safety of chemical batch reactors and storage tanks
TRANSCRIPT
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EURO
courses
RELIABILITY AND RISK ANALYSIS
VOLUME 1
Safety of
Chemical Batch Reactors
and Storage Tanks
edited by
A. Benuzzi a n d J. M . Za ldiva r
Kluwer Academic Publishers
for the Comm ission of the European Comm unities
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Safety of Chemical Batch Reactors and Storage Tanks
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RELIABILITY AND RISK ANALYSIS
Volume 1
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Safety of Chemical
Batch Reactors
and Storage Tanks
Edited by
A. Benuzzi
and
J. M. Zaldivar
Commission of
th e
European Communit ies,
Joint Re search Ce ntre ,
Inst itute for Safety R e search , Ispra, I taly
PARI EURCP B'.bi.V.H.
L J
f f
KLUWER ACADEMIC PUBLISHERS
DORDRECHT / BOSTON / LONDON
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Based on the lectures given during the Eurocourse on
'Safety of Chemical Batch Reactors and Storage Tanks '
held at the Joint Research Centre Ispra, Italy, April 1 5-1 9,1 99 1
ISBN 0-7923-1233-3
Publication arrangements by
Commission of the European Communities
Directorate-General Telecom mun ications, Information Industries and Innova tion,
Scientific and Technical Communications Service, Luxembourg
EUR 13457
©1 99 1 ECSC, EEC, EAEC, Brussels and Luxembourg
LEGAL NOTICE
Neither the Com mission of the European Com munities nor any person acting on behalf of the
Com mission is responsible for the use which m ight be made of the following information.
Published by Kluwer Academic Publishers,
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C O N T E N T S
1. Incidents in the chem ical industry due to therma l-runaw ay chemica l reactions
J. A. Barton and P. F. Nolan 1
2.
Fundam entals on Runaw ay Reactions: prevention and protection measures
J.M.ZaldivarComenges 19
3 .
Controlling Run-away Reaction hazards within the framework of the "SE VE SO -
Directive"
G. Drogaris
49
4. Labo ratory testing proced ures
P. Cardillo 79
5. Equ ipmen t characterisation
C. Barcons I Rises 99
6. M odelling and simulation for safety analysis of batch reactors and storage tanks
H. J. Hernandez 125
7. Risk assessment methodologies
N. Labath
147
8. Control technique s
C. Moussas
161
9. Early on-line detection of Runaw ay initiation
J. M. Zaldivar Comenges 201
10. Emergency relief system sizing: in-vessel fluid flows
J. Duffield 227
11. Emergency relief system sizing: vent line fluid flows
A.
Benuzzi 255
12 . Vent sizing for tempered vapor systems
J. C. Leung
285
13 .
Vent sizing for gassy and hybrid systems
J. C. Leung 299
14.
Calorimetry for Emergency Relief Systems design
J.L.Gustin 311
15 .
Treatment of relieved fluids
J. Singh 355
16. Runaway Reactions: a case study
T.J.Snee 371
17.
Reaction hazard evaluation
P.F.Nolan 391
18.
Outline of the modelling activities in venting
A.
N. Skouloudis 409
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INCIDENTS IN THE CHEMICAL INDUSTRY DUE TO THERMAL-RUNAWAY CHEMICAL
REACT
,
I«jNS
BARTON, J.A. (1) and NOLAN, P.F. (2)
1) Health and Safety Executive, Research and laboratory Services
Division, Harpur
Hill,
Buxton, SKL7 9JN
2) Department of Chemical Engineering, South Bank Polytechnic, London,
SE1 OAA
Introduction
Thermal-"runaway" is characterised by progressive increases in rate of
heat generation, temperature and pressure (the latter generally caused by
components in the reaction mass vapourising and/or decomposing to yield
gaseous products at the elevated temperatures involved).
Thermal-runaway begins when the heat generated by a reaction exceeds the
heat removal capabilities of the hardware in which the reaction is being
carried out. At first the accumulated heat produces a gradual temperature
rise in the reaction mass which causes an increase in the reaction rate.
This self-accelerating process may finally lead to an explosion. The
problem is that an increase in temperature has a linear effect upon the
rate of heat transfer but has an exponential effect on the rate of
reaction and subsequently on the rate of heat generation.
Runaway is a major problem in unsteady-state batch reactors, since the
task of specifying the design, operation and control of an apparently
simple kettle reactor with stirrer, heating/cooling coils, possibly reflux
facilities,
and emergency relief venting can be difficult, if all the
time-dependent parameters are considered. It is a task which requires a
systematic approach. The problem is often compounded because batch
reactors are frequently multi-purpose rather than dedicated to one
process. Due to economic factors a batch reactor may be used to carry out
many different chemical processes, and it is necessary to ensure that the
heat of reaction does not exceed the existing cooling capacity of the
vessel for each reaction.
A.
Benuzzi and
J.
M. Zaldivar (eds.). Safety of Chemical Batch Reactors a nd Storage Tanks, 1—17.
© 1991
ECSC.
EEC. EAEC.
Brussels
and
Luxembourg. Printed in the
Netherlands.
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Barton and Nolan (1,2) have previously examined case histories of
industrial incidents in batch reactors involving thermal-runaway chemical
reactions of the type A + B — > products (incidents involving thermal
stability problems with single components are not included) to determine
any apparent trends with a view to drawing general lessons from previous
mistakes,
having regard in particular to lack of knowledge of the process
chemistry, faulty design, e.g. scale-up procedures, and deviations from
operating procedures. This present paper updates the information from
that previously given and now covers the period 1962-1987.
The present analysis classifies the incidents in terms of:
(a) chemical processes;
(b) prime causes;
(c) industries involved.
Analysis of Incidents
Between 1962 and 1987, 189 incidents which occurred in industrial batch
reactors were reported to HM Factory Inspectorate (Health and Safety
Executive).
The information available on many of the incidents was not as
full as might have been wished. Even had the information on each incident
been complete the data presented below would have no statistical
significance because of the uncertainties of under reporting. Furthermore
it is not possible to say, for instance, that a particular process has a
poor record in comparison with others, because to be able to do so it
would be necessary to place the figures in context taking into account
such factors as numbers of reactors, production tonnages, unreported near
miss data, operating standards etc.
THE CHEMICAL PROCESSES
Eleven principal chemical processes were involved in the incidents as
shown in Table 1.
It was not possible to identify the chemical processes being carried out
in all of the 189 incidents, due to lack of information. However, 134
incidents could be classified.
From Table 1 it is apparent that polymerisation reactions featured in by
far the most incidents, followed by nitration, sulphonation and hydrolysis
reactions. Of the polymerisation reactions 20% (13) involved phenol-
formaldehyde condensations. In view of the number of incidents with
phenol-formaldehyde resin production the British Plastics Federation (BPF)
came forward with an exemplary approach to the problem in its publication
"Guidance for the safe production of phenolic resins" (3 ). Although the
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3
BPF document is specific to phenolic resins the general approach adopted
could be used elsewhere. It is perhaps significant that no phenol-
formaldehyde polymerisation incidents have been reported over the last few
years.
THE PRIME CAUSES
The prime causes which led to overheating and eventual thermal-runaway for
169 of the incidents (20 were without sufficient details for the
assignment of a prime cause) are classified below under the main
headings:
(a) process chemistry;
(b) plant design and operation.
(a) PROCESS CHEMISTRY
(i)
Reaction Chemistry/thermochemistry
Thirty-four of the incidents
are attributable to little or no study or research or development work
being done beforehand, with the result:
no appreciation of the heat of reaction on which
to base cooling requirements for the reactor
(scale-up) 8
- the product mixture decomposed 7
unstable and shock sensitive by-products
were produced 6
- the reaction was carried out en-masse (i.e. all
reagents added simultaneously at start) whereas
staged addition would have been appropriate 4
unintended oxidation occurred (instead of
nitration) 3
the reaction was carried out with reactants at
too high a concentration 2
the reaction was carried out at too low a
temperature resulting in accumulation of reactants
and subsequent en-masse reaction 1
the reaction accelerated due to:
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- catalysis by materials of construction of
the reactor 1
- unsuspected autocatalysis 1
a phase change of the product (to the vapour
state) occurred 1
34 (20%)
(ii)
Raw Material Quality Control
Fifteen of the incidents are
attributable to the use of out of specification materials:
- water contamination 9
other impurities 5
changed specification; a moderator should
have been used on start of new supply but this
change was not recorded in instructions 1
15 (9%)
(b) FIANT DESIGJ AND OPERATION
(i) Temperature Control
failure to control steam pressure or time of
application (includes one case of improper use
of steam to unblock vessel out-let, causing
decomposition of product) 6
- probe wrongly positioned to monitor reaction
temperature 6
failure of temperature control system (leading
for example, to cooling water being automatically
shut off; heating oil overheating; steam valve
remaining open) 7
loss of cooling water (not monitored)
(reactor 3 ; condenser 2) 5
error in manual reading of thermometer or
chart recorder 4
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failure
to
provide sufficient separation
distance between reactor
and
adjacent
hot
plant
2
too rapid heating
at
reaction initiation
1
thermocouples coated with polymer giving
slow response
1
32
(19%)
(ii)
Agitation
inadequate stirrer specification
-
mechanical failure,
for
example, stirrer
blades sheared
off due to
solidification
of
the "heel"
from previous batch;
although
an
overload switch
was
fitted
the
motor
was too
powerful
for the
paddle
securing bolts
operator either failed
to
switch
on
agitator
or switched
it on too
late,
the
nett result
was en-masse reaction
6
loss
of
power supply
2
agitator stopped
by
operator
to
make
an
addition (localised high concentration
caused liquor
to
boil
and
erupt)
2
17
(10%)
(iii) Mischarging of Reactants
overcharging (includes
2
cases
of
overcharging
a
catalyst
and one
where
the
metering device
was
faulty.
In 5 cases, the
total volume
of the
reaction mixture
was
incorrect
and the
cooling capacity
of the
reactor
was
inadequate.
In the
other
6
cases
the
reaction mixture contained
the
wrong proportions
of
reactants)
12
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too rapid addition (including
a
catalyst)
8
wrong sequence
of
addition
4
wrong material
5
vindercharging
3
improper control (use
of
hose-pipe)
2
addition
too
slow
1
(v)
Human
Factors
-
operator failed
to
follow written instructions
35
(21%)
(iv)
Maintenance
-
equipment leaks (scrubber
1;
valves
3 ;
cooling pipes/jacket
3 ) 7
blockages (vent pipes
2;
transfer pipes
3 ;
separator 1)
6
condenser solvent locked
due to
valve
in
reflux return line being closed following
shut-down
for
maintenance
3
residues from previous batch
2
water
in
transfer lines (including
one
case
of water siphoning from quench tank)
3
in situ replacement
of
closures (cracked
sight-glass
1;
cover plate 1) during
course
of
reaction
2
unauthorised modifications
1
-
loss
of
instrument
air
supply
1
25
(15%)
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- product run off before completion 3
deviations caused by poor communications at
times of staff changeover (change of shift,
holiday, sickness) 3
pTw^uct filtered at wrong stage of process 1
11 (6%)
INDUSTRIES INVOLVED
Batch reactors are ubiquitous in the chemical industry due to their
convenience and flexibility. The pattern of incidents, however, shows, as
might be expected, a preponderance to certain specific industries (Table
2 ) .
RECENT INCIDENTS
The analysis of Barton and Nolan (2) covered the period 1962-1984. The
data covering 1985, 1986 and 1987 can be summarised:-
A total of 47 incidents were reported, 3 in 1985, 16 in 1986 and 28 in
1987. Either there was a real upsurge in incidents in 1986 and 1987,
which seems unlikely, or, which seems more probable, the impact of the new
reporting regulations (Reporting of Injuries, Diseases and Dangerous
Occurrences Regulations 1985 [RIDDOR]) has resulted in improved
reporting.
The prime causes (3 incidents in 1987 were without sufficient information
for the assignment of a cause) of the incidents follow the familiar
pattern:
8 (18%) (ca. average) were due to little or no study or research or
development work being done before scaling up and going into production.
14 (32%) (well above the average) were due to mischarging of reactants of
which 4 were due to overcharging (1 catalyst); 4 were due to addition of
the wrong material, e.g. drums of wrong material were stored with drums of
one of the reactants and were charged in error; 3 to too rapid addition; 1
to wrong sequence of addition; 1 to undercharging of a reactant and 1 to
improper control (use of a hosepipe).
4 (9%) were due to temperature control failures.
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5 (11%) were due to the presence of impurities, particularly water
3 ) ,
in
raw materials.
5 (11%) were due to problems with agitation, 2 because the agitator had
not been switched on; 2 because the agitator was switched on late once the
error was realised and 1 because of mechanical failure.
6 (14%) were maintenance related; 1 was due to a blocked transfer pipe; 1
to a blocked separator; 1 to unauthorised plant modification; 1 to loss of
instrument air supply; 1 to a leaking cooling jacket and 1 to an
improperly secured cover plate; and
in 2 (5%) the operators failed to follow written instructions; in 1 they
failed to separate an aqueous phase from an organic phase before
proceeding and in the other, filtration was carried out at the wrong stage
of the process.
13 of the incidents occurred in the fine and intermediate organics
industry; 7 in the plastics, rubber and resin industry; 13 in the heavy
organics industry; 4 in the pharmaceuticals industry; 2 in the dyestuffs
industry and 1 in the metal processing indusry.
Of the chemical processes involved polymerisations accounted for 17
incidents. The polymerisations involved vinyl acetate; vinyl chloride
9 ) ;
polyester resins (2); butadiene/acrylonitrile; hydroxyethyl
methacrylate; and urea-formaldehyde (due to contamination of the urea with
ammonium
nitrate).
Other chemical processes involved were sulphonation (4 ); amination (3 );
nitration (2); halogenation (2); diazotisation (2); alkylation (1);
esterification (1) and hydrolysis (1).
9 persons were injured (8 operators and 1 fireman). In one incident
(runaway nitration) 20 people off-site were affected by acid-spray.
INJURIES AND DAMAGE
The result of the runaway incidents ranged from a simple foam-over of the
reaction mass to a substantial increase in temperature and pressure
leading to violent loss of containment, with in some instances the release
of large quantities (up to several tonnes) of flammable and/or toxic
materials into the environment. In a few cases where flammable materials
were released a fire and/or a secondary explosion followed. As a result 4
fatalities and 82 injuries (as defined in relevant health and safety
legislation (4)) occurred in the period 1962-1987.
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The injuries to operators were due, for example, to splashing by hot
liquors or the effects of blast, missiles or toxic fumes. They generally
occurred when the operators were attempting to regain control of a
reaction. Eleven injuries, one of which was fatal, occurred when manual
additions of ingredients were being made to the reactor and the reaction
mixture then erupted over the operator.
Plaiic usually suffered down-time at least and/or it was more or less
seriously damaged as also, in some cases, was the building housing the
plant.
In a small
number of cases, surrounding areas both on- and off-site were put at risk.
In one incident 20 people off-site were affected by acid spray.
General Lessons
The analysis indicates that incidents occur due to: -
(i) a basic lack of proper understanding of the process chemistry and
thermochemistry;
(ii) inadequate engineering design for heat transfer;
(iii) inadequate control systems and safety back-up systems (including
venting);
and
(iv) inadequate operational procedures, including training.
In order to deal with hazards it is first necessary to identify them, then
decide how likely they are to occur, and how serious the consequences
would be. A formal system should be used to study the plant, and identify
and record process hazards (see Appendix 1 ) . This area is further
developed by other speakers at the symposium. It is apparent from the
analysis of incidents that this is still not common practice for batch
reactors.
It is axiomatic that in order to avoid conditions for runaway arising it
is necessary to have knowledge of the chemistry and associated
thermochemistry of the desired reaction and potential side reactions and
also of the thermal stability and physical properties of reactants,
intermediates and products.
Some of this necessary information can be obtained from the literature or
from computer-based modelling of reactions. The thermal behaviour
characteristics of reactants, products and occasionally reaction
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10
intermediates/mixtures can be found using laboratory techniques. A
variety of laboratory techniques are available for use to acquire this
knowledge. The Association of the British RTarmaceutical Industry
developed a laboratory scheme (5) for screening new products and
processes. More sophisticated techniques include use of accelerating rate
calorimetry (6) or other adiabatic calorimetry systems. The study of
reaction mixtures is ideally carried out by using a heat flow calorimeter
7 ) . These techniques will be described in more detail by other speakers
at the Symposium. A thermal hazards assessment strategy is discussed
below.
It is also possible to obtain information relating to changes in heat
transfer coefficients and control parameters, due to changes in properties
such as viscosity and specific heat as the reaction proceeds, using heat
flow calorimetry (8 ).
The laboratory studies can provide data on the onset temperature of and
magnitude of exotherms. The detected onset of an exotherm is scale
dependent i.e. the larger the reaction
mass,
the lower the onset
temperature. From such information and a thorough examination of previous
plant operating experience, it is possible to set safety margins and hence
select the operating temperature for the given reactor charge size.
The ensured quality of the raw materials is vital to safe operation. The
analysis shows that the presence of impurities, water in particular,
appears to present a problem. The presence of water can cause additional
heat evolution, raising the total heat output above the reactor cooling
capacity, leading to temperature rise and increased rate of reaction
causing subsequent further increases in heat generation.
With reference to the prime causes relating to plant design and operation,
it is obvious that heat removal rate is an important criterion for batch
reactor design, to which adequate agitation, eg stirrer speed, is related,
particularly with regard to scale-up from laboratory data. Numerous
correlations exist for heat transfer in agitated, jacketed vessels (9,10)
and it is possible to scale-up data on inside film heat transfer
coefficients from heat flow reaction calorimeters to industrial size batch
reactor plant (8 ). It is imperative that the cooling capacity of the
designed plant can cope with the heat generation from all the chemical
processes envisaged.
It is unusual for batch reactor plant to be designed to resist any
calculated pressure rise resulting from a runaway reaction. Ideally, of
course, the objective should be for process control to eliminate any
runaway potential. However, pressure relieving of the reactor or dumping
the contents or quenching the reaction should be considered in case of
emergency. If pressure relief venting is considered, attention must be
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paid to the nature of the material likely to be released, e.g. its
toxicity and/or flammability, and it may be necessary to install catchpots
or other means of containment or entrainment to capture the released
material (11). The vent sizing of reactors has been advanced recently by
the work of the AIChE's Design Institute for Emergency Relief Systems
(DIERS) (12). This work has included the development of two-phase flow
equations: and the 'Satire' computer code for vent sizing of realistic
releases. For reactions not previously investigated or adequately covered
in the literature, the DIERS programme also produced a laboratory-scale
apparatus to provide the necessary information for input into the
developed models. Vent sizing for reactors is covered by other speakers
at the Symposium.
Many of the incidents resulted from the mischarging of reactants,
inadequate temperature control and poorly defined operating procedures and
operator training. The safe operation of plant can be aided by the use of
computer or other automatic control techniques; however, two of the
incidents in this analysis occurred due to the operator over-riding the
alarm signals.
Assessment Strategy
Runaway inside a batch reactor is characterised by the loss of thermal
control.
The purpose of a thermal hazards assessment strategy is to:
(a) identify materials and unit processes which are potentially
hazardous;
(b) quantify the hazards which arise from these with a rujiimum of
testing.
It involves a sequential approach, which cavers thermochemical evaluation,
reaction calorimetry and the effects caused by scale, accumulation and
cooling/agitator failure.
A typical strategy is shown in Figure 1 (13,14). This is discussed more
fully in the references given.
The thermochemical evaluation consists of data on the thermal stability,
heat of reaction and total heat capacity of reactants of the desired
reaction, the expected adiabatic temperature rise and any general process
hazards, e.g. flammability and toxicity of reactants.
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12
Reaction calorimetry, either in the form of heat flow or adiabatic Dewar-
based calorimeters allows the measurement of many process variables
(agitation, heating, and cooling requirements) and reaction
characteristics (kinetics, reaction enthalpy, heat release rates and
reactants
1
heat capacity) under known environmental heat loss conditions.
The reaction calorimetry stage of the assessment also allows for the
determination of adiabatic temperature rise and gas generation potential.
The heat release per unit mass or unit volume of reactants can be used
with the previously established plant cooling capacity to ascertain safety
margins for safe operation. It is also usually necessary to consider the
potential results following the failure of agitator and cooling systems,
along with the results from heat accumulation storage tests.
Conclusions
Despite the apparent knowledge which exists, the techniques which are
available and the commercial instruments on the market for the assessment
of potential runaway reactions, to aid process and plant design, control
and operation, incidents continue to occur due, in the main, to common
errors.
The hope is that more chemical manufacturers will introduce systematic
assessment procedures. A systematic approach should reduce the types of
common errors exemplified in the analysis. It is essential to have a
thorough understanding of the process chemistry and thermochemistry and
then to ensure adequate engineering design for heat transfer, adequate
control systems and safety back-up systems and adequate operational
procedures, including training.
An assessment strategy for chemical reaction hazards, has been outlined.
A need is perceived for coherent and concise guidance to be produced,
particularly for small and medium-sized companies, covering the areas of
thermal haz ards assessment, venting, and a formalised approach to process
control. HSE has now initiated, and in part, sponsored, the production of
a User Guide on safety in exothermic reactions by I Chem E. Other
sponsors have come from industry. The publication is being written by an
Industrial Fellow reporting to a Steering Committee. It will seek to
bring together information produced in the last few years on all aspects
of the subject, including thermal hazards assessment, process design, heat
transfer problems, process control, vent sizing and operator training. It
will not be a full text-book but should alert smaller to medium sized
companies to the problems in these areas and point out where to go for
further help and advice.
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REFERENCES
1 Barton, J.A., and Nolan, P.F., April 198 4. Runaway reactions in
batch reactors, in: The protection of exothermic reactors and
pressurised storage vessels, I.Chem.E. Symp. Ser. 8 5, Chester.
2 Vclon, P.F., and Barton, J.A., 1987. Some lessons from thermal-
runaway incidents. Journal of Hazardous Materials 1 4 , 233 -239.
3 British Plastics Federation; 1980. Guidelines for the safe
production of phenolic resins. BPF Thermosetting Materials Group,
London.
4 Factories Act, 196 1; Notification of Accidents and Dangerous
Occurrences Regulations, 1980; Reporting of Injuries, Diseases and
Dangerous Occurrences Regulations, 1985.
5 Association of the British Pharmaceutical Industry; 198 2. Guidance
notes on chemical reaction hazards analysis. ABPI London.
6 Townsend, D.I., March 1981. Accelerating rate calorimetry, in:
Runaway reactions unstable products and combustible powders,
I.Chem.E. Symp. Ser. 6 8 , Chester.
7 Brogli, F., Giger, G., Randegger, H., and Regenass, W., March 1981.
Assessment of reaction hazards by means of a bench scale heat flow
calorimeter in: Runaway reactions, unstable products and combustible
powders, I.Chem.E. Symp. Ser. 6 8 , Chester.
8 Steele, C.H., Ph.D. thesis, Heat transfer characteristics and scale-
up under isothermal and reflux conditions in batch reactors (in
preparation).
South Bank Polytechnic.
9 Chapman, F.S., and Holland, F.A., 196 5. Heat transfer correlations
in jacketed vessels. Chem. Eng. Feb 15 175.
10 Chilton, C.H., Drew, T.B., and Jebens, R.H., 1944 . Heat transfer
coefficients in agitated vessels, Ind. Eng. Chem. 3 6 , 510 .
11 Burgoyne, J.H., June 198 7. Safe disposal of relief discharges.
I.Chem.E. Symp. Ser. 10 2, 201-213, UMIST, Manchester.
12 Fauske, H.K., 1985. Emergency relief system design. Chem. Eng.
Prog. 8 1, 8,
53-56.
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14
13 Cronin, J.L., Nolan, P.F., and Barton, J.A., June 1987. A strategy
for thermal hazards assessment in batch chemical manufacturing.
I.Chem.E. Symp. Ser. 102, UMIST, Manchester.
14 Cronin, J.L., January 1987. A strategy for thermal hazard
assessment in batch chemical manufacture, Ph.D. thesis, CNAA (South
Bank Polytechnic).
15 KLetz, T.A., 1986. HAZOP & HAZAN - Notes on the identification and
assessment of hazards, I.Chem.E (Loss Prevention), Rugby.
16 The Chemicals Industries Associated Limited (Chemical Industry
Safety and Health Council of), 1977. A guide to hazard and
operability studies. CIA London.
17 Lees, F.P., 1980. Loss prevention in the process industries,
Butterworths.
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FIGURE I ASSESSMENT STRATEGY
CHEMICAL REACTION HAZARDS
THERMOCHEMICAL
EVALUATION
magni tude & rate of
hea t r e l ease
DESIRED PROCESS
reac t ion temperature
addi t ion t imes
ma x imum ho ldu p t ime
operating procedures
REDEFINE
CONDITIO
MODEL PROCESS :
REACTION
CALORIMETRY
kinetics, heat release
gas generat ion
N
PROCESS DEVIATION
REACTION
CALORIMETRY
magn i tude o f e xo the rm ,
adiabat ic temperature
increase,
gas genera t ion
secondary reactions
produc t s tab i l i ty
residual cool ing
r e q u i r e m e n t
THERMAL
STABILITY OF
REACTION
GOMPONENTS
PLANT
(OPERATIONAL
DATA
cool ing capaci ty
cont ro l parameters
PLANT FAILURES
&MALOPERATIONS
IDENTIFIED DURING
PROCESS ANALYSIS
PROCEED TO
PILOT PLANT
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Table 1
Number of incidents per specified chemical process
Chemical Process
Polymerisation
(including condensations)
Nitration
Sulphonation
Hydrolysis
Salt formation
Halogenation
(Chlorination and Bromination)
Alkylation using
Friedel and Crafts Synthesis
Amination
Diazotisation
Oxidation
Esterification
Number of Incidents
64
15
13
10
8
8
5
4
4
2
1
134
Table 2
Specific manufacturing industries, in which reported batch reactor
runaway incidents have occurred during the period 1962-1987
Manufacturing Industry
Fine and intermediate organics
Plastics, rubbers and resins
Heavy organics
Metallurgy and metal processing
Dyestuffs
Pharmaceuticals
Number of incidents
- including animal health products
Agricultural chemicals
Food and flavourings
Paint and varnish
Miscellaneous
51
41
20
13
13
13
5
5
5
23
189
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APPENDIX 1
IDENTIFYING HAZARDS
Among the better known formal systems are 'Hazard and Operability Study
1
(HAZOP), used to identify hazards, and Hazard Analysis (HAZAN), used to
quantiry hazards (15,16).
Having identified a hazard it is still necessary to decide what to do
about it. Ways must be found to reduce the probability of a runaway
occurring.
Where consequences are judged to be severe, or where the causes giving
rise to the hazard are many or interrelated, it is recommended that a
'fault-tree' (17) is constructed, showing the way in which various events
or faults can give rise to a hazard. When constructed the tree can be
used to see where the most likely causes of an incident lie, and where
additional precautions can be introduced to minimise the risks.
For the most rigorous examination it is necessary to allocate
probabilities to each event in the fault tree, allowing the total
probability of the final event to be calculated (HAZAN).
Where companies are not able to carry out such examinations of their batch
processes alone, they can call on the services of consultant practitioners
to assist them.
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FUNDAMENTALS ON RUNAWAY REACTIONS:
PREVENTION AND PROTECTION MEASURES
J .M . Z A L D I V A R C O M E N G E S
Com mission of the European Com munities
Joint Research Centre
Safety Technology Institute, Process Engineering Division
1-21020 Ispra(VA), Italy
ABSTRACT. The circumstances leading to accidents are often very complex but most of them
could have been foreseen by the use of laboratory tests, hazard analysis and chemical reaction
engineering technique s. In this paper, different approaches to imp rove the safety of chemical batch
processes and storage tanks will be studied, as well as emergency procedures to minimize the
effects of a thermal excursion of the reaction mixture. The objective is give a global vision of the
diversity of aspects that must be covered and the basic concepts to deal with them.
1.
Introduct ion
The rapid development of the Chemical Industry in the past decades has increased the complexity
of chemical plants, and the diversity of products. In parallel, there has been a corresponding
increase in the number of accidents and therefore, the quantity of human losses, material damages
and environment impact has augmented.
The study of accident case histories [1, 2] shows that the circumstances leading to accidents are
often very complex, involving human error, insufficient knowledge about the chemistry of the
process, poor training of the operator, inadequate instrumentation, etc. but it also shows, that the
accident probably could have been foreseen in a high percentage of the cases, by means of
laboratory tests, hazard analysis, and chemical reaction engineering techniques.
Loss of thermal control due to undesired or poorly controlled desired reactions, which can lead
to destruction and release of toxic materials, is a Chemical Engineering area, in which the main
contributions are to develop p rocess concep ts which prevent the loss of control of the reactions and
countermeasures to protect against runaway events. In any case, prevention and protection against
chemical reaction hazards is based on the understanding of the basic phenomena involved. In order
to achieve safety, the study of four different aspects is vital: the thermo-kinetic phenomena, the
physical and chemical properties of reagents and products, the equipment characteristics, and the
operating conditions.
In recent years, the search for inherent safety has been widely recommended [3]. A process is
inherently safe, in a rigurous sense, when no disturbance whatsover can cause an accident. In
practice, this is impossible to achieve. However, this concept should be an objective in process
design, since considerable reduction in the potential hazard can be reached at this stage, and even
19
A. Benuizi and J. M. Zaldivar (eds.). Safety of Chemical Batch Reactors a nd Storage Tanks,
19-47.
© 1991
ECSC.
EEC,
EAEC,
Brussels a nd Luxembourg. Printed in the Netherlands.
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the effects of disturbed operating conditions such as cooling system malfunction or agitator
stoppage can be assessed.
A detailed analysis on the probability of an incident and its severity cannot be effected in the
absence of data with regard to the phenomena involved. Then, this is an important condition that
should be fulfilled.
In this paper different approaches to improve the safety of chemical processes will be studied,
as well as emergency procedures to minimize the effects of a thermal excursion. The objective is
give a global vision of the diversity of aspects that must be covered and the basic concepts to deal
with them.
2. Runaway React ions and Thermal Explosion Theory
Reaction systems in which the heat removed from the reaction mass to the surroundings becomes
less than the heat generated by chemical reaction, will increase their temperature, and due to the
exponential dependence of the reaction rate on it, will self-accelerate and "runaway".
That means, they will produce a large amount of heat in a very short time, developing
temperature and pressure excursions of the reacting mass with the consequent danger for people,
installations and environment.
In order to gain basic understanding of runaway reactions it is convenient to study the theory of
thermal explosion. This theory stems from ideas of van't Hoff (1884), but the first mathematical
formulation of conditions for ignition, or explosion, in a gaseous self-heating system was given by
Semenov [4] during the 1930s. Its most extensive development - theoretically and experimentally -
with the application to runaway reactions in solids and liquids has taken place during the past 50
years [5-8].
Thermal
f l o w
Heat generation
rate
©
Tempera tu re
Figure 1. Therm al diagram
Thermal explosion theory is concerned with the competition between heat generation by
exothermic reaction and heat removal by conduction, convection and/or radiation from the reaction
mass to the surroundings. The heat generation depends exponentially on temperature while the heat
loss depend s linearly (see figure 1). W hen the heat generation ex ceeds the heat remov al capacity,
runaway will occur. Intersections of the two curves represent steady states in which the rate of heat
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loss equals the rate of heat generation in unit volume. The upper and lower steady states, of the
intersection between the sigmoid function of heat generation rate and heat removal rate in figure 1,
are stable to temperature perturbations while the intermediate one is not.
Acco rding to figure 1, in a thermal explosion it is possible to distinguish the following phases:
1/ Auto-thermal behaviour : Initially, the exothermic reaction is stable and under control. If for
some re°.i^ii iiie reaction becomes unstable, that is, it can no longer be held in check by normal
process control, then the temperature will gradually begin to rise.
2/
Initiation: The reacting mass reaches a temperature in which the heat generated is higher than the
heat disipated by the cooling system. Hence, there is a self-heating behaviour with an acceleration
due to the exponential depend ence on temperature of the reaction rate.
3 /
A cc ele rat ion : The reacting mass rises until it reaches a temp erature that triggers off the
deco mp osition reactions , characterised by their high exoterm icity and gas produ ction. The
pressure of the system increases suddenly due to gas production and/or vigorous evaporation of
the liquid phase.
4/ Explosion or reaction auto-controlled: If the reactions continue to accelerate, the pressure
reaches the limit of wall resistance of reactor and an explosion occurs. Otherwise, the reaction rate
sometimes can be controlled by reactants consumption or by diffusion rates if the mass transfer
phenomena plays an important role (e.g. oxygen diffusion for combustion reactions).
Representing the evolution of temperature versus time (see figure 2), it is possible to define
different parts. At the first stage the system is stable and completely defined by the initial
cond itions. The second and third stages are the early stages of an instability and it may be possible
to restabilize the reaction by taking unusual actions such as emergency cooling, addition of a
supressant, and quenching. At some point in time, no such restabilization method can bring the
reaction back under control. The reaction is said to runaway. The only recourse to avoid pressure
buildu p and possible explosion is venting.
Temperature
PREVENTION PROTECTION
Figure 2. Temperature-time history of a runaway reaction.
t ime
Depen ding o n the type of reaction involved in the runaway initiation, it is possible to distinguish
between two different cases; the former is a production process which becames unstable, while the
later is an unw anted reaction that goes out of control:
a/ Loss of control of the desired reaction. The behaviour of the wanted reaction may become
unstable by different causes: high reactant accumulat ion, high sensi t ivi ty to impuri t ies,
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22
degenerat ing operat ional condit ions (i .e . poor mixing, too high feed rates, wrong ini t ial
temp erature), failure of the cooling sy stem, etc.
b/
U ndesired reactions, fundamentally decomp osition and oxidation reactions that are unwanted.
The main possible causes are: reactive compounds mixed accidentally (e.g. cooling water that
penetrates into the reactor), the temperature of the reaction mass increases until decompositions are
triggered off, low heat dissipation capacity that even in very weakly active undesired reaction
systems -in the long term- runaway can be produced (i.e. storage tanks).
An other clasiffication on types of thermal explosion w as given by Bow es [9] in function of how
the unstable steady state point is reached. The first kind occurs at the point where the stable and
unstable steady states converge (see figures 4 and 5) and beyond which only high-temperatue
diffusion-co ntrolled steady states can exist, and the seco nd kind requires the self-heating system to
be forced through an unstable steady state with the aid of some other heat source for thermal
explosion to occur.
3 .
Safety measures against a runaway react ion
There are essentially two different types of measures and countermeasures that can be taken in
order to avoid runaway reactions depending on the region of the temperature-time history which
has been reached by the system (figure 3):
- Prevention mea sures: oriented to avoid situations that can lead to a runaway scenario.
- Protection measures: oriented to stop or to minimize the consequences of a thermal excursion
(region of abnormal behaviour).
/
O f f - l i n e ^
PREVENTION
On- l lne<
\
Calorimetric studies
Improving plant design
Analyt ical cr i ter ia
Simulat ion
New synthetic routes
- Instrumentation
- Improving control techniques
- Detection of initiation of runaway
s^ Simulation
-Full cooling
Stopping the '
r u n a w a y
P R O T E C T I O N
P r e s s u r e
^ Quenching'
rel ief
Add an inhibitor
Add cold liquid
Dump
C o n t a i n m e n t
Figure 3. List of the prevention and protection measures.
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Clearly, the prevention measures are the most desirable ones because they do not affect the
integrity of desired products. These measures can be divided into off-line and on-line. The former
is part of the systematic process analysis before carrying out the process in the plant and aiming at
the obtention of basic data as a prerequisite for understanding the process behaviour and the risk
associated. The later tends to avoid the loss of control of the process when operating and to detect
possible deviations from the safe operation at an early stage.
The p
r
oic^iion measures have as an objective to restabilize the control of the reactor, by means
of active emergency actions such as full cooling, fast injection of a supressant or dumping the
reactor contents; or at least to reduce the damage for people, installation and environment, by
means of passive measures such as containment. These measures are taken when the process is
outside of desired conditions, that means when the rate of heat generation has surpassed the rate of
heat remo val and the process is getting to a dangerou s state.
4. Prevent ion mea sures
4.1 . OFF-LINE AND ON-LINE TECHNIQUES
The logical way of obtaining knowledge about the process in order to prevent the potential hazard
of thermal explosion, begins with safety tests performed under laboratory conditions, using small
samples. Apart from basic data, such as physical properties and data related to process equipment,
the type of experimental information necessary for the evaluation of the thermal safety of a
chemical process, can be divided into different types [10].
The first type of tests to be performed concern the evaluation of the thermal stability of
substances and mixtures of substances. Typically, the mixed starting materials and samples from
intermediate process phases are investigated using mg. quantities (eg. DTA, Differential Thermal
Analysis).
For information on the desired reaction, heat flow reaction calorimetry has proved to be an
appropriate tool. The method provides information measured under conditions very similar to
industrial situations wh ich permits the gaining of know ledge about the process and the influence of
the operating conditions on its behaviour [11].
Other required experimental data concerns the heat evolution dynamics of secondary reactions.
Unwanted exothermic reactions can be characterised [12] by a small-scale thermal stability test
(e.g. DTA or DSC) using mg. quantities; adiabatic test (e.g. Dewar, ARC, PHI-TEC); isothermal
test; and test for deflagration. Exothermic secondary reactions are a particularly difficult safety
problem. When a reaction of this type has been established, it is important to determine the
temperature at which this reaction can be observed [10]. When this temperature is more or less the
same or lower than the desired reaction temperature, then it is practically impossible to run the
reaction safely and new operating conditions or synthetic routes must be studied.
The experimental data, obtained by the procedures described above, can be used to apply the
criteria and rules for the safe design of the process (see chapter 4.2) and/or to feed numerical
simulators. The advantage of the former is that it is easy and quick to apply but the information
obtained is relatively reduced when compared to numerical simulation. The advantages of using
mathematical modelling in hazard analysis evaluation are: to interpret the experimental data, to
reduce the num ber of expe rime nts need ed to establish an acceptable deg ree of und erstand ing , to
predict the dynamic behaviour of the reactor under conditions which are not easily achieved with
laboratory equipment and to perform the scale-up procedure [13].
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Complementary to off-line techniques there are other types of procedures to prevent the potential
hazard. These are called on-line supervision techniques because they are carried out in real time.
Furthermore to improve instrumentation devices (ie. double sensors for important measures like
reaction mass temperature) and/or to improve control procedures (i.e. introduction of adaptive
strategic); an important on-line prevention measure consists on the detection of potential hazardous
situations with sufficient time in advance to take necessary countermeasures to avoid the thermal
excursion. This can also be done by means of some rule or criteria, or by means of model-based
techniques involving on-line numerical simulation.
4.2.
ANALYTICAL CRITERIA
The mathematical modelling of the behaviour of compounds or mixtures that can lead to runaway
reactions has followed two different approaches. On one side, the theory of thermal explosion
which have been applied in the fields of combustion and explosion. On the other side and in
parallel, the concepts developed by this theory has been used in Chemical Reaction Engineering in
orde r to assess potentially dangerou s situations and to design chemical reactors for safe o peration.
In this chapter several main points of the thermal explosion theory will be presented. From the
simplest approach (Semenov Theory) that treats a system with uniform reaction mass temperature
and without reactant consumption, to more advanced theories that describe the effects of non
uniform reactant distribution temperature. A more detailed treatment of this theory is available
elsewhere [6,9].
4.2 .1 .
Semenov Model. The Semenov model [4] assumes an uniform temperature distribution
within the reacting system. This is more or less the case of homogeneous systems in stirred tank
reactors.
The theory considers a pseudo zero order exothermic reaction (A —> R) with an Arrhenius type
rate equation given by
-E.
d C .
RT
— A = -r . = - k - C . = - A e
m
C
A
dt A A A
(1)
It is assumed that the effect of decreasing concentration is negligible, compared to that of
increasing temp erature (which is the case for highly energetic reactants), that implies, C
A
=
C
A Q
.
In this case, the heat generated by chemical reaction is given by the following expression,
-E,
RT
^Generated =
V
^
H
R '
r
A
=
V
m - A H
R
- A - e
m
-C
( 2 )
o
The rate of heat production is mainly governed by the exponential term: exp(-E,/RTj.
Semenov further supposed an uniform temperature of the surrounding T
e
, which is smaller than
the temp erature of the reacting m ass. Assum ing that there is a cooling jacket, the heat transfer to it -
in accordance with Newton's rule- is given by
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^Removed
U-S (T
m
- T
e
)
(3)
Hen ce, the heat dissipated is a linear function of the temperature of the reacting m ass.
It is pos sible to repres ent the equ ation s in the so-ca lled therm al diagram and obtain three
different states, which are graphically show n in figure 4. They are subcritical, critical and
hypercritical states. In the straight line 1, there are two stationary states in which the heat
generation equals the heat removal rate, the points A and B. The operating point in the low
temp erature region is called stable and the other at higher tempe rature metas table. Any point
beyond the point B intersection represents a runaway condition. At any point below point B the
condition is stable.
There are two ways to affect the equilibrium:
a/ The coolant temperature can increase while the heat removed slope remains practically parallel.
If this occurs, the heat removed line moves parallel to itself until it becomes tangential to heat
generated line in the critical state and until there are no intersection points between both lines
(hypercritical states).
Therma
f low
Tempera tu re
c r c r ^
Figure 4. Semenov plot traces relationship for heat generation and removal. Influence of the
cooling temperature.
b/
The loss of heat transfer capacity, such as by the loss of cooling, or loss of mixing, will lower
the slope of the heat removed line, although the stationary cooling temperature remains the same
(see figure 5 ).
Thermal
f l ow
( U A ) > ( U A )
c r
(UA)< (UA)
c r
Tempera tu re
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Figure 5. Semenov plot traces relationship for heat generation and removal. Influence of the heat
transfer parameter.
The situation for the critical state can be described mathematically by equations (4) and (5):
q
G
= % (4)
d(
h _
d
q
R
dT
m
d T
m
(5)
At Tm,.,. the heat generation rate equals to heat removal rate, eq. (6), and also, the slope of the
heat gen erated line equals to the slope of the heat removal rate, eq. (7).
RT
m
V
m
A H
R
A e "
b
C
A
= U - S ( T
m c r
- T
e
)
(6)
^ ^ V ^ -
6 =US
R T
m
C
r
(7)
Substituting equation (7) into equation (6) and rearranging:
T - a
m c r -
2
R
1±
1
_ 4 R T
e
(8)
Eq. (8) shows that an exothermic reaction can lead to a runaway condition only if E
a
> 4 R T
e
, and
also, that ignition phenomena may occur only as long as T
e
lies in the range 0<T
e
S E
a
/4R. Thus
the maximum value of
Tmc,.
occurs when T
e
=E
a
/4R and is given by Tmc
r
=E
a
/2R which implies at
very high temperatures (i.e. 10
3
to 10
4
K). Hence, it is necessary consider only the lower of the
two critical temperatures given by equation (8). Expanding the square root of eq. (8) in a binomial
T
A
m
(9)
with b„=2,2,4,10,28,. .
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■ cr
RT?
T„+-—^
+
2
f 2 3\
v
E
> ;
' R T
+
5
F
V
a
J
(10)
and truncating the series after the second term [13]:
RT?
(11)
The Semenov number <> can be formulated:
rate of heat generation in a certain volume at T
e
(p=
rate of heat loss at a steady-state temperature excess AT=(T
m
-T
e
) by Newtonian cooling
< is a dimensionless heat flow number and can be defined in terms of the chemical and physical
properties
of
the
system.
For
a
zero-order
reaction
is:
AH„ A E . e
R T t
C ,
R
a
A .
US
RT?
(12)
It is possible to define
<J)
cr
by substituting th e critical condit ion, eq. (6), into eq. (12) and
rearranging as,
* « = ■
E
a
(Tn^- T
e
)
R
1 J_
T n w T ,
RT?
(13)
Developing
E
a
/RT
m
in
Taylor
series
for
T
m
=T
e
,
=
- ^ . _ ^ ( T
m
- T
e
)
+
^ i . ( T
m
- T
e
) . .. .
R T
m
R T
e RT?
(14)
RT:
truncating
the
series
after
the
second
term
(only
valid
if
E
a
>>RT
e
)
and
introducing
the
dimensionless
temperature
rise:
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Q
_ E
a
( T
m
- T
e
)
RT?
(15)
it is possible to define
but substituting Tm,.
r
by the aproximate equation (11):
0
c r
= 1 and (|>
cr
= e"
1
(16)
(17)
that means,
a
steady state exists
if
<t><<t>cr and
a
thermal exp losion will occur
if
<|>><t>
cr
. The
conditions at criticality can b e en capsulated into the values of two d imensio nless groups : the
dimensionless Semenov number which equals to e
1
and the dimensionless temperature excess 0„
which is unity.
The advantage of the Semenov model is its simplicity. It gives a clear picture of the occurrence
of a critical state and of the influence of several parameters and variables such as activation energy,
heat of reaction, heat transfer coefficient and temperature. However, in order to describe other
important cases, i.e. unstirred self-heated reactants (for instance, storage tanks), the assumptions
of the Semenov model are not valid and other approaches must be employed.
4.2.2.
Frank-Kamenestkii Model.
The Frank-Kam enetski i model assumes
a
non-uniform
temperature (T
m
) distribution as a function of an spatial variable [15] and it is based upon the
Fourier heat transfer equ ation for the conduction of heat in an isotropic me dium :
5T„
5 t C
Pn
1
f 2
5T,
n
r
5x
2
m G " T
m
5x
5>
^AH,r
:
i= l
(18)
where the geometric symetry is defined by o as , a = 0,1,2 for infinite slab, infinite cylinder and
sphere, respectively.
Then , for a zero-order reaction:
8T„
5t
C
Pn
1
r
5
2
T
m
+ c
5T
m
^
8x
2
x
5x
- A H
D
A e
R T m
C
A
R A„
(19)
with boundary conditions:
T
m
= T„ at x=x
n
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29
and
'm
d x
= 0 at x= 0
If dimensionless quantities and approximation given by equation (14) are introduced, eq. (19)
may K transformed into:
, 2 ,
'
9
5 9
=
j 5 _ e
+
J l 5 e
+
5 e l
1 + E e
; (20)
5x 6z
2 z
5z
with boundaiy conditions:
0=0 a t z= l
and
4^-=0 at z=0
dz
wh ere e is the dim ension less amb ient tem perature, x is the dimensio nless time, and z is the
dimensionless d istance from the centre :
e = ^ (21)
1 =
Xm t
(22)
Pm Cp
m
X
Q
z f (23)
x
o
Frank-Kamenetskii was the first to solve a simplified form of equation (20) for stationary state
(d9/dt = 0) and assuming that e< <l and 0 is not large:
d e
+
j r j d i
=
_ 5 e
9
( 2 4 )
d z
2 z
dz
where 5 is the dimensionless heat flow, called Frank-Kamenestkii number, that can be formulated
as,
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ra te of heat genera t ion in a given vo lume at T
e
5
=
rate of conduc t ive hea t loss at a steady-sta te t empera tu re excess (T -T
e
)
where Tm,, refers to th e temperature in th e centre. For a zero-order reaction this number can be
defined as ,
-E
a
A H
R
E
a
x
2
0
A e
R T
' C
A
5 =
_ _
\
(25)
^ .
m
R T
e
As opposed to the Semenov model where the heat resistance only occurs within the substance,
which
means
that
this
model
results
in
a
temperature
gradient
in
th e
substance
without
a
temperature difference across th e surface of th e reactant. For a symetrically heated system th e
temperature gradient in the centre of reacting mass is assumed to be zero, which also means that
the maximum temperature occurs in the centre.
4.2.3.
Thomas Model. The Frank-Kamenetskii model assumes that the reactant temperature equals
to the surroundings at the wall. Apart from the thermal resistance to heat flow due to finite thermal
conductivity,
Thomas
(16)
considered
the
case
where
there
is
heat
exchange
with
the
surroundings
following Newton's law. In fact, th e Thomas model is th e more general and it is possible to derive
the Semenov and Frank-Kamenetskii models as extreme cases.
The
Thomas
model
is
described
by
eq .
(18)
with
boundary
conditions:
■ ^ m l
' d T
m
dx
= U (T -T
e
)
X=X
^ 5 1 = 0 at x= 0
dx
where Tm,, refers to the temperature of the reacting mass at the surface.
Introducing
th e
dimensionless
numbers ,
it
is
possible
to
obtain
eq.
(20)
with
boundary
conditions:
_ d 0
=
B i e „ atz=±l whena = 0
dz °
at z= 1 when a = 1 or 2
^ i = 0 whenz=0
dz
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31
where 9
0
is the dimensionless tem perature rise at the surface and Bi is the Biot num ber, that can be
formulated as,
heat t ransfer reasistance of react ing mass
Bi =
heat t ransfer resistance at the surface (boundary)
and hence,
B i = ^-± (26)
The relationship between the theories of Semen ov, Frank-Kamen etskii and Thom as can be shown
by function of the Biot number. The Semenov and Frank-Kamenetskii models are two extreme
cases of Thom as theory [5].
a) Bi « 1 b) Bi => 1 c) Bi » 1
Figure 6. Temperature profile in staedy-state at critical conditions as a function of Biot number.
Thomas solved eq. (23) with the boundary conditions gived in (26). The results for
critical values of 5 and 6 as a function of the Biot number are given in figure 7.
When Bi
—*
0 (Semenov Model) then,
( o + l ^Bi
c r
e
If
Bi—>
<*> (Frank-Kamenetskii model) the critical conditions are:
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32
{
.8S
2.0
3.3
and 0„
■{
.19
1.39
1.61
for
o=
0 =
G =
0
1
2
(28)
2.5
0.5
pr
s
sphe re
s ^
cyl inder
slab
1
Bi
->
°o
5 ^ 3 . 3 2
Bi
- > ~
Bi
- >
M
6
->
0.88
1
e„
-
Bi
15
2.0
C
1.0
0
9
C
- > 1 . 6 1
_ ^ I 7 r , 3 9
■ 9 ^ 1 . 1 9
1
r 1
1 1 1
sphe re
cyl inder
slab
i
sphere
s lab
Bi
a)
The
critical
Frank-Kamenetskii
number
b)
The
critical
dimensionless
temperatures
9
c
(centre)
and
5
C
as function of the Biot number e
0
(surface) as functions of the Biot number.
Figure 7. Critical conditions as a function of Biot number [4].
4.3.
THE CHEMICAL REACTION ENGINEERING APPROACH
In th e last years batch and semibatch operations have become more popular due to their versatility
which
allows
the
obtention
of
special
chemicals
-
with
very
good
yields
-
in
small
amounts
(when
compared to those of continuous processes), and permits a rapid change from one process to other
with minor modifications.
However , th e study of accident case histories [1 ] shows that batch units are usually more
frequently involved in accidents (57% of cases) than continuous process plants (about 11% of
accidents).
These
results
ar e
not
surprising
because
batch
processes
are
usually
very
complex,
with
strongly nonlinear dynamics and with time-varying parameters. In a batch cycle there is no steady
state and therefore, batch operation requires continuous corrections and decisions to be made by
th e operator. Moreover , due to th e small production levels and th e variety of processes, the
understanding of reactor dynamic behaviour is usually not economically justified.
Consequent ly , th e optimization of such processes should take into account tw o different
aspects: performance and safety. From the performance point of view, the optimal process design
must allow the manufacture of products with the desired specifications in the minimum amount of
time and with low operating costs. From the safety point of view, optimum process desing must
significantly reduce the risk of thermal runaway, avoiding intermediate accumulation of hazardous
compounds ,
and
reducing
th e
effects
of
cooling
system
malfunction
or
agitation
stoppage.
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Obviously, the ideal situations would be those in which the process is inherently safe [3], that
means, w here no disturbances, whatsoever, can cause an incident.
Hugo, and Steinbach have determined some safety rules for assessing conditions under which
batch or semibatch processes cannot be carried out, and for selecting safe operating conditions,
that have been accepted as practical guidelines by Westerterp and co-workers [26]. In the next
chapter some of these criteria will be reviewed, but a more detailed treatment can be found
elsewhere [17,19-23,26] .
4.3.1.
Batch and Semi-Batch Processes. Two different discontinuous operating modes are usually
carried o ut: batch and sem ibatch. In the first case, the reactor is charged with all reagents, solvents
and catalyst. In the second case, only a part of the reagents is present from the beginning, and the
other part (a reagent or a catalyst) is added.
Reaction vessels for batch operation are normally provided w ith standard cooling/heating jackets
and/or internal coils, a stirrer, a condenser and, for semibatch operation, a feeding system. The
temperature development is controlled by means of removing the heat generated by exothermic
chemical reactions through a cooled heat transfer fluid that circulates in the jacket or in the case of
working at the boiling point through the removal of heat by evaporation by means of a condenser.
For strongly exotherm ic reactions, the heat removed capacity may be too small to keep the reacting
mass at the required reaction temperature, in the case of batch operation, and then the heat
generated by chemical reaction has to be reduced. This can be accomplished by adding one of the
reagents during a certain period of time (semibatch). That means, some additional control of the
reacting mas s behaviou r can be obtained regulating the metering rate.
Different phases [17] can be differentiated in a batch process:
- Phase of heating: The reactor is charged at the starting temperature Tm„ and the reaction starts. If
the reaction rate is suficiently high, this phase is performed in nearly adiabatic conditions (with the
heating/cooling system switched off),while if the reaction rate is not considerable at the starting
temperature, the content of the reactor is heating following a temperature ramp.
Temperature Temperature
Phase of
cooling
/
T i m e
u /
a/ b /
Figure 8. Exam ple of different tactics for cooled batch or semibatch processes, a/ Isothermal
operating mode (T con stan t), b/ Isoperibolic operating mode (T
c
^constant).
Time
- Phase of cooling: When the reacting mass reaches a pre-selected temperature, T„ cooling is
started. After a certain period of time the maximum temperature , T m „ „ is attained. There are
mainly two different operating modes: isothermal or isoperibolic. In the first case, the temperature
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34
of the reaction medium is kept constant by regulating the jacket temperature; in the second case, the
cooling temperature is constant (see figure 8).
It is evident that the mo me nt to start the cooling is critical. If it is started too soon (small T,), the
reaction time will be long and the performance will be reduced; moreover, low temperature can
produce accumulation of one of the reagents and consequently the formation of undesirable by
products (low yield or unstable compounds that can trigger off decomposition reactions). If the
starting is produced too late (high T,) the high temperature obtained can reduce safe operability
margins by triggering off secondary unwanted reactions with the risk of a thermal excursion.
Assuming the uniformity of concentration and temperature in the entire reactor and ideal
disolution [18], the mass and energy balance equations for batch and semibatch processes can be
written as
d t
dC.
2 ,
Q
S
B
S
k=l
n
r
r^ i F.
C
j d V
m
V
m
d t
; j = i . .» ,n
c
(29)
(30)
i=l
d T m _
i
d t r „
r n
r
^ i-1 J k=l
(31)
An important parameter for safety analysis is the adiabatic temperature rise, AT
a
d, which
indicates how much the temperature of the reaction mixture would rise if the reaction were to
proceed adiabatically (q=0) to completion. Replacing eq. (30) into eq. (31), rearranging and
integrating for the specie A with the initial conditions Tn^Tnjg and XA=0
a t t=
0> where % A *
S
^
relative conv ersion of A , defined by XA
=
1"
CA</CA>
it is possible to find that for batch
processes:
ad
C
A
Q
AH
R
p C p
(32)
and then, the relation between the temperature and the conversion in an adiabatic reactor is:
T
m
= T
m
+ A T . Y
ad
A
A
(33)
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4.3.2. Criteria for safe operation of a Batch process . Hugo [17] has determined some rules in
order to decide if a process could be carried out in batch, or semibatch should be chosen because
the heat removal capacity was too small to keep the reaction mixture at the required temperature.
The analysis was applied to a batch process in which the reaction starts adiabatically at the
temperature TmQ and when the reaction mixture has heated itself to the preselected temperature T„
the cooling is started. After a certain period of time the maximum allowable temperature Tm™, is
reachpj (.see figure 9).
From the safety point of view, it is only necessary to limit the study at the point at which the
system reaches the maximum temperature, Tm
m
„,and suppose that at this point the rate of heat
generation and removal are equal, then
U S ( T
m
- T
c
) :
ffl
R
V
D
r ( T
m
_
)
(34)
Temperature
Temperature
o L L l
Time ^ a * ^
n a x
Conversion
Figure 9. Temperature history and temperature-conversion trajectory in a batch reactor [17].
The problem for solving eq.(34) is that the conversion at the maximum temperature, XA
m a
, . '
s
unknown. An approximate value can be found by extrapolating the adiabatic line of conversion
given by eq. (33) to Tm™
x
(see figure 9), so
nimax
J
\nax
A T
(35)
ad
This value of conversion represents the fraction of the chemical heat production required to heat
the reaction mixture from T
m o
to Tm
m
„. The advantage of this formu lation is that XA
m a x
is
independen t of the switch-on point, but at the same time is a too conservative value of XA
max
-
Considering the following formal kinetic formulation:
r
A = -
k C
A
1
.
C
B (
1
- X A )
n
(36)
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it is possible to develop th e energy and mass balances corresponding to th e different operating
phases of the batch process.
For the adiabatic period (Tm<T,):
dt
■=-AT
a d
C
A
(37)
and
X
A
T - T
AT
(38)
ad
with the initial conditions Tm ^ u Q ,
XA=0
at t=0 .
During the heat removal period:
d T
m -U S
( T
m
- T
c
) - A T
dt r
m c
^ C
(39)
d
A
-
f
A
dt C
A
(40)
dividing eq . (39) by eq . (40) , it is possible to find the temperature-conversion trajectory:
U S C
A
(T
m
-T
e
)
d I
m ^ o
+ A T
r
m
r
A
(41)
but, at T
m
= T
m m a x
dT
m
/d t = 0 and d^A/dt * 0 then,
U S _ ~
A T
a d
r
A (
T
n w )
(42)
replacing eq . (42) in eq . (41),
— A T ,
dX
A
a d
r A ^ m ^ ) (T
m
-T
e
)
A ( ^ n v ^ ' ^ e )
(43)
,and introducing the reaction rate expression, eq . (36),
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d T
m
d%
A
AT
ad
T -T
T -T
1-%
A
rt
rr
i -x
A
' E
a
(
T n w
- T
m )
^
•exp
RT
m
T,
X a i
(44)
Hugo and co-workers [19] integrated numerically eq. (44) satisfying the condition given by eq.
(33 ; , for many different initial conditions of T
m
and %A and for many different combinations of
T
m
-T
e
and A . and they found the following em piric correlation:
r i - x
A
. >
K =
l
- x
A
a - V * )
n
V
where
<)
is a dimensionless parameter given by
T -T
( - X
A
) A T
ad
(45)
(46)
and with the correlation parameters m and K, where
m = 0.6 n + 0.8
and
K(3 = P + 0 .114
E a ( T
" ; "
T
l
s
)
( p
2
- l . 2 5
2
)
R T i
(47)
(48)
where p is the dimensionless temperature difference between reaction mass and heat transfer fluid:
E
a
Inserting this approximation in eq. (34), it is possible to obtain the following expression,
x)/
m ax
K p = ( l - x
A
)
n
( l - ^ )
m
(49)
(50)
with the two dimensionless variables P and y
m
ax given by,
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RT^us
¥ m a
* E
a
( - A H
R
) k
m a x
C
A
C
B
V
m
( 5 1 )
0 0
By applying eq . (50), the temperature set-point in order to ensure the control of the reaction can be
set. Once, the data set T
e
, T
m 0
, and T
s
has been established for a specific process, there are some
rules and criteria to be observed. The most imp ortant param eter is the temperature sensitivity of the
reactor, S, defined [17] as,
S = - ^ (52)
d T
e
S takes into account the variation of the maximum temperature respect to any change in the heat
transfer fluid tem perature as the critical param eter. This p aram eter gives a value of the influence in
the reactor temperature of changes in the operating conditions. For example, if S=3 a change of 4
°C in the heat transfer fluid temperature would produce 12 °C of increase in the maximum reactor
temperature that in some circumstances can be dangerous (i.e. triggering off secondary reactions).
Replacing eq. (36) in eq. (34), derivating in function of T
e
, and using the approximative
solution, eq. (50 ), to calculate the derivative of the con version,
S
=WHM)
( 53 )
with,
n m
2B(l-x
A i
)V* (1-V*)
(54)
where
B =
a a d
(55)
R T „
B is the thermal reaction num ber that gives information about the exothermicity and dynam ic of the
reaction. Hugo [17] defined two possible cases: if fx>
1,
S is always smaller than 1, and it
decreases when the temperature difference p increases, then, this is the stable cooling range; if
however
|0.<1,
then S will increase with (J, which means it is possible to go to critical regions
(S>1).
Since generally [3>1, the only requirement for maintaining control of the reaction is |J.>1.
From eq. (54) it is possible to define a B
c r
;
t
when u=l and then using the unfavorable case of
^'
A
max pl
o t the
divisory bo rder line betw een critical and non -critical region (see figure 10).
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0 .0 0 .2 0 .4 0 .6 0 .8 1.0
Figure 10 . Critical limits of B
cr
jt in function of A
m ax
[17].
4.3.3.
Criteria for safe operation of a SemiBatch Process. Steinbach [20-22] followed the same
type of procedure for semibatch processes and developed an empirical correlation based on
computer simulat ion results in order to discriminate between safe and dangerous operating
conditions,
- v
A
- k - C
B o
- t
V
add.
\
y
U - S - t
>
1
V
m
- C p - p
(56)
where V ^ is the volume feeded.
In this case, th e accumulation of unreacted reagents must be avoided, and for this reason, the
semibatch reactor should be operated in an ignited condition (opposite to batch reactor); that
means,
trying
to
maintain
the
reaction
rate
equal
to
the
feed
rate
as
in
an
infinitely
fast
reaction.
For these type of processes a very important point to be considered in the design phase is the
development of some type of interlock that switches off the feeding of reagent automatically in case
of
incident
(i.e.
breakdown
of
cooling,
stirrer
stoppage,
etc.)
Hugo,
Steinbach
and
Stoessel
[22]
showed that it is possible to find an opt imum temperature in order to guarantee th e lowest
temperature increase in case of breakdown of cooling (adiabatic reactor).
4.3.4. Application example. A simple reaction system has been chosen in order to illustrate by
means of an example the design principles explained before.
A
+
B
- > S
+
P
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The system investigated was
a 1:1
molar mixture
of
A and B. Th e objective
is to
assess
if
such
a
process can be carried out batchwise with
CA„=C
B( )
=
4.56 KmoL'm
3
.
The heat
of
reaction
(AHR)
was obtained from adiabatic tests
and is
equal
to
-64.9 kj/mol,
the
specific heat capacity
of
the
reaction mixture
(Cp)
is
2512. J/Kg-K,
and the
density
is
937.
Kg/m
3
, hence pCp=2354 kJ/m
3
K. From the same
set of
experiments
a
simple reac tion rate w as
fitted:
' A - * c
A o
- c
B o
. ( i -
3
t
A
) ( i - c
A o
^ . )
B
o
where k = 2 .446604-10
7
exp(-8348.7/T) m
3
K m o l Is.
The adiabatic temperature rise can be calculated from eq. (31):
A T
H
=
4
-
56
; 6
4
-
9
-
l o3
= 125.7 °C
a d
2 3 5 4 .
From DSC studies
it
was sho wn that an unw anted reaction
(C
—> products) can take place,
and
,
m a x
should
be
established 100 °C.
With this data B
c r
i
t
, eq. (54), can be calculated,
R
8348.7-125.7
7
<
A
From
the
diagram
of
figure
4.7 [17] it is
possible
to
read
A
m a x
that should
be at
least 0.68.
Hence, using eq. (34), the Tm,, can
be
obtained as Tm,, =T
mma x
-%'A
max
-ATad=14.0 °C.
Another important aspect
is
the ratio between the surface area and the volume
of
the reactor
at
the critical conditions, eq. (33).
P - c p . A T
a d
- k - c
B
( i - x ; ) d - c |^-)
S_
=
° _2l (57)
V
= U
(
T
n w -
T
e )
Assuming U=350 W/m
2
K, S/V= 21.4 m
2
/m
3
in
this examp le,
For an
small reaction calorimeter
(11) this ratio is higher, approximately S/V=3 1.4 , but for an standard installation it is too high
(S/V between
3-5
m
2
/m
3
). Th is indicates that this reaction may
be
carried
out in the
laboratory
with
a
small reactor (2
1) but if
it
is
transferred
to an
standard installation
a
runaway will occur.
In the case of semibatch processes, the control of the heat generated
can be
done
by
means
of
the cooling circuit
or by
regulating
the
metering rate.
If the
metering rate
is too
strong,
the
maximum allowable temperature can be overshot, but if it is too low, the reaction rate can be low
and the total reaction time
too
long, with the problem of accumulation
of
unreacted reagents into
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41
the reactor. Figure 11 shows an example of this situation. Normally, the optimum dossing time
can be calculated once the working temperature h as been selected by m eans of,
A H C
A
V
m
A
o
d° s U S ( T
m
- T
e
)
393
(58)
n 1 1 1 1 r
1320 1650 1980 23t) 2540 2970 3300
Time (s)
Figure 11 . Temperature-time profiles of a semibatch processes, modifying the metering rate.
4.3.4. Extension to heterogeneous systems. A great number of industrial processes involve
systems in which two partially miscible phases coexist, which are in general, organic and aqueous.
However, a considerable amount of incidents, concerning runaway reactions occur in this type of
system [2].
The analysis of reactions taking place between partially miscible liquids is further complicated
due to the mass transfer phenomena between the phases. The reaction usually takes place in one
single phase, which means one compound present in the non-reactive phase diffuses to the
interface, and then into the bulk reactive p hase; w hile diffusing into the reactive ph ase, it reacts to
form the product. Examples of this type of systems are nitrations, sulphonations, polymerisations,
hydrolisis, esterifications, alkylations, etc.
The formulation described above for homogeneous systems has been extended by Steensma and
W estertep [23,24] for liquid-liquid reactions.
In order to study these type of reactions the following simple reaction w as con sidered:
A + B
—>
products
According to the general theory of mass transfer combined with a chemical reaction [26], it is
possible to define the following two typical situations:
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42
Figure 12. Example of semibatch process with two liquid phases.
a/ B is present in the continuous phase (subscript c) and A is present in the dispersed phase
(subscript d) in form of droplets of different size.
Cont inuous
B
Dis p e r s e d
\ A+B — ► products
Figure 13. B is transfered into the dipersed phase where it diffuses and reacts with A. The reaction
occurs only in the dispersed phase.
b/ B is present in the dispersed phase and A is present in the continuous phase (see figure 14).
For these cases expressions for the overall reaction rate can be developed [26], depending on
th e
controlling
phenomena
(mass
transfer
or
chemical
kinetics)
and
consequently,
some
new
variables that did not exist in homogeneous systems have an important influence making the
develoment of the criteria more complex:
- The droplet size, which will determine th e interfacial area and thus affecting the overall reaction
rate in case of mass transfer control.
- The distribution coefficient between th e phases , which will determine th e maximum
concentration of the reactant in the reaction phase.
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43
- The phase inversion phenomena which is capable of producing abrupt changes in the reaction rate
during a semi-batch process [25].
C o n t i n u o u s
A+B products
D i s p e r s e d
B
Fig ure 14. B is transfered into the con tinuo us ph ase w here it diffuses and reacts with A. The
reaction occurs only in the continuous phase.
5 .
Protect ion m easures against runaway react ions
As previously stated, the protection measures are taken when the process is outside of desired
conditions and normally it is going to a dangerous state. The objective of these measures is to
restabilize the control of the reactor or at least reduce the danger for people, and the damage to both
the installation and the environment. The type of action required is highly dependent on the nature
of the reaction which must be kept under control and also on the reason for the potentially
dangerous situation.
5.1. STOPPING THE RUNAWAY
5.1.1.
Full cooling. In cases where the temperature of the reacting mass is high but the rate of heat
generated is still w ithin the heat remov al capacity of the reactor (see figure 15), then switching to
full cooling will suffice. Interlocking systems of this type must be implemented on reactors in
which potentially dangerous reactions are carried out.
Thermal
f l o w
Tempera ture
Figure 15. Effect of emergency full cooling in stopping the loss of control. The heat removal flow
capacity is increased from 1 to 2.
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44
5.1.2. Quenching, a/ Fast addition of a supressant: The method is based on the inerting in situ of
the reactive mixture through the injection of a calculated amount of inert diluent which reduces
reaction rate by cooling the mix ture and also by dilution, or a chem ical inhibitor which modifies
the reaction rate expression. The application of such a procedure requires that a number of
previous considerations and preparation be made:
- Choice of an appropriate liquid which does not react too exothermally with the reaction mixture.
The addition of an inhibitor requires also intimate knowledge of how the reaction rate can be
influenced
- Sufficient free volume in the reactor
- Technical installations which provide the addition of the liquid in due time.
b/
Dumping of the reactor contents: The reaction mixture is dumped into a vessel which contains
cold diluent with or without an inhibitor. This method requires again good knowledge of the
reacting m edium and technical installation to perform the dump ing procedu re.
5.2. PRESSURE RELIEF
The venting of the reaction mass is the most used safety measure. The main effect of pressure
relief is temperature stabilisation, due to the heat removed by evaporation. However, this system
has three main problems:
- the design of the relief system (vent area sizing and starting pressure)
- the containm ent of the ejected material
- its ineffectiveness for low vapor pressure systems
Th e sizing of the vent line is one of the most imp ortant aspects in safety of chemical reactors or
storage tanks, since a faulty design could lead to a catastrophic vessel failure with very serious
consequences. The adequacy of a particular relief vent depends on three factors:
- the accuracy in the determination of the "worst case" initial conditions,
- the accuracy with which the thermo-kinetics and physical properties of the reacting mass are
known,
- the accuracy with which the effects of the emergency device can be calculated.
5.3 .
CONTAINMENT
The objective of a containment system is to keep toxic chemical substances away from people
and environment, to protect the surroundings from missile generation, fires and pressure wave
effects, and to avoid chain incidents (domino effect).
F i n a l r e m a r k s
Due to the limited space available, this paper has only presented the main points. Some of the
aspects mentioned here will be covered in more detail by other contributions, however, the cited
literature is strongly recommended.
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N o t a t i o n
45
C
Cp
CPL
D
Ea
F
H
K
K
L
k
N
n
E
n
R
n
Q
q
R
R
r
S
T
U
US
V
Set of chemical species
orpre-exponential factor,
Molar concentration,
Specific heat capacity,
M olar heat capacity of a chemical species,
Diffusivity,
or diameter,
Activation energy,
Molar flow,
Molar enthaply (liquid),
constant,
Overall mass transfer coefficient,
Reaction velocity constant,
Number of species
Number of reactant feed streams
Number of independent reactions
Molar Hold-up,
Volumetric flow,
Thermal flow,
Rate of chemical production,
Radius,
or Gas constant,
Rate of reaction,
Surface,
or Sensitivity
Temperature,
Heat transfer coefficient,
Effective heat transfer coefficient,
Volume,
Molar volume,
Molar fraction
or distance from the center
depends on kinetics
mol -n r
3
J K g - ^ K "
1
J-mol-^K"
1
7
-1
m
z
-s '
m
J-mol-
1
mol-s"
1
J-mol-
1
n v s
- 1
depends on kinetics
mol
-,3.,
m
J
-s
_ I
W
mol-m
_3
-s
_1
m
J-mol"
1
-K"
1
m o l m "
3
-s
_ 1
m
2
K
W-m-2-K-
1
W-K"
1
m
3
m
3
-mol
_ 1
Greek symbols
X
r
y
Conversion
Thermal capacity,
toichiometric coefficient, reactant(-), product(+)
Thermal conductivity,
Dynamic viscosity,
partial order of reaction
J-K-l
W-nH-K"
1
k g - i r r ^ s "
1
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46
e
p
a
T
Parameter of a heat transfer correlation
Density,
Geometric simetry factor
Time constant,
k g m
m3
Subscripts
0
cr
e
i
L
R
s
w
Supersc
initial con dition
Critical
Heat transfer fluid
Reaction or Input
Liquid
Rem ove d, reaction
Set-point
Wall or Wetted part
riptS
ad
E
h
J
m
r
T
z
Adiabatic
Feed of reactants
Heating
Species
Reaction mixture
radial
Total
Axial
continuous phase
dispersed phase
reaction phase
R e f e r e n c e s
1.
Ras mu ssen, B. (1988) 'Occurrence and imp act of unw anted chemical reactions', J. Loss
Prev. Process Ind. 1, 92 .
2 .
Barton, J.A. and Nolan, P.F. (1984) 'Runaw ay reactions in batch reactors', The Protection
of Exhotermic Reactors and Pressurised Storage Vessels, IChemE Symposium Series, 85, 13.
3 .
Reg enass , W. (1984) 'The control of exotherm ic reactors', The Protection of Exhotermic
Reactors and Pressurised Storage Vessels, IChemE Symposium Series, 85, 1.
4 . Semenov , N.N . (1928), Z. Phys. Chem. 48, 571 .
5 .
Fran k-K am enets kii, D.A. (1969) 'Diffusion and heat transfer in chem ical kinetics', 2nd ed,
Translated by J.P. Appleton, Plenum Press, New York .
6. Gray , P. and Lee , P.R. (1967), 'Thermal Explosion theory', Ox idation and Com bustion
Reviews, vol. 2, Elsevier, New York .
7. M erzh ano v, A.G. and Du bov itskii, F.I. (1966 ) 'Present state of the theory of thermal
explosion' , Russ. Chem. Revs., 35 (4), 278.
8. Sem enov , N.N . (1959) 'Som e problem s of chem ical kinet ics and react ivi ty ' vol 2,
Translated by J.E.S. Bradley, Pergamon Press, London.
9. Bo we s, P.C . (1984) Self-heating: evaluating and controlling the hazard s, Dep artment of the
Environement, B uilding Research E stablishment, London .
10. Grew er, T., Klusacek , Loffler, H.U., Rog ers, R.L. .Steinbach, J. (1989) 'D etermination
and assessement of the characteristic values for the evaluation of the thermal safety', J. Loss Prev.
Process Ind., 2, 215.
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47
11 .
Riesen ,R. and Grob , B. (1985) 'Reaction Calorimetry in Chem ical Process D evelopment',
Swiss Chem., 7, 39.
12 . Grew er.T. (1975), Chem .-Ing.-Tech.
,51,231.
13 .
Go rdon ,M .D., O'Brien, G.J., Hensler , C.J., Marcali , K. (1982), 'Mathem atical M odeling
in Therm al Hazards Evaluation', Plant/Operation P rogress, 1, 27 .
14. Gra y, P. , Harp er, M.J. (1960 ) Reactivity of solids , Pro c. of the 4th Symp . on the
ReacH', iiy or Solids, Elsevier, Amsterdam, 283.
15.
Frank-Kam enetskii, D.A. (1939), Zuhr. Fiz. Khim., 13, 73 8.
16. Tho mas , P.H. (1958), Trans. Faraday Soc.,54, 60.
17.
Hu go, P. (1980) 'Start-Up and Operat ion of Exotherm ic Batch Processes' , Chem. Ing.
Tech., 52, 712.
18 . Fro me nt , G.F. and Bischoff, K.B. (1990) Chemical Reactor Analysis and Design, 2nd ed.,
J. Wiley & Sons, Singapore.
19.
Hu go, P., Konczella , M. and Mau ser, H. (1980) 'App roximation solutions for the design
of exothermic batch processes with indirect cooling', Chem. Ing. Tech., 52, 761 .
20. Hu go, P. and Steinbach , J. (1986) 'A Comp arison of The Limits of Safe Operation of a
SBR and CSTR', Chem. Eng. Sci . 41,4,1081-1087.
21. Hu go, P., Steinbach , J. and Stoessel, F. (1988) 'Calculation of the M aximum Temperature
in Stirred Tank Reactors in Case of a Breakdown of Cooling', Chem. Eng. Sci. 43, 8, 2147-
2152.
22. Steinbach, J. (1989) 'Fundam entals/Theory of Run away Chem ical Reactions', Conference
on Techniques for Assessment of Chemical Reaction Hazards, London 5/6 December.
23 .
Steens ma, M. and W esterterp, K.R. (1988) 'Therm ally safe Op eration of a cooled semibatch
reactor. Slow liquid-liquid reactions', Chem. Eng. Sci. 43, 8, 2125-2132.
24.
Steensm a M. (1990) ' Run away and Therm ally safe Op eration of batch and semi-batch
reactors', Ph.D. Thesis, Deventer.
25.
Al-Khud hairy, D., Barcons, C , Hernandez, H, and Zaldivar, J.M. (1989), 'Modell ing of
Two Liquid Phases with Chemical Reactions Applied to Toluene Mononitration', Technical Note
N° 1.89.57, Comm ission of The European C omm unities, Joint Reasearch Centre, Ispra (Italy).
26. Westerterp, K.R., Van Swaaij , W.P.M. and Beenackers, A.A.C.M. (1987), Chemical
Reactor Design and Operation, Student ed., J. Wiley & So ns, M anchester.
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CONTROLLING RUN-AWAY REACTION HAZARDS WITHIN THS FRAMEWORK OF THE
SEVESO-DIRECTIVE
Dr. G. DROGARIS
Institute for Systems Engineering and Informatics
CEC - JRC - Ispra Site
ABSTRACT. The requirements imposed by the Council Directive 82/501/CEC
on the major-accident hazards of certain industrial activities (SEVESO-
Directive) both on manufacturers and the national Competent Authorities
are briefly presented followed by a short reference to other relevant
EEC Directives, international conventions and other related activities
as well as various guidelines codes of practise etc. for accident pre
vention. Safety related standards are also discussed. A general
overview of the national approaches in the implementations of the
SEVESO-Directive with emphasis in tackling run-away reaction hazards in
the safety report (notification) is given. Major Commission activities
such as the Major Accident Reporting System (M.A.R.S.) and the Commu
nity Documentation Centre on Industrial Risk (C.D.C.I.R.) are described
and some lessons learned from accidents involving run-away and other
unexpected reactions and/or electrostatic loads are also presented.
1. Introduction
The EEC Council Directive 8 2/501/EEC [ 1] , or the so-called "SEVESO-
Directive" provides an effective tool for an enhanced accident and loss
prevention policy. This Directive was the response to a series of major
accidents occurred in the last few decades and which attracted the
interest of the public to the hazards presented by industrial installa
tions and highlighted the need for an improved European policy to con
trol potentially dangerous activities.
The accident of 1976 in Seveso, North Italy is mainly considered
as the initiating event for this directive. However it should be
reminded that the disaster of 1974 in Flixborough, U.K. had already
initiated reactions to this same end. Actually the legal frame for the
implementation of this directive in U.K. is based on acts and actions
49
A. B enuzzi and J. M. Zaldivar (eds.). Safely of Chemical Batch Reactors and Storage Tanks,
4 9 - 7 7 .
© 1991 ECSC, E EC, EAEC, Brussels and Luxembourg. Printed in the Netherlands.
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50
taken according to the recommendations of the Flixborough accident
investigations.
Up to now this SEVESO-Directive has been amended twice. The first
amendment was adopted in March 1987 as a response to the 1984 disasters
in Bhopal and Mexico City and mainly aimed to tightening up the provi
sions for certain very dangerous chemicals, including chlorine, MIC,
phosgene and sulphur trioxide.
In 1986 the accident in Basel demonstrated the need to strengthen
the requirements of the Directive for isolated storage installations.
The second amendment that was adopted in November 1988 extended sub
stantially the scope of the Directive to storage of dangerous sub
stances and/or preparations at any place. This amendment also attempted
to clarify requirements for risk communication to the public.
The publication cited here [1] contains the consolidated text of
the SEVESO-Directive after the first two amendments.
A fundamental revision of this Directive has been already initi
ated. It will be based on the experience gained after over five years
of application of the SEVESO-Directive, which came in force in July
1984. Requirements for controls on land-use planning both for new
installations and new urban developments around existing installations
will be included following a council resolution [2] .
Here below the objectives and the requirements of the SEVESO-
Directive are presented. Further the two main activities of the Insti
tute for Systems Engineering and Informatics of the CEC Joint Research
Centre at Ispra as part of its support to the Commission for the imple
mentation of this Directive, namely the:
- Major Accident Reporting System (M.A.R.S.), and
- Community Documentation Centre on Industrial Risk (C.D.C.I.R.),
will be discussed.
There are also other EEC Directives related to safety issues as
for example the Directive on health and safety at work and the classi
fication, packaging and labelling of dangerous substances. They will be
presented together with other similar international regulations as well
as rules and guides on the same subject recently developed in the USA.
The role of standards on industrial safety will be also discussed.
SEVESO-Directive as all Council Directives are addressed to the
Member States. This means that they are not automatically imposed to
the national legislation; on the contrary each Member State has to
develop a legislative framework in which the requirements of the Direc
tive will be implemented. A general overview on the national approaches
for the implementation of this Directive with emphasis on the safety
reports of installations is therefore necessary for getting an insight
in the practices for controlling major industrial hazards. Methods of
tackling run away reaction hazards in the safety reports will be dis-
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51
cussed separately.
Up to the end of 1990 almost 100 accidents have been registered in
M.A.R.S.
Run-away or other unexpected reactions have been identified
among the causes in 17 incidents or accidents. Their characteristics
and the lessons learned from these 17 accidents as well as from 7
acci
dents involving electrostatic loads conclude this presentation.
2. The SEVESO-Directive
2.1. Objectives
The objectives of the SEVESO-Directive, which are mainly based on the
objectives and principles of the Community's Environmental policy, can
be summarized as follows:
a) The protection of the public and the environment as well as of work
ers from the hazards connected with industrial activities involving
dangerous chemicals.
b) Convergence of legislative and practical national approaches to
industrial safety towards an enhanced level within the frame of a
free market.
c) Accident and Loss Prevention, mitigation of consequences of major
accidents.
2.2. Content of the SEVESO -Directive
2.2.1. Definitions-Application of this Directive.
This Directive covers
industrial activities
where
dangerous substances
are processed or
stored. Both terms are defined in Article 1 of the Directive. In gen
eral toxic, flammable, explosive and oxidizing substances are consid
ered as dangerous substances. Annex IV the Directive contains indica
tive criteria for characterizing substances as toxic, flammable, explo
sive or oxidizing according to their physicochemical properties. In
addition 180 dangerous substances are listed in Annex III with inven
tory threshold values. Annex II refers to storage of dangerous sub
stances (either isolated or associated to a process plant) and contains
a list of 28 dangerous substances (26 out of these are listed also in
Annex III) with respective inventory threshold values as well as inven
tory threshold values for the various categories of dangerous sub
stances .
Industrial activities for the purpose of this Directive is consid
ered any industrial installation involving, or possibly involving, one
or more dangerous substances. This implies that
manufacturers
(defined
as any person in charge of an industrial activity) should also consider
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52
the potential generation of a dangerous substance (e.g. generation of
nitrogen oxides as a result of uncontrolled and/or unintended decompo
sition of an even not dangerous substance).
Annex I contains also an indicative list of processes and unit
operations that are covered by this Directive (practically all widely
applied processes of organic and inorganic chemicals). This Directive
is not applied to nuclear and military installations, manufacturing and
separate storage of explosives, gunpowder and munition and mines.
Installations for the disposal of toxic and dangerous waste are also
excluded provided that are covered by other Community
Acts.
Since for
the time being no such Acts exist this exclusion is considered inac
tive.
The concept of
major accident
is rather fuzzy despite its defini
tion in the Directive as: "an occurrence such as a major emission, fire
or explosion resulting from uncontrolled developments in the course of
an industrial activity, leading to a serious danger to man, immediate
or delayed, inside or outside the establishment, and/or to the environ
ment,
and involving one or more dangerous substances".
Therefore a scale of "gravity indices" has been adopted for a two-
year trial period [2] . Three gravity indices, ranging in a scale from 1
(worth noting) up to 5 (catastrophic), describe:
- the actual or potential danger (based on the amount of dangerous sub-
stance(s)
involved);
- the extent of the consequences of the accident;
- the extent of intervention or safety measures external to the indus
trial activity.
But the scale has not yet been used to define a "threshold" of
gravity for notification purposes.
2.2.2. Notifications-Safety Repo rts.
The manufacturers of installations
are obliged to take all measures necessary to prevent major accidents
and to limit their consequences for man and environment. The manufac
tures have to prove to the Competent Authorities (see point 2.2.3.
below) that they have identified the major hazards and have taken all
proper safety measures and precautions. These obligations (defined in
Articles 3 and 4 of the Directive) are valid if the inventory of dan
gerous substances in an installation exceed the lower inventory thresh
old values specified in Annex II and III. Should the inventories exceed
the higher threshold values then manufacturers have to submit a notifi
cation containing information on dangerous substances, the installa
tion, major hazards and safety precautions (safety report). Annex V of
the Directive contains the minimum content requirements for this safety
report.
These installations covered by the requirements of the
Arti
cle 5 of the Directive are the so-called top tear sites.
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These requirements apply
to
both
new and
existing facilities.
Major modifications of existing installations are treated as new
installations.
2.2.3. Com petent Authorities. The
Member States have
to set up or
appoint the Competent Authority (or Authorities) responsible for
the
implementation of the Directive. The complete list of all Competent
Authorities has been given in [ 4 ] . Almost half of the Member Countries
have appointed more than one Competent Authority. Environmental Min
istries are the most common Competent Authorities (9 Member
Countries),
while the Ministry of Labour has been also appointed as one of the Com
petent Authorities in four Member Countries. In Ireland and U.K.
autonomous bodies (Health and Safety Executive
in
U.K., Occupational
Safety and Health in Ireland) are the Competent Authorities.
The Committee
of
the Competent Authorities (CCA) chaired
by the
Commission (DG XI/A/2) and composed of the national Competent Authori
ties meets regularly every four months and provides a wide forum for
exchange of experience and review of the progress in the implementation
of the Directive.
2.2.4. Information to the Public.
The Directive required that "persons
liable to be affected by a major accident originating in a notified
industrial activity within the meaning
of
Article
5
are informed
in an
appropriate manner of the safety measures and of the correct behaviour
to adopt
in
the event
of an
accident". Further all this information
disseminated to the public should be made available to the other Member
States concerned.
The second amendment of the Directive underlined the importance
of
this information flow to the public requiring that such information has
to be communicated to all persons liable to be affected in case of an
accident
without these persons
to
request
it and adding that this
information has to be repeated and updated at appropriate intervals and
shall also
be
made publicly available. Annex VII states
the
minimum
requirements for the information to be communicated to the public.
2.2.5.
Major Accidents.
Experience gained from accidents is precious
for
an
active prevention policy. Hence the Directive requires that
as
soon as
a
major accident occurs the manufacturer notifies the Competent
Authority providing adequate information for assessing the effects of
the accident on man and the environment and measures to prevent recur
rence of such an accident.
The Competent Authority
in
turn has to notify the accident
to
the
Commission. Minimum requirements to be supplied to the Commission for
major accidents are given in Annex V I.
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This notification procedure is the basis of the M.A.R.S. see
point 2.3. herebelow).
2.2.6.
Emergency Planning.
The
Competent Authorities examining
the
notification of installations submitted pursuant to Article 5 shall
ensure that internal emergency plans sufficient to cope with potential
major accidents have been drawn by the manufacturer.
Further they shall ensure that
an
emergency plan
is
drawn
up
for
action outside the establishment in respect of the information col
lected from safety reports.
It shall be clarified that the Competent Authority shall not nec
essarily draw up emergency plans but shall mainly ensure adequate
information flow to the emergency planning authority(ies).
2.2.7.
Exchange
of
Information
and
Experience.
Article 12 requires that
"the Commission shall set up and keep at the disposal of the Member
States a register containing a summary of the major accidents which
have occurred within the territory
of
the Member States, including
an
analysis of the causes of such accidents, experience gained and mea
sures taken, to enable the Member States to use this information for
prevention purposes".
Information obtained by the Competent Authorities and/or the Com
mission within the framework of this Directive are considered confiden
tial.
This confidentiality requirement, however, "shall not preclude
the publication by the Commission of general statistical data or infor
mation on matters of safety containing no specific details regarding
particular undertakings or groups of undertakings and not jeopardizing
industrial secrecy" (Article 13 ).
2.2.8.
Application Schedule.
The Council Directive 82/501/EEC required
Member States to take the measures to comply with it at the latest on
January 8
t h
, 1984. Submission of safety reports of existing installa
tions was to be due
by
latest July 8
t h
, 1989. In the mean time instal
lations covered by the requirements of Article 5 should submit a decla
ration (name, address, location, type of activity, dangerous sub
stances) latest by January 8
t h
, 1985.
Amendment 1 came in force 18 months after its publication (i.e.
September 19
t h
, 1988 ) but safety reports for existing installation sub
jected to the provisions of this Directive for the first time following
adoption of this amendment were to be submitted not later than
March 1 9
t h
, 1989.
The second amendment applies
to new
installations latest from
June
l
c
,
1990 and will become effective for existing installations
by
'latest June 1
s t
, 1991.
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Existing installati ons covered by the requireme nts of Article 5
for the first time following adoption of this second amendment have to
submit safety reports by latest June 1
s t
, 1994.
This directive can be amended by a majority of 45 vot es, the votes
of the Member States being weighted as provided for in Article 148(2)
of the Treaty.
2.3.
Ma jor Accident Reporting System (M.A.R.S.)
To store and retrieve the accident reports notified by the Member
States under a rticl es 10 and 11 of the SEVES O Directiv e (see point
2.2.5. above), the M.A .R. S. (Major Accident Reportin g System) data bank
has been established at the JRC/I SEI. The content of the information to
be supplied has been defined in consultation with the Committee of Com
petent Authorities (CCA), so that:
- all countries can use a uniform reporting procedure;
- the inform ation supplied is consist ent with the requiremen ts of the
Directive;
- the informatio n is adequate to under stand the primar y as well as the
underlying causes and circumstances of the accidents;
- information can be easily processed and stored in the M.A .R. S. infor
mations structure.
Special accident reporting forms , designed to meet the above
requirem ents, have been adopted and are now in use. Details of this
reporting form have been presented elsewhere [ 3 , 5 ] . The main topics
covered by it are:
1) general data of the accident;
2) type of accident and substances involved;
3) circumstances of the accident;
4) emergency measures taken;
5) analysis of causes;
6) nature and extent of damage;
7) preventive measures.
Accident notifications are , upon rec eipt, loaded into the M.A .R. S.
(working language of M.A.R.S. is English) and analysed in order to:
a) Classify the notified accidents according to var ious parameters
(country, year of occurrence, type of activity, type of accident,
consequences, substances involved).
b) Calc ulat e gravity indices (see also point 2. 2.1. above).
c) Identify the c ausat ive f act ors . This is a very import ant step
because it enables one to extract lessons to be learned from each
notified accident.
Finally, a feedback by the notifying Competent Authorities ensures
that essential features of the notified accidents are correctly inter-
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preted and that all important lessons to be learned from each notified
accident are identified.
Up to the end of 1990 , 98 accident notifications had been received
and loaded into M.A.R.S. Though the Directive requires notification of
major accidents only, in practice the tendency is, whenever important
lessons are to be learned from such events, to report also near misses
and incidents that had the potential to lead to serious consequences.
M.A.R.S.
enables the Commission to fulfil the requirements of
arti
cle 12 of the Directive by the preparation of the following documents
at regular intervals:
a) At each CCA meeting, a summary of major accidents notified, indicat
ing causes, consequences and measures to prevent recurrence of
simi
lar accidents and/or mitigate the consequences. This report as well
as the content of M.A.R.S. are confidential (see also point 2.2.7.
above).
b) A report on lessons learned from notified accidents containing also
some general statistical data. This report is purged from all confi
dential information so that it can be made periodically available to
the public. The first version of it has been recently published as
an EUR-report [3 ].
2.4. Com munity Docum entation Centre on Industrial Risk (CDC IR)
In addition to M.A.R.S., the CDCIR is a Commission activity aiming to
diffuse safety-related knowledge and experience to the public. The
objectives and tasks of the CDCIR have been defined as follows [ 6 ] :
"One of the most essential areas for action identified was the need for
a systematic diffusion of information concerning the practical imple
mentation of the Directive in the Member States, including the techni
cal rules and guidelines applied, the safety practices and the lessons
learned from major accidents. Therefore, the Commission decided to set
up a Community Documentation Centre on Industrial Risks (CDCIR). This
Documentation Centre is run by the European Commission, Joint Research
Centre,
Institute for Systems Engineering, at Ispra, Italy. Through the
Documentation Centre the Commission plays a very significant role as a
central point for the collection and classification of technical rules
and documents issued by national governments or produced by national or
international organizations, industrial and professional associations
and so on. Furthermore, the Centre also actively looks for any other
relevant issues in the field of industrial risks. The Documentation
Centre collects, classifies and reviews technical rules, guidelines and
documents concerning the requirements of the Directive 82/501/EEC, as
well as the safety of industrial installations run by governments,
administrative, scientific or technical bodies, national or interna-
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tional organizati ons and industrial or professional associa tions. Docu
mentation on major accidents in the form of reports and videotapes are
also collected and reviewed".
The documents collected in the CDCIR are classified as follows:
i) the SEVESO Directive requirements and related issues ;
ii) techni cal guid elin es or safety asses sment s specific to non pro
cess/facilities;
iii) technica l guide lines or safety as sessme nts spe cific to a process
or a facility;
iv) accident document ation;
v) other relevant issues.
This list contains only the five major categories. Details on sub
categories and on the CDCIR organization are available elsewhere [ 7] .
Up to now the number of documents collected by the CDCIR
approaches 10 0 0 . Four volumes of the inventory have been published (the
third one is a consolidated version containing the first two and the
fourth one is dedic ated to acciden t case historie s availab le in the
literatures.
Upon request the CDCIR may provide to any interest party:
a) a list of documents or other issues available for a specific subject
relevant to the CDCIR scope. In case of a general inquiry the pub
lished CDCIR catalogues will be forwarded to the party making the
inquiry, if these are not already in its possession;
b) copies of docume nts conta ined in it when these are not covered by
copyright or are not restricted in distribution. For documents cov
ered by copyright or which are restricted in distribution, the CDCIR
will advise on the proper contact address.
The CDCIR is also available for on site consultation upon request.
Inquiries of any type should be addressed to the attention of
Mr.
Wiederstein,
C.C.R.,
T.P. 6 32 ,
1-21020
Ispra (VA) , Italy.
3. Other Related Directi ves, Regulations and Standards
3.1. Other EEC Council Directives
One of the major issues in the SEVESO-Di rective is the characteriz ation
and identification of dangerous substances (see also point 2.2.1.
above). This same problem is also tackled by the so-called CPL
(Classification, Packaging and Labelling) Dire ctive [ 8 ] , where explo
sive, oxidising, easily flammable, flammab le, very to xic, toxic , harm
ful,
corrosive and irritant substances and preparations are defined.
Annexes of the CPL-Directive as well as its amendments contain list of
substances and preparations classified to one of the categories men-
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tioned above.
Another Council Directive related to prevention of major hazards
and amelioration of their consequences is the 89/391/EEC Directive [ 9] .
Though the objective of this Directive is limited to occupational
safety and health issues there are quif.e a few common issues with the
SEVESO-Directive (accident prevention, hazard identification, personnel
training,
etc.);
risk communication and consultation issues are however
limited to the labour force of the establishment concerned. Within the
framework of the Directive 89/391/EEC, another Directive [10] contain
ing the minimum safety and health requirements for workplaces has been
already issued and further actions are expected.
Different, minimum requirements are set for new and existing
installations; a 3 years period is given to existing installations for
conforming with the respective minimum requirements.
3.2. Regulations in USA
The OSHA is also preparing a new rule with reference to safety manage
ment of highly hazardous chemicals [11] . This proposed rule, which
makes reference to the SEVESO-Directive, mainly refers to a process
hazard analysis and gives emphasis to managerial issues (procedures,
personnel training, safety reviews, safety audits, incident investiga
tions, emergency planning and
response).
The primary requirement for on-site emergency response in USA is
the OSHA regulation 29 CFR 1910.120 "Hazardous waste operations and
emergency response", while the framework for off-site emergency plan
ning is the Title III SARA (the Superfund Amendments and Reauthoriza
tion Act) also known as the Emergency Planning and Community Right-to-
Know Act.
On an international level there are a lot of initiatives on Major
Accident prevention or related issues.
3.3 . International Gu idelines, Conventions, etc.
The OECD is very active on this area and work is carried out from an ad
hoc group of experts and in a series of workshops. Recent relevant OECD
publications include decision-recommendations on provision of informa
tion to the public and public participation in decision-making
pro
cesses,
exchange of information on accidents [12], good practices for
accident prevention [13 ], risk communication to the public and the role
of operators in accident prevention and emergency response [14] and
land-use planning under consideration of major accident hazards [15] .
The World Bank has also developed guidelines for identifying, ana
lyzing and controlling major hazard installations in developing coun-
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tries [16] and has developed a hazard assessment manual which provides
measures to control major hazard accidents affecting people and the
environment. A list of dangerous substances is included [17].
United Nations Environment Programme has also prepared a handbook
on the APELL Process [18] (Awareness and Preparedness for Emergencies
at Local Level). This process is designed to assist decision makers and
technical personnel in developing countries to identify hazards and
prepare emergency response taking into account local conditions.
International conventions for major accident prevention are under
preparation in the following forum:
- United Nations Economic Commission for Europe;
- Council of Europe (compensation for damage resulting from dangerous
activities);
- Nordic Council;
- International Labour Office (Code of Practice on the Prevention of
Major Industrial Accidents).
Codes,
guidelines or technical documentation under preparation at
international level include:
- code of conduct to promote economic developments focus on accident
prevention and on emergency response (United Nations Centre for
Transnational
Corporations);
- guidelines for disaster prevention including land use and prepared
ness (United Nations Disaster Relief Coordination);
- technical documentation on chemical spills at sea (International Mar
itime
Organisation);
- a PC-Safety Audit System for identifying, analysing and controlling
major hazard installations (World Bank);
- guidelines on external hazard, human error and common cause failure
(International Atomic Energy Authority);
Other relevant activities at international level worth mentioned:
- study on circumstances and causes of accidents associated with the
release of chemicals (World Health
Organisation);
- international programme for the promotion of working conditions and
the Environment-PIACT (International Labour Conference);
- preparation of Environmental Health criteria documents (International
Programme on Chemical Safety);
- studies on lessons learned from emergencies after accidents involving
dangerous substances (EEC-CDCIR);
- studies on environmental accidents (EEC-CDCIR);
- studies on effective provision of public information on major indus
trial accident hazards (EEC-JRC).
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3.4. Literature on Major Accident Hazards
Consequently there is also a very extensive literature on major
acci
dents hazards. The CDCIR inventory publications [19] give a good
overview of the available material. With reference to guidelines on
hazard and risk evaluations and on safe handling of dangerous sub
stances very active are the H.S.E. [20 ]. The Institution of Chemical
Engineers,
the American Institute of Chemical Engineers, which has also
created a "Center for Process Safety", U.S. EPA and OSHA. It is also
worth noted that manufacturers are giving an increased attention to
safety issues [3,21-25].
3.5. Safety Related Standards
There are standards specifically related to safety. However standards
covering various areas such as indicated herebelow are also related to
safety issues:
- fabrication of various equipment (pumps,
etc.),
- pressure vessel fabrication,
- steam boiler fabrication,
- construction,
- civil works,
- testing and inspection of equipment/installations,
- electrical apparatus/area classification,
- safety devices,
- fire protection,
- fire detection,
- fixed fire extinguishing systems,
- fire extinguishers,
- personnel protection equipment,
- safety at work places.
Each country has its own standardization organization (e.g. DIN -
F.R.G., AFNOR - France, BSI - U.K.,
etc.).
In some countries not all
subjects are covered by standards; for certain issues codes of prac
tices are issued instead (e.g.
U.K.).
Specific areas may be covered by
other organizations (e.g. in France the standardization organization is
AFNOR but electrotechnical standards are covered by UTE). Finally in
the U.S.A. standards are issued by various organizations (ASTM, API,
NFPA,
etc.).
Due to the historical development of the various standardization
organization various standards on the same subject may differ substan
tially. In areas that have been recently developed (e.g. instrumenta
tion and control systems) there exist ISO standards that have been also
adopted by most countries. This is not however easy for all areas. In
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the European level at least an harmonization of standards is needed to
remove trade barriers in view of an open European market. For this pur
pose the European Committee for Standardization (CEN - Comite Europeen
de Normalisation) has been created. CEN is an association of the
national standards organizations of 18 countries of the European
Eco
nomic Communities (EEC) and the European Free Trade Association (EFTA).
CENELEC (European Committee for Electrotechnical Standardization)
deals specifically with electrotechnical standards.
CEN and CENELEC member countries are Belgium, Denmark, F.R.G.,
France, Greece, Ireland, Italy, Luxemburg, Netherlands, Portugal, Spain
and U.K. (EEC), Austria, Finland, Island, Norway, Sweden, Switzerland
(EFTA).
Their official languages are English, French and German. Member
ship is open to the national standards organization of any European
country which is, or is capable of becoming, a member of EEC or EFTA.
The principle task of CEN and CENELEC is to prepare European Stan
dards (EN) . Other documents published may be Harmonization Documents
(HD) or European prestandard (ENV).
- An European Standard (EN) is a set of technical specifications estab
lished, in collaboration with and with the approval of the parties
concerned in the various member countries. It is established on the
principle of consensus and adopted by the votes of a weighted major
ity. Adopted standards must be implemented in their entirety as
national standards, regardless of the way in which the member voted
and any conflicting standards must be withdrawn latest by the date
fixed by the Technical Board.
- A Harmonization Document (HD) is drawn up and adopted in the same way
as an European Standard but its application is more flexible so that
the technical, historical or legal circumstances pertaining to each
country can be taken into account.
- An European Prestandard (ENV) can be prepared as a prospective stan
dard for provisional application in areas of technology where there
is a high level of innovation or where an urgent need for guidance is
felt,
and where the safety of persons or goods is not involved. The
time required for its preparation is therefore reduced; once adopted,
ENVs are subjected to an experimental period of up to three years.
Members have to announce their existence at national level in the
same way as for EN/HD. However, any conflicting national standards
may be kept in force.
CEN and CENELEC have also a certification task for either the
issuing of an European mark of conformity to standards, or the mutual
recognition of test results and inspection. The CEN framework European
Certification scheme is known as CENCER.
CENELEC has a Marks Committee dealing mainly with the certifica-
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tion scheme within the framework of the Low Voltage Directive (LVD),
within the CENELEC Certification Agreement (CCA) on the mutual recogni
tion of test results for approval of electrical equipment and household
appliances and the scheme for the marking of harmonized low voltage
cables and cords (HAR agreement).
CEN and CENELEC work on a contractual basis (General Guidelines,
Framework Contract) signed with the Commission of the European Communi
ties;
specific mandates for new standards may be also received in the
form of "Order Vouchers" for areas of concern where the Commission
wishes to resolve trade barrier situations which have been notified to
it by the Member States.
A review of the 1989 CEN catalogue [26] showed that only following
specifically safety related European Standards exist:
- EN2 : classification of fires,
- EN3 : portable fire extinguishers (5 standards),
- EN54 : components of automatic fire detection systems
(10 standards),
- EN-132 up to EN-149 : respiratory protective devices and Personnel
eye protection.
4.
Practical Application of the SEVESO-Directive
A detailed comparison of all aspects of the implementation of the
SEVESO-Directive in the Member Countries is hardly possible, since
there various framework for the application of this Directive. Some
countries (e.g. F.R.G., France) operated a full licencing scheme for
industrial installations while in some others (e.g. Ireland, U.K.) no
industrial installation licencing is required. The background from
which the implementation of the Directive started varied from one coun
try to another.
Furthermore in almost half of the countries there is only one Com
petent Authority charged with the task to implement the Directive
(F.R.G., Greece, Spain, France, Ireland, Portugal and U.K.), in the
others there two (Belgium, Italy, Luxemburg, Netherlands) or even three
(Denmark). Cooperation and coordination among the various Competent
Authorities is not always an easy task. In addition some countries
(e.g. F.R.G., Spain) have to face the problem of coordination of the
work of the local authorities operating in the federal regions.
A comparison of the national approaches to the safety report
(notification as per Article 5 of the Directive) performed by the JRC
[27] gives an opportunity for an in depth review of the application of
the SEVESO-Directive in the Member States since the safety report is
tiot a stand alone object. Safety is controlled by inspections, safety
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audits,
standards, etc.
The main differences observed in this comparison [27] are related
to the control/acceptance approaches applied.
The Netherlands has made probably the most extensive use of quan
titative risk studies of any of the EC countries. There are quantita
tive ri
<;k
acceptance criteria approved by the parliament and define
maximum permissible risk (action required of situation unacceptable)
and for negligible risk (no action required)
.
However, it should be
noted that these acceptability criteria are related to the "external"
safety report which is submitted to the Environmental Ministry and is
available to the public while there is also an "internal" confidential
safety report examined by the Ministry of Labour.
In Ireland and U.K. there is neither a specific requirement for
Quantitative Risk Assessment (Q.R.A.) nor a set of acceptability crite
ria.
Use of Q.R.A. is however not discouraged and is accepted as a sup
port evidence of qualitative conclusions and decisions taken by the
manufacturer. Further H.S.E. in U.K. itself uses Q.R.A. for land use
planning decisions.
In France the laws and regulations themselves are prescriptive and
do not give any quantitative acceptability criteria. No Q.R.A. is
required and the safety analysis has to follow the deterministic
approach. Results of probabilistic analysis, if submitted, are also
judged for the final decision.
F.R.G. represents the other extreme case in comparison to Nether
lands.
Safety analysis has to use a deterministic approach. The safety
report has to show that safety measures taken correspond to the "State-
of-the-art of safety technology" and has to prove that there is no dan
ger for men outside the plant. Even operators of nearby process
units/facilities of the same establishment are considered as "men
out
side the plant". However, Q.R.A. is accepted as a support for selecting
among various alternative safety solutions but is never used for a
whole plant or installations.
Contrary to these differences there are also some important points
of convergence such as:
- Though the limitations due to lack of data of a Q.R.A. analysis, this
method is useful for selecting among various alternatives or for
stating priorities.
- Compilation of the safety report by the operator of the plant is very
useful, since substantially contributes to the awareness of the
hazards inherent in the process.
- The safety report is not a stand alone object that is once compiled
and examined. It should be a part of a dynamic process of continuous
inspections from the authorities in order an ever improving level of
safety to be achieved.
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- Evaluation of safety reports is a multidisciplinary task. This
requires either the assistance of various specialized experts or at
least as an aid very detailed checklist containing the concentrated
experience of various experts.
- Human factors are very important and have to be addressed appropri
ately in the safety report, evaluation of human factor issues is not
an easy task [ 3 3 ].
4.1. Run-away/'Side/Decomposition Reaction Hazards
Generally batch processes are considered as more problematic in compar
ison with continuous operation processes since they involve much often
transient operations (start-up, shut-down, loading-unloading, transient
conditions, etc.). It should be noted that in all countries (with the
exception of Spain) hazard identification is required to be performed
for every plant state [27].
With reference to run-away/side/decomposition, etc. reaction haz
ards the answers of the Competent Authorities can be grouped together
in three categories:
a) No specific requirements because either such a hazard is not present
in any of the installations (Luxembourg) or the Competent Authori
ties have not yet been confronted with this problem.
b) general requirements such as that the manufacturer has to identify
conditions that may lead to a hazardous incident and hence identify
any risk of run-away reactions. If data are not available in the
literature experimental campaigns should be performed.
c) More specific requirements such as:
- Should a major accident hazard can be perceived to result from an
unwanted or uncovenanted reaction the implications of that sce
nario are to be investigated and the relevant safeguards de
scribed.
This also requires experienced inspectors who can be assisted by
referring to either general rules (e.g. attention to exothermic
steps such as polymerisations, nitrations, Grignards, etc.) or to
data from sources like:
. Brethick (1975) in
Lees'
Loss Prevention, p. 1080 [3 2] ,
. data bank DIMDI in FRG,
. NFPA guide,
. International Process Safety Analysis guidelines (if an y).
- Data to be supplied in this case may include:
. Process chemistry, thermochemistry rates of reaction, laboratory
techniques to determine reaction rates DSC, DTA, Dewer Calorime-
try, ARC tests,
. details of research work performed (if an y),
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impurity controls,
vessel design,
measures to prevent releases (justification of venting or not,
DIERS sys tems, venting and scrubbing/blowdown/flaves
systems),
other precautions to reduce such risks,
==sessment of consequen ces of a reactor ex plosio n including ri sk
to operator/other persons in nearest building/public.
5. Lessons Learned from Accidents Notified
By the end of 1990 a total of nine tyeig ht (98) accidents had been reg
istered in M.A .R. S. Competent Autho rities , having recognized the impor
tance of an exchange of experience for an active accident prevention
policy, notify also some not major accidents whenever this enables
extraction of important lesso ns. Accidents notified can be broken down
as follows:
Major accidents 69
Other accidents 20
Accidents occurred before 198 4 9
Total 98
The numbe r of accident noti ficat ion from each country largely
depends both on the efficiency of national control organizations, which
in turn is related to the background from which the implementation of
the Dire ctiv e sta rted, and on the interpre tation of the rather fuz zy
defini tion of "major acci dent " (see also point 2 .2.1. above).
As a result the accid ents included in M. A. R. S. do not represent an
uniform sample of process accidents and can hardly be used for statis
tical purposes. However, the characterization of the accidents by
vari
ous parameters *) leads to some useful remarks [3 ] that can be summa
rized as follows:
a) almost 2/3 of the accide nts involved the releas e of dange rous sub
stances;
b) main process u nits are more often involved in accid ents wherea s the
number of accidents in isolated storages is also significant;
c) almost 1/3 of the accidents occurred during maintenance, loading/un
loading, transfer, start-up, shut-down and other non-standard opera-
(*) Type of act ivit y, type of acc iden t, conseq uen ces, subst ances in
volved, gravity indices and causative facto rs, see also point 2.3 .
above.
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tions;
d) substances very commonly used (e.g. flammable gases and liquids,
chlorine, hydrogen) are most often involved in the accidents;
e) the vast majority of the accidents notified could have been
pre
vented by proper application of existing experience and diffused
knowledge;
f) managerial/organizational omissions could be identified among the
causative factors in about 90% of the accidents of which the causes
are known;
g) design modifications/improvements were suggested after the accident
in almost 70 % of the accidents of which the causes are known.
6. Accidents Involving Unexpected Reactions
6.1. Gen eral Characteristics
In 17 out of the 98 accidents unexpected reactions were identified
among the primary causes of the accidents. This is a significant
portions of the total number of accidents notified; furthermore it
should be noted that unexpected reactions are ranked as the third in
frequency primary cause of accidents after component failures (in 45
out of the 98 cases) and operator errors (in 25 out of the 98 cases) .
These accidents can be broken down according to their notification as
follows:
Major accidents 11
Other accidents 3
Accidents occurred before 1984 3
Total 17
Type of these accidents:
Explosion 2
Fire 1
Release 1
Explosion and fire 2
Explosion and release 3
Fire and release 1
Explosion, fire and release 7
Total 17
These tables show that in almost all cases (14 out of 17)
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explosion occurred while frequency of explosion occurrence is less than
45%
in the total 98 accidents.
The breakdown of the accidents according to the type of industrial
installation is as follows:
Type of Activity Accidents
Run-away All
Other industries
Refinery, petrochemical
Pharmaceutical
Halogen, alkali, etc.
Isolated storage
9
2
4
1
1
3 9
4 0
1 5
7
1 3
17 98
This breakdown shows that unexpected reaction hazards are higher
in pharmaceutical activities and rather low in storage activities in
comparison to the total number of accidents registered in M.A.R.S. Ten
of the accidents occurred in batch processes, five in continuous
pro
cesses and one during unloading operation in a storage installation.
6.1.1. Consequences of the accidents.
The consequences of th-°se 17
accidents are given herebelow together with the consequences of all 98
accidents included in M.A.R.S.
Such a comparison suggests that accidents involving unexpected
reactions show a higher tendency to inflict losses (fatalities,
injuries - especially operator injuries - and material damage) in com
parison to the average accidents in process industries. This should be
attributed to the higher frequency of explosions observed in this type
of accidents.
6.1.2.
Accident causes.
There hardly exist accidents with a single
causative factor. Causes of accidents can be further subdivided in
pri
mary and underlying causes. Identification of all causative factors for
extracting experience useful for a preventive policy. The classifica
tion of causative factors for accidents currently used is given in [ 3 ] .
The most dominant other primary causes that have been identified
in the 17 accident involving unexpected reactions are:
- component failures : 6 accidents (in 3 out of these 6 instrumenta
tion/control
failures);
- operator errors : 6 accidents (all 6 operations related errors).
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Consequences
None or negligible
Fatalities
on-site
off-premises
Injuries
on-site
off-premises
Material damage
within the establishment
off-premises
Environmental damage
Traffic interruption
Public evacuation
Plant evacuation
Public annoyance
Public deprived from potable water
Accidents
involving
reactions
2
4
4
12
12
3
15
15
6
1
2
2
1
1
(11.8%)
(23.6%)
(23.6%)
-
(70.6%)
(70.6%)
(17.7%)
(88.2%)
(88.2%)
(35.4%)
(5.9%)
(11.8%)
(11.8%)
-
(5.9%)
(5.9%)
Tot
ace
21
20
19
2
43
40
8
64
61
13
11
10
7
5
3
2
al
idents
(21.4%)
(20.4%)
(19.0%)
(2.0%)
(43.9%)
(40.8%)
(8.2%)
(65.3%)
(62.2%)
(13.3%)
(11.2%)
(10.2%)
(7.1%)
(5.1%)
(3.1%)
(2.0%)
15 (88.2%)
14 (82.3%)
14 (82.3%)
11 (64.7%)
3 (17.7%)
(17.7%)
(23.6%)
The most dominant underlying causes are:
a) Managerial/organiz ational omissions
- insufficient or unclear procedures
- design inadequa cy
. process inadequately analyzed
. design error
. codes applied provided for
limited prote ction only : 3
b) Appro priat e proc edure s not followed (short-cuts) : 4
The study of the causative factors of these accidents reveals the
conclusions drawn in [3] (see also point 5. above) and is in agreement
with other accident reviews [28 -30 ] underlying the importance of human
factors for accide nt prev enti on. A proper s afety manag ement system is
indispensable for an effective accident prevention policy. If a safety
culture exists then early identification of hazards with the help of a
structured hazard as sessm ent techniq ue (e.g. combina tion of a technique
mainly aiming to hardware such as HAZ OP, HAZ AN, FMEA with techniques
focussing mainly on manag erial and organ isatio nal aspects such as MOR T
[31]) is more effective.
It is worth noted that the recently published Cullen report "The
Public Inquiry into the Piper Alpha disaster" suggests that also off-
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shore installati ons to be covered by the requiremen ts of the SEVE SO-
Directive since a formal safety assessment is expected to enhance the
safety of such installations [30].
6.2. Lessons Learned from Accidents Involving Unexpected Reactions
The lessons learned extract ed from the acciden ts in M. A. R. S. are pre
sented in [3 ] grouped t ogether in the following categ orie s:
1) design/construction-related,
2) operation/maintenance-related,
3) emergency handling,
4) mobiliz ation after and emergency,
5) substance specific,
The lessons extracted from the 17 accidents involving unexpected
reactions are given herebelow; lessons of categories 3 and 4 are pre
sented together.
6.2.1. Design/construction-related.
a) Contro l rooms in plants whic h handle flammab le and/or explosive sub
stances should be able to withst and ex pected bla st (blast-proof
design) so that control room operato rs can take the prope r act ions
in the case of an emergency.
b) To a maximum p ossib le extent an inherent ly safe design must be
adopted whenever possib le. The application of this rule is illus
trated in the case where for vinyl chloride polymerization to PVC:
- a plasti ciz ing agent was used requiring heati ng by steam at 16 5"C-
175°C,
while latex starts to decompose at 14 0 °C;
- there was no means for the detec tion of the failure of the agita
tor and, consequently, it was not possible to automatically cut
off the steam supply when the agitator failed in order to avoid
the development of hot spots.
The same principle is also highlighted in another accident where a
by-pass on a control valve was installed without any possibility to
safely interlock this by-pass manually so that no dangerous situa
tion would arise in case of maloperation.
Accident investigation in a third case indicated that process modi
fication in the direction of an inherently safe design could prevent
similar accidents to occur (substitution of the wast e wate r trea t
ment method
employed).
c) The creation of explosive mixtures when handling flammable materials
must be avoided using inert substan ces (e.g. nitrogen). This very
well-known practice could have prevented a series of the reported
accidents (10 out the 98 reported accidents among which one involv
ing an unexpected reaction)
.
If for a certain case inert ing is not
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considered feasible, technical measures have to be taken to avoid
the presence of ignition sources (e.g. installation of flame
arrestors in piping connecting a system with a potential explosive
mixture to an environment where ignition sources can not be elimi
nated) .
d) Proper th ermoche mical data and ass ociated conditi ons mu st be
obtained for possible run-away reactions before any substance, sus
pected to cause or undergo such a run-away reaction, is used in a
substant ial quantity (e.g. even in pilot -plant scale trials).
e) Provi sions for safe disposa l or con tainme nt of the maximum fire
water flowrate, that could be used in the case of emergency, are
necessar y to avoid damage to the envir onment (this has been demo n
strated in at least 3 of the 98 acc idents one of which involving
unexpected reaction; this later case caused the cut-off drinking
water to 200,000 persons). Attempts to provisionally contain the
fire water led to flooding of the establishment and damage to
machin ery and electrical equipment in another cas e. On the other
hand, there are indications that this particular lesson has been
learned, since in five other recent a cci den ts, the containmen t and
the safe disposal of used fire-water has been reported.
f) Fire water supply faci lities m ust be designed in such a way that
adequate fire water supply is ensured in the case that even a single
failure occurs in the system.
6.2.2. Operation/Maintenance related
a) Extrem e care mu st be taken and pro cedur es must be accurately fol
lowed in order to avoid mixing of incompatible chemicals or invert
ing the order of introduction of chemicals in a reactor. There are 3
among the 17 acciden ts initi ated in such a way ; their caus alitie s
were personnel injuries and material damage and in one case one
fatality.
b) Proce dures for performing v ariou s analytical tests must alway s be
strictly followed; in one case deviation from the specified proce
dures masked the identification of a run-away reaction in operating
conditions.
c) Inadequat e perso nnel training has been identified among the cause s
of 9 out of 98 accide nts notified (2 of them involving also run
away reactions). Ho wever, even experienced operators may make errors
under condit ions of excessive w ork load or due to unclea r pr ocedur es
as is indicated in other 3 of the notified accidents.
6.2.3. Lessons Learned from Emergencies
a) The location of a release to the environment must also be identified
and monitored. Reference is made to an accident , where chloride and
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71
hydrochloric acid c oncentr ations, measured at the plant's fence,
were very low , but the location of emission of thes e gases to the
atmosphere was close to the air intake of the ventilation system of
an adjacent building. Due to the low levels measured, it was not
considered necessary to alert the population, but concentrated
fumes, sucked in by the venti latio n s ystem , affected 29 per so ns, 11
of whom needed to be taken into the hospital for observation.
b) The effective action of spray/deludge systems, automatically or man
ually operated, has been experienced in several cases both for
assisting in dispersing the emission of toxic substances (two acci
dent s both involving run-away exother mic reactions) or fi ghting
fires (three cas es one of whic h involving unexpec ted reaction) .
There is also a reported case where the activation of a sprinkler
system by the release of hot liquid hexane was not adequate to pre
vent the explosion of its vapours, since the ignition point was
obviously qu ite far from the release sou rce . The instal lation of a
water drench syst em was decided up on in at least one case aft er
accident investigation.
c) The appl icatio n of cooling w ate r, at an adequat e ra te , to storag e
tanks adjacent to a fire can effectively prevent the spreading of
the fire to the content of the tank as has been experienced in two
accidents one of which involving an unexpected reaction.
d) Following an explosion and fire in a chemical factory situated close
to the to wn (about 2 km away), a blast and smok e caused public c on
cern.
The manufa cture r soothed people' s fear by stating on national
radio and TV that the smoke was not toxic.
e) Delay s in getting skilled deci sion- maker s and neces sary fire fight
ing equipment and material at the scene of the accident may con
tribute to an unnecessary escalation of the accident. Therefore,
they must be accounted for in the emergency planning.
f) Fire fighting intervent ion teams must be in the posit ion to acti vate
quickly alter native external fire water sources since the good func
tioning of the fire water supply systems of the establishment cannot
always be guaranteed.
6.2.4.
Substance Specific Lessons Learned
a) Chlorin e: the use of hydrochloric acid , contaminated by traces of
methanol in chlorine/alkali electro lysis, may lead to methylnit rate
formation and, consequently, to danger of explosion. Hence, careful
analytical monitoring of raw materials is recommended. Reference is
made to an accident where an explosion attributed to this reason
caused injuries to 6 persons and material damag e.
b) Hydrogen peroxide: rapid exothermic decomposition of hydrogen perox
ide may occur in the presence of sulphur components and at pH higher
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72
than 7.5. Hence, the use of hydrogen peroxide for waste-water treat
ment in the presence of volatile flammable substances may be danger
ous.
Referen ce is made to an acc ide nt, wher e 1 person was killed and
large material damage was caused by an explosion and fire.
c) Hydro gen peroxide and pyri dine : a rapid exoth ermic reactio n may be
caused by excessive hydrogen peroxide addition rate to pyridine.
d) Nitro -orga nic com poun ds: this type of compounds is well known as
unstable and subject to run-away reactions. In four of the reported
accidents, nitro-organic compounds were involved.
Inversion of the order of introduction of sulphuric and nitric acid
in the synthesis of 3-methylthioa niline caused the formation of
methy lnitr ate which , in turn , initiated a run-away reaction leading
to an expl osio n, which caused injuri es to one person and large mat e
rial damage.
Still unknown catalytic effects (inorganic salts) caused an unex
pected run-away reaction in a nitroanthraquinone production plant
leading to an explosion, which caused the death of one person,
injuries to 5 perso ns and large materi al dam age .
The distillation of a crude product containing also orthonitroben-
zaldehyde (which had been formed by the oxidation of this product by
nitric acid) led to a run-away explosion which caused injuries to 2
persons and large material damage.
The run-away explosion during distillation of l-methyl-2-formyl-l-
nitro -imida z ole caused injuries to 2 pers ons and large materi al dam
age.
e) PV C: A run-away explosion in a polymerization reaction which caused
large mate rial d ama ge, was attri buted to the combina tion of the fol
lowing parameters:
- inadequat e ammoni a a ddit ion, which could not compe nsate the hy
drogen chloride produced;
- latex coagulation due to an excess of hydrogen chloride;
- mixer failure due to latex coagulation;
- no device had been installed to indicate mixer failure;
- local overheating due to no mixing;
- decom positi on of latex due to local over heating (steam at 165°C-
175°C was used due to the plasticizing agen t, while latex decompo
sition starts at 1 4 0 ° C ) ;
- attack of reactor material by an excess of hydrogen chloride.
The reactor burst although the steam supply had been interrupted and
external cooling started due to overpressure and the reduction of
wall thickness from 9.8 to 2 mm.
After this accident, the following was decided:
- the substitution of the plasticizing agent so that steam at maxi
mum 127°C can be used;
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- the installation of warning signals and a steam supply cut-out
system;
- batch analytical controls of the latex pH and its persulphate con
tent are required
f) Raney nickel: pyrophoric nickel material may ignite vapours from
flammable material. Reference is made to an accident where ignition
causing a flash-fire was attributed to this reason.
7. Accidents due to Electrostatic Hazards
7.1. General Characteristics
There are 7 out of 98 accidents for which electrostatic loads have been
identified among their primary causes. Only 1 out of these 7 is a major
accident according to the interpretation of the relevant notifying Com
petent Authority.
In all seven accidents an explosion occurred; in four of them a
fire was also broken thereafter.
Five out of the seven occurred in pharmaceutical industries, the
other two in installations specified as general chemical industry. All
seven occurred in batch processes.
Review of these accident characteristics suggests similarities
with the conclusion drawn for accidents involving unexpected reactions
(see point 6.1.
above).
In 3 out of these 7 cases persons were injured, in 2 of them the
plant was damaged and in one case plant evacuation was necessary. In 3
out of these 7 accidents consequences were negligible. However 6 out of
these 7 cases were incidents that have not been considered as major
accidents.
Only in three cases another primary cause has been identified, too
(component failure in all 3 ) .
With reference to underlying causes following was observed:
- Managerial/organisational omissions : 7 (100%)
- Lack of safety culture : 6 (85.7%)
- Insufficient/unclear operating procedures : 6 (85.7%)
- Design inadequacy : 1 (14.3%)
It should be noted that design inadequacy has been identified for
the only one major accident falling in this category.
Hence these 7 accidents suggest also the same conclusions with
reference to an active accident prevention policy as the ones drawn
from the whole of notified accidents (see point 6.1.
above).
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7.2. Lessons Learned from Acciden ts Caused by Electrostatic Loads
7.2.1. Design/Construction-related
a) The creation of explosive mixtures when handling flammable materials
must be avoided using inert substances (e.g.
nitrogen).
This very
well-known practice could have prevented could have prevented 6 out
of these 7 accidents as well as a series of others (see also point
6.2.1.C
above).
b) In the case of the operation of a vacuum drier with a flammable sol
vent,
the monitoring of its pressure is recommended. When the vacuum
falls to a pre-set value, the automatic stop of the rotation and the
start of the nitrogen purge are recommended.
c) Earthing of metal components is necessary to avoid electrostatic
charges in areas where flammable materials are handled. The failure
to comply with this well-known rule was identified among the causes
of four reported accidents.
7.2.2. Operation/Maintenance-related
a) Non-standard operations must be avoided. Whenever their execution is
inevitable, a careful review from a safety point of view should take
place before they start in order to assure that all the operators
involved are fully aware of the inherent potential danger. Reference
is made to an accident, where an explosion followed by fire occurred
when dry powder instead of the usual wet cake was added to a
flammable solvent for recrystallization.
b) Nitrogen purging is mandatory before starting to charge material to
vessels/equipment containing flammable solvents or whenever such
equipment are opened for sampling or similar operations. This
requirement was not fulfilled in four of the reported accidents, as
post-accident investigations showed.
c) Frequent inspections of equipment with rotating elements containing
flammable material (e.g. batch centrifuges) are recommended to
assure that there is no spark danger due to tear of the coating of
the metal parts. Reference is made to an accident where a friction
spark was among the possible explanations of the ignition sources of
the isopropanol vapours.
7.2.3.
Substance Specific Lessons Learned
a) Powders and flammable solvents: Handling powders in the presence of
flammable solvents must be performed with extreme care and with all
necessary precautions such as:
- inert (e.g. nitrogen) purging to avoid explosive mixtures;
- earthing of metal components to avoid static electricity build
up;
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- exclusion of other ignition sources (e.g. sparks).
Reference is made to five incidents where explosions and fires were
caused by not respecting these rules,
b) Styrene:
- all metal components in contact with styrene must be earthed;
- it is recommended for vessels containing gelcoat (polyester in 4 0 %
styrene) to locate safety valves on the pressurized air supply
pipe and not on the pressure vessel itself (reference is made to
an explosion and fire accident that caused large material damage).
5. References
[1] Commission of the European Communities (1990) "Council Directive
82/501/EEC on the major accident hazards of certain industrial
activities", EUR 12705, Luxembourg: Office for Official Publica
tions of the European Communities.
[2] Council resolution 8 9/C273/01, Official Journal of the European
Communities, No.
C273/1.
[3] Drogaris, G. (1990) "M.A.R.S.-Lessons Learned from Accidents
Noti
fied", EUR-(in press), Luxembourg: Office for Official Publica
tions of the European Communities.
[4] Otway, H. and Amendola, A. (1989) "Major Hazard Information Policy
in the European Community: Implications for Risk Analysis" 9. (4) 505.
[5] Amendola, A., Contini, S. and Nichele, P. (1988)
"M.A.R.S.:
The
Major Accident Reporting System" in "Preventing Major Chemical and
Related Process Accidents", I. Chem. E. Symposium Series No. 110 ,
EFCE Publication Series No. 7 0 , p. 455.
[6] Testori-Goggi, P. (1989) in the Preface of CDCIR, Vol. 1, Report
S.P./1.89.12 (JRC-Ispra).
[7] Rasmussen, K. (1990) "European Community Documentation Centre on
Industrial Risk", Toxicological and Environmental Chemistry 25 213.
[8] Commission of European Communities (1967) "Council Directive on
the approximation of
laws,
regulations and administrative provi
sions relating to the classification, packaging and labelling of
dangerous substances - 67/548/EEC", Official Journal of the Euro
pean Communities L 196/1, 16.08.67.
[9] Commission of the European Communities (1989) "Council Directive
on the introduction of measures to encourage improvements in the
safety and health of workers at work - 89/391/EEC", Official Jour
nal of the European Communities L
183 /1,
29.06.89.
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76
[10] Commission of the European Communities (1989) "Council Directive
concerning the minimum safety and health requirements for the
workplace - 89/654/EEC", Official Journal of the European Communi
ties L
393/1,
30.12.89.
[11] U.S. Department of Labour - OSHA (1990) "29 CFR Part 1910 -
Pro
cess Safety Management of Highly Hazardous Chemicals" Notice of
Proposed Rulemaking, Federal Register 5_5_, No. 13 7, July 17, 1990.
[12] OECD (1989) "Accidents Involving Hazardous Substances" Environmen
tal Monographs No. 24.
[13] OECD (1990) "Atelier sur la prevention des accidents lies aux sub
stances dangereuses. Bonnes pratiques de gestion" Environmental
Monographs No. 28.
[14] OECD (1990) "Atelier sur la communication d'informations au public
et le role des travailleurs dans la prevention des accidents et
1'intervention", Environmental Monographs No. 29.
[15] OECD (1990) "Workshop on the Role of Public Authorities in Pre
venting Major Accidents and in Major Accidents Land-Use Planning",
Environmental Monographs No. 3 0.
[16] Batstone, R.J. and Lepkowski, W. (1986) "World Bank Acts to Pre
vent Chemical Disaster", Technology Review.
[17] The World Bank (1985) "Manual of Industrial Hazard Assessment
Techniques", London.
[18] United Nations (1988) "Awareness and Preparedness for Emergencies
at Local Level. The APEL Process" United Nations Environment
Pro
gramme.
Industry and Environment Office.
[19] CEC-JRC-ISEI (1990) "Community Documentation Centre on Industrial
Risk", ISEI/SER-1899, S.P./I.90.18.
[20] H.S.E. (1990) "Library Information Service - Publication in Series
List"
H.S.E. Library and Information Services.
[21] CONCAWE (1989) "Methodologies for Hazard Analysis and Risk Assess
ment in the Petroleum Refining Industry".
[22] CEFIC (1987) "A Guide to Safe Warehousing for the European Chemi
cal Industry".
[23] LPGITA (1988) "Guide to the Writing of L?G Safety Reports".
[24] Chemical Manufacturers Association "Evaluating Process Safety in
the Chemical Industry".
[25] Chemical Manufacturers Association "Safe Warehousing of Chemicals".
[26] CEN (1989) "Catalogue" Ed. 2.
[27] Amendola, A. and Contini, S. (1990) "National Approaches to the
Safety Report. A Comparison" CEC-JRC-ISEI/SER, S.P. ISEI/SER 1761.
[28] H.S.E. (1987) "Dangerous Maintenance" ISBN 0 11 8 839578, London.
[29] Shortreed, J. (1990) "Recent Advances in Research and Future
Requirement", Plant/Operation Progress, 9_ (3 ), 198 .
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77
[30] Boniface, A. (1990) "Piper report set to reform", The Chemical
Engineer, No. 485
(15.11.90),
15.
[31] Smokas, J. (1988) "The Role of Safety Analysis in Accident Preven
tion", Accid. Anal. & Prev., 1Q (1), 6 7.
[32] Lees, F.P., (1983) "Loss Prevention in the Process Industries",
Vol. I and II, Butterwort, London.
[33J Amendola, A. (1990) "Human Reliability Models" CEC-JRC-ISEI, Tech
nical Note No. 1.90.23, PER 184 0/90.
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LABORATORY TESTING PROCEDURES
Paolo CARDILLO
Stazione sperimentale per i Com bustibili
V.le A. De Gasperi 3
20097 San Donato Milanese
Italy
ABSTRACT. In order to avoid conditions for thermic hazards it is neces
sary to have knowledge of the chemistry and associated thermochemistry
(kinetic and thermodynamic data) of the desired reaction and potential
side reactions and also of the thermal stability and physical properties
of reactants, intermediates and products. The various instruments and
testing methods currently used provide a means of assessing thermal ha
zard. Over recent years great progress has been made. New methods have
been developed and many new instruments have been offered to the market.
In addition, many institutions have codified the procedural aspects of
safety investigation.
1.Introduction
In any chemical process there is always the danger that the rate of heat
generation will be greater than the rate of heat removal so that the ma
terials will undergo an undesired temperature increase. At this higher
temperature, it will produce even more heat, and the temperature will
increase exponentially in the direction of a thermal explosion.
Essentially chemical reaction hazards are associated with loss of
control of exothermic reactions, gas evolution and/or decomposition phe
nomena.
Hazardous runaway reactions may occur in all operations in which
chemicals are involved including t
1
) :
- conversion of chemicals (desired reaction)
- unit operations (drying, grinding, distillation, etc.)
- storage and transportation of bulk chemicals.
Potentially dangerous heat formation can occur in the desired
pro
cess as well as in undesired consecutive and decomposition reactions
[2,3] .
The accumulation of starting materials or intermediate products
is, in many cases, the initial step of a runaway reaction: common causes
of reactant accumulation are wrong kinetic assumption, too high feed ra
te,
too low temperature, incorrect initiation, or insufficient mixing
and impurities that can affect the kinetics. Under disturbed operating
conditions (for example, loss of cooling), the energy release associated
79
A.
Benuzzi and J. M . Zaldivar (eds.). Safety of Chemical Batch Reactors and Storage Tanks, 79-97.
© 1991 ECSC. EEC. EAEC, Brussels and Luxembourg. Printed in the Netherlands.
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80
with the reactant accumulation can cause the batch temperature to rise
to a critical level where secondary, unwanted reactions are triggered.
In order to avoid conditions for thermic hazards it is necessary
to have knowledge of the chemistry and associated thermochemistry (kine
tic and thermodynamic data) of the desired reaction and potential side
reactions and also of the thermal stability and physical properties of
reactants, intermediates and products. Only a detailed analysis can
pro
vide quantitative, reliable data on the probability of an incident and
its severity. The key to success here is initiating a comprehensive ana
lysis at an early stage in project development.
It is not enough that the process steps have been carried out on
laboratory scale without incident, for plant conditions are different.
For example, metals are used in place of glass for the construction of
equipment, pressures and temperatures may be higher, residence times may
be longer, by-products may accumulate in recycle streams, or impurities
may be introduced by substituting commercial for reagent chemicals.
The scale of operation may also be an important factor, particularly in
batch operations.
The assessment strategy is to evaluate two types of hazard. In the
first case, one or more of the reactants, intermediates or products is
inherently unstable and limits have to be determined for the safe opera
tion of the process so the lowest possible temperature at which the on
set of decomposition can be detected is not reached. In the second case,
we must consider that any reaction which is exothermic is potentially
hazardous unless the plant used is capable of handling the heat load.
2.
Testing procedures
A testing sequence is required that screens processes for potential ha
zard, defines process conditions under which uncontrolled reactions
could be initiated, quantifies the consequences of such reactions, and
monitors the margin of safety between the normal operating conditions
and the onset of dangerous exothermic activity.
The questions that should be answered by a test program are:
. which process data do we have to know?
. by which methods can we determine the necessary data?
. what can we conclude from the test results?
In order to specify the safe operating conditions, the primary da
ta required are:
1. the rate of heat evolution
2. the cooling capacity of the plant
In order to determine the consequences of a runaway reaction, it
is necessary to determine:
1. the total heat of reaction
2. the specific heat
3. the adiabatic A T
4.
the boiling point of the mass
5. the temperature range in which secondary or decomposition reactions
can be expected and the heat of decomposition of such reactions
6. the amount and rate of gas or vapor evolution (pressure developed and
'rate of pressure increase)
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81
7.
effects of mischarging, impurities and errors.
If the intended reaction is exothermic, heat production is unavoi
dable and the corresponding cooling has to be provided.
Heats of reaction can be roughly assessed by calculation using
heats of formation, and for well-known reactions published data are so
metimes available f
4
-9]. For the majority of the processes under deve-
lopme^
1
", the reaction heat and the time profile of the heat evolution
rale has to be measured experimentally.
The instantaneous heat evolution rate of chemical process proves
to be an ideal property to measure. Not only it is indicative of whether
and how fast reactions are actually occurring but it is also directly
the risk-related quantity which can be easily transformed into a tempe
rature increase rate for the case of emergency loss of cooling.
An essential quantity for the estimation of the severity of a gi
ven chemical process will be the maximum temperature increase to be ex
pected under adiabatic conditions (adiabatic
/ \ T ) .
It allows us to
cal
culate the maximum final temperature in case of a runaway situation.
Comparing this final temperature to the temperature range of se
condary reactions and to the physical properties of the reaction mixture
under investigation such as melting point, vapor pressure and boiling
point, yield direct information about the consequences of a runaway
(Fig. 1).
Until a few years ago experimental determinations were all aimed
at establishing the temperature range in which decomposition occurs I
10
-
15] .
decomp. reac t ion
A H • 8 0 0 J / g
des i red reac t ion
A H - 170 J /g
50 C
90 C
A
Tad - 45 C
T e m p e r a t u r e
Figure 1. Simplified scenario of a thermal runaway.
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In reality, only very few substances have a clearly defined decom
position temperature. Exothermic decomposition starts at the temperature
at which heat generated exceeds the lower detection limit of the measu
ring instrument. Thus instruments with high sensitivity will indicate a
lower starting temperature for the same decomposition reaction than in
struments with a lower sensitivity [16-19]
#
When the decomposition temperature is given, it is essential to
describe the instrument used and the experimental conditions employed
(sample size, heating rate, sample holder, e c c ) .
The temperature at which the initiation of exothermic decomposi
tion is detected during thermal stability tests depends on several fac
tors.
These do not only concern the materials properties and the speci
fic decomposition reaction but can include the experimental systems'
characteristics and experimental parameters.
A good example of this is the thermal stability study of the "Se-
veso mixture". The Seveso accident (1976) has met with great interest in
the scientific world; it has probably never happened in the past that
such an effort was made to understand, from a physico-chemical point of
view, an accident occurring in a chemical plant.
Several authors studied the thermal stability of the mixture and
its components supposed present in the reactor. All available methods of
thermal analysis (1976-1983) were used: simultaneous thermogravimetry
and differential scanning calorimetry (TG/DSC) [20,2i]
j
differential
thermal analysis (DTA) [ 22] , miniautoclave, Sikarex, Dewar flask [23 ],
accelerating rate calorimeter (ARC) [24] under different experimental
conditions (dynamic, isothermal, adiabatic, isochoric, and
isobaric);
in
open platinum sample holder, in air or nitrogen; in closed crucibles of
nimonic, glass or gold.
The most significant results of these studies can be summarized as
follows:
. the atmosphere surrounding the sample and the material of the contai
ner does not affect the observed exothermic behaviour;
. the Seveso mixture kept at 160 °C does not show appreciable exother
mic reactions;
. the experiments in miniautoclave do not show exothermic reactions be
low 200 °C; self-heating of the mixture proceeds at an appreciable rate
only above this temperature t
23
l;
. DSC measurements with an instrument made in 1970 did not show any e-
xothermic behaviour below 230 °C t
2
° ] ;
. DSC/DTA measurements with more recent instruments show - both under
dynamic and isothermal conditions - slow and week (about 105 - 125 J/g)
exothermic behaviour starting a 180 °C; these phenomena were previously
unknown. These measurements also show other, known and more intense, e-
xothermic reactions above 230 °C [20-22].
. in the Sikarex calorimeter, under isothermal conditions and with open
sample holder, the self-heating proceeds at an appreciable rate only a-
bove 200 °C; under adiabatic conditions, with open sample holder at 160
°C, the temperature of the mixture increases by about 10 °C in four
days; at 180 °C only a small temperature gradient can be observed, which
gets exhausted after 24 hours t
2 3
) ;
'. under heat-accumulating conditions (Dewar flask) at 180 °C the tempe-
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83
rature increases
by 1-2 °C
only,
and the
rate
of
pressure rise
is 10
mbar/h I
23
l ;
.
the
adiabatic calorimeter
ARC
confirmed existence
of a
first exother
mic effect
at 180 °C (/\H 122 J/g) ,
strong enough
to
increase
the
tem
perature
by
about
60 °C
(under strictly adiabatic conditions)
and to
start
a
second, more violent, runaway reaction.
The ARC
test also showed
that.
° ove 180 °C, the mixture gets self-heated, always in adiabatic
conditions,
causing
a
pressure increase
of 4 bar (the
safety disk
at IC-
MESA was set at this value) in 8 hours I
24
l.
The ability to detect very low rates of self heating is of great
importance. This
is
illustrated
in Fig. 2.
j
O)
c
C O
C D
C O
B
Temperature T1
T2 T3
Figure 2. Simple exothermic reaction.
A relatively insensitive test method
(A)
will detect exotherm
at
temperature above T3. As the sensitivity of the method increases (B,C)
the detection temperatures drops (T2,Ti).
As can be
seen,
no
matter
how
sensitive the test method is, there will always be a reaction occurring
below
Ti.
It
is
important
to
note that
the
difference between
Ti and T3 is
typically 50-100 °C.
Under temperature control (cooling
and agitation), the low
rates
of heat evolution may be insignificant but under heat accumulation con
ditions,
then very
low
rates
of
heat evolution
may
give rise
to a ha
zard.
The example shown
in Fig. 2 was of a
simple exothermic reaction.
If the chemistry is more complex, then the need for high sensitivity can
be even greater
as
shown
in
Figures
3 and 4.
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Fig. 3 shows a typical system of two overlapping reactions. The
main thermal hazard is caused by the major peak. However, the hazard
from this major exotherm is triggered by a very small reaction at lower
temperature. Recognition of the small reaction is of absolutely crucial
importance in understanding and hence controlling the thermal hazard.
However, low sensitivity techniques will fail to recognize its existen
ce.
c
CO
0)
CO
B
r ^
I
Temperature
Figure 3. Two overlapping reactions.
T1 T2 T3
Fig. 4 shows another example where good sensitivity is of para
mount importance. In this case, the main exotherm is autocatalytically
induced. The instrument C is sensitive enough for this to be recognised
instantly (the steep initial slope is a sure indicator of autocataly-
sis),
but the others are not.
This is a serious defect of less sensitive techniques since the
recognition of autocatalysis is crucially important in thermal hazard e-
valuation.
When assessing the consequences of a runaway reaction, it is im
portant to remember that the real damage is caused by the effects of ex
cessive rate of gas and vapor evolution and that the exothermic events
only act as the driving force.
The pressure produced during decomposition is in turn determined
by the quantity of gas liberated and the decomposition energy, which is
decisive for the attainable final temperature. In addition, the decompo
sition rate, which itself is very much dependent on the temperature at
tainable during decomposition, is decisive for the rate of the pressure
'increase.
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85
c
'+*
0
.c
I
5 3
C O
B
Temperature
Figure 4. Autocatalytic reaction.
T1 T2 T3
Some modern instruments can now measure the temperature-pressure
curve under different conditions t
2 5
.
2 6
3 . Fig. 5 shows the ARC self heat
curve of a liquid monomer A. At least three reactions can be seen, the
initial exotherm being detected at 180 °C with a mechanism change about
6 or 7 °C later. The initial mechanism may be deduced to be autocataly
tic from the shape of the first part of the curve. The third reaction,
the decomposition of the polymer, is seen as the shoulder on the right
of the curve.
Fig. 5 also shows the pressure versus temperature curve making ap
parent that the last reaction, the small shoulder on the right is the
real danger.
3.INSTRUMENTS AND METHODS
The various instruments and testing methods currently used provide a
means of assessing thermal hazard. Over recent years great progress has
been made [27-36]
t
New methods have been developed and many new instru
ments have been offered to the market. In addition, many institutions
have codified the procedural aspects of safety investigation and come up
with more sophisticated testing systems. Progress continues, and new in
strumentation is expected. Also the methods already used for decades are
being improved. Also worthy of mention, are new interpretation methods
that enable us to make better use of the same readings; modern data
pro
cessing, in particular, offers possibilities by which data can be trea
ted mathematically and various extrapolations carried out. The number of
measurement being made is rising rapidly, partly as a result of growing
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86
safety consciousness and partly because of the aforementioned automa
tion, which is cutting the cost of such studies.
The test methods included here do not represent a complete "state-
of-the-art" but are those of which the author has practical experience.
+
e l f -heat ing
Pressure
_C
'+*
C O
C D
sz
I
C D
C O
T
- P
4 -
1
C D
W
C O
C
i
CD
F
11 i l l I I I I
Temperature
Figure 5. ARC self-heating and pressure curves of a liquid monomer.
3.1. Screening tests
Where a large number of samples has to be tested, a fast screening
met
hod is necessary. G enerally, screening tests determine only the rough i-
nitial temperatures for the exothermic decomposition reaction. In order
to fix a safe working temperature from these initial temperatures, safe
ty margins are necessary.
The first step in the identification of reactive chemicals hazards
is the evaluation of the thermodynamic potential of the system. This
will tell first, whether a reaction is thermodynamically possible and
second, how much thermal energy can be released by the reaction. The po
tential quantity of thermal energy released by the system can then be
related to increases in temperature and pressure within the system being
considered.
One can write balanced chemical equations for the reactions to gi
ve "maximum energy release" for which the heats of decomposition can be
estimated [
3 7
] . The heat of reaction/decomposition can be estimated by
computer programs and used to predict the possibility of explosion or
decomposition.
Yoshida [
3 8
] , for example, has studied different combinations of
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87
typical chemicals by carrying out computations with the program REITP2
(Revised Program for Evaluation of Incompatibility).
The use of computers as a prediction tool in chemical process ha
zard evaluation began in 1974 with the introduction of the CHETAH (Che
mical Thermodynamic and Energy Release) program '
3 9
1 . Since then, the
CHETAH program has been widely used in the chemical industry for hazard
evaluation.
Although its chief aim is to predict deflagration/detonation po
tential from molecular structure, it can be used to estimate heats of
reaction, heat capacities, and entropies of a pure chemical, a chemical
mixture,
or a chemical reaction.
Four criteria of energy hazard potential, based on classical ther
modynamics, have been developed and are included in the program.
For the first criterion of energy hazard potential, CHETAH uses
the amount of each element present and thermodynamic data in conjunction
with a linear programming technique to define those products which could
be formed from the reaction mixture and which would release the maximum
amount of energy. The program obeys the laws of thermodynamics and the
principles of stechiometry. For this criterion, the program lists the e-
nergy hazard potential as low if the maximum heat of reaction is more
positive than -0.3 kcal/g, as medium if the maximum heat of reaction is
between -0.3 and -0.7 kcal/g, and as high if it is equal to or more ne
gative than -0 .7 kcal/g.
The second criterion compares the difference between the heat of
combustion of the compounds in an excess of oxygen and the maximum heat
of decomposition to the maximum heat of decomposition.
The third criterion is based on the "oxygen balance" concept of
Lathrop and Handrix l*°i
.
If the oxygen balance is more positive than -24 0 or more negative
than -160, the energy hazard potential is rated as low. If the oxygen
balance is between + 240 and + 120 or -160 and -8 0 , the energy hazard po
tential is rated as medium. If the oxygen balance is between -8 0 and
+120, the energy hazard potential is rated as high.
The fourth criterion is represented by the following equation:
y = 10 A H
2
n
ax W/n
where /\Hmax maximum energy of decomposition
W = weight of compound in grams
n = number of moles
If y is greater than 110, the energy hazard potential is rated as
high.
If y is between 30 and 110, the energy hazard potential is rated
as medium. If y is below 3 0 , the energy hazard potential is rated as
low.
The program uses pattern recognition to classify the compound as
sensitive or insensitive. The program gives a sensitivity rating of
high,
medium or low each of four criteria, and then it gives one overall
rating (Energy Release Potential, ERP) for the compound or mixtures.
The exact details of operation of CHETAH can be found in the lite
rature [39,41-43] .
Because of its ability to predict the potential hazards of a mate
rial or mixture solely from a knowledge of chemical structure, CHETAH is
ideal for preliminary hazard evaluation (Table 1).
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TABLE 1. Examples of CHETAH application
c r i t e r i o n
1
k c a l / g
acetonitrile C2H3N = 1.25 C + 0.5 N2 + 0.75 CH4
-0.88 H -6.37 L -214.36 M 52.96 M HIGH
acrylonitrile C3H3N = 2.25 C + 0.5 N2 + 0.75 CH4
-1.09 H -6.70 L -226.14 M 89.37 M HIGH
p-benzoquinone C6H4O2 = 6.0 C + 2.0 H2O
-0.81 H -5.22 L -177.62 M 58.75 M HIGH
chlorotrifluoroethylene C2CIF3 = C + 0.25 CCI4 + 0.75 CF4
-0.42 M -0.87 M -34.34 H 34.43 M HIGH
diazomethane CH2N2 = 0.5 C + N2 + CH4
-1.90 H -3.40 M -114.17 H 304.05 H HIGH
e t h y l e n e
o x i d e
C2H4O
=
1 .5
C
+
H2O
+ 0 . 5
CH4
- 1 . 2 3 H - 5 . 3 8 L - 1 8 1 . 6 0 M 9 5 . 1 4 M HIGH
nitrobenzene C6H5NO2 = 5.75 C + 0.5 N2 + 2.0 H2O + 0.25 CH4
-1.11 H -4.78 M -162.46 M 108.22 M HIGH
phenyl isocyanate C7H5NO = 6.25 C + 0.5 N2 + H2O + 0.75 CH4
-0.62 M -6.14 L -208.19 M 33.03 M HIGH
styrene CsHs = 6.0 C + 2.0 CH4
-0.68 M -9.10 L -307.24 L 30.25 M HIGH
3.2.Thermal analytical ■ethods (DSC/DTA)
The theory and practice of DSC/DTA are well known and available from
many sources t
4 4
-
4 6
. These methods require small sample sizes, tipical-
ly, a few mg, and short analysis times (an hour or two at
most).
Thus, DSC/DTA are advantageous for first examinations of even the
most explosive unknown products or reaction mixtures.
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For a more detailed examination, these advantages often became di
sadvantages:
- the small sample size employed make accurate mixing difficult and the
composition of a sample of a few mg taken from a grossly heterogeneous
sospension, is not necessarily representative of the whole mass;
- the observed beginning of an exothermic reaction, i.e. the first de
flection from the zero line, is a function of the heating rate, shifting
tov'j.rd lower temperatures at lower heating rates;
- no additions can be made during a run;
- no agitation is possible;
- no measure of pressures generated in sealed pans is possible;
- only a limited range of sealable pans are available.
Recently, a special designed capillary tube and tube holder have
been developed for thermal hazard evaluation using DSC I
4 7
J. This capil
lary tube container has several important advantages compared to other
common sample encapsulation approaches. The glass container is inert to
most materials and is capable of withstanding pressures in excess of 200
bar and temperatures up to 500 °C. The vaporization effect, often pre
sent in DSC of liquids to high temperatures, is negligible because high
sample volume to total volume ratios are possible.
In spite of the difficulties in transfering the DSC results to
plant condition, we think DSC to be a very useful method to in many ca
ses get a quick view of the thermal stability of a substance I
4 8
"
5 0
.
The rate at which the energy is released is very important: thus a
sharp rise in the rate indicated by a steep slope of the exothermic
shows that the reaction may be haz ardous; a broad exotherm peak is
indi
cative of a slower reaction. The area of the peak is proportional to the
energy of the exotherm.
In the dynamic mode (temperature programmed experiment) f
51
l, one
obtains a quick overview of the entire temperature range of interest.
The observed initial temperature of the exothermic response permits a
first estimation of the temperature region in which the undesired reac
tion must be taken into consideration.
Isothermal measurements t
52
l in the region of the onset temperatu
re of the exothermic peak usually clarify, in a short time, wheter or
not a decomposition occurs by an autocatalytic mechanism. Key results
from isothermal experiments are heat evolution rates. Since heat evolu
tion rates vary with time, one may simple refer to their maxima, which
occur either at the beginning or, in the quite frequent cases with for
mally autocatalytic mechanism, after a time delay. Plotting the log of
the maximal heat evolution rates of a number of isothermal experiments
in an Arrhenius plot provides information on the temperature dependence.
The slope of the line is referred to as activation energy (Ea) t
50
.
3.3.Isoperibolic (quasi-isotheraal) Methods
The sample temperature is increased in pre-defined steps and is allowed
to equilibrate before being monitored for exothermic sel-heating.
The isoperibolic methods (Dewar flask, Sikarex, etc.) [23,32,33]
are generally more sensitive than micromethods and, therefore, make it
possible to determine if exotherms occur at correspondingly lower tempe-
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90
ratures. Also, they make it easy to recognize autocatalytic processes.
Large sample sizes are sometimes necessary, which is most disadvanta
geous when dealing with expensive or toxic substances.
3.4.Adiabatic calorinetry
The Accelerating Rate Calorimeter (ARC) is a commercially available
thermoanalytical instrument in which it is possible to examine the ther
mal characteristics of a material in a closed environment and in near
perfect adiabatic conditions. The ARC was initially designed by members
of the Dow Chemical Company and was first described by Townsend
t
28
J
in
1977. A considerable number of publications have appeared in the scien
tific literature: the design concept and thermochemical performance have
been described and a number of papers have outlined the basic ARC system
and its operation
[24,53-70]_
The adiabatic calorimetry is almost the ideal method for thermal
hazard investigations because the adiabatic course of a reaction pre
sents the thermal behavior under the most unfavorable conditions as far
as the safety is concerned.
There are two main modes of operation of the ARC. The most common
is known as the heat/wait/search mode. A sample is heated to a preset
start temperature. A wait period follows and, once equilibrium has been
established, a search period is initiated. During this time the sample
is held adiabatically. If the increase in the system temperature is be
low the preset value (0.02 °C/min) then the system is heated stepwise to
the next set point. The heat, wait, search cycle is repeated until the
temperature rise during the search period exceeds the preset value.
The ARC can also be used in isothermal mode and this method of o-
peration should be employed where unstable materials are likely to be
held for long periods of time at elevated temperatures.
In the recorded temperature/time and pressure/temperature curves,
all the thermal, kinetic, and physical property data of the reaction
mass are implicitly contained.
The risk of processes with normal residence time of the substances
can easily be evaluated with the helps of experimentally determined a-
diabatic time to maximum rate of the thermal decomposition.
The list below gives the data which can be obtained from an ARC
experiment:
. adiabatic rate of selfheating vs. temperature
. adiabatic time to maximum rate vs. temperature
. pressure rise or rate of pressure rise vs. temperature
. maximum rate of reaction and heat of reaction (or decomposition)
. activation energy
. pseudo rate constant
If the logP vs. 1/T graph is a straight line, this is likely to be
vapor pressure. If the graph is curved or there are variations then ot
her reactions can be implied. If a pressure is still left in the bomb at
the end of the experiment non condensable gas must have been formed. A-
fter suitable correction for the fill ratio (ratio of reaction volume to
freeboard volume), solubility, compressibility and vapor pressures are
made,
the quantity of gas generated can be established.
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3.5. Reaction calorinetry
At all stages in the development of a chemical manufacturing process,
thermodynamic and kinetic data pertaining to each of the process steps
are required. Early in the development process, before a synthetic pat
hway has been chosen, a reaction step that is obviously highly exother
mic may be encountered. A determination of the total amount of heat
dis
sipated in the step would enable a judgement to be made on the thermal
hazard posed by the step. Development work on the step could more easily
be halted at this early stage, before a significant investment is made
in the reaction. A pathway having been chosen, conditions must be iden
tified. Profiles of the instantaneous rates at which heat is dissipated
or absorbed throughout the course of each process step would indicate
the temperature range in which reaction runs to completion fastest, or
in which a runaway is a problem.
The desired reaction can generally be carried out only in a very
definite temperature range. At too low a temperature, the reaction is
either too slow or doesn't occur at all. At too high a temperature, the
formation of undesired by-products often occurs or a region of undesired
consecutive or decomposition reactions is eventually reached.
Many processes providing a high exothermicity of the reaction are
hence designed with a large safety margin (e.g. low reaction temperature
to be far away from the start point of dangerous decomposition). And a-
gain very often these preventive measures work against yield.
At the optimal reaction conditions, the maximum rates of heat dis
sipation and absorption for each step are required to determine the re
frigeration and/or heating capacity needed for plant reactors.
Reaction calorimetry allows to simulate plant conditions and to
simultaneously determine actual heat generation data.
A prerequisite for determination of the heat effects is equipment
suitable for dealing with the many varied problems which arise. In par
ticular the reaction enthalpies of chemical reactions should be measured
as stated in the operating conditions. Enthalpies of solution, dilution
and mixing also pose various safety related problems which must be sol
ved.
Reaction calorimetry is not a simple task, since it has to fulfill
a number of sometimes demanding requirements:
- for measuring of the heat of reaction, the investigated chemical syn
thesis has to be carried-out. Modern organic chemical processes demand
often precise maintanence of the reaction conditions, such as temperatu
res, dosing rates, pressures, reaction times, weights of added or di
stilled products, etc. Also the handling of the reaction mixtures is o-
ften specifically prescribed and basic unit operations are required,
i.g. stirring, distillation, boiling under reflux, etc.
- as a result of the measurement not only the net reaction enthalpy is
required, but sometimes also various other heat sources have to be con
sidered, i.g. dissipative energy of the stirrer, endothermic process in
the condenser, etc.
- besides heat of the reaction measurement, other information about im
portant engineering parameters are often requested, especially if their
changes influence the interpretation of the calorimetric measurements,
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92
i.g. values and changes of the heat transfer coefficient through the
wall of the reactor.
- during a reaction, a number of physical properties of the reaction
mixture can drastically change. A typical example is the change of vi
scosity due to forming and precipitation of unsoluble product and the
resultanting deterioration of the heat transfer on the inner
wall.
Many examples of applications of reaction calorimeters can be
found in the literature [29,30,71-81].
Now we can see some of the most frequent problems in routine expe
rimentation.
4.Selection of the substances or processes to be tested
It is not possible to test every substance for every possible type of
hazard. Obviously, there are intrinsic factors controlling the systema
tic procedure for thermic safety testing, such as:
- the type of problem/process to be evaluated, i.g. is it a matter of
assessing the hazards of a complete process; is it a matter of determi
ning the permissible storage conditions for a specific product or is it
a simple distillation to be evaluated, etc.
- the structure of the compounds involved in a process
- the instruments available.
A decision as to whether a material should be submitted for test
can be made by consideration of its chemical constitution, the oxygen
balance of the molecule £
40
J and its behavior in small scale heat tests.
For a molecule containing x carbon atoms, y hydrogen atoms and z oxygen
atoms the oxygen balance Bo is:
Bo = -1600 (2x + y/2 -z)/mol.wt
Oxygen balance for some compounds are reported in Table 2. DSC/ARC
tests have confirmed their instability.
Table 2. Examples of oxygen balance
o.nitro benzyl bromide -111.09
o.nitro benzyl chloride -139.87
o.nitro benzyl alcohol -151.50
o.nitro benzaldehyde -142.93
isoxazole -150.72
3-amino-5-methyl isoxazole -163.26
dimethyl sulfoxide -122.87
5-nitro imidazole -53.92
1,3-dibromo-5,5-dimethylhydantoin -61.55
N-bromosuccinimide -71.91
It is recommended that materials with an oxygen balance more po
sitive than
(-200)
should be tested for explosibility. This is an arbi
trary choice but is not unreasonable; it is recognized that it errs on
the side of safety
(82,83].
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The presence of certain chemical groups may indicate thermal in
stability. For example, groups such as nitrate ester, aromatic nitro and
nitramine are closely linked with explosibility; azo, azide, nitroso,
peroxide and acetylene are groups that can form part of explosive struc
tures t
1
J .
5.Selpf.tion of test method
If the nature of the hazard is not know, it is impossible to decide in
advance which test method wuold be most appropriate. The situation beco
mes critical when a chosen method would not show up the specific hazard
at all. The choice of method may often be governed by the availability
of the apparatus, by tradition or habit rather than by it's suitability.
The most powerful use of the instruments can be achieved, when
their limitations are known and when the plant conditions to be judged
are borne in mind during interpretation of results. This knowledge al
lows to apply simple procedures where these are adequate and to use more
extended tests where critical conditions in the plant are relatively
close to the expected real conditions.
Generally, results of safety measurements reflect only the beha
vior of the material under conditions of the experimental setup and te
sting procedure used in the instrument. Any other interpretations of the
results, or conclusions made for the manufacturing process, is an extra
polation. Unfortunatly, conditions in production plants are often signi
ficantly different from those used in testing instruments. Consequently,
there is a danger from thermal hazards which can remain undetected l
8 4
l.
Typical examples are: exothermicities masked through endothermic evapo
ration of solvent remainders, if tested in an open container; or oxida
tive reactions which cannot be properly detected by tests in closed
ves
sels.
Other parameters can effect the detection of the onset temperatu
re:
1. sample size (which affects the extent of heat accumulation within the
sample)
2. thermal inertia (which will cause heat to be absorbed limiting self
heating. The level of thermal inertia is dependent on sample size rela
tive to sample container size and material)
3. vessel material (which can either catalyse or inhibit the reaction)
4. heating rate (which can have an effect on the detection sensitivity,
with higher heating rates raising the detectable onset
temperature).
An often-used rule in thermal hazard evaluation which has been
perpetuated throughout the chemical industry is the "100 Degree Rule".
This rule states that if the operating temperature of a process is 100
°C away from the nearest detectable exotherm observed in a DSC experi
ment,
the operation will not "experience" this thermal event, and it is
not necessary to obtain more detailed information via a technique such a
ARC.
The "100 Degree Rule" failed for a large number of reactions which
commonly occur in the chemical industry [85,86]
_
6.Selection of samples for testing
Most safety testing is carried out prior to the start of large-scale
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94
production. The problem is to find a sample that will be representative
of the ultimate production material. This often proves difficult, becau
se:
- the material produced in a laboratory may have different impurities
than the production material. And even after production has been star
ted, apparently trivial changes, i.g. in a raw material, can produce a
significant modification of the thermal behaviour.
- some instruments are designed to handle such small amounts that the
sample cannot be considered representative.
- substance properties depend on the process itself. In other words, the
thermal behaviour of the substance changes depending on the treatment
undergone. Substantial differences in properties may be found if the
process conditions vary.
For example, recently in a fine chemicals factory a drum contai
ning about 100 kg of 3-amino-5-methyl isoxazole exploded I
8 7
. Samples
from the batch involved in the accident (A) showed a DSC purity of 96
X,
and samples from previous batches (B) gave a purity of 98 %. TLC analy
sis showed the presence of the isomer 5-amino-3-methyl isoxazole as main
impurity. From DSC and ARC tests, sample A appeared to be much more un
stable than the others (ToA = 62 °C, ToB = 106 °C).
7.Process and plant operation variables
The following indicate some of the variables which must be considered in
a testing sequence l
8 3
3 :
. effects of adding incorret quantities of starting materials, solvents
or catalysts;
. recycle and recovery streams;
. nature of by-products, still residues, waste and effluent streams;
. quality of raw materials, catalysts, solvents and reaction intermedia
tes;
. effect of scale of operation;
. catalytic action by materials of construction of the plant or products
of corrosion;
. ingress of heat transfer fluids in the reactor;
. extended heating times of reactants due to unforeseen circumstances.
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REFERENCES
[1] Bretherick, L. (1990) Handbook of Reactive Chemical Hazards, But-
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[3] Cardillo, P. (1988) Incidenti in ambiente chimico: discussione di
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[5] Stull, D.R., Westrum, E.F. and Sinke, G.C. (1969) The Chemical
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[10] Duswalt, A.A. (1968)
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[17] Cardillo, P. (1982)
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[18] Cronin, J.L. and Nolan, P.F. (1987)
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Hakl,
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[33] Rogers, R.L. (1989) in Internat. Synp. on Runaway Reactions,
CCPS,
Boston, p. 281
[34] Sing, J. (1989) in Internat. Symp. on Runaway Reactions,
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CCPS,
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[36] Laye, P.G. and Nelson,D.C. (1989)
Thermochim. Acta
153, 221
[37] Stull, D.R. (1977) Fundamentals of Fire and Explosion, AIChE Mono
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[38] Yoshida, T. (1980) Handbook of Hazardous Reactions with Chemicals,
Tokyo Fire Department, Tokyo
[39] Seaton, W.H., Freedman, E. and Treweek, D.N. (1974) CHETAH: The
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[4 0] Lathrop, W.C. and Handrix, C.R. (1949)
Chem. Rev.
44, 419
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Cahiers de Notes Docum entaires
105, 405
[42] Davies, C.A., Kipnis, I.M., Chase, M.W. and Treweek, D.N. (1985)
The thermochemical and hazard data of chemicals. Estimation using
the ASTM CHETAH program,
In J.M. Hoffmann and D.C. Maser
(eds),
Chemical Process Hazard Review, ACS Symp. Series 274, 81
[43] Fruip, D.J., Freedman, E. and Hertel, G.R. (1989)
Plant/Operat.
Progress
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[44 ] Wendland, W.Wm. (1986) Thermal Methods of Analysis, Wiley &
Sons,
New York
[45] Garn, P.D. (1965) Thermoanalytical Methods of Investigation, Aca
demic Press, London
[46] Mackenzie, R.C. (1970,1972) Differential Thermal Analysis, Vol.1
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[47] Whiting,L.F., Labean, M.S. and Eadie, S.S. (1988 )
Thermochim. Acta
136, 231
[48 ] Gygax, R., Meyer, M.W. and Brogli, F. (1980 ) in Proc. of the 6th
Internat. Conf. on Thermal Analysis, Bayreuth, p. 541,549
[49] Barton, J.M. (1983 )
Thermochim. Acta
71, 337
[50] Gygax, R. (1990)
Chem. Eng. Prog.
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[51] ASTM, (1976) Assessing the thermal stability of chem icals by met
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ASTM E 537
[52] ASTM, (1974)
Constant tempera ture stability of chem ical ma terials,
ASTM E 48 7
[53] Townsend, D.I. and Tou, J.C. (1980)
Thermochim. Acta
37 , 1
[54] Tou, J.C. and Waiting, L.F. (1981)
Thermochim. Acta
4 8, 21
[55] Cardillo, P. and Girelli, A. (1982)
Chimica e Industria
64, 231
[56] Waiting, L.F. and Tou, J.C. (1982)
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24, 111
[57] Duch, M.W., Marcali, K., Gordon, C.J., Hensler, C.J. and O'Brien,
G.J. (1982)
Plant/Operat.Progress
1, 19
[58] Waiting, L.F..Raykovitz, H.F.andTou, J.C. (1983 )
Thermochim. Acta
62, 65
[59] Cardillo, P. and Girelli, A. (1982)
Chimica e Industria
65, 611
[60] Huff, J.E. (1982)
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[61] De Haven, E. (1983 )
Plant/Operat. Progress
2, 21
[62] Cardillo, P. and Girelli, A. (1984)
Annali di Chimica
74, 129
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[63] Fenlon, W.J. (1984)
Plant/Operat. Progress
3, 197
[64] Cardillo, P. and Girelli, A. (1985)
Chimica e Industria
67, 403
[65] Coates, C.F. (1985)
Thermochim. Acta
8 5, 369
[66] Cardillo, P. and Girelli, A. (1986 )
Thermochim. Acta
85, 339
[67] Cardillo, P. and Girelli, A. (1986)
Chimica e Industria
68, 68
[68 ] Cardillo, P. (1988)
Chimica e Industria
70, 90
[691 Cardillo, P., Quattrini, A. and Vajna de Pava, E. (1989)
Chimica
e Industria
71, 38
[70] Kohllbrand, H.T. (1989) in Internat. Symp. on Runaway Reactions,
CCPS,
Boston, p.86
[71] Beyrich, J., Regenass, W. and Richarz , W. (1980 )
Chimin
34 , 244
[72] Schildknecht, J. (1981)
Thermochim. Acta
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[73] Hoppe, T.F. and Weir, E.D. (1981) in Proc. 13th NATAS Conf., Phi
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[74] Schulz.N.,
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V. and Schacke H. (1983)
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[76] Riesen, R. and Grob, B. (1985)
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7,39
[77] Weir, E.D., Gravenstine, E.D. and Hoppe,T.F. (1986)
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Progress
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[78] Riesen, R., Grob, B. and Vogel, K. (1987)
Thermochim. Acta
114,83
[79] Hoffmann, W. (1989)
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43,62
[80 ] Hoppe,T. and Grob, B. (1989) in Internat. Syap. on Runaway Reac
tions,
CCPS, Boston,
p.
132
[81] Steele, C.H. and Nolan, P.F. (1989) in Internat. Symp. on Runaway
Reactions, CCPS, Boston, p.198
[82] Gibson, N., Harper, D.J. and Roger, R.L. (1985)
Plant/Operat. Pro
gress
4, 181
[83] The Association of the British Pharmaceutical Industry, (1990)
Guidelines for Chemical Reaction Hazard Evaluation
[84] Hub, L.(1980 )
Can thermic hazards remain undetected?
in 3rd Inter
nat. Symp. Loss Prevention and Safety Promotion in the Process In
dustries, Basilea
[85] Hofelich, T.C. and Thomas, R.C. (1989) in Internat. Symp. on Ru
naway Reactions, CCPS, Boston, p. 74
[86] Health and Safety Executive (1977)
The explosion at the Dow Facto
ry, Kings'Lynn,
Her Majesty's Stationery Office, London
[87] Cardillo, P.(1988)
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1, 46
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EQUIPMENT CHARACTERISATION
C. BARCONS I RIBES
Chemical engineering department
Institut Quimic de Sarrid, Barcelona, Spain
Present address: JRCIspra Site
Safety Technology Institute
1-21020 Ispra(VA)
ABSTRACT. The manufacture of chemical products by means of batch processes has recendy become
very important due to the flexibility offered by this type of equipment in w hich they are carried out. The
proper characterisation of this equipment will allow die performance of a wide variety of chemical
reactions with a minimum risk. The response of the system depends basically on the heat capacity of the
vessel, heat losses, heat transfer availability and other sources of input/output heat. An approach for
determining them either theoretically or experimentally is described in this paper. The procedure to
determine the safe operating conditions is basically the same for every different process. A basic method
for scaling-up a chemical process is described as a result of the proper equipment characterisation. This
paper has been written with the purpose of helping engineers on the characterisation of their batch
chemical plants, in order to avoid accidents when there is a need to scale-up a laboratory process.
1 .-
I n t r o d u c t i o n .
The chemical Industry has become important in recent years due to the large number and variety of
chemical processes which have been developed. Human needs and the important evolution of
technology have encouraged the development many chemical processes without a basic knowledge
of the potential risk involved, thus leading to a large number of accidents.
Accidents in the chemical industry are often due to unexpected and/or undesired reactions,
resulting from an over-heating of the reacting mixture and leading to a thermal-runaway. This
happens when the heat generated by the reaction exceeds the heat removal capabilities of the
equipment in which the process is carried out. According to Rasmmusen [1], the largest number
of accidents within the chemical industry occur in batch and semi-batch processes, involving 57%
of cases against 11% in continuous processes.
A significant number of chemical processes, particularly where large scale production is not a
major req uiremen t, are carried out in batch chemical reactors becaus e of their versatility. This type
of equipment often allows the performance of many different processes with minor modifications.
For this reason, batch reactors have become very common in the Fine Chemicals sector.
The standard equipment for this type of processes consists of a vessel, which can be heated or
cooled by means of an external jacket and/or internal coils. An agitator is frequently axially
centered in the vessel and its paddles are placed close to the bottom of the vessel to provide good
agitation of the reacting mixture. External condensers are often available for processes involving
reflux or distillation. Th e temp erature evolution of the reactor contents depend s on the heat transfer
fluid temperature, circulation speed and properties. The heat transfer fluid can be temperature
99
A.
Benuzzi and J . M. Zaldivar (eds.). Safety of Chemical Batch Reactors and Storage Tanks,
9 9 - 1 2 3 .
© 1991
ECSC, EE C, EAEC, Brussels and Luxembourg. Printed in the Netherlands.
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100
controlled for isothermal processes or may have a constant inlet temperature for isoperibolic ones.
In semi-batch processes, the temperature control can be aided by the rate of addition of reagents
(and their temperature) in order to avoid a large quantity of heat accum ulated in the reaction mass.
This equipment is normally designed to work under small pressure. Many different probes and
devices for control and measurem ent purposes can easily be installed (temperatu re, pH , redox and
so on) according to the particular process requirements.
Barton and Nolan [2], analysed the incidents which occured in batch reactors due to
overheating of the reacting mass and concluded that these were due to:
- basic lack of knowledge of the process chemistry and thermochemistry
- inadequate en gineering for heat transfer
- inadequate control systems and safety back-up systems
- inadequate operational procedures
From this study, it is possible to conclude that a proper equipment characterisation and scale-up
procedure are important aspects in the design of these installations. This paper will cover these
subjects and special emphasis will be given to experimental and theoretical determination of the
heat removal capabilities of a process vessel. Further, the power input due to stirring, the heat
losses to the surrounding s and the influence of the addition of reactants will be considered, as well
as the heat capacity of the vessel and internal devices, in order to know how the characteristics of
the vessel can affect the process under dynamic conditions.
2 .-
Eva lua t ion o f t he rma l capac i t i e s and hea t l osse s .
An important parameter relating to a vessel in which a chemical process will be carried out is its
thermal capacity. Normally, thermal capacities of laboratory vessels have an important thermal
effect when a reaction is studied. In process vessels this thermal effect is less important because
the ratio between the thermal capacity of the vessel and the mixture is proportionally much small.
It is relatively simple to determine thermal capacities of vessels. Theoretical prediction is
accurate as they are built-up with well known materials and geometry. There are also easy
methods to perform experiments to determine thermal capacities.
It is more difficult to use available data to find out the value of heat losses as a function of
ambient temperature. It is also problematic to evaluate them experimentally, because of their small
value, how ever, they can be neglected if the reactor is properly insu lated.
2.1.
THEORETICAL PREDICTION OF THERMAL CAPACITIES AND HEAT LOSSES .
Chemical reactors are usually made of well known materials. Data describing the physical
properties of such materials is easy to find elsewhere [3].
Theore tical calculation of the thermal capacity of the vessel is made throug h adding together all
the thermal capacities of the different parts of the vessel in contact with the reaction mixture, which
means the reactor wall and all the probes and devices, such as stirrer, temperature, pH and so on.
n
r
t
= £ m,C
i =1
wh ere: i refers to every individual part in contact with the reaction mix ture.
t = ^ W " Y ° P ; (2-1)
i=1
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The prediction of the heat losses to the surroundings is more difficult to calculate than the
thermal capacity of the vessel. It will mainly depend on reaction mixture properties (vaporisation
and condensation of the mixture on the reactor walls), air circulation around the vessel (natural
convection) and on solid parts in contact with it (conduction). The importance of heat losses
should be checked and the possibility of a thermal insulation considered. If the reactor is insulated
and working conditions are not drastically far from ambient temperature, heat losses can be
ne ^c cte a, otherwise complex methods to evaluate them are described by Ku mana/Kothari [4] and
different approaches can be found in many heat transfer handbooks [5], [6].
2.2.
EXPERIMENTAL EVALUATION OF THERMAL CAPACITIES AND H EAT LOSSES.
Experimental evaluation of the whole thermal capacity and heat losses of a process vessel can be
done in several different ways using the energy balance for a closed system.
2.2.1.-
Electrical Heating
+
free cooling. Heat a know n am ount of pure liquid w hich has a very
constant (or very well known) specific heat capacity in the temperature range in which is going to
be used, i.e. water, with a constant power input and no cooling services.
Allowing a free cooling after the heating operation, time constant for heat losses can be
determined. Heat losses can easily be influenced if the mixture is stirred. For an approximative
calculation, free cooling without stirring can be allowed.
A combination of both effects using a non steady state temperature evolution analysis allows to
calculate both values accurately at the same time if accurate data of temperature evolution is
available. Using the energy balance of the system and assuming that the whole system is in
thermal equilibrium, the equation involved for this calculations is the following one:
dT
m
q
m
"i j _
(
r. + r
+
x . ' I
t r, + r
T
T
-1 a
t m
T„ - T
m
(2.2)
wh ere: Tt is the vessel thermal capacity
r
m
is the mixture thermal capacity
\ is the time cons tant for heat losses
qj is the power input
Du ring the free coo ling in w hich the electrical heating is off, the po we r input is restricted to the
one that is introduced by means of the agitation. Depending on the heat losses value, this can be
considered or neglected. If heat losses are important, they can be easily evaluated by means of a
very simple computer program using temperature evolution data without taking into account any
small pow er input. The v alue found can then be used to ma ke a precise calculation of the thermal
capacity of the system, and better results may be found if iterative procedures are used when other
small heat contributions as the stirrer effects are considered.
2.2.2.- Fast injection. A rapid addition of a cold/hot liquid to a hot/cold one (normally the same),
will produce a fast temperature change of the whole system, involving the liquid, the vessel and all
the inserts in contact with the liquid. Wa ter is also suitable in this cas e. The difference between the
theoretical final temperature if no thermal capacities other than liquid were involved and the one
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102
measured experimentally, is due to the thermal capacity of the whole equipment in direct contact
with the liquid. The first temperature inflexion is reached in a short time depending on the time
constant for the response of the system. At this moment, the vessel wall and the fittings in contact
with the liquid have reached the thermal equilibrium. The value of this temperature difference
allows the calculation of the thermal capacity of the reactor wall and inserts, which can be called
heat transfer barrier. This evaluation needs also no heat transfer fluid present inside the reactor
jacket.
n
i
= 1
r r
V
C „ - | T
i
- T ) =
P: ^ i
) ~
u
(2.3)
wh ere: i is refered to each amoun t of liquid.
T is the theoretical final temperature.
Th e am ount of liquid used should be enou gh to be in contact with the who le heat transfer area at
the end, and the temperature difference between both amounts before the injection should be as
large as possible. This method is reliable if heat losses are neglectible compared with the amount
of heat involved in the thermal changes of the system, and if thermal equilibrium is reached in a
short period.
2.3. APPLICATION EXAMPLE [8].
For a 100 L Pfaudler standard glass lined batch reactor [7], insulated from the surroundings, the
theoretical thermal capacity using material properties available data can be calculated as follows:
glass => m
g
- C p
g
= 3.6-800 (Kg-J/K g/K) = 2.9(kJ/K )
metal => m
m
- C
p m
= 471.4-500 (Kg-J/Kg/K) = 23 5.7(kJ/K)
wh ere: mj is the total mas s of every material type used.
Cpj is its heat capacity pe r unit mass.
Norm ally every supplier of these reactors gives information about the type of material the vessel
is made off and the thickness it has. For this particular case it has been calculated that the thermal
capacity of the vessel ( neglecting the inserts) is at about 238.6 kJ/K.
An experiment carried out heating amounts of 60 Kg of water with a constant power of 4 kW
and the vessel insulated (heat losses neglected), using the first technique (2.2.1) and using eq.
(2.2),
gave a value of 256 kJ/K for the whole thermal capacity of the vessel and inserts. Using the
fast injection method (2.2.2) to determine the value of the heat transfer barrier, with the reactor
properly insulated, a large variation between 23 and 431J/K was found between five experiments.
This experimental error is due to the small AT measured.
A calculation using data available for the thermal capacity of the heat transfer barrier was made
and the value found is 38.9 kJ/K
glass => n y C p g = 3.6-800(Kg-J/Kg/K) = 2.9(KJ/K)
metal => m
m
- C
p m
= 72-500(Kg-J/Kg/K) = 36.(K J/K)
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Comparing these values, it is possible to conclude that the theoretical prediction of the thermal
capacities is rather accurate in accordance with the values experimentally found, taking into
account that the thermal capacity of the inserts was not calculated.
3 .-
Ca lcu lation of heat transfe r coefficients
3 . I . L N I K O D U C T I O N
Almost all the operations carried out in chemical reactors involve either the production or the
absorption of heat. The knowledge of the equipment capacity for heat transfer is very important
for the characterisation of the dynamic behaviour of the system and is, therefore, of great
importance for the safe and economic design of the process.
Heat flow is defined as the speed at which heat is exchanged from a hot source to a cold
receiver. Both systems are usually considered indepently because their heat transfer dynamics are
different There are three main distinct mechanism s in which heat can be exchange d: conduction,
convection and radiatioa
Many different types of vessels and cooling/heating systems are used in chemical processes.
For batch ch emical reactors, external jackets and internal coils are the most co mm on methods to
control the reaction mixture temperature. This chapter will deal with jacketed vessels, but all the
items described hereafter are also applicable with slight modifications for coils and for other
similar types of equipment.
Heat transfer in a stirred chemical reactor with an external jacket can be represented in a
generalized form as is shown in figure 3.1.
Figure 3.1. Heat transfer from a chemical reactor to an external jacket.
The general equation to describe heat transfer dynamics is the energy balance, which can be
described as the time evolution of reactor tem perature:
dt r
L
ff '
m i = l
removed
(3.1)
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Newton's law defines the heat removed through a wall as a proportional part of the temperature
difference betwe en both sides, which is called driving force (3.2 ). This p roportionality involves
the overall h eat transfer coefficient, U, and the heat transfer area, S):
^removed = U -S-(T
m
- T
e
) (3.2)
The magnitude of the driving force depends on the operating mode. There are three main
modes: adiabatic, isoperibolic and isothermal. In the adiabatic mode, no heat exchange occurs
betw een reaction mass and surroundings, that means qrem oved = 0- The isoperibolic mode is
characterised by a constant inlet temperature in the jacket, whereas in the isothermal m ode the
reac tor tempera ture is controlled by mean s of adjusting the jac ket tem per ature . In the latter case,
the dynamics of the heating/cooling circuit becomes important.
For jacketed chemical reactors, the main heat transfer phenomena is forced convection, which is
produced either by stirring effects inside the vessel or by the circulation flow of the heat transfer
fluid through the jacket. Heat conduction through the wall may be important, depending on the
material of w hich the reactor is made .
The exchanging of heat by means of forced convection can be described simply with the
following equation:
dq =
h-SdT
(3.3)
The proportional constant h is referred to as the partial heat transfer coefficient. For a jacketed
reactor, h is applied to the internal and external sides of the reactor w all. Th e internal heat transfer
coefficient depends on the reaction mixture properties and on the stirring characteristics while the
external depends on the heat transfer fluid properties and its fluid-dynamics regime inside the
jacke t. These coefficients mu st be evaluated experimentally [9].
The final parameter is the heat exchange area. This is practically constant for batch processes
because its changes are due only to density variations in the reaction mixture. However, for
semibatch processes the heat transfer area will increase as a function of the feed rate. Further,
there is also an increase of the heat transfer area due to the vortex generation in reactors that do not
have baffles inside, and this will depend on the stirrer characteristics and physical properties of the
fluid [10].
The main objective of this chapter is to show how to predict from dimensional analysis the
overal l heat t ransfer coefficient , and to describe the procedure with which evaluate i t
experimentally. After the heat transfer coefficients are modelled or experimentally evaluated for a
small laboratory chemical reactor, a procedure to scale-up the process to a pilot plant and/or to a
larger production vessel is presented.
3.2. HEAT TRANSFER IN AGITATED VESSELS
For a tank within which a chemical process is carried out, the heat exchanged with the heat
transfer fluid is calculated by taking into account all the thermal resistances between the reaction
mix ture and the heat transfer fluid. Th e overall heat transfer coefficient, U , introduc ed before, is
determ ined by two different partial or individual heat transfer coefficients and the wall resistance,
or in other term s, the overall resistance to remove he at can be described as the add ition of three or
mo re resistances. Thes e are attributable to:
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- Internal film from reaction mixture.
- Wall thermal conductivity.
- External film from circulating heat transfer fluid.
Th e gen eral expression for overall heat transfer resistance is:
U " h
+ H w +
D h (
3
.
4
)
o 1 1
Where: hg and hj are the partial heat transfer coefficients related to the internal and external
films respectively, and R
w
is the wall resistance. The term
D Q / D J
is the ratio of areas to take into
account the diameter difference betwe en the inside and the outside of the reactor w all.
It should be noticed that every liquid can produce a layer or deposit of extraneous materials on
the heat transfer surface, which will provoke a time-modification of both partial heat transfer
coefficients. In these cases, the heat transfer resistance increases considerably due to the fact that
this type of materials normally have a lower thermal conductivity. This effect is referred to as the
fouling or dirt factor, and should be avoided or, if this is not possible, taken into account as a
further resistance to heat transfer.
3.3.
THE DETERMINATION OF THE INTERNAL HEAT TRANSFER COEFFICIENT
From dimensional analysis, using the Nusselt equation (3.5), it is possible to correlate empirically
the internal partial heat transfer coefficient as a function of operating conditions and mixture
properties by means of equation (3.6).
Nu = f (Re, Pr, Vi) (3.5 )
h
0
= a
0
N
a
9 2
° (3.6)
w here : otQ is a cons tant.
According to equation (3.6), only the stirrer speed can modify the value of the internal partial
heat transfer coefficient for a given reactor, with the same mixture and temperature conditions
inside it The value of
OLQ
is described by dimensionless analysis (Nusselt equation) with equation
(3.7):
Da-Pn
- o - ^ o ^ P ^ V l '
4 0
-
K
where : 0 IQ, 620 ^30> ^40
a r e
constant for every system.
(3.7)
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When the power generated in the reactor mixture is small, the viscosity number (Vi) can be
neglected , if temperature difference between the mixture and the heat transfer fluid is not so large.
Assum ing that
O Q
has a constant value u nder the conditions previously men tioned, it is possible
to determine experimentally the value of hg, using the Wilson plots [11]. For every vessel, the
values of hg and
(XQ
must be experimentally d etermined in orde r to derive the characteristic values
for a specific system. The correct values of II Q and
< XQ
can be simply obtained using eq. (3.4).
W ith the sam e operating conditions in the jacket, R
w
and hj will not change, and hg can be
mo dified varying only the stirrer speed. A straight line can be plotted in a graph using eq. (3.8):
1
U
f
R
+
- ^
A
V
1 1
+
^LN
920
a
o
a
(3.8)
The experimental procedure to evaluate the overall heat transfer coefficient, U, is described in
section 3.7.
If the stirrer speed pow ered at -620 is plotted against the reciproca l of U, a graph such as that
shown in figure 3.2 is produced. The slope of the straight line is the reciprocal of
<XQ.
When the
stirrer speed has no effects on the value of ho (N—»°°), 1/U gives the constant value for the wall
and partial external heat transfer resistance due to the heat transfer fluid film.
U
- T
_ R
w
+
"
D l
h .
Na
20
Fig. 3.2.- Wilson ploter for hg experimental determination.
Ex tensiv e characterisation work has been carried out by B ourn e et al. [14] for different agitator
types. Th e values of the constants reported are given in table 3 .1. The values found in their work
for the exponents and constants were contrasted with those found in the literature, and a standard
deviation for the predicted and the experimental ho was calculated for all cases.
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Table 3.1- Exponents and standard deviation for different impellers and Re regimes.
impeller
turbine
turbine
anchor
ar-ch^i
anchor
pfaudler
pfaudler
gate
gate
Re range
8<Re<46000
8<Re<46000
5<Re<70
70<Re<600000
70<Re<600000
9<Re<55000
9<Re<55000
12<Re<300000
12<Re<300000
OlO
0.42
0.42
1.0
0.29
0.35
0.27
0.33
0.55
0.47
620
0.694
2/3
0.38
0.678
2/3
0.7
2/3
0.65
2/3
630
1/3
1/3
1/3
1/3
1/3
1/3
1/3
1/3
1/3
640
0
0
0.14
0.14
0.14
0
0
0.14
0.14
s %
3.2
8.4
11.3
4.2
6.9
4.5
9.8
5.6
6.9
3.4. THE DETERMINATION OF WALL RESISTANCE
Theoretical evaluation of wall resistance is normally straightforward for standard chemical
reactors, because of the specifications provided by the manufacturers. These specifications
normally include the type of material used in the construction of the vessel, the thickness of the
walls and the type and characteristics of possible paints or coating covering the walls in order to
protect the reactor from corrosive agents.
W all resistance is described w ith the following equation:
R
w
=
R
0
-Lnh/D
0
)
(3.9)
wh ere: ^ is the thermal cond uctivity of the wa ll.
DQ and Dj are respectively the internal and external diameters of the cylindric wall.
If the wall of the reactor is made of different films of different materials, each resistance should
be calculated separately for every one, and the addition of these will give the overall resistance
value. Detailed information about the thermal conductivity ^ , of the mo st comm on materials used
to build chemical reactors can be found in the literature [3].
3.5.
THE DETERMINATION OF THE EXTERNAL HEAT TRANSFER COEFFICIENT
Determination of the external partial heat transfer coefficient for a given vessel can be done
following the dimensional analysis mentioned previously for the calculation of the internal one.
Again, the Nusselt equation (3.5) can be used to correlate empirically the influence of the flow of
the circulating heat transfer fluid through the ja ck et T he N usselt equation gives:
h
1
= a
1
Q
e
21
(3.10)
where: a\ depend s on the heat transfer fluid properties and the shape of the jack et
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From the equation (3.10), and assuming that a\ is kep t in such a cond itions that there are no
temperature changes, the variation of Q
e
is the only parameter that can modify the value of the
external partial heat transfer coefficient, due to the film of the heat transfer fluid. The value of a j
is a function of the heat transfer fluid properties and is defined by dimensional analysis with
equation (3.11):
e„
a . = 0
11 D
^-Pr
3 1
- V i
4 1
P.-D,
S
f
- H
f * e
21
(3.11)
where:
G J J ,
62 1, 63 1, B41 are coastant for every system.
Following the procedure used for the linearisation of the internal heat transfer coefficient as a
function of the stirrer speed, it is possible to represent the external partial heat transfer coefficient
as a linear function of the heat transfer fluid flow if it is pow ered to the correct ex pone nt for each
system. The expression to plot is:
1_
u
\
V ° J
D
r°S
• Q ,
21
(3.12)
The experimental procedure to evaluate the overall heat transfer coefficient, U, is described in
section 3.7.
A graph similar to the one proposed by Wilson can be produced, with the heat transfer fluid
flow powered to -621 against the reciprocal of U. This also produces a straight line whose slope
is proportional to the reciprocal of ctj, and it gives a constant value when the heat transfer fluid
flow has no influence on U (high Re num bers), comp ared with the partial internal heat transfer
coefficient and the wall resistance. This plot is show n in figure 3 .3 .
Fig. 3.3 .- Wilson plotter for hj experimental determination.
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M any different autho rs [12, 13 , 14, 15] have reported stud ies on Nusselt 's dimens ionless
equation for different systems through a large range of Reynolds numbers (Re), and have often
reported similar values for the exponents ©21 • ®31
a n (
^
®4\-
T h
e
typical values for 02
\
631 and
041 are respectively 2 /3 , 1/3 and 0.14. The constant 6 J J which is used to multiply the whole
equation have been reported to range from 0.2 to 0.8, mainly varying due to system geometry. In
the same system, it varies with the fluid dynamics regime, increasing at about 40% from the
laminar flow (Re<400) to the fully developed turbulent flow (Re>10000). The exponent for the
Prandtl Number (631) is set to 1/3 in nearly all the main relevant works, and the viscosity number
is usually found to be 0.14, though different values have been reported ranging from 0 for small
process vessels to 0.18 for bigger ones.
3.6. THE DETERMINATION OF THE OVERALL HTC DURING A CHEMICAL REACTION
In som e cases it may be useful to know the variation of the overall heat transfer coefficient during
a chemical process. It might happen during a chemical reaction that the physical properties of the
mixture change drast ical ly and, with them, i ts heat t ransport characterist ics. Under such
con dition s, the internal heat transfer coefficient m ight decre ase due to the variation of the reaction
mixture properties, and a larger quantity of heat than expected can be accumulated in the reactor,
increasing the temperature of the mixture. In such cases, undesired reactions may take place and,
in the worse case, reaction mass can lead to a thermal runaway.
In order to avoid this situation, the evaluation of the heat transfer coefficient time dependence
during a chemical process can be done. This technique was p roposed for the Mettler RC1 reactor
calorimeter [20], and it has been tested for a simple chemical reaction. Its performance is now
described.
The desired reaction is carried out under normal conditions, and the temperature profiles of the
reaction mass and the heat transfer fluid (also the temperature of the reagents added if the process
is semi-batch) are stored in a computer file. After this, the reaction is performed again under the
same conditions, but adding a well known and constant ammount of heat (qh) to the mixture, by
means of an electric heater, during the whole process. This heat flow input should be small
enough in order not to affect the reaction conditions, (basically the temperature), but it must
produce a significant change between reactor and jacket temperature. Temperature data is also
recorded in this case.
Using the equation for the energy balance (3.1) for both cases, and subtracting one from the
other, it is possible to obtain equation (3.15).
dT
m s
dt
dime
dt
1 [q
x
- US(T
m s
- T
e s
) - K ^ T ^ - T
a
) - Q
a d
Cp(T
m s
- T
a d s
) ]
1 [q
x
- US(T
m c
- T
ec
) - r y -T ^ - T
a
) - Q
a d
Cp(T
m c
- T
gdc
) + q
h
]
(3 .13) , (3.14)
whe re: s and c refer to the experimen t without and with qh respectively.
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no
To develop this equation (3.15), it is assumed that the chemical reaction occurs exactly in the
same way and rate, the heat input by the stirrer and any other different inserts are the same in both
cases, as is the ambient temperature.
U S =
dTn
d t
dTm
d t
q
h
- K / T ' V
T m
c) -Q
a d
C p (
T
a d c -
T m
c -
T
a ds
+ T m
s )
A T
S
-
A T
C
(3.15)
where: q^ is the heat input
r is the thermal capacity of the reactor and its contents
dTm i/dt is the derivative of reactor temperature w ith (c) and w ithout (s) heat input
AT] is ( T
m
- T
e
) with (c) and without (s) heat input
T
a
di is the temperature of addition, with (c) and w ithout (s) heat input
Ki is a constant for the heat losses to the surroundings.
Using this equation with all the points of both experimental profiles, it is possible to obtain a
good time profile of the heat transfer coefficient, even the noise introduced when calculating the
derivative of the reaction m ixture temperature (see figure 3.4).
Continous heat transfer coefficient calculation using equation (3.15) has been performed for
two different experiments on isothermal and isoperibolic mode, when adding 0.500 Kg of water
during 30 min. to 1.000 Kg of water.
1100
10.50-
10.00-
7.00
6.50
6.00
180 360 540
T T
US (IS0THERMAL. MODE)
US (ISOPERIBOLIC MODE)
US
(EXPERIMENTAL DATA)
T
720
900 1080 2 6 0 1440 1620
Fig. 3.4.- Calculations under isoperibolic mode (light line), isothermal mode (thick line)
and from previous and posterior evaluation (straight line).
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I l l
This method can be applied under either isothermal or isoperibolic modes. If it is applied under
isoperibolic mode, it should be taken into account that the additional heat input will increase the
reactor mixture temperature. In order not to modify the reaction rate, jacket temperature should be
reduced on the same amou nt
The value of the constant for the heat losses should be determinated for every process at the
final temperature, using the experimentally evaluated heat transfer coefficient and the energy
balance for the steady state (eq. 3.16 ). It will be mo re accur ate if all the hea t input sources are
experimentally measured.
K
_ US(Tm - Te) + q
a ( 3 1 6 )
1
(Ta - Tm )
where: q
a
is the po wer inp ut by the stirrer.
3.7. PRACTICAL EXAMPLES
The re are two different metho ds to measure the overall heat transfer coefficient using calorimetric
principles. The first one uses a control system to keep the reactor temperature constant while a
kno wn pow er is given to the mixture, which causes a decrease of jacke t temp erature. The second
one is in isoperibolic mode, where a known power is given to the mixture and the reactor
temperature is allowed to reach a steady state. In both cases the measure of the AT generated will
be used to determine the value of U. The overall heat transfer coefficient can then be calculated
using equation (3.17):
US =
s
A T
m r
A T
, n o '
AT, .=
In
AT
e
. m eo .
(3.17)
where: AT[
n
Q and A T
m
j are the temperature difference betw een the mixture and the jacket
before and during the power input (when reactor temperature steady state is reached)
respectively.
Experimental Wilson plots with different liquids were carried out with a reaction calorimeter
using the first technique [16]. A plot for toluene at different temperatures and 5 different agitator
speeds is shown in figure 3.5.
The second technique described has been used to determine U for water in a 100 1 standard
chem ical reactor [ 17]. Th e results of this experimen tal
OQ
evaluation and the Reynolds exponent
are shown in figure 3.6.
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y . 0.0076 » 0.0022X
y - 0.0076 * 0.002X
y - 0,0074 . 0.0022X
y - 0.0072 ♦ 0.0O25X
y - 0 , 0 0 6 7 * 0.0031
R-0,99
H - 0,96
R.0 .96
R-1.00
H-0.99
°.
5
Na
A
-.694
Figure
3.5.-
1/U
vs.
Na for
toluene
at
different
Temperatures.
1/U
1AJ -0 . 0 016 » 5,803e-4 Wa -0.7 R - 0.98
Na
A
-0.7
Figure 3.6. 1/U vs. N a
u
' ' for water at different stirrer speed.
4 .-
T he
c h a r a c t e r i s t i c s
of
mix ing
dev ices .
4.1.
TYPES OF EQUIPMENT.
Many different types of stirrers ar e used to agitate chemical mixtures. Among them, impeller,
anchor, turbine and gate are th e ones mainly used. For batch and semibatch reactors, normally
only one stirrer is used and it is generally axially centered in th e reactor with th e paddles close to
th e bottom of i t
The anchor agitator is normally operated at a few rpm. It generates tangential flow which can be
accompanied with axial flow depending on the mobility of the product. It is placed in the centre of
the reactor and has the shape of the vessel outline, ensuring a low wall clearance. The height of the
tw o blades usually ranges from 0.5 to 0.8 of the agitator diameter.
The
impeller
agitator
obtain
optimum
results
at
an
agitator
diameter
of
0.5
to
0.8
of
the
vessel
diameter. It usually rotates at more rpm than the anchor. It is normally arranged in the centre of the
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reactor, and with a minimum of bottom clearance. The agitator sucks in the product axially and
ejects it radially. By installing baffles in the vessel, the efficiency is considerably improved,
especially in the lower viscosity range. It is considered to be a reliable all-purpose agitator over a
wide viscosity range.
The gate agitator produces a double ring turbulence conveying the product out of the middle of
the blades and deflecting it at the vessel wall to both sides. Suction is produced both from the
re^Cujr DOLtom and from the liquid surface. Moreover, it develops a uniform shearing head above
the entire filling height. It is applied for homogenizing services throughout the whole viscosity
range. This type of agitator is specially suitable for the high-viscous range with good results even
at small Re (Reynolds number) with a relatively low power input
Th e turbine ag itator covers ap proxim ately 1/3 of the reactor diam eter and can be fitted w ith a
variable number of blades. The conveying flow is normally ducted to the vessel bottom. It is
especially suitable for dispersing services. Power consumption is only slightly affected by
viscosity increase.
Often, baffles are installed in stirred tanks in order to cut the liquid flow inside the reactor,
allowing a better mixture. The baffles can be placed in many different places and in many different
ways.
The use of baffles is optional but they are efficient and advantageous in mixing throughout the
whole turbulent flow range. Depending on their size and position they more or less convert the
tangential flow into an axial flow. Moreover, they increase the turbulence within the vessel and
reduce the formation of vortices, although this is at the expense of power consumption.
The use of probes and other types of inserts in the reactor will also produce a non
homogeneous flow, and vortex generation (if no baffles are present) can be really different,
depending on the whole reactor geometry.
For homogenizing tasks, all the stirrers can be used, but there is, however, an optimum Re
range for each agitator, where shorter mixing times can be obtained with less power consumption.
The application limits of every agitator depends on the minimum Re number required by means
of the physical properties of the mixture. Baffles are recommended in the turbulent flow range
whereas they may be omitted in the laminar range.
4.2. POWER INPUT BY M IXING.
The calculation of the power input disregarding mechanical loss is calculated using the following
equation:
P = N e N
3
- d
5
- p
(4.1)
In the first instance, power calculation is reduced to defining the dimensionless Ne number
(power num ber).
N e = f( agitator shape , Re, d/D, b/d, H/D) ,4
2
)
where: P = power requirem ent
Ne = power number.
N = agitator speed.
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d = agitator diameter.
p = density of the mixture.
Re = Nd
2
p/|J-
D = vessel diameter,
b = height of blades.
H = height of the vessel.
Normally the course of the Ne is plotted against Re. The influence of baffles in mixing
processes is more important at large Re num bers, having no effects o n pow er consumption w hen
Re has sm all values.
The power transmitted by an agitator to a mixture in agitated vessels has mostly been
determined mechanically by measuring the torque transmitted by the shaft. If it is not possible to
.do this, a calorimetric m easurement can be carried out.
With a properly insulated vessel in which heat losses are negligible, the following equation can
be applied to calculate the power given to the mixture:
U-SAT
=
- (
m
m
-
C
p m
+ n
V
C
P
t } - ^ + P (4.3)
In a steady state (dT/dt = 0), and without any external power input, the agitator is the only
pow er input source. Then, i f the U S value is know n (previously evaluated), and the AT
generated is measured, it is possible to calculate the power input by means of agitating.
Data for predicting the power given by different stirrers can be found either from the
manufacturing company or from the literature [18].
4.3.
HEAT TRANSFER AREA INCREASE DUE TO VORTEX G ENERATION.
The stirring speed in chemical reactors does not only modify the internal partial heat transfer
coefficient, but can also produce an important change of heat transfer area. This is applicable for
the vessels that do not have baffles or inserts inside (see figure 4.1). Heat ex chang e area increases
with stirrer speed, and thus, the proportional factor that multiplies the temperature difference in
Newton's law for heat transfer also increases.
The heat transfer area is defined as the surface wetted by the reaction mixture. It can be
calculated as a function of the volume of the ma ss added plus the stirring effects (vortex) with the
following expression:
2(V
- V J
S = S +
m B
- + AS (4.4)
B R v
v
'
wh ere: S = who le heat transfer surface.
S B = reactor bottom surface.
ASy = increase of surface du e to the vortex.
V
m
,
VB
= Mixture and bottom volume respectively.
Rfj = vessel internal radio.
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A theoretical model to predict the increase of heat transfer area due to the vortex generation was
developed [19] using the modified Navier Stokes equations. This model is valid for a steady
rotational laminar flow of a newtonian fluid around a vertical axis, and without radial and vertical
speed. The expression deduced from this equations is:
N?R
S
H
v
=-
2g
(4.5)
where: H
v
= increase of height due to the vortex generation.
N
a
= stirrer speed.
RO = reactor radio,
g = gravitational strength
Figure 4 .1.- heat transfer area increase due to the vortex.
The validity of this model for a common chemical reactor is very restricted, due to many non-
ideal agitating effects. These non-ideal effects are caused by the vertical and radial movement of
the fluid produced by the stirrer, the interaction of the reactor fittings that cut the rotational flow,
as well as the interaction of the fluid with the reactor wall, which may depend on the mixture
physical properties such as viscosity and surface tension.
4.4. MODEL OF INFLUENCES ON HEAT TRANSFER AREA INCREASE.
In accordance with the theoretical result given by equation (4.5), it is possible to describe the
increase of heat transfer area due to vortex formation with the assumptions previously numbered
as equation (4.6).
AS = (2JIR J H
v
v
0 v
(4.6)
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Experimental results show that this increase in the heat exchange area is not independent of
liquid volume, type of agitator, and physical fluid properties. In order to correct the non-idealities
of such an assumption, the value of N
a
in the equation (4.5) was multiplied by a factor, f, that
depends empirically on all the characteristics mentioned above. Hence, eq. (4.6) can be write, for
a determined reactor and geometry, as follows:
A S ^ K ^ f N f (4.7)
wh ere: K i is a constant that depends on the geometry of the reactor
f is a correction factor for the non -idealities
According to [18] the factor must be correlated with the discharge rate which depends on the
power number given by equation (4.8). Substituting f by this term and rearranging equation (4.7)
the following relationship is obtained (4.9):
K
3 \
Po = K -(Re) -(F r) (4.8)
AS
V
= C
1
R e
C z
F r°
3
N* g(V
m
) (4.9)
wh ere: g(V m) is a function of the reaction mass volum e.
Intuitively, this function has to follow an exponential inverse behaviour, that means with less
volume the increase in height must be bigger than with more volume present in the reactor. The
correlation that fits the experimental data best is:
9 (V
m
) =
V
- V
T m
V
T
C
4
(4.10)
where: C i , C 2 , C3 and C4 are constants that were calculated ex perim entally for four
different agitators using several different fluids and mod ifying th eir vo lum e, the temperature and
the stirrer speed [21].
5.- The Scaling-up of batch reactors .
5.1. INTRODUCTION.
In the Chemical Engineering Industry, one of the main problems to solve is how to carry out a
chemical reaction in a produ ction plant under the same c ond itions as in the laboratory. The
manufacturing of a product requires large vessels in order to be economically viable for the
company, which can lead to unforeseen problems in the laboratory, i .e. heat released, mass
transfer.
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There is a procedure which should be followed through the laboratory experimentation to the
industrial production which can contribute substantially to safe reactor design thus avoiding
accidents.
This procedure concerns the full calorimetric study of the mentioned reaction, beginning with
small amounts of reagents (for example using DSC or adiabatic calorimetry), followed with bigger
quantities (i .e. using heat flow calorimetry), and scaling-up from this reactor to the plant one,
s o ^ n m e s also going through a pilot plant reactor stage before produ cing the final design.
Tem peratu re control of the reaction vessel is essential for the safety an d performa nce of a given
process. The proper knowledge of the heat transfer coefficients play an important role for a
satisfactory scale-up procedure, because often it is necessary to ensure that the temperature
evolution in the large vessel will be the same as that in the laboratory one. Thus, once the thermal
respo nse of the vessel and the heat of reaction (from calorimetric studies) are kno wn , the scale-up
procedure can be applied. For the first larger runs, a large safety margin should be conserved in
order to account for any unexpected behaviour of the reaction mixture during the process.
5.2. RULES FOR BATCH AND SEMIBATCH REACTORS SCA LE-UP.
The two main phenomena in which special care has to be taken for scaling-up from laboratory to
plant reactors are heat and mass transfer. The main parameter for the former is the overall heat
transfer coefficient, while for the latter the interfacial area through which the diffusion of chemical
species takes place is of great importance.
The mass transfer phenomena will not be considered in this chapter, but the most important
thing to remember is that the interfacial area per unit volume should be constant in both reactors
for the right scale-up of a process. If the main limiting factor for a chemical reaction is the
diffusion of the species from one phase to the other, the reaction rate will change in the same
proportion that it has changed the interfacial area per unit volume.
5.2.1.- Scaling-up to a geometrically similar plant reactor. For this case it is necessary to conserve
geometrical similarity (shape factors, i.e. relations between diameters and height, blades, inserts)
and thermal conditions (reactor and jacket temperature).
It is not so difficult to design a bigger reactor geometrically similar to the laboratory one, but for
the overall heat transfer coefficient approximation, a complex experimental work should be
performed.
It has been defined previously a general procedure to determine the film heat transfer coefficient
for a chemical reactor with equations (3.5), (3.6) and (3.7).
For the plant reactor (P) as well as for that of the laboratory (L), these equation s are applicable.
If Sjo p is not kno wn b ut the vessels are geometrically sim ilar, the ratio of Nusse lt analogies of the
plant and laboratory reactors may be applied. Since the properties of the reaction mixture remain
constan t for the same process at the same tem perature, this ratio can be drastically simplified.
Rearrang ing of the equations and using hoL determined w ith the laboratory reactor, hQp for the
plant reactor is calculated at the same tem perature using equation (5.1):
fD.VcO
4 / 3
h
0P
= V '
v S
v
L
y
V
2 / 3
,
N
L
' V i
p
>
0.14
Vi.
(5.1)
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In the case of geometrically similar reactors and if hydrodynamic conditions remain the same
(Newtonian fluids), scale-up involves only a change of heat transfer area and the results can be
viewed with confidence.
With the procedure presented before it is enough to scale-up a process even if no data is
available for the plant reactor.
5.2.2.- Scaling-up to a non geometrically similar plant reactor. More accurate calculations should
be performed if possible to use the material properties. With this information there is no need to
have geometrical similarity between reactors. The use of Nusselt's relation for the film inside the
reactor can be expressed in the following manner
h
0L = V
4
o
d N a
2
0
Y I / 3
go
J
J
V^
2
c
D
g
0 / 3
,
2 / 3
Na„
(5.2)
The first therm involves the geometry of the reactor and inserts (Rn), the second refers to mixture
properties (Mp) and the third is a relation between the stirrer speed and a reference o ne.
The calculations involve the experimental determination of 6 J O L by means of the Wilson
method, using a low viscosity solvent with a well behaved boiling point and vapour pressure.
9 J O P
is determined following the same procedure used for
0JOL-
The overall heat transfer
coefficient U can be experimentally determined as it is proposed for heat flow calorimeters [ 16]
and described in section 3.7.
1
U
9
10P
R
n
3
Mp^[
Na/Na,
R
+
- ^
A
1 1P
(5.3)
Fo r the develo pm ent of this equation it has been assum ed that 620 = 2/3 , 630 = 1/3, and that
the viscosity number can be neglected. The last therm of this equation is called the apparatus
resistance. Now, for the plant reactor, it is possible to get the 9iop value from the slope of the
Wilson plot, because either Rn and Mp are known (Mp can be calculated from the bench scale
reactor Wilson's plot). Once it is evaluated, any unknown Mp can be calculated if a new plot is
done with the same reactor, with the goal of avoiding any possible lack of mixture properties data.
For accurate data acquisition, the vessel should be insulated from the surroundings. Viscosity
data is necessary at the reaction temperature and at the estimated wall temperature, if there is a
large temperature difference between reactor and jacket temperature.
Th e best results are obtained if the linearisation with the Wilso n plot using a Reyno lds exponent
2/3 is good and heat transfer measurements have been accurately carried out in the plant reactor.
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5.3. DOSING CONTROLLED REACTIONS (SEMI-BATCH).
With the known resistances due to the reaction mixture (h^p) and the apparatus (h^p), the overall
heat transfer coefficient can be calculated. The maximum heating/cooling power can be estimated
with the larger reactor and jacket temperature difference. The heat transfer area can be calculated
using the reaction mixture volume inside the reactor, thus available power (q
a v
) is obtained by
means of.
q
a v
= U S - ( T
m
- T
e
)
( 5 4 )
Heat of reaction and proper reaction temperature are known approximately from laboratory
experiments, by means of the different types of calorimetric analysis. From the available power
plus data on the heat of reaction, a minimu m dosing time for an isothermaly controlled reaction can
be approximated by:
t _
A H
dos q
a v
(5.5)
This applies for an addition of a liquid at the same temperature of the reaction mixture. It is
possible sometimes to add a warmer or a colder fluid depending on the requirements of the
reaction, having a heating or cooling influence according to the needs of the process. The heat
involved in this case should be added to the available po wer as it is described in equa tion (5.6):
q
a v
= U S ( T
m
- T
e
) + q ^ C p
d o s
- (
T
m "
T
d o s
) (5.6)
5.4. SCALE-UP APPLICATION EXAMPLE.
An exam ple of scale-up from a 2 1 laboratory reactor to a 100 1 pilot plant reactor will be done in
this section. Data from a calorimetric study carried out by Bourne, Buerli and Regenass [14] using
a heat flow calorimeter with a Pfaudler stirrer will be used in order to calculate the internal heat
transfer coefficient of a Pfaudler reactor, using the same type of stirrer [7].
The evaluation of
HQ
for the plant reactor has been done in troducing a know n electrical power to
the water inside the reactor and waiting for all temperatures to reach the steady state. Using
equation (3.13 ), U was calculated and the plot show n on Fig. 1 represents the reciprocal of U
against the reciprocal of Na raised to the power of 0.7.
Bourne et al. adjusted eq. (5.7) for the 21 reactor. Calculations of hg at the temperatures of 19
and 25 °C stirring water at 100 rpm are presented in table 5.1.
N u = 0 . 2 7 - R e
0 7
P r
1 / 3
( 5
.
7
)
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1 / U - 0.0018 ♦ 6.074a-4 Na«-0.7 R - 0.98
1/U - 0,0019 < 5 .M3« -4
-
Na* -0 .7 R - 0.99
EI 1/U(25 C)
• 1/U(19 C)
1. 2
NaM) .7
Figure 5 .1 . - 1/U vs. Na~0-7 for the 1001 reactor filled with 80 Kg of water.
Table 5.1.- Values used in eq . (5.5) to calculate hg.
values
Re
P r
k/D
ho
calculated
T=19°C
7273
7.220
5.219
1375
T=25°C
8378
6.154
5.305
1463
Using data from Figure 5.1, rig evaluated for th e 100
1
reactor agitating at 50 , 100 and 150 rpm
at 19°C and 25°C are compared with the ones obtained scaling-up from the 21 reactor to the 1001
one,
by means of equation (5.1). The same exponent for Re used in (5.7) has been used to rise the
relation between stirrer speed for both agitators. The equation used in this case ha s been
5.1.
This
comparison is shown in table 5.2.
Table 5.2.- comparison between scaled-up/evaluated hg values.
RPM
hO
scale-up
(19)
hO evaluated (19)
hO scale-up (25)
hO evaluated (25)
50
1762
1588
1875
1449
100
2797
2580
2976
2354
150
3665
3426
3900
3127
These calculations have been carried out considering for the calorimetric reactor d=0.067 and
D=0.114 , and for the 100 1 reactor d=0.350 and D=0.508, where d is th e stirrer diameter and D is
the reactor diameter.
N O T A T I O N
c
:
parameters
for
correlations.
Cp : Specific heat capacity, J-Kg
l .
K
- l
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121
d,D
f
g
h
H
K
L
m
M p :
N
N
a
Q
q
p
R
Rn
S
T
t
U
U S
V
G r e
a
r
A
e
X
n
p
X
S u b
0
1
a
B
dos
e
g
i
J
: diameters
empirical factor for vortex increase
gravitational acceleration, nvs"2
partial heat transfer coefficient
Molar enthalpy (liquid), J-mol"^ orHeight.m
dimensionless constant or Coefficient of heat losses, W-K"
1
laboratory
mass,Kg
mixture properties
Nu mb er of species, stirrer speed
Stirrer speed s~*
Volumetric flow, m^-s"
Thermal flow, W
power, plant
Rad ius, or resistance
reaction number
Surface, m^
Temperature, K
time,
s
Heat transfer coefficient, W-nT^-K'l
Effective heat transfer coefficient, W-K"l
Volume, rrP
ek symbol s
Constant in a heat transfer correlation,var. dim.
Thermal capacity, J-K"'
difference, variation
Param eter of a heat transfer correlation
Thermal conductivity,
W-m"^-K"'
Dynamic viscosity, kgm~l-s~l
Density, kg-m^
Time constant, s
s c r i p t s
A t the surface, internal side m
At the surface, external side P
Stirrer or ambient R
Bottom r
Dosing T
Therm ovector, heated loop t
glass v
Input w
Species x
Reaction mixture, metal
plant
Reactor
radial
Total
tank
Vortex
Wall
reaction
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L : Liquid, laboratory
Dimensionless groups
Fr
Ne
Nu
Pr
Re
Po
Vi
6.-
: Froude number,
: power number
: Nusselt number,
: Prandtl number,
: Reynolds number,
for stirred tank,
: Power number,
: Viscosity ratio
References .
Axial
N
a
2
-D
a
-g- l
u-D-r
1
t i - C p - r
1
p
m
-Q-D-S-l -Li - l
P m - N a ' D a
2
- ^ "
1
q a - P m ^ - N a "
3
^ -
5
R j u l k ^ a t w a l l
( 1) Rasm ussen , B. (1988) 'Occurrence and impact of unw anted chem ical reactions', J. Loss
Prev. Process Ind., 1, 92.
( 2) Barton, J.A. and Nolan, P.F . (1989) 'Incidents in Chem ical Industry due to Therm al-
Runaway Chemical Reactions', Chemical Reaction Hazards, London Press Centre, London.
( 3) Dubb el (1981) Taschenbuch fur den Maschinenbau, Auflage, Springer.
( 4) Ku man a, J.D., Kothari, S.P. (1982) 'Predict storage-tank heat transfer precisely', Chemical
Engineering, March, 127-132.
(5 ) R.H . Perry and C.H. Chilton (1973) Chemical Engineers Ha ndbo ok, 5th ed., M c Graw-
Hill, New York.
( 6) M cCa be, W .L. and Smith, J.C. (1956) Unit Operations of Chem ical Engineering ,
Mc Graw-Hil l , New York.
(7 ) Pfaudler reactor Type: AE-100
( 8) Private comm unication from Dr. Hernand ez, H. FIRE S Project, J.R.C. Ispra (VA ), Italy.
( 9) Kern, D.Q . (1950) Process Heat Transfer, Mc Graw-Hill, New Yo rk.
(10) Zaldivar, J.M., Hernandez, H. and Barcons, C. (1990) 'Developm ent of a Mathematical
Mo del and Num erical Simulator for a Reaction Calorimeter FISIM , RC1 Version', technical
note n° 1.90.109, J.R.C. Ispra (VA), Italy.
(11) Wilson, E.E. (1915) Trans A.S.M.E. ,37-47.
(12) Ch apm an, F.S. and Holland, F.A. (1965) 'Heat Transfer Correlations for Agitated Liquids
in Process Vessels', Chemical Engineering, 1, 153-158.
(13) Ch apm an, F.S . and Holland, F.A. (1965) 'Heat Transfer Co rrelations in Agitated Vessels',
Chemical Engineering, 2, 175-182.
(14) Bo urne , J.R., Buerli, M. and Rege nass, W. (1981) 'Heat transfer and power measurements
in stirred tanks using heat flow calorimetry', Chemical En gineering Science, 3 6, 347-354.
(15) Bro oks , G. and Su, G.J. (1959) Che m. Eng. Prog .,Oct., 54.
(16) RC 1 Operating Instructions (1986) Mettler Instrumente AG , CH-860 6 Greifensee.
(17) Private comu nication from Zaldivar, J.M., FIRES Project, J.R.C. Ispra (VA ), Italy.
(18) Uh l, V.W . and Gray, J.B. (1966) M ixing: Theory and Practice, vol 1&2 , Academ ic Press,
N e w Y o r k .
(19) F.A. Holland (1973 ) Fluid flow for Chem ical Enginee rs, Edw ard Arnold, L on do n.
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123
(20) Hoffman W . (1989) 'Qdos Qflow Qaccu and all these things', RC 1 3rd International User's
forum.
(21) Zaldivar, J.M., Hernandez, H. Barcons, C , Nom en, R. and Semp ere, J. (1990), 'Heat
Transport for Immiscible Liquids in Agitated Vessels', Proceedings of the 5th Mediterranean
Congres on Chemical Engineering.Barcelona, 1,176-177.
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MODE LLIN G AND SIMULATION FOR SAFETY ANAL YSIS OF B ATCH
REACT ORS AND STORAGE TANKS
H.J. HERNANDEZ
Joint Research Centre,
Institute for Safety Technology
Process Engineering Division,
21020 Ispra (Va), Italy
ABSTRACT. The application of mathematical modelling and numerical
simulation to hazard analysis is discussed. The principles of
mathematical modelling are described, with particular reference to
batch reactors and storage vessels where runaway reactions can take
place.
Two representative cases are presented in order to show the
applicability and limits of numerical simulation in assessing the
safety of a batch process by calculating critical operating conditions.
1 . I n t r o d u c t i o n
Process analysis can be based on experimental investigations or
mathematical modelling, whereby the behaviour of a system can be
simulated either experimentally or by solving a mathematical model.
In this manner, the design and optimization of industrial processes
can be supported by appropriated techniques where the objective is to
reproduce the desired behaviour of the system under "normal" operating
conditions.
The safety assessement of processes can also be based on simulation
techniques, but this requires additional information about the
"off-normal" functioning of the system. However, in this case the
experimental work must employ specialised equipment and/or reduced
scales,
because the consequences of the associated hazards. Therefore,
the mathematical modelling becomes an important tool as guide and
complement of the experimental research and to carry out the scale-up
of the process, respecting the safety constraints.
Nevertheless, whenever a mathematical model is used to asses the
safety of a process, special attention must be paid because of the many
assumptions usually introduced during the formulation of the model. In
fact,
safety calculations are frequently made by applying conservative
assumptions that do not always guarantee a safety improvement, because
of complex interdependencies between the process variables.
The objective of this work is to describe the principles of
mathematical modelling based on a Chemical Reaction Engineering
125
A.
Bemtizi and J. M. Zaldivar (eds.). Safely of Chemical Batch Reactors a nd Storage Tanks, 125-145.
© 1991
ECSC.
EEC,
EAEC,
Brussels a nd Luxembourg. Printed in the Netherlands.
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126
a p p r o a c h , a n d t o f i n d o u t t h e a p p l i c a b i l i t y a n d l i m i t s of t h i s
t e c h n i q u e t o t h e h a z a r d a n a l y s i s o f b a t c h p r o c e s s e s . F i r s t l y , a
g e n e r a l mo d e l i s p r e s e n t e d i n o r d e r t o d e m o n s t r a t e t h e c om p l e x
i n t e r a c t i o n i n v o l v e d , an d t h e l a r g e q u a n t i t y of d a t a t h a t i s r e q u i r e d .
S e c o n d l y ,
t h e
f o r m u l a t i o n
a n d
a p p l i c a t i o n
o f
s p e c i f i c
mod e l s
f o r
a
b a t c h r e a c t o r a nd a s t o r a g e v e s s e l i n wh i c h r u n away r e a c t i o n s c an t a k e
p l a c e a r e d e s c r i b e d .
2 . M a t h e m a t i c a l m o d e l l i n g
2
.
1
GENERAL MODEL
Consider a system consisting of a mixture of (Nc) chemical species
confined in a volume (Vm) of fixed coordinates.
The state of the system, represented by the temperature(Tm), the
pressure(p), and the concentration of different species
(Cj),
changes in
time and space according to the chemical reactions taking place, and to
the transfer of
mass,
energy and momentum. These phenomena are
interdependant, and so must be considered simultaneously. However, for
the systems studied here, the transfer of momentum is not strongly
coupled, and may be determined separately (e.g. by means of
dimensional analysis).
Let consider first, the characteristics of these phenomena, that
will be introduced into the fundamental equations.
2 .1.1. Chemical reaction.
A chemical reaction is characterised by the
kinetic function that expresses the rate of matter transformation,
which depends on the state of the system (see complete description of
symbols in section
4
:
r. = r. T
m
,C.,p (1)
The knowledge of the rate of reactions and the stoichiometric
coefficients Vj:, allows the calculation of the net rate of production of
each
species[1]:
Nr
/
V . r.
X ^ *■
1
Rj = ; , V
H
r
(
; j=l,...,N
c
(2)
i = l
Where Nr is the number of independant chemical reactions.
2.1.2.
Mass transfer.
The mass transfer is mainly due to velocity and
concentration gradients.
For each species j, the molar flow can be defined as:
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127
N. = C. v + J. ; j = l,
. .
.,N
C
(3)
Where the two terms represent respectively the molar flow of
species j by convection and conduction.
In the case where the difussional terras due to temperature and
p r e s s u r e radients are negligeable, and where the total concentration
is constant, the conduction term may be expressed by:
i i J : 3 - 1 / • •
•
/N
c
(4)
Where Dj is the difussivity coefficient of j within the mixture
2.1.3. Energy transfer. The relevant impulsive forces leading to the
energy transfer are the gradients of velocity, temperature and
pressure. A concise form of the equation for the energy flow within
this system is [3]:
e = p
m
(U + l/2v
2
)v + N
w
+ n • v (5)
Where,
the three terms represent respectively the internal and
kinetic energy flow by convection, the thermal energy flow and the work
done by the system.
The mathematical representation of the state variables of the
system is based on the fundamental principles of conservation, which
can be expressed as mass and energy balances. These balances can be
written in the following form:
Mass balance for each species j
3c.
- ^ = R. - V • N. ; j = l, ..,N
C
(6)
Energy Balance
§ = -
v
. V U - - U V . N
w
+ p V • v]
(7)
Equations 6 and 7 are strongly coupled, and their solution needs the
following information:
state equations for
U=U(p,Tm,Cj),
p=p
(p
m
, T
m
, Cj)
and
ri=ri( T
m
,Cj,p) ,
expressions for the mass and energy flows as functions of
gradients and transport coefficients
• expressions to take into account the variation of all parameters
with temperature, pressure and composition.
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128
2.2.
PARTICULAR MODELS
2.2.1.Storage Vessel.
Consider a vessel of symetric geometry specified
by CT, (where
<T=0,
1 or 2 for a slab, cylinder, or sphere), containing
an isotropic medium where physico-chemical processes may take place.
The characteristics of such a system permit to assume one-dimensional
transfer of mass and energy.
The mass balance equation is obtained directly from equation 6,
introducing the characteristics of this system: no velocity gradients
and mass flow by diffusion expressed by:
V • N.
a
2
c
3x
2
3c.
£
\_
x
3x
(8)
Where Dj= constant
Then equation 6 becomes:
3c.
:
3t
3
2
c.
3c,
l
+ - ^
3x
2 x
3x.
;j=l,...,N
r
(9)
With the boundary condition at the center of the vessel, x=0 :
= o
; j = l, . . . ,N
C
(10)
The temperature time-profile is obtained by modifying the energy
equation 7, as follows:
• cancelling the velocity terms:
v»Vu, and pV»v/p
m
,
• replacing the internal energy by the enthalpy function:
3u
_ 3H
3t
3t
V-
dp
dt
(11)
and neglecting the term Vdp/dt, which is small compared with the
enthalpy term,
• introducing the enthalpy change of the mixture and substituting the
concentration variation by the mass equation 9,
• introducing the Fourier law for heat conduction,
N.,
A .
m
V
T
(12)
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and the definition of enthalpy change due to reaction:
A H
C
. = / V . ,H . ; j = l , . . . , N
r
j = i
( 1 3 )
129
The t i m e - p r o f i l e of t e m p e r a t u r e r e a d s :
3 T „
dt Cp„
3x
2 x
3x_
r
i = l
( 1 4 )
With the boundary conditions at the center of the vessel, x=0 :
3x
0
(15)
and, at the wall of the vessel, x=Xo,
5T
m
3 T
P
_ u
K
~d^
"
x
?~d^ X
p
( T e
"
T
^
(16)
2 . 2 . 2 .
S t i r r e d Batch Reac tor.
In a typical batch reactor, the
diffusional phenomena are negligeable, due to the elimination of
composition gradients by the stirring.
The integration of the continuity equation 6 over the reactor
volume Vm, including the mass input from the surroundings, gives the
time-profile of composition for each species j:
dC,
"dt
3
R.
+
^
3
V „
(F,
F
c
) - C
dV
m
i
dt
;j=l,...,N
C
(17)
The temperature profile is obtained, by simplifying the energy
balance (eq. 7 ) , as in the case of the storage vessel, adding the terms
corresponding to the exchange of mass and heat with the surroundings:
dt
r
m
+r
/
c
(T - T ) - V
j = l
\
r.AH.
+ q
(18)
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130
3 . Application cases
3.1. SYNTHESIS OF ETHYL GLYCIDATE
The objective of this study is the optimization of an existing process,
taking into account the potential hazard of thermal explosion. The
process is described in detail in the reference [4], where emphasis was
placed on obtaining the thermo-kinetic data required for the solution
of the mathematical models.
3.1 .1 . General description and thermo-kinetic data.
The ethyl glycidate
is obtained by epoxydation of the ethyl acrylate by the
peroxycarboximidic acid, which is prepared "in situ" by the action of
hydrogen peroxide on the acetonitrile in an alkaline medium. The raw
materials and products are:
raw materials
H2C=CH-COOC2H5
CH
3
-C H
2
OH
CH3CN ========
H2O2 CO3K2
A nd e t h a n o l a s s o l v e n t
p r o d u c t s
CH2-CH-COOC2H5
CH3-C0-NH2
o
2
The reaction scheme is the following:
1) CH3 CN +
H
2
02
>
2) CH
3
-COOH=NH + H
2
02
3) CH
3
-COOH=NH + H
2
C=CH-COOC
2
H
5
>
4) CH
3
-COOH=NH >
5) H
2
C = C H - C O O C
2
H
5
)
CH
3
-COOH=NH
CH3-CO-NH2 + H
2
0 + 0
2
CH
2
-CH-COOC
2
H
5
+ CH3-CO-NH2
decomposition product
decomposition product
The main problems of this process are the high exothermicity and
instability of the peroxycarboximidic acid, which decomposes (reaction
4 ) , and reacts with the hydrogen peroxide at low temperatures (side
reaction 2) . The objective is to determine the optimal operating
conditions, (temperature and initial composition), that minimize the
reaction 2 and 4 and the decomposition of ethyl acrylate (reaction 5 ) .
The thermo-kinetic parameters were obtained by "thermal flux"
calorimetry[4]
.
These results are presented in table 3.1.
This process is implemented in a standard 500 1 glass lined reactor
in semi-batch operation mode. The main characteristics of such reactor
are described in table 3.2.
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131
TABLE 3.1. Thermo-kinetic parameters. Ethyl glycidate synthesis
N ° r e a c t .
1
2
3
4
5
A H i ( k J r a o l
- 5 4 , 4 3
- 2 5 5 , 3 9
9 , 6 3
- 1 0 2 , 9 6
- 6 7 , 8 3
-1 )
A i
1 , 90 - 108
6 , 2 6 - 1 0
2
°
1 , 21 - 1014
6 , 86 -1020
3 , 0 6 - 1 0 6
E i ( k J i n o l
- 1
)
4 5 , 0 2
1 1 7 , 6 5
8 3 , 3 2
1 2 4 , 3 5
1 2 2 , 6 7
f i ( c o n e . f u n c t i o n )
f i = c
A
- c
B
f
2
=
C
B
- C R
f 3
=
C
C
- C R
f
4
= c
R
0 / 5 5
f 5 = C
C
TABLE 3.2. Equipment data. Ethyl glycidate synthesis
Glass lined reactor
dimensions: hight, H R = 0,8 m
ceramics film: thick., Ei = 0 002 m
steel
wall:
thick., E2 = 0,013 m
heat capacity, T R = 51,7 kj K~l
Heat exchanger
jacket diameter =
0 027
m
diameter, D R = 1,0 m
conduct., X \
=
1.2 W m-lR-l
conduct.,
X.2 =
6.5 W m-iK
-1
Cp
c
Pc
^c
Thermo-vector:,
heat capacity,
density,
viscosity,
thermal conductivity,
X
c
temperature range, Tc
flow, Q
c
T e m p e r a t u r e c o n t r o l l e r
P . I . D . c o n s t a n t s : p r o p . = 7 , i n t . = 12 0 s ,
J k g
k g m
kg irf
■IK-
'S
-1
I s - 1
W m
_ 1
K~
K
m
3
s
1
-1
Water
4 , 1 9
1 0
3
1 . 1 0
3
1 1 0
- 3
0 , 6
Brine.
2 , 7 8 1 0
3
1 , 2 5 1 0
3
1 1
1 0
- 3
0 , 5
T m i n = 2 8 3 Tm i n = 2 5£
2 , 0 8 1 0 ~
3
d i f f . = 60 s
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132
3.1.2. Typical operating procedure.
The normal conditions for this
process are indicated in the following recipies:
• Charge the the reactor with a mixture (225 1) of following
composition:
- 1 mol of Ethyl acrylate per 1.72 mol of acetonitrile
- 2.5 vol. of ethanol per 1 vol. of ethyl acrylate
• Put stirring at 1.67 s~l, and maintain the mixture at a
temperature of 303 K
• Introduce, over 3.5 h, 70 1 of a mixture with composition:
-
1.95 mol of
hydrogen peroxide
(30
%wt)
per mol of
ethyl
acrylate introduced.
3.1.3. Simulation.
This system was simulated, by solving numerically
equations 17 and 18 , which have been modified to include the algorithms
of
a
temperature controller
and the
influence
of
operating conditions
on the heat exhanged [4] .
The results of the simulation, with the operating conditions
described above, are shown in Fig. 3.1, which contains the time-profile
of the relevant variables:
3.1. a/ temperature of the reaction mixture and of the external
cooling,
3.1.b/ thermal fluxes generated and removed,
3.1.c/ concentration of reactants and
3.1.d/ concentration of products.
Thereafter, the critical conditions have been found by means of
succesive simulations with different temperature set-points
and
different feeding rates of the hydrogen peroxide. Selected results of
these simulations are presented
in
the figures
3.2 to 3.6.
3.1.4. Concluding remarks.
Under normal operating conditions, this
process is carried out at a low temperature (< 303
K) ,
generating a
moderate thermal flow that may be removed with a low cooling capacity.
However, the process is very sensitive to slight modifications of the
operating conditions, which easily activate the side reactions, leading
to a thermal excursion. Additionaly, the release of oxygen can cause an
overpressurisation of the system.
In general, safety improvement
of
this process result
in a
reduction in yield. A compromise between the safety and performance
criteria could be achived by increasing the proportion of hydrogen
peroxide, both with a slower rate of introduction.
Finally, a higher cooler capacity (e.g. with sodium chloride
solution), is recommended, which allows a larger margin of safety.
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Taav wat ur B ( C )
3 . 1 .
a
Thermal f low fcw)
6 4 . 0 -
SHNEHET REMOVED
Concentration (nol/lt)
5.00.
4.0i
0 25 50 75 100 125 150 175 200 225 250
— - — - - Tim e (rnn)
CH3CN H2 02 ACflYLATE ACID E-fl
Concent r a t i on ( r ao l / l t )
2.00r
1 . 2 0 -
0 . 00
AC-AMIOE SLYCIDTE FW C*
FIGURE 3.1. Simulation results of ethyl glycidate synthesis with "normal operating conditions".
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Tannarature ( C) 3.2.a
Thermal flow (kVO
32.0-
lB.O-\
MIXTURE THEBMOVE
-25. V-
5.00-
Concentration (ml/It)
Concantratlon (rnol/lt)
2.00 i
1.00-
0 29 SO
C H 3 C N
-
H 202
75 100
"*>» 1 i i JBBU.VSI
125 190 179 200 229 290
Tlaa tan)
1 . 6 0 -
1 . 2 0 -
0 . 4 0 -
0 29 90 79 100 129
AC^MUDE 6LYCUJTE BM C« "
175 200 229 250
T I M tun)
ACHYLATE ACDJE-H
FIGURE 3.2. Simulation results of ethyl glycidate synthesis with T
set
=303 K, Feed rate H
2
0
2
=35 1/hr
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B4.0
4S.0
32.0
16.0
0.0
r«apsr*tura
\
A
Co
—j 1 1~
9
1 i
3.1
,
/
. m u m
29 SO 75 100 IBS ISO 173 200 223
— — TlaB 0m)
MIXTUFE THEHHOVE
S.O
Tharml flow (kH)
1 . 0 -
-a.o-
—I u-
5.0"
*-
0 23 50 79 lOH I B 150 173 200
SHOVED
Tlao (an)
9.00]
Concentration tool/It)
3.3 .C
O.Ol
2.001
Concsntnatlon taol/ltl
1.20-
0.80-
0.40-
190
178 BOO 223 250
Tlae (on)
0 25 80 73 100 12S ISO 170 200 228 250 0 25 90 73 100 125
CHSCS
-
" H 20 2~ ~ ACHYLATE AC IBM "* "" ACHWIOE 6LYCHJTE 5* '~
C* '
FIGURE 3 . 3 . S i m u l a t i o n r e s u l t s o f e t h y l g l y c i d a t e s y n t h e s i s w i t h T
s e t
=2 98 K, Feed ra te H
2
C>2=20 1/hr
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Tmparatura (*C)
3 . A.»
64.0-
16.0
\
0.0^
0 25 SO 73 100 125 150 173 BOO 225 250
. - - - - - T i n * (on)
MIXTURE TWHMOVE
5.0,
Ttwoml flow IkW
3 . 4 . 6
5 . 0&
Con c«n t r«t lon ( ao l / l t )
3 . 4 . c
3 . 0 0 -
2.00 i
1 . 0 0 -
JSaMLyoJ
28 50 75 100 1 2 3 1 5 0 173 2 0 0 2 2 5 2 5 0
Tlaa (on)
C o n c e n t r a t i o n t a o l / l t )
2 . 00r
3 . 4 . d
1 . 2 0 -
0 . 4 O -
O.OO
25 50 73 100 123 150 175 200 225 2fi
AC AMWe BLYKOTE SS CK ™ ""
H3CN H 20 2 ACHYUkTE ACIOE-R
FIGURE 3.4. Simulation results of ethyl glycidate synthesis with T
set
=298 K, Feed rate H
2
0
2
=35 1/hr
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Taaporatura
( CI
SO.Of-
6 4 . 0 -
S . S . a
TTisml flow tkX
- 7 . 0 -
-11 .0 -
-1S.0
1
0 24 48 72
G E N E R E T R E M O V E D
Concentration
(asl/lt)
Concentration (Ml/It)
a.OOr
i . a o -
0.00'
0.40-
0.00*-
168
192
216 240
T i m
(an)
0
24 48 72 96 120 144 1M 192 216 240 0 24 48 72 96 120 144
EHSCN" SaniT" ACHYLATE A C ID M " " AC^AMIDE 6LYCH>TE BM ci
FIGURE 3.5. Simulation results of ethyl glycid ate synthe sis with T
s et
=293 K, Feed rate H
2
O
2
=20 1/hr
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Tsaparaturs C)
Tharm l flaw (kW
3.B.0
-83.0
1
GENBST REMOVED
Concentration (Hol/lt)
Concentration tol/lt)
S.B.d
CH3CN H202
ACHYLATE ACIDE-fl
1.60-
l.ao-
0.80-
o.ooi
AC-AMIDE BLYCIDTE
R*
FIGURE 3.6. Simulation results
of
ethyl glycidate synthesis with T
set
=293
K,
Feed rate H
2
0
2
=3 5
1/hr
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139
3.2. STORAGE OF CYCLOPENTADIENE
The cyclopentadiene, in liquid state, is an intermediate reagent in
many organic syntheses. However, this product is very unstable even at
low temperatures, when it dimerizes exothermically to dicylopentadiene,
which is the stable form until the boiling point, 170°C (see ref. [5]) .
The objective of this study is to determine whether is worth to
store the cyclopentadiene, by predicting its stability under storage
conditions.
3.2.1. G eneral description and thermo-kinetic data.
The dimerization
reaction of cyclopentadiene is:
2C
5
H
6
====> C10H12 + AH
(2) cyclopentadiene dicyclopentadiene
The thermo-kinetic parameters were determined by calorimetry [4]
and compare favourably with those reported in reference [5]:
• Heat of reaction, AH: -3,86 9-10
4
J-mol"
1
• Heat capacities, Cp: cyclopentadiene dicyclopentadiene
1,71 1,64
J-g-l-K-l
• Rate of reaction, r:
r = A-exp(-E/RT)-C
s
With: A =
1,34-106
s
-l ,
E = 6,47-10^
J-mol-l
,
T he t h e r m a l c o n d u c t i v i t y was c a l c u l a t e d u s i n g t h e f o l l o w i n g
c o r r e l a t i o n fo un d i n r e f e r e n c e [ 6 ] :
X =
3 , 5 9 - 1 0 - 3 - C p - (p 4 /3 ) / ( M l/3 )
W h i c h g i v e s :
C y c l o p e n t a d i e n e , X = 0 , 1 1 3 W - m - l -K
- 1
D i c y c l o p e n t a d i e n e , X = 0 ,1 1 0
T h e d i f f u s i v i t y c o e f f i c i e n t w as c a l c u l a t e d a s s u m i n g , a
s e l f - d i f f u s i o n p hen om en on u n d e r i d e a l c o n d i t i o n s [ 6] :
D
=
=
n
KT
v
v
*y
O b t a i n i n g , D
s
= 4 , 3 3 - 1 0 "
9
m Z - s "
1
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140
3.2.2. Calculation of storage conditions.
This
case
was
simulated,
by
solving numerically equations 9 and 14. The critical conditions are
determined
by
means
of
succesive
simulations,
fixing
the
characteristics of the vessel and following the behaviour of the
mixture
for
different
storage
temperatures.
The following case was used as a reference:
steel spherical vessel: storage conditions:
radius,
X() = 0,10 m concentration C
s
=12157 mol-lt
-1
surface,
So = 0,27 m
2
coefficient of heat exchange:
thermal
capacity,
r
R
=l-103
J-K-I
U
=
35
W-m-2-K-l
The
results
of
the
first
simulation
run
with
a
storage
temperature,
T
c
=283
K,
are
shown
in
the
figures
3.2.1
and
3.2.2,
which
show how the temperature and concentration profiles, change with time.
It can be seen that the reaction runs away after nine hours.
Succesives
simulation
runs
with
lower
storage
temperatures
lead
to
the
critical
values:
T
c r
=
279
K,
for
Xo
=
0,10
m
The t e m p e r a t u r e p r o f i l e s f o r t h e s e c o n d i t i o n s a r e shown i n
f i g u r e s 3 . 2 . 3 and 3 . 2 . 4 .
I t i s i n t e r e s t i n g t o c omp a r e t h e s i m u l a t i o n r e s u l t s w i t h t h e
a n a l y t i c a l
c r i t e r i o n
o f
F r a n k - K a m e n e s t k i i [ 7 ] w h i c h
e x p r e s s e s
t h e
c r i t i c a l s i z e of a v e s s e l a s :
8 • • RT^
r
cr m cr
cr
AH ■ E ■ A ■ exp(-E/RT
cr
)
This
criterion
yields
the
following
critical
storage
conditions:
T
C
r
=
275.8
K,
for
Xo
=
0,10
m
Finally,
the
previous
calculations
were
repeted
for
vessels
of
different sizes. The critical values found by simulation and by the
Frank-Kamenestkii
equation
are
shown
in
the
Figure
3.2.5
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141
350
Temperature (K)
TIME (hr)
3 3 4 . 0 -
31B.0
3 0 2 . 0 -
2 B 6 . 0
2 7 0 . 0
0 . 5 0 .5 R
R ad iu s (R 0 .10 m)
C o n c e n t r a t i o n ( m o l / l t )
3 . 7 . 0
TIME (hr)
15.00
12.80
1 0 . 6 0 -
B.40
6 . 2 0 -
4 . 0 0
0 . 5
0 . 5
FIGURE 3 . 7 . S i m u l a t i o n r e s u l t s o f c y c l o p e n t a d i e n e s t o r a g e
T
storage
=283
K
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142
320.0
310.0
300.0-
290.0-
280.0
270.0
Temperature (K)
3.8.a
TIME (hr)
0.92
2.93
4.90
6.85
8.83
10.82
12.74
14.47
16.29
18.28
20.27
22.21
24.17
26.12
28.02
30.01
32.00
33.93
0.5
0.5 R
Radius (R 0.10 m)
320.0
310.0
300.0
290.0-
2B0.0
270.0
Temperature (K)
3 . a . b
TIME (hr)
33.93
35.95
3 7 . 7 1
39.65
4 1 . 5 8
43.5B
45.5B
47.55
49.52
5 1 . 4 1
53.38
55.32
57.34
59.28
6 1 . 2 3
63.02
0 . 5
0 . 5 R
Radius (R 0 .1 0 m)
FIGURE 3 . 8 . S i m u l a t i on r e s u l t s o f c y c l o p e n t a d i e n e s t o r a g e
T
s t o r a g e
=279
K
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143
FIGURE 3 . 9 . C r i t i c a l c o n d i t i o n s o f s t o r a g e o f c y c l o p e n t a d i e n e .
C o m p a r i s o n o f s i m u l a t e d a n d F r a n k - K a m e n e s t k i i r e s u l t s .
300.0
X )' 10'
Critical temperature
(K)
3.2.3
Concluding remarks.
Under adiabatic conditions, dimerization of
cyclopentadiene will produce a temperature rise of approximatively 350
K. This means that secondary reactions that become significant at
temperature greater than 550 K, may be activated by the main reaction,
leading to a thermal explosion.
The above discussion confirm the high potentail hazard of
storing important amounts of cyclopentadiene, which requires a
relatively low storage temperature.
As far as possible, the processes where the cyclopentadiene is
an intermediate, should be integrated, in order to avoid the storage of
this compound.
Concerning the difference between the two calculation methods
presented here, it is due to the fact that the Frank-Kamenestkii model
does not take into account the influence of extent of the reaction
neither a resistance of heat exchange with the sourroundings, while,
both were included in the numerical simulation.
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144
4
Conclusion
The m a t h e m a t i c a l m o d e l l i n g for hazard p r o c e s s analysis appears
particularly attractive and beneficial because the difficulty of carry
out appropiate experimental investigations under dangereous conditions.
However, the formulation of a model for safety assessement should
be oriented to the representation of the significant features of the
process, with an awareness of the implicit assumptions from a safety
point of view.
The main limitation in applying the t h e o r e t i c a l approach
presented here is the lack of knowledge of the chemical process. A
reliable model would require a large quantity of data, which are rarely
available.
In
practice,
accurate
data
are
only
found
for
a
limited
range of process variables and do not provide enough information for
the
safety
study.
In
the
future,
the
problem
of
lack
of
data
may
be
reduced
by
the
application of identification and estimation techniques, which provide,
on-line or off-line, determination of parameters of the model.
5 N o t a t i o n
A
C
Cp
Cp
L
D
E
e
F
H
J
K
N
Nw
N
Na
n
P
q
R
r
S
T
U
U
V
v
v
X
Pre-exponential factor
Molar concentration,
Specific heat capacity,
Molar heat capacity of a chemical species,
Diffusivity,
Activation energy,
Energy flux,
Molar flow,
Molar enthaply
(liquid),
Molar flux by conduction,
Chemical equilibrium constant,
Molar flux by convection and conduction,
Heat flux,
Number
Stirrer speed
Molar
Hold-up,
Pressure
Thermal flow,
Rate of chemical production,
or Gas constant,
Rate of reaction,
Surface,
Temperature,
Internal energy,
Heat transfer coefficient,
Volume,
Average
velocity,
Local velocity,
Radius,
depends on kinetics
mol-m
3
J Kg l K l
J mol i K l
m
2
■s-1
J -mol
-1
W-m-2
mol• s
_ 1
J mol
m o l - m
-
2 • s
_ 1
depends on k
mol-m
-
2• s
1
W-m-2
m o l
K g - m - 1
W
m o l
m
J - r n o l
m o l
m2
K
J
W-m
m
3
m -
s
m -
s
m
m-
-2 .
-1
■ l
3
1
3
K
2
S
K
s
1
1
1
1
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G r e e k s y m b o l s
145
r
n
v
n
P
Thermal capacity, J-K~l
Thermal conductivit y, W-m
_1
-K~
Dy namic vi scos ity, Kg-rrrl-s
Stoichiometric coefficient, reactant(-), product(+)
Partial order of reaction
Mo me nt um flux, Kg-irrl-s
Density, Kg-m
3
Vessel geometry, 0=slab, l=cylinder, 2=sphere
S u b s c r i p t s
c
e
i
m
R
S
heat transfer fluid
External
Reaction
Reaction media
Reactor
Output
E
h
J
P
s
X
Input
Heating
Species
Wall
Set-point
Radial
6.References
[1] LEVENSPIEL 0. (1972), Chemical Reaction Engineering, John Wiley,
New York.
[2] TREYBAL
R.E.
(1955),
Mass transfer operations,
Mc
G raw-Hill,
USA.
[3] BIRD R.B., STEWART N.E. and LIG HTFOOT E.N. (196 0), Ttransport
Phenomena, John Wiley, New York.
[4] HERNANDEZ H. (1987), "Contribution a la Simulation de Systèmes
Chimiques orientee vers
l'Analyse
de Securite", Ph.D. thesis,
U.T.C., Compiegne.
[5] WILSON P.J. and WELLS J.H. (1944), "The chemistry and utilisation
of cyclopentadiene", Chemical Review, N o . 3 4 , pi, Pennsylvania.
[6] REID R.C., PRAUSNITZ J.M. and SHERWOOD T.K. (1958), The Properties
of Gases and Liquids, Mc G raw-Hill, New York.
[7] GRAY P. and LEE P.R. (1967), "Thermal Explosion Theory", Oxidation
and Combustion Review, vol. 2, Elsevier, New York.
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RISK ASSESSMENT METHODOLOGIES
N.A.LABATH
Consultants in Advanced Technologies
Via L. Maggiore 41
21038 Arolo di Leggiuno (VA)
Italy
1. Introduction
Qualitative and Qualitative Risk Assessment have been applied
to new and existing installations to ensure that the hazards
associated with the plants are acceptable to employees and
the public. Quantitative Risk Assessment expresses the
magnitude of a hazard on an absolute numerical scale thereby
providing plant designers and management with the necessary
data to take measures aimed at reducing the risk to
acceptable levels. It is frequently used to compare the
effects of alternative safety measures.
The assessment methods can be broken down into three areas,
as follows :
- Methods used to identify sources of accidents and the
ways in which they could occur.
- Methods used to estimate the likelihood of occurrence
of accidents.
- Methods used to estimate the potential consequences of
accidents.
Only the first two areas will be covered in the following
sections.
Accidents can be prevented by anticipating how they may
occur.
Having identified how accidents could occur, several
other questions may then have to be considered. What is the
likelihood of the accident occurring ? What would be the
consequences of such an accident ? What measures could be
taken to eliminate the particular hazard or if this is not
possible to reduce the likelihood or consequences of the
accident ? Would implementation of such measures be
justified ? The identification stage remains the most
important step in safety assessment however, if the
existence of a hazard is not identified, no action can even
be contemplated. This essential stage in the assessment
prodedure involves rigorous consideration of all situations
in which the potential for harm may exist in order to
identify those which are hazardous, followed by a
disciplined analysis of the combinations or sequences of
147
A. Benuzzi
and
J. M.
Zaldivar
(eds.).
Safety of
Chemical Batch Reactors
a nd
Storage
Tanks, 147-159.
© 1991 ECSC, EEC, EAEC, Brussels a nd Luxembourg. Printed in the Netherlands.
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events which could transform this potential into an
accident.
This stage in the assessment of an installation is called
hazard identification. It is essentially a qualitative
process,
although aspects may be revealed which require
calculation, for example, analysis of transients to
establish the boundaries of safe operation.
2. Hazard Identification Techniques
Many hazard identification methodologies are available to be
applied at differrent steps of the project. Most of them are
listed in Table 1.
Table 1 : Hazard Identification Methodologies
Process/System Checklists
Safety review
Relative ranking : DOW and Mond Hazard Index
Preliminary Hazard Analysis
What-if analysis
Failure Mode and Effect Analysis
Hazard and Operability Analysis
Fault Tree Analysis
Human Error Analysis
The first four methodologies are normally applied in the
initial steps of an engineering project.
The others are preferently used when most design features
and details are defined.
This paper deals mainly with the last procedures and their
possible developments or extensions.
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3. Hazard
a n d
O p e r a b i l i t y A n a l y s i s
3.1 GENERAL DESCRIPTION
The method of hazard and operability studies (HAZOP) is now
well established as a means of identifying at the detailed
design stage potential hazards and operability problems.
HAZOP is a technique for systematically considering
deviations from the design intent, by the application of
guide words, to an operation or a process flowsheet. It can
be carried out at an early stage on a conceptual flowsheet,
in which case only safety aspects are usually noted, or at
the detailed design stage line by line on a Piping and
Instrumentation Diagram (P & I) . In this case all deviations
which are undesirable, either for safety or for operability
are noted.
The technique can be applied to an existing plant but in
this case the scope for action will be limited whereas
during plant design options should, as far as possible, be
kept open until the process has been studied in this
rigorous manner. One particular situation where the
technique is found to be particularly useful, in the case of
existing plant, is where modifications are under
consideration. If a HAZOP study has been carried out on the
original design and adequate records are kept then only a
limited amount of work would be required to consider the
implications of the modification.
The study is based on a very generalised procedure capable
of application in a wide range of circumstances and which
generates a number of searching questions. These questions,
of the "What happens if?" type, are asked in an ordered but
creative manner which ensures a thorough and systematic
coverage either by an individual working alone or by a
multi-disciplinary team.
The method adopted is to search the proposed design,
systematically looking for every notional deviation from the
norm and to decide whether these deviations are trivial
ones,
operational problems or constitute a potential hazard.
It is usually applied to flow diagrams whether these are
detailed P & I diagrams, block charts for unit operations or
flow charts describing an operational activity. This search
is done by the application of a carefully chosen list of
guide words or standard phrases to the process parameters
for each integral part of the design or system. Such a list
of guide words should promote unrestricted, free ranging,
logical thought to detect virtually all conceivable process
abnormalities. The method can be applied to any type of
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plant or operation, irrespective of the degree of
complexity, provided that only a suitable list of guide
words is selected. There are several variations of these
lists of guide words. Some are intended for specific
situations and the guide words will reflect
this.
Other
lists are designed to be far more wide ranging in
application.
Table 2 : A comprehensive list of guide words
Process variables
Main guide words
FLOW
PRESSURE
TEMPERATURE
LEVEL
PHASE CHANGE
COMPOSITION
NO SUPPLY
DISCONTINUUS
OPERATION
LEAKS
EXTERNAL EVENTS
Low / High / No / Reverse
Low / High / Vacuum
Low / High / Below 0 °C
Low / High
Vapour / Liquid / Solid
Contaminants / Composition
Change
Energy / Compressed Air /
Nitrogen / Cooling water /
Vacuum / Steam
Start-up / Shut-down /
Emergency Shut-down /
Maintenance Activities
Flanges / Small Pipes /
Pump Gaskets
Tube Rupture / Vessel
Rupture
Vehicle Collision / High
Winds / Flooding / Fire
Earthquakes / Aircraft
Crash
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A rather comprehensive list of guide words and their
possible "states" is presented in Table 2 for most important
process variables and other events of interest.
Each guide word is applied to the "integral part". How each
deviation might be caused and what the possible consequences
of it may be, are then considered. The kind of questions
that ought to be asked at this stage of the procedures are :
- Could there be no flow ?
- What are the consequences of no flow ?
- Are the consequences hazardous or do they prevent
efficient operation ?
- If so, how could it arise ?
- How will the operator know that there is no flow ?
- If so, can we prevent no flow (or protect against
the consequences) by changing the design or method of
operation ?
- If so, does the size of the hazard or problem
justify the extra expense ?
Having completely examined one part of the design and
recorded any potential hazards associated with it, or
remitted for detailed separate consideration, the study
progresses to focus attention on the next part of the
design.
The examination is repeated in the same fashion
until the whole section of the design, etc. under
consideration has been reviewed.
3.2 FAULT PROPAGATION IN HAZOP STUDIES
The objective in HAZOP studies is to identify deviations
from design intent which may give rise to safety or
operability problems. This necessarily involves some
exploration of the possible causes and consequences of the
deviations.
It is not, however, the purpose of the study to
make a detailed analysis of these causes and consequences.
If this is considered necessary, it is carried out as a
separate exercise using such techniques as fault trees.
Nevertheless, since a HAZOP study does involve in some
degree the detection of fault paths, the method may be
regarded as one of a member of techniques developed in
recent years for the exploration of fault propagation in
process plants. The fault tree aspects of HAZOP studies are
illustrated by work described by Lihou
(1) ,
who has
developed a method of encoding the written results of a
hazop studiy to produce a set of fault trees for the plant.
The completeness of the fault trees so produced necessarily
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depends on the completeness of the fault propagation
information produced by the HAZOP study.
In normal HAZOP studies the exploration of fault
propagation by the study team is unsystematic and
fragmentary. This is to be expected, since the systematic
determination of the fault propagation pathways is not the
object of the HAZOP study. These considerations indicate
that there are likely to be difficulties in constructing
fault trees from HAZOP study records.
3.3 OTHER FEATURES
The main advantages of the procedure are :
- Several minds with different engineering
backgrounds address the problem.
- Very detailed results
and the drawbacks :
- Considerable time and manpower required.
- Not all causes are investigated.
Many interesting comments regarding other important
features of HAZOP studies as well as some application
examples can be seen in references (2) and (3 ).
4.
Fault Tree Analysis
4.1 GENERAL DESCRIPTION
It is a deductive technique that focuses on one particular
accident event and provides a method for determining causes
of that accident event. The fault tree itself is a graphic
model that displays the various combinations of
equipment/component failures and human/operator errors that
can result in the accident event of interest. These diagrams
must start from an event which has been identified by some
other method.
The technique is essentially binary, i.e., the events or
states in a fault tree are generally assumed to be those
which can be identified as existing or not existing. In
reality there is a whole spectrum or multiplicity of failure
possibilities, some will constitute a state of partial
failure others may be total. Decisions must be taken about
what degree of partial failures constitutes a "failure" in a
fault tree.
The result obtained is a set of combinations of
failures/conditions (cut-sets) that being present
simultaneously produce the accident event. These cut-sets
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may be limited by the number of component failures to
consider or by its probability of occurrence, in order to
minimise the work of result analysis.
These sets can also be ranked qualitatively (number of
failures/errors required to produce an accident) or
quantitatively (probability of having an accident).
The strength of Fault Tree Analysis as a qualitative tool
is its ability to break down an accident into basic
equipment/component failures and human errors.
It requires a complete understanding of how the
plant/system functions, the interconnections between the
different components or subsystems, operating procedures,
failure modes of every component and their effects on the
plant.
4.2 PROBABILISTIC EVALUATION.
Fault trees also provide a basis for quantification of the
frequency or probability of the undesired event, provided
data is available for the frequency or probability of the
various events or states appearing in the fault tree. Even
if this data is very limited, the important contributory
factors can often be identified. This enables effective ways
of reducing the likelihood of the top event to be
determined.
4.3 FAULT TREE CONSTRUCTION
The construction of a fault tree follows a rigorous and
methodical process. Starting with the top event the analyst
poses the question "What are the immediate precursors or
causes of the event or system state?". This question is then
applied to each of these sub-events until the analyst is
quite satisfied that all credible root causes, which could,
albeit in combination with other causes in the tree, lead to
the realisation of the top event, have been discovered and
included.
In the construction of fault trees, the analyst makes use
of various symbols. Symbols known as gates describe the
logical combination of input parameters necessary for an
output to be propagated up the tree. The two most widely
used gates are the "OR" gate and the "AND" gate :
- OR : An output is propagated from an "OR" gate if any
one or more of the inputs exist at any time.
- AND : An output is propagated from an "AND" gate if
all the inputs exist at the same time. Note that this does
not mean that these input events or states must happen
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simultaneously. If, for example, a protective system is
failed on demand, the time at which the protective system
became unable to react to demand is irrelevant.
There are more complex gates which are sometimes used to
show conditions or sequences. The use of certain gates can
complicate quantification of a fault tree. Examples of these
complex gates are the "EXCLUSIVE OR" and the "SEQUENTIAL
AND"
gates. Take for instace the "EXCLUSIVE OR" gate, if an
input A or an inut B exists then the output will be
propagated but should both inputs A and B exist, then the
output will not be propagated. A "SEQUENTIAL AND" gate,
sometimes known as a "PRIORITY" gate, can be used in
situations where the output, for example an explosion, will
only propagate if one of the inputs, an inflammable gas
release,
is closely followed by a second input, an ignition
source (note the flammable gas must be in the combustible
range).
4.4 USE OF FAULT TREES IN HAZARD IDENTIFICATION
The main use of fault trees in the overall context of hazard
identification is to structure the failure logic although
they are also used for identification of the causes of top
events. Fault tree construction provides a powerful prompt
to the analyst to consider ways in which situations
appearing in a fault tree can arise thereby identifying
causes.
This prompting action is not structured and so
cannot be guaranteed to be exhaustive. For this reason it
may be wise to apply "bottom-up" techniques, such as FMEA or
HAZOP to parts of the system to improve the likelihood that
all important causes are included.
Because Fault Trees are labour intensive, i.e., require
specialist expertise to perform the analysis and can involve
very detailed analysis of components and operations, their
use in the process industry has mainly been limited to the
analysis of critical areas. Hazard and operability studies
can provide an exhaustive way of going through deviations
but it does not provide any structure for combinations of
events. The techniques are therefore complementary and
should not be seen as alternatives.
Fault trees tend to be equipment oriented therefore the
analyst must be aware of this and ensure that sufficient
attention is given in other areas for instance human errors.
Human errors can be incorporated into the technique but the
main problem here is in identifying them.
Fault tree analysis provides a powerful technique for
identifying and structuring the contributory causes to a
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given top event. The analyst must be aware that causes
appearing in the tree could lead to other top events which
may be just as serious. This is another good reason for not
relying solely on one technique to provide a thorough
analysis of the situation.
Some application examples can be seen in references (2) and
(4).
5. Plant Dynamic Simulation to Evaluate Top Event Conditions
(DYLAM Methodology)
The increasing complexity of chemical sites nowadays,
combined with the diversity of dangers in various parts of
them, calls for a more synthetic and representative way of
plant and process description for risk and safety analysis
as well as fault detection purposes. Towards this direction
the DYLAM methodology offers a solution since it takes
account at the same time of process physics and system
performance, two domains which are normally separated by
current probabilistic techniques.
Since accidents proceed according to the values assumed by
certain physical variables, such as temperature, pressure,
concentrations, etc.
,
as a function of time and to the
occurrence of logical events such as lack of intervention of
protective systems, control actions, human operator faults
(which happen at random
times),
dynamic analyses are more
appropriate for representing such phenomena because they
depict more adequately the real accident sequence. This
advantage is greatly reinforced when responses of control
systems and/or of human operators are of concern because the
real time period for their intervention can be quite
precisely defined.
In such a way, design parameters and operating procedures
can be analysed in detail, helping the decision making
process and the fault diagnosis for accident prevention.
5.1 DYLAM TECHNIQUE
The DYLAM technique and its related computer program is a
methodology which has been developed at the Joint Research
Centre of the European Community, Ispra, Italy, and it is
still under amelioration. The basic characteristics of the
method have been extensively described elsewhere (5-6) and
in this lecture we are going to shortly summarise and stress
these aspects which become important for the elaboration of
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our example, as they are synthetically represented in Table
3.
The technique has two main parts. The first one (steps 1 to
4) consists of generating all the possible system state
configurations by the combination of the different component
states. Every one of these configurations is finally
represented by giving appropriate parameter values to a set
of parameteric equations, which contain both logical and
physical information. The second part (steps 5 to 7) solves
numerically the corresponding equation set in order to
foresee the physical consequences of the event sequences
generated, and it verifies whether the TOP conditions are
satisfied
(i.e.,
if some physical variable has reached
certain threshold value).
The process under analysis is described by a set of
component models, obtained by a quantitative failure mode
and effect analysis, resulting in logical analytical
relationships characteristic of each component. Such models
should be developed for each single component, but if this
tends to be very CPU-consuming by increasing considerably
the number of sequences to be analysed, the grouping of
single components in macro-components is advisable.
DYLAM provides all the nominal sequences that produce one
or more TOP conditions and the evolution of the physical
variables of interest for those sequences. On the other
hand, the probability distributions of the top conditions
are given as a function of time, taking into consideration
both statistical and functional failure dependencies. It
must be stressed that the functional dependency
consideration is made possible just because of the step-by-
step procedure in the evaluation of the physical variables
along the transient state and is has been implemented in the
new version (DYLAM 2) of the code (6 ).
In order to minimise the number of numerical solutions,
which are generally most CPU consuming, steps 2, 3 and 4 of
Table 3 are performed as soon as an event sequence has been
generated and before proceeding to the physical consequence
evaluation. In that sense, the maximum order of simultaneous
failures to be considered and the cut-off probabilistic
limits are key factors in the total CPU time of the
analysis.
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T a b l e
3 :
S t e p s
o f
D Y L A M p r o c e d u r e
1) Event sequence generation (based on component models).
2) Sequence are generated until the maximum order specified
is reached.
3) Analysis of passive states to cancel those sequences
where all components are in passive state.
4) Verification that sequence probability is not lower than
the cut-off value established by the user.
5) Numerical solution of equation set or dynamic simulation
of the plant to predict the physical consequences of the
respective sequence of events.
6) Verification of TOP event conditions and selection of
minimal TOP TIME PATTERNS.
7) Results :
i) Reliability parameters.
ii) Physical evolution of every minimal sequence that
reached at least one of the TOP event conditions.
The first and the fifth steps presented in Table 3 are
strongly interrelated because components should be modelled
according to the way in which the numerical solution
requires parameter values to calculate the system
performance.
The numerical solution of the equation set, characteristic
of each system, may be performed in several ways according
to the complexity of the system, as applications in the
nuclear and chemical field can show. Main alternatives are :
a) The process equipment is represented by simplified
formulas including some delay times to take account of
transient situations.
b) The system is represented by transient simulators,
the running times of which are considerably low as to be
used directly, without simplification. The requirement of
this alternative is that the simulation running time must be
reduced to as little as possible for any combination of
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failures. The accuracy of this code should be compatible
with the uncertainties which are present in the other steps
of risk assessment.
5.2 CASE STUDY
An application of DYLAM to chemical plants falling in the
second case indicated above is described elsewhere
(6) .
The
chemical plant analysed is a batch plant for sulfolane
production; it is divided into two parts : the addition unit
and the hydrogenation unit. The process can be summarised in
the following chemical reactions :
Addition reactor :
S02 + C4H6 > Sulfolene
C4H6 : butadiene
Hydrogenation reactor :
Sulfolene * H2 > Sulfolane
Sulfolane : tetrahydroditiofene-1-1 dioxide.
The first reaction is exothermic and reversible; the higher
the temperature, the smaller the amount of products
obtained.
The second reaction is irreversible, exothermic, and needs
a catalyser to proceed at an acceptable rate.
The DYLAM methodology was applied only to the addition
reaction and the respective facilities.
5.3 RESULTS OBTAINED
Two complete analysis were made, the difference between them
lying in the consideration or not of the operator corrective
actions for certain emergency situations.
The following parameters were considered :
- 13 components and event variables (without operator
corrective
actions).
18 components and event variables (with operator
corrective actions)
- Maximum top event seguence order : 4
- Sequence probability threshold : 1.0 x 1 0
- 8
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Different top event conditions were assumed, regarding
maximum pressure to be obtained for all failure combinations
generated by DYLAM. Results obtained and discussion are
detailed in reference (7).
It was concluded that with DYLAM method olo gy, t he complet e
prob abili stic and physical related info rmation for all the
possible and significant combinations of failures or
compo nent states were obtained, giving thus the p aram eter s
which help the reliability engineer to judge about the
adequacy of the different design alternatives from the
standpoint of plant safety.
The simulation of a large number of possible accidental
sequences which is made possible by the automated technique
implemented in DYLAM, offers the designer a very strong body
of knowledge to understand malfunctions and their effects.
Therefore, it may give a great aid in applications directed
towards operator support systems and fault diagnosis.
References
1. Lihou, D. (1980) Oyez Publications Symposium on Safety
Promotion and Loss Prevention in the Process
Industries, London.
2.
Lees,
Frank P. (1980) Loss Prevention in the Process
Industries,
Butterworths, London.
3. Roach, J. and
Lees,
F. (1981) The Chemical Engineer,
456-461.
4. Labath, N. ,
Real,
M., Huespe, A. and Masera M. (1986)
Reliability Engineering 14 , 223 -24 3 .
5. Amendola, A. and Reyna, C. (1984) EUR 9224 EN
6. Amendola, A. and Reyna, C. (1987) T.N.I.87.128, JRC;
Ispra
7. Amendola, A., Labath, N. , Nivolianitou, Z. and Reyna, C.
(1988) The Int. J. of Quality & Reliability Management
5, 48-59
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C O N T R O L T E C H N I Q U E S
C. MOUSSAS
Control Systems Laboratory
University ofPatras, Patras, Greece
Present address: J RC
Ispra Site
Safety Technology Institute
Ispra (VA), 1-21020
ABSTRACT. In this paper, first a description of the general configuration of a batch process computer-
controlled system is given. Then, some process control techniques are reviewed. Emphasis is plased on
the so-called
adaptive
control
techniques
which appear to be very effective in controlling batch processes
over a large range of operating conditions. In fact, the need for adaptive control arises from the fact that
the traditional feedback controllers (State Feedback, PID, e.t.c.) may work well for a given application,
but they need to be retuned whenever the conditions of the underlying process, or the process itself,
change. Fine chemical plants represent typical examples. The basic concepts of the various design
methods are presented, without getting into many technical details and mathematical derivations.
1 . Introduct ion
The introduction of digital comp uters to chemical process plants has been started approximately 3 0
years ago. Even in the first applicat ions, improvements in product quali ty and process
reproducibility were immediate, since the sequencing of the process steps was being done in a
more consistent and systematic way. With the increasing development of microelectronics, digital
computers became smaller, more powerful, and less expensive. At the same time, new theoretical
results in control theory, specially suited for computer-controlled systems, appeared in the
literature. As a result, advanced controllers can now be implemented in a fast and inexpensive
manner. Also, the substitution of many process units by microprocessors led to the idea of
distributed control systems, where specific control functions are imp lemen ted by means of
microprocessor-based devices which are supervised by a general-purpose digi tal computer.
Because of their complexity, batch chemical processes lend themselves to the application of such
advanced control systems. Major improvements include increased production, better product
quality, cost reduction, and safer plant operation. O n the other han d, there is an inevitable increase
in the complexity of the overall system which dictates the need for better personel training, and
elevates the role of process operators
[1].
2 . Batch Process Com puter Control
2 .
1
.
BATCH PROCESS DESCRIPTION
161
A.
Benuizi and J.
M.
Zaldivar (eds.). Safety of Chemical Batch Reactors and Storage Tanks, 161-200.
© 1991 ECSC, EEC, EAEC, Brussels and Luxembourg. Printed in the Netherlands.
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Batch chem ical processes consist in the manufacturing of
a
product by proces sing raw materials in
a discontinuous way. Usually, the batch reactor includes an agitator, a cooling/heating jacket, a
condenser and a feeding system. Important batch process variables are, among others, the reactor
temperature, the jacket temperature, the reactor press ure, and the feed rate. In all cases, the reactor
temperature, as well as its variations, play an important role in both the quality of the
manufactured product and the safe operation of the plant, and they can be directly controlled by
means of the fluid tem perature circulating in the jacket. In the case of highly ex othermic reactions,
temperature control may also be performed by controlling the reactant feeding rate, i.e. semi-batch
operation. Other control variables can also be controlled indirectly, since the reactor temperature
definitely affects the reaction rate, as well as the pressure. However, difficulties in controlling the
above m entioned quantities arise form the following facts.
First, some of the process variables may not be easy to be measured, and thus they have to be
inferred by using other available measurements.
Second, many of the process variables vary considerably throughout a batch, and they never
achieve a steady state. This is an unavoidable situation, since it is inherent in every batch process.
Third, startups and shutdowns are normal procedures which have to be automated effectively,
since they represent one of the most difficult phases with respect to control.
Finally, a batch process plant must be able to operate in a wide range of operating conditions,
so that various desired products can be manufactured.
In spite of the above difficulties, batch chemical processes can be effectivelly controlled with a
high degree of reliability and safety, by a proper selection of a process control system [2]. This
requires a good understanding of the batch process characteristics, and a careful consideration of
the process control needs. In the following section we discuss some common control system
configurations, paying more attention to the so-called Distributed Control Systems which are
mostly used today.
2 . 2 . BATCH PROCESS CONTROL SYSTEMS
2.2.1.
Classification. Commonly, the existing batch process control systems can be classified into
the following three general categories [2] :
1. Systems based on P rogramm able L ogic Controllers (PL C).
2.
Direct Digital Control (DDC) Systems.
3 .
Distributed Control Systems (D CS).
In the first category, the control system is build around microprocessor-based programmable
controllers w hich sequence the process and they can handle a limited amou nt of control functions.
These systems are suitable for small to medium scale batch processes, and where there do not
exist frequent changes in the manufactured product specifications. The main reason is that PLC
units provide two-state(on/off) control functions, and thus, complex controllers are more difficult
to be both programmed and modified. However, as long as no advanced control techniques are to
be implemented, they represent simple, well-functioning, and highly reliable control systems.
They can also be easily expande d by the introduction o f either new PLC u nits or just I/O
hard w are. It is imp ortant to men tion that PL C's are beco ming mo re and more powerful and they
can now be equiped with A/D and D/A modules in order to implement special analog control
functions, such as PID controllers.
In the second category, the control system uses a minicomputer for direct control. That is, a
computer handles all the required control actions, and its output control signals act directly to the
specific final control elements, or other process units. Whenever continuous time signals are
involved, the necessary transformations are performed by means of A/D and D/A converters. Note
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that these functions can also be implemented on the computer. Futhermore, by appropriate
programming, advanced control techniques can be easily applied. DDC systems are suitable for
medium to large scale batch processes, having complex requ irements. A mon g their drawbacks is
their poor expand ability. Also, their complex harware and software usually requires highly trained
personel.
In the third category, microprocessors, designed to perform specific tasks, are responsible for
all the required functions of the control system. Through a communications link they are all
connected to a general-purpose computer which acts as a supervising unit. The supervising
computer does not act directly to the various process elements, but it rather sends appropriate
requests to the specially designed microprocessor-based units which, subsequently, transform
these requests into actions applied directly to the process. Similarly to DDC systems, distributed
control systems are appropriate for medium to large scale batch processes. Furthermore, they are
far more expandable. They also provide more standard functions and they require less
programming skil ls. With respect to PLC based systems, they provide more sophist icated
operaror interface, and they are able to implement advanced control algorithms as well as better
recipe handling functions. On the other hand, PLC based systems tend to be less expensive for
smaller plants. On the wh ole, distributed control system s are mu ch mo re flexible than PLC and
DDC systems, and they are the most appropriate for processes where either the product
specifications are frequently changing, or different products are manufactured.
The main idea in a DCS is that the implementation is totally distributed, and supervision of the
various units is performed through levels of increased centralization. This leads to the notion of
different levels of functionality in a batch process control system. According to the previous
discussion, we can identify two main levels of functionality which will be referred to as the
regulatory control level and the superviso ry control level, respectively [3]. Specifically, the
regulatory control level contains the microprocessor-based units as well as any existing manual
control functions, while the supervisory control level contains the supervising computer together
with its peripherical units. In the following subsection we discuss these two levels in more detail,
and we identify the specific control functions that each one of them can handle.
2.2.2. Functiona lity Levels. Figure 2.1 show s a distributed con trol system which has been
divided into three basic levels of functionality. Level 1 contains the various process elements, that
is , valves, pumps, agitator, measuring elements e.t .c, level 2 represents the regulatory control
functions, and level 3 the corresponding supervisory control functions. In order to make a clearer
distinction between levels 2 and 3, we now consider some general control functions which are
common to all batch chemical processes. A predefined recipe which determines the specific
product to be produced and also selects the appropriate operations which are to be performed, will
contain the following actions [4] :
- feeding of the raw materials
- strirring of the reactor components at certain speeds
- following a desired temp erature profile
- measuring various process variables
- checking the proper function of valves, pumps, e.t.c.
- discharge of the product
- reporting, during and after the batch
The execution of the above actions can be obtained by a combination of sequence and
continuous control, including the following b asic control functions :
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- actuation
- sensing
- interlocking
- regulatory (continuous) control
- recipe handling
- sequencing
- failure detection
- data handling and reporting
Terminals
^ i a p
> ^
V*
SUPERVISING
COMPUTER
t
LEVEL 3
J
* l
\
Pr in te r 1
Disc
J
Terminals
s a
MICROPROCESSOR-BASED
UNITS
- Operator Interface
- Single Loop controllers
- Weighting subsystem
- A/D converters
- ' - . L J .
mrm
Communicat ions
Link
LEVEL 2
Panels
PROCESS
LEVEL 1
Figure 2.1 - Functionality levels
Actuation, applies electric signals to pumps and valves, required for the feeding of the
components, or the discharge of the product.
Sensing, includes all the data aquisition d evices, as well as A/D and D /A converters.
Interlocking, prevents different valves to be open at the same time, whenever this is not
permitted.
By regulatory, control we mean the application of control algorithms for controlling important
process variables such as temperarure, pressure, flow, e.t.c.
Recipe handling, manages the execution of a specific recipe through the process units, and
sequencing, determines the steps to be followed within each of the process units.
Failure detection, handles any irregularities which are detected in the process, actuates alarms,
and takes recipe-based corrective actions.
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Data handling and reporting, is the function which organizes data from various devices, and
makes them available as reports, or it transmits them to other systems.
We now turn to the classification of the above control functions with respect to the
functionality levels. As we can see in figure 2, the regulatory control level, or level 2, is directly
connected to the process equipment and to other output devices, while the supervisory control
level, or level 3, acts on the process by giving specific requests which are subsequently executed
by level 2. That is, it is not directly connected to the process. Thus, actuation and sensing
definitely belong to level 2. Simple, well-defined regulatory control functions (e.g. PID), are also
included in level 2, as well as safety interlocks which should not be bypassed by a plant operator.
On the other hand, recipe handling, data handling and reporting functions usually belong to level
3 ,
together with any advanced regulatory control algorithms and any flexible interlocking
functions. Sequencing and failure detection control functions, can be divided between the two
levels, depending mainly on the complexity of each function. The equipment used in level 2 must
be totally error-free, thus requiring low complexity. It must also be protected against changes. On
the other hand, level 3 equipment can be quite complex and it should be able to change whenever
operation conditions, product specifications, or safety measures, change.
2.3. BATCH TEMPERATURE CONTROL
In this section, we discuss in some more detail the regulatory control function. As we mentioned
above, this part of the batch control system deals with the application of control algorithms for
controlling important batch process variables. The m ost important controlled variable is the reactor
temperature, which plays an important role in the quality of the manufactured products and in the
safety of the operation. Therefore, varying temperature profiles from batch to batch, lead to
inconsistent, or unacceptable, product quality. In the beggining of a typical batch reaction, heat is
introduced, so that the reactor temperature is initially raised until a specific value, called the set
point, thus initiating the reaction. Then, for an exothermic reaction, cooling is applied to keep the
temperature close to the set point. Towards the end, heating may be necessary in order for the
reaction to be com pleted.
This heating/cooling procedure can be performed by manipulating the temperature of the fluid
circulating in the jacket of the reactor. To this end, either two fluids, that is steam for heating and
water for cooling, or just one fluid which is externally heated or cooled, can be used. In the letter
case the jack et tem perature is changed by opening and closing va lves. Wha tever the case is, the
control algorithm has to provide a value for the jacket temperature, given values of other process
variables such as reactor temperature, reactor pressure, feeding flow, e.t.c. For the design of such
control algorithms, various techniques are discussed in the next chapter. Emphasis is placed on
the so-called adaptive control techniques which appear to be quite effective in controlling chemical
processes.
3 . Contro l Techniques
3 . 1 . INTRODUCTION
3.1.1.
General Control Considerations.
Control systems are found in all sectors of industry, such
as chemical industry (quality control of desired product), space technology (flight control), power
system s (energy co nsum ption ), robotics and others. In fact, our every-day life is greatly affected
by some type of control system (car, air-conditioning, electronic devices e.t .c). The design of
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such a system consists in determining the appropriate control signals which will be applied to a
specific p roces s, so that its output satisfy som e prescribed p roperties.
In the chemical industry, process means the operations necessary to put together raw materials
and cause them to react in a prescribed fashion in order to produce a desired end-product.
Generally speaking, the process can be described by an equation of the form
Y = f (X,U,t )
(3 .1)
where Y represents the desired properties of the end product, and it will be referred to as the
output of the process. The letters X and U represent the variables on which the properties depend.
Specifically, let U represent the variable(s) which we can control directly, i.e. the input of the
process. The control system, or controller, can also be described by an equation of the form
U = g (X,Y, t )
(3.2)
where g is a function which realises the following strategy :
1.
Measure the variables X, U, Y of the process at a given time instant.
2. Compare the output Y with the desired value, i.e. the set point, and find the error.
3 .
Based on 1 and 2 above determ ine a new value for the input variable U , in order to
correct any deviation of the error from zero (Controller Design ).
4. Feed the new value back to the process.
A simplified block-diagram configuration of the above procedure is illustrated in figure 3.1.
Set Point
e
A
Controller
u
Process
y
— w
Figure 3.1 - Feedback Control System
According to the above discussion, it is clear that the design of the controller should be done in
such a way so as to eliminate the error, e, in a reasonable period of time. Typically, the design of
the controller is based on some assumed process model as in 3.1. If the model is known, then the
design can lead to satisfactory results. But a complete knowledge of the model, requires a
complete knowledge of the process parameters for all possible operating conditions. If these
param eters are not known, or if they change w ith time, then the performance of the controller will
deteriorate. Unfortunately, industrial processes exhibit time varying parameters, nonlinear
dyn am ics, and mo delling unc ertainties. Since a com preh ensiv e theory for the treatment of
nonlinear systems does not exist, we realise that the controller design for such processes becomes
a very difficult task. In fact, this is where the adaptive control systems come in to the picture. A
typical block-diagram representation is shown in figure 3.2. The controller parameters can be
adjusted by means of the adjustment mechanism, and they usually depend on the difference
between the actual and the desired performance of the overall control system. We can distinguish
two main loops; loop 1, which is the same as that in figure 3.1, and loop 2, which is used to
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adjust the controller parameters. If the process parameters change, then loop 2 will take a
corrective action by chan ging the param eters of the controller.
Set Point
Loop 2
Controller
Adjustment
Mechanism
Process
Loop 1
Figure 3.2 - An Adaptive Control System
Two very important adaptive control schemes which lead to such control system
configurations are :
1. Self-Tuning Controllers (STC) [5],[6]
2.
Model Reference Adaptive Systems (MRAS) [5],[6],[7]
For the rest of this report we shall be concerned with these two categories. For information about
other important adaptive control schem es see [5].
3.1.2. Self-Tuning and Model R eference Adaptive Control. A block diagram of a self-tuning
control system is shown in figure 3.3.
Desired
Performance
Set Point
^
i
r
Design
i
r
Controller
u
Estimation
Process
. _
y
_ ^
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Figure 3.3 - Self-Tuning Control System
An assumed dynamic model is associated to the process. Based on this model and on a
controller design procedure, a specific controller can be derived. This controller, which obviously
depends on the model parameters, is then applied to the process. At each time instant the
parameters of the model are estimated from input-output data, and based on these estimates, the
parameters of the controller are computed according to the specific design procedure. We see that
a variety of self-tuning controllers can result from this scheme by co nsidering different structures
for the controller and the estimator. Typical design procedures include the recursive least squares
and projection algorithms, for the estimator design, and the minimization of a quadratic cost
function and pole-placeme nt techniqu es, for the design of the controller.
A block diagram of a model reference control system is shown in figure 3.4. In this case the
desired performance of the control system is described in terms of a reference model. We again
have to assume that the process is described by some mathematical model. The goal is to
determine the adaptive mechanism which changes the values of the controller parameters, so that
the output y of the process be close to the desired ou tput y
m
.
STC systems where originally developed for discrete time systems [9],[10], while MRAC
systems were developed for continuous time systems [11],[12],[13]. Also, MRAC as shown in
fig. 3.4, represent the so-called direct schemes because the controller parameters are directly
updated from the adaptive mechanism. On the other hand, STC as in fig. 3.3, are indirect
schemes in the sense that first the model parameters are estimated, and then the new controller
parameters are computed. However, as we can see in these figures, the two configurations are
quite similar. In fact, we can design MRAC for discrete time systems and STC for continuous
ones ,
as well as, indirect MRAC and direct STC which, as we shall see later in this paper, in
some cases result in identical adaptive control schemes [5],[6],[7].
Desired
Performance
Set Point
w
Reference
Model
1
r
Controller
y
m
u
Adaptive
Mechanism
t
Process
y
*
Figure 3.4 - Model Reference Adaptive Control System
The design of an adaptive control system of the form illustrated in figures 3.3-3.4 is
conseptually simple. As we have already mentioned, the design will result in different schemes
depending on the specific choises of the controller and the estimator. Whatever the choise is, the
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overall system must satisfy some stability and convergence requirements. Specifically, we require
global stability, which means that the process inputs and outputs remain bounded for all time, and
that the error between the process output and the desired one go asymptotically to zero. Also, in
the case of constant process parameters we require that the estimates converge to the real values.
Since, in principle, adaptive control systems are nonlinear systems, their analysis is quite
complicated and global stability and convergence proofs exist only for some cases and under ideal
situations. An overview of the current stability and convergence results can be found in [5],[6].
Issues associated with the application of adaptive schemes to real nonideal situations, as well as
general guidelines for resolving some practical problems are discussed in [5],[19],[20],[21].
3.1.3 .
Digital Control and Process M odelling.
Nowadays, digital computers play an important
role in the implementation of adaptive schemes. Recent achievements in microelectronics was one
of the main reasons for the developm ent of many different adaptive algorithm s, since their testing
through simulations could be done in a very fast and inexpencive way. Since many processes are
inherently continuous-time, some kind of conversion from continuous-time values to discrete-time
values, which can be direcdy processed by the computer (and vice-versa), is needed. This is done
by using analog-to-digital (A-D) and digital-to-analog (D-A) converters. A block diagram of such
a computer controlled system is illustrated in figure 3.5.
z(t)
h -
A-D
z(k)
Digital
Controller
u(k
D-A
u(t)
Process
y(0
w
measurements
input
output
Figure 3.5 - A Computer Controlled System
One way to design a digital controller for this system would be, first to design an appropriate
continuous-time controller based on the continuous-time process model, and then to make a
discrete-time approximation. The best results that we can expect by applying this approach are the
ones obtained by the continuous-time controller, and in the case that we sample the process fast
enough. In many cases, however, much better results can be achieved if one uses the theory of
discrete-time systems. This will, also, enhance the class of controllers available for a specific
application, as well as it will lead to a better understanding of inherently discrete-time processes.
For a more detailed discussion and representative examples see [14],[15]. For the above reasons,
it is necessary to develod discrete-time models for the continuous-time processes, and then base
the design of digital controllers on them. In the context of adaptive control the usual approach is to
consider that the process is described by the so-called AutoRegressive Moving-Average with
auxiliary input (i .e. the control signal u) model, or ARMAX [5],[6], which for a single-input
single-output process is given by the following equation
A(q"') y(k) = B(q"
1
) u(k-d) + Cfq"
1
) e(k)
(3.3)
where u and y are the process input and output, respectively, e is a stochastic noise variable (white
noise process), and by definition
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q'VG Osyfc-l) . (3.4)
Any delay between the input and output of the process is expressed through the integer d, for then
d > 1. The polynomials A, B, and C are defined by,
n
A q
1
) = l
+
2 ^ a . q -
i
(3.5)
i= l
m
B(q"
1
)
= X
b
i
q
"
i ( 3 6 )
i=0
n
C t q V ^ C . q
1
•
(3
-
7)
i=0
Th e coefficients a;, bj , and q , represe nt the para me ters of the mo del. At first glance, one
would say that this model cannot represent a highly nonlinear process, such as a chemical
process, since 3.3 is a linear difference equation. However, by allowing the parameters a;, b;, q,
to change (time-varying parameters), we introduce a nonlinear behaviour into our model. In the
adaptive control case, this is done by the estimation mechanism which continuously updates the
model parameters. The use of ARMAX models is furthermore justified by the fact that when
combined with appropriate control and estimation schemes, they lead to adaptive algorithms for
which stability and convergence results can be established. For these reasons ARMAX models
have been extensively used in the literature [5],[6],[17],[18].
3.1.4. Applications. In a recent article, surveying the design of adaptive control system s [2 7], the
author begins with the phrase :
" Adaptive control is now finding its way to the market place after many years of effort"
In fact, even if the first applications of the adaptive control systems appeared in the 1950s in
the context of aircraft flight control, it was only in the 1980s where the development of both the
theory and the computer hardware, allowed for a systematic application of various adaptive
control schemes to the industry. As reported in [5], it was estimated that in May 1988 there were
at least 7000 0 industrial process loops in which adaptive techniques w ere used. A description of
various commercially available industrial adaptive controllers, announced in the 1980s from
com panies in Europe, No rth Am erica and Japan, can also be found in [5]. At least half of them are
based on the PID controller structure, which is the most common technique applied to industrial
processes, and provide automatic tuning of the PID parameters. They are very useful, since it
appears that even today many industrial PID controllers are poorly tuned [27].
Som e recent applications of adap tive control to chem ical reactors are reported in [25], [28]-
[31].
In [25], the generalized minimum variance self-tuning controller (sec. 3.4.2.4) was applied
to a batch chemical reactor (Real Plant). The results showed a smoother temperature profile, than
that obtained by a PID controller, as well as insensitivity to reactant quality. In [28],[29],[30],
applications of various adaptive control techniques to a batch polymerization reactor are described,
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both to simulated [28],[29],[30] and to pilot plant [30], experiments. The techniques included,
among others, minimum variance and generalized minimum variance self-tuning control (sec.
3.4.2), as well as adaptive pole-placement (sec. 3.4.3). Their performance was showed to be
either
equally
good,
or
better
than
the
performance
of
well
tuned
PID
controllers.
Various
control
objectives were considered, such as isothermal operation, constant rate operation, constant weight
average molecular weight , and specific monome r conversion profile. Finally, in [31], a
modification of the basic minimum variance self-tuning controller (sec. 3.4.2.3) was applied to a
simulated continuous stirred-tank reactor, where it was demonstated that it was more effective
than the basic method. Other numerous applications of various adaptive control schemes can be
found in the survey parers [21], [27] and [32].
3.2. PID CONTROLLERS
Even today, PID feedback controllers are th e most widely used controllers in the industry. The
reason
is
that
they
perform
quite
well
whenever
th e
process
is
of
reasonable
complexity
and
the
control specifications are not very tight. Among their features are th e integral action, which
eliminates steady state errors, or offsets, and the derivative action, which improves the stability of
the closed loop system. Their function can be described, in its simplest form, by the equation
r ■
I
„(,) . KI
e
M
+ Y |=W
d s + T
d T I , (3.8)
L ' » J
where u(t) is th e control signal, e(t) is the control error which equals the difference detween the
output y(t) and the set point y
r
(t), and K, Tj and T j are the so-called PID parameters, namely, the
proportional gain, th e integral t ime, and th e derivative t ime, respectively. In Laplace transform
representation, the above equation can also be written as
U( s ) = K
1 + T ^ - + T .
s
T. s
d
E(s) . (3 .9)
In practice, the algorithm described by 3.8 is subject to various modifications which improve its
performance.
For
examlpe,
in
the
case
of
pure
proportional
control
we
have
u(t) = K e ( t ) . (3 .10)
Since th e goal is the elimination of the error e(t), and since 3.10 implies that u(t)=0 whenever
e(t)=0, we realize that in most cases there will exist a non-zero steady-state error between the
output and the se t point. For this reason, instead of 3.10 we frequently use the equation
u(t ) = K e(t) + A (3 .11)
where
A
is
a
constant
corresponding
to
the
control
signal
when
e(t)=0.
In fact, th e main function of the integral term is the elimination of such offsets. To see this,
consider that instead of 3.11 we use a PI controller, i.e.
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r i i
u(t) = K |
Z(Q
+ Y
e(s)ds
| .
( 3 1 2 )
L
' »
J
Now
assume
that
after
a
time
instant
t'
we
are
in
steady
state
with
u(t)
=
u(t')
=
u',
while
e(t)
=
e(t') = e' * 0, for t > t'. That is , a non-zero offset. Then, for a t > t' equation 3.12 gives
r r I
I , i f . , . e '-(t - t' ) I
u(t) = K |
e
+ — e ( s ) d s + |
;
f
o r t > t
. (3 .13)
L
°
j
J
Note , however, that the third term of the above expression is not constant, but it depends on the
time
t.
Consequently,
u(t)
is
not
constant.
But
this
contradicts
ou r
hupothesis.
On
the
other
hand,
we se e that for e' = 0 the control signal equals
r}
(s )
ds
0
which
is
constant.
A problem associated with th e integral action of a PID controller is th e so-called
integral
windup,
or
reset
windup,
which appears whenever th e control signal drives an actuator, or final
control element, having limited range. Then, when th e actuator reaches its upper limit, it will
remain there even if the control signal is increasing. Simultaneously, th e control signal will keep
increasing, since the error is not zero and the algorithm cannot detect that the non-zero error is not
due to the magnitude of th e control signal, but rather to th e saturation of th e actuator. This
situation has th e following consequences. When, at some time t, th e error becomes zero, the
integral part stops integrating, but the control signal is so big that the output of the process will
still be increasing, and it will take time before it s derivative changes sign. Therefore, this
behaviour
leads
to
large
overshoots
and
long
settling
t imes.
One
way
to
avoid
this
problem
is
to
use the integral part only when the error is sufficiendy small, thus avoiding the actuator saturation.
Another way is to stop updating the integrator when th e actuator saturates, or keep its value
bounded. This can be done, for example, if we use the following modified form of the integral
part
t
t
■ £-
fe(s)ds
+
^ fe
t
(s)ds
(3 .14)
In
this
case,
the
second
term
integrates
the
error
e
t
(t )
defined
as
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e
t
( t ) = v( t ) - u ( t ) , (3 .15)
where u(t) is the control signal, and v(t) is the actuator signal. In normal conditions, v(t) = u(t)
and therefore e
t
(t) = 0. On the other hand, when the actuator saturates, e
t
(t) becomes negative and
keeps the integrator output bounded.
As we have already mentioned, the derivative action improves the stability of the closed loop
system. Intuitively, this can be understood if we rewrite the derivative part as
deffl e(t
+
A t ) - e ( t )
d
dt
d
At
This expression implies that the derivative term provides anticipatory action, for the error at time
t+At, thus improving the performance of the controller and the stability of the overall system. If
high frequency measurement noise is present, the derivative term will result in flactuating control
signals whose amplitude will be an increasing function of the frequency. For this reason, the
deriv ative term is often filtered th roug h a first order filter. The n, in Lap lace transform
representation, tthe derivative term becomes
D
=
T 7 T W
E ( S )
<
3
-
17
>
d
where N is an integer, and Tj/N is the time constant of the filter.
Derivative action can also lead to large control signals, and thus to large overshoot, when the
set point changes. Since after such a change, usually, the new value remains the same for a
relatively long period of time, and since the derivative of a constant is zero, it is a common
technique to replace the error e(t) by e^ t) = -y, only in the derivative term . Th e oversho ot can be
even more redu ced, if in the proportional part w e replace e(t) by e
p
(t) = b y
r
- y, w here 0 < b < 1.
Taking into account the above modifications, a more realistic PID controller can be described,
in Laplace form, by the following equation
U(s) = K E
D
(s) +
fE(s)+fE,(s)
T . s T
t
s
K T
d
s E
d
(s)
1+T. s /N
d
(3 .18)
where
E
p
(s) = b-Y
r
(s) - Y( s) (3.1 9)
E(s ) = Y
r
(s) - Y(s ) (3.2 0)
E
d
( s ) = -Y (s ) (3 .21 )
E
t
(s) = V(s) - U( s) (3 .22 )
N is an integer in the range 3-10, T
t
is a rather small constant, and K , Tj , T j are the PID
parameters. The implementation of the PID algorithm on a digital computer requires a discrete-
time model, which must be equivalent to that of equation 3.18 when the sampling period is small
enough. There are many methods to derive such a discrete-time model [14],[38]. In the case
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wh ere an Euler appro ximation for the integral part and a backw ard-difference approx imation for
the derivative part are used, equation 3.18 becomes
u(k) = Ke
p
(k )+
Khe(k) he
t
(k)
T
;
(q-1) T
t
(q-1)
T
d
( q - l ) e
d
( k )
(3.23)
where k represents the discrete time, and h is the sampling period.
In the following, we present two well known methods for tuning the PID parameters, namely,
the Ziegler-Nichols open loop, or transient responce, method, and the Ziegler-Nichols closed
loop, or ultimative sensitivity, method. [14],[38]. The first method is based on the form of the
process step responce. Specifically, it is assumed that the responce is similar to that shown in
figure 3.6, where R is the maximum slope of the responce and L is determined by drawing the
tangent at that point.
y(t)
Figure 3.6 - Process Step Responce
Then, the PID parameters are obtained as shown in table 3.1.
Table 3.1 - PID parametrs (open loop method)
Controller
Type
P
PI
PID
K
1/RL
0.9/RL
1.2/RL
T
i
3L
2L
T
d
0.5L
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The second method is a frequency responce method. First, a proportional controller, as in
3.10, is applied to the process. After, the proportional gain is increased until the output of the
process oscillates periodically. At that point, let K
c
be the gain of the proportional controller and
T
c
be the period of the oscillations. Then, the PID parameters are obtained by means of table 3.2.
Table 3.2 - PfD parameters (closed loop methodt
Controller
Type
P
PI
PID
K
0.5K
C
0.4K
C
0.6K
C
Ti
0.8T
C
0.5T
C
T
d
0.12T
C
The PID parameters obtained by using either of the two methods have to be considered as a rough
estimate, and based on them, more accurate values must be derived manually. A more detailed
discussion of the above methods, as well as methods for automatic tuning of PID controllers, can
be found in [38] .
3 . 3 .
PARAM ETER ESTIMATION
3 .3 .1 .
Introduction. As we have already discussed in section 3.2 , estima tion of param eters is a
very important part of an adaptive control system. In the indirect schem e the estimator com putes at
each sampling instant the current parameters of the process model, while in the direct scheme it
computes directly the new controller parameters. We see that a kind of system identification is
performed, where the system to be identified is either the process or, in some sense, the
controller. In both cases, it is assumed that the system can be described by an ARMAX model, so
that the method of least squares can be easily applied. The methods which we discuss in the rest
of this section, namely, Recursive Least Squares (RLS), Projection Algorithm, and Extended
Least Squares (ELS), belong to the so-called on-line, or real-time, parameter estimation methods,
as opposed to the off-line ones. A complete discussion of the various identification schemes can
be found in [6],[16].
3 .3 .2 . Least Squares. Con sider the problem of estimating the param eters of a system whose
behaviour is described by the mathematical model
y(k) = e ^ O O + 9
2
x
2
(k)
e
r
x
r
(k) ,
(3.24)
wh ere y(k) can be thought of as the output of the system , and xi (k) x
r
(k) are combinations
of other variables which can be measured. We w ant to estimate 0 i , . . . ,0
r
, given measurements
of the functions xi (k),. . . , x
r
(k) , so that the output of the real system y (k) be as close to the
variable y(k) as possible. In the context of least squares, as close as possible means that the error
k
e (k )
=
X
[ y ( i )
y + ( i ) ] 2
(3.25)
i=l
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is minimum. The estimated parameters, at time k, should minimize this error. Equations 3.25 and
3.24 contain the two most important features of the least squares formulation, namely, the
minimization of a squared error criterion, and the linear fashion in which the parameters are
introduced into the model. These two facts allow for an analytical solution to exist. Specifically,
let
x(k) = [
X j
(k ) x
2
(k) - x
r
(k) ]
T
, (3 .26 )
and
e = [ e
1
e
2
- e
r
]
T
>
(3.27)
which will be referred to as the
regression vector
and the
parameter vector,
respectively. Then,
3.24 can be written as
y ( k ) = _ x
T
(k )_9 , (3 .28)
which will be called the regression equation. At time k, the estimate which minimizes the error
e(k) can be show n to be the solution of the equation (see [16],[22])
R( k)- 8(k ) = p(k) , (3 .29 a)
or
where
6(k) = K
1
( k ) p ( k ) , ( 3 . 2 9 b)
m =
2^_x(i)x
T
(i) (3.30)
i = l
and
p(k)
=
2^y*(i)-x
T
(i) , (3.31)
i = l
a matrix of dim ension (r x r) and a vector of dimen sion (r x 1), respectively. A s far as the notation
is concerned, the underscore indicates a vector, the double-underscore a matrix, and the
superscript T the transpose of either a vector, or a matrix. Equation 3.29b implies that,
theoretically, we are able to compute the solution if the matrix R is inversible. However, the
amount of computation needed for inverting this matrix, for large r, makes this approach not
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feasible for real-time ap plications w here time is an impo rtant factor [22]. For this reason, in many
practical applications the vector 6(k) is computed recursively, and its value at time k depends on
the previous e stimate, at time k -1 , plus new information available at time k -1 . The idea is the
recursive computation of the matrix R and the vector p
a
in 3.29b, based on their values at time k-
1. This leads to the so-called Recursive Least Squares (RLS) algorithm which provides the basis
for many different recursive identification algorithms. In what follows we discuss the application
of the RLS, ELS, and projection algorithms, in the parameter estimation of processes described
by ARMA X m odels.
3 .3 .3 . On-line Estimation Algorithms. The AR MA X m odel, which was introduced in section
3.1.3 , is described by the set of equations 3.3-3.7. Assume that e(k)=0 for all k's (deterministic
case),
so that the process is approxim ated by the model
A C q
1
) y(k) = BCq
1
) u(k-d) , (3 .3 2)
which can be written also as
y ( k ) + a y ( k - l ) + - + a
n
y ( k - n ) = b u ( k - d ) + - + b
m
u ( k - d - m ) , ( 3 .3 3 )
y (k) = -a
1
y ( k - l ) - - a
n
y ( k - n ) + b
0
u ( k - d ) + - + b
m
u ( k - d - m ) . ( 3 . 3 4 )
We see that, for
e
i
=
- V
e
2 = -
a
2 ' - - - '
e
r =
b
m (3-35)
and
Xj(k) = y(k - l ) , x
2
(k) = y(k-2) , . . . , x
r
(k) = u(k -d-m ) , (3 .3 6)
3.34 yields 3.24. Therefore, the application of least squares is straightforward and the solution is
given by 3.29. In the sequel we present its recursive version, i.e. the RLS algorithm, in the case
where the error to be minim ized is given by
k
e(k) =
2 /
k
' [
y(0 " y*W ]
2
• (3-37)
i = l
which is a generalization of that in equation 3.25 .
3.3 .3 .1 .
Recursive Least Squares Algorithm.
Let
9(k) = [ -aj( k) - -a
n
(k) b
0
(k ) - b
m
(k ) ]
T
(3 .38)
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and
u ( k -l ) = [ y * ( k - l ) - y * ( k - n ) u ( k - d ) - u ( k - d - m ) ]
T
. (3 .3 9)
The argument k-1 in the definition of the vector u indicates that all its components are available at
the samp ling time k- 1 , or before. W ith the above notation, the recursive least squares equations
are as follows ([16],[22]):
9 ( k ) = e ( k - l ) + g ( k ) [ y * ( k ) - _ u
T
(k - l ) _e (k - l ) ] , ( 3 .40)
where
P ( k - l ) - u ( k - l )
g ( k ) =
U u T ( k - l ) . P ( k - l ) - u ( k - l )
( 3
-
4 1 )
and
P(k) = -L[P(k-D-g(k)-u
T
(k-l)-P(k-i)] _
( 3 4 2 )
A.
Equation 3.40 implies that the current estimate depends on the previous estimate, plus the error
y (k) -u( k-l )9 (k- l) resulting by the use of the previous estimate multiplied by a time-varying gain
£(k).
This gain is determined by 3.41 and 3.42, where the matrix P(k) is being interpreted as the
covariance matrix of the estimation error. For the algorithm to work, initial values of the parameter
vector £(0) and the covariance matrix P(0) are needed. Usually, P(0) is chosen to be the unit
matrix multiplied by a constant. A large value of this constant indicates that 6(0) is a poor
estimate, and vice-versa. This w ill, initially, cause rapid chan ges in the estimated parameters Q(k).
The constant X, taking values in the interval
(0,1],
is called the forgetting factor. The choise X=l
will equally weight all the measurements from k=0, while a value of
\< l
will discard old
measurements by weighting more heavily the recent ones. The smaller the value of X. the less
weight into the old measurements wil be assigned. This will allow for parameter tracking in the
case where the parameters are not constant but rather drift. For more details concerning the
specific choise of X, as well as other techniques dealing with time-varying parameters such as
covariance reseting or use of variable forgetting factors, see [5],[6],[19],[21]. Another important
issue associated with the RLS algorithm is parameter convergence. As we have said, the criterion
is the minimization of the error in 3.37. We notice that no requirements about the parameter
behaviour are included in this criterion. This can very well lead to the case where the error goes to
zero,
while the parameters do not converge to the real values. This situation can be avoided if the
vector u(k) possess the so-called persistent excitation prop erty (for a formal definition see
[5],[6],[16]). Practically speaking, a persistently exciting sequence should contain a sufficient
number of frequencies, in its frequency spectrum, so as to allow for parameter updating
[5],
[6],[19],
[21].
Lack of this property can also lead to various
bursting phenomena
[20].
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3.3.3.2. Projection Algorithm. The above recursive computat ion of th e solution to th e least
squares problem considerably reduces th e computat ional complexity, by avoiding th e matrix
inversion. It is probable, however, that further reduction of th e computation effort be required,
depending
on
the
application
and
especially
in
th e
case
where
the
dimension
of
the
vector
j
is
too
large. Then a frequently used simplified algorithm is the projection algorithm described below.
g ( k ) =_6(k- l )
+
n
, - f
1
„ [ y* (k ) -uT (k - l ) - _6 (k - l ) ] p . 4 3 )
p + u H k - l ^ u t k - l )
where 0 < a < 2 and
3
> 0 .
We see that the step of updating the matrix P(k) has been eliminated, and this yields in a less
complex algorithm. Instead, its rate of convergence will be slower than that in the case of the RLS
algorithm [6],[16].
3.3.3.3.
Extended
Least
Squares
Algorithm.
In the beginning of this section we had assumed that
th e process is described by th e model 3.3 with e(k)=0 for all k. Assume now that th e noise
variables are not zero and that C(q ^)=l . Then the process model becomes
ACq
1
) y(k) = BCq
1
) u(k-d) + e(k) . (3.44)
If {e(k)} is white noise, then the RLS estimates, as described adove, will converge to the true
parameter values. But, if e(k) is a sequence of correlated random variables, then it will produce
biased parameter estimates [16],[18]. This correlation in th e noise sequence is expressed through
the
polynomial
C(q~l)
which
leads
to
a
process
model
as
in
equation
3.3,
with
c,
*
0
for
some
i
>
1, and {e(k)} being white noise. In th e fol lowing we describe th e extended least squares
algorithm (ELS) which, based on this model, produces unbiased parameter estimates [16],[18].
First, we rewrite 3.3 as
y ( k ) + a
1
y ( k - l ) + - + a
n
y ( k - n ) = b
0
u ( k - d ) + - - - + b
m
u ( k - d - m ) +
+ c
0
e ( k ) + c
]
e ( k - l ) + - + c
n
e ( k - n ) . (3 .45)
Then, by defining
9 = [ -a , -a ■•■ -a „ b ••• b
m
c ••• c
n
] (3 .46)
-
L
1 2
n
0
m
0
n
and
u(k- l ) = [ y* ( k - l ) - y* ( k - n ) u ( k - d ) - u ( k - d -m) e ( k ) - e ( k - n ) ]
T
, (3.47)
3.45
yields
y(k)
=
u
T
( k - l ) - e
.
(3.48)
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Therefore, the RLS algorithm can be directly applied, where now the vector 0 contains also the
correlation coefficients of the noise. No tice, how ever, that the regression vector u ^ k - l ) , which is
supposed to be know n, contains the variables e ( k ) , . . . , e(k-n), for which measurem ents are not
available. For this reason, in applying the RLS we have to replace these variables by
approximations. A possible choise is
e (k ) = y * ( k ) - u
T
( k - l ) - 6 ; k - l ) ; V k ( 3 .4 9 )
i.e. the prediction errors. The method which results by applying the set of equations 3.40-3.42 for
the estimation of the parameters in 3.48 with the above modification in the regression vector, is
referred to as the extended least squares method [5],[6],[16]. Finally, in order to give an example
for the presence of correlated noise, consider the following situation. Let the process model be
deterministic, that is, as in 3.32. Assume that the measurements of the system output are
corrupted by additive white noise. Then, our modelled output is not y(k) but rather y'(k) where
y'(k) = y(k ) + e(k) . (3.5 0)
By substituting 3.50 into 3.32 we get
A ( q "
1
) [y ' (k) - e (k)] = B(q '
1
) u(k- d) , (3.5 1)
A ( q
4
) y '(k) = B(q"
1
) u(k-d) + A(q
_ 1
) e(k) , (3. 52 )
which yields 3.3 for C(q
_ 1
) = A(q
_ 1
) and y(k) = y'(k).
3 .4 . ADAPTIVE CONTROL TECHNIQUES
3.4.1. Introduction. Th e design of adaptive control system s is base d on the idea of simultaneou s
parameter estimation and control. Therefore, by using different parameter estimation methods and
different control design procedures, many adaptive control schemes can be produced. Since
parameter estimation was treated in the previous chapter, we shall now discuss some control
design procedures together with their adaptive versions. Two main categories are considered in
the following sections. In the first category (section 3.4.2), the desired performance of the overall
system is expressed by means of a quadratic cost function, and the design of the controller is
based on the minimization of this function, while in the second category (sections 3.4.3 and
3.4.4), the desired performance is expressed by specifying some characteristics of the closed loop
transfer function which, also, determine the structure of the controller. We shall always assume
that the process is described by an ARMAX model as in equation 3.3 which we rewrite below as
A ( q - ' ) y ( k ) = q - f y q
1
) u(k) + C(q "
) e(k ) , (3.5 3)
with A (q" l) being a stable polynom ial, that is, having all its roots inside the unit circle.
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In every case which we present below, the resulting controller will be a special case of a
general linear controller described by an equation of the form
V ^ q
1
) u ( k ) = V ^ q
1
) y
r
(k ) - V^q"
1
) y(k) , (3 .5 4)
where u is the output of the controller, y
r
the set point and y the process output. V j, V2 and V3
are polynomials of the backward shift operator q~l.
3.4.2. Generalized Minimun Variance Self-Tuning Controllers.
3.4.2.1. Deterministic One-step-ahead Self-tuning Control. We begin with the deterministic case.
We assume, also, that the process delay is d= l. Then , the process model becomes
A ( q -
1
) y ( k ) = B ( q -
1
) u ( k - D . ( 3 .5 5 )
Let y
r
(k) be the set point, not necessarily constant. Also, define a polynomial P(q~') as
P ( q "
1
) = l+p
1
q -
1
+ - + p
I 1
q -
n
. (3.5 6)
Then, our goal is to determine a control law u(k) which minimizes the following quadratic cost
function:
2
j(k+i) = L
p
(q"
1
)[y(
k + 1
)-yr(k+i)]J
;
k> o . (3.57)
P(q"l) determines the dynamic behaviour in which y(k+l) approaches y
r
(k+l). The way to
minimize J(k+1) is to take its first partial derivative with respect to u(k) and set it equal to zero. In
this case, how ever, w e can simplify the calculations if we notice that the minimum value of J(k+1)
can be m ade equal to zero by requiring that
P(q"
1
) [ y ( k+ l ) - y
r
(k + l ) ] = 0 ; k> 0 , (3 .5 8a)
or, equivalently
P ( q "
1
) y ( k
+
l ) = P ( q -
1
) y
r
( k + l ) ; k>0 . ( 3 .58b)
In order to proceed with the derivation of u(k), we define A (q"
1
), B ( q
- 1
) a n d P ( q "
1
) by the
following equations
A (q
1
) = l+ q - ' A V ') (3-59)
B ( q -
1
) = l + q "
1
B V
I
) (3-60)
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P(q
_1
) = l + q V f o "
1
) (3.61)
Then, 3.58 can be written as
[ l + q
1
P * ( q
1
) ]y (k+ l ) = P( q
1
) y
r
(k + l) , (3 .62)
y(k+l) = P(q
1
) y
r
( k +l ) - P V ) y (k) . (3 .63 )
By adding the term A (q~*)y(k) in both sides of
3.63
we obtain
A(q"
1
) y (k+ l ) = P (q ' ) y
r
(k +l)+ [A V ) " P V ) ] y(k) , (3 .64)
and using 3.55 we get
B ( q
1
) u(k) =
?(q
l
)
y
r
( k + l) + [A V ) " P V ) ] y(k ) , (3 .6 5)
which yields the following control law :
u ( k ) =
X [P(q-
1
)y
r
(k
+
l)
+
[ A* ( q -
1
) -P*(q
1
) ]y (k) -B*(q-
1
)u(k-l)] .
( 3
.
6 6 )
b
0
We see that the controller output at time k is a function of the set points y
r
(k+l), y
r
(k ),. . . , of
the process outputs y(k), y (k -l ), . . . , and of the previous controller outputs u(k- l), u(k -2) ,. . .
Equation 3 .66 can be written also as
u(k ) = — L - [P (q -
1
)y
r
(k+l)+[A*(q-
1
) -P*(q-
1
)]y(k)] , (3.67)
B (q
1
)
which implies that the roots of B(q~l), i.e. the process zeros, should lie inside the unit circle or, in
other words, the process should be
minimum phase.
This is necessary, in order to have a stable
control law which will remain bounded when disturbances are present. The transfer function of
the closed loop system can be derived by substituting 3 .67 into 3.55, and this gives
A(q '
1
)y(k+l) = P(q-
1
)y
r
(k+l) + [AV
1
) - P * ( q "
1
)]y (k) - (3.68)
By subtracting 3.61 from 3.59 and substituting above, and by defining
y
P
r
(k+l) = P(q"
1
)y
r
(k+l) (3.69a)
and
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we get
y
P
( k + l )
=
P ( q "
1
) y ( k + l )
,
(3 .69b)
ACqbyCk+l) = y
P
r
(k+l) + q[A(q"VP(q
)]y(k)
,
(3.70)
P ( q
1
) y ( k + l )
=
y
P
r
(k+l)
.
(3 .71)
Therefore,
the
pulse-transfer operator
is
given
by
H( q
1
) = ^ - = V , (3.72)
y
P
( k + l ) P ( q "
1
)
that
is, the
roots
of
P(q~l)
are the
poles
of
the closed loop system,
and
they have
to be
inside
the
unit circle
so as to
result
in a
stable closed loop system.
If
the
model parameters, that
is, the
coefficients
of
A(q" l )
and
B(q" l ) ,
are
known, then
the
computation
of
the control
law
u(k), given
by 3.66, is
straightforward.
If
not, then
we
need first
to estimate them , using
one of
the methods described
in
section 3.3,
and
then com pute
u(k) as in
3.66 where instead
of aj , a2, . . . a
n
,
bQ,
bj , . . . , b
m
, we put
their estimates. This
can be
repeated
in
every sam pling instant
and it
leads
to a
so-called indirect adaptive control schem e.
The
name
is due to the
fact that
the
controller parameters
are not
estimated directly,
but
rather
indirectly, through
the
controller design procedure. Another approach, which leads
to a
direct
scheme,
is
described below.
We
notice that, using
3.69 and
3 .61 ,
the
process model
in 3.55 can
be w ritten
as
y
P
( k + l )
=
B(q"
1
)u (k )
- [A*(q
V p V ) ] y ( k )
•
(3 .73 )
Let
us
define
the
vectors
9
and u(k)
as
6 = [ b
0
- b
m ( a i
-
P i
) - ( a
n
- p
n
)
]
T
(3 .74)
and
_u(k)
= [ u(k) -
u ( k - m )
-y(k) -
- y ( k - n + l )
]
T
,
(3 .75 )
respectively. Th en,
3.73 is
also written
as
y
P
( k + l ) = _ u
T
( k ) _ 9
,
(3 .76)
which
has the
form
of
the regression equation
as in
2.28. Then,
the
parameter estimation methods
of section
3.3 can be
directly applied
for the
estimation
of
the controller param eters. This
can be
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done in every sampling instant, and it leads to a direct adaptive control scheme. Notice that in both
methods, indirect and direct, the number of the estimated parameters is the same, and equal to
m + n + 1 . We see that in the indirect case the controller design step (i.e. the computation of the
controller parameters from the estimated process parameters), has been eliminated, thus resulting
in a simpler method. This, however, will not be always the case as we shall see in the sequel.
We now turn to the case where the process delay d is greater than one. The process model will
be
A( q
1
)y (k ) = B(q-
1
)u( k-d) , (3.77)
and the control law u(k) should minimize the cost function
J(k+d) = [ P(q
_1
) [ y(k+d) - y
r
(k+d) ] ]
;
k>0 (3.78)
which corresponds to 3.57. Let us proceed as previously, that is, define 3.59 - 3.61 and try to
satisfy 3.58 where instead of k+1 we put k+d. By following exactly the same steps, the
corresponding controller equation of 3.65 will be
B(q"
1
) u(k) = P(q-
l
) y
r
(k+d) +
[ A V V P V ) ]
y(k+d-l) . (3.79)
By solving it with respect to u(k), as in 3.66, we see that u(k) depends on the set points y
r
(k+d),
y
r
(k+d-l), . . . , on the previous controller outputs u(k-l), u(k-2), . . . , and on the process
outputs y(k+d-l), y(k+d-2), . . . Thus, the output of the controller at time k will depend on the
output of the process at future times, and this is an undesirable situation since it leads to a
noncausal controller, or in other words, to a control law which depends on outputs of the process
not yet available. This difficulty arises from the fact that in 3.77 the output at time k+d is
expressed as a direct function of the previous outputs at times k +d -1 , k+d-2, . . . In order to
overcome this problem we can transform the model in 3.77 in another equivalent one, where now
the output at time k+d will be a function of the output at the times k, k - 1 , . . . This can be done by
expressing y(k+d) as a function of y(k+d-l), y(k+d-2), . . . , then, expressing y(k+d-l) as a
function of y(k+d-2), y(k+d-3),. . . , and so on, until we arrive at the point where everything is a
function of y(k), y(k- l) , . . . A more systematic and compact way of performing the above
transformation is the following. First, we solve a polynomial identity of the form
P(q"
1
) = A(q
) S(q"
1
) + q"
d
Ttq"
1
) (3.80)
which has a unique solution for S(q
_1
) and T(q
_1
) (see [6],[14]), defined by
S(q"
1
) = l + s ^ + ' - H - s ^ q - " *
1
(3.81)
and
K q '
1
) =
V
T
1
q "
1
+
- + T
n l
q -
n + 1
, (3.82)
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respectively. We define, also, the polyno mials BS (q~l) and BS (q" l) by the equation
BSCq"
1
) = BCq-^SCq"
1
) = b
Q +
q 'B S V ) . (3 .83)
Then, the steps corresponding to 3.62 - 3.64 are as follows. Substituting 3.80 into
PCq'
1
) y(k+d) = PCq'
1
) y
r
(k+d) (3 .84)
yields
[A(q"
1
)S(q"
1
)+q"
d
T(q"
1
) ] y(k+d) = P(q
l
) y
r
(k+ d) , (3 .85 )
or
A ( q "
1
)S(q"
1
)y (k+d) = P(q
1
) y
r
( k + d ) - T ( q "
1
)y(k ) . (3.8 6)
Using 3.77 and 3.83, the last expression becomes
B(q"
1
)S(q"
1
)u (k ) = P(q
1
) y
r
( k + d ) - T ( q ' ) y ( k ) ( 3 .8 7 )
and
[ b ^ q ^ B S ^ q -
) ] u ( k ) = P ( q '
1
) y
r
( k + d ) - T ( q
1
)y (k ) , ( 3 .88)
respectively. Then, the control law is given by
u(k) = - L [ P(q -
1
)y
r
( k + d ) - T ( q -
1
) y ( k ) - B S * ( q -
1
)u (k - l ) ]
( 3
. 8 9 )
b
0
where, now, u(k) is a function of the set points y
r
(k+d) , y
r
(k+d-l), . . . , of the process outputs
y(k),
y(k-l), . . . , and of the previous controller outputs u(k-l), u(k-2), . . . , i .e. it represents a
causal controller. Notice that 3.89 reduces to 3.66 when d=l.
For the adaptive controller based on 3.89, it is interesting to consider the direct and indirect
schemes in more detail. Specifically, for the indirect case we have the following algorithm :
Algorithm 3.1 (Indirect Schemel
1) Estimate the model parameters (coefficients of A(q~l), B (q "'))
2) Compute T(q "
) and S(q"
J
) by solving 3.80
3) Compute u(k) as in 3.89
4) k=k+ l ; go to 1
We see that the controller design is now rather complicated, when compared with that in the case
of d=l, since the solution of the equation 3.80, at each sampling instant, is required. For the
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direct case we proceed as follows. First, we multiply both sides of 3.80 by y(k+d). Then, by
combining the result with the model equation 3.77, we get (compare with 3.73)
PCq^yOc+d) = BS(q"')u(k) + TCq^yCk)
wh ich, by defining approp riate £ and u(k) vectors, can be transformed to a regression equation
similar to 3.76. Therefore, as in that case, the parameter estimation methods of chapter 2 can be
used in order to directly estimate the controller parameters Tj and bsj. Thus, we have the following
algorithm:
Algotithm 3.2 fDirect Schemel
1) Combine 3.77 with 3.80, and form a regression equation
2) Estimate the coefficients of this equation (controller parameters)
3) Compute u(k) as in 3.89
4) k= k+ l ; go to 2
Therefore, we don't need to solve 3.80 at each sampling instant, and this fact greatly simplifies
the computational effort of the adaptive scheme. On the other hand, we notice that the number of
estimated parameters in the indirect scheme is less than that in the direct one. Specifically, in the
indirect scheme we need to estimate n+m+1 parameters, while in the direct one the corresponding
number is n+m+d. Thus, it may happen that the computational effort introduced by step 2
(algorithm 3.2), is bigger than the simplification that the algorithm provides, and as a result, its
overall performance can be worse than the performance of an indirect scheme. That is, there is a
trade-off between the two algorithms, and the choise depends on the specific degrees of the
polynomials B(q~l) and A(q~l) and on the delay d, as well as on various robustness and stability
considerations [5],[6].
At this point a comm ent on the sam pling rate is in order. Assum e that the model 3 .77 describes
a continuous-time process w ith a delay of D seconds. Then, by approximating it by a discrete-time
model we introduce the delay d which, clearly, depends on the sampling rate and it increases
when the sampling period decreases. In order to be more specific, if h is the sampling period,
such that D is a multiple of
h,
then
d = ^ + 1 . ( 3 . 9 0)
h
Since we are interested in reducing the compu tational effort of the parameter estim ation algorithm
as much as possible, we must not choose a very small value of h. On the other hand, we must
keep its value small enough, so that the discrete model adequately describe the process. More
details on the selection of the sampling period in implementing discrete-time control systems, can
b e f o u n d i n [ 5 ] , [ 1 4 ] , [ 2 1 ] .
The controller described by 3 .89 is usually referred to as the one-step-ahead controller because
the criterion which is based on, takes care only of one step ahead ((k+d)th sampling instant).
Criteria including the system behaviour for a set, or horizon, of future sampling instants lead to
control techniques such as Model Predictive Control [23], or Generalized Predictive Control [24].
3.4.2.2. Weighted Control. Frequently, the method described above produces control signals
whose magnitude is quite large. This is due to the specific form of 3.78 which does not include
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any requirements about u(k). One way to put a weight on it, is to consider a cost function of the
form
2
J
1
(k+d)= [ P(q
_1
)[y(k+d)-y
r
(k+d)] J + l-
u
2
(k) ; 1>0 , (3.91)
and minimize it with respect to u(k). Intuitively, this criterion implies that a situation like
y(k+d)=y
r
(k+d) being achieved by a lagre value of u(k) will be avoided, since even if the first
term of the right-hand side of 3.91 is zero, the second one will result in a very large value of
Jj(k+d). Therefore, it may be preferable to reduce the absolute value of u(k) in order to produce a
smaller value for Jj(k+d). For the same reason, a control law based on 3.91 can produce an offset
in the steady state responce of the closed loop system. A slight generalization of the cost function
wh ich alleviates this problem is given by the following :
J
2
( k + d ) = [ P ( q "
1
) [ y ( k + d ) - y
r
(k+d ) ] ] + l . [
u
( k ) - u ( k - l ) ]
2
; 1>0 . (3.92)
W e see now that the weighting is placed on the increm ents of the control signal, rather than on the
signal itself. The term u(k)-u(k-l) can be rewritten as (l-q"')u(k) and by defining Q(q~l)=l-q~l,
3.92 becomes
2
J
2
(k+d)= L P(q"
1
)[y(k+d)-y
r
(k+d)] J + l.[Q(q
1
)
u
(k)]
2
; 1>0 . (3.93)
This form leads to different criteria when different expressions of Q(q~^) are applied. The general
case will be treated later in the context of stochastic self-tuning controllers. For this special case of
J2(k+ d) it can be show n, by diffentiating with respect to u(k), that the control law is given by
u ( k ) =
J _ [ l u ( k - l )
+
b
0
[ P ( q -
1
) y
r
( k + d ) - T ( q -
1
) y ( k ) - B S * ( q -
1
) u ( k - l ) ] ]
( 3
.
9 4 )
b
0 +
l
Notice that if 1=0, then equation 3.89 results. Also, if we just remove the term lu(k-l), then the
resulting controller equation is the one which minimizes Jj(k+d). As both cases are simple
generalizations of the controller in 3.89, their adaptive versions can be obtained in exactly the
same manner as described before. Their application will produce control signals of reduced
magnitude with respect to the previous cases, and for this reason they are useful when constraints
on these signals exist. We must keep in mind, however, that specific maximum or minimum
values of u(k) are not included in 3.93.
The controller equation 3.94 can also be written as
u ( k )
, P ( q -
1
) y ^ d
)
- T ( q ^ ) y ( k )
B ( q -
1
) S ( q -
1
) + ( l / b
n
) ( l - q
1
)
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which implies that it is not necessary for the process to be minimum phase, as long as, the roots
of the denominator of 3.95 are inside the unit circle. Also, by substituting 3.95 into 3.55 we can
easily obtain the closed loop pulse-transfer o perator, given by
H ( q ' ) - - ^ = , / ^ ,
r
. (3.9 6)
yP(k+d) BCq-^PCq-Va/boXl-q-VCq-
1
)
which implies that also the roots of B(q~ l)P(q~l)+(L /bo)(l-q~l)A(q "l) should lie inside the unit
circle, in order for H(q"') to represent a stable closed loop system.
3.4 .2 .3 . Minimum Variance Self-tuning Control. So far we considered the deterministic case,
where C(q"l)=0. In the stochastic case we assume that disturbances are present, which can be
mod elled as a random noise process, say
{h(k)}.
This leads to a process model as in 3.53. In that
model, {e(k)} is a white noise random process and C(q~l) is a polynomial representing any
correlation betw een the random variables of
{h(k)},
whose roots should be inside the unit circle.
We can also assume that co=l[17],[18]. Furthermore, we assume that the random variables e(k)
have zero means and finite variances. Thus, the output of the process y(k) will also be a random
variable and therefore any criterion describing its desired behaviour should include some kind of
probabilistic expectation. In the simplest case, the control law u(k ) mu st minim ize the expectation
J(k+d) = E{ [y(k+d) - y
r
( k + d ) ]
2
} , (3.9 7)
given measurements available at time instant k. Notice that for y
r
(k+d)=0 V k (regulat ion
problem), the criterion becomes the minimization of the output variance. The resulting controller,
when co mbined with the RLS parameter estimation method, leads to the minimum variance
self-
tuning regulator, originally proposed in [9].
In order to minimize the expectation in 3.97 we proceed as follows. First, we determine two
polynomials S(q~l) and T(q~l), defined by 3.81 and 3.82 respectively, by solving the polynomial
equation (compare with 3.80)
C(q"
1
) = A(q-
) S ( q
1
) + q
d
T t q
1
) . (3 .98)
Then, a multiplication of both sides by y(k+d) yields
C ( q "
1
)y (k+d) = A(q"
1
)S(q"
1
)y(k+d) + T(q"
1
)y(k) , (3 .99)
or, equivalently
y
( k + d ) =
A ( q
"
1 ) S
1
( q
"
1 )
y (k + d) + ^ - y (k ) , ( 3. 10 0)
C ( q
1
) C ( q
1
)
and using 3.53 we have that
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y (
k + d
) = 4 r % ^ u (k )+ S( q-
1
)e (k+d)
+
^a
:
l
y ( k )
.
CCq
1
)
CCq"
1
)
(3 .101)
Thus, 3.97 equals
B S
^ ( k ) 3 ^ y ( k ) -
y r
( k
+
d )
-,2
CCq
1
)
CCq
1
)
+EnS(q-
1
)e(k+d)] (3.102)
because {e(k)} and {u(k)} are assumed to be independent, and furthermore, y(k) is independent
of each one of the random variables e(k+d), e(k+d-l), . . . , e(k+l). Finally, since the second
term of 3.102 does not depend on u(k), we require that
^ml
m+
ml
yik)
.
yik+d)=0
CCq"
1
) CCq"
1
)
which yields the control law
(3.103)
u(k)
= J -
[C(q-
1
)y
r
(k+d)-T(q-
1
)y(k)-BS*(q-
1
)u(k-l)]
,
(3.104)
b
0
i.e. the same as that in 3.89 if we chose P (q "') =C (q "') . The m ain difference is that while in the
deterministic case this control law sets the error P(q~l)[y(k+d)-y
r
(k+d)] to zero, in the stochastic
case the minimum value of J(k+d) (eq. 3.97) is given by
W
k + d
) =
E
{ [
s
( q
1
)
e
(
k
+
d
) ]
2
.
= V a r [ e ( k + d ) ] + S j V a r [ e ( k + d - l ) ] + - + s ^ j V a r [ e ( k + l ) ] . (3 .1 05 )
However, the various assumptions pertinent to the stability of both the control law in 3.89 and the
overall closed loop system in the deterministic case, apply also to this case for C(q~l)=P(q~l).
The adaptive version, or minimum variance self-tuning controller, will be a combination of the
controller in 3.104 with a parameter estimation technique. If C(q~l)=l then the RLS algorithm
will suffice, while if C(q"l) is a polynomial of a degree greater than zero, then the ELS method
should be used. As before, either the direct, or the indirect schemes can be applied.
3.4.2.4.
Generalized Minimum Variance Self-tuning Control.
We now present a generalization of
the above controller, which has been introduced in [6], based on the cost function
J(k+d)
=
E {
[P(q-
1
)y(k+d)-R(q-
1
)y
r
(k+d)]
2
+
[Q(q
1
)u(k)]
2
) (3.106)
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which generalizes 3.97. P(q"'), R(q"^) and Q(q"^) are polynomials in q~l where, generally
speaking, Q(q"*) weights the control signal, R(q~l)y
r
(k+d) represents a filtered version of the set
point, and P(q ) greatly affects the dynam ics of the closed loop system . The expectation is
conditioned on system input-output data available at time k. If we remove the expectation, we
have a generalization of 3 .93 for the deterministic case.
The control law which minimizes 3.106 can be shown ([25]) to be given by
Rfa-VOc+d) - (^(k+d/k)
u(k) = —
i
— ^ \ , (3.107)
(q
0
/b
0
)Q(q
1
)
where qo=Q(0), brj=B(0), and <j)
v
(k+d/k) is the least-squares prediction ([22]) of P(q"^)y(k+d)
given data up to k, and it is given by
.
=
T V W + B S ^ M k )
" C(q"
1
)
where BS(q
_ 1
) has been defined in 3 .83. T (q
_ 1
) and S(q"
1
), defined by 3.81 and 3.82
respectively, are determined by solving the polynomial aquation
C(q"
1
)P(q"
1
) = A(q
1
) S ( q "
1
) + q ^ q
1
) . (3 .109 )
By combining 3.107 and 3.108 we get
C ( q W
W
. T ( q ' ) y ( k )
;
B S ( q
1
) + (q
0
/b
0
) Q ( q -
1
) C ( q -
1
)
and the closed loop system output is given by
[ B S ( q -
1
)
+
( q
0
/b
0
) Q ( q -
1
) C ( q -
1
) ] e ( k ) + B ( q -
1
) R ( q -
1
)y
r
(k)
y(k ) = : i ; ; • (3 .111 )
P ( q -
1
) B ( q
1
) + (q
0
/b
0
) Q ( q -
1
) A ( q -
1
)
Thus, this method can be applied also to non-minimum phase processes for which the roots of the
denominator polynomial of 3.111 are inside the unit circle. Notice that if in 3.110 we set C(q"
1)=1, then the resulting control law will be either the one which minimizes 3.106 when the
process model is given by 3.44 with e(k) being white noise, or that which minimizes 3.106 in the
deterministic case (i.e. drop the expectation) where the process model is as in 3.77.
The adaptive version is obtained by combining 3.110 with one of the parameter estimation
algorithm s described in section 3.3 . In the indirect case one has to estimate the coefficients of the
polynomials A, B and C at each sampling instant, and then apply 3.110 by using their estimates.
In the direct case the controller param eters, that is the coefficients of T(q "' ), B S(q
_1
) and C(q
_ 1
) ,
can be estimated by means of 3.108 which can be written as
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n
^/k+d/k) = T C q^ y C y+ B S C q V C k )- ^ c.cfyk+d-i/k-i) . (3.112)
i=l
Thus, upon defining vectors Q and ]i(k), by
-
9
= ^ 0 V V l
b S
0 ^ f
b S
m +
d - l "
C
l " V "
C
n ]
T
(
3
-
113
)
and
u(k) = [ y ( k ) - y ( k - n + l ) u ( k ) - u ( k - m - d - l )
< | > y ( k + d - l / k - l ) - < t ) J ( k + d - n / k - n ) ]
T
(3 .114)
respectively, it becom es
(fyk+d/k) = u
T
(k ) -9 (3 .115)
which is a regression equation, as in 3.28, hence the RLS method can be applied. Notice however
that <t>
v
(k+d/k) is not known because it depends on the parameters, and for the same reason the
vector u.(k) is not completely known. Therefore, an approximation of these quantities has to be
used (compare with ELS). Specifically, we can put instead,
ty(k+d/k) = u
T
( k ) 6 ( k ) ( 3 . 1 1 6 )
where f)(k) is the previous parameter estimate and the symbol "
A
" ov er u i mp lies that the <>-
components in 3.114 have been calculated also by 3.116. Finally, once the estimates of T(q~l),
BS(q"l) and C(q"l) are available, the control law can be readily computed by 3.110.
The choise of the polyno mials P(q"^), R(q ) and Q(q "') depen ds on the specific requirements
of the closed loop system behaviour. A s we mentioned above, P(q"^) affects the closed loop poles
and if, for example, Q(q~l)=0 then equation 3.111 shows that the roots of P(q"^) become poles of
the closed loop response. In the case of sudden set point changes, R(q"*) can be chosen, for
example, as
R(q"
1
) =
T
-—
(3 .117)
1 - rjq"
1
so that to filter the set point. This will be advantageous in many cases since it will reduce the
magnitude of both the control signal and the overshot, at the expense of slower tracking. In this
case r should be chosen such that P(1)=R(1) in order to avoid a steady state offset. Finally, Q(q"
1) is used in order to reduce the magnitude of the control signal. Equations 3.91 and 3.92
represent two such examples forQ(q"^)=l and Q(q"')=l(l-q"'), respectively. More details on the
choise of the above polynomials can be found in [6], [21], [25], [33] and [34].
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3.4 .3 .
Adaptive Controllers B ased O n Pole Placement. In section 3 .4.2 we presented a class of
adaptive controllers which were based on control laws having the form of equation 3.54. In all
cases, these control laws were the result of a minimization of a quadratic cost function as, for
example, in 3.106. In this section we follow a different approach. We assume from the beggining
that the controller is described by an equation as in 3.2 which, by changing the notation, we
rewrite as follows
P(q
_1
)u(k) = R(q
_1
)y
r
(k) - TC q^M k) . (3.118)
Our goal will be to determine appropriate polynomials P(q"^), R(q~') and T(q"'), such that the
closed loop responce possess desired prorerties. For example, we can ask that the poles of the
closed loop transfer function be in prespecified locations (pole placement). The closed loop
responce can be determined by combining 3.118 with the process model 3.53. This gives
q
d
B ( q -
1
) R ( q -
1
) y
r
(k ) + C(q-
1
) P ( q -
1
) e (k )
( 3 u 9 )
A(q-
1
)P(q
1
) + q^BCq-^IXq
1
)
The specific degrees of P(q~l), R(q~*) and T(q~l) depend on the imposed requirements. Note that
we can always take prj=P(0)=l.
In the sequel we discuss the pole placement self-tuning controller, following the approach
which is used in [5] (originally proposed in [35]). For other approaches and more details see also
[6],[21],[36]. The main idea is to place the poles of the closed loop system in some desired
locations by an appropriate choise of the polynom ials P(q~*), R(q ) and T( q" l). From 3.119 we
see that the closed loop poles are the roots of the polynomial (A P+q "^B T)(q" l). Therefore, P(q"^)
and T(q"l) can be determined by equating this polynomial with another one, representing the
desired pole locations, and then solving an algebraic equation with respect to P(q"^) and T(q"l).
By choosing only the poles, however, the behaviour of the closed loop system is not completely
known from the beggining, since the polynomial P(q~l) appears also in the numerator of 3.119.
The same holds for T(q"^), since in some cases we select R(q~l)=T(q~l). Thus, if we want that
the imposed requirements completely specify the behaviour of our system, then the closed loop
zeros must be specified as well.
We consider the deterministic case, for then 3.119 becomes
y « - ,
q
y ? " ' ,
, y , « . (3-.20)
where the process model is given by 3.77 (For extensions to the stochastic case see [5],[6]). Our
objective is to choose the P (q
_ 1
) . T(q
_ 1
) and R(q
_ 1
) such that
y ( k ) =
q d B m ( (
;
}
y
r
(k ) , ( 3 .121)
where B
m
( q "
1
) and A
m
(q "
1
) represent the desired zero and pole locations, respectively. That is,
we require that
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y(k) q^B(q-
1
)R(q-
1
) q X C q '
1
)
( 3 m )
Yr(k) A(q
1
) P ( q -
1
) + q
d
B ( q
1
) T ( q -
1
) A ^ q "
1
)
By comparing the nominators of the above equation we see that, first, some (or all) of the zeros of
the open loop system (roots of B(q~ l)) can beco me zeros of the closed loo p system, and second,
other zeros can be added by means of R(q~l). On the other hand, roots of B(q"l) which are not
desired as roots of B
m
(q~l), have to be cancelled by the denominator of the middle term of 3.122.
Hence, they should be included in P(q~l). Specifically, let B~(q~l) contain the open loop zeros
which appear also in B
m
(q~l), and let B+(q~l) contain those which are cancelled. Then according
to the above discussion we must have that
B(q'
]
) = B V ' j B - f q
1
) (3.123)
and
P ( q
1
) = P
1
(q -
1
)B
+
(q -
1
) . (3 .12 4)
Furthermore, notice that the controller equation 3.118 can be written as
u ( k ) = ^ J - y
r
( k ) - ^ 3 J . y ( k ) . (3.125)
P (q
_ 1
) P(q
_ 1
)
This implies that the roots ofP(q"l) should be inside the unit circle, for the control law to be
stable. Therefore, B
+
(q~l) must contain only well-damped zeros of the open loop transfer
function. That is, only these zeros can be cancelled. The rest must be included in the zeros of the
closed loop transfer function. For this reason B
m
(q~l) will be given as
BJq"
1
) = ffJq^B V) . (3.126)
where B
m
'(q"^) contains additional desired zeros. As we mentioned before, these will be
provided by the polynomial R(q~'), for then
RCq
1
) = R ^ J B ' J q
1
) . (3.127)
We didn't take just R(q"
1
)= B
m
' (q"
1
), because the term Rj(q"l) will be useful afterwards. In the
light of the above definitions, the left-hand side of 3.122 b ecom es
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y ( k
) q -
d
B
+
(q -
1
) B - ( q -
1
)R
1
(q -
1
) B ^ ( q -
1
)
y
r
(k) A ^ P , ( q ^ B V
1
) V B V ^ B X q ^TCq
1
)
(3.128)
q^B^q-^R.Cq"
1
)
AC q^P ^q
1
) + q^BCq-^TCq
1
)
Until now we dealt with the closed loop zeros. The corresponding poles can be determined by
the denominator of 3.128. Normally, we would equate this term with A
m
(q"l) and solve with
respect to P i( q "' ) and T(q~l). A slight generalization is to solve the equation
A C q -b P /q ^ + q V C q ^ T C q ^ A J q - b R j C q "
1
) . (3.129)
This will assure that a solution exists independently of the order of A
m
(q "
1).
Notice that R \ (q" *)
has already been included in the nominator of 3.128 (by means of R(q~l)), so as to be cancelled.
Hence, w e have that
y(k) _ q-Xtq-Xtq-
1
)
Yr(k) A
m
( q -
1
) R
1
( q
1
)
dr> /„-l>
(q .e .d .) . (3 .1 30 )"
a
B
m
(q~')
AJq"
1
)
The above procedure can be applied also to non-minimum phase systems, since only well-
damped zeros are cancelled. Equation 3.129 is the so-called Diophantine equation, and it is
discussed extensively in [5],[6],[14]. Note that it is a generalization of 3.80. In fact, many of the
control design procedures presented in section 3.4.2 can be shown to be special cases of this zero-
pole placement technique [32].
An indirect self-tuning controller based on the above procedure can be summarized in the
following algorithm :
Algorithm 3.3 (Indirect scheme)
1) Specify polynomials A
m
(q
_ 1
), Bjjj'tq"
1
) and Ri(q
_ 1
)
2) Estimate A(q~l) and B(q~l) (model parameters)
3) Determine B+fq"
1
) and B-(q
_1
)
4 ) So l v e 3 .1 2 9 f o r P
1
( q -
1
) a n d T ( q -
1
)
5) Calculate Ptq"
1
) and Rfa"
1
) by 3.124 and 3.127
6) Compute u(k) by 3.125
7) k= k+ l ; go to 2
In order to get a direct scheme we first multiply 3.129 by y(k), and then combine the result with
the process model in 3.77. This yields the equation
A ^ q ^ R / q ' ^ y C k ) = q
d
B - ( q "
1
) [ T ( q -
1
) y ( k ) + P ( q
1
)u ( k ) ] . ( 3 .131)
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The idea is to use this equation in order to directly estimate the controller polynomials T(q"l) and
P ( q " l ) . But as we can see, 3.131 is not linear in the parameters (i.e. it doesn't have the linear
form of equation 3.28) because B~(q"l) multiplies both T(q~l) and P(q~l). In the simplest case,
we can make it linear by taking B"(q"l)=l, but now the method is not applicable to non-minimum
phase systems since all the process zeros are cancelled. Other approaches dealing with this
nonlinearity are described in [5],[27],[32].
3.4.4. Model R eference Adaptive Controllers. A block diagram of a model reference adaptive
control system (MRAS) is shown in figure 3.4 (sec. 3.1.2). The idea is to express the desired
behaviou r of the closed loop system by means of a reference mod el, and then design the controller
in such a way so that the closed loop system "follow" the reference model as close as possible.
Originally, model reference adaptive control systems were developed in the continuous-time
domain where the process was described by state-space equations [11],[12],[13]. Later, the
interest was moved more to the transfer function representation and also to the discrete-time
domain [5],[6].
Traditionally, the design of MRAS was based on stability criteria, which means that the
adaptive control laws were being derived in such a way so as to assure the stability of the closed
loop system. In order to illustrate the early ideas we now present an example where the design of
the adaptive controller is based on the Lyapunov stability criterion [37 ]. As sum e that the process
is described by a first-order differential equation
y( t ) = -a y( t ) + bu( t ) , (3 .1 32 )
where y(t) is the process output, u(t) is the process input, and a,b are constant but unknown
parameters. The problem is to find an adaptive control law such that y(t) follow the output y
m
(t)
of a reference mo del, given by
y
m
W = -a
m
y
m
( t )
+
b
m
u
m
( t ) . (3 .13 3)
We see that a controller of the form
u(t ) =-Cj( t )y( t ) + c
2
( t )u
m
( t ) , (3 .13 4)
when applied to 3.132 yields
y(t) = -[a +b
C l
( t ) ]y ( t ) + [bc
2
( t ) ]u
m
( t ) . (3 .13 5)
The above equation implies that if a and b were known, then a choise of C2(t)=b
m
/b and
c i ( t )= (a
m
-a)/b would suffice. But, since a and b are unkown constants, we proceed as follows.
We first define
e(t) = y
m
(t) - y(t) , (3 .1 36 )
to be the output error. Then , by combining 3 .133 with 3.135 we get
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e(t) = -a
m
e ( t ) - d
1
( t ) y ( t ) + d
2
( t ) u
m
( t )
where
and
dj(t) = a
m
- a - bCj(t)
d
2
(t) = b
m
- b c
2
( t ) .
( 3 .137)
(3 .138)
(3 .139)
Our goal is to appropriately adjust dj(t) and d2(t) so that e(t)—»0, dj(t)—>0 and d2(t)—>0 as
t—>+°°.
Le t d^(t) and d2(t) satisfy differential equa tions of the form
d,( t ) = g
L
(e, y, y
m
)
d
2
(t) = g
2
(e, y, y
m
)
Then the quadratic function
V(e,d
1
,d
2
) = l
b - s g n ( b ) - e
2
( t ) + ^ - d j ( t ) ^ - d
2
( t )
(3 .140)
(3 .141)
,X
x
X
2
>0 (3 .142 )
is a candidate Lyapunov function for the dynamic system described by the equations 3.137, 3.140
and 3.141 [7]. Th is system will be stable, accord ing to the Ly apu no v stability criterion, if the
derivative of V(e,di,d2) with respect to time is negative semidefinite, and this is achieved by
choosing [7]
and
d
1
(t) = X
1
[ b s g n ( b ) ] e ( t ) y ( t )
d
2
( t ) = - y b s g n ( b ) ] e ( t ) u
m
( t ) .
Then, cj(t) and C2(t) will be given by
6
1
(t) = -X
1
s g n ( b ) e ( t ) y ( t )
and
(3 .143 )
(3 .144)
(3 .145)
c
2
( t ) = X
2
s g n ( b ) e ( t ) u
m
( t ) , ( 3 .146)
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respectively, and they represent the adaptive laws. Notice that the sign of the parameter b is
assumed to be known. Also, in order to get a uniformly asymptotically stable system, further
properties on the reference input signal u
m
(t) must be imposed. Finally, since the adaptive laws
3.145 and 3.146 directly adjust the controller parameters, the above procedure corresponds to a
direct MRAS. For details, as well as extensions of the above method to more general cases, the
reader is referred to [7].
We now consider the case where the process is described by a transfer function model, in the
discrete-time domain. Specifically, we assume that the process model is given by 3.77 which we
rewrite below as
A C q
1
) y(k) = q^BCq'
1
) u(k) . (3 .14 7)
The objective is that the process output y(k) follow a reference output y
m
(k) determined by a
reference model given below
A
m
( q
4
) y
m
( k ) = q '
d
B
m
( q
1
) u
m
( k ) . ( 3 .148)
In order to derive a suitable controller form, let Pj(q"l) and T(q~l) be polynomials satisfying
the algebraic equation
AmCq"
1
) = P / q V t q '
1
) + q"
d
T(q
X
) . (3 .149 )
Multiplication of both sides of 3.149 by y(k) yields
A
m
( q ' ) y ( k ) = P / q ' l A t q ' l y f k ) + q
d
T ( q -
1
)y ( k ) , ( 3 .150)
and using 3.147 we get
A
m
(q "
1
)y(k) = q"
d
[P
i
(q -
1
) B ( q "
1
)u(k) + T(q"
1
)y(k)] . (3 .15 1)
By comparing 3.151 and 3.148 we see that a controller of the form
P
1
(q
1
)B(q-
1
)u(k) = B J q ' V ^ ) - TXq-'jyOO (3.152)
would cause y(k)=y
m
(k), in the case of known model parameters. If they are unknown, they can
be estimated using equation 3.148 together with a parameter estimation method. This procedure
results in a indirect MRAS. If, on the other hand, equation 3.151 is used instead, then the
controller parameters can b e directly estimated, thus resulting in a direct sch eme.
By comparing equations 3.149 and 3.152 with 3.129 and 3.118, respectively, we notice that
the above model reference adaptive control scheme can be considered as a special case of the pole
placement design technique, by taking u
m
(k )=y
r
(k), B~(q~l)=l and Ri(q~l)=l, corresponding to
the case where all process zeros are cancelled and no additional zeros are introduced.
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4 . C o n c l u s i o n s
Adaptive control systems result from the combination of two basic techniques, namely, controller
design and parameter estimation. In the general case, the resulting system is a time-varying
nonlinear dynamic system which may be very difficult to analyse. For this reason, theoretical
results exist only for some classes of adaptive control systems.
In the previous chapters we gave a description of self-tuning controllers and model reference
adaptive systems which represent two of the most important classes of adaptive systems for which
stability and convergence results have been established. Also, numerous applications of these
schemes have revealed that they are quite effective in controlling a large number of industrial
processes. Both methods require the existence of a mathematical model which should adequately
describe the process. Usually, the model is given in discrete-time representation since the
implementation is done by means of digital computers. Typical examples are the so-called
ARMAX models. Based on such models, various controller design methods can be applied, as for
example, general ized minimum variance, pole placement, model fol lowing, e .t .c . Final ly,
identification schemes based on the recursive least squares (RLS) are usually applied since they
appear to be the most appropriate for real time applications.
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Vol. 124, No. 10, Oct. 1977.
[35] K. J. Astrom and B. Wittenmark, Self-tuning controllers based on pole-zero placement ,
Proceedings of IEE, Vol. 127, pp. 120-130, 1980.
[36] D. W. Clarke, Model following and pole-placement self-tuners ", Optimal Control
Applications and Methods, Vol. 3, pp. 323-335, 1982.
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200
|37 ] K. S. Narendra and P. Kudva, Stable adap tive schem es for system identification and
control
", IEEE Trans, on Systems, Man, and Cyb ernetics, Vol. SM C-4, No. 6, Nov.
1974.
[38] K. J. Astrom and T. Hagglund,
Automatic Tuning of PIDControllers
", ISA, 1988.
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EARLY ON-LINE DETECTION OF RUNAWAY INITIATION
J .M. ZALDIVAR COMEN GES
Commission of the European Communities
Joint Research Centre
Safety Technology Institute, Process Engineering Division
1-21020 lspra (Varese), Italy
ABSTRACT. In the early stages of a runaway reaction, when the rate of heat generation exceeds
the rate of heat removal by a small amount, it may be possible to restabilize the control of the
reactor by taking emergency actions. The problem is to detect these potentially hazardous
situations in sufficient time to allow the necessary counter-measures to be taken. In this paper, a
general overview of the different techniques for early detection of potentially dangerous situations
will be given and the advantages and disadvantages of each technique w ill be discussed.
1. Introduct ion
Normally, the temperature of a reactor in which exothermic reactions take place is controlled by a
cooling system. If, for some reason (e.g. loss of cooling, loss of mixing, etc.), the rate of heat
generation exceeds the rate of heat removal, the temperature of the reacting mass will begin to rise.
This will cause an increase in the rate of heat generation, due to the exponential dependence of the
reaction rate on the temperature, and the process will continue to accelerate producing a large
amount of heat in a very short time with the consequent dangers for people, installations and
environment.
However, in the early stages, when the rate of heat generation exceeds the rate of heat removal
by a small am ount, it may be possible to restabilize the control of the reactor by taking emergency
actions such as full cooling, fast injection of a suppressant or dumping the reactor contents. The
problem is to detect these potentially hazard ous situations in sufficient time to allow the necessary
counter-measures to be taken to avoid temperature and pressure excursions associated with the loss
of control of such processes. The early detection of these potentially hazardous situations is,
consequently, of great importance in the safe and economic design and operation of a plant.
Control of potential thermal explosion hazards once had to rely on laboratory measurements of
process chemistry and direct control of process variables within fixed limits on the plants. In recent
years,
new techniques have been developed allowing a better understanding of the chemical
reaction [1,2] and improving the methods to control it.
Although the so called off-line tests, performed under laboratory conditions, are necessary, and
should be carried out for each new process, there are some disadvantages which must be taken into
account when the results are evaluated [31. Off-line tests are not totally representative because the
properties of materials being used in the plant are never exactly the same as those of a laboratory
201
A.
Benuzii
and J. M.
Zaldivar
(eds.).
Safety of
Chemical Batch Reactors
and
Storage
Tanks, 201-226.
© 1991
ECSC,
EEC,
EAEC,
Brussels a nd
Luxembourg.
Printed in the Netherlands.
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202
sample. Another disadvantage is the fact that in these tests there is an implicit assumption that the
"worst case" conditions have been identified, and consequently there is the possibility that
unexpected hazards will remain undiscovered. Moreover, in the real processes there are
unpredictable disturbances that affect the process behaviour and can not be simulated in the
laboratory tests. However this can be partially compensated by performing the tests under
conditions (temperature, pressure, initial concentrations, etc.) more severe than those forseen for
the process.
Complementary to these tests, there is another type of procedure to recognize the potential
hazard. These procedures are called on-line supervision, and are carried out in real time, with the
real reaction mixture, equipment and operating conditions. Because of the development and the use
of digital computers, the level of sophistication has increased from simple supervision of directly
measurable variables to complex signal analysis, treatment, and estimation techniques that allow
prediction of state variables or parameters, not directly measurable, to be included in the criteria for
hazard detection. The disavantage of on-line methods is that the information appears only when the
process is outside of the desired conditions and normally in a dangerous state. From all these
considerat ions, i t can be shown that both techniques (off-l ine and on-l ine) should be
complementary.
Ta ble 1. Differences betw een off-line and on
Offline
laboratory
sample
simulated conditions
without disturbances
sensitive to the choice of test conditions
conditions more severe than real process
information obtained before process design
line prevention measures [3].
On-line
actual process materials
process equipment
real conditions
with disturbances
non sensitive
information appears only when the
process is outside desired
conditions
There is a fundamental requirement that early detection should provide sufficient time for plant
operators to correct the deviation from safe operation. However early on-line detection of
hazardo us states is difficult [4] because a chemical process is described by a large num ber of state
variables, such as temperatures, pressures, concentrations, etc. and only some of these can be
measured on-line with an acceptable response time to allow the information to be used for the
detection procedure. Particularly for batch chemical reactors, the difficulties are increased due to the
wide range of processes that are carried out, and their complexity, strong non-linearity and time-
dependen ces (in a batch cycle there is no steady state).
2 . Early on- l ine Detect ion Techniques
2.1.
DETECTION SYSTEM
A process (see fig. 1) can be described by an equation of the form:
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y =f{x, n, w, ©}
(1)
where n(t) and y(t) are the measurable input and output variables, w(t) represents non-measurable
disturbance signals from the process and its manipulating and measuring equipment, © non-
measurable process parameters, and x(t) non-measurable state variables. The process parameters
are constants or slow time-variable coefficients, while the state variables are time-dependent.
Disturbances
Control
va r iab les
T ><
( t ) |
Figure 1. Representation of a process with measurable input variables a, measurable output
variables y and non-directly measurable disturbance variables w, process parameters © and state
var iables St.
If a process fault (a non-permitted deviation of a characteristic property which leads to the
inability to fulfil the intended purpose) appears, it has to be detected as early as possible. In order to
accomplish this objective, the detection system (see fig. 2) consists of the following parts:
- Interface with the process in order to acquire data (monitoring).
- Criteria to distinguish between dangerous situations and non-dangerous ones (detection)
- Procedure for triggering off the alarms (diagnosis and evaluation)
After the detection system has found a fault in the process, the decision abou t the co unter-measures
to be adopted has to be made .
D i s t u r b a n c e s
Control
var iables
i
PROCESS
DETECTION
SYSTEM
Measured
var iables
r
A l a r m ?
Figure 2. Block diagram of a detection system.
The methods for early on-line detection can be divided into two categories depending upon the
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quantities being used [5]:
- Measurable signals.
- Non-measurable state variables, process parameters or characteristic quantities.
In the former case, measurable information about the status of the process is used in order to detect
a malfunction. In the latter case, it is necessary to develop estimation methods and process models
in order to calculate the non-measurable quantities that will be used afterwards in the criteria for the
detection system.
2.2. MEASURABLE SIGNALS
2.2.1.
Limit checking. Measurable input iu(t) and output y(t) variables can be directly used to
monitor changes in the process. The method consists of on-line measurement of a determined
variable checked against preselected limit values. The hazard identification criterion is:
y
(
<yXt) < y
;
2)
This is referred to an absolute value check. If the measured variable exceeds the set limit, alarm
or automatic counter-measures must be initiated. The most common is temperature supervision [3],
but recent theoretical studies show that detection procedures based on pressure are more suitable in
certain conditions [6]. However for practical applications the sensitivity and reliability of the sensor
play an important role to determine the choice of the detection system.
A number of other variables: pH, viscosity, thermal conductivity, etc. are also easily measurable
and can be used for some processes, for example, oxidation can be a dangerous secondary reaction;
therefore the oxidation-reduction potential (Redox) of the reacting medium is a good measure in
order to detect initiation of these reactions at its earliest stage.
The limits are usually so set that a large enough distance to the non-return point is retained on the
one hand, while avoiding false alarms on the other. In general these measures are easy and cheap to
install and can have good predictive capacity, but they are completely dependent on knowledge of
the process and are unsuitable for detection of unexpected dangers.
2.2.2. Supervision of the rate of increase and/or acceleration. The limit check can also be applied to
the derivative of the signal. The hazard identification criteria in this case is:
dy=
dt
dy
;
< — <
dt
ty
dt
3)
for the rate increase, and
o V ,
< J .
2
J
4<
dt
2
^
dt
A
4)
for the acceleration.
The loss of control of exothermic batch or semibatch processes is characterised by thermal and
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205
pressure excursions of the reacting mass due to the large amounts of heat released in a very short
time. That means that the derivatives of temperature and pressure or derivatives of the rate increase
can be used to predict the runaway excursion.
Th e m ethod of supe rvising the rate of temperature or pressure rise is not as cheap or as simple as
temperature or pressure measurement, because amplification and filtering are necessary before
reliable derivative can be calculated. Since the "safe" temperature or pressure need not be specified,
the independence and selectivity of this method is higher, but depends also on specific kovvledge of
the system in order to define the limits.
The method of monitoring the acceleration is similar to the previous method; the predictive ability
is however higher.
2.2.3. Frequency analysis. A physical process can be described either in the time domain, by the
value of some quantity as a function of time, or in the frequency domain, where the process is
specified by giving its amplitude as a function of frequency. The method to change from one
representation to another is by m eans of the Fourier transform equations:
y(co) = y( t) -e
i r a t
-dt
y(t)
J
y(co)e"
1 C D t
-dco
(5)
(6)
Output signals Y(t) often consist of lower frequency components with large magnitudes which
mainly determine the nominal values of the signal, and higher frequency components with small
amplitudes which give additional information on the inner state of the process. Some attempts have
been made to identify frequency signal patterns and to pinpoint process errors from the changes in
their corresponding frequency behavior. A simple approach [7] consists of representing the
frequency response by its amplitude ratio and phase angle (see fig.3) and then defining the upper
and lower limits tolerated in the case of a change in the typical pattern obtained when the process is
operating under normal conditions.
Real axis
Figure 3. Polar representation of the transfer function with the tolerance limits.
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206
Simple bounds at one frequency are not very effective for fault detection. Instead, fault
dictionaries need to be prepared in which bounds are placed at several different frequencies or more
comp lex characteristics need to be examined [8].
2.2.4.
Recipe-based supervision.
Th e hazard identification criterion is the devia tion of some
characteristic values, or of status of different parts of equipment from the "recipe". The procedure
consists of observing the time record of one or more process variables or parameters, computing
simple statistics of the variables, and carrying out elementary tests to detect faulty operation.
Normally the practical application of this method is through control charts [7], which are a
graphical means of representation and analysis (see figure 4).
When the process is subject only to variations due to random fluctuation, such as that
engendered by environmental changes, internal mixing conditions, etc. then it is possible to say that
it is "in statistical control". If some change takes place via a non-random change, such as
engendered by a deterministic component added to the process variable, the process is "out of
statistical control". Consequently, "in control" means that the same probability distribution will
continue to represent the observed variable as the process goes on. The objective of control charts
is to provide a visual observation of the measured variable and to detect the category change as
soon as possible after it occurs.
•
• m
•
• •
• m
Upper control limit
. . ' •
• •
Lower control l imit
T i m e
Figure 4. A process quality control chart.
This method is completely specific for a process, fully dependent on knowledge, data available,
and judgements. For these reasons it is better for continuous processes at steady-state rather than
for batch processes in which all the variables change with time and there is no steady-state that can
be used as a reference.
The predictive ability and selectivity are given by the quality of the evaluation and specification of
the hazard limits.
2.2.5. Detection of the progressive increase of heat evolution. The hazard identification criterion is:
'Generated
r\
(7)
dt
where qc.eneraied '
s t n e
P
o w e r
generated by chemical reaction. The principle applied is based on a
simple heat balance:
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F
dt
U S ( T
m
-T
c
)
(8)
Power generated = power used to increase the temperature of the reaction mixture + power
removed by the jacket.
From expression (8) it is possible to obtain:
dt
P
d t
2 dt
supposing MCp and US independent of time.
^ d ( T
m
- T
c
)
(9)
.......
t
.. .
>o
mm
^Potent ia l ly dangerous
Jzone J~r
d r
Figure 5. Delimitation of the potentially dangerous region [9].
The criteria of eq. (7) defines two different regions separated by the line dq^dt =0. The region in
which the heat output of the reaction declines can be considered non-hazardous. However two
other zones in the region in which the heat output of the reaction inc reases, can be discarded from
the potentially dangerous region (see fig.5). In the former, the power accumulated in the reaction
mixture increases and the power removed through the jacket decreases; this is due to deliberate
heating of the heat transfer fluid by the control system and, in principle, is not dangerous. In the
latter, the heat removed increases and the heat accumulated decreases, so in this situation the
reaction is under control. Hence, for the purpose of hazard recognition it is sufficient to check the
following two expressions:
d
2
T
n
d t
2
> 0 and
d ( T
m
- T
c
)
dt
(10)
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208
For the evaluation of these criteria there is a comercially available system, that was developed by
Hub [3], and is called OLIWA. Figure 6 shows an idealized form of the flow diagram of the
OL1WA system.
OLIWA MONITORING
SYSTEM
Figure 6. Diagram of the OL IWA (On-LIne WA rning) system.
The strong point of the OLIWA system is its independence of knowledge about the supervised
process. It is the only on-line method, which in principle does not require any setting, adjustment,
or information on the process or equipment. A nother advantage is that only the measurement of two
temperatures is necessary for the hazard identification. The disavantage is that disturbances, always
superimposed on the measurement signal, become amplified and considerably affect the result of
the evaluation. Hence, digital filters of high order and also various auxiliary algorithms must be
employed to smooth out the differential coefficients and to avoid false alarms.
In practice, positive values of the derivatives are allowed up to upper limits Ei and £2, and the
alarm is triggered off only if these limits are exceeded by a time interval greater than
A t
m
j
n
.
The
variables E\, £2
a n
d
At
nl
j
n
must be adjusted for each process [9].
2 . 3 .
NON -MEASU RABLE STATE VARIABLE S, PROCESS PARAM ETERS OR
CHARACTERISTICS QUANTITIES
If a mathe matical model of the process exists, the state of the reactor can be reconstructed from
measurable variables, which will allow predictive calculation of the future status or at least,
evaluation of new criteria based on these non-measurable quantities. That means that highest
predictive power and selectivity can be reached and hence better early detection of hazardous states
can be ob tained.
Figure 7 illustrates the general structure of a model-based detection system. Firstly, all the
know n inform ation about the process is put in the form of a ma them atical m odel that normally
consists of a set of algebraic and differential equation s. This m odel is solved on-line by num erical
procedures in order to obtain the whole state of the batch reactor.
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In addition to the available measured variables, the model-based detection system must be
supplied with all the control variables, and the initial and operating conditions. The simulated
variables must be compared with the measured variables; a non-zero difference will indicate an
incorrect calculation in the model that can be due to unknown disturbances, unknown initial
conditions, erroneous parameters, etc. Consequently, the model must be corrected from process
measurements. The method to correct these deviations is by minimizing the error using estimation
techniques, for instance, a state variable observer (deterministic case) [10] or state variable filter
(stochastic case) can be used [11].
Control
va r iab les .
1
PROCESS
Disturbances
Measured
v a r i a b l e s ^
Error between
predicted and
0
bserved respons
Mathemat ica
model of the
process
State var iables,
paramete rs ,
x i i a iac te r i s t i c
Est imat ion
techniques
quar tities
Pattern
recognit ion
(Cr i te r ia )
*
M o d e l - b a s e d
d e t e c t i o n s y s t e m
Alarm ?
Figure 7. Block diagram of a model-based detection system.
Once the whole state of the system is estimated and the error between predicted and observed
responses has been minimised by modifying parameters in the model, different criteria can be
applied using data estimated.
It is possible to divide these m ethod s, depend ing on the type of quantities in which the safety
criteria is based [5]:
- Non-measurable state variables
- Non-measurable process parameters
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- Non-measurable characteristic quantities
2.3.1.
Non-measurable state variables. As was pinpointed before, once all the state variables of the
system are known, different criteria based on non directly measurable parameters can be applied.
For instance, Gilles and Schuler [12] developed another criterion for the definition of dangerous
reaction states by examination of the inflection of phase trajectories for dimensionless temperature
and conversion variables:
C - C T T"
A
0
A l
m
- l i r ^ E
a
x, = — , x„
C
4
'
2
T _ R T
m
(11)
They demo strated that for a batch reactor in which a simple reaction, with decom position behaviour
(nA
—»
products) , takes place and in which a proportional controller regulates the temperature of
the jacket, the phase trajectories show a positive inflection when the reaction is self-accelerating,
and that all points in the phase plane for which the conditions:
dx_ d x„
— - > 0 an d — - ? - > 0
d x
i dx^
(12)
apply are dangerous reaction states.
Similar procedure, based on conversion, can be applied if the criteria of eq. (7) is used and q
G
is
defined as:
q „ = V
m
-AH-r (13)
lG ~ ' m
and hence,
dq,
^ T = V
m
A H . |
(14)
supposing that the volume of the reaction mixture does not change considerably during the reaction
(approximately true for batch processes).
This type of criteria can be extended and applied only if the conversion can be measured or
inferred on-line. The measurement of this variable is difficult or expensive in most cases,
consequently model based techniques for estimating the conversion are necessary for the use of
such as criteria.
An other similar approach was followed by Bonvin and Saner [1 3]. They developeded an on-line
procedure for supervising the operation of batch reactors with the aim not to detect runaway
initiation but the entrace of a disturbance in the system . Th e general procedu re was based on the
estimation of the rate of heat production by two different methods. The former used kinetic
reconstruction from temperature and time measurement, eq. (13), to infer the conversion and the
heat evolution of the reaction. The latter used calorimetric reconstruction based on a model of the
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211
reactor to estimate the total heat which evolves in the reactor, eq. (8). The difference between the
two estimates indicated that a disturbance had entered the system. For example, if during a reaction
there is a disturbance in the heat transfer coefficient (U) due to a stirring problem, the estimation of
the rate of heat production using the calorimetric approach will not be correct because it is based on
the calculated value of U by simulation, while the kinetic approach does not depend on the reactor
model, and consequently will not be affected.
2.3.2. Non-measurable process param eters. Process parameters are constants or slow time-
dependent coefficients which appear in the mathematical description of the relationship between the
input and the output of the mathematical model, i.e. overall heat transfer coefficient (U), heat
transfer area (S ), kinetic parameters, heat capacity (Cp), etc.
There are no applications in literature for tine use of these parameters for safety criteria for batch
or semibatch chemical process, but for instance, if the kinetic parameters are changing it is normal
to infer that an unexpected reaction has taken place and this could be used for detecting
decomposition reactions. The following method, practically the same as that for non-measurable
process variables, should be used for this purpose [5]:
- Establishment of the process equation for the measurable input and output variables by theoretical
modelling.
Y ( t ) = f { U ( t ) , © } (15)
- Determination of the relationship between the model parameters 6; and the physical proce
coefficients pj:
© = f(p ) (16)
- Estimation of the model parameters 9; as results of measurements of the signals Y(t) and U(t).
- Calculation of process coefficients:
P = f '(© ) (17)
and determination of their changes Apj.
- Possible process fault can be pinpointed if there are changes in the Apj coefficients.
2.3.3. Non-measurable characteristic quan tities. Normally the checking.of characteristic quantities
can give im portant inform ation on the inner state when s upervisin g larger plants 15], but for small
installations such as those used in batch or semibatch processes they do not seem to be very
adeq uate. Examples of characteristic quantities are:
- Efficiency (e.g. all types of engines and mach ines, heat exc hange rs)
- Energy consumption per unit time (e.g. stirrer, pumps)
- Wear per unit time
These characteristic quantities must be determined from measurable variables:
:SS
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n = g{u,Y}
Mostly, static relationships are sufficient.
(18)
3 . Experimental and Analyt ical results
3.1.
DESCRIPTION OF EXPERIMENTS
3 .1 .1 . Materials and Method. The reaction ch osen for this set of expe rime nts to test the
possibilities of early detection of runaway initiation, was the esterification between propionic
anhy dride and 2-bu tanol [14]. This reaction has some ad vantages that mak e it very interesting for
safety studies:
- Hom ogeneous reaction
- No danger of decomposition reactions.
- Reaction rate variable in function of catalyst (strong acid, i.e. sulphuric acid)
- Autocatalytic behavior for 0.8% sulphuric acid, in the sense that the maximum of the reaction rate
is reached at approx. 5 0% of conversion . This imp lies that the early detection is more difficult due
to this accelerating phenomena.
( C H J - C H J - C O ^ O
H +
CHj-CHOH-CH^CH
CH -CH -COOH
3 2
CHj -CH2-COOCH-CH -CH
CH
The system investigated was a 1:1 molar mixture of 2-butanol and propionic anhydride. The
process was carried out in a RC1 reaction calorimeter [2] of 2
1
of volume. Initially the =6.8 mols
of 2-butanol containing 0.8% in weight of sulphuric acid were added to the reactor, and allowed to
reach thermal equilibrium, the same number of mols of the propionic anhydride were then rapidly
introduced (=10 s.). Different series of experiments in isoperibolic (modifying the jacket
temperature) and isothermal conditions (varying the reactor temperature set-point) were performed.
3.1.2. Isoperibolic experiments [14]. Figure 8 represents a set of isoperibo lic experime nts
(constant jacket temperature).
The initial drop in the temperature of the reacting mass is associated with the endothermic
mixing of the reagents. The effect of jacket temperature on the rate of reaction can be seen from the
changes in the reactor temperature-time profiles, with high temperatures leading to exothermic
runaway.
Table 2. Jacket temperature for the different isoperibolic experim ents.
Experiment
El
E2
E3
E4
E5
E6
T e H O
293.9
295.7
298.2
300.7
303.2
308.2
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n 1 1 1 r
0 1200 2400 3 6 0 0 4 8 0 0 6 0 0 0 7 2 0 0 8 4 0 0 9 6 0 0 tBOO 12000
Time (s)
Figure 8. Esterification reaction: Isoperibolic experim ents.
3.1.3 . Isothermal experiments [14]. Figure 9 represents "isothermal" experiments m odifying the
reactor temperature set-point.
~\ 1 1 1 T 1 1 1 r
1300 2600 3900 5200 6500 7800 9 t» tt+ 00 11700 13000
Time (s)
Figure 9. Esterification reaction: Isothermal experim ents.
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Table 3 . Jacket temperature for the different isothermal ex periments.
Experiment
E7
E8
E9
Tm set point (K)
296.4
304.2
313.2
Figure 10 shows the experiment E9. The "strange" behaviour of the cooling jacket temperature
is explained due to the fact that when the RC1 alarm system started (the maximum reactor
temperature parameter was set at 100 °C), the emergency cooling programme was triggered off and
the safety valve was opened to increase the cooling power. Afterwards, when the reactor
temperature was decreasing and the emergency was cancelled, the RC1 tried to mantain a 50 °C
difference between T
m
and T
e
in order to protect the glass reactor against breakag e.
410
1
150
I
300
I
450
1 1 1
600 750 900
Time (s)
1
C50
I
1200
050 S »
Figure 10. Esterification reaction: Isothermal experiment E9. Temperature-time profiles for the
reactor (Tm) and jacket (T
e
) respectively.
3.2. OLIWA TESTS
The OLIWA system was tested using the esterification reaction described above. The OLIWA
system has three different alarm levels [15]: a/ Pre-alarm (flashing light with increasing on-time
and constant cycle), b/ Alarm (acoustic signal and flashing light together, with increasing on-time
and constant cycle), c/ Extreme danger alarm (continuous acoustic and optical signals).
Two independent temperature sensors were placed in the reaction calorimeter in order to
measure the reactor and jacket temperature, and connected to the OLIWA system. The signals of
these two m easu res, the first and second deriv atives of reactor tem pera ture, as well as the first
derivative of the temperature difference between reactor and jacket, and the alarm level were
recorded independently of the RC1 data acquisition system.
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376
"T
752
T
1128
n 1 1 1 r
« H B 80 2256 2632 3008 3384 3760
Time(s)
Figure 11. Reactor and jacke t temperature of the experimen t E5.
10
d 2 T m / d t 2 « W
^f-
Akrm level
T n 1 ^ T
-
^ 1 1
1128 "604 B80 2256 2632 3008 3384 3760
Time(s)
Figure 12. Values of the two variables of the criteria used by the OLIWA system and alarm level in
experiment E5.
Figure 11 and 12 show a typical isoperibolic experiment and the OLIWA results. There are two
alarm s, the first at approx. 927 s and the second at approx. 1408 s, which con vert into an extreme
danger alarm, while the time for the maximum temperature is approx. 1969 s.
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The results of the OL1WA experiments show that potentially dangerous reaction states can
be detected in the early stages if the reactions proceed slowly at the beginning. In the case of
autocatalytic or radical type behaviour the time for taking counter-measures is reduced due to the
fact that the self-heating process is enhanced by the effect of the concentration in the Arrhenius
expression for the reaction rate and in some circumstances the OLIWA is not useful.
M oreove r, the existence of an alarm does not imply that the system will runaway (see figure 8,
E l ) ,
because perhaps all the reactants will be consumed. Consequently, the installation of such a
device should provide a warning, but should not substitute the judgment of the people in charge of
the plant.
3 .3 . DEVELOPMENT OF AN IN-HOUSE WARNING SYSTEM
The OLIWA system is a dedicated equipment with its own micro-processor and can be used
simultaneously for five reactors or storage tanks. In the case of a single system, if a reliable on-line
estimate of both temperature derivatives can be made, then the criteria given by eq. (10) can be
used as a part of the warning system of the installation, and this can be carried out in a personal
com puter or as part of the control system.
3.3.1.
Signal treatment and noise suppression. The numerical methods for differentiation, i.e. eq.
(19) for five centered points and eq.(20) for nine centered points are affected by the disturbances
superimposed on the measurement signal. This can lead to rate estimates that amplify this effect
making the use of these values for early warning detection very difficult (see figure 13.a).
f (
X
) = _L_ [f(V
2 h
) -8f(x
0
-h)+8f(x
0
+h)-f(x
0
+2h)]
( 1 9 )
0
12h
fYv
^
- 1 F3f(x
n
+4h)+16f(x
n
+3h)-36f(x
n
+2h)+48f(x
n
+h)-48f(x
n
-h)
U
°
;
" 2 8 0 h o o o o o
f-36f(x
0
-2h)-16f(x
0
-3h)+3f(x
0
-4h)] (20)
where h is the interval between successive x values.
There are many available techniques for minimizing the noise in the calculation of the
derivatives, but only very simple digital filters will be considered in this section. A more
comprehensive treatment of digital filtering is available elsewhere [16, 17].
- Exponential filters: If we denote the samples of the measured variable as x
n
_i, x
n
... and the
corresponding filtering values as y
n
_i, y
n
... where n refers to the current sampling instant, the eq.
(21) gives the filtered measurement as a weighted sum of the current measurement x
n
and the
filtered value at the previous sampling instant y
n
.i . This is a single exponential smoothing (see
figure 13.b)
y
n
= a x
n
+ ( l - a ) y
n l
(21)
a is defined as ,
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217
a =
(22)
At
+ 1
where At is the sampling period and if the time constant of the filter. Limiting cases for a are: oc= 1
(no filtering), a=0 (the measurement is ignored).
Another similar filter is the double exponential or second-order filter, which offers some
advantages for eliminating high-frequency noise (see figure 13.c).
y
n
= Yaxn+(
2
-Y-a)y
n
_
r
( l-a)( l-y)y
n 2
(23)
a and y
are
defined in the same way as previously
r-
» ■
6
4
2
0
-2
-4
■6
-t
-D
lETm/dO' ld
- 1 1 1 r
-
85
370 555
740 525 110
Tn»(i )
a/
1295 H80 66 5
y dflm-Te)/«
• U 2
(CTm/dO*
1*3
»
370 555
740 925 II I
fine (a)
H » 1565 B50
b/
(CTm/dt2*l*3
IB 370 555
- 1 1 1 T
740
925 110
TVre(i)
C/
C-j
0
- 4 -
-6 -
■ « -
- t -
^
*
dam-T«)/dl'l i2
(OTm/iM'UJ
J
_v
K80 B65 - B50 o K 370 555
740
925 II D
Trt»(j)
d/
1295 1460 K 5 850
Figure
13.
Derivatives
of
criteria
from
eq.
(10)
in
experiment
E5.
a/
Single
exponential
filter,
Tp=20
s,
b/
Double
exponential
filter
tpi=
7
s
and
Tp2=
8
s,
c/
Moving
average filter,
=
20
points.
-
Moving
average
filter:
This
filter
averages
a
specified
number
of past
data
points,
by
giving
equal
weight to each data point (see figure 13.d).
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218
y
n
:
n
i=n- j+ l
(24)
where
j is
the number of past data points that are being averaged.
Comparing
the
three different filters and using
the
same arbitrary margin
for
th e level
of
derivatives and
for
th e time interval
in
which they must exceed these limits,
the
detection
is
achieved at 1556, 1504 and 1400 s respectively. The same type of treatment was carried out for
exper iment E9,
the
results
are
shown
in
figure
14. In
this case
the
t ime
for the
maximum
temperature was 556
s.
Using the same criteria, th e detection
is
achieved
at
364, 348 and 328
s
respectively.
Better results can be obtained applying adaptive filters similar to exponentials bu t using variable
averaging weights [18]
or
Kalman filters [11]. The disadvantage
is
that extra computat ion
is
required
but
they
provide
standard
error
estimates
that
ca n
be
used
in
formulating
decision
rules,
reducing the false alarm risks.
T
« -
36-
24 -
E -
- 0 -
- 24 -
- 36 -
- 48 -
1
.
91
dCTm-WUtf
1
<tZrm/*2 U3
112
63
204
255
306
Tn«(i )
357
40B
A
■y
459
5
6 0 -
4 8 -
36 -
24 -
0 -
0 -
- 0 -
- 24 -
- 36 -
- 4 8 -
D
(
51
dCIm-T.y*'li2
/ ( B W d B ' U J
IK
83
204
255
306
Trab)
357
403
-^y
459
5
a/
b/
6 0 -
4 t -
36 -
2 4 -
0 -
-a-
- 24 -
3 6 J
- 4 8 -
1
\
V
1
51
dCIrn-W*
•
U2
/ <ZI>n/iK'U3
IQ
E3
204
255
306
T imd)
d
357
405
459
5
6 0 -
4 8 -
36 -
2 4 -
0 -
0 -
-B -
- 24 -
n36-
- 4 8 -
0
0
1
51
dCTm-T.Vdl
•
U2
\
/
/
dTIm/da l*
112
B3
204
255
306
Th»W
d/
357
l
408
J
/
459
5
Figure
14.
Derivatives
of
criteria
from
eq.
(10)
in
experiment
E9.
a/
Single
exponential
filter,
Tp=20 s, b/ Double exponential filter TFI= 7 s and Tp2= 8 s, c/ Moving average filter, j = 20 points.
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219
Moreover, in order to avoid false alarms due to the noise, it is necessary to define a certain limit
value greater than zero. However, this will reduce the sensitivity for small values of derivatives,
that means, the slow starting self-heating processes will be detected later. In order to correct this
problem is interesting also to evaluate [15]:
± f
2
d t > e .
d t
z
(25)
ps
™ I ^ d t > £ ,
dt
4
(26)
3.4. MODEL-BASED APPLICATIONS
A numerical simulator able to reproduce the dynamic behaviour of chemical processes carried
out in a RC1 reaction Calorime ter was developed [29]. Th e results of experimental and simu lated
data of experiment E9 are shown in figure 15.
41) •
1
160
I
320
1
480
1 1 1
64 0 800 960
Time
(s)
I
1120
I
1280
1440
1600
Figure 15. Exp erimental and simulated temp eratures of the reacting mass and the heating/cooling
jack et in a runaway scenario in the RC1 Reaction Calorimeter for experiment E9.
3.4.1. Off-line application. As the simulator exists, the application of criteria given by eq. (10) and
other criteria based on conversion or another non-measurable state variable or parameter may be
carried out. The advan tage of this approach is that the experimental noise can be eliminated. Figure
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220
16 shows the application of the criteria given by eq. (10) to the simulated results.
dfJm-Te)/dt«te2
Simulated
I I
204 255 306 357 408 459
Time(s)
Figure 16. Derivatives of criteria from eq. (10) using simulated data.
5t)
Figure 17 shows the evolution of derivatives of criteria given by eq. (12).
60
n i i i i i r
0.02 0.03 0 J0 4 0.04 0.05 0.06 0.07 0.08 0.08 0.09
x1
Figure 17. Derivatives of criteria from eq. (12) using simulated d ata.
3.4.2. On-line developments . Up to now, the model-based criteria for early detection of runaway
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221
initiation have been applied off-line, but this technique has been developed to solve on-line the
mathematical model of the process and to correct it by comparison with the real measurement [19-
22].
Some applications for incipient fault diagnosis in chemical process have been reported [23], and
particularly, Gilles, King and Schuler [4,12, 24] who studied the application to detect hazardous
states in a batch chemical reactor.
The first step for a development of such system is the reconstruction of the state of the system
and/or the estimation of some parameters. In order to achieve it, the most common method is the
Kalman filter [11], but other methods can be used (i.e. Lainiotis filters [25], etc.).
Th e mode l of a chem ical pro cess , in this case a batch reactor, can be be represe nted by the
following expression:
x = F ( x
r
x
2
, . . . , x
n >
Q
V
Q
T
...,9
p
) (27)
where x; are the state variables and 0j the model parameters. Through linearization by Taylor series
around any operating point, it is possible to obtain the following stochastic state-space model:
x(t) = Ax (t)+ E n( t) (28)
y(t)=Mz(t)+v(t) (29)
where x is an n dimensional state vector of the process, n is an r dimensional vector of inputs to
the proc ess; y is an m dimensional ind epend ent me asurem ent vec tor; and v is an m dimensional
gaussian random noise vector for the measurements; A,B and M are coefficient matrices with
appropriate dimensions.
The linear model given by eq. (28) and (29) can be discretised under the assumption that a is
constant over a sampling interval. Hence,
\
+
l = *
X
k
+ r
\
+ W
k (30)
y
k
=
M
k
X
k
+ V
k (3D
where, 4>= e
A A l
, T= A-\fy-'iyB and w is an r dimension al gaussian random noise for the inputs.
The equations of discrete Kalman filter recursive algorithm are summarized in Table 4. A more
detailed and rigorous de scription is available elsewhe re [2 6,2 7]. Th e discrete K alman filter gives
an estimate x of the state x at the time sam ple k +1 . This estimate is based on the previous estimate
x
k
and the previous measurement y
k
. K
k
is the filter gain vector that minimizes the covariance P of
the estimation error. Moreover, if some parameters 9, need to be estimated along with the original
state vector, the Kalman filter algorithm can be extended by introducing these parameters in the
state vector [26,27].
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222
Table 4. Summary of discrete Kalman filter recursive algorithm
- Prediction:
*
k+
i
=
* k
+
i V
r
A
p
k + 1
= i W L i
+
Q
k
. Q
k
= § K - » f }
- Correction:
K
= P
M
T
M. .P. ,ml ,
+R.
,] R
^ k + 1 ^ k + l ^ k + l l
k+1 k+1 k+1 k+U . ^k
\
+
l
=
\
+l
^J
y
-
M
*^
P
k
+
, =
P
k
+
, -
K
k
+
l
M
k
+
,
P
k
+
l
=
^ V
V
k}
King
and
Gilles
[4,24],
in
order
to
take into accou nt that different fault mode s have
to be
considered,
and
that the w arning system
in
order
to be
efective shou ld
be
able
to
distinguish
betw een the m, applied different filters for every po ssible fault mo del (see figure 18) and using the
information provided
by
the filter abou t the qu ality
of
estimates
it
was possible
to
discriminate
between rival models using the Bayes rule [28].
Process
Filter 1
Normal process
Filter
2
Fault type
1
Filter 3
Fault type
2
Filter 4
Fault type
3
Figure 18. Multiple filter method
for
fault discrim ination using the Baye s rule
to
determine the
model which fits best the measurements.
5 . C o n c l u s i o n s
Early warning detection based
on
temperature derivatives
is
feasible
and
should serve
as a
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223
warning for plant operators. Moreover, it can be easily implemented on a microcomputer linked to
ordinary measurement devices.
On-line model based measuring techniques have the highest predictive power and selectivity.
Even though the development of a mathematical model is time consuming, once it has been built-
up, it can be applied not only for safety but also for optimization purposes increasing the yield and
minimizing the time for each batch, and consequently can be justified economically.
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224
N O T A T I O N
A
A
B
C
Cp
E
a
H
k
K
IP
q
M
M
R
r
S
T
U
US
m
V
V
<w
%
y
pre-exponential factor
Dynamic matrix of the state
Input matrix
Molar concentration
Specific heat capacity
Activation energy
Molar enthaply (liquid)
Reaction velocity constant
-space model
Ga in vector of the Kalm an filter
Covariance matrix
Thermal flow
Mass
Measurement matrix
Gas constant
Rate of reaction
Surface
Temperature
Heat transfer coefficient
Effective heat transfer coefficient
input vactor
Noise vector of the measurem ents
Volume
Noise vector of the state
State vector
Measured output vector
depends on kinetics
mol-m"
3
J K g - ^ K "
1
J-mol"
1
J-mol"
1
depends on kinetics
W
Kg
J-moH-K"
1
mol -m '^s"
1
m2
K
W-m-2-K-
1
W K "
1
m
3
Greek symbols
Discrete state transition matrix
r
T
e
V
p
X
CO
S u b s
A
a
B
Thermal capacity
Discrete input m atrix
Process parameter vector
Stoichiometric coefficient, reactant(-), product(+
partial order of reaction
Density
Time constant
Frequency
c r i p t s
Actu ator or External cold source L :
Stirrer or inserts m :
Bottom M :
J-K-i
)
Kg-m-
3
s
rad.s"
1
Liquid
Reaction mixture
Measurement
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225
c
d
E
e
h
i
J
0
1
Thermovector, cooled loop
Dry part
Feed of reactants
Thermovector, heated loop
Heating
Reaction or Input
Species
At the surface, internal side
At the surface, external side
P
R
r
sp
T
t
V
w
z
Inert gas at inlet
Reactor
radial
Set-point
Total
Hydraulic
Vortex
Wall or Wetted part
Axial
R E F E R E N C E S
1. Grew er, T., Klusac ek, H., Loffler , U., Ro gers, R.L., and Steinb ach, J. (1989)
'Determination and assessment of the characteristic values for the evaluation of the thermal safety
of chemical processes', J. Loss Prev. Process Ind. 2, 215.
2 .
Riesen, R. and Gro b, B. (1985) 'Reaction Calorimetry in Chem ical Process D evelopmen t',
Swiss Chem. 7, 39-43 .
3 .
Hu b, L. and Jone s, J.D. (1986) 'Early On-Line Detect ion of Exo thermic Reactions' ,
Plant/Operation Progress 5, 221.
4. Kin g, R. and Gilles , E.D . (1986) 'Early detection of hazar dou s states in chem ical reactors
with model-based measuring techniques', 5th International Symposium "Loss prevention and
Safety in the Process Indu stries", Cann es 15/19 Septem ber.
5 . Isermann, R. (1984) 'Process Fault Detection Based on M odeling and Estimation Methods-
A Survey', Automatica 20, 387 .
6. Tufa no, V. (1988) 'Mod eling runaw ay reactions in reactors protected with suppression
systems ', J. of Hazardous Materials 19, 225 .
7. Him melb lau, D.M . (1978) Fault Detection and Diagno sis in Chem ical and Petrochemical
Processes, Elsevier, Amsterdam.
8. Tow ill , D.R. and Payne , P.A. (1971) 'Frequency domain approach to automatic testing of
control systems', Radio and Electron. Engr.41, 51 .
9. Cas adei, R. (1977) 'Autom atisierungstechn ik im W andel durch M ikroproz essoren ' in M.
Syrbe and B. Will (eds.), INT ER KA M A-K ongreb , Springer, Berlin, 179.
10. Luenberg er, D.G. (1966) 'Observers for M ul tiv ar iat e System s', IEEE Trans, on Automatic
Control 11, 190 .
11 . Kalm an, R.E. (1960) 'A New App roach to Linear Filtering and Prediction Problem s', J.
Basic Eng. 82 D, 35-45.
12 . Gilles , E.D. and Schuler, H. (1982), 'Early Detection of Ha zardo us States in Chemical
Reactors', Ger. Chem. Eng. 5, 69.
13 .
Bon vin, D. and Saner U. (1988) 'On Line Proce dures for Superv ising the Ope ration of Batch
Reactors', Comput. chem. Engng. 12, 371-376.
14 . Snee, T. (1991), in this course.
15.
OLIW A manual (1985), System Technik AG .
16. Op penh eim, A.V . and Shafer, R. W. (1975) Digital Signal Processing , Prentice-Hall ,
Englewood Cliffs, NJ.
17.
Sebo rg, D. E., Edgar, T.F . and M ellichamp D .A. (1989) Process Dyn amics and Control,
Wiley , New York.
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226
18 .
Spe nce, J.P. and No ronha, J.A. (1988) 'Reliable Detection of Run away R eaction Precursors
in Liquid Phase Reactions', Plant/Operation Progress 7, 231 .
19 .
Seborg D .E., Edgar T.F., Shah , S.L.(1986) , AIC hE Journal 3 2, 88 1.
20.
P. de Valliere and D. Bonvin, Application of estimation techniques to batch reactors-II.
Experim ental studies in state and param eter optimization , Co mp . Che m. Eng., 13,11 (1989 ).
21 . Soliman, M. A. and Ray, W. H. (1979) 'Nonlinear State Estimation of Packed-Bed T ubular
Reactors', AIChE Journal 25, 718-720.
22. Kuru oglu, N.R ., Ram irez, W .F., Clough , D.E . (1981) 'Distributed Param eter Estimation
and Identification for Systems with Fast and Slow D ynam ics', Chem. Eng. Sci. 36,1357 (1981).
23 .
W atanab e.K . and Him melblau D.M . (1984) 'Incipient fault diagn osis of nonlinear processes
with multiple causes of faults', Chem. Eng. Sci. 39, 491-508.
24. King , R. (1985) 'Multiple Kalman filters for early detection of hazard ous states', Proceeding s
of Industrial Process Modelling and Control, Hangzhou, 6-9 June.
2 5 .
Lainio tis, D.G . (1971) 'Optimal Ad aptive Estim ation: Structure and Param eter Adaptation',
IEEE Trans. A utomatic Control 2, 160-169.
26. Jazwins ki, A.H. (1970) Stochastic Processes and Filtering Theo ry, Academic Press, New
York, 269.
27.
Gelb, A. (1974) Applied Optimal Estimation, MIT Press, Cam bridge.
28.
An derson , B.D .O. and M oore, J.B. (1979) Optimal Filtering, Prentice-H all, Englewood
Cliffs, N.J.
29.
Zaldivar, J.M., Hernandez , H. and Barcons C. (1990) De velopm ent of a Mathematical
Model and Numerical Simulator for a Reaction Calorimeter. FISIM, RC1 version, Technical Note
N° 1.90.109, Comm ission of The European C omm unities, Joint Reasearch C entre, Ispra (Italy).
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EMERGENCY RELIEF SYSTEM SIZING:
IN-VESSEL FLUID FLOWS
J . S . Duffield
CEC Joint Research Centre.
Ispra E s t a b l i s h m e n t
I - £1020 Ispra (Va)
Italy
1. I N T R O D U C T I O N
The occurrence
of an
uncont rol led chemica l runaway reac t ion
in a
ba tch type reac tor
or
storage vessel
is a
frequent event
in the
chemica l indust ry .
The
consequences
of
such
an
event can be benign (but still costly in t e r m s of lost product ion) when the p r o d u c t s are
safely vented
to a
d u m p t a n k
or
similar device,
or can be
d i sa s t rous
in
t e r m s
of the
effect
on
the
env i ronment when
the
p r o d u c t s
are
released
to the
a t m o s p h e r e ,
as for
example
in
the case of the acc idents at Seveso and Bhopa l .
An uncontrol led release to the a tmosphere usual ly occurs due to vessel failure, which
often results from
the
fac t tha t
the
emergency rel ief system
is not
correc t ly sized. Tra
di t ionally
the
emergency rel ief systems were designed assuming single-phase condit ions
in
the vent l ine, whereas in rea l ity often two-phase condi t ions prevai l. Co mp ared to relief
systems designed
to
handle single-phase vapour, two-phase flow requires vent sizes that
are
2 - 1 0
t imes la rger .
An
addi t iona l compl ica t ion ar i s ing f rom two-phase discharge
is
t he r equ i rement to insta l l spec ia l equipment to t r e a t the relieved fluids if they are toxic or
imflamm able . This spec ia l equipm ent
(a
fol lowing lecture wil l t reat this subject
in
more
deta i l )
may
consist
of
knock-out dru ms , vapour- l iquid sepa ra to rs , ca tch tank s, condensers ,
e tc . W h a t e v e r the sys t em the cost of such equipment is not insignificant , therefore it is
i m p o r t a n t
to
opt imise
the
size
of the
relief lines
and
duc t ing ,
i.e.
they should
be
large
enough
to
ensure t ha t
the
peak pressure stays within safe l imits during
relief, but not too
l a rge in order to minimise the a m o u n t of relieved fluid to be t r ea t ed .
In view
of
this interest , much effort
has
been expended over
the
las t decade
in an
a t t e m p t
to
improve
the
unde rs t and ing
of the
basic phen om ena assoc ia ted wi th emergency
relief. For example , the chemica l indust ry has performed m any exper im ents some of which
have been described
in the
open l i t e ra tu re ,
the JRC has a
f ramework prog ram me dea l ing
wi th " Indus t r i a l Haza rds" ,
and a
major effort
has
been
the
work performed
in the
D I E R S
227
A .
enuzzi and J
M
Zaldivar (eds.) . Safely
of
Ch emical Batch Reactors
and
Storage Tanks, 227-253.
©
1991 ECSC. EEC EAEC.
russels
and Luxem bourg. Printed in t he Ne ther lands.
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(Design Inst i tute for Emergency Relief Systems) project . DIERS consists of a consort ium
of 29 companies under the auspices of the American Inst i tute of Chemical Engineers and
was formed to generate experimental data on large-scale vessels undergoing ei ther runaway
reac tion s or exte rna l heat ing (e.g. by extern al f ires or loss of coo ling), and to develop
m eth od s for the safe design of emergency relief system s to handle the se even ts. Significant
progress has been made but th is knowledge i s by no means comple te .
This lec ture wil l conc ent ra te on wh at hap pen s wi thin th e vessel dur ing emergency
relief,
and an a t tempt wi l l be made to highl ight the basic phenomena tha t a re present (and tha t
have to be modelled) during the transient and how they interact and affect the course of the
t ransient . Reference wi l l be made to the computer code RELIEF, which i s current ly be ing
developed a t the JRC to model such s i tua t ions and most of the i l lust ra t ive ca lcula t ions
presented in this lecture have been made using this code.
The important aspect of two-phase cri t ical f low through the vent l ine wil l be left to the
next lec ture . I t is perh aps w orth men t ioning however, tha t i t i s the beh aviour w i thin the
vessel that determines the entrance condit ions to the vent l ine, and the errors associated
with calculat ing these condit ions usually have a much greater effect on the calculated vent
flow th an the likely spre ad of values th a t would res ult from usin g different crit ical flow
models .
2.
REACTOR RELIEF PH EN OM EN A
The s i tua t ion under considera t ion can be a ba tch reac tor or s torage tank conta ining a mul t i -
component l iquid mixture in which a chemical (usually exothermic) react ion occurs. If due
to malfunctioning the generat ion of react ion heat in this mixture exceeds the heat removal
capacity of the equipment a thermal runaway process wil l occur which is strongly enhanced
by the Arrh enius- type tem per a tu re dependency of reac t ion ra t e . W hen this s i tua t ion can
not be cont rol led by opera t ional measures , the tempera ture wi l l r i se to leve ls where the
vola t ile com pone nts of the liquid reac tan t mix ture s ta r t to evap ora te . At h igh tem pe ra tu re
levels also gas may be produced as a result of undesired secondary decomposit ion react ions.
This volume product ion leads to an increase of system pressure and in order to prevent
over-pressurisat ion of the reactor vessel i t is necessary to discharge the fluid mixture from
the vessel at an adequate rate . For sizing the emergency rel ief system, required by safety
rules,
i t i s necessary to dispose of adequate computa t ion models which must be based on a
correct descript ion of the chemical conversion, of mass transfer between l iquid and vapour
phase, of two-phase fluid dynamics and of the interact ions between these processes.
2 .1 LEV EL SW ELL
Chemical react ions can be the cause of a r ise in pressure in a closed system by increasing
the vapour pressure of the system and/or by genera t ing non-condensible gases as reac t ion
or unw anted decom posi t ion pro duc ts . Even endo therm ic reac t ions can cause a pressure
increase if the react ion products are gases, or l iquids which are more volat i le than the
reac tants . Exothermic reac t ions a re potent ia l ly more dangerous as in addi t ion they ra ise
the tempera ture of the reac tants and hence acce lera te the chemica l reac t ion.
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Often in the l i terature dist inct ion is made between the mechanism of this pressure rise
so tha t s impl i f ica t ions can be made to the mathemat ica l t rea tment of re l ie f system siz ing.
The fol lowing dist inct ions are usually made:-
(a) "Vapo ur pressure" or " temp ered" system s, in which the pressure gene ra ted by the
reac t ion i s due to the increasing vapour pressure of the reac tants , products and/or
iner t solvent as the te m per a tu re r i ses .
(b) "Gassy" sy stem s, in which the pressure is due to the produc t ion of a per m ane nt gas
by the reac t ion.
(c) "Hybrid" systems, in which the pressure rise is due to both an increase in vapour
pressure and permanent gas genera t ion.
For such systems a number of analyt ical tools and formulae can be used to calculate the
vent s ize for a par t ic ular overpressure . These "hand ca lcu la t ional" me thod s usual ly t r ea t
the vessel as a single calculat ional node having uniform propert ies. The obvious difficul ty
arises when this assumption is not val id and when i t is not known a priori w ha t t ype
of sys tem is exp ected . An excellent review of exist ing vent sizing m eth od s of this ty pe is
given by Duxbury and Wilday [1,2].
When a runaway react ion is in progress there is a volumetric source in the l iquid phase
resul t ing f rom evapo ra t ion an d/ or reac t ion gas prod uct io n. T he bubbles of vapo ur an d/ or
gas generated within the l iquid tend to rise through the l iquid and disengage at the l iquid
surface. If the rise velocity is sufficiently high then d rople t entr ain m en t can o ccu r.T he
bubbles during their residence in the l iquid occupy volume and so cause the l iquid level to
rise or "swell" . Figu re 1. shows quali tat ively this ph eno m eno n.
W hen th e set pressu re is reached and the re acto r or sto rag e vessel relieves the n the
pressure fal ls and the evaporat ion or "flashing" increases markedly. This causes the l iquid
level , or to be more precise the "two-phase mixture level"*, to r ise further and if this level
reaches th e vent pos i t ion two -phase venting wil l occu r. Th e dep ress uris at ion rat e of a
system is direct ly proport ional to the volume flow rate exit ing the system and since this,
under c r i t ica l f low condi t ions, i s inverse ly propor t ional to the mixture densi ty enter ing the
vent l ine the capacity to reduce the system pressure by venting is strongly reduced when
the mixture level reaches the vent posi t ion. In a runaway si tuat ion if the volume production
ra te due to evapora t ion and/or gas product ion i s grea ter than the vented volume f low ra te
the system press ure will increase. Therefo re, the abil i ty to describe th e m otio n of the
two-phase mixture level is one of the most important aspects of reactor rel ief modell ing.
2.1.1
Interfacial Mom entum Transfer
Th e genera l a rea of in te rfac ial mo m entu m t ransfer in pool systems conta ining arbi t ra ry
fluids an d subject to depre ssuris at ion is st i l l an open ar ea of resea rch. Th ere is a pau city
of experimental data part icularly for high viscosi ty fluids from which real ist ic models can
be developed. Th e problem reduces to the descr ipt ion of the mo t ion of bubb les wi thin a
The two-phase mixture level
separates
the region which is predom inately liquid (possibly containing
vapour
bubbles)
from the region which is predominately
vapour
(possibly containing liquid droplets) and
is
usually deSned as the position
where there is a discontinuity in the axial void fraction profi/e
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cont inuous l iquid phase and the mot ion of drople ts wi thin a cont inuous vapour phase , and
how this motion changes with void fract ion. In a bubbly l iquid in a pool where wall effects
are negligible, the frict ion or drag exerted by the l iquid on the bubble surface determines
how fast the bubb les rise with in the l iquid. Th is fr ict ional force in com pariso n to th e
buoyancy force decreases markedly as the bubbles increase in size. As the void fract ion
increases the rate of sl ip of the vapour past the l iquid increases unti l the si tuat ion arises
when the l iquid begins to break up in to drople ts and the vapour becomes the cont inuous
phase. The drag between the droplets and the vapour increases as the droplet size decreases
and so the sl ip decreases. At the extremes of al l l iquid and al l vapour flow the sl ip must
obviously be zero, and at some intermediate void fract ion the sl ip wil l be a maximum where
the bubbles have their maximum size. Therefore, the phasic veloci ty difference should vary
with void fraction in a way similar to as is shown in figure 2.
To descr ibe th is mot ion one has to look a t the phasic momentum t ransfer . The equa
t ions that describe this process are usually formulated in terms of mixture or drif t f lux
mo del [3] or a two-fluid mo del
[4].
In the dr i f t f lux model the phasic momentum equat ions a re replaced by a mixture
momentum equation and the relat ive veloci ty between the phases is described by a steady
st at e corre lat ion . I ts val idi ty is l imited to si tu at io ns wh ere accelerat ion and wall fr ict ion
forces can be neglected. For most pract ical cases i t has been found that an equation of the
form:
U
r
= U
v
-U, = ^
0 0
a
m
( l - a ) "
(1)
correlates experimental data for bubbly flow in vert ical pipes well , where
Uoo
represents the
term ina l r ise velocity of a single bub ble. Th e depe nden ce of /«, up on fluid prope rt ies has
been de term ined exper imenta l ly by Pebbles and G arber[5] , and for bubbles of d iam eter up
to 1 or 2 cms is given by,
Uoo
= 1-53
For bubbles wi th a la rger d iameter than
g c r A g
1 / 4
(2)
r
b
Z
2c
9Ql
1 / 2
(3)
then
Uoo = y/gn
(4)
T he two-fluid m odel uses a se pa rate par t ial differential equ ation to describe the m otio n
of each phase and if one assumes that the pressure difference between the vapour and l iquid
phases is negligible, the momentum equations averaged over a constant cross sect ion can
be wri t ten in the form:
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dag
v
U
v
dag
v
U
v
2
dp da . ,
-
V
\-a—
+
A
m
+ p
int
—
=
-n
-
F
wv
- a e „ f f + r
m
t / ,
n t
15)
dt az az az
for
t h e
vapour
phase
and ,
9(1
—
a)piUi
9 ( 1 -
a)giUi'
2
.
.dp
da
,
.
„ . . . . .
—
'
+
—
'
+
(1
-
a)-f-
-
A
m
- p
in t
—
=
Ti-F
w
,-(l-
a)etg
- T
m
U
int
(6)
at
az
az
az
for th e liquid phase .
where th e t e rms: -
- r
m
{7,-„
t
represents th e momen t um t ransfer due to phase change .
-
A
m
is th e added mass t e rm re la ted t o iner t ia l effects. I ts value is impo r t a n t only
for high velocity accelerat ing flows.
- r; is t h e interfacial drag force per uni t volume .
■ ^iu(v,i) i
3
'
n e
phasic wall friction force.
- Pint f f is a differential t e rm appea r ing in non establ i shed flow.
T he interfacial drag force r< is th e force t h a t develops when one of th e phases a t t emp t s
to move faster t h a n t h e othe r and acts so as t o re t a rd t h e faster moving phase . The
magn i t ude
of
th is
force
depends
on
th e
shape
of
th e
vapour- l iquid
in terface ,
th e
relat ive
velocity and th e phasic prope r t i e s .
To solve th is sys t em one has to specify a corre la t ion for th e interfacial drag force. If a
force balance is made on a single bubble it can be shown t h a t
[6]:
3ag,U?C
d
n = - — (7)
8 rf,
The basic empir ic ism of t h e two-fluid mode l enters in de te rmin ing th e values of C j and TV
In th e par t i cu l a r case of pool boil ing or flashing in la rge diame te r vessels (such as
ba tch
reac to r s
or
s to rage
t anks)
th e
velocities
are
low
and
th e
t empo ra l ,
accelera t ion
and
convective t e rms in th e momen t um equa t ions can be neglected as to o can th e t e rms re la ted
to wall friction and momen t um t ransfer due to phase change . Thu s in th is case t he re is
l i t t le to choose between th e drift flux approach and th e two-fluid mode l except t h a t th e
drift flux mode l general ly requires less comput ing t ime .
We have chosen for th e i l lustrat ive compu t a t i on s presented in th is pape r to a dop t th e
drift flux approach , and to descr ibe th e phasic velocity difference as a function of void
fract ion. The expression chosen is given below which incidental ly is equivalent to figure 2.
a
m
1 -
a)
U
v
U
t
=
Upool
■
_
J (8)
maxK
1
max)
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where
a
max
is th e void fraction w hich gives th e te rm a
m
( l - a ) " i t s m axim um value .
The denomenator is a scal ing factor which ensures that the maximum value of the sl ip is
given by
U
poo
i
irresp ective of the value of void fraction at which it occ urs . T he coefficients
m and n describe bubbly flow and droplet f low respectively, they have been fi t ted to ex
pe r imenta l da t a .
U
poo
i
is closely related to equa tion (2) and con tains a physical pro pe rty
sz±±£
a n
d
c a n
be thought of as a characterist ic bubble veloci ty representat ive of
a pool s i tua t ion.
With the constant 1 .53 , U
pool
i s ident ica l to equat ion(2) and corresponds to the churn-
turbulent regime as defined by Zuber [7]. This defini t ion has much success in describing
drift f lux experiments where gas is bubbled through a l iquid column in reasonably small
diameter tubes, say up to lOcms. However, there is a general awareness that this value
significantly underpredicts the rise veloci ty in flashing pool si tuat ions. For a more detai led
discussion reference should be made to the fol lowing art icles by, Fi l imonov[8], Styirkovich
[9],
G ard ne r [10], and K atao ka and Ishi i [11]. Pres ently we are using a co ns tan t t h at
has been obtained from fi t t ing equation (8) to data from available flashing experiments.
To improve the modell ing further more experiments are required, part icularly for viscous
fluids.
2.1.2 Effect of Level Swell on Vessel Depressurisation
Recently a number of vessel depressurisat ion experiments have been carried out in the
Mult iphase Mult icomponent (MPMC) test faci l i ty of the JRC [12]. Shown in figures 3 and
4 are two similar tests with water, where the only difference was the ini t ial f i l l ing of the
vessel. In figure 3 the initia l filling was 98% which ens ured s ignificant tw o-p has e v en ting ,
whereas in figure 4 the fi l l ing was 65%. Subsequent analysis has indicated that at a f i l l ing of
65 %
the two-phase mixture level did not reach the top of the vessel and al l vapour venting
occu rred. Th us a com pariso n of figures 3 and 4 indica tes w ha t effect two-p hase venting
has on the depr essu risat io n. I t is clearly seen th at th e rate of dep ress urisa t ion is strongly
reduced when two-phase condi t ions occur in the vent l ine . This becomes more important
when the ini t ial condit ions are not as in the tests i .e . an inert f luid at steady state , but a
chemically react ing fluid undergoing a thermal runaway.
2 .2 M U L T I C O M P O N E N T E Q U I L I B R IU M
So far we have restric ted our discussion to a single com pon ent f luid, w here as in the p rocess
indust ry we are usua l ly dea l ing wi th mul t icomponent mixtures made up of f lu ids of
signif
icantly different volat i l i t ies and physical pro per t ies. To add ress this pro blem we assum e
th a t th e mul t icom ponen t m ixture consis t ing of l iquid and sa tur a te d vapou r i s in phase
equil ibrium. This may be expressed as:
X
vi
= KtX
H
(9)
where X
v
i is the mole fract ion of com pon ent t in th e vapou r phas e, Xu that in the l iquid
phase and
K{
is the phase equil ibrium rat io. If the vapour mixture behaves as an ideal gas
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th e par t i a l pressure p,- of componen t i in th e vapour mix tu r e is p ropo r t i ona l t o th e mole
fraction X„< resul t ing in :
Pi = pX
vi
(10)
If
th e
liquid
mix tu r e
also
behaves
ideally
and
follows
Raou l t ' s
law
t h e
pa r t i a l
pressure
Pi
is p ropo r t i ona l to th e liquid mole fract ion
Xu
and to t h e vapour pressure of th e pure
componen t a t th e same t empe r a t u r e :
Pi = P.iXu (11)
As appea rs from eqs(10) and (11) for ideal mixtures th e phase equi l ibr ium ra t io Ki is :
Ki = *± (12)
P
For
ideal
gas
behav iour
of
th e
vapour
mix tu r e
th e
mole
fract ion
X„,-
is
equa l
to
t h e
volume
fract ion ¥ „,•. Eq (9 ) t hen can be t r ansfo rmed i n to :
Y,i = KiXu (13)
The re la t ions between th e componen t mole fract ions and th e componen t concen t ra t ions
are:
x
i^h^
{14)
M
>
2^ i M(
■ i
L- i
u
{
where Mi is th e componen t molecular weight .
Given th e componen t mole fract ion mix tu r e t he rmophys ica l prope r t i e s such as en tha lpy ,
densi ty , specific hea t etc . can be calculated using th e usua l mixing rules .
For non-idea l liquid mixtures e qu a t i o n ( l l ) is replaced by
Pi = P.i-XiiT,- (16)
where n is th e activi ty coefficient of componen t t .
The above descr ipt ion can be displayed graphical ly by wha t is known as a phase equi-
l ibr ium d i ag r am . Figure 5 shows a typical phase equi l ibr ium d i ag r am for a bina ry mix tu r e
of componen t s A and B. Suppose t h a t we have a liquid in which th e liquid mole fract ion
of componen t
A
XAU
=
0.25 and t h a t th is mix tu r e has an in i t ia l t empe r a t u r e
T\.
If th e
fluid is hea ted , vapour begins to be formed a t th e so-called bubble po in t t empe r a t u r e
(,„(,.
The
vapour
formed
has
a
much
higher
concen t ra t ion
of
componen t A {
in
th is
case
th e vapour mole fraction Xx„,- is a round 0.7) . If, similarly, we had s t a r t e d wi th a vapour
of compos i t i on
X*
v
i
= 0.25, and the vapour was cooled i t would begin t o condense a t th e
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"dewpoint" Tdcw In this case, the condensed l iquid wil l have a composit ion XAH of around
0.05.
2 .3 C H E M I C A L R E A C T I O N
An ongoing chemical react ion is a potential source of both volume (due to the genera
t ion of new prod uc ts) and he at . Consider a general chemical process in the l iquid pha se
which involves two reactants A and B undergoing an irreversible react ion according to the
stoichiometr ic formula
n
A
A + n
B
Bi— *n
c
C + n
D
D (17)
The instantaneous conversion ra te of reac tant A can be expressed by an Arrhenius type
t empera tu re dependency :
n,A = k
0
\C,^\
m
\C,^]
n
exp[-E/RT) (18)
where : k
0
is an empirical factor, m and n are the react ion orders for A an d B, E is the
ac t iva t ion energy ( in J /kmol) , R i s the gas con stant and X is the ab solute tem pe ra t ure .
The heat source if the react ion is exothermic, or the heat sink if i t is endothermic is
obtained from the enthalpy change of the react ion or from the differences in the heats of
format ion of the reac tants and products .
2 .4 N O N - E Q U I L I B R I U M E F F E C T S
Thermal non-equi l ibr ium has been observed in many vesse l depressur isa t ion exper iments
containing non-reacting fluids (see for example Friedel et al [13] and Friz [14]. This non-
equil ibrium is often referred to as the boil ing delay, and results from the fact that , fol lowing
the opening of the vent the vapour space depressurises but there is a delay before bubbles
are formed in the l iquid and boil ing occurs to bring the system back towards equil ibrium.
In react ing "vapour pressure" systems a significant boil ing delay would mean there
would be a delay in the cooling effect by evaporat ion and the react ion rate would continue
to rise. Fortunately, in react ing systems the means by which the system pressure rises in
the vessel in the first place is usually by the boil ing of the more volat i le components and/or
the produ ct ion of gas f rom the reac t ion. Th is mean s tha t wi thin the l iquid phase th ere
already are plently of nucleat ion si tes and sufficient interfacial area to l imit the departure
from equ il ibrium . It is expe cted therefore, tha t the rm al non -equil ib rium effects with in the
vessel will have a negligible effect on the venting process.
3. MO DEL LING PRINCIPLES
Having described the key phenomena associated with reactor rel ief we wish to provide some
i l lusta t ive computa t ions to highl ight the importance of these phenomena. For th is we wi l l
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make use of the code RELIEF, which is being developed here at the JRC; the sal ient features
of which wil l be described below. Ha nd calcu lat ional m eth od s, derived from the D IER S
pro gra m m e, wil l not be discussed here and the read er is referred to pape r of D ux bu ry and
W ilday [1,2] for furth er de tail s.
In modell ing the in-vessel f luid behaviour an at tempt is made to separate as far as possible
the physica l , physico-chemica l and thermokine t ic phenomena assoc ia ted wi th the mul t i -
component phase-equi l ibr ium and wi th the exothermic l iquid phase chemica l reac t ion f rom
the phenomena per ta ining to the two-phase f lu id dynamics. The ra te of vesse l depressur i -
sat io n and th e rate at which fluid is discharged from the vessel dep end on the fluid d yn am ic
phenomena in the vent l ine and on the two-phase f low behaviour of the mul t icomponent
mixture inside the vesse l . Both phenomena are model led but major a t tent ion needs to be
given to the mult icomponent two-phase fluid behaviour in the vessel because the vent mass
flow rat es depen d strong ly on fluid dyn am ic con dit ions at th e entran ce to the vent l ine. In
the i l lustrat ive calculat ions shown later a simplified cri t ical f low model has been selected
to compute the mass f low through the vent l ine , taking the s tagnat ion pressure and f lu id
mixture densi ty as the pr ime governing parameters .
The treatment of volume production in the vessel , which is due to evaporat ion of volat i le
components from the l iquid and to gas production by chemical react ion, is an element of
key importance in the ana lysis . Vapour product ion dur ing the vent ing process i s assoc ia ted
wi th externa l hea t input , a l iquid phase volumetr ic hea t source due to ongoing exothermic
chemical reac t ion and the change of system pressure w i th t ime. Ga s pro duc t ion can resul t
f rom the ongoing chemica l reac t ion or through secondary decompost ion reac t ions.
The key features of the in-vessel fluid flow model are:
* Vert ical discr et isat io n of the vessel into control volume elemen ts for which c ons erva tion
laws per ta ining to the separa te phases a re appl ied.
* Formula t ion of mass conserva t ion equat ions for individual components in each of the
phases .
* Formula t ion of phasic energy equat ions for the component mixtures .
* Descript ion of the relat ive motion between phases with an algebraic phase sl ip (drift-
flux) model.
* Irreversible chemical react ion in the l iquid phase formu lated as one of arb i tra ry o rder in
te rms of reac tant concent ra t ions wi th a tempera ture dependency given by an Arrhenius-
type expression.
The fol lowing hypotheses and assumpt ions a re present ly made:
- miscibi l i ty of al l components in the l iquid phase
- uniformity of pressure over the flow cross section
- the wall fr ict ion and accelerat ion terms in the momentum descript ion can be neglected
- the kinet ic energy terms in the energy equations can be neglected
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- axial conduction and axial mass diffusion in the fluid can be neglected
- thermal equi l ibr ium between l iquid and vapour phases (no superhea t a t onse t of the
depressur isa t ion process)
- d is t r ibut ion of components be tween phases governed by phase equi l ibr ium re la t ions
- phase equil ibrium relat ions based on ideal gas behaviour (Dalton's law) and on ideal
l iquid solut ion behaviour (Raoul t ' s law)
I t i s wo rth point ing ou t tha t most of the above assump t ions do not represen t l imi ta t io ns
of the analy sis. Th eir el imination however requires specification of add it ion al rela t ions
conta ining para me ters th a t have to be de termin ed expe r imenta l ly (e .g . in case of non-
equil ibrium, interphase areas and interphase transfer coefficients, for non-ideal l iquid mix
tures act ivi ty coefficients etc .) .
3 .1 C O N SE R V A T I O N E Q U A T I O N S
Conservation laws are applied to the separate phases in one-dimensional Eulerian fini te
volum e elem ents. For the sole pur pos e of simplifying the pre sen tat io n of equ ation s th e
assumption is made that f low cross sect ions at the inlet and outlet boundaries of a f ini te
volume element are equal .
3 . 1 . 1 . Mass Conservation
Here mass conservation for component i is expressed in terms of concentrat ions per unit of
mixture mass. This formulat ion al lows one to separate the concepts of change in chemical
composi t ion and change of mixture densi ty and enables the der iva t ion of phasic mixture
energy conserva t ion equat ions conta ining hea t source te rms, assoc ia ted wi th chemica l re
ac t ions.
The vapour mass conservation equation in discret ized form for a component t can be
wri t ten as:
A(ag
v
fi
vi
)
_
A(G
vf
i„j)
^ y + r
m i
+ a r „ i (19)
A similar equation for the l iquid phase is:
A((l-a)
eifMi
) A ( G ,
W ;
)
^ = y T
m i
+
(1
- a)ru (20)
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In the above equat ions a re :
Q„
and
QI
the m ixtu re densi ty in the v apour and l iquid
phase, /*„,- and fin the component mass concent ra t ions in mass per uni t of mixture mass
(which is equivalent to the component mass fract ion) in vapour and l iquid phase, G„ and G/
the vapour and l iquid mass flow rates, T
m
; t he componen t i n t e rphase mass t r anspor t r a t e
per unit of element volume, r„,- and ru the component mass product ion ra te in the vapour
and the l iquid phase per uni t of phase volume, g iven by equat ion( l8) . Physica l parameters
on the right hand side of equations(19) and (20) represent t ime average values during the
t ime s tep ( t ime centered va lues) . Pa ram eters und er the di fference op era to r a t the r ight
hand side pertain to the inlet and exit boundaries of the element.
3 . 1 . 2 . Energy Conservation
Neglec t ing the cont r ibut ions of k ine t ic energy and of axia l conduct ion to energy t ranspor t
the energy conservation equations formulated in terms of enthalpies, in discret ized form,
are for the vapour mixture :
H^BvK) A(G „/i„) Ap„
^ = y + n.„,r
m
+ qh
v
+
a
~^ I
2 1
)
and for the l iquid mixture:
A ( ( l - a ) e i M A (G iM .
r
. . . . .
>A
PI
-£1 y n
v
,T
m
+ qhi +
(l-a)—
(22)
W h e r e qh
v
and qh[ are the external he at inp ut pe r unit of elemen t volum e to vap our
and l iquid respectively, the mixture enthalpies are given by :
hv =J2^i
h
" (
2 3
)
i
h
i = ^2^ihii
(24)
where h
v
i i s the compo nent entha lpy in the vapou r phase a t system pressu re and tem
pe ra tu re and hn the component l iquid phase entha lpy a t the prevai l ing l iquid tempera ture
and componen t sa tu ra t ion p re ssure , and h„ , i s the vapour mixture sa tura t ion entha lpy a t
the vapour-l iquid interface.
The left hand term and the first r ight hand term in equations (21) and (22), represen
ta t ive of energy accumula t ion and energy convect ion, conta in a change in mixture entha lpy
(over t ime and distance respectively).
The above equat ions can be developed fur ther by taking in to considera t ion tha t the
component composi t ion in the separa te phases may change due to occurrence of chemica l
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reac t ions and mas s t ransfer processes . The a im is to de termine th e to ta l volume p rodu ct ion
ra te per e lement . This can be wri t ten as:
'/'tot =
$p +
V'chem + V W (2 5)
Equat ion(25) expresses tha t the to ta l volume product ion ra te per e lement foot is due to
changes of pressure and temperature in the gas phase (\£>
p
) , a volume source term associated
wi th chemica l conversion (V^m) and volume product ion by phase change (il>
va
p)-
The ra te a t which components a re produced by chemica l reac t ion [r
v
f,r
ti
) is direc tly
related to the reactant conversion rate taking account of the stoichiometry of the react ion
equat ion. Note tha t i f the te rm rpciiem dominates equat ion(25) then even an endothermic
react ion can cause a r ise in pressure.
The to ta l volume product ion ra te in the vesse l can be found by summing the cont r ibu
t ions for al l e lements in the vessel . Equating the total volume production rate in the vessel
to the total volumetric f low rate exit ing the vessel yields the value of the depressurisat ion
rate within the vessel .
3 .2 A X I A L D I S T R I B U T I O N O F V O L U M E F L O W , V O I D F R A C T I O N A N D
C O M P O S I T I O N
With the known va lue of the e lementa l volume product ion ra te the mixture volumetr ic
flow rat es a t the element b oun darie s can be successively evalu ated a nd from p hase sl ip or
interfacial fr ict ion relat ions, as described in sect ion
2 .1 .1 ,
the phasic e lementa l volumetr ic
flow rate s and the elemen t void fract ion can be calcu lated . Th e elem ental com pon ent
dis t r ibut ion over the vapour and l iquid phases can then be ca lcula ted using the component
mass conserva t ion equat ions and the phase equi l ibr ium equat ions.
4. ILLUSTRA TIVE CALCU LATIONS
Calcula t ions wi l l be presented tha t sequent ia l ly inc lude the phenomena tha t have been
descr ibed above . Th e a im is to highl ight the imp ortanc e and re levance of cer ta in par am eter s
dur ing vent ing and to demonst ra te the complexi ty of the process .
4 .1 H Y D R O D Y N A M I C A N D M U L T I C O M P O N E N T A S P E C T S
The hydrodynamic capabi l i ty of RELIEF has been extensive ly tes ted in a recent benchmark
exercise carried out at the JRC [12]. Here various blowdown experiments using pure com
ponent fluids in different sized test facilities operating at different pressures were compared
to various code calculat ions. Some of these calculat ions were performed "blind". Figure 6
shows a comparison of such a bl ind predic t ion using RELIEF wi th the exper imenta l va lues
for the depressurisat ion of a vessel ( top venting) containing the refrigerant R114.
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In the following eight figures (7
-
15) the importance
of
pha se equ il ibrium , interfacial
frict ion and vent locat ion wil l be considered. In all these cases chem ical reac t ion is a b
sent so the vapour p roduc t ion and subsequent level swell are due only to phase change
and vapour expansion. The s i tua t ion considered
is
the vent ing
of a
typica l type
of
ba t ch
reac to r or s torag e tank . The vesse l is cylindrical and po si t ioned vert ical ly with the vent
posi t ioned e i ther at the top of the reac tor or at the bo t to m . Th e vesse l was given the
fo l lowing d imens ions : he igh t=4 .17 m, i n t e rna l d i ame te r=0 .305 m, ven t d i ame te r=0 .02
m.
It was descret ised into 100 axial elements. In pr inc iple any n um ber of com ponen t s can
be t rea ted wi th the model but for these ca lcula t ions we wi l l res t r ic t our a t ten t ion to two
components and wil l chose fluids that have dissimilar vapour pressures.
The
fluids chosen
are the refrigerants R-l l and R-22; f igure 7 shows the vap our press ure curve s for these two
subs t ances . In all the calcula t ions the vessel is ini tial ly filled to a relat ive height of 60%
w i t h
an
in i t ia l mix ture comp osi t ion
of
20% (mass)
of
the vola t i le comp onen t and 80% of
the less volat i le component .
To test the importance of l iquid-vapo ur eq uil ibrium the re sults of two calcu lat ion s wil l
be shown.
The
f irst t rea ts the b inary mix ture
as a
t rue m ix tu re
in
which th e com posi t ion
changes dur ing the t ransient due to pha se equ il ibrium effects, the second keeps the com
posi t ion constant (pseudo one-component ) wi th the proper t ies kept equal to t hose of the
b ina ry mix tu re
at
the in i t ia l condi t ions. Figures
8
a nd
9
show the pressure and tem pera
ture histories for the two cases. Notice that the pressure of the pseudo one-component f luid
remains always above the two component f luid but t ha t t he t em pera tu re a lways rema ins
below.
4 . 1 . 1 .
Phase Slip and Vent Location
Of crucial importance is the abil i ty to describe th e ext ent of th e l iquid "swell ing' ' which in
turn defines the onset and durat ion of two-phase condit ion at the e nt ranc e to th e vent l ine .
In figures (10
-
15), the important effect
of
pha se sl ip and v ent loc at ion
is
d e m o n s t r a t e d .
In these figures two si tuat ions are considered, ie . both top and bottom venting of a vessel
conta ining a t rue mix tu re of the two refrigerants R - l l and R -22. To i l lus trate th e effect
of interfacial fr ict ion two values of sl ip have been taken; the first calculated using equation
(8) and is labelled "with slip" in the figures, the second is rep rese ntat ive of a hom ogeneous
m i x t u r e or foam, obta ine d by pu t t ing s l ip to zero and is labelled "no sl i p" .
Figure 10 shows the vessel void fraction evolution for the case
of
to p ven ting w ith sl ip.
The initial swelling of the liquid is clearly seen and after about 5 seconds t he m ixt ur e level
reaches the top of th e vessel; this signifies th e be gin nin g of two-phase ven t ing. No te th a t
a secondary mixture level
is
formed near th e m iddle
of
the vessel after ab ou t 10 seconds
which s teadi ly moves upwards and af te r about 50 seconds reaches the to p of th e vessel.
At th is t ime there is a significa nt axia l void profile in the vessel. La ter in t he t r ans i en t at
t im es bey ond 100 seconds (not shown
in
th e figure
so as to
avoid confusion) the m ixtu re
level moves downwards from the top and stops when the blowdown is complete, giving the
final si tuat ion with the remaining l iquid in the lower p ar t of th e vessel. Fig ure 11 shows
the same void fract ion evolut ion when sl ip
is
p u t
to
zero (homogeneo us condi t ions) and
a
cha racte rist ic foamy b ehav iour is seen. After 20 seconds the vessel is com pletely fi lled w ith
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a uniform mixture, and the void fract ion becomes a function of t ime only and not vessel
height . No set t l ing out of the fluid wil l occur at the end of the transient .
Figures 12 and 13 i l lust ra te wha t happ ens in the identica l case wi th b ot t om vent ing.
For the case where there is phase sl ip one again sees a moving mixture level but in this case
i t steadily moves downwards at an almost constant speed. At about 40 seconds the vessel
is voided and the vessel pressure will then fall rapidly (see figure 14). For the homogeneous
case with no sl ip the transient is characterised by the mixture level remaining at the height
of the ini t ial f i l l ing and with a constant void distr ibution below this level .
The consequence of there being an interphase sl ip on the global parameters is vividly
shown in figures 14 and 15. Th e system pre ssure histo ries are shown in figure 14 and
de m on str ate s the stron g influence of bo th vent pos i t ion and phase sl ip. O ne shou ld no te
th at th e curves for top and bo tto m venting show even a quali tat ively different beh avio ur,
and that for a certain period of t ime top venting can result in the highest pressure. Figure
15 show s th e correspon ding norm alised m ass inventory histories where significantly different
masses are vented. This can have major consequences when one has to consider the design
of dow ns t ream equ ipment .
4 .2 C H E M I C A L R E A C T I O N T Y P E A N D S C A L E D E P E N D E N C Y
Two types of chemical react ions wil l be considered, the first is typical of a polymerisat ion
react ion where the more volat i le component is converted into the less volat i le component ,
the second i s a decomposi t ion reac t ion forming a gaseous product . Calcula t ions were per
formed where sl ip was modelled, again using by equation(8) and where sl ip was put to zero.
The two components had vapour pressures that differed by a factor of ten and the ini t ial
m ass fract ion for each com pon ent was set to 80% for the mo re volat i le com po nen t an d 20%
for the less volat i le com po nen t . Th e vent l ine was posi t ion ed a t the to p of the vessel and the
relief valve was set to open at an o verpressure of ab ou t 10%. Fig ure 16 show s the influence
of phase sl ip on the pressure history, and demonstrates that for this type of react ion a sl ip
between the phases reduces the tendency for runaway.
T he influence of vessel dim ensio n is show n in figure 17 wh ere calc ula tion s have b een
performed for two vessel having th e same volume b ut wi th different le ngth s ( 0.4m and
4.0m ). A comparison of figures 16 and 17 leads one to believe that the effect of reducing
the vessel height has a similar effect to th at of increasing th e pha se sl ip. Th e ph ysical
explanation for this scale effect is that within the vessel bubbles rise with the same veloci ty
independent of vessel height so their residence time in the liquid is larger for longer vessels.
This results in an increase in the "swelling" of the liquid for the longer vessel and hence
increases the probabil i ty of obtaining two-phase flow condit ions at the entrance to the vent
l ine.
Th is in turn reduces significantly th e pressure rel ieving capab il i ty of a given vent
geometry.
It is interest ing to see whether these conclusions are universal ly val id or are specific
to react ion typ e. Figu res 18 and 19 show similar calcu lat ions for the deco mp osit ion of
hyd roge n pero xide. Th is react io n has been studied in deta i l beca use we have recently
performed such exper iments here a t the JRC. Here one sees tha t the tendencies a re exac t ly
the reverse of those seen with the polymerisat ion react ion.
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To explain this one has to appreciate that the l iquid mixture is ini t ial ly subcooled
and the gaseous phase i s pr imari ly composed of oxygen f rom the decomposi t ion reac t ion,
which has no late nt heat of vap orisat io n associated with i t . There fore, the pressu re an d
temperature within the vessel are effectively decoupled. Once the relief valve opens (sa 100
seconds into the transient for a rel ief set pressure of 2 bar) the vessel pressure remains close
to the outer pressure unti l the onset of runaway, and oxygen is vented from the vessel . For
homogeneous condit ions (zero phase sl ip) or for sl ip when we consider the longer vessel
more l iquid swell ing occurs. If the mixture level reaches the elevation of the vent l ine then
two-phase fluid wil l be vented and since the temperature and pressure are decoupled there
is no feedback on fluid temperature (and hence react ion rate) of any increase in vessel
pressure due to th is ear ly two-phase vent ing. Of importance however , i s tha t reac tant mass
is vented in this case. Th us when run awa y occurs the re is less hyd roge n perox ide in the
vessel if hom ogen eous co ndit ion s or the longer vessel are consid ered. Th is the n res ults in
lower peak pressures than the corresponding cases where inter phase sl ip is modelled or a
shorter vessel is considered.
4 .3 VE N T SIZING
As an example of how RELIEF can be used to size a venting system, or to calculate the
consequences of using an exist ing system for a given react ion, we wil l consider the hydrogen
peroxide decompostion now in more detai l . The results presented here refer to a vessel of 1
m
3
with an ini t ial f i l l ing of 60%. The l iquid composit ion is 20% H
2
0
2
and 80% H
2
0. The
rel ief valve was set to a very small overpressure so that the vent can be assumed to be open
at a t ime close to zero. Figures 20 and 21 show the results from calculat ions using three
different vent diameters. The first assumes a zero vent diameter and therefore represents
the closed adiabatic case. The other two calculat ions have vent diameters of 2cm and 5 cm
respectively.
Figu re 20 shows the tem per a tu re his tor ies and wh at is imm edia te ly app aren t i s th a t the
vent size has a negligible effect on the ini t ial heat up ph ase (say up to 6 m in ). Th erea fter,
up unt i l the maximum tempera ture i s achieved, the di f fe rences a re mainly be tween the
closed vessel and the vented vessel . This means that for a vented vessel the t ime for the
ons et of runaw ay is to a fi rst app rox ima tion in dep end ent of th e vent area. On e should also
note th at th e value of peak te m pe rat ur e is l i t t le affected by the ventin g process, ra ngin g
from 184 C for the adiabatic case to 175 C for a vent diameter of 5cm.
Figu re 21 show s the corre spo nding pressu re histories and here one sees th at vent size
has a significant effect on the press ure. Th e tem pe ra tur es an d pressure s are effectively
decoupled. The reason for th is i s tha t dur ing the hea t up and runaway the system pressure
is always above the saturat ion value of the mixture, which means that the gaseous phase is
virtual ly entirely made up from the oxygen l iberated from the decomposit ion react ion. In
fact boiling of the liquid only occurs after all the H
2
0
2
has been consum ed and the pressure
fal ls below the saturat ion value. This occurs at 7min 40sec for the 5cm vent and at 8min
35sec for the 2cm vent where a dist inct change in the gradient of the temperature trace can
be seen.
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Norma. operation
h
Mixture level
i<
o o
O O (
Runaway situation
£
Vapou.
r generation
Fig
1.
M i x t u r e level does no t reach
vent location, practically al l
vapour venting
Reactor level swell
Mixture level reaches vent
location, two-phase ver.tin
_
>
o
>
LJ
u
ex
u .
u .
a
£
o
o
_ l
Lu
>
I/ ]
a
0 .50
0.
40
0 .30
0.C0
0 .10
0 .00
■
/ \
■ / \
:
/
V
/
-
. . I . . . . F . . . . 1 . . 1 - . . . t
0.
20
0 . 50
0 .
70
VOID
FRACTION
Fig
2. Phasic velocity difference as a function of void fraction
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243
2. 40
2 . 20
2 . 00
1.80
1.60
1.40
1.20
1.00
fV
^
■
\
•
\
:
N .
\ . ;
^ - ^ _ _
:
TIME
I s a c )
Fig
3. Depressurisation history for two-phase venting
2 . 4 0
2 . 2 0
2 . 0 0
1.80
1.60
1.40
1.
20
1.00
\
N .
^ ^ ^ - .
•
-
-
-
-
_ ^ ^
~~ ~~-
4 0 . 0
TIME I s o c l
Fig
4. Depressurisation history for all vapour venting
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244
' d ew
h
T
bub
T)
l \
-X \
1 ' >v
-
r
- - t - - ^
- f
_
r
i i
r-£t*„
i
'
* . , , ;= 0.25 1
I I . I I
= 0.7
100%
B
100%
A
Fig 5.
Phase
equilibrium
diagram
for
a
binary
mixture
of
components
A
and
B
-z .
n-
i
ft
I d
u.
0-
7.00
6.00
5.00
2.00
1.00
0.00
K
- ^
•
\ ,
\»
\ \«
\
¥
»
-
_
E X P E RIME NT
/
V P R E D I C T I O N
^ ♦
^ - - V
TIME
( S )
Fig
6.
Vessel
depressurisation
of
refrigerant
R114;
blind
prediction
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245
*
-
S
S -
•s ^ ^
R-22/ sS^
y ^ ^
/ ^^
s^
/ >^
y^
/ y^
/ ys
/ j r
R-iy
/
240.
280. 320.
Temperature (Kalvin I
Fig 7. Vap our pres sure of R-ll and R-22
Timm ( s e c o n d s )
T n*e t seco nds 1
Figs 8. & 9. Pressure and t empera tu re histories for a
pseudo one-component Quid and for a two component Quid
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246
Vo i d F r e c t io n
Fig 10. Axial void profile evolution
Top venting - with phase slip
60 . 0
50 . 0
40 .0
30 . 0
20 . 0
10 . 0
:
;
0
se
' I i
■
1
2
1 j
i
]
5s
■ r ' '
l
'
JJ J
/ :
1 j — '
1
i i
i i
;
1 i
i i
i i
j 10 s j 20 s
■
i
j 1
i i
i i
i
| i
i
1
i , i .
-* - • ■ 7 1 ' '
T
1
I
i
i
|
i 5 0 s
1
0 .<0 0. CO
Vo i d F r a c t I o n
Fig
11 . Axial void profile evolution
Top venting - without phase slip
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eo.o
8 0 . 0
7 0 . 0
SO.
0
4 0 . 0
3 0 . 0
2 0 . 0
1 0 . 0
0 . 0
:
:
- /
/
/
/
/
/ /
/ /
-
i
0
sec.
10 s
20
s
30 s
40
s
i-»
r
■
i
i
■
|
■
i
■
.
-
.
■
;
jS — ;—-
r
--7—-;-- . . .
0. «0 0 . 60
V o i d
F r o c t I o n
Fig 12. Axial void profile evolution
Bottom venting - with phase slip
BO.
0
BO.
0
70 . 0
50 .
0
40 . 0
30 . 0
20 . 0
10.0
0 .0
:
:
-
:
-
0
,
. . . . . . . . .
sec.
r
10 s\
1.
. . . . .
20 s
. . . . i
■ ■ ■
30 s
i i . i ■ ■ ■
-
-
.
/
s j
|
i
:
0.40 0.60
Void FroctIon
Fig
13. Axial void profile evolution Bottom venting
-
without phase slip
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248
60 .
120.
T l « « ( s e c o n d s )
Fig 14. Pressure histories
for
different inter phase slip
and
venting modes
0 so
0. BO
0.70
0 . 60
0. 50
0.
40
0 . 30
0 . 20
0 . 10
0
00
^ \
\
^
^
- \ \ ^ ^ ^ \
\
\
^ ^ ^ ^ ^ ^
top
venting/with slip
' \ \ ^ ^ _ _ J
\
\
:
\\
x
\\ \
\ \ top
venting/no slip
\\
^
\\
^
\\
N :
\
\
x
\ \
x
\ \ \
; \ \
ottom \ \ \
with slip \ \
s
\
~~\
—
N
-
\ \ n o slip """""--^
v_ \ .
6 0 . 120.
T i r>« ( s e c o n d s ]
Fig 15.
Mass inventory histories for different inter ph ase slip and venting modes
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249
ao.
120. lco. 20a.
TIHE ( seconds )
Fig 16. Influen ce of inter p h a s e slip on the pressure history
a. 10- o
Polymerisation reaction
long vessel
BO.
1 2 0 .
rinE I atconda )
Fig 17. Influence of vessel length on the pressure history
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250
90 . 0
BO.
0
70 . 0
60 . 0
50 . 0
40 . 0
30 . 0
20 . 0
10 . 0
0 .0
■ ■ ■ , . . . . | i ■ i . ] ■
|
i
ecomposition reaction
|
1
1
1
1
//
h
/
/
J
■
with slip
■
\
\
\
\
\ \ n o slip
T l f l E s t c o n d a
Figl8 . Influence of inter phase slip on the pressure history
9; 20 . 0
400.
500.
TIME I s e c o n d s
Fig
19. Influence of vessel length on the pressure history
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251
1 1 ] ■ ■ ■ ■ ■
0 cm
.X
ii \ ■
\
1 V S cm
:
4 :00 0 :00
Fig 20 . Influence of valve size on the t emper a tu r e history
Fig 21 . Influence of
va lve
size on the pressure history
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252
REFERENCES
1) H.A. Du xbu ry, A .J. Wilday, ICh em E Sy m p. Series No 102, 175-186, 1987.
2) H .A. D uxb ury , A .J. Wilday, "Efficient design of reac tor relief sys tem s"
Interna t ional Symp. on Runaway React ions, Boston, Massachuse t t s , March 1989.
3) W .B . Wal l is , "One-dimensional Two-phase Flow ", M cGraw Hi l l , New York 1969.
4) M . Ishii "The rmo -Fluid Dyna mic Theory of Tw o-Ph ase Flow ", Eyrol les , Par i s . 1975.
5) F.N . Peebles , H.J . Ga rber , Ch em E ng Prog r , Vol49, 88-97, 1953 .
6) M. Ishi i , N. Zuber, "Drag coefficient and relat ive veloci ty in bubbly, droplet or part ic
ulate f lows", J.AIChE, Vol25, No5, 843-855, 1979.
7) N. Zub er , J . Hench, Rept n o. 62G L100, Genera l Elec t r ic Com pany, Schenectady, N.Y . ,
1962.
8) A.E. Fi l imonov, M.M. Przhiylkovski , E .P. Dik, I .N. Pe t rova , Teploenerge t ika 4(10) ,
22-26 ,
1957.
9) M .A. Styr ikovich, A.V. Surnov, Y .G. Vinok ur , Teploenerge t ika 8(9) , 56-60, 1961.
10) G.C. Gardner , "Frac t ional vapour content of a l iquid pool through which vapour i s
bubbled", Int . J. Mult iphase Flow, Vol 6, 399-410, 1980.
11) I . Kataoka, M. Ishi i , "Drift f lux model for large diameter pipe and new correlat ion for
pool void fract ion", Int . J. Heat and Mass Transfer, Vol (30) 1927-1939, 1987.
12) A.N. Skouloudis, "Fifteen benchmark exercises on vessel depressurisat ion with non-
react in g fluids", E U R 12602 EN , 1989.
13) L . Fr iede l , 5 th In t . S ym p. on Loss Preve nt ion, paper 4 3 , Can nes, 1986.
14) G. Friz , W. Riebold, W. Schulze, "Studies on thermodynamic non-equil ibrium in flash
ing water" , OECD Specia l i s t s meet ing on t ransient two-phase f low, Toronto, Aug 1976.
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253
NOM E NCLA T URE
C
C
P
E
Y
G
U
h
P
R
r
ffc
T
V
X
9
F„
C
d
D
H
K
Concen t ra t ion
specific heat at constant pressure
act ivat ion energy
volume fract ion
axial mass flow rate
velocity
entha lpy
pressure
gas constant
component mass product ion ra te per uni t of phase volume
bubble radius
abso lu t e t empera tu re
volume of computa t ional e lement
component mole f rac t ion
accelerat ion due to gravity
wall friction force
drag coefficient
hydraul ic d iameter
phase equi l ibr ium ra t io
k g m "
3
J k g ^ K -
1
Jkinol"
1
m
3
/ m
3
k g s -
1
m s "
1
J k g -
1
N m "
2
J k m o l ^ K -
1
k g m
- 3
s
_ 1
m
K
m
3
kmol/kmol
m a
- 2
k g m
- 2
s
- 2
m
Greek symbols
a
vap our volume fract ion m
3
/ m
3
T
m
phase change in t e rphase mass t r ansp or t r a t e kg m
_ 3
s
_ 1
\i com pone nt mass concen t ra t ions
g densi ty kg m
- 3
surface tension N m
- 1
<7
r f
volume prod uct ion ra te m
3
a
_ 1
n interfacial dra g force k g m
_ 2
s
- 2
7 ac tiv ity coefficient
Subscr ipts
t component
/ l iquid pha se
v vapour phase
s sa tu ra t ed
in t interface
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E M E R G E N C Y R E L I E F S Y S T E M S I Z I N G : V E N T L I N E F L U I D F L O W S
A .
B E N U Z Z I
Institute of Safety
Technology,
JRC Ispra,
Commission of the European Communities
21020 Ispra.
(VA), Italy.
A B S T R A C T . This lecture is a review of the methods developed to calculate the critical flow during the
emergency pressure relief of a chemical reactor or a storage tank. The fundamentals of the single-phase
and two-p hase critical
flows
are discussed but the emphasis is put mainly on the simplified formulations
recently developed (DIERS) in order to provide quick and simple-to-use vent sizing methods appropriate
for safety requirements.
1 .
I n t r o d u c t i o n
Th e scope of t h i s l ec tu re is t o r ev iew th e ca l cu l a t ion me th od s cur re n t ly employed
to eva lua te the c r i t ica l mass f lux G ( = pu ) i n t h e ven t ing l i ne wh en for some reaso n
( runaway reac t ion o r ex t e rna l f i r e ) t he p re ssure i n t he reac to r (o r s to rage t ank) r eaches
the "se t" va lue or the va lue a t which the pressure re l ie f device wi l l be ful ly open. I t i s
we ll know n th a t u nd e r t hese cond i t i ons two -pha se f low wi ll m os t l ike ly occur / l / and
tha t t h i s s i t ua t ion repre sen t s t he mos t seve re r equ i rement fo r t he ven t s i z ing . In f ac t ,
t he p re ssure r i se i n t he reac to r i s r e l a t ed to t he vo lume inc rease p roduced by vapour o r
gas genera t ion due to the e ffec t of the energy sources . Pressure re l ie f requi res a ba lance
b e t w e e n t h e v o l u m e t r i c v a p o u r / g a s g e n e r a t i o n r a t e a n d t h e v o l u m e t r i c d i s c h a r g e f l o w
r a t e . F ig . 1 t ak en from / 2 / an d re fe r red to s ty re ne p rop e r t i e s a t 0 .5 M P a , shows t h a t
bo th the mass f l ux
G
a n d t h e t w o - p h a s e d e n s i t y
p
decr ease as th e in le t void f rac t ion a
inc reases . In con t ra s t , t he vo lume t r i c f l ow
G/p
i s found to increase as
a
increases; for
pure gas f low (a = l ) G/p i s ab ou t 20 t im es la rger th an for a l l - l iquid (a = 0) flow.
As a consequence , two-phase f lows need l a rge r ven t a rea s compared to pure gas f l ows ,
in ord er to assu re the sa m e rel ie f capa c i ty . I f a l imi ted pre ssu re increase ( e .g: 20% of
the se t p re ssure ) i s t o l e ra t ed dur ing the ven t ing , a s ign i f i can t r educ t ion in t he ven t
area wi l l be possible . Therefore the eva lua t ion of the mass f lux G for two-phase f low
con di t i on s repre sen t s a key s t e p in t he emergency re li ef sys t em s (ER S) des ign . Th i s
lec ture wi l l be l imi ted to f lows in the fol lowing boundar ies (see Fig . 2 ) :
Tubes ( l ong p ipes ) wi th cy l indr i ca l o r annu la r geome t ry , cons t an t o r va r i ab l e
c ross sec t ion and a rb i t r a ry inc l ina t ion . Fr i c t i on losse s a re a lways impor t an t .
Nozz le s cha rac t e r i zed by va r iab l e c ross sec t ion (con ve rg ing /d ive rg ing ) an d
shor t length which de termines negl igible f r ic t ion losses .
255
A. Bemtzzi and J. M . Zaldivar (eds.). Safely of Chemical Batch Reactors a nd Storage Tanks, 255-284.
© 1991
ECSC,
EEC,
EAEC,
Brussels a nd Luxembourg. Printed in the Netherlands.
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256
Ori f i ce s (d i aphragms) which a re supposed to r epre sen t t ubes wi th ze ro -
length . Specia l cases a re rupture disks , sa fe ty re l ie f va lves and wal l breaks
which a re r epre s en ted by com bina t ions of t he p rev ious ly ment io ned e l em ent s .
1.1. UNSTEADY-STATE SINGLE PHASE CRITICAL FLOW
A lth ou gh t he the ory of s ingle -phas e cr i t ica l flows is wel l kn ow n, ne ver th e less i t is
worthwhi le to reca l l here i t s basic aspec ts in order to make easier the extension of the
form ula t io n to two -ph ase cr i t ica l f lows. Co nsid er ing a f low sy ste m formed by a pipe
a t t ached to a cons t an t p re ssure r e se rvo i r on one end and to a l a rge rece ive r on the
o t h e r e n d , w h e n t h e d o w n s t r e a m p r e s s u r e is r e d u c e d b e l ow t h a t of t h e u p s t r e a m v a l u e ,
a p re s sure g rad ien t i s se t up in t he p ip e an d th e f low beg in s . A s t ea dy -s t a t e i s r eached
when the pressure gradient forces a re ba lanced by the f r ic t iona l and iner t ia l forces . I f
t he t he rmodynamic s t a t e o f t he f l u id i n t he ups t ream re se rvo i r i s kep t cons t an t , de
c reas ing the downs t ream pre ssure wi l l p roduce an inc reased f low ra t e un t i l a max imum
va lue is r eache d . A t t h i s po in t , fu r the r r e duc t ions in t h e do w ns t rea m pre s sure wil l p ro
du ce no effec t. T he ma xi m um f low ra te va lue is ca l led "cr i t ica l" an d rep res en ts a l imi t
in t he d i scha rge p rocess t ha t has t o be de t e rmined wi th accuracy in many eng inee r ing
p r o b l e m s .
The c r i t i c a l f l ow usua l ly occurs when the Mach number i s equa l t o one a t t he
sma l l e s t c ross sec t ion o f t he p ipe . In t h i s cond i t i on a do w ns t re am pe r tu rb a t i on (e .g :
change o f p re ssure ) canno t be t r ansmi t t ed ups t ream and the f l ow ra t e i s no longe r
inf luenced by the changes in the rece iver presssure . Le t us consider the se t of par t ia l
di f fe rent ia l equat ions descr ibing the t ransient compressible f low in a rec t i l inear p ipe of
var iable c ross sec t ion A and inc l ina t ion 0 wi th re sp ec t t o t he hor i zon ta l p l an e .
at ( M ) + h ( M « ) = 0 ( M a s s )
f t (pAu) + j ^ (pAu
2
) + f^ (Ap) = -x
T
w + Apg cos 0 ( M o m e n t u m )
j
t
[Ap (h + £ ) ] + f
z
[Apu (A + T ) ] = X9w + ApgucosO ( E n e r g y )
(1)
w h e r e p, u , p and h a re f lu id densi ty , ve loc i ty , pressure and spec i f ic entha lpy, respec
t i ve ly . In add i t i on , T
W
a n d q
w
a re shear forces and he a t f lux a t th e wal l of th e pip e , x i s
a coe f f i c i en t ob ta ined th rough appropr i a t e cor re l a t i ons and g is t h e g rav i ty acce l e ra t ion .
Equa t ions 1 ) have to be coup led wi th t he cons t i t u t ive l aw:
P = f(p,h) (2)
t o c lo se t h e s y s t e m . E q u a t i o n s l ) c a n b e e x p r e s se d in m a t r i x fo r m / 3 / :
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257
(4)
a n d A , B , r a re funct ion s of p ,
u, h
Eigenvalues of the system 3) a re given by the solut ion of :
det(B - AA ) = 0 (6)
which i s a t h i r d o rde r po lyno mia l . Th e roo t s o f 6 ) dep end on th e co m po ne n t s of
/ . T h e s o u r c e t e r m s r e p r e s e n t e d by r do no t p lay any role in eq ua t io n 6 . T he rea l
pa r t o f any roo t A( r ) j g ives t he ve loc ity of s igna l p ro pa ga t io n a long the cor r e sp ond ing
c h a r a c t e r i s t i c p a t h i n t h e z, t p l ane . Th e ima gina ry pa r t o f any com plex roo t A( i)
t
-
g ives t he ra t e of g row th o r decay o f t h e s igna l p rop ag a t in g a long i t s r e spec t ive pa th .
For a hype rbo l i c sys t em in which a l l t he roo t s o f 6 ) a re r ea l and non-ze ro , t he number
o f b o u n d a r y c o n d i t i o n s r e q u i r e d a t a n y b o u n d a r y p o i n t c a n b e s h o w n t o e q u a l t h e
num ber o f cha rac t e r i s t i c l ine s en t e r ing t he so lu t ion reg ion a s t increases . I f system 1)
is appl ied in the par t icular spa t ia l region 0 < z < L a n d t h e b o u n d a r y c o n d i t i o n s a t
z = L a re exa m ine d, i t fo l lows th a t as long as any A,- i s less th an zero , som e bo un da ry
in form a t ion m us t be supp l i ed in o rde r t o ob ta in t h e so lu t ion . If, on the o the r h an d , a l l
t h e A,- a re g rea t e r t h an o r equa l t o ze ro , t he n no bo un da ry co nd i t i o ns a re needed a t
z = L a nd th e in t e r io r so lu t ion is una f fec ted by con d i t i on s bey ond th i s bo un da r y . A
c r i t ica l ( choked) cond i t i on ex i s t s w hen no in fo rm a t ion can p ro pa ga te in to t he so lu t ion
reg ion f rom the ex t e r io r . Such a cond i t i on ex i s t s a t t he bounda ry po in t z = L w h e n :
Ay = 0 for so m e j' < 3 (7)
A, > 0 for all i f j (8)
These a re t he ma thema t i ca l cond i t i ons sa t i s f i ed by the equa t ions o f mot ion fo r a
f lowing f lu id when reduct ion in downst ream pressure ceases to cause an increased f low
r a t e .
I t i s wel l -known tha t the choked-f low condi t ion for s ingle-phase f low occurs when
the f lu id ve loc i ty just equals the loca l sound speed.
1.2. STEADY-STATE SINGLE PHASE CRITICAL FLOW
For s t eady-s t a t e f l ow the t ime de r iva t ives i n equa t ions 1 ) become ze ro and the ma t r ix
equa t ion 3 ) r educes t o :
B
A
f = r
(9)
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258
and the f low is c r i t ica l when the fol lowing condi t ions a re ful f i l led somewhere a long the
pipe :
det[B) =
0 (10)
det
( B P > ) = 0 t ' = 1 ,2 ,3 (11)
W h e r e B ^ is t h e m a t r i x o b t a i n e d by s u b s t i t u t i n g in ( B ) t h e i co lumn wi th r .
F ig . 3 t aken f rom / 4 / shows in a (p , z ) p l ane , for a nozz l e , t h e curve de t (B ) = 0
a long which the ve loc i ty a ssumes the c r i t i c a l va lue , sepa ra t ing the uppe r subc r i t i ca l
reg ion f rom the lower supe rc r i t i c a l r eg ion . In t he same d i agram the curve det (Ti^
1
') =
0 i s t h e l ocus o f m ax im um v a lues for t he p re s sure i n t h e supe rc r i t i c a l r eg ion an d
th e locus o f m in im um va lues for t he p re ssure in t h e subc r i t i ca l r eg ion . Th e p o in t
S{Pa
z
c) rep res en ts con di t io ns 10) an d 11) s im ul ta neo usly fulf il led . E qu at io n 11) i s
a compa t ib i l i t y cond i t i on which ensure s an inde t e rmina te i ns t ead o f an imposs ib l e
solut ion of 9) a t the c r i t ica l sec t ion.
I f f r ic t ion and head effec ts a re negl igible and the c ross sec t ion area i s constant , the
ene rgy ba l an ce equa t io n can be w r i t t e n fo r s t ea dy s t a t e t u r bu len t flows / 5 / a s fo llows:
udu + vdp = 0 (12)
w h e r e v = l / p i s th e spec if ic volum e of th e flu id an d the co nt in ui ty eq ua t ion c an b e
expressed a s :
Gv = u wh ere G i s t h e ma ss flux (kg /m2 s) (13 )
di f fe renc ing 13) wi th respec t to p , one obta ins:
du dG dv . .
dp dp dp
c o n s i d e r i n g t h e m a x i m u m o f G wi th respec t to p i .e .
d
Z,
0
wh ich is th e c r i t ica l
cond i t i on , we ge t :
du dv . .
T
P
= Gmax
Tp
( 1 5 )
and combin ing wi th 12 ) we ob ta in :
dv , .
v + uG
max
— = 0 (16)
o r
~ dv
v
+
Gl
ax
v-=0
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,2 l '
d v
\
259
G
» » = - U J
(17)
w h e r e G
max
i s th e c r i t ica l m as s flux, an d p an d
v
t he p re ssure and spec i f i c vo lume ,
respec t ive ly , a t the exi t of the discharging l ine .
2 .
P e c u l i a r i t i e s o f T w o - p h a s e C r i t i c a l F l o w s
Two-phase c r i t i c a l f l ow of a s ing le -componen t mix tu re i s much more compl i ca t ed than
t h e c o r r e s p o n d i n g s in g l e p h a s e flo w d u e t o a n u m b e r of p h e n o m e n a / 6 / . T h e s e a r e :
1) change of phase , boi l ing ( f lashing) or condensa t ion; 2) s l ip or re la t ive ve loc i ty be
tween the phases; 3 ) f low pat te rn (or f low regime) and 4) possible depar ture f rom
t h e r m o d y n a m i c e q u i l i b r i u m . T h e fir st of t h e s e p h e n o m e n a o c c u r s b e c a u s e t h e r e is a
p re ssure va r i a t i on a long the l i ne . Gene ra l ly , t he ex i t qua l i t y (pe r cen t vapour by mass)
increases for low ini t ia l qua l i ty va lues and decreases for h igh in i t ia l qua l i ty va lues , i f
t h e expa ns ion i s a ssu me d to be i sen t rop ic / 7 / . S l ip t akes p l ace ma in ly becau se th e
vapour phase i s l e ss dense than the l i qu id phase and , t he re fo re i s more in t ens ive ly ac
ce l e ra t ed by the ac t ing fo rces . Fr i c t i on be tween the phases and l i qu id en t ra inment by
the va po ur t end to r educ e th e re l a t i ve ve loc i ty be tween th e pha ses . T hes e p he no m en a
are s t rongly inf luenced by the f low pat te rns ( f low regimes) or , in o ther words, by the
topo log ica l s t ruc tu re o f t he i n t e r face be tween the phases . In F ig . 4 t he ma in f low pa t
t e r n s a r e d e p i c t e d . I t is e v i d e n t t h a t m a s s , m o m e n t u m a n d e n e r g y e x c h a n g e s b e t w e e n
the phases wi l l be s t rong ly dependen t on the f l ow reg ime occur r ing . However t he f l ow
reg ime p red ic t ion and the eva lua t ion o f t he f l ow reg ime t r ans i t i ons a re p rob lems which
s t il l need more re sea rch work . Lack of t he rm od yn am ic equ i l i b r iu m, h as been shown to
exis t in or i fices an d nozzles or , in gen era l , in sh or t p ip es (L < 0 .1 m ) / 5 / . In s ingle-
ph as e cr i t ica l flows, even if th e ve loc i t ies a re high, mo lecu lar re laxa t ion ph en om en a
a re su ff ic ien tly r ap id for t he vap ou r t o be rega rd ed a s i n t h e rm od yn am ic equ i l i b r ium .
For two-phase cr i t ica l f lows, on the cont rary , re laxa t ion t imes for the format ion of new
in te r faces (nuc lea t ion) , hea t , mass and momentum t ransfe r , and the evo lu t ion o f f l ow
pa t t e rns a re comparab le wi th t he t ime spen t by the f l u id i n t he c r i t i c a l r eg ion o f r ap id
p r o p e r t y c h a n g e . W i t h a s a t u r a t e d o r s u b c o o l e d l iq u i d , d e p a r t u r e f r o m t h e r m o d y
namic equi l ibr ium can occur because of the de lay in in i t ia t ion of boi l ing as the f lu id
flows in to a reg ion in which the p re ssure is be low i t s sa tu ra t io n t em pe ra tu re . Th i s
de lay can occur because of the lack of nuclea t ion s i tes for evapora t ion or because of
the shor t t ime o f expans ion , o r bo th . In t he ca se o f sa tu ra t ed vapour which i s coo l ing
dur ing an i sent ropic expansion, nuc lea t ion s i tes a re needed. I f the radi i of the nucle i
a re sma l l , l a rge subcoo l ing can be reached . In t h i s s i t ua t ion a "condensa t ion shock"
or the sudden format ion of a c loud of f ine l iquid drople ts , can develop, g iving r i se to
a
press ure pulse . Ne ver th e less for long pipe s (L > 0 . 1m ) th e e ffec ts of th e lack of
t h e r m o d y n a m i c e q u i l i b r i u m a r e , in g e n e r al , n e g li g ib l e / 7 / . F i g . 5 i l l u s t r a t e s t h e t y p i
ca l p re s sure p ro fi le in a l ong p ipe and the p re sence of equ i l i b r iu m a nd non equ i l i b r ium
regions for two-phase f low.
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2.1. G O V ERN I N G EQ U A TI O N S F O R TW O - P H A S E CRI TI CA L F LO W S
For uns t eady , compress ib l e , two-phase f lows , t he ba l ance equa t ions cor re spond ing to
th e sys t em 1) a re l i s ted in Tab le I / 8 / t oge the r wi th t h e exp lana t io n o f t h e t e r m s . Th e
va r i ab l e a r ep re sen t s t he vo lum e t r i c f r ac t ion o f t h e pha se A; ( J ^
a
k = 1) )• N ot e
tha t t he number o f equa t ions i s 6 ( i nd ices k an d i vary f rom 1 to 2 , an d rep res en t l iquid
(1) an d vap ou r (2 ) ) ; t he subsc r ip t s I ,g an d m cor re spo nd to l i qu id , ga s (vapou r ) a nd
mix tu re , r e spec t ive ly . The equa t ions o f Tab le I have to be comple t ed wi th appropr i a t e
c o n s t i t u t i v e r e l a t i o n s h i p s d e s c r i b i n g t h e m a s s , m o m e n t u m a n d h e a t e x c h a n g e b e t w e e n
th e phases an d be tween t he pha ses an d th e bo un da r i e s an d wi th t he e .o. s . o f t he l i qu id
an d vapou r . Th e sys t em of equ a t ion s dep ic t ed in Tab le I can be expressed in m a t r ix
form:
w he re th e t ra ns po se of / i s g iven by:
f = ( p . u ^ h ^ U g . h g . a ) (19)
and r i s the source te rm vec tor which i s the r ight hand s ide of the s ix equat ions given in
Tab le I . The ma thema t i ca l c r i t i c a l f l ow cond i t i ons fo r uns t eady and s t eady-s t a t e f l ows
a re fo rma l ly t h e sam e a s t hos e o f t h e cor re sp ond ing s ing le -ph ase ca ses ( eqn s 6 , 7 , 8 ,
9 , 10, 11) , exce pt for th e fac t th a t th e order of th e poly no mi als is 6 ins tea d of 3 . T h e
mo de l p re sen ted in Tab le I , c a ll ed "mech an i s t i c " o r "Tw o- f lu id" , i n p r inc ip l e ap pe a rs
capab le o f r epre sen t ing a l l t he r ecogn ized nonequ i l i b r ium phenomena occur ing in two-
pha se c r it i c a l f lows. I t ha s been used , w i th mino r modi f i ca t ions , i n va r ious com pu te r
cod es re la ted to nucle ar reac to r safe ty ana ly sis . T he f lu id consid ered i s w ate r which is
ve ry we l l cha rac t e r i zed fo r t he rmophys i ca l and fo r exchange p rope r t i e s i n t he two-phase
region . T his i s no t th e case for o th er s ingle-co mp one nt f lu ids, a nd p ar t ic ular ly , for the
m u l t i c o m p o n e n t m i x t u r e s e n c o u n t e r e d i n t h e c h em i c a l i n d u s t r y . Fo r s u c h s y s t e m s t h e
"Two-f luid" approach, due to the lack of knowledge on the coeff ic ients of the equat ions
sho wn in Tab le I , i s d i ff icult to use . Ne ver th e less , f rom th e the ore t ica l p oin t of v iew
the re is no do ub t t h a t it i s t h e more rigorous m e th od .
2.2.
S I M P LI F IED F O RM U LA TI O N S ( H EM , H F M , ERM )
A current s impl i f ica t ion made for the eva lua t ion of the c r i t ica l mass f lux i s the as
su m pt i on th a t t he two-p hase m ix t u r e i s an hom ogen eous flu id wi th li qu id an d va po ur
h a v i n g e q u a l v e l o c i t i e s a n d t e m p e r a t u r e s ( H o m o g e n e o u s E q u i l i b r i u m M o d e l - H E M ) .
The spec i f ic volume of the mixture i s g iven by:
v = v
t
(l - x) + v
g
x (20)
Where x i s the vapour qual i ty . The s tandard expression for the c r i t ica l f low 17)
i s coup led wi th a m om en tu m conse rv a t ion (Be rnou l l i ) / 7 / equ a t ion which fo r a nozzl e
t akes t he fo rm:
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" i L Jpo
dp
261
(21)
w h e r e s u b s c r i p t s 0 a n d 1 i n d i c a t e s t a g n a t i o n a n d e x t e r n a l ( d o w n s t r e a m ) c o n d i
t i ons , r e spec t ive ly . For a l ong p ipe the Be rnou l l i equa t ion t akes t he fo rm:
2po
vi
(
1 _ M _
JUL f
H
n
*dH
V
1
Vaj viPo Jo
P
H
J
0
L
' v*dL*+ K
0
v*
0
+2{v{-
v*
0
)
(22)
w h e r e v*,p* a re dim ensio nless speci fic volu m e an d den si ty , respe c t ive ly . L* —
4./L/D i s a d imens ion le ss l eng th (f is t h e Fan n ing fac to r , D is t h e d i a me te r an d L the
length of the pipe) , H i s the ne t change in e leva t ion and
K
0
is th e en try loss coefficient.
T h e t e r m 1
— p\jp
0
r e p r e s e n t s t h e t o t a l p r e s s u r e d r o p b e t w e e n s t a g n a t i o n (0 ) a n d
ex ter na l ( l ) co nd i t io ns . T he s im ul ta ne ou s solu t ion of 17) an d 21) for a nozz le or of
22) for a p ipe de termine the choking f low G
c
and the c r i t i c a l p re ssure r a t i o r\
c
. F ig .
6 i l lu st ra tes th e grap hic solut ion of th e eq ua t io ns 17) an d 21) for a nozz le for f lashing
wa te r . The equa t ion 17) combined wi th equa t ion 20) g ives :
dv
g
dx dvi
(23)
to :
For a s ingle component f lu id 23) can be eva lua ted a t loca l condi t ions according
dv
g
dp
IP
'xX-wr-^
dx^
dp /
h
-±CT
h
2
(24)
(25)
(26)
dvi (vi
dp \
a
f
(27)
In equat ions 23) through 27) 7 i s the i sent ropic coeff ic ient , vi
g
a n d h\
g
a re t he
spec i f i c vo lume and en tha lpy change f rom vapour t o l i qu id s t a t e , r e spec t ive ly , C i s the
l iquid specific heat , T is t h e a b s o l u t e t e m p e r a t u r e , a n d aj i s th e so un d speed in the
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262
l iquid pha s e . In 25) a n d 26) t h e eva l ua t i on of
dx/dp
is pe r fo rmed a long i sen t rop ic
a n d i sen tha lp i c p a t h s , respect ive ly . T h e loca l qua l i t y wi t h reference t o s t a gn a t i o n
cond i t i on s can be a pp r ox ima t e d by:
h
lgo
T
CT
(T
x),
^x
0
f —
+ — In [ —
nig
J o
n-ig
\1
0
(29)
<:)h
hlgo ,
■Ig
Hg
(To - T)
(30)
T h e choice d e p e n d s on t h e app l i c a t i on . Acco rd i ng t o / 7 / , fo r a nozzle c on s t a n t
en t r opy
a n d
fo r
a
p ipe
c on s t a n t
en t ha l py
a re
r e c ommend e d .
T h e
Cl a p e y r on
e qu a t i o n :
dp
dT
Tv
lg
(31)
dvi/dp h a s been ut i l ized in a r r i v i ng a t e qu a t i o n s 26 ) , 27) a n d 29 ) . Using 24 ) ,
25) a n d a s s um i ng dvi/dp = 0 , t h e H E M l oca l choking cond i t i on in t h e s imp l e s t form
becomes :
xvg vf
g
(CT-xh
lg
)
IP
+
t.
(32)
In Fig . 7 a compa r i son be tween two - ph a s e cr i t ica l flow mode l s is i l l u s t r a t e d . Cr i t -
ical ma s s fluxes ve r su s s t a gn a t i o n p re s su r e ca lcu la t ed by different mode l s a r e s h own .
T h e H E M p red i c t i on s r e p r e sen t t h e lower b o u n d of all t h e mod e l p red i c t i on s . For ven t
sizing pu r po s e s t h i s is conse rva t ive .
In t h e Hen r y Fauske nonequ i l i b r i um Mode l ( H FM ) / 7 / t h e flow is also homoge -
n e ou s b u t wi t h no ma s s t r ansfe r be tween t h e s t a gn a t i o n a n d t h e chok i ng po in t ( i = i o )
a n d t h e r a t e of flashing a t t h e choking po i n t is s ome specified f rac t ion [N ) of t h e equ i -
l i b r i um
va lue :
xv
g
vf
g
(CT-xh
lg
)
IP
+ N
?
(33)
T h e p a r am e t e r
N
is given by:
N
=
*i
2Ap
Pl
K vf
g
TC
+ 10L
(33a )
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263
w h e r e KQ is a dis ch arg e coefficient ( = 0.6 for sh ar p edges orifices) a nd A p th e to ta l
ava i lable press ure dr op be tw een the vesse l an d the end of th e pip e . T he di ff icul ty
assoc i a t ed wi th t h i s mode l i s t ha t N (usua l ly N < < 1 for nozzle flows) is se ns itiv e to
the f low geomet ry . In t he Equ i l i b r ium Ra te Mode l (ERM) i sen tha lp i c cond i t i ons a re
a s s u m e d w i t h N = 1 :
x
0
v
r
v,„CT
0
V
g
Vjg
IP
K
(34)
As a spec i a l bu t i n t e re s t ing ca se , we cons ide r t he sa tu ra t ed in l e t cond i t i on s
[XQ
=
0) and we ge t :
G
c
o r c o n s i d e r i n g t h e C l a p e y r o n e q u a t i o n
h i
(35)
dp (T
dT\C
3 .
M u l t i c o m p o n e n t T w o - p h a s e F l o w s w i t h E n e r g y S o u r c e s
Th e phys i ca l p ro pe r t i e s o f a m ul t i c om po nen t mix tu r e can be de r ived f rom the p rop e r
t i e s o f each componen t accord ing to t he fo l lowing s imple re l a t i onsh ips :
hi
g
= ^ Yi
h
l
gi
vi
g
E
r
« ^ . E*'
C
<
w h e r e Y{ a n d X{ a re t he vapo ur and l i qu id mas s f r ac t ions o f t h e i t h com po ne n t , r e
s p e c t i v e l y . T h e r e f o r e , t h e H E M c o n c e p t c a n b e e x t e n d e d t o m u l t i c o m p o n e n t m i x t u r e s
which are the f lu ids to be considered in the vent ing process of ba tch reac tors .
4 . D I E R S M e t h o d o l o g y
T h e D e s i g n I n s t i t u t e fo r E m e r g e n c y R e li ef Sy s t e m s ( D I E R S ) / 9 / o f t h e A I C h E h a s
d e v e l o p e d r e s e a r c h p r o g r a m m e s t o :
reduce the f requency , seve r i t y and consequences o f p re ssure p roduc ing acc iden t s
p romote the deve lopment o f new t echn iques which wi l l improve the des ign o f ERS
DIERS was fo rmed in 1976 by 29 US and European Organ iza t ions and so fa r has spen t
in r e sea rch work approx ima te ly $1 .6 mi l l i on . The ma in re su l t o f t he DIERS work was
the deve lop me nt o f an ER S s i z ing me th odo logy based on :
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264
a b e n c h - s c a l e e x p e r i m e n t a l a p p a r a t u s ( V SP)
a d e s i g n c o m p u t e r p r o g r a m m e ( SA FI R E )
simpl i f ied ca lcula t ion procedures
Due to t he re l evance o f t he re su l t s ob ta ined by DIERS i t i s i n t e re s t ing to r ev i ew he re
br i e f ly t he concep t s on which th i s me thodo logy i s founded .
A de qu a te s i z ing of ER S to p ro t ec t aga ins t R R i s o f ten d i ff icu lt due to unc e r t a in t i e s
(o r l ack o f knowledge ) r ega rd ing chemica l k ine t i c da t a and the rmophys i ca l p rope r t i e s .
Fur the rmore , t he f l u id dynamic behav iour o f RR sys t ems in r e l i e f cond i t i ons depends
s t rong ly on the phys i ca l p rope r t i e s o f r eac t ion p roduc t s which a re p re sen t even in
m i n u t e a m o u n t s .
In t hese cond i t i ons , ca l cu l a t ion me thods a lone canno t g ive re l i ab l e p red ic t ions due
to insuff ic ien t d a t a fo r sys t em ch a rac t e r i za t ion . The re fo re , t he r e is t h e need to t e s t t he
RR sys t em on a sma l l sca l e ( t o r educe the cos t s ) r ep re sen t ing cor rec t ly wha t would
happen a t fu l l sca le in the rea l reac tor .
Fo r t h i s p u r p o s e D I E R S h a s d e v e l o pe d t h e a d i a b a t i c c a l o r i m e t e r V S P / 1 0 / w i t h
the in t en t ion o f mee t ing the fo l lowing requ i rement s :
Handle l a rge ly unknown sys t ems wi th ene rgy re l ea se ra t e s r ang ing f rom 0 .1 to
WW/g.
A sma l l t e s t sample (100ml ) t o a ssure sa fe and easy hand l ing
Direc t ext rapola t ion to la rge sca le : safe but not over ly conserva t ive
Re la t ive ly inexpens ive
The key fea ture of the equipment i s the use of a low hea t capac i ty tes t ce l l (see
Fig . 8 ) which is m a in t a ined in ad i aba t i c cond i t i ons t h ro ug h e lec t r i ca l hea t ing p rov ided
t o k e e p t h e w a l l t e m p e r a t u r e e q u a l t o t h e s a m p l e t e m p e r a t u r e . T h i s s h o u l d r e p r o d u c e
in the ca lo r ime te r t he behav iour o f a " sma l l vo lume e l ement " o f t he rea l r eac to r cha rge
wi th undesidered sca l ing effec ts .
The VSP can be used to measure homogeneous ( foamy) ve r sus non- foamy be
hav iour dur ing re l i e f o f a RR and to d i sc r imina te be tween " t empered" ve r sus "gassy"
s y s t e m s . T h e a p p a r a t u s c a n a l so m e a s u r e t h e r m a l q u a n t i t i t e s a n d o t h e r R R d a t a
( t e m p e r a t u r e , t e m p e r a t u r e r a t e a n d p r e s s u r e t i m e h i s to r i e s a n d h e a t o f r e a c t i o n v e r s u s
t e m p e r a t u r e ) . T h e i n f o r m a t i o n o b t a i n e d b y t e s t i n g t h e R R s y s t e m i n t h e V SP a l l o w s
th e iden t i f ica t ion o f t he rel ie f beha v iour ( t he rm a l and f lu id dy nam ic ) an d p e rm i t s t he
use o f t he compute r code o r o the r ca l cu l a t ion me thods , wi th t he appropr i a t e se l ec t ion
of models .
SA FI R E ( Sy s t e m A n a l y s i s For I n t e g r a t e d R e li ef E v a l u a t i o n ) is t h e c o m p u t e r c o d e
d e v e l o p e d b y FA I / l l / u n d e r a D I E R S c o n t r a c t w h i c h i n c o r p o r a t e s m o s t o f t h e D I E R S
ana ly t i ca l m e th od s . Th e code desc r ibes t he m ul t ip ha se flu id dynam ics o f a ba t ch - typ e
chemica l r eac to r o r s to r age vesse l wi th an E R S . M ix tu re phys i ca l p ro pe r t i e s , r eac t ion
s to i ch iome t ry and k ine t i c s , ve sse l and ven t l i ne geome t ry a re i npu t by the use r . F lu id
d y n a m i c m o d e l a s s u m p t i o n s a r e a l so m a d e b y t h e u s e r. SA FI R E c a n c a l c u l a t e t h e
m i x t u r e b e h a v i o u r ( t e m p e r a t u r e a n d p r e s s u r e r e s p o n s e ) , p r i o r t o r e l i e f s y s t e m a c t u
a t ion a s we l l a s t he subsequen t vesse l mix tu re d i scha rge p rocess t h rough the ERS.
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265
T e m p e r a t u r e d e p e n d e n t p h y s i c a l p r o p e r t y d a t a r e q u i r e d
by
SA FI R E inc lude : l iqu id
and vapour spec i f i c vo lume , hea t capac i ty
and
v i scos i ty : l a t en t hea t
of
v a p o r i z a t i o n ,
su r face t ens ion
and
s a t u r a t i o n p r e s s u r e - t e m p e r a t u r e r e l a t i o n .
The
c o d e
is
e x t r e m e l y
ve rsa t i l e
but two
ma jor l im i t a t i ons sho u ld
be
ta k e n i n t o a c c o u n t :
l) the
i nab i l i t y
to
a n t i c i p a t e
the
vapo ur - l i qu id flow reg im e
in the
vessel
for
u n k n o w n s y s t e m s ;
and 2) for
m a n y p r a c t i c a l s y s t e m s e n c o u n t e r e d n e i t h e r
the
r e a c t i o n c h e m i s t r y
nor the
p r o p e r t i e s
of
the
re a c t io n p r o d u c t s
are
sufficiently kno wn
to
fully utilize
the
f lu id dyn am ic m e th
o d s c o n t a i n e d
in
S A F I R E . T h r o u g h
the use of the
e x pe r im e n t a l a p p a r a t u s
VSP
m o s t
of
the
a b o v e - m e n t i o n e d u n c e r t a i n t i e s
can be
r e m o v e d
and the
a p p r o p r i a t e c a l c u la t i o n
m o d e l
can be
se l ec t ed . The re fo re ,
the
c o m b i n e d
use of VSP and
S A F I R E ,
or
s impl i
f i ed fo rmula t ions ,
is the
D I E R S r e c o m m e n d e d a p p r o a c h
to the ERS
s i zing un de r
RR
c o n d i t i o n s
or
ex te rn al f ires.
4.1.
SIMPLIFIED FORMULATIONS.
B a s i c a s s u m p t i o n s
are:
homogeneous equ i l i b r ium (equa l ve loc i ty
and
e q u a l t e m p e r a
t u r e
in
b o t h p h a s e s ) , c o n s t a n t m a t e r i a l p r o p e r t i e s
and
m i x t u r e c o m p o s i t io n d u r i n g
the
v e n t i n g t r a n s i e n t . A c c o r d i n g
to
L e u n g
/ 12/ who has
deve loped
the
f o r m u l a t i o n s
of
t h i s
sec t ion ,
a
s i m p l e r e l a t i o n s h i p
of the
form:
e —
1 =
w ( l / r ? —
1)
w h e r e
r\ = p/po and e = V/VQ)
c an
be
used
to
correlate f lashing choked flow
in
d u c t s
or
nozz les .
The
cor re l a t i ng
p a r a m e t e r
has the
fol lowing simplified form :
,2 r T^, 2
XoVlg
|
CTpvf
g
CTpvf
g
i
2
r^- = a
0
+ -JS- (38)
v
0
hf
a
v
0
hf
T h i s p a r a m e t e r b a s e d
on
s t a g n a t i o n p r o p e r t i e s ,
is
fo rmed
by two
s e p a r a b l e t e r m s :
the f i r s t r ep re sen t s
the
compress ib i l i t y
of the
m i x t u r e
due to the
ex i s t i ng vap ou r f r ac
t i o n a l v o l u m e
and the
second repre sen t s
the
compress ib i l i t y
due to
p h a s e c h a n g e
(or
f lashing) u po n de pre ss ur iz a t io n.
For
flashing flow systems,
the
s e c o n d t e r m
in 38) is
d o m i n a n t u n t i l
a
0
a p p r o a c h e s u n i t y
(all gas
i n l e t ) .
For
non- f l a sh ing f low sys t ems ,
the
s e c o n d t e r m v a n i s h e s
(no
p h a s e c h a n g e )
and w
r educes s imply
to a
0
. In
t h i s
way,
solu
t i ons deve loped
for
flashing flows
can be
e x t e n d e d
to
non- f l a sh ing s i t u a t io ns . Nozz le :
For
a
nozz l e f l ow, subs t i t u t ing equa t ions
37) and 38)
i n to
21) and
u p o n i n t e g r a t i o n ,
w e
get:
G
.
=
{-2
[a;
In
ry
+ - l )
( 1 - 7 ? ) ] } *
W
( i - 1 )
+ 1
(
>
w h e r e
G* =
G / ( p o / i > o )
2
is
a
d imens ion le ss ma ss f lux. C hok ing con d i t i on s
are
found
by
seek ing
the
m a x i m u m
of G (or G*) as p (or
TJ)
is
dec rea sed . Th i s cond i t i on
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266
l e ads t o t h e fol lowing t r a n s c e nd e n t a l equa t i on fo r
77
r a t i o :
T]
c
,
t h e so called cr i t ica l p re s su r e
■nl +
w(w
-
2 ) ( 1
- r]
c
)
2
+ 2u
2
lnr]
c
+
2 w
2
( l
-
r?
d
)
=
0
(40)
Afte r 77
c
is f ound , i t s va lue can be s u b s t i t u t e d i n to equa t i on 39) t o ob t a i n G*.
Al t e rna t i v e l y , t h e loca l choking c r i t e r ion given by:
U
c — —j=
(41)
can be used t o ob t a i n t h e s am e r e su l t . The s e so l u t i on s fo r choked flow t h r o u g h a
nozzle a r e r e p r e sen t ed graph ica l ly in Fig .9 , whe r e b o t h flashing a n d non- f l a sh ing flows
a re
di sp layed .
A
cor re l a t ion
deve loped
by
/ l l /
gives
r e su l t s
in
close
a g r e emen t
wi t h
t h e p rev i ous m e t h o d : For w > 4 (low qua l i t y r e g i on ) :
G*
= [0 .6055 + 0 . 1 356 ( l nw ) - 0 . 0 1 3 1 ( l nw )
2
] /w
0
8
( 41a )
a n d fo r
C J
< 4 . (high qua l i t y r e g i on ) :
G*
=
0 . 6 6 /w
0
-
3 9
(416)
Fu r t h e rmo r e , fo r t h e all- l iquid in le t cond i t i on , t h e cor re l a t ion m ay be rep laced by:
G
= 0 . 9 G
L
(41c)
whe r e
GL
is called t h e l imi t ing flow a n d is given by equa t i on 35 .
Hor i zon t a l p ipe : For a ho r i zon t a l long pipe wi t h c on s t a n t cross sec t ion , i n se r t i ng
e qu a t i o n s 37) a n d 38) i n t o 22) we ge t :
4 /
D
2
G *2
»7i - f?2
w
+
(1
- 2 In
w)
2
In
(1 —u)ri2 + w
(1
-
W)T7I
+ C J
(l-u>)r)
2
+ C J
/771
( l - w ) » 7 i + w \772
(42)
whe r e 4fL/D is t h e t o t a l equ iva len t pipe r e s i s t a nc e , 771 = P i / p o a n d 772 = P2/P0 (see
Fig . 10) . In o rde r to ca lcu la t e flow di scha rges f rom a l a rge re se rvo i r , b o t h t h e in le t
a n d exi t cond i t i on s have t o be known . For t h e in le t , G* a n d 771 a r e r e l a t e d t h r o u g h
t h e r e l a t i on sh i p 39 ) , wi t h
77
= 77
Loss en t r y effects c an b e i n c o r po r a t e d i n t o t h e t e rm
4/L/D. For subson i c or unchoked exi t cond i t i on s , P2 = p
a
whe r e p
a
is t h e amb i e n t
back
p r e s s u r e .
For
ex i t
choking
cond i t i on s ,
e qu a t i o n
41)
wi t h
77
c
=
772c
prov ides
t h e
r e l a t i on sh i p be tween G* a n d t h e cr i t ica l exi t p re s su r e r a t i o , 772c- In t h i s way, fo r a
given 4fL/D,
we
have
t h r e e e
e qu a t i o n s
fo r
t h e
t h r e e
u n k n own s , G*, rji,
T)2
C
-
Fig .
10
di sp lays t h e r a t i o of
G
c
fo r p ipe flow t o
GQ
C
co r r e spond i ng t o a nozzle , as a func t ion of
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4fL/D, for va r ious va lues o f t h e pa ram e te r u> , cover ing bo th flashing an d non -f lashing
f low condi t ions.
Inc l ined p ipe : Gene ra l i zed so lu t ions have been ob ta ined by us ing a d imens ion le ss
" F l o w i n c l i n a t io n " n u m b e r :
gDcos9 p
0
gLcos8 . .
Fi
= — =
j
(43)
w h e r e 6 i s the angle of inc l ina t ion to the ver t ica l . F{ i s a m e a s u r e of t h e d e p a r t u r e
f rom the hor i zon ta l ca se (F { = 0 ) . T h e n o n - d i m e n s i o n a l iz e d m o m e n t u m e q u a t i o n t o
be solved is:
L f
V, [[1-W)V
2
+UTI] \l-G'
2
p]dT]
4f— — — — (44)
which reduces t o equa t ion 42 ) fo r Fi = 0 . Fig . 11 i l lu st ra tes th e e ffec t of an inc l in a t ion
F{ = 0 .2 by com par i son w i th F ig . 10 repre s en t ing the Fi = 0 case . For more de ta i l s
an d for th e exte nsio n of th e "o m eg a" m eth od to inc lu de the effec ts of sub coo l ing in le t
cond i t i ons and the e f fec t s o f t he p re sence o f noncondensab le gases i n t he mix tu re , see
/ 1 2 / .
4.2. VENT SIZING FORMULAE
In th i s sec t ion the mos t com mo nly used me th od s for t he des ign /ve r i f i ca t ion o f E R S a r e
pre se n ted . Th e ca se o f pu re vap our ven t ing is no t cons ide red bec ause i t ha s l imi t ed
app l i cab i l i t y / 1 3 / . Tw o-ph ase flow can usua l ly be expe c ted to occur from a runaw ay
reac to r ven t and the a ss um pt io n o f two -phas e f low shou ld usua l ly be m ad e a s a sa fe
case .
I t i s r eca l l ed tha t t he des ign /ve r i f i ca t ion o f an ERS in such cond i t i ons requ i re s an
a p p r o p r i a t e c h a r a c t e r i s a t i o n of t h e ch e m i c a l s y s t e m c o n c e r n i n g t h e t h e r m o k i n e t i c a n d
f lu id dy nam ic a sp ec t s . Th i s can be ach ieved on ly th r ou gh ad i ab a t i c ca lo r im e t ry t e s t i n g
/ 1 0 / . O ne of th e lec tures of th is Co urs e i s dev oted t o th is top ic . I t is usua l ly preferab le
tha t t he r e l i e f dev ice can ope ra t e a t a p re ssure va lue p
g
("set" value) well below the
m ax im um a l lowable work ing p re ssure (M AW P) of t he reac to r vesse l. In add i t i on ,
the p re ssure dur ing the ven t ing t r ans i en t may be a l l owed to r i se up to a f i xed va lue
Pm{Pm = l - 2 p
s
) before s t a r t in g th e decay pha se . In doin g so , a s igni f icant red uc t ion
of t he ven t a rea a s compared to t he ca se o f ze ro ove rpre ssure (Ap = p
m
— p
a
= 0) can
b e o b t a i n e d .
In order to dec ide which methods are appl icable in a g iven case , i t i s necessary to
def ine the chemica l system as one of the fol lowing types:
a ) "V apou r p re ss ure sys t em s" (or " t e m pe red " ) , i n which the p re s sure gen e ra t ed by
the runa w ay i s du e to t he inc reas ing vapo ur p re ssure of t he com po ne n t s o f t he
r e a c t o r m i x t u r e .
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b) "Ga ssy sy s t em s" , i n which the p re ssu re is due to t he non -con den sab le gases gen
e ra t ed by the re ac t ion .
c ) "H ybr id sys t em s" , i n which the to t a l p re ssu re i s du e to bo th vap ou r p re ss ure and
gas gene ra t ion .
" V a p o u r p r e s s u r e s y s t e m s " . I n F i g 12 t h e p r e s s u r e a n d t e m p e r a t u r e t i m e h i s to r i e s
of a runaw ay reac to r in ven ted (do t t ed l ine ) an d non-v en ted (con t inou s l ine ) con d i t i ons ,
a r e s h o w n / 1 4 / . I n t h e v e n t e d c a se t h e m a x i m u m p r e s s u r e v a l u e p
m
is reached in a t ime
r
p
= At
p
+ At
v
w h e r e At
v
i s t he t ime requ i red to gen e ra t e hea t for vap ou r fo rm a t ion
d u r i n g v e n t i n g a n d At
p
i s th e t im e (ad iab at ic r ise t ime ) needed to reach p
m
in th e
non-ven ted ca se . I f t he vo la t i l i t y o f t he sys t em does no t change dur ing the ven t ing ,
t h e t u r n a r o u n d i n p r e s s u r e o c c u r s a t t h e s a m e t i m e o f t h e t u r n a r o u n d i n t e m p e r a t u r e
( r
p
= r
t
). Th e gove rn ing equ a t ion s for t h e rel ie f t r ans i en t can be ob t a ine d cons ide r ing
the mass ba l ance :
dm/dt = -GA
45)
o r m = m o — GAt
w h e r e m = pV a n d V i s t he vo lume of t he reac to r {m
3
);
and the ene rgy ba l ance :
mCdT/dt = mq- GAVh
lg
/[mvi
g
) 46)
w h e r e
q
i s th e speci fic power (W /k g) ge ner a te d by th e reac t ion ;
In wr i t i ng equa t ion 46) t he fo l lowing a ssumpt ions have been made :
vapour sens ib l e hea t t e rms a re neg lec t ed
vapour mass i s neg l igeab le
q i s cons t an t ( a su i t ab l e ave rage o f t he va lues a t T
a
a n d T
m
shou ld be used)
G i s cons t an t
hom ogen eous vessel beha v iou r ( two -phase f low w i th no vap ou r d i sen gage me nt )
c o n s t a n t m a t e r i a l p r o p e r t i e s
By combin ing eqns 45 ) and 46) a f t e r i n t egra t ion , we ob ta in :
r = r
a +
g -
vh
'° , (47)
Dif fe ren t i a t i ng equa t ion 47) wi th re spec t t o t ime and pu t t i ng dT/dt = 0, we get :
T=?±-( *-)* 48)
GA \v,
g
qGAj
V
'
by subs t i t u t ion o f t h i s va lue in to equa t ion 47) we ob ta in :
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269
^ ^ , (4 9 )
w h e r e A T = T
m
— T
a
is t h e " o v e r t e m p e r a t u r e " c o r r e s p o n d i n g t o t h e " o v e r p r e s s u r e "
A ? = p
m
— p
e
- T he zero ove rpre ssu re case i s g iven by:
m
0
qvi
g
Gvhio
(49a)
Fig . 13 / 1 4 / d i sp l ays t he ven t a rea ve r sus A p show ing th e bene f i t s in t h e red uc t io n
of th e ve nt a re a wh ich can be achieved w i th a l lowanc e of a sm al l ov erp res sur e . Al l -
vapour and a l l - l i qu id ven t ing repre sen t , r e spec t ive ly , t op and bo t tom ven t ing modes
w i t h c o m p l e t e v a p o u r - l i q u i d p h a s e s e p a r a t i o n o r d i s e n g a g e m e n t . T h e t r e a t m e n t i s
s imi lar as the one previously descr ibed; the only di f fe rence in equat ion 46) i s the ra t io
V/m repla ced by V| or v„ . For the zero overpressure , in the case of a l l -vapour f low the
required flow area is given by:
T h e r e c o m m e n d e d v a l u e f o r q i s g iven by /14 / :
q = 0.5C{[dT/dt)
m
+ {dT/dt)
a
)
(50)
w h e r e dT/dt va lues a re me asu red w i th t he ad i a ba t i c ca lo r im e te r . K ey pa ram e te r s fo r
the use o f t h i s me thod a re : V, m o , C, hi
g
, v\
g
, and P — T d a t a .
For a non- reac t ing sys t em sub jec t t o a cons t an t ene rgy inpu t Q(VK) repre sen t ing
the ca se o f a s to rage t ank exposed to an ex t e rna l f i r e , equa t ion 46) becomes :
mCdT/dt = Q - GAVh
lg
/(mvi
g
) (51)
which a f te r us ing a t r e a tm en t s imi l a r t o t ha t i n t he runaw ay reac t ion ca se , y i e lds t h e
fo l lowing express ion fo r t empera tu re :
T
°
c £ c
l n
GA
L GA
V hig t
™o Cvi
g
( g j -
t)
(52)
and the fol lowing impl ic i t equat ion for the vent a rea A:
-
1
4-
m
0
Cvi
g
Q
AT =
T
m
-T
e
=
W
,m
0
QVi
g
GAC
which has t o be so lved th ro ug h i t e ra t ive m e th od s
+
-FT—
(
5 3
)
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270
"G ass y sy s t e m s" . Le t us cons ide r t he ca se o f an idea l gas ( accu ra t e enou gh for
low pre ssure cond i t i ons ) i ns ide the co n ta im ent vessel o f an ad i ab a t i c ca lo r im e te r :
n =
pV
c
/RT
c
(54)
wh ere n i s t h e num ber o f moles , V
c
i s t he con ta inment vesse l vo lume (m
3
) a n d T
c
is
t h e c o n t a i n m e n t a m b i e n t t e m p e r a t u r e . D i f fe r e n ti a ti n g y i e ld s :
dn/dt ~ V
c
/(RT
c
)dp/dt (55)
L e t rh g deno te t he gas gene ra t ion ra t e i n kg/s, t h e n :
m
g
= M
w
dn/dt (56)
a n d c o n s i d e r i n g t h a t :
we ge t :
v
g
= RT
p
/[p
p
M
w
) (57)
Q
g
= m
g
v
g
= V
c
T
p
/{p
p
T
c
){dp/dt) (58)
w h e r e M
w
i s th e mo lecular weight of th e gas , p
p
i s t he peak p re ss ure , T
p
i s t h e t em
p e r a t u r e a t p e a k r a t e , a n d
Q
g
i s t he vo lum e t r i c gas gen e ra t ion ra t e eva lua t ed a t t he
peak p re s sure dur in g ven t in g . For an ad eq ua te ven t si ze, we equ a te t h e vo lu me t r i c
gene ra t ion ra t e t o t he vo lume t r i c d i scha rge ra t e :
A = m
0
Q
g
/{m
a
Gv) (59)
w h e r e
m,Q
i s t h e r eac to r cha rge (kg) , m
a
i s th e tes t ce ll cha rge (kg ) , v i s t he homoge
neous two-phase spec i f i c vo lume
— V/mo
w h e r e
V
i s t he r eac to r vo lu me (m 3) , an d
G
i s t he two-phase d i scha rge mass f l ux [kg/m
2
s) , or:
A = m
2
0
Q
g
/{m
e
VG) (60)
Combin ing 60) and 58) we ge t :
A = m
2
0
V
c
T
p
/{m
a
VGp
p
T
c
){dp/dt)
max
(61)
I f t he d i scha rge f low i s eva lua t ed wi th t he incompress ib l e Be rnou l l i ' s equa t ion :
G
g
= (2Ap/v)i (62)
w h e r e A p = p
p
— p
am
b, equ a t ion 61) becom es :
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A = V
c
T
p
/{m
3
p
p
T
c
).{dp/dt)
max
{m
3
J{V2Ap)*
271
(63)
"Hybr id sys t ems" a re t hose in which a non-condensab le gas i s p roduced bu t some
of t he reac to r con ten t s vapor i ze du r ing the runaway , p rov id ing a t em pe r in g ef fect . Th e
vent s ize formula i s the equat ion 49) modif ied to account for the fac t tha t the to ta l
p re ssure i s t he sum of t he pa r t i a l p re ssure s o f t he vapour and the gas (p = p
v
+ p
g
)-
T h e t e r m hi
g
/vi
g
i s replac ed by (T p
v
/p)dp/dt / 1 5 / an d the equ a t ion 49) becom es :
A =
qm
0
( ^ ) * + (CAr)i]
2
(64)
T h e t e r m
(p
v
/p)dp/dt
m a y b e f o u n d t h r o u g h a d i a b a t i c c a l o r i m e t r y , a n d
G^
is
g i v e n b y / 1 5 / :
n
i , ,Pv dp
2
T
G
»
+ (
7 A ' C
(65)
4.3.
PRACTICAL EXAMPLE
T h i s e x a m p l e h a s b e e n t a k e n f r o m / 1 4 / a n d / 1 6 / a n d c o n c e r n s a t a n k o f s t y r e n e
m o n o m e r u n d e r g o i n g a d i a b a t i c p o l y m e r i s a t i o n a f t e r b e i n g h e a t e d i n a d v e r t e n t l y t o 7 0 C .
T h e M A W P o f t h e t a n k i s 0.5MPa. T h e p a r a m e t e r s of t h e p r o b l e m a r e :
V
m
0
Ps
T
B
T
a
Pm
T
=
13.16
= 9500
= 0.45
= 482.5
= 0 .493
= 0.54
= 492.7
= 0.662
m 3
kg
MPa
K
K/s
MPa
K
K/s
They have been ob ta ined v i a ad i aba t i c ca lo r ime te r t e s t i ng ,
p rope r ty da t a have been used :
Th e fo llowing m ix tu re
For p = 0A5MPa:
vi = 0 .001388
v
g
= 0 .08553
C = 2470
hi
g
= 310.6
m
3
/kg
m
3
/kg
U/kgK
kJ/kg
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272
For p = 0 . 5 4 M P a :
vi = 0 .001414
v
g
= 0.07278
C
= 2514
hi
g
- 302 .3
m3/kg
m3/kg
kJ/kgK
kJ/kg
B a s e d on t w o - p h a s e h o m o g e n e o u s v e s s e l v e n t i n g , the ca l cu l a t ion p rocee ds as fol
lowing:
F r o m e q u a t i o n 50):
and f rom equa t ion 49):
AT = T
m
-T
a
= 10.2K
q
=
1.426kJ/kgs
9 5 0 0 X 1426 , ,
GA = 2 = 256kg/s
{ ( 9 5 0
1
O
6
X
X
O
3
O B 4 M ) ' + (2470X10.2)*}
The two-phase mass f l ux is e v a l u a t e d w i t h e q u a t i o n 41c):
3 1 0 6 0 0 / 1 \ , ,
G = 0.9 = 3 0 4 0 f c o / m
2
s
0 . 0 8 4 1 4 \ 2 4 7 0 x 4 8 2 . 5 , /
y/
A
2
p
= ^ ^ = 0 . 0 8 4 m
2
and D
2
p = 0 . 3 2 7 m ( t w o - p h a s e v e n t i n g )
U s i n g the m o r e t r a d i t i o n a l v a p o u r - v e n t i n g m o d e l , the ze ro ove rp re ssure ca se (equa
t ion 49b) gives:
9 5 0 0 x 1219 x 0 .0 8 4 1 4 , .
GA = = 37kg/s
3 1 0 6 0 0 x 0 .0 8 5 5 3 * '
a n d the c r i t ica l mas s flux, eva lua t ed wi th equ at io n 41b) and w i t h u> = 1.4 gives:
= 1 3 1 0 f c o / m 2 s
0 .66 / 41
1.4
0
-
39
\0.
3 7
= 0 . 0 2 6 m
2
and D
v
= 0 . 1 8 9 m
1310
(a l l -vapour ven t ing)
In
Fig. 14, the
p re ss ure t im e h i s to r i e s , dur ing ven t ing
and
ca l cu l a t ed us ing
the
t w o - p h a s e h o m o g e n e o u s v e s s e l m e t h o d , v e n t d i a m e t e r s D
2
p and Dv, are s h o w n . It is
e v i d e n t t h a t the ven t s ize based on al l-vapour flow wil l lead to vessel fai lure .
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Table I: Two Phase Flow Equations
Iner t i a
+ c o n v e c t i o n
d
k
d t
d 7 (
A
«kOk)
A
D
k t
i
h
A«KL>k
D (
Aa
he k
fh
k
+ -^-1
P r e s s u r e
+
A «
k
—
+ Pk
A d d e d
M a s s
+
B
k
In ter fac ia l
P r e s s u r e
+ A p , — —
o z
P h a s e
C h a n g e
= A r
k
= A / '
k
[v,-v
k
)
=
A r
k
( h
k
+ - ^
In ter fac ia l
F r i c t i on
+ Ar
l k
Wal l
F r i c t i on
—
*
k
^
k
w
Inter fac ia l
heat
t rans fer
+
A q
k l
Wal l
heat
t rans fer
+
*k<Pwk
Grav i ty
+ A a
k
y
k
g
z
+ A a
k 0 k
g
z
u
k
C r o s s
S e c t i o n
C h a n g e s
+ R
k
I-a
;i-b
[I-c
d
k
fi d
Where:
—— =
— + — u
k
dt ot oz
n„
ut
=
o
dt
+ u
k
fl
OZ
/ V - l - i r r
r
ik
=
( -D
k
'V
i
B
k
= ( - 1 ) A^n,a
g
i<
m
v,
D g ?>g D| l ' |
_
A
f l a ^ p
+ A p
O ^
fit ot
R
k
=l R (l-«
k
)p,4^
4 oz
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274
u>
E
ra
.*:
m
O
O
X
D
"-
(/I
«)
ra
10
6
4
2
-
.
-
-
—
c
CD
TJ
03
W
CO
Q .
n
«:
I -
1<-
10
3
600 -
400 -
E
g
200
at
100 -
60 "
40 -
2 0 -
10
-
- ^ ^ ^ »
-
-
^^^
-
I
e ^
i i i
Styrene
g = 500 kPa /
1 -
G/Q^C \
\ -
100
60
40
20
10
H
4
2
—
w
E,
Q ;
O
CO
m
CO
. w
c
^
ci)
Q .
>.
O
ra
t i
CO
o
"a:
0)
i _
CI)
E
o
0.2 0.4 0.6
Inlet void fraction
0.8
1.0
Fig.
1 : Variation of two-phase density
Q ,
mass velocity G, and
volumetric flow per unit area
G/Q,
with inlet void fraction
(from reference 121).
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275
Tubes (long pipes)
Nozzles
y y "if"
Orifices (diaphragms)
Fig. 2 : Ge om et r ies con s ide red fo r c r i t ica l f l ows .
Fig . 3 : Ty pic al (p,z) di ag ra m for a noz zle (from reference /4/).
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76
Slug
or
p lug
f low
^
Fig. 4 : Flow patterns in vertical upward f low.
X
o
o Q
O
o
^ 0 ° O
a a
a
o 0
0
o
O
0 o
O
a
o
Non
o
o
—■
-
—
- —
I
-equilibrium . |
\ ^ t
Equi l ib r ium
- L
>
0.1
m -
Lenght ,
L
Fig. 5 : Illustration of typical pressure profile and equil ibr ium and
nonequil ibr ium regions fo r f lashing f lows in constant area
p i p e s f rom re ference HI .
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10.
8. -
re
6
6.
x
W
E
O
2.
-
H
2
0 Hom ogeneous Equilibrium
P
0
= 1.1 MPa
x
o
=0.001
r rP -\ 1/2
G = -
2 / vdP
L
y
P
0
J
\ V
i i i i
X
G -
r d v i
dP .
i
-1/2
I
G
c
-
^V/-"
s' \ \
1 \
1 \
1 \
1 \
1
1 1
^ = 0 . 8 8
i I
1
1 '
1
1
1
1
l i
0.20
0.40 0.60
V
_P_
P.
0.80
1.0
Fig.
6 : HEM solut ion for cr i t ical f low of f lashing water through a
nozzle under a pressure drop of
1
MPa (from reference
HI).
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278
Experimental
o
LVD
=
0
■
LVD
=
3
A LVD = 3.5
a
LVD
=
6.5
• Friedrich
* Uchida Narig
o Zaloudek
T
•
T
*
LVD
LVD
LVD
LVD
LVD
LVD
LVD
= 12 I
=
I
= 18 I
=
29
I
= 1.5
= 12
=
6
Fauske D = 6 i
Sozzi a nd Sutherland
D
=
12.7
mm
D = 6.0 mm
D = 4.0 mm
D =12 . 7 mm
Mode l
Predictions
i Upper bound flow (Frictionless)
Homogeneous Equilibrium Model (Frictionless)
Moody
(Frictionless)
12
O r
Henry
Fauske
(Frictionless)
Edwards LVD = 12
Henry LVD = 12 (Frictionless)
10.0
9.0
o
- 8.0
X
o
a
7.0
15 30 45 60 75 90 105 120
Stagnation pressure (bars)
Fig.
7 : Discharge of saturated water th rough orif ices, nozzles and
pipes: compar ison between mode l predictions and
experimental
da ta .
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279
EXHAUST
& SUPPLY
TYPE I TEST CELL
CLOSED SYSTEM
THERMAL DATA
TYPE II TEST CELL
OPEN SYSTEM
VENT SIZING &
FLOW REGIME DATA
TYPE III TEST CELL
OPEN. SYSTEM
VISCOUS EFFECTS
DATA
F ig .
8 : Sm a l l - sca le tes t eq u ip m en t w i th c lose d and o pe n tes t ee l
designs (from reference /10/).
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280
1.2
1.0
0 8
0 6
0.4
0 2
n
_
-
: -r\
- T
D
:
-J
i i
Non- f lash
^ _ P c
• — Gc
/
1
n g
I
f low
1 1
—
1 1 1 1
—
V
Flashing f low
P
c
/Po
^ '
G
c
^ ^
Po Co ^ ^
I 1 1 I 1 1 1 1 1 1
0.01 0.1
0)= n
n
1 10 100
u> = a
0
+ Q
0
C
P
T
0
P
0
(v
ve o
/h
ve o
)z
Fig . 9 : F l a sh i n g a n d n o n - f l a sh i n g ch o ck e d f l o w t h r o u g h n o zz l e s
/12/.
u
100
4fU/D
Fig .
10 : Ch ok ed f l ow d is ch arg e f rom h or i zon ta l p ipe s /12 /
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281
u
o
100
4fL/D
F ig . 11 : Ch ok ed f l ow d isch arg e f rom inc l i ned p ip e , w i th F i 0 .2
/12/.
System type
Sealed
Venting
Time into venting
Fig .
12 : Cha rac te r i s t i c t im e in ven ted and no nve n ted runa way s
/14/. /16/ .
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282
u.o
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Styrene example
13.16 m
2
9500 kg
-
Computer simulation
[ (SAFIRE)
i i i i i i
0 10 20 30 40 50 60 70
Percent overpressure
i i i i i i
4.5 5.0 5.5 6.0 6.5 7.0
Maximum pressure bar abs.
Fig. 13 : Vent area versus ove rpressure for styrene polym erisation
/14/.
90 120
Time (s)
180
Fig.
14 : Styrene po lyme risation: pressure t ime histories in the
reactor du ring two-ph ase v enting, for two flow areas.
-©•D=0.327 m, and -a-D =0 .189 m .
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283
5 . R e f e r e n c e s
/ l /
F i s h e r , H .G . ; ( 1 9 8 5 ) , C h e m . e n g . P r o g r . , A u g u s t , 3 3
/ 2 /
L e u n g , J .C . , F i s h e r , H .G . ; ( 1 9 8 9 ) , J . L o s s P r e v .P r o c e s s I n d . , A p r i l , V o l.
2
/ 3 /
T r a p p , J. A . , R a n s o m ,V .H . ; ( 1 9 8 2 ) , I n t . J. M u l t i p h a s e F l o w , V o l. 8 N . 6 pp 669
- 681
/ 4 /
G i o t , M . ; ( 1 9 8 8 ) , E x p . H e a t T r a n s f e r ,F lu i d M e c h a n i c s a n d T h e r m o d y n a m i c s ;
Shah , Gan ic and Yang Ed i to r s ; E l sev ie r Sc i ence Pub l i sh ing Co .
/ 5 / Faus ke , H. K. ; (1962) , AN L - 6 6 3 3
/ 6 / Wal l i s , G. B . ; (1980) , In t . J. M u l t i p h a s e F l o w , V o l. 6 p p 9 7 - 112
PI Fa u s k e & A s s o c i a t e s ; ( 1 9 8 3 ) , FA I / 8 3 - 2 7 ( D I E R S A I C h E )
/ 8 /
S h e p h e r d ,
I.
M. ; (1989) , Pro c .
of
N U R E T H
-
4 , K a r l s r u h e , O c t o b e r 10
- 13
/ 9 / F i s h e r , H . G . ; ( 1 9 8 8 ) , Sp r i n g N a t . M e e t i n g A I C h E , N e w O r l e a n s , M a r c h 6 - 10
/ 1 0 / Fa u s k e , H . G . , L e u n g , J. C; ( 1 9 8 5 ) , C h e m . E n g . P r o g r . , A u g u s t , 8 1 ( 8 )
/ l l / G r o l m e s , M . A . , L e u n g , J. C; ( 1 9 8 5 ) , C h e m . E n g . P r o g r . , A u g u s t , 8 1 ( 8 )
/ 1 2 / L e u n g , J. C . ; ( l 9 9 0 ) , J. L o s s P r e v . P r o c e s s I n d . , J a n u a r y , V o l. 3
/ 1 3 /
D uxb ury , H. A. , Wi lday , A. J . ; (1989) , In t . Sy m p. on Ru naw ay Re ac t io ns , Bo s ton ,
M a r c h 7 - 9
/ 1 4 / L e u n g , J. C; (1986) , A IC hE Jo ur na l , Vol 32 , N . 10 , pp 1622-34
/ 1 5 /
Fa u s k e
&i
A s s o c i at e s ;( 1 9 8 4 ) , F A I / 8 3 - 4 3 ( D I E R S - A I C h E )
/ 1 6 /
Huff,
J. E . ; ( 1 9 8 2 ), P l a n t / O p e r a t i o n P r o g r e s s , V ol. 1 N . 4 , p p 2 1 1 , O c t o b e r
6 . N o m e n c l a t u r e
o Speed o f sou nd m/s
A Sur face a re a m
2
A M a t r i x of th e coeffic ients of th e t im e-d er iv a t ive t e r m s of th e eqns of m ot i on
B M at r i x of th e coeffic ients
of
t he space -d e r iva t ive t e rm s o f t h e eqn s
of
m o t i o n
C Liqu id spec if ic he a t
J/kg.K
D C r o s s s e c ti o n d i a m e t e r
m
f Vector
of
u n k n o w n v a r i a b l e s
in
t h e eqns o f m ot io n
/ Fr i c t i on fac to r (Fann ing)
Fi F low inc l ina t ion num ber
G M as s f lux kg/m2.s
g Acce le ra t ion o f g rav i ty m/s2
h Specif ic en th a lp y J/kg
H E l e v a t i o n m
K Discharge coefficient
L L e n g t h m
n
N um be r o f moles
m M a s s
kg
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284
N Non-equi l ibr ium coeff ic ient
P
q
Qw
R
T
Q
Qs
s
t
T
u
V
X
X
Y
z
P r e s s u r e
Specific power
,
H ea t f lux
G a s c o n s t a n t
Source t e rm vec to r i n t he eqns o f mot ion
Po w e r i n p u t
j Vo lume t r i c g as gene ra t io n ra t e
Specific entropy
T i m e
T e m p e r a t u r e
Velocity
Speci f ic volume
V a p o u r q u a l i t y
Liquid mass f rac t ion
Va pou r m ass f r ac t ion
Sp a t i a l c o o r d i n a t e
Pa
W/kg
W/m2
m2Js2K
W
m3/s
J/kg.K
s
K
m/s
mZ/kg
6.1.
G RE EK S Y M BO LS
a Vo lume t r i c f r ac t ion
j3 Coeffic ient of th e ad de d ma ss te rm s in th e eqns of mo t ion
7 Isentropic coefficient
e Dim ensio nless speci fic vo lum e
r Coeff ic ient of th e in t e rp ha se exchan ge te r m s in th e eqn s of m ot io n
kgm/s
9 A n g u l a r c o o r d i n a t e
77 Dime nsio nles s pressu re
A E igenva lue o f t he ma t r ix o f t he eqns o f mot ion m/s
u>
C o r r e l a t i o n p a r a m e t e r
p D e n s i t y kg/m
3
X Coe ff ic ien t i n t h e wa l l exchan ge t e r m s o f t h e eqns o f m ot ion l / m
T
T im e in t e rva l s
r
t K
Sh e a r s t r e s s Pa
6.2. SUBSCRIPTS
0 Ini t ia l va lue
c C a l o r i m e t e r
t Co m po nen t (1 ,2 )
k C o m p o n e n t ( 1, 2)
j Co m po nen t (1 ,3 ) o r (1 ,6 )
g V a p o u r / g a s p h a s e
v V a p o u r p h a s e
/ L iqu id ph ase
m
M a x i m u m v a lu e
max M a x i m u m v a lu e
s "Se t" va lue
p peak va lue
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VENT SIZING FOR TEMPERED VAPOR SYSTEMS
J.C.LEUNG
Fauske & Associates, Inc.
16W070 West 8 3rd Street
Burr Ridge, Illinois 60521 U.S.A.
Introduction
This paper and the accompanying paper address the pressure relief
vent sizing methods for runway reaction systems. In addition, the
fire emergency sizing for non-reactive (storage) systems will be
included because of its prominence in the chemical industry. Runaway
reaction systems can generally be classified as tempered or non-
tempered types, see Table 1. A tempered system is one in which the
reaction heat can be removed by latent heat of vaporization, thus
controlling the runaway reaction from escalation in temperature.
This of course is accomplished by pressure relief venting. Many of
these systems are in fact normally operated in the refluxing mode for
temperature control. The latent heat can be provided by either the
reactant(s) or the solvent(s). However, the latter case presents
special concern If the system loses its solvent via boil-off due to
fire. Note that a tempered system can accommodate a reaction that
gives off noncondensable gases as long as the reaction temperature
can be controlled, we call this type a tempered hybrid system. On
the other hand, a non-tempered system exhibits little or no latent
heat of cooling at all, this is typical of a low vapor pressure
system. If the reaction products are also of low vapor pressure, the
pressure relief requirement can be quite small. But quite often the
reaction product(s) are noncondensable gas(es), these are so-called
"gassy" systems. For these non-tempered systems, the heat release is
largely retained in the runaway reaction mass and if left unattended,
without cooling re-initiation, quenching or dumping, may lead to very
large temperature and pressure excursions.
As might be expected, the vent sizing methods differ depending on
the system type. In this paper only the tempered vapor (or sometimes
being called tempered volatile) system will be addressed. The other
systems will be covered in the accompanying paper.
In the past, several methods of calculation have been proposed for
sizing emergency relief system (ERS) for runaway reactions. One
common, but frequently nonconservative method, is based on vapor
venting alone. As noted by several early observers (Boyle, 1967;
Harmon and Martin, 1970; Huff,
1973),
the most realistic case should
285
A. Benuzzi and J. M. Zaldivar (eds.). Safely of Chemical Batch Reactors a nd Storage Tanks, 285-298.
© 1991
ECSC,
EEC,
EAEC,
Brussels a nd
Luxembourg.
Printed in the Netherlands.
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286
be based on the release of a vapor-llquid mixture with two-phase
discharge in the relief system. This conclusion was supported in
part by actual pressure relief experience from industry. This was
also the recommendation of the Design Institute of Emergency Relief
Systems (DIERS) (Fisher, 1985; Huff,
1988),
a consortium of 29 com
panies under the auspices of AIChE formed in 1976 to develop improved
methods for ERS design. The methods presented here are either taken
from this technology or extensions of it.
Theory of Pressure Relief
Simply stated, pressure relief of a runaway reaction requires a
balance between the volumetric vapor generation rate V and the
volumetric discharge flow. This criterion can be derived from first
principles via consideration of mass and energy balance (Leung,
1986).
The above statement must be satisfied at the maximum
(turnaround) pressure during relief. Codes may require this maximum
pressure not to exceed 1.1 times or 1.21 times the design (gage)
pressure of the vessel. In equation form this criterion can be
written as
W
V - - - GA v (1)
v p ^ '
where W is the so-called relief vent rate (kg/sec), G is the dis
charge mass flux (kg/m
sec),
A is the vent area (m ) , p is the fluid
density (kg/m ) discharging from the reactor, and v is the fluid
specific volume
(1/p).
In general the two-phase fluid density
depends on the vapor volume fraction,
a
(or void fraction) via
p - a p
v
+ (1 -
<*)P
£
= (1 - *
P j i
(2)
where
p
and
p.
are the vapor density and liquid density, respec
tively. The discharge mass flux in Eq. (1) also depends on the fluid
conditions and is often limited by the choking (sonic or critical
flow) phenomenon at the minimum discharge flow area.
The volumetric vapor generation rate necessary to remove the ex
othermic reaction heat is given by
Q m q,-, rxn ^rxn ...
V - r - — v (3)
v h
.p
h „ v
v
'
vi v vi
where Q is the total heat release rate
(J/sec),
q is the
specific neat release rate (J/kg»sec), m is the reacting mass at the
point of pressure turnaround, and h . is the latent heat of vaporiza
tion.
Strictly speaking, Eq. (3) should be written as V =
(Q /h „)v „ where v „ denotes the net increase in volume per unit
rxn'
vi' vi . vi
n
_
^
n
p
-
mass upon vaporization. But at low pressure v . - v - v . - v and
Eq. (3) results. The traditional vapor vent sizing formula can be
obtained from Eqs. (1) and (3) with
p — p
and m - m , the reacting
mass at the start of relief venting, i.e.,
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287
m q
o
n
rxn
._. ,,
x
W — — r , vapor venting (4)
vi
whereas for a more general two-phase flow condition,
, two-phase venting (5)
m q
o^rxn
h
o
The corresponding equation for vent area with no overpressure, A , is
m q
p
m q
o
n
rxn o ^rxn
. o -rxn o -rxn r , , , .
-i
(6)
vi
p
v vi *v
According to this formula, the term
G/p
, which can be regarded as the
volumetric flow per unit area, plays a key role in determining the
vent size. It is therefore of interest to examine its variation for
a wide range of two-phase flow inlet conditions.
Using styrene properties at 500 kPa, Fig. 1 shows that both the
choked flow mass flux G and the fluid density
p
decrease with in
creasing void fraction a entering the relief piping. In contrast,
the volumetric flow term
G/p
is shown to increase rapidly with in
creasing void fraction. For example, we find in this illustration
that the volumetric flow per unit area is nearly 20 times larger for
all-vapor venting
(a —
1) than for two-phase venting with a = 0.2.
This would translate to vent area of 20 times larger for this two-
phase venting case than for vapor venting, if in fact no overpressure
(i.e.,
pressure above relief set pressure) is permitted. As will be
shown,
by allowing for overpressure, this difference in vent size can
be greatly reduced due to rapid mass (chemical "fuel") depletion in
the case of two-phase venting. By the time the pressure turnaround
criterion is approached
(i.e.,
Eq. (3 )), the mass remained can be
significantly less than the Initial mass prior to venting (i.e., m «
m
Q
) .
Venting With Overpressure
The simplest method of incorporating the effect of overpressure on
vent size is that due to Boyle
(1967).
He defined the required vent
area as that size which would empty the reactor before the pressure
could rise above some allowable overpressure. This can be repre
sented mathematically as
m
^ G A T
(7)
P
Here the emptying time, equated to the pressure rise time At , is
based on the pressure history obtained from adiabatic runaway "com
putation or data in a non-vented system (see Fig. 2 ) . Thus according
to Eq. (7), the vent area continues to decrease with increasing
overpressure. However this method does not yield realistic result as
no overpressure is approached. For the case of zero overpressure,
Eq. (7) would give an infinite vent size (since At - 0) which is at
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288
odds with the result presented earlier, Eq. (6 ). This discrepancy is
due to the neglect of the energy balance consideration in Boyle's
method, i.e., the effect of tempering and latent heat cooling has not
been considered. This limitation was overcome in Leung's formula
tion. The relief sizing formula for homogeneous-vessel (or uniform
froth) venting is given as (Leung, 1986 ),
m q
o ^
h 1
1 / 2
m v
n
where
(V
T
)
(8)
q " 0.5 C
p
|^ | + |^ | | (9)
Here q represents the average heat release rate during the overpres
sure venting period, (dT/dt) and (dT/dt) are the self-heat rates
corresponding to the set pressure (temperature) and the turnaround
pressure
(temperature),
respectively (see Fig. 2 ) . For no allowable
overpressure (AT -
0 ) ,
Eq. (8) reduces to Eq. (6) exactly.
The effect of overpressure on vent size can be clearly illustrated
by Eq. (8) together with the experimental data reported by DIERS.
Figure 3 is a dimensionless plot of A/A versus AP/P showing the
homogeneous-venting prediction of Eq. (8) and the styrene relief data
observed in both large (2000
£)
and small (32 i) scale facilities
(AIChE/DIERS,
1986a).
The agreement is encouraging. The discrepancy
is due to the observed vapor-liquid disengagement behavior which
results in lower overpressures than the idealized (homogeneous-vessel
venting) case. Note that by allowing for an overpressure correspond
ing to AP/P of 0.1, Eq. (8) suggests a vent area reduction of about
six times from the no overpressure case (i.e., A/A — 0.15). This
reduction is quite significant and is mostly due to the mass deple
tion via venting, resulting in a much lower total energy release at
the pressure turnaround point.
Figure 3 also depicts that at higher overpressure the relative
reduction in vent area becomes increasingly smaller. This portion of
the curve is in essence operating on Boyle's emptying time theory
with most of the energy release being stored as sensible heat in the
reacting
mass.
The ultimate turnaround in pressure is due primarily
to the emptying of the reactor. Due to the Arrhenius behavior
typi
cal of most reactions, the simple averaging approximation for q, as
suggested by Eq. (9), gets progressively worse at higher overpres
sure,
resulting in some cases a minimum in the area versus
overpressure curve (see Leung and Fisher, 1989). For these situa
tions better approximation of the non-linear heat rate can be given
by
AT
q - C — (10)
P
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289
where At is based on the pressure history obtained from adiabatic
runaway computation or data in a non-vented system. An alternative
would be to borrow the results from thermal explosion theory
(Townscend and Tou, 1980) where
P E
A
2 2
T T
s m
(dT/dt)
s
(dT/dt)
r
(11)
can be used to approximate the pressure rise time in Eq. (10 ). Here
E is the apparent activation energy and E /R can be obtained from
the slope of an Arrhenius self-heat rate plot. It is worth noting
that Eq. (8) in combining with Eq. (10) would reduce to Boyle's
formula, Eq. (7) as high overpressure is approached. The above-
mentioned vent sizing methods require the evaluation of two-phase
mass flux G. We shall postpone this discussion towards the end of
the accompanying paper where a complete and generalized treatment for
the mass flux will be presented.
Finally, a very simple method for sizing was advanced by Fauske
(1984a, 198 4b) and this has come to be known as the nomograph method.
In the most recent form it can be represented by (FAI, 1989)
m (dT/dt)
A = 1.5 x 10 — — (12)
s
2
where the particular units are: A[-] m , m [-] kg, dT/dt[=] °C/min,
P [=] psia. This equation was developed based on an overpressure to
set pressure ratio AP/P of 0.2. Note that this is different from
the traditional meaning or 20 % overpressure since by convention the
percent overpressure is defined based on the gage set pressure.
Vapor-Liquid Disengagement
The homogeneous-venting model is an idealized flow regime with no
phase separation at all inside the reactor (Huff, 1982). Because of
its simplicity in treatment and its conservatism, this uniform-froth
model offers a useful tool for ERS design. While a real venting
process falls somewhere between all-vapor venting and homogeneous
venting, the amount of phase separation or disengagement depends
largely on the particular fluid behavior and the vapor superficial
velocity. From studies of gas sparging through liquid columns, two
rather distinct flow regimes have been identified - the bubbly and
the churn-turbulent regimes. These flow regimes are best described
by the drift flux model (Zuber and Findlay, 1965; Wallis, 1969) and
have been used extensively to characterize the in-vessel fluid be
havior during the course of the DIERS research program (AIChE/DIERS,
1986b).
The complete vapor-liquid disengagement criterion can be
stated as follows. If the vessel free-board volume fraction (void
fraction)
a
exceeds the disengagement void fraction
a
, then vapor
venting is predicted. The latter is governed by the following drift
flux relationships for bulk heating:
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290
^ - - a
(1 -
a
) for bubble flow (13)
J*.
2 a
D
U 1 - a
n
CO D
for churn flow (14)
where j is the superficial vapor velocity at the top of the vessel.
At the turnaround condition, j is given by
. rxn
n
rxn
■ \ z \
J
g=> h
,p
A h .p A
Ci:>;
° vi V X V* V X
where A is the vessel cross-sectional area. Here U is the bubble
rise velocity given by
U -
^
a
Pjl - P
w
)
1 / 4
r
i V 4
(16)
where the coefficient Ak according to Wallis, ranges from 1.18 for
bubbly flow to 1.53 for cnurn flow. Here
σ
is the surface tension
and g is the gravitational acceleration. Upon solving for aD,
a
D
- 0.5 -
Jo.
25
-
ip
for bubbly flow (17)
a
D
=
2 + IA f
o r c h u r n
flo
w
(18)
where
ip = Q / ( h . p A U ) ,
can be defined as the dimensionless
rxn vi v x
^
superficial velocity. These solutions are presented graphically in
Fig. 4. If a > a
n
, vapor venting (complete disengagement) is
predicted. If a < a., then two-phase discharge upon relief opening
will occur. Under such situations, analytical equations have been
developed (Leung, 1987) for both the bubbly flow regime and the churn
flow regime. However, these solutions are not as simple or explicit
as Eq. (8) for the homogeneous-vessel venting case, but they can be
readily solved by numerical method.
Figure 5 is an illustration of the influence of flow regime on vent
size based on a styrene runaway example (Leung, 1986; Leung,
1987).
Note that the bubbly regime yields nearly the same vent size as the
homogeneous regime. The churn regime, on the other hand, yields
significantly smaller vent size, and in this example the vent size is
nearly the same as the all-vapor venting area if a 40% overpressure
is allowed.
Finally, some useful approximations for these flow regimes are
given here. For bubbly flow the venting process resembles closely to
that of the homogeneous-vessel case particularly when
ij> >
0.25.
According to Fig. 4 or Eq. (17), no vapor disengagement is possible
when the dimensionless superficial velocity
ip)
is greater than 0.25.
For churn flow, significantly more vapor disengagement takes place.
An asymptotic solution was suggested which yielded both simplicity
and acceptable accuracy. The vent area as given by Leung (1987) is
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291
^SS[* -
2
^ -
->
- a^ ry t r^ ) ] (")
where
1 r ) - J
|V2
The quantity (1 - T ) is in fact the fraction of mass remaining in the
reactor at the pressure turnaround point. This asymptotic solution
is recommended for AP/P of greater than 0.1. For more discussion
the reader can consult the original publication and a more recent
paper (Leung et al., 1988 ).
Fire Emergency Sizing for Non-Reactive System
The pressure relief system for storage vessel of non-reactive chemi
cals such as solvents is typically designed for fire emergency. The
total heat input from fire exposure Q„ is the product of the wall
heat flux q„ and the wetted heat-transfer area A :
^F w
% - < F \
(21)
Crozier (1985) has summarized various sizing formulae for fire emer
gencies which were all based on vapor venting assumption. His
discussion dealt mainly on the underlying fire heat fluxes assumed in
these formulae. The NFPA (1984) chart was found to be most widely
followed. For a wetted area of less than 19 m (200 ft ), the
average fire heat flux is 63 kW/m (20,000 Btu/h-ft ) . For larger
vessels with A > 19 m , the average fire heat flux actually falls
off due to the fact that larger vessels are less likely to be fully
exposed to fire. It should be noted that a local fire heat flux as
high as 110 W/ra (35,000 Btu/h-ft ) has been measured (API, 1976;
Moodie and Jagger, 1987). This value applies to direct flame im
pingement situations only. Unless the whole vessel is fully engulfed
by the fire, the average flux of 63 W/m is widely accepted (A < 19
m
) .
The fire emergency sizing also depends on the flow regime behavior
of the liquid under consideration. First of all, if the liquid is a
foamy fluid, i.e., the regime is in bubbly flow, then the relief
sizing treatment resembles closely to that for the runaway reaction.
In the case of fire, the dimensionless superficial velocity TJ> is
given in terms of
Q
F
^ - h - T ^ A - i r <
22
>
V f V X <*>
If the available free-board volume fraction
a
is greater than the
disengagement void fraction a
n
, sizing for vapor venting is adequate,
i.e. ,
a
Q
> a
D
- 0.5 - Jo.25 - i> (23)
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292
If
ip >
0.25, homogeneous-vessel venting is a close enough approxima
tion. The required vent area is given implicitly by the following
equation (Leung, 1986)
AT -
GAC
in
m
o
Q
F
V
vi
V GA h
vi
V hVi
m C v .
o p vJ
(24)
If TJ>
<
0.25, the venting behavior in bubbly regime can differ
substantially from the uniform-froth case. For lack of any better
method, the relief sizing equations for constant heating in bubbly
regime as given by Leung (1987) are suggested. At present insuffi
cient data exists for further refinement (although preliminary data
suggests that the above methods yield too conservative vent sizes).
For non-foamy system or churn-turbulent fluid, the influence of
external wall heating differs significantly from that of bulk heat
ing.
The vapor is found to nucleate on the vessel wall and upon
detachment forming a boiling two-phase boundary layer, see Fig. 6.
An analysis that describes the void distribution and thickness of the
boundary layer, both of which increase with vertical distance along
the wall has been presented (Grolmes and Epstein, 1985). The amount
of liquid swell as a result of the rising bubble in the boundary
layer was found to be significantly less than the case where bubbles
are created and rising throughout the bulk of the liquid. In fact, a
reported experimental investigation suggests that in venting assess
ments of liquid-filled vessels subjected to external fire, it is
acceptable even to ignore the effects of liquid swell for non-foamy
liquid (Fauske et al.,
1986).
However, the possibility of two-phase
flow to the vent still exists if the velocity of the venting vapor
within the free-board volume is such that a droplet spray is pulled
off the liquid surface and carried by the vapor to the vent (Epstein
et al., 1989). Usually this occurs at a very high quality (vapor
mass fraction) flow condition. Nonetheless, it causes a significant
increase in pressure drop across the vent and particularly detrimen
tal to atmospheric-type storage tanks where allowable overpressure is
very limited. Epstein et al., (1989) has developed a criterion for
the onset of two-phase venting via entrainment consideration, see
Fig. 6. From this criterion, a minimum head space clearance h . can
,
D
, . ,
r
min
be derived,
2 p h ,U„
v vi E
1/2
(25)
where U is the entrainment velocity (or critical vapor velocity for
droplet fluidization) as given by the Kutateladze (1972) correlation
" g P ,
1/4
(26)
Thus if the available head space separation h is greater than h . ,
vapor venting is assumed and the sizing is according to vapor relief
requirement,
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293
111
tr
I —
<
DC
H I
0 .
LU
I -
~^
1X1
cc
ID
CO
CO
H I
tr
0_
T IM E I N T O R U N A W A Y
Figure 1. Nomenclature for runaway in unvented system.
J C L B 8 1 0 3 1 H A
£
1 0 — ,
6 0 0 -
Q :
£ 2 0 0
CO
z
LU
Q
— X 6 0
- i
1
4 0
t
ra
CO
O
*-
o
X
o
CO
CO
<
6 -
4 —
2 —
I I I
rn
<
X
n
o
5
i -
- 1
;-
~ ^ -~~~
~
-
"
—
—
-
~ ' ^ - - -
"
~
l
l l l
P
^
4 —
1 1
I 1 I 1
S T Y R E N E
P
0
= 500 kPa
G//3 . , / \
G
1 1 1 1 1
/—
j -
-
—
—
-
\ -
\ -
0.2 0 .4 0 .6 0 .8
INLET VOID FRACTION, a
<
L U
C C
<
CC i'
10 LU E
6
0
a
o
>
Figure 2. Variation of two-phase density (p), mass
flux (G ), and volumetric flow per unit area (G/p)
with inlet void fraction.
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294
0.5
0.4
0.3
<
•v.
<
0.2 —
0.1
—
—\
I
O N
0
|
I I
D I E R S I C R E S e r i e s
0
•
D
S c a l e ( J )
V e n t i n g
3 2
Top
3 2
B o t t o m
2 0 0 0 Top
H o m o g e n e o u s V e s s e l
J~
V e n t i n g
o
• ■
o
I
O
—
-
0.1 0.2
AP/R,
0.3 0.4 0.5
Figure
3.
Comparison
of
homogeneous vessel
prediction versus DIERS styrene relief data.
8
<
a
o
»
0.1
0 .01
=—r—
—
-
—
—
—
-
/
'
I
' I ' I ' i
B u b b l y
F l o w
I . I , I .
—
-
—
—
-
—
T
T
m
0.2
0.4
0.6
0.8
1
DISENGAGEMENT
VOID FRACTION,
X
Figure 4. Disengagement void fraction for bubbly
and churn-turbulent flow regimes.
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295
0.05
PbAK PRESSURE, bar (abs)
5 5.5 6 6.5
S t y r e n e P o l y m e r i z a t i o n
9500 kg in 13 .16 m
3
T a n k
H o m o g e n e o u s
V e n t i n g
V a p o r
- V e n t i n g
A r e a
i
Bubbly
Churn
20 40 60
PERCENT OVERPRESSURE
Figure 5. Vent area versus overpressure for
styrene runaway example in different venting
regimes.
V a p o r
I C L . 0 1 0 2 0 4 C .A
Figure 6. Sketch of boiling boundary layer
under external fire heat flux and minimum
head space clearance for vapor relief.
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296
TABLE 1. Classification of reactive systems
TYPE CLASS SOURCE OF PRESSURE
Vapor System Tempered Vapor (partial) pressure as
driven by temperature
effect.
Hybrid System Tempered Both vapor pressure and gas
pressure.
Hybrid System Non-Tempered Dominated by gas pressure.
Gassy System Non-Tempered Gas pressure due to gas
accumulation within reactor.
Q
F
A
= h - ^ >
f 0 r h > h
m i n <
27
>
where G is the vapor mass flux (G
~
0.61 |P p for vapor choked
flow). On the other hand, if h < h . , then an alternative is to
enlarge the vent area such as to stay just below the droplet entrain-
ment velocity within the vent (Fauske et al.,
1986),
Q-F
A = — . „ , for h < h . (28)
P h „U_, m m
v vi E
Conclusion
This paper provides a state-of-the-art summary of practical vent
sizing methods for tempered vapor systems. Both runaway reaction and
fire emergency of non-reactive storage have been discussed. The
effect of two-phase discharge on vent size can be elucidated and
recommendations are provided for different venting flow regimes.
References
American Institute of Chemical Engineers (1986a), "Phase III
Large Scale Integral Tests, DIERS
III-5,
Experimental Results
for Series III Tests, DIERS
III-6,
Experimental Results for
Series IV Tests, Analysis and Program Summary", Reports sub
mitted by Fauske & Associates, Inc. for AIChE/DIERS.
American Institute of Chemical Engineers
(1986b),
"Emergency
Relief Systems for Runaway Chemical Reactions and Storage
Vessels:
A Summary of Multi-Phase Flow Methods", Report
submitted by Fauske & Associates, Inc. for AIChE/DIERS.
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297
American Petroleum Institute (1976), API
RP-520,
Fourth
Editions, "Recommended Practice for the Design and
Installation of Pressure-Relieving Systems in Refineries, Part
I - Design and Part II - Installation", API, Refinery
Division, Washington, D.C.
Boyle, W. J., Jr. (1967), "Sizing Relief Area for Polymerization
Reactors", Chem. Eng. Prog., 63 (8 ), p. 61 (August).
Crozier, R. A., Jr. (1985), "Sizing Relief Valves for Fire
Emergencies", Chem. Eng. Prog., p. 49, October 28 issue.
Epstein, M., Fauske, H. K., and Hauser, G. M. (1989), "The Onset
of Two-Phase Venting Via Entrainment in Liquid-Filled Storage
Vessels Exposed to Fire", J. Loss Prev. Process Ind., Vol. 2
(1),
P- 45.
Fauske & Associates, Inc. (1989), "Reactive System Screening
Tool (RSST) System Manual - Methodology and Operations", FAI
Report No. FAI/89-73.
Fauske,
H. K. (1984a), "A Quick Approach to Reactor Vent
Sizing", Plant/Operations Prog., 3 (3 ), p. 145.
Fauske, H. K. (1984b), "Generalized Vent Sizing Nomograph for
Runaway Chemical Reactions", Plant/Operations Prog., 3 (4 ), p.
213 (October).
Fauske, H. K., Epstein, M., Grolmes, M. A., and Leung, J. C.
(1986), "Emergency Relief Vent Sizing for Fire Emergencies
Involving Liquid-Filled Atmospheric Storage Vessels",
Plant/Operations Prog., 5 (4 ), p. 205.
Fisher, H. G. (1985), "DIERS Research Program on Emergency
Relief Systems", Chem. Eng. Prog., 81 (8 ), pp. 33 -36 (August).
Grolmes, M. A. and Epstein, M. (1985), "Vapor-Liquid
Disengagement in Atmospheric Liquid Storage Vessels Subjected
to External Heat Source", Plant/Operations Prog., 4 (4 ), pp.
200-206.
Harmon, G. W. and Martin, H. A.
(1970),
"Sizing Rupture Discs
for Vessels Containing Monomers", Paper preprint No. 58A, 67th
Nat.
Mtg. AIChE (February).
Huff, J. E. (1973), "Computer Simulation of Polymerizer Pressure
Relief", Chem. Eng. Prog., Loss Prevention Tech. Manual, Vol.
7,
p. 45.
Huff,
J. E. (1982), "Emergency Venting Requirements",
Plant/Operations Prog., 1 (4 ), p. 211
(October).
Huff, J. E. (1988), "Frontiers in Pressure-Relief System
Design", Chem. Eng. Prog., 84 (9), pp. 44 -51 (September).
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Kutateladze, S. S.
(1972),
"Elements of the Hydrodynamics of
Gas-Liquid Systems", Fluid Mechanics - Soviet Research, Vol.
1. P. 29.
Leung, J. C. (1986), "Simplified Vent Sizing Equations for
Emergency Relief Requirements in Reactors and Storage
Vessels",
AIChE Journal, 32 (10 ), pp. 1622-163 4.
Leung, J. C. (1987), "Overpressure During Emergency Relief
Venting in Bubbly and Churn-Turbulent Flow", AIChE Journal, 33
(6), pp. 952-958.
Leung, J. C , Buckland, A. C., Jones, A. R., and Pesce, L. D.
(1988), "Emergency Relief Requirements for Reactive Chemical
Storage Tanks", Institute of Chemical Engineers Symposium
Series, No. 110, p. 169.
Leung, J. C. and Fisher, H. G.
(1989),
"Two-Phase Flow Venting
from Reactor Vessels", J. Loss Prev. Process Ind., Vol. 2, p.
78.
Moodie, K. and Jagger, S. F. (1987), "Flow Through Pressure
Relief Devices and the Dispersion of the Discharge", Inst, of
Chem. Engrs., Symp. Series No. 102, p. 215.
National Fire Protection Association (1981), "National Fire
Codes",
NFPA-30 Flammable and Combustible Liquids Code, NFPA,
Quincy, MA.
Townscend, D. I. and Tou, J. C. (1980), "Thermal Hazard
Evaluation by an Accelerating Rate Calorimeter", Thermochimica
Acta,
Vol. 3 7, p. 1.
Wallis, G. B.
(1969),
One-Dimensional Two-Phase Flow. Chapter 4,
McGraw-Hill, New York.
Zuber, N. and Findlay, J. (1965), "Average Volumetric
Concentration in Two-Phase Flow Systems", Trans. ASME J. Heat
Transfer, Vol. 87, p. 453.
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VENT SIZING FOR GASSY AND HYBRID SYSTEMS
J.C.LEUNG
Fauske & Associates, Inc.
16W070 West 8 3rd Street
Burr Ridge, Illinois 60521 U.S.A.
Introduction
In the previous paper, vent sizing methodology for tempered vapor
systems has been presented. In this paper the gassy system and the
hybrid system are examined. As indicated in Table 1 of the previous
paper, two general types of hybrid system can be found. The type
that does not exhibit any sustained tempering is the non-tempered
type (either due to solvent boiled off or insufficient latent heat of
cooling) and this system exhibits essentially the same characteristic
as the gassy system - the source of pressure is dominated by the
evolved gas mostly. The other is the so-called tempered hybrid
system and as expected, this system exhibits similar tempering
(latent heat of cooling) characteristic as the vapor system.
However, if not properly relieved, the accompanying gas evolution can
cause the reactor pressure to rise much more rapidly. We will ex
amine the relief requirement for these systems and the sizing methods
in this paper.
Theory of Pressure Relief
In general the pressure relief of a runaway reaction requires a
balance between the volumetric vapor/gas generation rate and the
volumetric discharge flow. This criterion can be represented mathe
matically as
m q
o^rxn
,
— T + m m
W \t ° 6
- — ^ — r (l)
or in terms of the required vent area with no allowable overpressure,
[°(P
V
+ P
e
) + (1 - a) pj
A
o
m
0
q
n
r x n •
u +
N
:
' v
+
'
g
>
(2)
299
A.
Benuizi and
J.
M. Zaldivar
(eds.).
Safety of Chemical Batch Reactors a nd Storage Tanks, 299-310.
© 1991
ECSC,
EEC,
EAEC,
Brussels and
Luxembourg.
Printed in the Netherlands.
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300
where
p
and
p
are the vapor and gas density, respectively. From
ideal gas law,
p
S
- P M y'RT and
p
- P M /RT. Again the above
equations apply to the case of no^overpressure with an initial batch
size of i , It should be noted that according to the partial
pres
sure definition, the total volumetric generation rate is not equal to
the sum of the vapor volumetric rate (V - m q /h
„ p )
and the gas
volumetric rate (V = m m
/p ) .
In Eqs. (1; and (2; , m denotes the
specific mass rate of gas evolution. Experimentally it ^can be es
timated from pressure rise rate data via
VM
-m ,
Ut /
m
t
°
v
-'meas
where V is the free-board volume the gas occupies in the test ap
paratus, (dP/dt) is the measured pressure rise rate, and m is
the test sample
mass.
Note that in the case of vapor relief, the
vent rate requirement is simply
q
w f
V a
P °
r
m
JventingJ o
rxn
r + m
W
But for homogeneous-vessel (uniform-froth) venting, which
sidered the most conservative, the required vent rate is
.[
m
o
q
r x n . •
r + m
Kl 6
i
o m o g e n e o u s
v e n t i n g I ~ (P M + P M ~)/RT
°
J
V wv g wg
(5)
Thus the difference in relief vent rate between homogeneous venting
and vapor venting is very large and can be given by
..(homogeneous^ _.
,.
.
W ° m /V (1 -
a )p
I venting I
o'
o
r
w
vapor
1
^ventingj
P
(6)
p + p p + p ^ '
v
H
g
H
v
H
g
where
a
is the initial free-board volume fraction in the reactor.
In what follows we will discuss the vent sizing implication and the
merit, if any, for allowing for overpressure in both gassy and hybrid
systems.
Gassy System Vent Sizing
The non-tempered gassy runaway system is deficient in latent heat of
cooling which is used in vapor system to control the runaway by
venting. For the gassy system, the temperature runaway history
remains essentially identical to the adiabatic case even in a vented
environment. Figure 1 illustrates a typical venting scenario for a
gassy system. Due to the continued accumulation of gas given off
from the runaway reaction, the rupture disk soon reaches its relief
pressure and causes the reactor to depressurize quickly to ambient
pressure or to the back pressure imposed on the downstream equipment
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(Pt.
1 in Fig. 1) . Two-phase flow is not expected since the gas
evolution rate is quite low at this early stage. The assumption of
two-phase discharge would be non-conservative (unsafe) here since it
causes early emptying of the reaction
mass.
After this initial
"blow-off" of the gas, the reactor temperature continues to rise
while the system remains at the prevailing back pressure (Pt. 2 in
Fig.
1 ) . Note that the use of a reclosure-type relief valve would
keep the system pressure at close to the set point with periodic
opening to bleed off the excess gas, but the temperature heatup
profile remains unaltered. As the reaction approaches the maximum
rate prior to complete conversion (decomposition), pressurization of
the reactor will take place (Pt. 3 in Fig. 1 ) , and this will most
likely be accompanied by two-phase discharge. The worst case to
consider is therefore the onset of homogeneous-vessel venting
coinciding with the peak reaction rate (as indicated by maximum dT/dt
or dP/dt
rate),
see Fig. 2. Here the general vent rate equation, Eq.
(5), for gassy system reduces to
m m
o g.max
W
max
p
g
m
o
(7)
Evaluating this requirement at the maximum allowable pressure P
(after substituting Eq. (3) into (7)) yields,
m V /-.„-> max
m
w
_ _o _cfdP]
max m P Idtl
t m
v
J
\
(8)
To estimate the required vent size for the allowable overpressure (AP
= P - P ) ,
m s
W
A = f (9)
where G is to be evaluated at P and at the reactor loading of m /V.
For gassy system, the two-pnase flow can be characterized as non-
flashing flow discharge; this is in total contrast to the flashing
flow regime for the vapor system. A unified treatment for both
regimes has been developed and will be presented later on.
Starting with Eq. (8) and after making a number of conservative
approximations, Fauske arrived at a simple formula in terms of the
maximum pressure rise rate measured in either the RSST (FAI, 1989) or
the VSP equipment,
m (dP/dt)
A
v
_° meas ,, .„
A
-
K
.
—^Jl <
1 0
>
m
where the coefficient K is 3 x 10" for the RSST and 3.3 x 10" for
the VSP (this difference accounts for the different containment
vessel free-board volume). Here the particular units are: A[=] m ,
dP/dt[=] psi/min, P [-] psia.
So far no attempt nas been made to account for the mass loss due to
decomposition and venting. The latter involves a transient
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(unsteady) calculation during the venting process. This effect is
expected to result in about a factor of two reduction in vent size
from the above methods. Early venting prior to the peak rates re
quires significantly more analysis and physical (flow regime)
characterization. This is best investigated experimentally by the
direct scaling approach as discussed below.
The so-called area-to-charge direct scaling approach (Leung and
Fauske,
1987) offers an alternative method which usually yields a
smaller vent size than the calculational methods given above. This
is because early loss of reactant from the reactor due to two-phase
flow is an advantage for non-tempered systems. Since this loss is
always more effective in the reactor than in the test apparatus due
to much larger superficial velocities, direct scale-up in apparatus
like VSP using top venting is hence possible. A vent size that allow
safe venting of the test sample and empties its content completely
(this is most important) can be safely extrapolated to full scale
based on area-to-charge scaling. Often a number of tests may be
required to narrow in on the size that limits the overpressure to
just below the allowable level.
It should be mentioned here that the Boyle's emptying time formula
(Eq. (7) of previous paper) can yield nonconservative results also if
the pressure rise time At is evaluated at a point where the rate is
substantially less than the peak reaction rate. On the other hand,
it has been found that if the peak reaction rate (m ) was used to
2 max
calculate At , the resulting vent size would be overly conservative.
Hybrid System Vent Sizing
The tempered hybrid system possesses volatile or condensable
component(s) which can be counted on to control the runaway tempera
ture via latent heat of cooling. Figure 3 illustrates a typical
venting scenario for a hybrid system. Although this illustration
uses a reclosure-type relief valve (PSV), the general venting trend
is not much different in the case of a rupture disk. Here PSV would
"lift" first when the system pressure attains the relief set pressure
and bleed off the accumulated gas (Pt. 1 of Fig. 3 ) . The lifting and
reclosing of the PSV might occur many times while the vapor pressure
of the volatile component(s) continues to increase due to rising
temperature. It is not anticipated that two-phase discharge would
occur during these early periodic relief intervals. However, as the
tempering point is approached, the vapor pressure contribution
noticeably increases and the total vapor and gas volumetric rate
rises rapidly. Typically this is the point when two-phase discharge
simultaneous with overpressure venting would take place (Pt. 2 of
Fig. 3 ) . For an adequately sized vent, the pressure would turn
around before the maximum allowable pressure and the temperature
would turn around also. Due to the effect of gas accumulation, the
pressure turnaround and the temperature turnaround do not occur at
the same time (Pts. 3 and 4 of Fig. 3 ) .
The so-called tempering condition is achieved when the evaporative
cooling becomes equal to the reaction heat release. This condition
is attained at the temperature turnaround point (Pt. 4 of Fig. 3 ) .
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The tempering condition can be determined experimentally in apparatus
like the VSP or RSST. Mathematically we can write the ratio of the
partial pressures as
P
-g _
P x /M
v
v
x /M
g
w
g _
m
- g _
M
.
W
S.
q
^ r x n
h .M
vx . wv
(11)
pressure P,
T \
For vent
In addition, these partial pressures add up to the system total
sizing purpose, one is most interested in
emperature T at the relief device set
pressure P . Thus with P„ equal to P , we can solve for the temper
ing temperature T__ which yields the following vapor pressure
(12)
(T ) -
1 +
This procedure has been demonstrated to yield excellent agreement
with experimental result for hydrogen peroxide decomposition, a
well-
known hybrid system.
The conservative venting scenario is to assume homogeneous-vessel
venting after the reacting mixture has attained the tempering tem
perature corresponding to the relief set pressure (see Fig. 2) .
Analytical sizing equations for such a venting scenario have not been
put forward yet, mostly because of equation complexity. Equation (5)
is ideally suited to estimate the vent rate requirement for no over
pressure, but such a case is deemed overly conservative. Another
somewhat less conservative approach is to modify the former vapor
system sizing formula by Leung (1986)
A -
m q
o ^
m
o \£
1/2
+ (C AT)
P
1/2
(13)
by incorporating the gas accumulation effect on overpressure (Leung
and Fauske, 1987). For a given allowable overpressure AP, the cor
responding "over-temperature" is calculated based on a non-vented
situation, i.e..
AT
AP
(dP/dT)
AP
vi
Vvi
m m RT
° g
a
VM (dT/dt)
o wg 's
(14)
in
ote that in terms of experimental measurement, the second term
the denominator can be replaced by (m V / m a V)(dP/dt)
Typically this term dominates and the available°Af and° hence
A T ^ I S
governed by gas accumulation. The result is quite similar to Boyle's
theory
(1967).
The discharge flow of a hybrid mixture lies somewhere between
flashing flow (for vapor system) and non-flashing flow (for gassy
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system). A recent development based on simple mixture consideration
has been suggested for the calculation of the discharge mass flux G
in Eq. 13). This will be presented in the next section.
Another vent sizing method for hybrid system is that based on the
RSST technology and the simple equation approach FAI, 1989; Creed
and Fauske, 1990)
suggested:
Based on AP/P of 0.2, the following formulae are
-6
m dP/dt)
A - 5 . 6 x l 0 —
1.5 x 10
p
3/2
s
dT/dt)
for RSST only)
15)
16)
where the units are: A[=] m , m
psi/min, and dT/dt)
[ ]°C/min.
-] kg, P [■
. , The larger
suggested for design. Note that Eq. 15) contains
tion of
psia, dP/dt)
g
[-]
of the two areas is
slight modifica-
the gassy system sizing formula, Eq. 10) while Eq. 16) is
simply the vapor system sizing formula FAI, 1989).
Gassy and Hybrid Flow Discharge
In most of the vent sizing equations presented in this paper and the
previous paper, a two-phase discharge mass flux G appears explicitly
in the vent size equation, such as in Eqs. 9) and 13). In fact for
these analytical vent sizing methods, the procedure can be broken
down to two rather distinct steps. The first step is to calculate
the required vent rate W which is entirely independent of the
dis-
charge flow through the relief device. The second step is to obtain
the required vent area A which, according to Eq. 9), requires the
evaluation of the discharge mass flux. For completeness a general
treatment for evaluating such two-phase discharges is summarized here
Leung, 1990a). The present unified method has the attributes of
yielding the two limiting cases, namely the flashing flow limit for
the vapor system and the non-flashing flow limit for the gassy
sys-
tem. The solution for nozzle flow can be characterized by the
following dimensionless physical groups, evaluated with properties at
inlet stagnation conditions:
a +
1 -
a )p.C
T P
o o
r
SL
p o vo
a inlet void fraction)
o
vlo
vio
a + 1
o
o s
y - P /P
o go o
G* --==£=
0 * 0
P /P eas mole fraction)
vo
o
V 6
normalized mass flux)
Here u is a measure of the flow compressibility of the flashing
component while
a is a measure of the flow compressibility of the
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305
non-flashing component. The relative amount is conveyed by the inlet
gas mole fraction y in the vapor phase. The generalized solution
for the normalized two-phase mass flux in a nozz le is given by (Leung
and Epstein, 1991)
G *
a y I n r r
6
- + (1 - a )y
o
y
g o P o - 'go
go
6
g°J
w ( l
"P
V
l n
p ~
+ (1
" vo
+ 1
« ) d - y
g 0
>
1/2
( 1 7 )
For given inlet conditions (i.e., P , T , a , u> , y ) , an additional
expression relating the two partial pressures, P ana P , is needed
before Eq. (17) can be solved for G*. This relationship is
The Dalton's partial
nozzle exit pressure P
(18)
pressure law can be written in terms of the
and the partial pressures:
g°
+ (1
g°
V
(19)
Eqs.
(18) andhus with the downstream pressure slightly below P ,
(19) can be solved for P /P and P /P , which can then be sub
stituted into Eq. (17) for calculating G*. This G* will correspond
to unchoked (subsonic) flow condition. However, as the downstream
pressure is reduced, G* reaches a maximum at the so-called choking
condition. By definition further reduction in downstream pressure
has no effect on G*. At this choked condition, the exit pressure is
given by the choked or critical pressure which is found from the
f o l l o w i n g e x p r e s s i o n
P
- a y I n r
2
- + (1
o
J
go Pgo
P
- «-(i -
y
g 0
)
l n
f~
° vo
1
2
y
g°
a
o
fP 1
- g -
P
I g°J
2
( 1
+
- a )y
o •'go
r p
)
1
- i * -
l g°J
+ ( i - « ) d - y
g 0
)
- y
R
0>
u
fP 1
V
P
0
.
2
1
P 1
V
P
v o
(20)
-.2
+ 1
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306
TIME
Figure 1. Typical venting scenario for gassy system.
Homog e n e o u s
Ven t i n g
ca
o
CO
o>
o
•E
a.
T7
■a
T3
N o n - T e m p e r e d
S y s t e m
( G a s s y )
T e m p e r e d S y s t e m s
( V a p o r / H y b r i d )
■TP
'M R
TEMPERA TURE ( R e c i p r o c a l S c a l e )
Figure 2. Sizing approach for tempered and non-tempered systems.
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PSV
LU
c c
I -
<
DC
LU
Q_
L U
I -
^
LU
CC
Z)
CO
c o
L U
c c
CL
TIME
I C L . 9 0 0 4 1 6 A . A
Figure
3.
Typica l venting scenario
for
tempered hybrid system .
1.4
1
1 I I I
lll|
1 1 I I I
^ - ^ N o n - F l a s h i n g F lo w
I I l l l | 1—I I I I I I I
F l a s h i n g F l o w _
0.8
0 .6
0 4
0.2
1 10
w
- - a
0
+
P o
C
P
T
o
p
o ( W h
v l o
)
100
2
Figure
4 .
Non-flashing
and
flashin g choked flow solu tion s
for
frictionless noz zle discharge.
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j _
_L
0.2 0.4 0.6
INLET VOID, a
Q
0.8
1.0
Figure 5. Normalized mass velocity and critical pressure
ratio versus inlet void fraction for u) = 10
(y - 0, pure flashing flow; y = 1 , pure
non-flashing flow).
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This is a transcendental equation for either P /P or P /P as it
R EO v V O
is to be solved simultaneously with Eq. (18) for
6
these critical
pressure ratios.
The solution for flashing flow (y - 0) and non-flashing flow (y
- 1) can be represented quite compactly for all inlet conditions is
shown in Fig. 4 (Leung,
1990b).
At the transition point between
these two regimes is the isothermal gas flow solution (G - 0.606
(P
p
) at u -
a -
1.0). A useful approximation for the flashing
choked flow regime when u> > 10 (for low quality inlet typical of most
homogeneous-vessel venting case) is simply (Leung, 1986)
G - 0.9 - ^ ■
1
(21)
C V
vio T C
J
o
p
Figure 5 illustrates how G* and P /P depends on
a
at various gas
mole fraction, y . At a fixed u — 10 (see definition of co for
a
,
this figure displays the shape of the G* versus
a
curves and the
P /P versus a curves for the entire range of y values (entire
C O O 2 Q
hybrid
regime).
It should be noted also that at the
&
limit of a - 0
(absence of both vapor and gas in the inlet), the current solutions
are in perfect agreement with the choked flow solution for subcooled
liquid inlet (Leung and Grolmes,
1988).
Conclusion
This paper, together with the previous paper, provide a state-of-the-
art summary of practical vent sizing methods for both tempered and
non-tempered systems. Significant advances in the area of two-phase
relief have been made in the past decade and these methods should
serve as valuable tools in ERS design. In addition, correlations and
equations have been developed for calculation of flashing flow, non-
flashing flow, and flashing flow with noncondensable gas through
relief devices. Finally, the tempered hybrid system should deserve
further study as such a development would provide a smooth transition
between the volatile vapor system and the gassy system.
References
Boyle,
W. J., Jr.
(1967),
Sizing Relief Area for Polymerization
Reactors , Chem. Eng. Prog., 63 (8), p. 61.
Creed, M. J. and Fauske, H. K (1990), An Easy, Inexpensive
Approach to the DIERS Procedure , Chem. Eng. Prog., 86 (3), p.
45
(March).
Fauske & Associates, Inc. (1989), Reactive System Screening
Tool (RSST) System Manual - Methodology and Operations ,
Report No. FAI/89-73.
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310
Leung, J. C. (1986), "Simplified Vent Sizing Equations for
Emergency Relief Requirements in Reactors and Storage
Vessels",
AIChE Journal, 32 (10 ), p. 1622.
Leung, J. C. and Fauske, H. K.
(1987),
"Runaway System
Characterization and Vent Sizing Based on DIERS Methodology",
Plant/Operations Progress, 6 (2), p. 77.
Leung, J. C. and Grolmes, M. A. (1988), "A Generalized
Correlation for Flashing Choked Flow of Initially Subcooled
Liquid", AIChE Journal, 3 4 (4 ), p. 68 8.
Leung, J. C. (1990a), "Two-Phase Flow Discharge in Nozzles and
Pipes - A Unified Approach", J. Loss Prevention Process
Industries, Vol. 3, p. 27.
Leung, J. C. (1990b), "Similarity Between Flashing and Non-
Flashing Two-Phase Flows", AIChE Journal, 36 (5), p. 797.
Leung, J. C. and Epstein, M. (1991), "Flashing Two-Phase Flow
Including the Effects of Noncondensable Gases", ASME Trans. J.
of Heat Transfer, 113 (1), pp. 269-272 (February).
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CALORIMETRY FOR EMERGENCY RELIEF SYSTEMS DESIGN
J.L. GUSTIN
RHONE-POULENC INDUSTRIALISATION
24, AVENUE JEAN JAURES
69151 DECINES CEDEX B.P.166
FRANCE
ABSTRACT. This paper gives an overview of the DIERS methodology for vent sizing
for runaway react ions. The DIERS vent sizing methods rely on experimental data
obta ined under adiaba t ic con dit ions . The theoret ical ba ckg roun d of prac t ical interest
for pseu do-adiab at ic calor imetry is given. This theore t ical ba ckg rou nd provides
methods to correct the data obtained in pseudo-adiabat ic calor imetr ic devices to true
adiabat ic condi t ions.
The experimental methods available for the system characterizat ion and data
acq uisit ion are des cribe d. These experimental m ethods are :
The Accelerating Rate Calorimeter (ARC),
The Vent Sizing Package (VSP),
The closed Dewar experiment,
The Reactive Systems Screening Tool (RSST).
The results obtained with the various methods are compared and the relevance of
these methods to vent sizing is discussed on an experimental and theoret ical basis.
311
A.
Benuzzi and J. M. Zaldivar (eds.), Safety of Chemical Batch Reactors and Storage Tanks, 311-354.
© 1991 ECSC, EEC, EAEC, Brussels and Luxembourg. Printed in the Netherlands.
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312
1 - INTRODU CTION
Emergency Relief Systems (E.R.S.) are provided on vessels containing a
chemical compound or a mixture prone to undergo a runaway react ion, to
prevent these vessels from exploding.
Normally these vessels cannot resist the pressure generated by a runaway
react ion.
The Design Institute for Emergency Relief Systems (DIERS), a working party of
the AlChE, has issued vent sizing guidelines which take into account the
occurence of two phase f low when the E.R.S. is actuated.
The previous methods issued by the A.P.I, which only took into account gaseous
release could lead to undersizing by a factor of 6-10, should a runaway react ion
be init iated (1).
The DIERS Methodology for vent sizing includes the fol lowing basic steps
Step 1 : Def init ion of the worst cred ible deviat ion of the proces s, to p rovide the
design case for vent sizing.
Step 2 : Characterization of the react ing system behaviour, using pseud o-
adiabat ic experimental techniques. The react ing systems are divided in
three classes :
- High vapor systems
- Gassy reac tions
- Hybrid systems.
Step 3 : Acq uisit ion of the exp erimental data necessary for vent s izing . The
nature of the data required depends on the nature of the react ing
system. The data must be obtained under condit ions close to adiabat ic
for a correct simulat ion of the runaway behaviour.
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Step 4 : Choice of the vent sizing method and of the two phase f low calculat ion
method, according to the system behaviour.
The purpose of this paper is to describe the experimental methods available for
the system characterizat ion and data acquisit ion for vent sizing and to discuss
the relevance of the various methods on an experimental and theoret ical basis.
The def init ion of the worst credible deviat ion of the process and the discussion
of the choice of the most suitable method for vent sizing and two phase f low
calculat ions, are beyond the scope of this paper.
CHARACTERIZATION OF THE REACTING SYSTEM
Three classes of react ing systems are considered in the DIERS methodology.
1) High vapor systems
High vapor systems are react ing systems where the pressurizat ion of the
enclosure is due to a vapo r- l iquid e qu il ibr ium . The vapor pres sure may be
that of the solvent, the reactants, the products or the react ing mixture.
The vapor- l iquid equil ibr ium must apply during the t ime necessary for the
E.R.S. actuact ion. This must be checked on an experimental basis under
runaway condit ions.
High vapor systems are tempered systems : If E.R.S. actuation allows control
of the pressure in the vessel, the temperature is also control led because the
pressure vs temperature relat ionship is imposed by the vapor- l iquid
equi l ibr ium.
The control of the temperature during the vent actuat ion al lows the control of
the react ion rate in the react ion mixture, provided that the react ion fol lows
the ARRHENIUS law.
These features al low the thermal runaway to be easily control led. The vent
area required is usually less for a high vapor system than for a gassy
react ion.
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For high vapor systems, the pressure in the vessel does not depend on the
f i l l ing rat io. This al lows laboratory experime nts to be p erform ed in a closed
test
cel l ,
with a high f i l l ing rat io, giving nearly adiabat ic condit ions yet no r isk
of cel l rupture.
For high vapor systems the vent area is est imated by considering the
adiabat ic heat rate at the temperature Tg related to the vent set pressure P
s
by the vapor- l iquid equil ibr ium.
The fol lowing data is required for vent sizing :
- the adiabatic heat rate curve of the reaction m ixtur e,
- the pressure vs tem perature relat ions hip.
2) Gassy reactions
Gassy react ions are react ions in the condensed phase which produce non-
condensable gases l ike CO, C0
2
, N
2
, NO, NgO, 0
2
...
The pressure in the enclosure is due to non-condensable gases only. There is
no vapor- liquid equi l ibr ium.
Consequent ly, the system is not tempered, even if the pressure in the
enclosure is controlled by an E.R.S. there is no vaporization heat sink, the
temperature r ise is unaffected and the chemical react ions speed up with
temperature.
For gassy react ions, the pressure in the vessel depends on the f i l l ing rat io.
The higher the f i l l ing rat io, the higher the pressure r ise and the pressure r ise
rate. In laboratory experiments using closed cells, the f i l l ing rat io must be
kept low to prevent cel l rupture. As a consequence, the experimental
condit ions are far f rom adiabat ic.
Vent sizing for gassy reactions is based on the maximum rate of gas
generat ion measured under adiabat ic condit ions. I t is safe to consider that
this rate is obtained even if the vent is actuated, and to design on this basis.
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3) Hybrid systems
A hybrid system is a tempered system where non-condensable gases are also
produced by the runaway react ion. Neither the vent sizing equat ions nor the
two phase vent f low equat ions are well established or val idated.
Due to tempering, the vent size is est imated by considering the heat rate and
the non-condensable gas generat ion rate at tempering condit ions e.g. at the
temperature T
s
related to the vent set pressure Pg by the vapor- l iquid
equil ibr ium. The discussion of the vent sizing equat ions for hybrid systems is
beyond the scope of this paper.
In addit ion the behaviour of several hybrid systems may be considered.
Systems with a polymerizat ion fol lowed by a decomposit ion react ion of
the polymers producing n on-con dens able g asses. As long as the
monomers are present, the system is tempered. I t may change to a gassy
react ion when the monomers are consumed. Vent ing is best achieved
when the monomers vapor pressure is available.
Systems where a react ion produces non-condensable gasses in the
presence of a solvent vapor pressure. An example could be the
decomposit ion of an organic peroxide in a toluene solut ion.
The system is tempered (and hybrid) as long as the solvent is present.
In the previous, example, if there is not enough solvent, the solvent is
boiled off and the system behaviour changes to a gassy reaction as in
case 1.
In any case it is necessary to check on an experimental basis that tempering
is available during the time necessary for the E.R.S. to operate. This must be
done under nearly adiabat ic condit ions.
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3 - PSEUP O-ADIABA TIC CALORIMETRY
3.1 Th erm al Inertia
Experimental methods in calor imetry where the sample enclosed in a test
cel l ,
is al lowed to react with no heat exchange with the outside, are cal led
"Pseudo-Adiabat ic Techniques". This is to emphasize the fact that i t is the
sample and the test cel l which are under adiabat ic condit ions.
In these techniques the heat produced by the chemical react ion causes a
temperature r ise in both the sample and the test
cel l .
The experimental set up is usually able to prevent any heat loss from the
test cel l by maintaining the temperature of the surroundings equal to the
sample temperature or to the test cel l wall temperature.
The way the heat produced by the sample causes an increase in i ts own
temperature and that of the test cel l is characterized by the Phi factor :
Heat capacity of the sample + test cell
$
=
Heat capacity of the sample alone
Under true adia batic con dit ion s, (J) = 1
The Phi factor is greater than 1, provided that there is no heat input from
the outside to the sample.
When a runaway reaction occurs in a chemical plant, the Phi factor is 1.05
or less.
The use of pseudo-adiabat ic techniques to provide data for vent sizing
relies on the possibility of achieving a Phi factor close to 1 and/or
correct ing the experimental data to true adiabat ic condit ions.
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The experiments are performed by charging the cold react ion mixture in the
test cel l and then by slowly raising the temperature to init iate the react ion.
When the sample exhibits self heat ing, the apparatus assumes adiabat ic
condit ions for the sample and the test
cell.
3.2 Onset tempe rature
The smallest exotherm which can be detected depends on the sensit iv i ty of
the apparatus. I f a given react ion is studied in dif ferent types of apparatus,
the onset temperature observed wil l be lower in more sensit ive apparatus.
The maximum heat rate is also reduced in the most sensit ive equipment,
due to more reagent deplet ion before this point is reached.
The maximum heat rate observed in dif ferent types of apparatus must be
adjusted to the same onset temperature.
3.3 Th eore tical basis
The theory by D.I. TOWNSEND and J.C. TOU [2] for the Accelerating Rate
Calorimeter (A.R.C.) holds for the other pseudo adiabat ic techniques. This
theory assumes that the temperature r ise observed is proport ional to the
degree of conversion and that the rate constant depends on the
temperature according to the ARRHENIUS law. The theory provides a
method of determining the kinet ic parameters of the ARRHENIUS law from
the experimental data e.g. the heat rate curve, dT/dt in log.scale vs T in
reciprocal scale.
The Phi factor is introduced to take into account the deviat ion from
adiabat ic condit ions due to the heat capacity of the cel l .
This theoret ical background provides methods to correct the heat rate curve
dT/dt vs T for the deviat ion from true adiabat ic condit ions.
The adiabat ic temperature r ise A T * _
1
is obtained f rom the exper imental
temperature r ise 4 T * - by the st raight forward relat ion
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4 T < D
= 1
= 0 .
4 T ( ] ) > 1
The adiabat ic f inal temperature Tf is deduced from the onset temperature
To by
Tf = To + 0 . ATQ^
Furthermore, near the onset temperature To or i f the react ion is zero order,
(i.e.
reactant consumption has no effect on the react ion rate), the adiabat ic
heat rate is obtained from the experimental heat rate by :
For zero order only
A method is proposed to correct the whole heat rate curve but this method
is not satisfactory.
It is necessary to be familiar with the theory by D.I. TOWNSEND and
J.C. TOU to have a good unde rstanding of the correc t ion me thods , de spite
the fact that few f indings of this theory are used for vent sizing purpose.
When the experimental heat rate must be corrected to adiabat ic condit ions
at a temperature far f rom the onset temperature where the react ion is not
"O " order, a method proposed by H.G. FISHER (3) after J. HUFF (4) is best
used.
In this method, the experimental onset temperature or f irst measured
temp erature T ^ is corrected to take into account the deviat ion fro m
adiabaticity :
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1 R
— + — Ln 0
T
M
E
where
T
o =
T
M =
R =
E =
0 =
adiabat ic onset temperature
f irst measured temperature
ideal gas constant
activation energy
Phi factor
This correct ion takes into account the fact that for a given onset detect ion
sensit iv i ty of the experimental device, the onset temperature would have
been lower if the Phi f ac to r was 0 = 1 .
Then the heat rate curve is corrected for the Phi factor.
The adjusted temperature T» for 0 = 1 is obtained for every measured
temperature T^| by :
T
A
= T
n
+ 0 n \ , - T
n
)
'A " 'o M V
The corrected heat rate /dT \
dt 0 = 1
is obtained f rom the measured
hea t rate / dT \ by
I dt/0
>
1
dT
—
d t _
0 = 1
= 0 -
EXP
E
—
R
/ 1
( - -
\ T
'M
' A / J
dT
dt
0> 1
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.20
Correct ion for a dif ferent onset temperature
The react ion rate at any temperature above the onset temperature is
inf luenced by the onset temperature.
The onset temperature of the react ion may be determined experimental ly by
a temperature scan in a pseudo-adiabat ic apparatus. In this case, the onset
temperature depends on the onset detect ion sensit iv i ty of the experimental
device. No exotherm can be measured below the base l ine heat rate on the
heat rate curve. The base line heat rate is given by the rate of temperature
scan.
As dif ferent experimental techniques may produce dif ferent onset
temperatures due to different onset detection sensit ivit ies it is necessary to
correct the measured heat rate to the same onset temperature and to the
same Phi factor, to compare the experimental results.
I f the react ion is init iated by a process deviat ion "by introduct ion", the
react ion is immediately fast whereas in a laboratory experiment, the react ion
is init iated by a temperature scan on the react ion mixture loaded cold in the
test
cell.
The react ion rate under process condit ions can be obtained from this
measured heat rate, adjusted for the dif ference in the onset temperature
and in Phi factor.
The fol lowing correct ion method can be used :
1) The experimental onset tempe rature is correc ted to take into acco unt
the deviation from adiabaticity as previously :
1 1 R
— = — + — . Ln (J)
T
o
T
M
E
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2) I f a dif ferent onset temperature T^ is considered, any measured
temperature is adjusted for this new onset temperature :
T
A
=
T
o
+ <
f - r r
M
- T
0
)
Then the adjusted heat rate is obtained by :
This correct ion method seems realist ic for simple one step ARRHENIUS
react ions. I t al lows the correct ion of the whole heat rate curve and does
nothing more than changing the onset temperature on the "O" order l ine
once corrected by the Phi factor.
This correct ion method derived from the thermal theory of D.I .TOWNSEND
and J.C. TOU, can also be used to correct the n on-c ond ens able gas
generat ion rate. This is straightforw ard i f the kine t ic param eters for the
gas generat ion are the same as for the heat generat ion.
I f not, the gas generat ion rate must be adjusted using this method in the
absence of any other method.
3.4 Pressure
In addit ion to the kinet ic data the pseudo-adiabat ic techniques al low the
characterizat ion of the system behaviour.
For high vapor systems, the pressure (corrected for inert gasses) in
log.scale is a l inear funct ion of the temperature in reciprocal scale.
The pressure increase during the runaway is also inf luenced by the Phi
factor as the f inal temperature is higher under true adiabat ic condit ions.
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A deviat ion from an init ial vapor pressure curve may indicate the product ion
of non-condensable decomposit ion gasses.
Alternatively polymerization of the reaction mixture will give a lower
pressure than expected from the init ial pressure curve.
For gassy reactions, experiments in closed cell will often lead to cell rupture
for reasonable f i l l ing rat ios. A prel iminary experiment using an autoclave
wil l provide information on the system behaviour and al low the choice of a
fil l ing ratio which will avoid cell rupture even if the reaction is gassy. A
prel iminary examinat ion of the react ion using DTA and the autoclave should
be carr ied out before any pseudo adiabat ic experiment.
THE EXPERIMENTAL TECHNIQUES
The pseudo-adiabat ic techniques available at the moment are :
- The Accelerating Rate Calorimeter (A.R.C.) manufactured by Columbia
Scient if ic Instruments,
- The Vent Sizing Package (V.S.P.) man ufac tured by FAI an d FIKE,
- The closed Dewar apparatus made from a commercial stainless steel
Dewar f lask,
- The Reactive System Screen ing Tool (RSST) m an ufa cture d by FA I.
We now describe these types of equipment and discuss their relevance for vent
siz ing.
4.1 The Acc elera ting Rate Calorime ter (ARC)
The A.R.C. is manufactured by Columbia Scient if ic Instruments a small f irm
of 75 workers situated in Austin Texas.
The original design was derived from the laboratories of DOW Midland. I t is
the most wide spread pseudo-adiabat ic technique. More than 100 ARC
instruments have been sold.
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Description of the ARC
The basic pr inciple of this apparatus involves maintaining the sample and
the test cel l under adiabat ic condit ions once an exothermic react ion is
detected.
The calorimeter jack et and the spherical test cel l are show n in f igu re 1. The
test cel l normally contains between 1 and 10 g of l iq uid or sol id m aterial.
The test cel l is connected to a pressure transducer (operat ing range 0-2500
PSIA) and suspended inside a calor imeter jacket constructed from Nickel-
platted copper. The jacket contains eight heaters and three thermocouples.
A fourth thermocouple is attached to the outside of the test cel l . The
operat ing temperature range is 0-500°C. All ARC operat ions are control led
by a microprocessor. The results are obtained on a line printer (raw data)
and on an X-Y plotter (graphs).
Figure 2 shows the heat-wait-search operat ion of the accelerat ing rate
calorimeter.
The sample is f irst weighed in the test cel l to determine the value of the Phi
factor. The test cel l is connected to the l ine to the pressure gauge inside
the jacket and the number three thermocouple is attached on the test cel l
wall.
The user inputs the various parameters which describe the desired
experiment which wil l be carr ied out automatical ly.
The sample undergoes a series of Heat Wait-Search cycles unt i l self-heat ing
is detected through the test cel l wall temperature.
At that point, the condit ions for the test cel l and the sample are
automatical ly kept adiabat ic while the data (Temperature - Pressure - Time)
is stored in the microprocessor.
At the end of the experiment the computer wil l process the data. The
fol lowing graphs are obtained :
- The observed temperature versus t ime f ig.3,
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PRESSURE
TRANSDUCER
CELL THERMOCOUPLE
THERMOSTAT JACKET
TEST CELL
FIGURE 1 : ACCELERATING RATE CALORIMETER
TEMPERATURE
WAIT
SEARCH
PSEUDO ADIABATIC
TIME
FIGURE 2 : THE HEAT-WAIT-SEARCH OPERATION OF ARC
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TEMPERATURE
FIG. 3
-TEMPERATURE VERSUS TIME
TIME
F I G . 4
HEAT-RATE VERSUS TEMPERATURE
HEAT RATE
(LOG. SCALE)
TEMPERATURE (RECIPROCAL SCALE)
ACTIVATION
A ENERGY
FIG. 5
ACTIVATION ENERGY
VERSUS TEMPERATURE
TEMPERATURE
A. PRESSURE
LOG.
SCALE
FIG. 6
PRESSURE VERSUS TEMPERATURE
TEMPERATURE (RECIPROCAL SCALE)
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A
dP/dt (LOG.SCALE)
TEMPERATURE
(RECIPROCAL SCALE)
FIG. 8
PRESSURE RISE RATE
VERSUS HEAT RATE
A k (LOG.SCALE)
5»
TEMPERATURE
(RECIPROCAL SCALE)
FIG. 7
RATE OF PRESSURE RISE
VERSUS TEMPERATURE
dP/dt
A (LOG.SCALE)
dT/di
j.
(LOG.SCALE)
FIG. 9
PSEUDO CONSTANT k
VERSUS TEMPERATURE
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d T / d t
(LOG.SCALE]
- >
TEMPERATURE
(RECIPROCAL
SCALE)
FIG.
10 : HEAT RATE VERSUS TEMPERATURE
CORRELATION OF EXPERIMENTAL DATA
TEMPERATURE
(RECIPROCAL SCALE/\
> ■
TIME (LOG.SCALE)
FIG. 11 : TIME TO MAXIMUM RATE VERSUS TEMPERATURE
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- The observed heat rate in Log.scale versus the temperature in reciprocal
scale f ig.4,
- The act ivat ion energy versus the temp erature f ig.5 ,
- The pressure in Log.scale versus the temperature in reciprocal scale f ig.6,
- The rate of pressure rise in Log.scale versus the temperature in reciprocal
scale f ig.7,
- The rate of pressu re rise versus the heat rate bo th in Lo g .scale f ig.8 ,
*
- The pseudo constant k in Log.scale versus the tempe rature in recip rocal
scale f ig.9,
- The correlation of the heat rate data by an estimated heat rate curve
f ig.10,
- The t ime to maxim um rate in Log .scale versus the temp erature in
reciprocal scale f ig.11.
Kinetic interpretation
The act ivat ion energy is obtained from the curve in f ig.5 or from the slope
of the heat rate curve in f ig.4. The order of the react ion is obtained from
the fol lowing relat ion :
E
A
n =
(If "
T
i
R T
M
2
where
Tf = f inal temperature
T
Q
= onset tempe rature
T
M
= temperature at maximu m rate
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The estimated value of n is checked by the linearity of the plot of pseudo-
constant versus reciprocal temperature in f ig.9.
If the linearity is not satisfactory the value of n needs further adjustment.
Then the adjusted heat rate curve may be compared with the observed heat
rate curve as in f ig.10.
Results of practical interest
The heat rate curve and the kinet ic interpretat ion wil l provide the kinet ic
parameters of the ARRHENIUS law k , E, n, near the onset temperature.
Due to low onset temperature and high Phi factor the heat rate curve may
show that the reaction splits in several separate steps. This is an interesting
result.
The P versus T curve wil l al low the system characterizat ion in the
experimental temperature range.
The heat rate versus pressure rise rate curve may prove that the heat
release and the gas generat ion are due to the same react ion.
If the reaction is a simple one step ARRHENIUS reaction the heat rate curve
and the pressure rate curve can be corrected to true adiabat ic condit ions.
Comment on the results of an ARC run
The results can only be obtained if the experiment comes to complet ion i .e.
I f the test cel l does not rupture. To operate the ARC properly the sample
thermal stabil i ty and the decomposit ion behaviour must f irst be measured
using DTA/DSC and Autoclave experiments.
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Phi factor
I f the sample react ion produces non-condensable decomposit ion gasses,
the fil l ing ratio of the test cell must be low enough to prevent cell rupture
i.e. to keep the pressure in the ope rat ing range . The sam ple w eight may be
as low as 1 g and the Phi factor 5 to 8 using a S.S. bomb.
If the sample reaction behaves like a high vapor system in an autoclave
experiment, the f i l l ing rat io in the ARC test cel l may be high enough to
achieve a Phi factor as low as 1.2 using a t itanium bomb.
Sensit ivity of the onset detection
Due to the heat - wait - search procedure, the heat rate sensit ivity threshold
for the exotherm onset is as low as 0.02°C/mn. Depending on the sample
heat capacity, the sample mass and the Phi factor, the sensit ivity is better
than 1 wa tt /kg sam ple. This is better than m ost DTA/DSC eq uipm en t.
Effect of Phi factor and sensit ivity of onset detection
The ARC is an apparatus with a good onset detect ion sensit iv i ty. The onset
temperature where the apparatus assumes a pseudo adiabat ic behaviour is
very low compared to other techniques.
The Phi factor typically ranges from 2 to 5 (extreme values 1.2-9).
The Phi factor is high compared to other techniques.
These two features will cause low measured heat rates and will allow
decoupling of complex kinet ics al lowing the separat ion of complex
reactions into separate steps.
Experimental temperature range
In an ARC experiment the onset temp erature T of the exotherm is low due
to the good onset detect ion sensit iv i ty compared to other equipment.
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The experimental temperature r ise (T
f
- T
Q
) = A T
A B
/ 0 is redu ced due to a
high Phi factor.
The experimental temperature range of the exotherm is shif ted toward lower
temp eratures. This may cause a subseq uent e xotherm not to be inclu de d in
the runaway, which would have been tr iggered in adiabat ic condit ions.
Let us take an example :
I f the onset temperature of an exotherm measured in the ARC is 30°C and
the exper imental temperature r ise 100°C with 0 = 3 , the exper imental
temperature range is 30°C - 130°C.
In a less sensit ive but more truly adiabatic device, the onset temperature of
the same exotherm may be 60°C and the experimental temperature r ise
cou ld be 300°C with <J) ~ 1. Then the e xpe rime ntal te m pe ratu re range is
60°C - 360°C.
In these two experimental temperature ranges, the react ion is not the same.
Further decomposit ion react ions may be tr iggered between 130°C and
360°C wich wil l increase the heat rate and the exotherm. In such a case, the
runaway behaviour is not satisfactorily measured with the ARC.
Conclusion on the relevance of ARC data to vent sizing
The advantages and disadvantages of the ARC experiments in providing
data for vent sizing may be exemplif ied by considering the heat rate curve
of f ig.12 obtained for the phenol + formaldehyde runaway react ion with the
recipe of ref.5.
This heat rate curve shows al l the above mentionned features
- low onset tempe rature
- low ma ximu m heat rate
- de cou pling of several reaction steps
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ARC
N 208 - 209
.0)
.M
or/ut
I'HEHOL
'
FORMALDEHYDE REACTION
J
— ' — ' — I A J
- J — I — I — I I I
ldu -
1
-
— - ^ E L M -
C O
Fig.12 : Phenol I Formaldehyde runaway reaction with the recipe of Ref 5
measured in ARC. Note the onset temperature and the maximum
heat rate.
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333
and cannot be corrected to adiabat ic condit ions by the known simple
correct ion methods.
In conclusion the ARC is not well suitable for vent sizing because it
operates too far f rom adiabat ic condit ions and gives onset temperatures
and maximum heat rates which are too low.
The other pseudo-adiabat ic techniques are more suitable for vent sizing.
On the other hand the ARC is st i l l a valuable tool for obtaining thermal data
near the onset temperature and detect ing complex react ions which may
look simple under runaway condit ions.
4.2 The Ven t Sizing Pack age (V.S.P.)
The V.S.P. is the commercial version of the DIERS Bench scale apparatus
designed to operate under nearly true adiabat ic condit ions. The f irst
manufacturer was FAUSKE Associates Inc. (FAI), a consultant f rom
Burr.Ridge (I l l inois). After some t ime the manufacturing l icence was given to
Fike,
a
rupture disks manufacturer. At that point some design changes were
incorporated which caused unwanted problems. This has since been
rect i f ied.
25 VSP have been sold so far. The last apparatus was purchased by
Rhone-Poulenc. No other VSP have been sold in the past two years.
A VSP clone is proposed by Dr.SINGH from the Brit ish Fire Research Center
and at least one has been sold to the JRC in Ispra.
The reasons for this lack of interest in the VSP are probably the following :
Some weaknesses in the design of the apparatus.
The VSP cannot be used alone but as a complement to a well equipped
laboratory. The VSP tests are the last to be done in safety studies where
an ERS is needed.
Once the VSP design is understood, the apparatus can be buil t at less
material cost and with more technical ref inement than the commercial
model .
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The demand for the product is l imited by the high level of expert ise
required to operate it and interpret the results.
The same results may be obtained through closed Dewar f lask
experiments.
Description of the VSP
A descript ion of the VSP and of the test procedures is given in ref.6 see
also f ig.13.
The key feature of the equipment is the use of a low heat capacity test cell
to reduce the Phi factor. The test cel l volume is 116 ml and the wall
thickness is 0.13 mm. A Phi factor of 1.05 is achieved provided that the
temperature control of the heat ing device is correct. The weight of the test
cell is 20 to 30 g. The test cell is enclosed in a containment vessel designed
to withstand pressures up to 200 bar in Europe. The weakness of the test
cel l is compensated by maintaining the pressure in the containment vessel
equal to the test cell inner pressure to prevent cell rupture.
Alternatively an open test cell can be used, especially for gassy reactions.
The heat ing device is a heat ing coi l separated from the test cel l by an
insulation assembly. The auxiliary heater is used to heat the test
cel l ,
when
in temperature scan mode, with a minimum heat rate of 0.3°C/mn. The
outer guard heater is placed on the outside wall of an aluminium can
separated from the can by a uniform layer of insulat ion. A thermocouple is
attached to the inner surface of the aluminium can.
Once the sample heat rate is higher than the temperature scan heat rate,
the auxiliary heater is switched off but the guard heater is used to keep the
temperature of the surroundings equal to that of the test
cel l .
The original design of the VSP did not include a Heat - Wait - Search
rout ine.
The heater temperature and containment vessel pressure are control led by a
computer .
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PRESSURE
BY PASS
TEST CELL
OUTER CAN
THERMOCOUPLES
NITROGEN
EXHAUST/SUPPLY
®
GUARD HEATER
INNER HEATER
INSULATION
CONTAINMENT VESSEL
FIGURE 13 : VENT SIZING PACKAGE (V.S.P.)
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336
Test procedure
The VSP can be used to characterize runaway chemical react ions in a
closed cell as well as in an open or a vented
cel l .
The experimental
information obtained includes Thermal data (closed cell) and f low regime or
viscosity characterization (open cell).
Obtent ion of thermal data
The sample is loaded cold into the closed test
cel l .
The runaway react ion is
init iated by slowly raising the temperature. A constant heat rate mode is the
best choice.
When the exotherm onset temperature is reached, the sample heat rate
becomes higher than the temperature scan heat rate. The guard heater is
then switched on to ensure adiabat ic condit ions for the test
cel l .
The pressure in the containement vessel is control led to fol low the test cel l
pressure.
When the react ion is completed, the power is turned off to the guard heater
and the sample is allowed to cool slowly.
The thermal data includes :
- The temperature T^ versus time curve
- The pressures P^ and
?2
versus time curve
- The heat rate curve
- The pressure rate curve
- The pressure versus temperature curve.
The closed cell procedure is suitable for obtaining thermal data for high
vapor (tempered) systems where the pressure is due to a vapor- l iquid
equi l ibr ium.
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337
For gassy reactions or hybrid systems the closed cell bursts readily due to
the high f i l l ing rat io. This exemplif ies the need for a prel iminary test using
an autoclave to detect the product ion of non-condensable gasses. Only the
high vapor systems should be used in a VSP closed cell test.
For test ing gassy and hybrid systems in the VSP the "constant volume
mode" is best used where the gas product ion rate is obtained from the
pressure build up in the containment vessel using a open top
cel l .
To demonstrate the use of the VSP in obtaining thermal data, the heat rate
curve of the phenol+formaldehyde runaway react ion with the recipe of ref .5
is given f ig.14. Note the high onset temperature and the high maximum
heat rate obtained in the VSP experiment.
Flow regime test ing
Flow regime characterizat ion is obtained from blow-down tests using a top
vented test cell.
For the current test cell design, the vent line diameter of 2.5 mm leads to
linear f low ve locit ies of 30 - 60 cm /s. No rmally 40 % to 60 % of the liqu id
wil l be lef t behind fol lowing blowdown transient i f non-foamy behaviour
prevails.
If a foamy regime prevails, no liquid is left behind in the test
cel l .
The test procedure is the following : (see fig.15)
- The containment vessel pressure is set to the value Pg.
- The runaway react ion is init iated and al lowed to reach tempering at Pg.
- The containment vessel pressure is decreased to atmospheric, thereby
init iat ing the blowdown process.
- Whe n the test cel l pressure is equal to atm osp heric, the con tainm ent
vessel is immediately repressurized to prevent further mass loss from the
test cel l . The sample mass lef t behind in the test cel l is determined by
weighing it af terwards.
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338
a
en
LL : 1 I LI
L I.I i I..I.I
1
1
1
1 1 1 1 1 L l
1
_43T
I I I 1
I I
I I I 1 I 1 I I I I I 1
I
1
i i i i i i i i i i i i i i l i i i i i i i i n n i i i i i i i i i i i u i
■ ■ r
—
\
jg r
l i .
. . . . . | . . . . . . . _ _ _ .
1
1
-
c F
£°
f
n
z
r;
:
;
:
iV-Z-t~:';E?
'~~ Jr
i
*f \
*r 1
^
4? ' -a -
1
m
3
0
3
~ f
□
D
rff *
- -
&k ~
'•
I l l
6(
«
a
3
I I
] 8(
1 , 1
1 ' , 1
J_LLi . J.L .
:
I
1
I
1 M 1 I I I 1
M I i i m i l H I
1
1
l l l l M l i
r 11
M M M
1
r
) 100 120 HO 170 200
°C)
Fig.
14
Phenol + Formaldehyde runaway reaction with the recipe
of Ref. 5,measured in the VSP. Note the onset temperature
and the maximum heat rate.
Reaction initiated by a temperature scan.
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339
r
Ts
,
TEMPERING
- ^
- X
l\
P
'W
\ \
?< , te
R E P R E S S U R I Z A T 1
BLOW DOWN
/
TIME
FIGURE 15 : BLOW DOWN TEST FOR FLOW REGIME TESTING
BLOW DOWN
TIME
FIGURE 16 : BLOW DOWN TEST USING BOTTOM VENTING FOR VISCOSITY TESTING
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340
Viscosity testing
The VSP experiment using a bottom vented test cel l and the blowdown
technique is used to characterize the f low regime (turbulent or viscous). A
vent line with L/D ~ 30 and a line length = 100 m m is used to assure
equi l ibr ium f lashing f low condi t ions.
The test procedure is the following : (see fig.16).
Following tempering the by-pass valve is opened to al low a pressure
equalizat ion between the test cel l and the conta inm ent vess el. Then the
blowdown process is init iated.
The f low rate is obtained by measu ring the em ptying t ime A t^ .
The measured f low rate is compared with the two phases f lashing cr it ical
f low rate G given by the ERM model :
dT Y C p
L
If the experimental f low rate is less than the ERM value the flow is viscous.
Comment on the VSP
Advantages of the VSP design
The VSP achieves a Phi factor close to 1 and condit ions close to the
adiabat ic.
Realist ic runaway simulat ion is obtained using the close test
cel l ,
thus
providing suitable data for vent sizing for high vapor systems. Heat rates as
high as 2500°C/mn can be measured.
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341
Drawbacks of the VSP
Open cell test ing appears to be expensive because of damage to the
heat ing device.
The heat rate base line corresponds to an onset detection sensit ivity of
0.3°C/mn. This is a poor sensit iv i ty compared with the ARC. Constant
temperature exposures are dif f icult to achieve because of the temperature
drift of the VSP.
The pressure fol low-up in the containment vessel could be better.
VSP clones
Once the basic design of the VSP is understood the performance of the
apparatus can be easily improved by the users. It would be unfair to present
these improvements as a new concept which could just i fy a trade
compet i t ion.
These modif icat ions can be divided into :
- improvem ents to the com puter program
- improvements to the hardware.
The improvements to the computer program are the fol lowing :
- Improvement to the onset detection sensit ivity through a heat - wait -
search rout ine
- Supp ression of the tempe rature dr if t during cons tant temp erature
exposure by better temperature control
- Improvement of the pressure control in the containment vessel to reduce
or delay cel l rupture by fast react ions. This is done by reducing the
control loop cycle t ime in the computer program
- Improvements to the data output, curve print ing
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342
- Pressure correct ion for the Nitrogen p ad .
The improvements to the hardware are the fol lowing
- Replace the pressure gauges by piezoelectric gauges, easy to clean with
a range 0-200 bar
- Improve the pressure control in the containment vessel by increasing the
pipe size for nit rogen input, providing a Nitrogen compressor and a
Nitrogen balast close to the containment vessel.
Possibly measure directly the differential pressure between the test cell
and the containment vessel.
- Improve the st irr ing rel iabi l i ty by redesigning the containment vessel and
choosing a better dr iving magnet
- Improve the insulat ion p acking repro duc ibi l i ty by p roviding a sol id
insulat ion block
- Improve open cell and blow-down test ing condit ions by providing a
pressure resistant catch tank outside the containement vessel thus
allowing the test to be aborted if the pressure increases to 200 bar.
To encourage improvements to the VSP we give in f igs 17-19 the results
of a closed cell test on an aqueous solut ion of hydroxylamine sulfate 44 %
by weight. It is a high vapor system. A heat rate as high as 2000°C/mn
and a pressure rate as high as 25 bar/s were measured without cel l
rupture.
Conclusions on the VSP
The basic p r inciple of the VSP is quite in terest ing . The VSP cap abil i ty ca n
be improved by a better design. We are quite conf ident about the future
of this apparatus.
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343
10"
103
_
10
2
r
IO
1
10 "
=
lo-'b
10-2
H E A T R A T E
r. '^rrpts^SfrrfK.-f.,
-
rr
p*-f***n: '
l
n" '
- 1 0 0 0 / T ( K )
-3
-2.8 -2.6 -2.4 . -2.2 -2 -1.8 -1.6
.4
(. _ 1.—(.
1—4—|—|—(—J—k_J—I—I—|—l_J__+_4—;--»--l--t-4-l-4-4-+
100 150 200 2 5 0 300 350
F i g u r e
17
103
1 0
2
10 '
inn
P r e s s u r e = f(T)
, . . /
^
-looomK)
-
:
:
1 \.—+-
-2.6 -2.4 -2.2 -2 -1.8 -1.6
4—J....4-4—4—4— 4—4—1~4~-1—l~4-J-4-4-4-4-4--l"M-4-4-4-4
100
150
Figure 18
200
250 300 350
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344
DP/Dt = r m
1 0
J
1 0
3
102
1 0 '
h
. 3
c
10"
10-'
io-2
10-3
1 0
J
_
1 ' " " '
..-y^f
.-"""
,*'
"
_
"
- 1 0 0 0 / T ( K )
-2 .8 -2 .6 -2 .4 -2 .2 -2 -1 .8 -1 .6
4-—+—[ —; —I J—i— —J— I—1-—-i—I—1— k—I—1— 4-4—4-4—^-1-4-4-4-4-;-
100 150
2 0 0 2 5 0 3 0 0 3 5 0
Figure 19
Fig. 17-18-19 - VSP closed cell test on 44 % by weight
aqueous solution of Hydroxylamine Sulfate.
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345
4.3 The closed Dewar experiment
The closed Dewar experiment was formerly used to determine react ion
onset temperature and adiabat ic induct ion t ime. For this reason it is a wide
spread test ing method.
The use of closed Dewar experiment to provide the experimental data for
vent sizing has been emphasized more recently by R. ROGERS (I.C.I.) (7)
an d the author (Rh one-Poulenc) (5). This is ma de pos sible by the availability
of low Phi factor stainless steel Dewar f lasks achieving a Phi factor of 1.1.
In cont inental Europe the best Dewar is made from the domestic i tems sold
in the superma rkets by Cam ping G az. The same items are also sold in
England by Thermos. These Dewar f lasks are manufactured in Japan and
Korea. The price for 1 I f lask is 300 F.F. The plastic cap on the original item
is replaced by welding
a
thread to hold a cap eq uippe d with
thermocouples, a pressure gauge, a rupture disk and a blow-down valve.
The Dewar f lask is heated in a furna ce the tem pera ture of w hich is
control led so as to be equal to the sample temperature, thus el iminat ing the
heat losses which are essentially from the cap.
The whole assembly, Dewar and furnace can be shaken if necessary and is
shown in f ig.20.
This apparatus must be located in a protected area, and cannot be used in
a convent ional laboratory because of the explosion hazard associated with
its use.
The value of the Phi factor is derived from water experiments.
Glass Dewar f lasks may also be used if necessary but have a larger Phi
factor of 1.8.
The temperature control and data acquisit ion is as good as in the VSP
using the same computer program.
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346
The pressure is corrected for the Nitrogen pad.
The outputs include :
- The heat rate curve
- The pressure versus tempe rature curve
- The pressure rate curve
The product ion of non-condensable gasses or the polymerizat ion of the
sample are detected by the deviat ion of the pressure curve from the
previously obtained vapor pressure curve.
The rate of non-condensable gas product ion is derived by the fol lowing
approximate equat ion :
1 d T \
T dt /
derived from the perfect gas law.
To il lustrate the use of the closed Dewar to provide the experimental data
for vent sizing, the heat rate curve and the pressure vs temperature curve
obtained for the Phenol + Formaldehyde runaway react ion with the recipe of
Ref.5 are given figs.21 and 22.
Comments on the Dewar f lask tests
The results obtained with the Dewar f lask are quite similar to the results
obtained with the VSP using the closed
cell.
The pressure resistance of the Dewar f lask is limited to 25 bar which is
enough for most process safety studies. There is nevertheless a need to
determine the further decomposit ion steps to obtain information on the
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3 4 7
S A F E T Y V E 1 T
B LO W D O W N
V A L V E
V O ^ * SAMPLE
PRESSURE GAUGE
^ T E ^ T U R E
F U R N A C E
[ I T E H R A T U R E
. - . . 1
F i g u r e 2 0 _ j ) E i A R F L A S K E X P E D I E N T
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348
S u l 9 t
Ficni iP :
PHENGL
/ FO nHO L
a: 2 9 0 6 9 0 ( Eaea l au 2B / 6 / 9 0 )
Teago r a tu r a loC)
1
I
■
■
■
?
l a l Mo 1
Lo g
P - « . 2 3 9 3 3 - 2 0 9 1 . 2 8 /
■•
da
a a c o a o o a l t l o n
:
38
1
(T+2271
;y
J <
\ A
i
• , / 1 1
1 . V I I
1
1
/
i
i
i i i
/
i
I
/
1
/
1
/
I
1
i
i -t
/[
/ /
,
> i i
i
i
1
i
T e m o e t a t u r e
l o c i
Sutat
:
PHENOL
/ FORMOL
F l cnu r : a : 2 S G 6 9 0 ( Eaaal mj 2A/B/90 1
Fig.
21 and 22:Phenol + Formaldehyde runaway reaction, with the
recipe of Ref 5. Heat rate curve and pressure vs tenroerature
curve. Reaction initiated by introduction of the catalyst. Dewar
flask experiment.
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349
consequences of the uncontrol led runaway react ion.
In some cases where very fast react ions are obtained with moderate f inal
pressure, the Dewar f lask is the best choice because the VSP closed cell
ruptures during the fast pressure build up. A typical example of these fast
reactions is the bulk polymerization of vinyl acetate init iated by a peroxide.
4.4 The Reactive System Scre enin g Tool (RSST)
The designer and manufacturer of the RSST is FAUSKE and Associates Inc.
I t is a simple and low priced piece of apparatus which provides some of the
capa bil i ties of the VSP. The fol low ing data can be ob tained with the RSST :
- The heat rate in a low Phi factor experiment,
- The vapor pressure versus temperature relat ionship,
- The non-condensable gas generat ion rate.
At the moment 30 RSST machines have been purchased.
Description of the RSST
An open, small spherical glass test cel l 10 ml in volume, with a low Phi
factor ( <> = 1.04) is placed in a pressure resistant containment vessel, (see
f i g .
23 and Ref.8).
The apparatus provides a record of the sample temperature and of the
containment pressure. There is a magnetic st irrer. Addit ional reactants can
be introduced into the test cel l during the experiment.
The test cel l holds a single heat ing element that compensates for heat
losses and al lows a temperature scan in the test cel l .
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350
FILL
_r
HEATER
TEST CELL
CONTAINMENT.
VESSEL
= 3
.THERMOCOUPLE
®
RESSURE
GAUGE
I PSV
NITROGEN
SUPPLY
-INSULATION
ASSEMBLY
FIG. 23 : SCHEMATIC OF THE RSST
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351
The heater is control led by the sample temperature measurement, to
overcome the heat losses and produce a specif ied temperature r ise rate at
that temperature. Nevertheless the temperature control is not by a feed
back loop but by a pre-programmed heat ing.
For a reactive system the linear heat up rate is added to the reaction energy
release so that the heat rate is measured under external heat ing condit ions.
The manufacturer claims that heat rates as low as 0.1°C/mn can be
obtained.
The apparatus must be connected to a regulated Nitrogen supply. The
control unit contains the temperature and pressure amplif iers and the
heater power supply. This unit is connected to a computer to record the
t ime, temperature and pressure during the test.
The apparatus can be easily transported to plant sites, a feature of great
interest when the shipment of the samples is not possible.
Test procedure
High vapor systems
The heat rate data is obtained by sett ing the RSST containment pressure to
some Maximum Allowable Pressure and let t ing the react ion be init iated by a
tempe rature scan . Then the heat rate is measured unde r co nd it ions close to
the adiabat ic or under external heat ing condit ions.
When the boil ing point of the sample under the test pressure is reached,
the vaporizat ion heat sink compensates for the heat rate this al lowing the
detect ion of the boil ing point.
Gassy reactions
For gassy react ions, the non-condensable gas generat ion rate is obtained
from constant volume mode experiments as in the VSP.
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352
Hybrid systems
A hybrid system is characterized by repeated tests under dif ferent back
pressures. If the heat rate and the gas generation rate are influenced by the
preset back pressure, the system is hybrid in nature.
Comments on RSST tests
The author is not famil iar with the RSST and so these comments are based
on the experience of other workers.
The results of the Round Robin-test on 25 % Hydrogen Peroxide solut ions
show a good agreement between heat rates obtained in RSST and VSP
experiments.
It is nevertheless likely that as with the VSP, a low heat rate base line
cannot be obtained with the RSST.
The heat rate data obtained with the RSST are influenced by :
- The heat rate of the temperature sca n,
- The insulat ion packing,
- The posit ion of the heat ing resistance with respect to the thermocouple in
the test
cell,
- Any detai l which may inf luence the heat exchange between the test cel l
and the outside.
Given that adiabat ic condit ions are dif f icult to produce and that so many
details may influence the heat rate and gas generation rate data, the results
obtained from RSST experiments look surprisingly good.
In a well equipped process safety lab the VSP is the better choice. The
RSST could be purchased to take advantage of i ts possible operat ion on
plant sites.
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353
CONCLUSION
This paper demonstrates the need for experimental techniques achieving
operat ing condit ions close to the adiabat ic for vent sizing purpose.
Due to condit ions far f rom the adiabat ic, the ARC should not be used to obtain
data for vent sizing.
A good experimental device should achieve :
- a goo d onset dete ction sensit ivity,
- a low Phi facto r,
- a fast data acquisit ion al lowing the fol low -up of fast react ions,
- a wide operat ing range to measure the ult imate consequences of
uncontrol led runaway react ions,
- a constant tempe rature exposure capab il ity with no tem pera ture d rif t ,
- the simultaneous acquisit ion of the temp erature and pressure history.
The VSP can sat isfy most of these requirements, once improved by the
customer.
The close Dewar experiment is also a valuable tool but with a pressure range
restricted by the pressure resistance of the Dewar f lask.
The RSST may be useful as a screening tool and is of interest for measurements
on plant sites. The VSP is a more useful device than the RSST.
One should never rely on one technique to produce data for vent sizing. Tests
using at least two or preferably three techniques, including the ARC, provide the
opportunity to detect unexpected react ion changes as well as geli f icat ion
processes which would compromize the rel iabi l i ty of the ERS design.
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354
The sample must go through DTA and autoclave tests before using pseudo-
adiabat ic techniques to detect extremely fast react ions and to adjust the
experimental procedure taking into account these basic results.
Hopefully the reader has been convinced of the great util ity of pseudo-adiabatic
techniques in the process safety laboratories.
L I T E R A T U R E
(1) H.G. Fisher, DIERS, an overview of the prog ram .
Loss Prevent ion Symposium.
AlChE Houston National Meeting - March 1985.
(2) D.I. Tow nsen d and J.C. Tou
Thermochimica Acta n°37, PP 1-30, 1980.
(3) H.G. Fishe r, 5
t h
DIERS Users Group Meeting Seattle, Mai 1989.
(4) J.E. Huff, Plant, Op erations Progress
Vol 1 n°4 pp 221-229 O ctobre 1982.
(5) J.L. Gus tin, 6
t h
Symp. Loss Prevent ion and Safety Promotion in the Process
Industry.
Oslo Norway June 19-22 1989 Paper n°75.
(6) H.K. Fauske, J.C. Le ung . CEP Aug ust 1985 p.10.
(7) R.L. Roge rs, The advantages and limitations of ad iaba tic Dewar calo rime try in
chem ical hazard test ing.
Internat ional Symposium on Runaway React ions March 7-9, 1989 - Cambridge
Massachusetts pp 281-292
(8) H.K. Fauske, G.H. Clare, M. Jo Creed , Labo ratory tool for cha racte rizing
chemical systems.
Ibid p.364-371
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TREATMENT OF REL IEVE D FLUIDS
Dr.
Jasbir Singh
Hazard Evaluation Laboratory
Ltd.
Fire Research Station Site
Melrose Avenue - Borehamwood
Herts WD6 2BL
1. INTRODUCTION
Runaway chemical reactions are a potential problem in many sectors of the
chemical industry.
The
typical hazard scenario involves
a
batch
(or
6emi-batch) chemical reaction where,
due to an
operator error
or
instrument failure,
the
reaction temperature begins
to
accelerate
rapidly. The rise in temperature is, of course, accompanied by a rise in
pressure and in order to prevent vessel rupture, some means of protection
must be provided.
The common approach for overpressure protection in the industry is to fit
a relief device
to the
reactor vessel
in
question;'the device opens
at a
predetermined pressure and if it is sized correctly, the maximum pressure
can be kept within acceptable limits. The Design Institute for Emergency
Relief Systems
(DIERS),
organized through
the
auspices
of the
AIChE
(ref
1) undertook several years
of
research
to
develop methodology
for
sizing
relief systems to cope with runaway reactions.
The DIERS project however, was completed over five years ago and was
started almost 15 years ago. The emphasis in industry is now changing
such that companies are interested in avoiding the release of chemicals to
the environment in addition to preventing equipment damage. Design
techniques must now be extended to cover the containment of fluids.
There
are two
main approaches
for
achieving these objectives
-
either
to
contain the thermal runaway in the reactor vessel or, vent into an
external tank where the reaction is suppressed (eg. by
quenching).
The
first option is theoretically preferable but not always practical,
particularly for existing units. Venting into an external quench tank,
essentially a compromise between total containment and relief to open
air, has received much support (ref 2, 3) . In order to design such
systems,
it is
necessary
to
generate
the
kinetic
and
physical property
data, under conditions
of the
runaway.
The DIERS work showed that
in
order
to
size relief systems,
the
most
expedient method
is to use
suitable bench-scale equipment together with
simplified design equations. The purpose of this paper is to explore
the use of a similar approach in the design of disposal systems and
discuss a bench-scale device that appears to be suitable.
355
A.
Benuzii
and J. M.
Zaldivar
(eds.).
Sa fety of
Chemical Batch Reactors
a nd
Storage
Tanks, 355-370.
© 1991
ECSC,
EEC.
EAEC,
Brussels a nd Luxembourg. Printed in the Netherlands.
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356
2. FLUID CONTAINMENT EQUIPMENT
Equipment for handling vented fluids, typically a two-phase
mixture of vapour and liquid, are referred to by a variety of
names including blowdown drum, knock-out drum and catch tank.
The objectives of the equipment are typically one or more of
the following:
. separate vapour (or gas) and liquid
. collect the separated liquid
. condense vapour
. cool liquid
The most common device is a knock-out drum, a simple
cylindrical vessel with inlet and outlet nozzles sized
primarily to ensure that the vapour and liquid are
successfully separated. The vessel may be horiz ontal or
vertical (see figure 1 ) , depending primarily on space
limitations.
In either case, the diameter is chosen to be
large enough to ensure that the vapour velocity is below the
terminal velocity of liquid droplets and the length must
provide sufficient time for separation.
The separation efficiency through knock-out drums may be
improved by installation of a wire mesh demister before the
vapour outlet.
A more compact arrangement, frequently more efficient in terms
of separation, is a cyclone connected to a catch-pot; the
cyclone performs the separation and liquid accumulates in the
catch-pot.
In order to reduce the amount of vapour leaving the separation
device still further, it is possible to condense the vapours
by venting the fluid directly into cold liquid (see figure 2 ) ,
so called passive quench, which is commonly used in the
chemical industry. The quench fluid will also serve to cool
(and dilute) the liquid portion - this may be an important
feature of the design in the case of reactive systems because
it will slow any reaction that may still persist.
G enerally, vapour consensation is extremely efficient provided
the quench fluid is at least 10°C below the condensation
temperature.
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3. VAPOUR DISPOSAL
It is rare for vented fluids to be totally contained in a
downstream knock-out drum or quench vessel. More frequently,
the gas/vapour is vented directly to atmosphere or routed to
a suitable treatment device.
The cheaper option, direct release to atmosphere, is becoming
less common because of increasing environmental concerns.
However it may be still an acceptable alternative in many
cases, depending on the likely frequency of incidents and the
amount and composition of the vapour. Careful selection of
discharge point in terms of height above ground and separation
from buildings, and a high exit velocity to promote rapid
dilution are the two most important design considerations.
If venting to atmosphere is not possible then a number of
options are available in order to treat the gas/vapour:
. vent condenser
. scrubber or absorber
. flare
. incinerator
A vent condenser is simply a dedicated method of removing
small quantities of particularly toxic or corrosive vapours.
The discharge temperature of the remaining gas is selected by
reference to the vapour pressure of the liquid being
condensed; in order to reduce the composition to sufficiently
low levels, cooling with a refrigerant may be necessary.
Scrubbers or gas absorbers may be used in a number of
different situations for treating large quantities of gas
containing a mixture of vapours. Applications are limited to
situations where a suitable solvent for the vapours is readily
available and of course the solvent must then be reclaimed or
suitably discharged. Ideally, emergency relief systems need
to be connected to a unit that is continuously available - for
example, scrubber that is used for routine process streams
with spare capacity. If this is not possible, the dedicated
unit must be continuously operated since it is not possible to
bring it on stream in time, following relief actuation.
Flares systems are the most common method for disposing of
large streams containing flammable gases. The flare itself is
a section of pipe with a specially designed combustion tip.
The tip consists of a pilot light which ignites the gas
flowing through the end of the flare pipe. The flare achieves
the desired objective firstly by converting bulk of the
chemicals to harmless gases (C0
2
, H
2
0 ) , and secondly by
releasing hot gas at a high elevation.
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Most flares are able to convert close to 99% of hydrocarbons
but other chemicals (e.g. HCN) may be only poorly treated. In
such instances, incinarators may be used. These subject the
gases to a more controlled temperature history and give a
minimum residence time necessary to achieve conversion. Als o,
catalysts are frequently employed to deal with species that
are difficult to treat by heat alone.
4. DESIGN CONSIDERATIONS
4.1 Knock-out-drum
The primary consideration is the velocity of the gas/vapour
leaving the vessel relative to the liquid being separated.
For a vertical drum, this must satisfy:
V* k[(p
L
- s>
g
)/
Pg
\^
2
m/s
with V
TtD
2
/4
where V is the gas velocity through the drum,
p
is the density
L
of the liquid, g of the gas) , Q
g
is the gas flow rate
(m
3
/s) , D is the drum diameter (m) and k is an empirical
constant typically about 0.03 to 0.05. The height of the drum
can be related to the diameter, typically L/D - 3. Horiz ontal
drums are sized in a similar manner, the constant k being
somewhat higher.
The unknown quantity in equation 1 is the gas rate Q
g
from the
drum and this depends on the nature of the reaction vented and
the physical properties of the chemicals.
4.2 Quench Tank
If it is necessary to cool or condense the vented fluids
before separation of the phases, then the amount of quench
fluid M
q
may be calculated from:
M -
M
r
C
r <
T
r ~ T
f
)
+
M
z
X X
C
q
(T
f
- T
0
)
l
'
where M, is the mass of reactants vented, C
r
specific heat of
the liquid reactants, T
r
the reactant temperature (in the
reactor) , T
f
the final temperature in the quench drum, T
0
the
original temperature of the quench fluid, C
q
the specific heat
of the quench fluid, x the weight fraction of vapour in the
reactor and X is the latent heat of vapourization of the
reactants at the reactor venting conditions. This equation
assumes that the amount of non-condensible gas is negligible
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359
assumes that the amount of non-condensible gas is negligible
which is usually acceptable for design purposes.
As stated earlier, T
f
should be at least 10°C lower than the
expected condensation temperature of the reactant vapours.
The vapour/gas leaving the quench tank will now be determined
by:
. non-condensible gas from the reactor
. uncondensed vapour
. further continued reaction in the quench drum
The tank volume above the liquid will act to separate this
gas/vapour from entrained liquid. If the flow rate of this
gas/vapor is known, then the top section of the drum can be
sized as a knock-out drum using equation (1).
If it can be shown that the reaction does not produce
non-condensible gas and if the reaction is suppressed after
quenching, then it is possible to totally contain the
incident.
4
. 3
G as/Vapour Disposal Units
4.3.1 Flow From Knock-out drum
The operation of vapour handling equipment such as absorbers,
scrubbers and flares is dependent primarily on the flow rate
from the knock-out drum or the quench device. The composition
may also be important for more detailed considerations but
overall specification can be completed from a knowledge of the
flow rate.
In the case of a simple knock-out drum, operating close to
atmospheric pressure, the first consideration is the flash
from the reactor down to atmospheric pressure. The amount of
vapor produced following adiabatic flashing may be calculated
from:
X
-
C
r< V
r
» >
(3)
where x is the weight fraction of reactants vapourized in the
drum and Tb is the adiabatic flash temperature (the boiling
point of the mixture.) Thus the amount of vapour generated in
the drum is XMr, and the resulting liquid and vapour will be
at a temperature Tb.
After the initial flash down to atmospheric pressure, the
liquid remaining in the drum may continue to react and
generate further gas/vapour.
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360
Equation (3) is applicable if the reactor is vented at a
temperature above its atmospheric boiling point (i.e. T
r
> T
b
) .
If the reverse is true the liquid will remain at the reactor
temperature T
r
(no flash cooling) and the gas will be that
vented from the reactor plus further reaction in the drum.
Also, in such cases the reaction rate will be exactly the same
as in the reactor since the reactants are not cooled.
For the situation where the reactants flash down to a lower
temperature, the reaction rate will be quite different in the
knock-out drum, normally much lower corresponding to the
reduction in temperature. If the activation energy E for the
reaction is known, then the self-heat rate in the drum (dT/dt)
d
may be obtained from that in the reactor (dT/dt)
r
using:
i-m,'
l -HSrIBtf
El
1
R[ T
z
T
b
( 4 )
where R is the universal gas constant.
The vapor rate M, resulting from the self-heat is then given
by:
C A (1 -
x) (dT/dt)
d
(5)
M„ =
:
The above equations assume that there is no change in
composition in going from the reactor to the drum, which in
practice will not strictly be true. (This is equivalent to
assuming that the reaction rate is independant of
concentration i.e. zero order.)
4.3.2 Flow From Quench Drum
The gas/vapor rate from a quench drum will of course be lower
than from a knock-out drum depending on the final quench
temperature T
q
.
If the reactants vented into the drum are totally condensible,
then the vapours generated may be calculated from equations
(4) and (5) , with T
b
replaced by T
q
. By venting directly into
the quench fluid, vapours from the initial flash (equation 3 )
are avoided. The vapor rate calculated in this manner is
conservative since reduction in reaction rate due to dilution
by the quench fluid is not considered.
If the amount of quench fluid is large enough then T
q
may be
sufficiently low to prevent further reaction and hence permit
total containment.
If the reaction produces non-condensible gas (typical for
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361
d e c o m p o s i t i o n r e a c t i o n s ) , the n clea rly thi s ga s wi ll need to
be rel iev ed from the que nch drum. Th e rate of flow wil l be
identical to that from the reactor plus further gas generated
with in the quenc h drum if the liquid conti nues to rea ct. The
rate of reaction will be determined by the extent of cooling
and dilution by the quench fluid.
5. TESTING OP REAC TOR/ QUEN CH COMBINAT ION
5.1. Runaway Reaction Simulation
Ideall y, a benc h-sc ale unit should prov ide data whi ch can be
interprete d easily and applied simply wit hou t need for c omple x
mod el li ng . Thi s ha s bee n achie ved to a large ext ent in the
case of runaway reaction venting following the work of DIERS.
A device that incorporates essential aspects of the DIERS
equip ment is PHI- TEC I I, shown in figure 3 (ref 4 ) .
This consists of a sample container approximately 130 cm
3
capa city wh ich is susp ende d in the centr e of a set of meta l
p l a t e s . The pla tes totally surround the sample cont ainer and
are elect rical ly heat ed. When a test sample underg oes
reac tion leading to a rise in temp erat ure, the heated plat es
are contro lled to mat ch this temp erat ure, thus elimi natin g
heat losses from the sample.
The sampl e container used in mos t experimen ts is of
0.006
inches wal l thi ckne ss which result s in a very low the rmal mas s
in rel ati on to the ma ss of the tes t sam pl e. Th is aspec t is
normal ly expresse d in term s of the Phi- fact or:
phi = 1 + (MCp),/ (MC p),
where M is the mass and Cp the specific heat, subscript t
refer s to the test cell and s to the samp le mate ria l.
The value of phi in a large scale plant is close to 1.0; using
thin-w alled t est cel ls , PHI-TE C is able to achie ve very
similar values.
In order to prevent the thin test cell from rupturing when the
vapour pressure in the reacting sample rises, a nitrogen
pres sure is exerted out side the
cell. Thus,
as the reaction
p r o c e e d s ,
pressu re equal iz ation is mainta ined by an elect ronic
contro l system. The resul t of thes e desi gn features is that
it is pos sib le to test runaway react ions usin g PHI-TE C and
apply the results directly to large scale equipment.
Extra polat ion of test data is not re quired .
The device can be used for a number of purposes including
chemical reaction screening, kinetic assessment of runaway
reac tions and emerge ncy relief sizing. In term s of exotherm
ons et det ect ion and haz ard scr een ing , it is at least as
sen sit ive as th e AR C (ref 5.) Ho we ve r, wh er ea s the AR C is
limited to maxi mum s elf-he at tracking rate s of 10 to
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362
15°C/minute, PHI-TEC II can reach up to about 200°C/minute.
5.2.
Disposal Drum Simulation
In order to simulate the disposal tank connected to a reactor,
low thermal capacity ratio (reflected in the phi-factor) and
adiabaticity constraints need to be observed. Moreover, the
test unit must be capable of being attached directly to the
reaction cell within PHI-TEC. A design that allows this is
shown in figure 4.
This consists of a small pressure vessel containing another
thin-wall
cell.
The vessel is electrically heated and is
held at a temperature identical to that of the thin-wall
cell.
The cell itself is connected directly to the reaction can
within PHI-TEC, the two being separated by a solenoid valve.
The pressure vessel containing the quench cell is fitted with
a small solenoid valve which can be opened or closed as
needed.
Typically, when the valve to the quench cell is opened, the
hot reactants flash down to atmospheric pressure and the
resulting temperature is measured by the thermocouple.
Immediately, the pressure vessel is heated to match this
temperature.
Thus,
the reactants are contained in the
thin-walled cell and the reaction not suppressed by the
thermal mass and at the same time, heat loss is avoided.
If the thin quench cell is left open within the heated vessel,
much higher pressures can be simulated. Normally the
objective is to find conditions under which pressure rise can
be avoided and so even the thin cell is sufficiently strong.
A number of different tests can be conducted with the unit in
figure 4. In all cases, a runaway reaction being studied is
first initiated within the PHI-TEC test cell and at the
appropriate time, the interconnecting valve is opened. The
quench cell can be operated in one of the following
ways:
* the first test could be performed with the vent valve on
the quench open; this would simulate the atmospheric
flashing of the reactants and provide the boiling point
of the flashed reactants.
* in a second test, the valve could be closed after the
initial flash to simulate the runaway reaction that
would ensue after
flash cooling.
* depending on the results, some suitable quench medium
could be added to the cell in further tests to slow down
the reaction still further. Different quantities (and
types) of quench fluids may be examined.
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If a decomposition reaction is being studied this will be
clear from the results and the rate of gas generation can be
measured.
6. APPLICATION TO A SIMPLE FIRST ORDER REACTION
6.1. Description of Reaction System
The exothermic reaction between methanol and acetic anhydride
has been studied extensively and is found to initiate at
atmospheric temperature (ref 4 ) . If stoichiometric amounts of
the two reactants are mixed in an ice bath and then allowed
to stand, the mixture will self-heat (under adiabatic
conditions.)
The pressure and temperature-time data for a closed
(adiabatic) thermal runaway of this reaction is shown in
figure 5. This shows a characteristic shape - very slow rise
initially and increasing exponentially with temperature. The
rate of temperature rise against temperature is shown in
figure 6. The reaction rate is found to be well represented
by a first order dependence on concentration with the
following Arrhenius parameters:
A = 4.57 x 10
17
sec"
1
E = 17.1 kcal/mole
6.2. Quench Test
The venting and subsequent quenching of this reaction was
studied by allowing the reaction to adiabatically runaway
within the PHI-TEC test cell and then venting into the quench
system at 102°C, 1.85 bar (27 psia) . At this point, the rate
of temperature rise was 21°C/minute. The reactants were vented
into an initially empty quench
cell.
The PHI-TEC venting was
performed through a 3mm dia pipe which was dipped into the
test can. A few seconds after venting, the intermediate
solenoid valve was closed. The quench cell was open to
atmosphere when the venting was initiated, but then closed to
allow adiabatic runaway of the flashed liquid. The questions
to be addressed by the test were:
* temperature following adiabatic flash
* rate of reaction after flash cooling
* quantity of quench solvent needed to reduce the reaction
rate to a safe level.
The temperature-time data for the reaction cell and the quench
cell is shown in figure 7. The vent valve was opened after
about 13.8 minutes into the exotherm - this is clearly
indicated - and then closed a few seconds later. When the
vent was opened, note the rapid initial rise in temperature
within the quench cell as it suddenly warms up from ambient.
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364
When the vent valve was shut, the contents in the reaction
cell continued to self-heat, as did the quench cell contents.
The initial information derived from this test is:
* self-heat rate goes down from 21°C/minute in the reactor
to about 7°C/minute in the quench cell
* reactants flash down from 102 to 72°C
* approximately
7 0
of the reactants were vented into the
quench
cell.
At the end of the test about 8 0 % of the
vented material was still in the quench
cell,
hence, the
fraction flashed (ie x) = 0.2.
Hence,
the parameters to be calculated from equations 1 to 3
are immediately available from a single test.
It is interesting to see whether indeed the calculated results
agree with the experimental. Consider first equation 1.
Using the kinetic parameters listed earlier and ignoring the
reduction in reaction rate as given by the concentration term:
(dT/dt)
Q
= 21Exp
1 7
-
l x l
°
9
(_i-\ - (-1-)
» *1 1.987 \3 75/ 1345J
(6)
= 2 .9°C/minute.
This is compared with the experimental value of about
7°C/minute. The difference is at least partially due to the
fact that when the reactants were flashed in the quench
cell,
lighter components will be preferentially stripped. Thus the
concentration will be quite different and extremely difficult
to calculate.
6.3. Effect of Quench fluid
With the data from the above test available, it is possible to
design the quench system. The undiluted (but flash cooled)
reactants still self-heat at 7°C/minute - hence the mixture
must be further cooled and diluted. The effect of quenching
with different quantities of solvent can be assessed directly
from the data. Using equation 2, the degree of cooling can be
calculated and then using equation 1, reduction in the
self-heat rate obtained. The result is shown in figure 8 ;
with the quench fluid equal to the reactant quantity, the
self-heat rate is reduced from 7°C/minute to 0.56°C/minute.
It is quite possible to allow the reaction to continue slowly
in the quench tank and simply vent the vapors that are
generated. The vapor quantity produced at different amounts
of quench is shown in figure 9. In this case the quench unit
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365
could for example be directly connected to the flare.
6.4 . Disposal System Design
The degree of cooling required to ensure a safe disposal
system depends on the balance between the self-heat rate and
the heat loss from the tank.
If heat loss from the quench tank due to natural convection is
Q
L
, then at any self-heat rate the amount of vapour generated
^ is:
M =
(M
r
+ M
Q
) (dT/dt)
q
C
p
- Q
L
)
( 7 )
For total containment, the dilution quantity must be chosen
so that the heat generation rate is less then Q
L
(ie H, = 0 ) .
In some instances, in order to completely contain the
reaction, an excessive amount of diluent is needed. In the
case of methanol-acetic anhydride for example, the quench
fluid needs to be several times more than the amount of
reactant. This is clearly impractical for large scale units.
If this situation occurs, then the quench drum itself has to
be provided with a small vent, the size of the vent being
governed by the vapour rate given by equation 7. It is
necessary in such instances to ensure that the venting is slow
enough to prevent liquid carry-over.
Since the vapour rate can be reduced to a low value, it is
possible to vent the vapours to flare, an absorber or
scrubber. The use of equation 6 directly provides the vapour
flow that would be vented to such units.
7. CONCLUSIONS
Design of disposal equipment to treat fluids relieved from
chemical reactors requires the use of standard chemical
engineering design methods in conjunction with the physical
and chemical property information about the reactants and
products.
Pertinent data is difficult to obtain under
realistic conditions without the use of specially devised
instruments. This article has discussed the use of an
adiabatic calorimeter PHI-TEC II for simulation of the
reaction and evaluation of the disposal system. The test data
can be used directly in standard design equations to specify
knock-out drums, quench drums, absorber/stripper columns and
flares.
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3 6 6
F R O M R E A C T O R
T O F L A R E ,
A B S O R B E R E TC .
F IG 1 : T Y P I C A L K N O C K - O U T D R U M F O R V A P O R - L I Q U I D S E P A R A T I O N
F R O M
R E A C T O R
C L O S E D V E N T
_ J — t
Q U E N C H L IQ U I D
F IG 2 : P A S S I V E Q U E N C H O F V E N T E D R E A C T A N T S
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367
S o l e n o i d
Va lves
n
Ni t rogen
1.
Th r o © R o d l a n l H o s i e r s
1. S i m p l o T h e r m o c o u p l e
3 . M a g n e t i c B a r
P r e s s u r e C o n t a i n m e n t V e s s e l
.
To o
I C e l l
5 . U M a g n a
0 . V e s a u l P r e s s u r e T r a n a d u c o r
7 . B a m p le P r e a t u i t t r a n s d u o o r
F IG 3 : P H I - T E C II R E A C T I O N C A L O R I M E T E R
HEATING COIL
F IG 4 : B E N C H - S C A L E D I S P O S A L C E L L C O N N E C T E D TO P H I - T E C
FROM
PHI-TEC
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368
FIG 5:CL0SED VESSEL RUNAWAY: MEOH-ACETIC ANHYD.
PRESSURE
&
TEMPERATURE
Vs
TIME
UJ
en
40 50
TIME[min]
60 70
in
tn
en
FIG 6: METHANOL-ACETIC ANHYDRIDE REACTION
RATE
OF
TEMPERATURE RISE
Vs
TEMPERATURE
80.0
60.0
2 40.0
Li_
O
£
20.0
0.0
I I I L O
i i 1
~r
1 \
i i .v _i i L
i t- — *s- 1 1 L _
25.0
55.0
85.0 115.0
TEMP C)
145.0
175.0
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369
FIG
O V E R A L L V I E W
OF Q U E N C H T A N K
AND R E A C T O R
TEMPERATURE
Vs
TIME
■ .
130.0
8.0
12.0
TIME min
20.0
FIG
8 :
VENTING
OF
METHANOL-ACETIC
ANHYDRIDE
EFFECT OF QUENCH QUANTITY ON SELF-HEAT RATE
U J
5
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370
F IG
9 :
V E N T I N G
OF
M E T H A N O L - A C F J I C A N H Y D R I D E
EFFECT OF QUENCH ON VAPOR VENTING RATE
2
fe
0.6
0.6
0.4
0.2
0.0
NO QUENCH
J
[ M q
=
1 ' 1 1
Q U E N C H
Q
A N T I T Y ,
M =
R E A C T A N T S V E N T E D ]
' j i
0.5
1.5 2.0
Mq/Mr
2.5
3.0
3.5
REFERENCES
1. H G Fisher, DIERS - An Overview of the Program, AIChE
National Meeting, National Meeting, March 19 8 5, Houston,
Texas, Paper no 55a
2. A G Keiter, Emergency Pressure Relief Discharge Control
by Passive Quenching, International Symposium on Runaway
Reactions, March 7-9, 1989, AIChE
3. S S G rossel, An Overview of Equipment for Containment
and Disposal of Relief System Effluents, J. Loss Prev.
Process Ind., 1990 , Vol 3, Jan
4. J Singh, PHI-TEC: Enhanced Vent Sizing Calorimeter -
Application and Comparison with Existing Devices,
International Symposium on Runaway Reactions, Boston,
March 7-9, 198 9, AIChE
5. Townsend, D I and Tan, J C, Thermo chimica Acta, 37
(1980),
1-30
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RUNAWAY REACTIONS: A CASE STUDY
T. J. SNEE
Health
and
Safety
Executive
Buxton
Derbyshire SK17 9JN
UK
ABSTRACT . A simple chemical reaction is used to illustrate the application of thermo-
analytical techniques and theoretical models in determinig critical conditions for exothermic
runaway
in
a
batch
reactor.
A
range
of
thermo-analytical
techniques
are
described
and
compared. Methods of determining th e thermo-kinetic parameters of th e reaction from
thermo-analytical data are discussed. Experimental results are used to predict th e conditions
which can lead to a runaway exothermic reaction in a pilot-scale reactor. The predictions are
compared with the results of experimental studies of exothermic runaway in a 250
1
glass-
lined reactor.
1.
INTRODUCTION
A wide range theoretical and experimental techniques can be used to evaluate hazards
associated with runaway exothermic reactions. This paper illustrates how some of these
techniques are applied to a batch chemical reactor. A reaction system with well established
physical and chemical properties has been chosen in order to demonstrate how thermo-
analytical data can be used to determine safe operating procedures. The methods discussed in
the present work would form part of a formal hazard evaluation procedure.
♦present address: Commission of the European Communit ies, Joint Research Centre,Ispra
(VA),
Italy.
371
A.
Benuzzi and J. M. Zaldivar (eds.). Safety of Chemical Balch Reactors and Storage Tanks,
371-389.
© 1991
ECSC.
EEC.
EAEC.
Brussels and Luxembourg. Printed in the Netherlands.
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372
NOTATION
sym bol quantity units
t
to
tf
m
me
m
s
T
T
m
T
e
T
0
A T
a d
AH
E
A
k
n
X
^g
qi
s
u
h i
h0
R
w
£
^
S
V
4>
Vc
R
time
onset time
final time
mass
container mass
sample mass
temperature
reactant temperature
jacket temperature
onset temperature
adiabatic temperature rise
heat of reaction
activation energy
pre-exponential factor
reaction rate constant
order of reaction
conversion
rate of heat generation
rate
of
heat loss
surface area
heat transfer coefficient
external heat transfer coeff.
internal heat transfer coeff.
thermal resistance
of
wall
specific heat capacity
specific heat
of
sample
specific heat of container
thermal dilution factor
critical Semenov number
universal
gas
constant
s
s
s
kg
kg
kg
K
K
K
K
K
k J k g "
1
kj mol"
s-1
s-1
k J s "
1
k J s "
1
m^
W m -
2
W i n "
2
W m "
2
m
2
W -
;
kJkg-1
kJ
kg-1
kJ
kg"
1
1
K-l
K-l
K-l
' K
K-l
K-l
K-l
k J m o l - t K
l i f - 1
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2.
REACTION SYSTEM
In order to illustrate the principles discussed in this paper it was necessary to choose a
reaction system with the following characteristics:
* a simple reaction system which produces good thermo-analytical data providing reliable
source terms for the theoretical models.
* a reaction system w here reliable data on the physical prop erties of the reagents and
products are available.
* a reaction system in wh ich the rate of heat generation could be controlled by the addition
of small quantities of catalyst to allow a systematic study of the conditions which can lead to
exothermic runaway.
A simple esterification reaction was chosen to meet these requirements so that the salient
features of exothermic runaway can be explored:
C H
3
C H ( O H ) C H
2
C H
3
+ (CH3CH2CCO2O -> C
2
H
5
C02(CH3)C2H5 + C
2
H
5
C 0
2
H
sec.butyl alcohol propion ic anhydride sec. butyl propion ate prop ionic acid
This moderately exothermic reaction can be catalysed by the addition of small quantities of
sulphuric acid.
3 .
HAZARD EVALUATION
Systematic determination of the risk and possible consequences of exothermic runaway should
ensure that safe and cost effective measures for controlling the hazard or mitigating the
consequences can be established. A typical theoretical and experimental assessment would pass
through the following stages:
* Determ ination of the exothermicity of the desired reaction and of any undesired side reactions. (If
the total potential energy release is very low, the risk of exotherm ic runaw ay can be discounted, and
further evaluation is unnecessary.)
* Estimation of the maximum temperature and pressure that could be achieved if the heat from
exothermic reaction were released very quickly (with no heat loss). In this way it is possible to
assess whether, under "worst case" conditions, there is a risk of vessel rupture, release of toxic
reagents or products, secondary reaction, auto-ignition or detonation etc. (If maximum temperatures
and pressures are relatively low, it may be possible to accept the risk of runaway, while ensuring
that the specifications of the reaction vessel are sufficient to achieve total containment.)
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* Determination of the temperature dependence of the rate of heat generation and the rate of heat
loss so that the critical conditions w hich can lead to exotherm ic runaway can be predicted in order
that suitable control measures can be identified.
* Assessment of the reliability of control measures and the hazard assessment procedure. (If there
remain s a significant risk of loss of control, it is necessary to adopt additional meas ures to m itigate
the consequences of exothermic runaway. These additional measures could include the provision of
an emergency pressure relief system, scrubbing systems, additional containment or plant isolation.)
The information required for the hazard evaluation can be divided into four main areas:
1) Physical properties of reagents and products - usually from published data or simple
measurements.
2) Specifications for process vessels etc. - from data supplied by manu facturers.
3) Reaction exothermicity and kinetic constants.
4) Heat transfer characteristics of reactor.
Physical properties, vessel specifications and heat transfer data are usually readily obtainable.
Definition of the thermo-kinetic properties can be more problematical. The present discussion will
place particular emphasis on the the determination of the thermo-kinetic parameters of an exothermic
reaction from thermo-analytical data.
As a simple example of a hazard evaluation procedure, a proposal to carry out the esterification
reaction in a 250
1
glass-lined reactor will be examined.
4 .PHYSICAL PROPERTIES
Relevant physical properties, and flammability and toxicity data for the reagents and products of the
esterification reaction are listed in Table 1. This type of information is readily obtainable for simple
chemicals. However, in the case of more complex reactions it may be necessary to determine some
of these quantities experimentaly. Uncertainties in, for example, the toxicity data for complex
subs tances, may necessitate additional safety measu res which are not appropriate for simple
substances with well established properties.
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TABLE 1. Physical properties and flammability and toxicity data for reagents and products of
esterification reaction.
boiling point
(°C)
specific heat
( k J k g K "
1
)
latent heat
(kJ kg"
1
)
flash point
(°Q
long term
expos, limit
(mg m
- 3
)
short term
expos, limit
(mg. m"
3
)
sec.butyl
alcohol
99.5
2.848
544
24
300
450
propionic
anhydride
169
1.796
306
74
(open test)
20
(acet. anh.)
20
(acet. anh.)
sec.butyl
propionate
132
1.944
283
32
(n-butyl)
950
(s.butyl acet.)
1190
(s.butyl acet.)
propionic
acid
141
2.119
431
54
30
45
5. PLANT SPECIFICATIONS
The p resent d iscussion will consider a proposal to perform the esterification as a pilot-scale (250 1)
batch reaction. The specifications for a standard, industrial, glass-lined, jacketed reactor are listed in
Table 2. Specifications for auxiliary equipment such as pumps, feed vessels and pipework, and the
standard operating and handling procedures would form part of a general safety assessment.
Hazard evaluation procedures concerned specifically with runaway reactions would focus particular
attention on the temperature and pressure rating of the reactor and possible catalytic effects from the
materials of construction.
It will be assum ed, for the purposes of the prese nt discuss ion, that the tem pera ture of the heat
transfer fluid in the reactor jack et can be chosen according to the results of the hazard ev aluation
and the requirement for efficient and economic chemical production.
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TA BL E 2. Specifications of a standard industrial pilot-scale reactor.
working pressure
(barg)
design pressure
(bar g)
test pressure
(barg)
temperature range
(°Q
capacity
(litres)
6 t o - l
6.6 to-1
11.4
-25 to 200
250 (nominal)
334 (total)
jacket
6 t o - l
6.6 to -1
11.4
93
material
glass-lined mild steel
mild steel
6 . THERM AL ANALYSIS
Four types of apparatus have been chosen to illustrate how thermal analysis can be used to
determine the thermo-kineteic parameters of an exothermic reaction:
Differential Scanning Calorimetry (DSC)
Accelerating Rate Calorimetry (ARC)
Adiabatic Calorimetry with Vent Sizing Capability (VSP, PHI-TEC)
Heat Flow Calorimetry (RC1)
6.1 Differential Scanning Calorimetry [1]
The DSC sample (around 10 mg) is held in a sealed container and placed in a measurement cell
whose temperature is increased at a constant rate. The rate of heat evolution (or absorption) from
the sample is measured as a function of temperature with respect to an inert reference material.
6.2 Accelerating Rate Calorimetry [2]
The sam ple for ARC analysis (around 10c) is placed in a container (designed to withstand
substantial pressures) which is subject to stepwise heating, but is held in an adiabatic state between
each temperature step. Adiabaticity is achieved by matching the temperature of the surroundings to
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that of the sample container. Exothermic reaction or decomposition is detected when, after a
temperature step, the temperature of the system continues to rise due to self-heating of the sample.
If the rate of temperature rise exceeds the detection threshold (0.02 K min"l), stepwise heating is
suspended and an adiabatic environment is maintained as temperature and pressure are recorded as
the reaction proceeds.
6.3 Adiabatic Calorimetry and Vent-Sizing
The operation of the VSP [3] and PHI-TEC [4] is similar to ARC, but thin-walled sample
containers are used so that that the experim ental data is not significantly influenced by the thermal
mass of the container. Rupture of the sample container is prevented by applying external pressure to
match the pressure developed inside the container. These instruments are provided with special
facilities for the design of emergency pressure relief systems for chemical reactors.
6.4 Heat Flow Calorimetry [5]
The rate of heat generation is measured using heat-flow reaction calorimmetry by determining, in a
small jacketed reactor (capacity approx. 2 1), the rate of heat transfer from the reactants to the
surrounding heat transfer fluid. The rate of heat flow is proportional to the difference between the
reactor and jacket temperature. This difference can be related to rates of heat generation, after the
heat transfer characteristics of the vessel have been determined by calibration using electrical
heating.
7 REACTION EXOTHERMICITY
A range of therm o-analytical techniques can be used to determine the heat of reaction. The choice of
technique depends on factors such as: available sample size, required temperature range, maximum
temperature and pressure etc.
7.1 Heat of reaction from DSC
Th e D SC scan for the esterification reaction is show n in Figure 1. Th e reaction is first detected at a
tempera ture of 40°C (the onset temperature) w hen the rate of heat evolution is sufficient to cause a
discernable departure from the baseline. As the temperature is increased further, the rate of heat
generation reaches a maximum value at 75°C and then subsides as the reagents become depleted
until the trace returns to the baseline at 120°C.
The heat of reaction can be determined by integrating the rate of heat generation between the onset
temperature and the final temperature.
1 ^
A H = - J q
g
.d t (1)
to
This integral is given by the area between the DSC curve and the baseline.
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378
i
o
CO
0>
o
64 72 80 88
T e mp e ra tu re 'C
96 w
112 120
Figure 1. DSC scan for the reaction between propionic anhydride and sec.butyl alcohol catalysed
by 0.8% H 2SO4 (scan rate 8 K min"
1
).
"E
n
D P - J
1)-^
10"
300
+
PH-TECdota
x ARC data
^ ^ H + H H + ^ ^ H f . , .
- 1 —
312
324 336 348 360 372 384
Temperature
(K)
T
+
+
+
+
T
396 408 420
Figure 2. ARC and PHI-TEC plots of self-heat rate against temperature for the reaction between
prop ionic anhydride and sec.butyl alcohol (no added H2SO4).
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7.2 Heat of reaction from ARC
The AR C plot of self-heat rate against temperature for the esterification reaction is shown in Figure
2.
Th e reaction is detected at 310 K whe n the rate of self-heating excee ds the detection threshold.
Under adiabatic conditions, the rate of temperature rise increases to a maximum and then decreases
until a final temperature of 392 K is reached when the reaction is comp lete. The total heat evolved
is distributed between the sample and the sample container and the heat of reaction can be calculated
using the expression:
AH = <j).AT
ad
.C
p ( 2
)
where
ms .Cps + mc .Cpc
* =
EIT^I
<
3
>
A typical thermal dilution factor (<j)) for an ARC experiment would be 1.4.
7.3 Heat of reaction from PH I-TEC
The PHI-TEC plot of self-heat rate against temperature for the esterification reaction is shown in
Figure 2. Th e detection sensitivity and the form of the self-heat rate plot is similar to ARC data.
However, the lower thermal dilution factor for the PHI-TEC gives rise to higher self-heat rates and
a larger adiabatic temperature rise. The heat of reaction can be evaluated using Equation 2. PHI-
TEC measurements can be made with thermal dilution factors close to unity.
7.4 Heat of reaction from RC1
Temperature records for the esterification reaction in the RC1 are shown in Figure 3. The reaction
was performed as a semi-batch process (metered addition of the anhydride to the alcohol) with the
reactor tem peratu re m aintained at 75 °C . At the start of the addition, the jac ket tem perature rises
above the reactor temperature in order to compensate for the addition of cold fluid to the hot reactor.
After 60 minutes the addition is complete and the jacket temperature falls below the reactor
temperature to compensate for the heat generated as the exotherm ic reaction proceeds .
The heat of reaction is determined by integrating the difference between temperature of the reactor
and the jacket multiplied by the heat transfer coefficient with corrections for the heat required raise
the temperature of the anhydride to 75°C.
A H =
m JU.S.(T
m
-T
e
).dt (4)
to
At a reactor temperature of 75°C, heat losses to the surroundings through the lid of the vessel are
substantial, and this introduces large uncertainties in the calculated heat of reaction, when the rates
of heat generation are relatively low. At 75°C, with no catalyst, the rate of esterification, and
therefore the difference in temperature between the reactor and jacket, is relatively low and the
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exothermicity is not determined accurately by heat-flow calorimetry.
343
340
reactor temperature
jacket temperature
— 1 1 1 1 1 1 1 1 —
2 8 0 0 5 6 0 0 8 4 0 0 11200 1 4 0 0 0 1 6 8 00 1 9 6 0 0 2 2 4 0 0 2 5 2 0 0 2 8 0 0 0
Time (s)
Figure 3 . Tem perature records from semi-batch esterifictation in RC1 reaction calorimeter (no
added H2SO4).
8. EXOTHERMICITY DATA AND PRELIMINARY HAZARD EVALUATION
The results of calorimetric measurement of the exothermicity of the esterification reaction are
summarised in Table 4. Large variations can be seen in the values obtained using different
techn ique s. Detailed asses smen t of the reliability of each method is not the subject of the present
work, but Table 4 illustrates the importance of applying a range of techniques, and repeating
measu rements in order to obtain accurate data.
The exothermicity data indicate that if the esterification reaction proceeds rapidly, with no
significant heat losses or thermal dilution, the temperature of the reaction mixture will rise by
approximately 130 K. The consequences of such a temperature rise can be assessed with reference
to Tab les 1 and 2. Th e AR C and PH I-TE C data indicate that an initial temp erature of at least 20°C
would be required for the reaction to proceed at a significant ("economic") rate. A rapid runaway
from this initial temperature would reach the boiling point of the product and give rise to potential
flammability and toxicity hazards (from Table 1). However, the temperature and pressure
specifications of the reactor (Table 2) would be unlikely to be exceeded, so there would be no
significant risk of vessel ruptu re. Such a reactor no rmally w ould be provided a reflux conden ser
and a vent to atmosphere (possibly via a scrubbing system) which would substantially reduce the
potential release of flammable or toxic material. However, assuming somewhat artificial plant
conditions, the exothermicity data indicate that the consequences of thermal runaway would be
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hazardous but not catastrophic. The preliminary hazard assessment indicates that reaction kinetic
and heat transfer data should be obtained in order to identify the critical conditions which could lead
to exothermic runaway, so that suitable control measures can be adopted.
TABLE 3. Comparison of reaction exothermicities evaluated using various thermo-analytical
techniques.
heat of reaction
(kJ kg"
1
)
differential scanning calorimetry -26 1
accelerating rate calorimetry -28 1
adiabatic calorimetry with vent sizing -3 01
reaction calorimetry -3 06
9. REACTION KINETICS
The rate equation for a simple chemical reaction or decomposition can be written in the form:
£-k.(l-x)* (5)
The temperature dependence of the rate constant (k) can often be predicted using the Arrhenius
equation:
k = A.ex p(-E/R T) (6)
Under adiabatic conditions ,with constant Cp, reactant conversion is directly proportional to the
change in temperature
T - T
0
x = (7)
A T
a d
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hence the rate of self-heating under adiabatic conditionsis given by :
dT dx AH AH .A.( l -x)
n
1W =
W — .exp(-E /RT ) (8)
d t
<* Cp.<j> Cp.<j)
at low conv ersion (x « 1)
log (dT /dt) = log(AH.A/Cp.<t>) - E/R T (8a)
The critical conditions which can lead to exothermic runaway are normally reached before reactant
depletion causes a significant reduction in the rate of heat generation. This means that, for the
purpose of hazard evaluation, the kinetics of exothermic reaction can be specified by determining
the Arrhenius constants A and E using thermal analysis. The addition of small quantities of
sulphuric acid to the esterification reaction mixture shows how the kinetic parameters can be
strongly influenced by catalytic effects.
9.1 Reaction kinetics from DSC
DS C traces for the esterification reaction catalysed by various concentrations of sulphuric acid are
shown in Figure 4. The increase in reaction rate with increasing acid concentration is seen as a
progressive reduction in the onset and peak temperatures and a progressive increase in the
maximum rate of heat generation.
The shape of the DS C curve is strongly influenced by the concentration depen dence of reaction rate.
DSC is relatively insensitive to the low rates of heat generation at low temperatures or low
conversion of reagents. Interpretation of DSC data can be difficult due to complex heat transfer
between the sample, the sample container and the measurement cell. Although, in principle, it is
possible to determine reaction kinetic constants from DSC [5], adiabatic techniques such as ARC
and PHI-TEC provide a more reliable means of determining the Arrhenius parameters from self-
heat rate data at the start of the reaction.
9.2 Reaction kinetics from ARC
ARC plots of ln(self-heat rate) against reciprocal temperature are shown in Figure 5. These results
show the same dependence of reactivity on sulphuric acid concentration as had been observed using
DS C. The increase in reactivity with increasing acid concentration is seen as a progressive reduction
in the onset temperature (at which the self-heat rate exceeds the threshold value - 0.02 K min"l)
and, at concentrations greater than 0.05% H2SO4, as an increase in the rate of self-heating at the
initial sample temperature.
A linear relationship between ln(heat rate) and reciprocal temperature is predicted by Equation 8a.
The initial sections of the ARC plots are approximately linear, so the Arrhenius parameters for the
reaction can be obtained by linear regression.
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i
o
o
0.KH2S04
02%H2S04
0.4%H2S(H
0.S5H2S04
0 320 330 340 350 360 370 380 390 400 4 0
Temperature (K)
Figure 4. DSC scan for the reaction between propionic anhydride and sec.butyl alcohol catalysed
by various concentrations of sulphuric acid.
E
2*:
iu -
:
uU
10°^
10-1
-
-
in"
2
HJ
0.4%H2S04
0ZUQSM,
0
0.KH2SO4"
0.05% H2S04 "
«* ° ° o ° o ° ° « ^ ° °«
o° ^ o° o°° c^" ")
0° „°
a
„=°°
y
o^°
o °
c
o o ^ t S >
°
Q
°° o°° 0O°°
."' /
o
„-""
„° „ : 0% H2S04
0.025% H2S04
1 1
1 1 i i i i i
-3.50 -3.40 -3.30 -3.20 -3.10 -3.00 -2.90 -2.80 -2.70 -2.60 -2.50
-1000/T (K-1)
Figu re 5. AR C plots of log(self-hea t rate) against recipro cal temp erature for the esterification
reaction catalysed by various concentrations of sulphuric acid.
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Reliable ARC data could not be obtained at sulphuric acid concentrations greater than 0.4 %
becaus e, w ith a reactive com positions, significant reaction occurs during the time required to install
the sample in the instrumen t. This effect causes a reduction in the measure d adiabatic temperature
rise.
(The addition of sulphuric acid would not be expected to affect the heat of reaction or the
temperature rise that occurs if adiabatic conditions are established at the start of the reaction.)
9.3 Reaction kinetics from PHI-TEC
The PHI-TEC allows reagents to be introduced into the sample container after it has been installed
in the apparatus. Reactive compositions can be studied by operating in adiabatic mode as soon as
the sample has been assembled. Figure 6 shows PHI-TEC data for the esterification reaction
catalysed by 0.8
%
H 2 SO 4. The difference b etw een initial and final temp erature (110 K)
coresponds closely to the temperature rise measured for less reactive compositions (Figure 2). This
indicates that adiabatic conditions have been maintained from the start of the reaction and during the
course of the reaction when the rate of temperature rise reaches a maximu m value of 500 K min" 1.
9.4 Reaction kinetics from RC1
Figure 7. shows the experimental record for batch esterification reaction (catalysed by 0.8%
H2SO4) in the RC1 with the reactor temperature maintained at approximately 31°C. Equation 5
predicts that, at constant temperature, the maximum rate will occur at the start of the reaction (x =
0).
Figure 7 indicates a maximum rate of heat generation only after substantial proportion of
reagents have reacted (x = 0.5), indicating auto-catalytic kinetics. Auto-accelerating reactions can
result in supercritical (runaw ay) conditions at temp eratures low er than those predicted assum ing
normal kinetics. Detailed discussion and quantification of this effect will be discussed elsewhere.
Figurre 7 shows how reaction calorimetry can be used to determine the concentration dependence of
reaction rate. Reaction calorimetry can be used to deterrmine the temperature dependence over only
a limited temperture range due to the substantial temperature dependence of the heat loss
characteristics of this type of apparatus and problems associated with the detection of rapidly
changing temperatures. The adiabatic techniques (ARC and PHI-TEC) are, in general , more
suitable for determining the Arrhenius parameters of an exothermic reaction.
9.5 Kinetic parameters for the esterification reaction.
The initial sections of the ARC and PHI-TEC plots of ln(heat rate) against reciprocal absolute
temperature (Figures 5 and 6) are approximately linear, indicating that the temperature dependence
of the reaction rate can be predicted by the Arrhenius e quation. V alues for the activation energy and
pre-exponential factor evaluated for the esterification reaction are listed in Table 4
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10
3
^
10
2
^
10
2
0XH2SO+
0.025* H2S04
3.50
-3.38 -3.26 -3.14 -3.02 -2.90 -2.78 -2.66 -2.54 -2.42 -2.30
-1000/r
( K - 1 )
Figure 6. PH I-TE C plots of log(self-heat rate) against reciprocal tempe rature for the esterification
reaction catalysed by various concentrations of sulphuric acid.
40
E
37-1
34
31
28
25- |
22
19-1
16
13
X)
reactor temperature
jacket temperature
—
1 1 1 1 1 1 1 1 —
850
1700
2550 3400 4250
5100
5950 6800 7650 8500
Time (s)
Figure 7. Temperature records during esterification reaction catalysed by 0.8% H2SO4 carried out
as a batch process in the RC1 reaction calorimeter.
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TA BL E 4 . Therm o-kinetic parameters evaluated from ARC and PHI-TEC data for the esterification
reaction.
sulpihuric
acid cone.
(%)
0.1
0.2
0.4
0.8
activation energy
(kJ mol"
1
)
ARC
94
97
95
-
PHI-TEC
95
94
94
98
pre-exponential
(s -
1
)
ARC
3 . 6 * 1 0
n
1.8*10
12
1.8*10
12
-
factor
PHI-TEC
4 . 6 * 1 0
n
6 . 6 * 1 0
n
7 . 9 * 1 0
n
7 . 5 * 1 0
1 2
10.
HEAT TRANSFER CHARACTERISTICS
The critical conditions which can lead to a runaway exothermic reaction are determined by the
temperature dependence of the rate of heat generation (from thermal analysis) and the temperature
dependence of the rate of heat loss (from the heat transfer characteristics of the process vessel).
Heat transfer coefficients for a jacketed chemical reac tor can be determined by calculation or,
experimentally, by determining the rate of heat transfer between the contents of the reactor (heated
electrically) and the heat transfer fluid in the reactor jacket.
The rate of heat loss from a well stirred jacketed reactor can be predicted assuming a Newtonian
cooling equation of the form:
qi = U .S . ( T
m
- T
e
)
(9)
where the heat transfer coefficient (U) comprises contributions from the thermal resistance of the
reactor wall and the internal and ex ternal film heat transfer coefficients :
J _
_ 1 _ _J_
U ~ h
0
w +
lu
( 1 0 )
Techniques for determining U are discussed elsew here [6]. A value of U= 180 W m"
2
K~l would
be typical for an organ ic med ium in a standard indus trial glass-lined reactor.
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387
11 CRITICAL CON DITIONS
Conditions in a well-stirred jacketed reactor correspond closely to those assumed in the Semenov
model [7] for predicting the critical conditions for exothermic runaway. Under these conditions
(assuming Arrhenius-type temperature dependence for the rate of heat generation) the critical jacket
temperature is given by:
m.AH.A.E.exp(-E/RT
e
) i
V c =
UZRTT
=
e (
u
>
This expression assumes that the critical conditions are reached before the depletion of reagents has
had any significant influence on the rate of heat generation (pseudo-zero order kinetics).
Th e S emenov model has been used to predict the critical conditions for the esterification reaction in
a 250 1 glass-lined reactor. Critical jacket temperatures calculated using ARC and PHI-TEC data are
listed in Table 5.
TABLE 5. Critical jacket temperatures calculated for the esterification reaction in 250
1
glass-lined
reactor.
sulph uric acid critical jacke t temperature (K)
concentration (%)
ARC data PHI-TEC data
0.1 296.0 295.8
0.4 285.1 288.9
0.8 285.6
It is not normally possible to test this kind of prediction experimentally, because of the attendant
hazards. However, in the case of the esterification reaction, where the properties of reagents and
products are well established, experiments to determine the critical conditions which could lead to
exothermic runaway could be performed safely in an isolated 250 1 reactor. The temperature-time
profiles which were observed when the esterification was performed as a batch reaction with water
circulating at 285 K (12 °C) through the reactor jacket are shown in Figure 8.
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388
p
CL.
E
C L
OJ -
68-
51-
34-
17-
0 -
I 0.8%H2S(H
i i
i i i
0.4% H2S04
^ — - \ 0.1% H2S04
i i i i
0 4800 9600 14400 19200 24000 28800 33600 38400 43200 48000
T i m e (s)
Figure 8. Temperature records during esterification reaction (catalysed by various concentrions of
H2S04) as a batch process in a standard industrial , pilot scale reactor (250 1 capacity) with the
jacket temp erature maintained at approximately 295 K .
Th e dro p in temp erature wh ich can be seen at the start of of each of the expe rimen tal records
(Figure 8) is due to endothermic mixing of reagents.
The results for
0.1%
H2S O4 show that, after the initial mixing of reagents,the tem perature of the
reactor contents remain at approximately the same temperature as the water circulating through the
jacket. (Analysis of the contents of the reactor after 48 hours indicated that the reaction had
proceeded isothermally to completion.) At a sulphuric acid concentration of 0.4% exothermic
reaction causes the temperature of reaction mixture to rise above the jacket temperature but the rate
of cooling is sufficient to prevent a large increase in the temperature of the reactor contents. At a
sulphuric acid concentration of 0.8% the rate of cooling cannot prevent an acceleration in the rate of
heat generation and a runaway excothermic reaction was ob served.
The experimental data indicate that for the 250
1
reac tor at a jack et tem peratur e of 295 K the critical
acid concentration which can lead to a runaway reaction lies between 0.4% and 0.8%. This result is
broadly in accord with the prediction of the simple Sem enov criterion (Equation 11) using thermo-
analytical data from AR C or PH I-TEC (Table 5 ) .
Au tocatalys is detected using isothermal reac tion calorime try (Figure 7) wo uld lead to critical jacket
tempe ratures low er than those predicted in Table 5. Experim ents over a wider range of acid
con centra tions and jack et tempe ratures than those reported here would be necessary in order to
quantify this effect.
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12 CO NCLUSION
The application of a simple theroretical model can provide a reasonably reliable prediction of the
critical conditions which can lead to exothermic runaway in a batch reactor. More sophisticated
treatments which take account of the concentraion dependence of reaction rate would provide a
more accurate prediction of the critical jacket temperature. A range of thermo-analytical techniques
should be applied in order to determine reliable input parameters for the theoretical models.
REFERENCES
1) Rogers R.N. and Smith L.C., (1970) 'Application of scanning calorimetry to the study of
chemical kinetics', Thermochimicha Acta, 1, 1
2) Townsend D.T. and Tou J.C., (1980) 'Thermal hazard evaluation by an accelerating rate
calorimeter', Thermochimica Acta, 37, 1.
3) Fauske H.K. and Leung J.C., (1985) 'New experimental techniques for characterising runaway
chemical reactions', Chemical engineering progress, 81(8), 39..
4) Singh J., (1989) PHI-TEC: Enhanced vent sizing calorimeter application and comparison with
existing devices', International Symposium on Runaway Reactions', AIChE, 313.
5) American Society for Testing Materials, (1979) 'Arrhenius kinetic constants for thermally
unstable materials', ASTM E698-79, Nov. 79, Committee E-27, SCE27.02.
6) Ch apm an F.S . and Holland F.A ., (1985) 'Heat transfer correlation s in jack eted vessels',
Chemical Engineering, 15, 175-182.
7) Semenov N.N, (1928) Z. Phys. Chem.,48, 57 1.
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REACTION HAZARD EVALUATION
P. F. NOLAN
Department of Chemical Engineering
South Bank Polytechnic
Borough Road
London SE1 OAA
UK
ABSTRACT. The available calorimetric methods are discussed in terms of
the data, which they provide in relation to the stages in the
development of a process. The data produced from calorimetric and other
thermal methods is placed within an overall assessment strategy
incorporating literature searches, calculations and formal quantitative
hazard assessment procedures and these may lead to the definition of a
basis for safety. Against this background a procedure is outlined which
will allow a beginner to establish a chemical reaction hazard assessment
laboratory for an industrial company.
1. INTRODUCTION
The majority of reactions carried out in the fine and speciality
chemical industries are exothermic and have the potential for over
heating to occur in their normal batch or semi-batch methods of operation.
The safety record of the chemical industry is generally good when placed
against the background of the number of reactors in operation and the
quantities and types of materials processed. However, problems have
occurred in the past [1,2] due to:
a. inadequate understanding of the process chemistry and thermochemistry
b.
inadequate engineering design for heat transfer
c. inadequate control systems and safety back-up systems
d. inadequate operational procedures, including training.
Various categories of hazard are inherent in chemicals manufacture.
These can be defined as chemical, operational, toxic and environmental.
The potential for such hazards, singly or in combination, can be present
during the stages of manufacture. (see Table 1)
Incidents have occurred in each of the stages below and hence it is
necessary to be in a position to predict any hazard producing potential
at every manufacturing stage. In particular, it is essential to have an
assessment strategy which links the nature of the chemical reagents, the
reaction with the equipment/plant in use and the operating procedures.
In general, chemical reaction hazards arise from:
391
A. Benuzzi and J. M. Zaldivar (eds.), Safety of Chemical Batch Reactors and Storage Tanks,
391—408.
© 1991 ECSC, EEC, EAEC, Brussels and Luxembourg. Printed in the Netherlands.
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TABLE 1. Stages in Chemicals Manufacture
Assembly/storage of raw materials
Chemical reaction
Holding of reactive substances
Purification of the reaction product
Treatment of waste/cleaning/recovery
Storage of product
Drying/formulation/packaging
Transportation
a. thermal instability of reactants, reaction masses and products
b.
rapid exothermic reaction, which can raise the temperature to
decomposition temperature or cause violent boiling of the batch
c. rapid gas evolution which may be associated with thermoneutral,
exothermic or endothermic processes.
Essentially, an assessment procedure for chemical reaction hazards will
initially define:
a. the chemistry for each stage of the process
b.
the plant design and operating conditions
c. the normal variations in process/plant procedures.
The second stage involves:
a. an evaluation of the potential hazards
b. the specification of safety measures
c. the preparation of a detailed report.
The implementation of the safety measures and their inclusion into the
process and plant design needs to be compatible with production and the
economics of manufacture. Finally, it is necessary to regularly monitor
the safety measures and ensure that they remain adequate.
2. STAGES IN PROCESS DEVELOPMENT
Gibson [3] has defined the stages in the assessment procedure against
the background of the normal development stages of a process. Process
development usually occurs in four stages, primarily defined by the
scale of operation - concept, laboratory bench, pilot plant and
manufacturing scale plant. At each stage, the potential reaction hazard
requires definition. Such continuous definition and in some cases re
definition leads to a comprehensive knowledge of the reaction at the
final,
manufacturing stage. Whilst a continuous development of safety
considerations is recommended, it has to be recognised at the outset that
a substantial amount of the experimental work on reaction hazard
evaluation occurs, in practice, between laboratory bench and pilot plant
scale operations.
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2.1. Laboratory Scale Development
After the conceptual stage of reaction design, it will be necessary to
carry out some bench-scale work in a fume cupboard. However, prior to
such activity it is necessary to:
a. check the literature for data on potential chemical hazards e.g. use
of Bretherick [ 4 ], NFPA [5] and Austin [6 ]
b.
calculate the heat of reaction and the adiabatic temperature rise for
instantaneous reaction. The latter will enable the maximum
attainable process temperature to be calculated
c. ensure that the materials being handled will not detonate or
deflagrate and that the process does not involve a violently
exothermic reaction. The initial screen can involve:
i. an examination of the chemical structure of the molecules
involved. Groups such as aromatic, nitro, nitrate ester and
nitramine are closely linked with explosibility and azo,
azide, nitroso, peroxide and acetylenic groups can also form
part of explosive structures
ii. calculation of the oxygen balance. Almost all of the
recognised explosives have balances between -100 and + 4 0 , but
any balance more positive than -200 should be regarded as a
potential high risk
iii. use of a computer program, such as CHETAH [7 ]. This allows
the estimation of the heat of reaction, thermodynamic
properties of individual substances and the prediction of
whether the compound or mixture has the tendency to propagate
a deflagration or detonation.
Other calculations may also be useful. Craven [ 8] described how the
approximate exothermicity of a reaction or decomposition can be predicted
from the atomisation energies of the reactants and the assumed products.
Atomisation energies can be determined from the summation of average bond
energies given in the literature [9]-
At this stage, it is also necessary to carry out some initial screening
tests (see Section 3.1) to answer specific questions on the exothermicity
of the proposed reaction. The main questions are:
a. What are the normal rates and quantities of heat and gas evolution?
b.
At what temperature will runaway commence?
c. What are the consequences of runaway in terms of heat and gas
evolution rates?
Therefore, any sequence of initial screening tests must be able to
provide the following basic information:
a. temperature for onset of thermal decomposition
b. quantity and rate of heat release
c. rate of gas evolution as decomposition proceeds
d. catalytic effects caused by potential materials of construction of
the envisaged plant
e.
autocatalytic effects
f. induction time effects
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g. decomposition rate, including any secondary decompositions.
2.2.
Pilot Plant
Following successful laboratory development, pilot plant scale operations
should be carried out. Under the normal, human supervision associated
with pilot plant scale work, it is necessary to demonstrate that the
process can be operated safely both as defined and with the individual
company's accepted normal variations which could occur in practice. The
experience of the company and of the individuals running the plant will
play an important role at this stage.
The basis of safety, i.e. use of preventative and/or protective measures,
requires the consideration of the reaction hazards and the influence of
the plant and its operation on those identified hazards. Ideally, a
formal hazard assessment will call for a clear definition of the process
prior to scaling-up in a pilot plant. This definition will include data
on the process
a. as written with fixed parameters
b.
with acceptable variations found in manufacture
c. with faults known to occur in normal processing, e.g. charging errors
d. with all potential faults.
Essential data at this stage, prior to pilot scale operation is given in
Table 2.
TABLE 2. Data for Reaction Hazard Evaluation
Heat of reaction
Heat capacity
Rate of heat production
Rate of heat removal
Heat transfer properties of reaction mass
Kinetics with regard to accumulation of
reactants/heat
Temperature range and nature of any
decompositions
Factors which affect accumulation
Effects of mischarging, impurities, errors
and those caused by materials of construction
of plant
Kinetics (autocatalysis) of decomposition
reactions
Rate and quantity of gas evolution
The prime objective of supporting calorimetric laboratory studies (see
Section 3.2) is to obtain information that can be evaluated in relation
to the conditions which occur in the plant. The design of preventative
and protective measures will require details of the deviations which may
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occur from the normal process definition. The information required to
characterise a runaway or decomposition is:
a. the onset temperature for the specific plant system being studied
b.
rate of heat evolution at runaway
c. rate of gas evolution at runaway
d. maximum pressure developed in a closed vessel when runaway occurs.
2.3. Manufacturing Scale Operations
Following bench scale and pilot plant operations, a number of further
decisions need to be made. The assessments carried out at the two
previous stages will need to be re-evaluated and some further testing
may be required to relate the data to the specific plant and operating
conditions.
The manufacturing scale plant can be:
a. an existing reactor
b.
a multi-purpose reactor, with possibly some modification to
accommodate the process
c. a new purpose-designed and built reactor.
The effect of scale of operation is a very significant factor, although
it is not always fully appreciated. Many incidents occur when processes
are scaled up, some having been performed successfully for years on a
slightly smaller scale. The reasons are clear when the following are
considered:
a. the rate of heat generation increases exponentially with temperature
b.
the total heat generated is proportional to the batch volume (a cubic
term)
c. the rate of cooling is proportional to the surface area (a squared
term).
Any increase in batch size will substantially increase the total heat
generated. Unless the cooling capacity is increased accordingly then
the reaction temperature will rise. This leads to an increase in the
reaction rate and the reaction can go out of control.
The required cooling area for batch operation can be calculated by a
number of methods. The method described by Hugo [10] requires data on
the rate of reaction and the adiabatic temperature rise. Depending on
the reactor size, 2 - 5 m m can be installed in reaction vessels with
only jacket cooling and 4 - 8 m m if the vessel is also provided with
an internal cooling
coil.
The determination of the required cooling area
may mean taking the decision about moving from batch to semi-batch
operation. The latter allows the option of feed control to minimise
potential runaway conditions.
Any available safety system must be adequate for all situations, which
may arise. The bench scale studies can define the most suitable
agitator, the inside film heat transfer coefficient for use in scale-up
correlations and the design of normal operating and emergency relief
systems. The materials of construction of any plant needs careful
consideration, since it may catalyse undesired side or secondary
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reactions. Laboratory scale tests may include samples of the materials
of construction or their decomposition products, e.g. rust.
The design of a reactor and the chosen operational procedures should be
accompanied by a series of formal hazard assessments. The easiest
technique for the non-specialist is the use of HAZOP [11]. The Hazard
and Operability study can be carried out at various stages of the process
development. More quantitative techniques, e.g. the application of fault
tree analysis [12], require some specialist knowledge.
The manufacturing scale also raises the possibility of designing for
inherent safety; however, where this is not possible then reliance must
be placed on process control and associated safety back up systems, where
necessary. The basis of process control is set by the experimental
results from calorimetric investigations. These include the definition
of onset of exotherm temperature, the safety margins, amount of cooling
required, the temperature limit to prevent accumulation of unreacted
material and the effect of loss of agitation.
2.4. Modified Processes
Many incidents follow modifications to plant and/or process. Any
assessment procedure must cater for on-going changes in the running of
processes and plants. If a hazard assessment of the plant and process
is available and the modification does not invalidate the basis for safe
operation then the formal recording of this decision and the reasons for
it are all that is required. Alternatively a detailed evaluation and
possibly alternative or additional recommendations to ensure safe
operation of the modified process or plant may be necessary. It is
essential that for any suggested modification, checks must be made on the
chemical and operational hazards and the basis of safety clearly re- ■
defined.
There is currently no standard procedure or no one test for the assess-
ment of reaction hazards; however, the type of data required, calls for
the use of calorimetric instrumentation.
3. CALORIMETRIC AND OTHER INSTRUMENTATION
Calorimeter is the generic term for a range of instruments used for
gaining thermodynamic, kinetic and heat transfer data to aid process and
plant design and operation. Calorimetry ranges in complexity from basic
heating tests to the sophistication of simulating an entire, as written,
process in a model bench-scale, computer-controlled batch or semi-batch
reactor. The main types of equipment, which can be used, after the
preliminary calculations and any necessary explosibility screening tests
are:
a. basic screening tests - These are used primarily at the laboratory
scale development stage and prior to any studies outside the
laboratory environment.
b. isothermal calorimetry - This is used to gain data on the normal,
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desired reactions, in terms of kinetics, thermodynamics and heat
transfer.
c. adiabatic calorimetry - This is used to gain data on the runaway
potential of reactions and individual compounds.
d. reactor venting instrumentation - This is used to gain data to enable
the calculation of emergency vent sizes, but they also provide some
thermal data.
3.1. Basic Screening Tests
These tests tend to use small samples and hence can be used during the
laboratory scale development programme. They can be used to examine the
effects on stability of the presence of materials of construction and
their decomposition products, e.g. rust and any ageing effects caused by
the reaction mass being held for prolonged periods at elevated
temperatures. From some of the tests, it is possible to gain ideas on
the initial exotherm temperature, adiabatic self-heating rate,
activation energy for decomposition, adiabatic temperature increase,
overall energy release during decomposition, adiabatic induction time,
estimates of the initial exotherm temperature for a larger size of
reaction mass and the volume of gas evolved on decomposition.
Many test methods have been developed "in-house" and are described in the
literature
[13,14].
Particularly useful test methods employ gramme size
quantities. Some companies use commercial DSC/DTA as a screening tool
employing milligramme quantities. For reaction hazard evaluation it is
recommended that use is made of:
a. sealed pressure resistant capsules
b.
heating rates of 1 to 5 C min
c. sample mass of 5 to 10 mg
d. temperature range of 30 3 to 623 K
when using conventional DSC/DTA.
The unfortunate "100 Degree Rule" is often misused in the evaluation of
reaction hazards. The rule basically states that if the operating
temperature of a process is 100 C higher than the detectable exotherm
found in a small scale test, then the process operation will not
experience this thermal event [ 15]. Based on experience, it is known
that many factors influence the temperature dependent rates of heat
generation as detected by screening test methods [16 ]. These include the
physical aspects of the test procedure, such as heating rate, sample size,
thermal inertia, sensitivity for the particular type of substances
involved, the agitation and the activation energy. The sensitivity of
the small scale test needs to be viewed in relation to the large scale
operation. Safety margins should only be used as guides and not for
defining a basis for safety.
Recently a number of commercial, relatively low cost screening tests have
become available. These include the Radex [17] and the RSST (Reactive
System Screening Tool) [ 18 ]. The latter also provides data for the
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sizing of emergency relief vents. The advent of commercial equipment
will aid the individuals/companies who are unable to develop their own
instrumentation, due to lack of workshop facilities or internal working
practices. However, the literature contains some very detailed
descriptions of easy to construct and use equipment, which can provide
the fundamental data on thermal stability and this includes onset
temperature, magnitude of an exotherm and its induction time. From such
data the size of the potential problem and the time available to correct
it can be estimated.
When expensive commercial instrumentation, such as the Seteram C-8 0,
Thermometries Thermal Activity Monitor, Columbia Scientific Industries
Accelerating Rate Calorimeter, is available some companies use them as
basic screening tests, although they are usually more expensive to run
and can take longer to provide the preliminary data. Although, of course,
they also provide additional data to that obtainable from the other
cheaper tests and instrumentation.
3.2. Reaction Calorimeters
Numerous commercial and "in-house" reaction calorimeters exist and the
choice of one particular instrument over another very much depends on the
type of data required (and the money available). Nearly all reaction
calorimeters can be said to operate in a number of modes, e.g. isothermal
and adiabatic. However, despite claims by some instrument manufacturers
their actual suitability for use in one or more modes can only be defined
for each specific study undertaken. Many of the instruments have common
features,
although the method of gaining the calorimetric data may vary
slightly.
Dewar-based calorimeters are easy and cheap to construct [19]. Due to
their basic construction they can simulate the thermal characteristics
of the plant and measure the heat output of the reaction by measuring the
changes in the batch temperature. Experiments to determine the cooling
rates of large reaction vessels [20] have shown that the rate of heat
losses from 0.5 to 2.5 m vessels correspond to those from 250 ml and
500 ml Dewar flasks. Hence, measurements of the temperature rise when
reactants are charged to Dewar flasks at known rates enables the rate and
quantity of heat evolved in large scale plant to be found.
In the simple isoperibol calorimeter, the heat transfer medium in the
jacket is held at a constant temperature and the heat flow measured by
the change in reactant mass temperature. Unfortunately, it is usually
non-linear at high power outputs and both reaction kinetics and heat
capacity are affected by allowing the temperature to rise. The results
are only approximate. Power compensation calorimeters [21,22] are
relatively easy to design, construct and operate. The temperature of the
heat transfer medium in the reactor jacket is set below the desired
reaction temperature which is maintained by a heater in the reactants or
base.
Any change in heat flow is compensated by a corresponding change
in the electrical power to the heater, which provides a direct measure of
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399
the heat flow caused by the reaction.
Heat flow calorimeters monitor the temperature difference between a
rapidly moving heat transfer medium, e.g. silicone oil, in the reactor
jacket and the reaction
mass.
The heat (power) output of the reaction
is quantified by measuring the flow of heat between the batch and the
heating/cooling system. Heat balance calorimeters monitor the
temperature difference between the inlet and outlet points of the heat
transfer medium, which is flowing at a measured slow rate in the jacket.
All the above types of reaction calorimeters are ideal for studying
desired, normal reactions. They can provide temperature-time curves for
reactions,
provide evidence of self-heating and can provide the data for
calculating heats of reaction and heat capacities. If assumptions can
be made about the reaction mechanisms, then it is possible to gain some
thermokinetic data on the reaction. The simplest type of analysis
assumes that the rate of reaction is proportional to the power output or
rate of temperature rise and is based on dimensionless rates and
concentrations. They can also be used to model semi-batch operation.
The heat flow calorimeter is an ideal instrument for gaining data on the
inside film convective heat transfer coefficient, which can be used as a
basis for scale up, in the standard heat transfer correlations in stirred,
jacketed vessels [23,24]. Geometric factors for the different types of
agitators can also be obtained from experiments using heat flow calori
meters [ 24 ]. However, it must be remembered that this is only possible
with reasonably mobile systems; too viscous materials cause a breakdown
of the necessary heat transfer paths between reactant-reactor wall-heat
transfer medium.
Reaction calorimeters can also be used to examine the problems of
accumulated heat, inhibition of the desired reaction and delayed
initiation. They are increasingly used for process development and
optimisation. It is possible to examine reactions under reflux
conditions with the addition of further equipment [25]. Reactions, which
generate limited amounts of gas can also be studied. Gas evolution
during a normal, desired reaction can be measured using an upturned
measuring cylinder filled with a suitable collecting fluid. Timing the
rate of gas collection can provide a quick assessment of the evolution
rate. An automated gas burette has been developed by staff at ICI pic
[26].
Lambert and Amery [27] have described the use of a thermal mass
flowmeter for measuring the gas evolved in both reaction calorimeters and
on full scale plant.
Commercial reaction calorimeters include the Toledo-Mettler Reaction
Calorimeter RC 1, the Thermometries Reaction Monitor RM 1 and the
Columbia Scientific Industries QRC (Quantitative Reaction
Calorimeter).
However, numerous individuals and companies have designed and use their own
reaction calorimeters to great effect. These incorporate reflux
facilities [25] and the use of pressure vessels to extend the range of
reactions which can be studied [28 ]. Steele et al [24 ] has converted a
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400
-3 3
675 x 10
m
computer-controlled pilot plant reactor to operate as a
heat flow calorimeter.
3.2.1. Adiabatic Calorimeters
Uncontrolled reactions can originate from:
a. the desired reaction going out of control
b.
a secondary reaction
c. a decomposition
The screening tests give some indication when runaway occurs but because
of the low heat loss conditions on industrial plant the accurate deter
mination of the minimum temperature at which self-heating will start on
the plant requires the use of adiabatic calorimeters. While a number of
calorimeters can operate under an adiabatic mode, some specialist
instruments are available for examining the runaway condition.
Test methods can fail to detect the onset of an exotherm due to heat loss
from:
a. the sample to its surroundings
b.
the sample to the test
cell.
The latter is particularly important when the thermal capacity of the
test cell is large compared with that of the sample. A parameter, 0 is
used to characterise the effect and is termed the thermal inertia
0
w h e r e M
1
=
+ M C
c vc
M C
s vs
mass (
C = specific heat at constant volume
v
subscripts s and c relate to the sample and container respectively
An analysis of the importance of the thermal inertia term is given by
Townsend and Tou [29].
Techniques operating under adiabatic mode for the study of runaway
conditions include the use of stainless steel Dewars, fitted with
pressure-tight lids [ 3 0 ]. The large sample size and the low heat
capacity of the Dewar means that a low value of the thermal inertia is
obtained. The sensitivity can be further increased, by placing the
Dewar in an adiabatic environment, i.e. in an oven, in which the
temperature follows that recorded in the sample.
The bench-mark, commercial adiabatic calorimeter is the accelerating rate
calorimeter from Columbia Scientific Industries. A 10 g spherical sample
container is suspended within a copper vessel containing heaters and the
whole assembly is enclosed in a steel safety casing. The instrument is
normally operated in an isothermal mode or in a step-wise temperature
regime, the heat-wait-search sequence. At each temperature step, the
A.R.C.
is programmed to detect any self-heating above a specified
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401
threshold, now down to 0.01 C min , i.e. any thermal excursion above
this threshold is recognised as an exotherm. The instrument is then
maintained under adiabatic conditions and temperature-pressure-time data
under runaway conditions is obtained. The data can be manipulated to
provide pseudo-kinetic information [29] as well as all the data offered
by the basic screening tests. Mores [31] has used ARC data, in
combination with self heat models, to gain self accelerating decomposition
temperatures [32] and for the modelling of sequential and parallel
reactions.
A number of other commercial instruments can provide similar data to the
ARC,
e.g. Sikarex. The latter instrument can be operated under both
adiabatic and isothermal modes of operation. Pressure-temperature-time
data can also be obtained from instruments, which have been primarily
designed for the acquisition of information needed to size emergency
relief vents using the DIERS methodology [33,34]. Considerable attention
must be paid to the sensitivity of instruments over their defined range
of application and in terms of the type of substances investigated.
3.3. Instrumentation for Emergency Vent Sizing
The AIChE sponsored Design Institute for Emergency Relief Systems
produced a calorimeter, which uses a pressure equalisation system and a
weak test cell, with a low thermal inertia. The original Vent Sizing
Package (VSP) [33] uses a 120 ml heated test cell with a pressure control
system which balances the internal and external cell pressure and hence
the integrity of the test cell is maintained. The cell can operate in a
closed or open mode, the latter using a vent pipe into an outer contain
ment vessel. Temperature-pressure-time data can be obtained, together
with the flow behaviour of the discharging runaway reaction masses. The
experimental data is combined with data from the actual plant (i.e.
ullage,
total reactor volume and relief set pressure) and physical
properties of the reaction
mass,
i.e. density, to allow the calculation
of the size of the emergency vent. It is possible to simulate the
presence of an external fire on a reactor.
A similar device is the Phi-tech from Hazard Evaluation Laboratory Ltd.
Fauske and Associates, the originators of the VSP have now developed the
RSST [ 18 ]. This is a relatively cheap instrument, which operates in a
quasi-adiabatic mode. It is necessary to use some modified equations
from the DIERS programme for vent sizing. The vast majority of the
original VSP users have carried out substantial development work to
create improved instrumentation, yet retain the basic concept of
pressure equalisation to maintain the integrity of thin walled containers.
Whether a low thermal inertia factor results from this technique is
debatable. Some very sophisticated instruments now exist in the
specialist laboratories of industrial companies and academic establish
ments. Most developments are readily made available to others wishing
to modify existing equipment or to build their own vent sizing equipment.
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A. BASIS OF SAFETY
The data from calorimetric experiments and the adoption of formal hazard
assessment procedures permit decisions relating to the safe design and
operation of the process and plant. Safe operation can be achieved by
preventative and protective measures. In order to select such measures,
it is necessary to define the worst case condition. The possible
measures include:
a. process control
b.
process control + containment
c. process control + emergency venting
d. process control + inhibition of runaway reactions
A reactor can be designed to withstand the maximum pressure produced in
the runaway situation or alternatively a normal reactor can be installed
in a concrete and steel bunker. Since the products of a runaway can be
toxic, flammable, corrosive or foul smelling, containment offers the
possibility of restricting their release into the environment. Venting
is a normal operation in the course of chemical manufacture. Relief
vents sized to cope with gas pressure and/or fire engulfment are rarely
if ever adequate to provide protection against uncontrolled runaway.
The sizing of relief vents for worst case conditions has been covered by
the DIERS programme, although it is becoming increasingly important to
consider alternatives to emergency relief venting, due to economics, the
containing/disposing of the relief discharge and the problems of dealing
with the rate of rise in pressure found with some reactions. Inhibition
can take several forms. Quenching and dumping are common methods. The
sizing of dump tanks has been addressed by Grossel [3 5] . Occasionally,
it is possible to use reagents to remove free radicals from the reaction
mass.
In any considerations relating to the definition of the basis of safety,
it is necessary to always consider the reliability of the operators and
the instrumentation.
Process control can employ hard-wired instrumentation and micro
processors. Duplication of sensors monitoring key parameters is usually
recommended. The correct level of protection can be defined by the use
of Hazan [3 6 ].
5. ESTABLISHING A REACTION HAZARD EVALUATION LABORATORY
With the ever increasing legislation requirements and the quest for
better manufacturing routes to both old and new products, there is a
great need to support such developments with appropriate data on the
potential hazards and to provide information for the specification of
the design and safe operation of processes and plants. However, it is
easy to recognise that a need exists but it is a problem to actually
satisfy that need. It is important to establish "in-house" testing,
primarily because the individual company should know its processes
better than any external consultants and because the use of a hazard
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403
assessment schedule also requires the incorporation of local process and
plant experience. Simultaneously, such testing may provide opportunities
for process development and optimisation. The initial steps are always
the most difficult because they involve the identification of the
problems of the individual company concerned. The literature and the
advertisements for commercial equipment can be confusing to the novice
in the field. Once the problems of the company have been identified,
the next stage is normally to seek advice from others, who have already
started such work. They will normally suggest the use of simple, cheap
methods presented in the literature or in specific publications e.g. the
ABPI Guidelines for Chemical Reaction Hazard Evaluation. Some of
Europe's major companies have their own "in-house" test methods and all
are prepared to give advice on tests, their results, the limitations and
their interpretation with respect to company activities in general terms.
The construction and use of cheap but effective methods for reaction
hazard screening will give confidence to the staff in an embryonic
hazard evaluation laboratory and it will be possible to see how the
measured data relates to past process and plant operating experience.
It is also possible to "calibrate" the obtained data by comparing the
results obtained on well defined materials with those given in the
literature for the same materials but found using more sophisticated
equipment. Based on experience, conversations with specialists and
comparative studies the level of confidence in the application and inter
pretation of data should grow.
At this stage, a decision must be made as to whether further equipment
and methods are needed. If developments are required, then the choice
of either purchasing commercial equipment or designing specific
instrumentation must be made. The work at the South Bank Polytechnic,
in London and its associated reaction hazard specialists based in
industrial companies has shown that it is possible to design, construct
and successfully use every type of calorimeter, including the next
generation of all-purpose calorimeters. Obviously, the development of
"in-house" instrumentation takes resources but they can be specifically
designed to solve particular problems. The purchase of commercial
equipment reduces the instrument development time but they all require
time for training of operators and for gaining sufficient experience to
apply the manufacturers operating instructions to specific industrial
reactions. An "in-house" instrument is usually easier to maintain and
modify. It must be stressed that in order to solve particular industrial
problems it may be necessary to operate commercial instruments in a
variety of configurations, other than that described in the manual of
operation. User forums certainly help the beginner to appreciate the
variations of operation and interpretations of data which are possible.
Gradually, the beginner is accepted as a specialist and user of
particular methods and a number of groupings have established themselves
for the free exchange of information. The European DIERS group meets to
discuss the uses of equipment, methods, data and designs. It is open to
industrialists and academics with practical experience. It is not
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404
involved in training or in the promotion, marketing, sales of
commercial equipment. However, the people involved in reaction hazard
evaluation tend to meet regularly and exchange their experiences. They
have an open policy to welcome and guide new people into the subject area.
Experience of the very latest commercial equipment or some new idea to
permit the measurement of say, the rate of gas evolution is readily
discussed. The basic steps of setting up a reaction hazard evaluation
laboratory are given in Table 3.
TABLE 3. Setting-up a Reaction Hazard Laboratory
i. identify the problems in the company. There
is no need to build or buy a reaction
calorimeter if all the problems relate to
the storage of thermally instable products
ii. discuss what methods are available to solve
the identified problems with some specialists
iii. gain some experience with easy to construct
and use equipment
iv. relate the acquired data to past experience
of processes and plant
v. integrate the methods and results into an
assessment programme, involving personnel
from other parts of the company
vi. assess the accuracy of the data obtained and
question whether it needs to be improved to
define the basis of safety
vii. define the need or otherwise for more
sophisticated equipment
viii.
decide whether commercial equipment can
provide a reasonably ready answer or on the
need to design and construct "in-house"
equipment which will provide the means to
gaining data of a level of acceptability
defined by the company
ix.
always keep records of the methods employed
and the resulting data and where possible
carry out calculations to check that the
values found bear some relation to that
expected, say for heats of reaction given
the fact that the extent of the particular
reaction studied can be found by chemical
analysis of the product (i.e. employ good
laboratory practice)
x. relate all the available test methods,
their results and the interpretation in the
reaction hazard evaluation laboratory to
process and plant experience to decide on
the most suitable methods of assessment for
each stage of the process development
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405
6. CONCLUSIONS
Reaction hazard evaluation must be considered at each stage of
development and scale of operation of a process. The details relating
to potential hazards need continuous expansion and re-definition. A
considerable number of methods and associated calorimeters exist and
their selective use can gain data, which can either directly, or when
used in appropriate formulae define a basis of safety for the
manufacturing scale plant.
The results from reaction hazard evaluation need to be combined with the
findings of formal hazard assessment procedures, e.g. HAZOP, FTA and
HAZAN, to define the worst case condition and the level of protective
measures required.
The basic steps of setting up a reaction hazard evaluation laboratory
include the identification of manufacturing problems and the acquisition
of raw and manipulated data. Confidence in the use of such data to
design and operate new plant and processes can be established on the
basis of relating laboratory-generated data to the past experience of
plant and process operations of the manufacturing company.
7.
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8. Craven A. D.
(1987).
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(1984). Chemical Reactor Design and Operation. Wiley. Chichester.
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Kletz T. A.
(1984).
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and assessment of hazards. IChemE (Loss Prevention). Rugby.
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(1987).
Engineering Safety Assessment. Longman.
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Cronin J. L. and Nolan P. F.
(1987).
Laboratory techniques for the
quantitative study of thermal decompositions. Plant/Operations
Progress 6, 2, 89 - 97.
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Guidance Notes on Chemical Reaction Hazard Analysis.
ABPI.
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Lambert P. G. and Amery G.
(1989).
The use of DSC as a screening
tool in chemical reaction hazard analysis. IChemE Symposium Series
No.
115. Hazards X Process Safety in Fine and Speciality Chemical
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16.
Cronin J. L. and Nolan P. F.
(1987).
The comparative sensitivity of
test methods for determining initial exotherm temperatures in thermal
decompositions of single substances. J. Hazardous Materials 14, 293 -
307.
17. Hub L. (1986). Experiences with the TSC 500 and Radex Calorimeter.
IBC Conference on Control and Prevention of Runaway Chemical
Reaction Hazards. Amsterdam.
18. Fauske H. K., Clare G. H. and Creed M. J. (1989). Laboratory tool
for characterising chemical systems. AIChE/IChemE International
Symposium on Runaway Reactions, Cambridge, Boston.
19- Harris M. T. G. (1991). Adiabatic Dewar calorimetry. PhD CNAA South
Bank Polytechnic, London.
20 . Wright T. K. and Rogers R. L. (1986). Adiabatic Dewar calorimetry.
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21. Wright T. K. and Butterworth C. W. (1987). Isothermal heat flow
calorimeter. IChemE Symposium Series No. 102. Hazards from Pressure.
Manchester.
22. Blitz J. L.
(1989).
The design and construction of a power
compensation heat flow calorimeter for the study of fermentation
processes. PhD CNAA South Bank Polytechnic, London.
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for agitated liquids in process vessels. Chemical Engineering 1,
153 - 158.
24 . Steele C. H. (1988). Calorimetric techniques for reflux analysis
and scale-up for the design and operation of batch reactors. PhD
CNAA South Bank Polytechnic, London.
25. Steele C. H. and Nolan P. F. The design and operation of a reflux
heat flow calorimeter for studying reactions at boiling.
26 .
G ibson N., Maddison N., Rogers R. L.
(1987).
Case studies in the
application of DIERS venting methods to fine chemical batch and
semi-batch reactors. IChemE Symposium Series No. 102. Hazards from
Pressure. Manchester. Pergamon Press.
27. Lambert P. G. and Amery G.
(1989).
Assessment of chemical reaction
hazards in batch processing. AIChE/IChemE International Symposium on
Runaway Reactions. AIChE Center for Chemical Process Safety,
Cambridge, Boston, MA.
28 .
Tee D. G.
(1991).
Heat flow calorimetric studies of ethylene oxide
reactions.
PhD CNAA South Bank Polytechnic, London.
29.
Townsend D. I. and Tou J. C.
(1980).
Thermal hazard evaluation by
an accelerating rate calorimeter. Thermochimica Acta 37, 1 - 3 0 .
30. Rogers R. L. (1989). The use of Dewar calorimetry in the assessment
of chemical reaction hazards. IChemE Symposium Series No. 115.
Hazards X Process Safety in Fine and Speciality Chemical Plants.
Manchester. Pergamon Press.
31. Mores S. (1991). Enhanced control and data evaluation for
accelerating rate calorimetry. PhD CNAA South Bank Polytechnic,
London.
32. Mores S. and Nolan P. F.
(1991).
Determination of SADT from thermal
stability data generated using accelerating rate calorimetry.
Submitted to Journal of Loss Prevention in the Process Industries.
33. Fauske H. K. and Leung J. L. (1985). New experimental techniques
for characterising runaway chemical reactions. Chemical Engineering
Progress 8 1, 8, 39 - 4 6.
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408
34. Fisher H. G. (1985). DIERS research program on emergency relief
systems.
Chemical Engineering Progress 81, 8, 33 - 3 6.
35.
Grossel S. S.
(1990).
An overview of equipment for containment and
disposal of emergency relief system effluents. Journal of Loss
Prevention in the Process Industries 3, 1, 112 - 124 .
36. Lees F. P. (1980). Loss Prevention in the Process Industries.
Butterworth-Heinemann. Oxford.
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O U T L I N E O F T H E M O D E L L I N G A C T I V I T I E S I N V E N T I N G
A. N. SKOULOUDIS
Process Engineering Division, JRC Jspra,
Commission of the European Com munities
21020 Ispra. (VA), Italy.
A B S T R A C T . The present work describes various aspects of modelling the loss of containment and
covers several problems which could be encountered in the theoretical calculations with several numerical
models (codes). The key features of four different codes which are suitable for the analysis of venting
transients are illustrated and the parameters which characterise the emergency relief of the reactor vessel
are identified. Six practical venting problems are analysed and comparisons are made with the data
calculated by the relevant codes.
1 . G e n e r a l A i m s
T h e c o n t a i n m e n t o f m u l t i c o m p o n e n t m i x t u r e s in v e ss el s u n d e r h ig h t e m p e r a t u r e a n d
pressure has been a lways an impor t an t sub jec t fo r t he sa fe ty o f Chemica l Indus t r i e s .
The re a re seve ra l p rocesses occur r ing dur ing the emergency ven t ing o f vesse l s which
a re d i rec t ly r e l a t ed wi th t he in i t i a l cond i t i ons which a re f r equen t ly c lose to sa tu ra t ion .
Thus, a f te r the opening of a re l ie f device the contents of reac tor vesse l a re empt ied
unde r mul t iphase f low cond i t i ons . The fo l lowing a re t yp ica l p rocesses i den t i f i ed dur
ing top ven t ing t r ans i en t s (1 ,2 ,3 ) . As soon a s t he re l i e f va lve opens vapour con ta ined
in the f reeboard volume of the pressure vesse l wi l l be re leased and the pressure fa l l s
rap id ly . Th e l i qu id pha se can no t fol low th i s r ap id chang e o f p re s sure wi th a p ro m pt
c h a n g e in t e m p e r a t u r e a n d t h e l iq u i d b e c o m e s s u p e r h e a t e d . T h i s l e a d s t o t h e r m o
dy nam ic d i sequ i l i b r ium b e tween th e pha ses which i s r e -e s t ab l i she d a f t e r a sho r t t im e
by v igoro us re -eva pora t io n o f t h e l i qu id . D ur in g th i s pe r iod the h igh de pres sur i sa t ion
ra t e i s r edu ced . Th en a ma rke d p re ss ure r ecove ry m igh t occur wh en the vap ou r vo l
ume produced by evapora t ion exceeds the vo lume of t he mix tu re which f lows ou t o f
th e vesse l. Th i s r ecove ry is ve ry p ro nou nced if a l a rge an d s t ee p p re ss ure decay has
occu r red a t t h e fir st s t ages o f t h e t r an s i en t . Va pou r is s t il l d i scha rged th ro ug h the
ven t - l i ne t oge the r wi th some drop le t s en t ra ined f rom the in t e r face sepa ra t ing the p re
dominan t ly l i qu id and the p redominan t ly vapour r eg ions o f t he vesse l . As soon a s t h i s
l eve l r eaches t he ven t - l i ne a d i s t i nc t two-phase mix tu re wi l l be d i scha rged wi th l a rge
l iq u i d c o n t e n t . N e v e r t h e l e s s , t h e e v a p o r a t i o n p r o c e s s e s c o n t i n u e a n d t h e t h e r m o d y
nam ic d i sequ i l i b r ium i s r edu ced . Th e in t e r face level is g ra du a l ly co l l aps ing so th a t t he
ven t - l i ne wil l be no longe r b locked . Th en a p re do m inan t ly vap ou r mix tu re wil l aga in
l eave the vesse l wi th seve ra l l i qu id d rop le t s en t ra ined . Dur ing th i s p rocess t he p re ssure
in the vesse l fa l l s cont inuously unt i l a new sta te of equi l ibr ium has been establ i shed
w i t h t h e s u r r o u n d i n g s .
409
A. Benuzzi and J. M. Zaldivarfeds.), Sa fely of Chemical Batch Reactors a nd Storage Tanks, 409—429.
© 1991
ECSC,
EEC.
EAEC. Brussels a nd Luxembourg. Printed in the Netherlands.
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410
T h e m a g n i t u d e a n d t h e i n t e r a c t i o n o f t h e p r o c e s s e s m e n t i o n e d a b o v e d e p e n d o n
a n u m b e r of g e o m e t r i c a l , o p e r a t i o n a l a n d p h y si c o -c h e m i c al p a r a m e t e r s . T h e s e p a r a m
e te r s a re i den ti fi ed in s ix exam ples which a l so de m on s t r a t e t he i r im po r t a nc e . Th e
exper imenta l da ta repor ted here have been obta ined a t four tes t s i tes in f ive di f fe r
ent vesse ls . T h e wo rking f luids have been e i ther w ate r or re f r igera nt R 114 and the
ope ra t ing p re ssure a re up to 7 .2 MPa . The theore t i ca l ca l cu l a t ions have been ca r r i ed
o u t w i t h t h e c o d e s R E L A P , S A F I R E , R E L I E F a n d D E E R S . D e t a i l s a b o u t t h e i n p u t
op t ions used by each code a re desc r ibed ind iv idua l ly i n each example .
2 .
I n t r o d u c t i o n t o t h e N u m e r i c a l C o d e s
Al l the codes tha t wi l l be used in ana lysing the vent ing examples which fol low have
been dev elope d for d i f ferent typ es of ap pl ic a t io ns and a l tho ug h in pr inc iple solve s im
i la r se t s o f conse rva t ion equ a t ion s fo r t he ma ss , m om en tu m an d ene rgy th ey a ll have
signi f icant ly di f fe rent fea tures for desc r ibing th e ph en om eno log y of th e t ra ns ien t . Here
a t t h e J .R .C . w e h a v e a v a i l a b l e t h e A m e r i c a n c o d e s R E L A P, SA FI R E a n d D E E R S
toge the r wi th t he code RELIEF (o r ig ina l ly ca l l ed VESSEL) which has been deve loped
loca lly . The ore t i ca l ca l cu l a t ions f rom a l l o f t he s e codes a re dem on s t r a t e d in t he n ex t
sec t ion however , i t i s useful to descr ibe here the key fea tures of these codes and to
iden t ify t he i r mo de l l i ng capab i l i t i e s fo r t he emergen cy ven t in g of chem ica l r e ac to r s .
The ma in code fea tu re s a s used in t he Benchmark Exe rc i se s (5 ) a re shown in Tab le 1 .
TA BL E 1 : The ma in fea tu re s o f t h e codes
N a m e
of the
C O D E
R E L A P 5
S A F I R E
R E L I E F
D E E R S
N o d e s
in the
Vessel
Severa l
1
Severa l
Severa l
N o d e s
in the
Vent- l ine
Severa l
8 or 50
1
Severa l
No of
C h e m i c a l
R e a c t i o n s
-
10
10
4
No of
C o m p o
n e n t s
1
10
10
6
E x t e r n a l
H e a t
F l u x e s
Yes
Yes
Yes
Yes
T w o - p h a s e
Flow
M o d e l s
Accord ing to
Flow Reg ime
Two Dr i f t -
f lux models
Drift-f lux
Dri f t - f lux
Al l t he abov e men t ioned codes employ d if fe ren t t yp es of tw o- ph as e flow mod e l s .
Th i s i s a c losure r e l a t i onsh ip which depends on the f l ow pa t t e rn o f t he l i qu id -vapour
m i x t u r e a n d c o r r e l a t e s t h e t w o - p h a s e p a r a m e t e r s i n t h e m a s s , m o m e n t u m a n d e n e r g y
conse rva t ion equa t ions . In p r inc ip l e , fo r t he two-phase f low a long a channe l wi th o r
wi thou t ex t e rna l hea t i npu t t he fo l lowing re l a t i onsh ip i s app l i cab le
(Pa
1
—
x ot u> 1
—
a
1
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This i s d i rec t ly der ived f rom the def ini t ion of the qual i ty , x, a s t he ra t i o of vap ou r t o
the to ta l mass-f low-ra te and f rom the def ini t ion of the void f rac t ion, a, as the ra t io of
a re a occup ied by the vap ou r t o t h e t o t a l f low a rea . I t is usua l ly poss ib l e t o express
x
as a funct ion of the loca l spec i f ic entha lpy f rom the energy conserva t ion equat ion
t o g e t h e r w i t h t h e a s s u m p t i o n of t h e r m o d y n a m i c e q u i l i b r i u m b e t w e e n t h e tw o p h a s e s .
W h a t i s s t i ll necessa ry in de t e rm in in g the o th e r pa r am e te r s inc lud ed in equ a t ion 1
i s e i t he r a r e l a t i onsh ip be tween x a n d a, o r a r e l a t i o nsh ip be twee n the vo id f rac t ion
an d th e ra t io of th e va po ur to l iquid average ve loc i t ies . T he re is a wh ole ran ge of
such re l a t i onsh ips which a re e i t he r o f pure empi r i ca l o r ig in o r o the r more soph i s t i ca t ed
re l a t ionsh ips which a re based on the de t a i l ed phenomenology o f t he f l ow.
Most o f t he codes p re sen ted be low, use a pure ly empi r i ca l r e l a t i onsh ip fo r t he
veloc i ty di f fe rence be twe en the va po ur and l iquid phas es (dr i ft - f lux mod el ) or they
employ a typica l dr i f t - f lux corre la t ion. In the dr i f t - f lux te rminology the re la t ive ve loc i ty
be tween the two phases i s d i rec t ly r e l a t ed to t he cor re spond ing d r i f t ve loc i t i e s u
gj
- and
u/_j
accord ing to
Ug-U l = U gj - U(,j . [2]
For each phase the re la t ive dr i f t - f luxes a re expressed as :
jgl = a Ugj [3]
jig = (1 - a) u
t
j [4]
which mus t obey the fo l lowing con t inu i ty equa t ion
kg + jgl = 0 • [5]
Th i s equa t ion s t a t e s t ha t t he re i s no ne t d r i f t t h rough a p l ane moving wi th t he to t a l
superf ic ia l ve loc i ty of the two phases . From equat ions 2 to 5 i t fo l lows tha t :
• , 1 1 ^
Ug-U
t
= Jgl { - + ) 6
a 1 — a
There a re severa l dr i f t - f lux models (10) which re la te the vapour dr i f t - f lux to the loca l
vo id f rac t ion . However , t he se a re aga in empi r i ca l co r re l a t i ons which mus t be deduced
from exper iments carr ied out wi th di f fe rent f lu ids under var ious f low regimes wi th
s t e a d y s t a t e o p e r a t i n g c o n d i t i o n s .
O t h e r p a r a m e t e r s d i r e c t l y r e l a t e d w i t h t h e v e n t i n g c a l c u l a t i o n s a r e t h e n u m b e r o f
con t ro l vo lum es (nodes) em ployed and the s ize o f t h e t im e s t ep used . I t i s r equ i re d th a t
the numer i ca l so lu t ions a re i ndependen t bo th f rom the number o f nodes and f rom the
size of th e t ime s te p. T he la t te r i s easi ly achieved in m os t of th e codes by in tern a l ly
a d j u s t i n g t h e t i m e s t e p b e tw e e n p re - sp e ci fi ed m a x i m u m a n d m i n i m u m v a l u e s . T h e
former can be solved only w i th conse cut ive ru ns wi th gr ids of red uc ed s ize .
2.1.
THE RELAP5-EUR/MF CODE
T h i s c o d e o r i g i n a t e s f ro m t h e N u c l e a r I n d u s t r y , a n d t h e v e r s io n R E L A P 5 - E U R / M F
has been subs t an t i a l l y modi f i ed a t t he J .R .C . I sp ra i n o rde r t o improve i t s pe r fo rmance
and fo r us ing f lu ids di ffe ren t f rom wa te r . I t de sc r ibes t r ans i en t s in g le - an d tw o- ph as e
flows in com plex ne twork s on the bas i s o f a one -d im ens ion a l app roa ch . I t ha s been
or ig ina l ly deve loped fo r t he p red ic t ion o f t r ans i en t s i n t he coo lan t sys t em of p re ssur i zed
wa te r r eac to r s w i th t yp ica l p re ssur e va lues i n t he range be tween 16 M P a > p > 1 M Pa .
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There fore , mos t o f t he code a sse ssment work has been concen t ra t ed on sepa ra t e e f fec t s
and in t egra l t e s t da t a i n t he h igh p re ssure r eg ion .
T w o - p h a s e f l o w c o n d i t i o n s i n R E L A P a r e t r e a t e d u s i n g s e p a r a t e m a s s a n d m o
m e n t u m e q u a t i o n s f o r t h e i n d i v i d u a l p h a s e s ( t w o - f l u i d s m o d e l ) . D u e t o t h e a s s u m p t i o n
th a t t he l ea s t mass ive phase is a lways sa tu ra t ed on ly one ene rgy equa t io n i s needed
for t he two -pha se m ix tu re . Th e app roac h se lec t ed can desc r ibe cond i t i on s o f non-
ho m og en eou s f low (di ffe rent ph ase ve loc i t ies) , an d the rm al dise qu i l ibr iu m effec ts d ur
i n g t h e p h a s e t r a n s i t i o n ( e v a p o r a t i o n , c o n d e n s a t i o n ) . M a s s , m o m e n t u m a n d e n e r g y
exchange be tween the two phases a re ca l cu l a t ed by cor re l a t i ons which a re f l ow reg ime
de pe nd an t . Speci fic mo dels exis t for th e pred ic t ion of c r i t ica l f low co nd i t io ns (choking)
bas ed on th e sonic ve loc i ty in th e s ingle or two-p has e f lu id .
T h e R E L A P 5 - E U R / M F c o d e i n cl u de s t h e d es c r ip t io n of o n e - d i m e n s i o n a l h e a t
conduct ion in the vesse l wal l and the hea t t ransfer be tween the sol id vesse l wal l and
th e flu id . T he hea t t r ans fe r i s ca l cu l a t ed u s ing the t em pe ra tu re d if fe rence be tw een the
wal l and the f lu id and a hea t t ransfer coeff ic ient based on the concept of a "boi l ing
curve" . The l a t t e r i nc ludes cor re l a t i ons fo r s ing le phase na tu ra l and fo rced convec t ion ,
subcoo led and sa tu ra t ed nuc lea t e bo i l i ng , c r i t i c a l hea t - f lux , t r ans i t i on bo i l i ng , min i
mum hea t - f lux , annu la r and d i spe r sed f i lm bo i l i ng . The hea t t r ans fe r co r re l a t i ons a re
au toma t i ca l ly se l ec t ed based on loca l f l ow pa rame te r s and wa l l su r face t empera tu re s .
Also, the loss coeff ic ient due to abrupt a rea change a t the exi t of the vesse l i s ca lcula ted
inte rna l ly by th e cod e . T he sam e i s t r ue for th e f r ic tion be tw een f lu id an d wal l an d
the f r i c t i on be tween the phases .
The physica l model l ing of the code resul t s in a system of f i rs t -order par t ia l d i f fe r
ent ia l equat ions which are solved numerica l ly by an eff ic ient semi- impl ic i t numerica l
t echn ique . The concep t o f f r ee noda l i sa t ion g ives t o t he code the capab i l i t y t o desc r ibe
a la rge var ie ty of sys tem s w i th di ffe rent degre es of geo me tr ica l de ta i l and m ake s i t
cap ab le of han d l ing whole p l an t ca l cu l a t ions . How ever , a t t he mom en t it does no t
a l low for chemica l reac t ions dur ing the vent ing process; thus i t s d i rec t re levance to the
ana lys i s of chemica l r eac to r s t r ans i en t s is r a t he r l imi t ed .
2.2.
T H E S A F I R E C O D E
Th e ma in fea tu re o f S A F IR E i s i t s ab i l i ty t o hand le u p to t en s im ul t an eou s chem ica l
reac t ions wi th t en com po nen t s . Th i s code can on ly desc r ibe re l a t ive ly s imple vessel
geome t r i e s wi th nozz l e s o r l ong p ipes se rv ing a s ven t ing dev ices and which can be
a t t a ch ed e i the r a t t he t op o r a t t h e bo t to m of t h e reac to r vesse l. S A FI R E so lves t he
o n e - d i m e n s i o n a l m a s s , m o m e n t u m , a n d e n e r g y c o n s e r v a t io n e q u a t i o n s in t h e v e n t - l in e
but uses a s ingle cont rol volume for descr ibing the vesse l .
T h e flow regime inside th e vesse l is chosen by the user an d on ce spec i fied i t does
no t a l t e r t h ro ug ho ut t h e du ra t ion of t he t r ans i e n t . Th e use r m ay op t for e i t he r no
vapour / l i qu id d i sengagement coup led in t he ven t - l i ne wi th e i t he r an homogeneous f low
reg ime o r wi th a cons t an t p re spec i f i ed ex i t mass qua l i t y . Al t e rna t ive ly , t he use r may
se l ec t t he pa r t i a l vapour / l i qu id d i sengagement op t ion wi th a "churn" o r "bubb le" f l ow
regim e. T he se regim es are bo th typica l dr i f t- f lux mo dels in wh ich th e va po ur dr i f t -f lux
and the bubble r i se ve loc i ty a re descr ibed by :
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Bubbly f low
_ u
a
( 1 - Q )
2
f 7
,
Jg i
~ °° ( i _
a
3 ) l
7
J
U
OQ
= 1.18 [
g g
^ - ^ ] ° -
2 5
[8]
P«*
C h u r n t u r b u l e n t
Jgt
U
0
U
ao
= 1.53 [
g < 7 ( P
V
P g )
]
0
'
2 5
[10]
Ra dia l va r ia t ion s of ve loc i ty and void f rac t ion a re tak en in to acco un t v ia an em pir ica l
d i s t r i b u t i o n p a r a m e t e r C
0
. If C
0
i s se t to 1 th ere i s no t var ia t io n ass um ed in th e ra dia l
d i rec t ion . Va lues be tw een 1 and 2 shou ld be se t a t t he code in pu t . Th e use r has
a lso the possibi l i ty for se t t ing the two-phase f r ic t ion fac tor for the vent - l ine by e i ther
se l ec t ing a va lue which i s kep t cons t an t dur ing the t r ans i en t pe r iod o r by ac t iva t ing
an op t ion which ca l cu l a t e s t he f r ic t ion fac to r au tom a t i ca l ly . W he n a tw o- ph as e flow
m ix tur e is expe c t ed in t h e ven t - l i ne t hen th i s f r ic t ion fac to r i s ca l cu l a t ed p r ima r i ly
f rom s ing le -phase f low re l a t i onsh ips based on ly on the l i qu id phase v i scos i ty .
The phys i ca l p rope r t i e s mus t be p rov ided by the use r i n t he i npu t da t a i n t e rms
of t he coe f f i c i en t s co r re spond ing to t he cor re l a t i ons i nc luded in SAFIRE. A cons t an t
t im e s t e p i s a l so requ i red a t t he i np u t which i s kep t cons t an t dur in g the t r an s i e n t . Th e
size of th is t ime s tep must be spec i f ied a t the input .
To a ce r t a in degree the use o f seve ra l i npu t op t ions i n cha rac t e r i s ing the ven t ing
process m akes the code user de pe nd an t . For t h i s r ea son in t h e exam ples des c r ibed
be low, two ca l cu l a t ions f rom the SAFIRE code has been inc luded which a re con t r ibu ted
by di f ferent u sers (11 ,12 ) . B ot h ca lcu la t ion s a re s ti l l firmly bas ed on th e or igina l
ve r s ion o f SAFIRE g iven to t he J .R .C I sp ra , howeve r , i n SAFIRE-2 ca l cu l a t ions t he re
a r e i n c l u d e d s o m e s t r u c t u r a l a l t e r a t i o n s . T h e s e a l t e r a t i o n s a r e m a i n l y a d d r e s s i n g t h e
conve rgence p rob lems enco un te red wh en the f r ic t ion fac to r is ca l cu l a t e d au t om a t i ca l ly
by the code . In these cases there a re some di f fe rences in the way the coupl ing equat ion
be tween the vesse l and the ven t - l i ne se l ec t s t he r i gh t ex i t -qua l i t y when more than two
numer i ca l so lu t ions a re found by the code .
The ma in comment s which re f l ec t our expe r i ence f rom the use o f SAFIRE a re
tha t some a l t e ra t ions migh t be necessa ry fo r t he numer i ca l scheme to t he code (12 ) . A
tw o- ph as e v i scos i ty shou ld be used ins t ead o f t h e li qu id v i scos i ty which h as been used
in the or igina l vers ion of the code (even i f the mixture in the vent - l ine was conta ining
vapour up to 98%) . However , i t mus t be po in t ed ou t t ha t t h i s code has been deve l
oped pr imari ly for vent -s iz ing ca lcula t ions and has been a lso used successful ly for the
in t e rp r e t a t i o n of t h e re su l t s f rom the D IE R S pro j ec t w i th chemica l ly r eac t in g flu ids.
2.3.
THE J.R.C. CODE "RELIEF"
T h e c o d e R E L I E F i s u n d e r d e v e l o p m e n t a t t h e J .R .C . I s p r a . A s u s e d fo r t h e B e n c h
m ark E xe rc i se s (5 ) i t ha s employed th e opp os i t e appro ach t o SA F IR E . I t ve ssel was
discre t i sed in severa l cont rol volumes but a s ingle cont rol volume was used for the
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ven t - l i ne . The c o d e has the capab i l i t y to hand le chemica l r eac t ions of a r b i t r a r y o r d e r
a n d can desc r ibe the v e n t l i ne h y d r o d y n a m i c s if it is t h o u g h t n e ce s s ar y . E x t e r n a l h e a t
t r a n s f e r t h r o u g h
the
vessel
and the
ven t l ine
can be
a l so inc luded .
T h e m o d e l l i n g in R E L I E F is b a s e d on the fol lowing pr inc ip les and a s s u m p t i o n s
as desc r ibed
by
Friz
G. (13) and
Duffield
et al (14).
T h e r m o d y n a m i c e q u i li b r iu m
has
b e e n a s s u m e d b e t w e e n the p h a s e s . The p r e s s u r e d r o p in the vesse l due to frict ion,
and acce l e ra t ion fo rces
is
a s s u m e d
to be
negligible
and a
dr i f t - f lux m ode l
has
been
used as a c losure r e l a t i onsh ip . The kine t ic en ergy and a x i a l c o n d u c t i o n t e r m s in the
e n e r g y e q u a t i o n
are
a l so a s s u m e d
to be
negl igible .
For the
num er i ca l so lu t ion
of the
c o n s e r v a t i o n e q u a t i o n s a modi f ied "donor -ce l l " t echn iq ue which cons ide r s c on t inu i ty
waves
is
a d o p t e d .
The dr i f t - f lux model
is
d r a f t e d
in
t e r m s
of
t h e re l a t i ve ve loc i ty be twee n
the
p h a s e s
s u c h t h a t ,
a
m
( l - a )
n
. .
U
°-
U
> =
U
>°°> « J » ( 1 - «
M
) » M
w h e r e otM is the void f rac t ion wh ich gives to the t e r m a
m
( l — a)
n
its m a x i m u m v a l ue .
T h e d e n o m i n a t o r
is a
sca l ing fac to r which ensure s t h a t
the
m a x i m u m v a l u e
of the
slip
is given by U
poo
i i r r e spec t ive of the va lue of void f rac t ion at which it o c c u r s . The
coefficients m and n desc r ibe bu bb ly f low and drople t f low respec t ive ly and have been
fitted to exp e r im enta l da t a .
U
poo
i can be
t h o u g h t
as a
cha r ac t e r i s t i c b ub b le ve loc i ty
w h i c h is c lose ly re la te d to the t e rm ina l ve loc i ty of the l a r g e s t b u b b l e in the s y s t e m and
c o n t a i n s the p h y s i ca l p r o p e r t y g r o u p [goAp/pi)
1
'
4
.
In the B e n c h m a r k e x e rc i se s the mass flow in the ven t - l i ne was m o d e l l e d in a
s impli f ied ma nn e r t ak ing in to accou n t b lowdow n expe r im ent s pe r fo rmed
at the
J . R . C .
T h e r e the mass f low in b o t h the supe r -c r i t i c a l and sub-c r i t i c a l r eg ion is ca l cu l a t ed in
a s imi lar way as in the gas d y n a m i c t h e o r y u s i n g the u p s t r e a m s t a g n a t i o n p r e s s u re
a n d
the
m i x t u r e d e n s i ty .
The
frict ion
at the
en t r anc e reg ion
and
a long
the
ve nt l ine
is
cons ide red and the c r i t i c a l p re ssu re r a t i o , used for the t r a n s i t i o n to sub-cr i t ica l f low, is
t aken f rom the i dea l gas r e l a t i o n s h i p . W i t h the a s s u m p t i o n of h o m o g e n e o u s c o n d i t i o n s
a t
the
e n t r a n c e
of the
ven t - l i ne
the
vo lum etr ic f low
is
ob ta ine d f rom
the
m ass f low
us ing the m i x t u r e d e n s i t y t a k e n f ro m the ce ll which adjo ins the ven t - l i ne .
2.4.
THE
D EERS CO D E
T h e D e s i g n and E v a l u a t i o n of Em erge ncy Re l ie f Sy s t em s code (D EE R S) so lves the
o n e - d i m e n s i o n a l m a s s , m o m e n t u m and e n e r g y c o n s e r v a t i o n e q u a t i o n s as d e s c r i b e d by
Klein (15). T h e s e e q u a t i o n s are solved in the axia l d i rec t ion of the flow for the vessel
a n d
for
va r ious conf igura t ions
of the
ven t - l i ne
all the way up to the end of the
ca tch
t a n k .
I t
can
h a n d l e
up to
four chemica l r eac t ions w i th
six
co m po ne n t s . Di f fe ren t t em
p e r a t u r e , p r e s s u r e
and
c o n c e n t r a t i o n
of
t h e s e c o m p o n e n t s
are
a l lowed a long
the
axis
of
the
flow. Along
the
vessel
the
fluids
are
a l lowed
to
exis t
in
d i ffe ren t com bin a t ion s
of liquid
and
v a p o u r m i x t u r e s
and
chemica l r eac t ions
can
occur e i t he r
in the
l iquid
o r / a n d
in the
v a p o u r p h a s e
of the
v a r i o u s c o m p o n e n t s .
Nozzles
or
d i ffe ren t c om bina t ions
of
long pipes
can be
t a k e n i n t o a c c o u n t
in the
ven t - l i ne which can be at the top a n d / o r at the b o t t o m of the rea c t io n vesse l and can
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be ve r t i ca l o r i nc l ined to t he hor i zon ta l . In add i t i on to t hese va r ious rup tu re d i sks can
be placed a t any cont rol volume a long the reac tor vesse l .
The two-phase mode l employed by th i s code re l a t e s t he vo id f rac t ion to t he re l a t i ve
ve loc i ty be tween the two phases accord ing to :
u
t
= sj 10 A
d
[ ap
g
+ (1 - a)pi ] a
[121
where the empi r i ca l f ac to r Aj, is referred to as the interface sl ip coefficient and has
d im ens io ns o f m K g s . Th i s coef fi ci en t has been t e s t e d aga ins t exp e r im enta l
d a t a from th e M P M C te s t fac il it y o f t h e J .R .C . I sp ra (7 ) for s imple non - reac t ing flu ids
and the fo l lowing va lues were p roposed :
A
d
= 8.0 X 1 0 ~
4
(Non -foamy l iquids)
Aj. = 1.5 X l 0
- 5
(Foam y l iquids)
A j = 0 .0 ( H o m o g e n e o u s m i x t u r e ) .
S imi l a r t o t he SAFIRE and the RELIEF codes th i s mode l i s no t a l l owed to a l t e r
th roughout t he dura t ion o f t he t r ans i en t and has been used fo r vo id f rac t ions f rom
0 to 1 i r r e spec t ive of t h e flow reg imes . Co mp ar i so ns have been m ad e (16 ,17) wi th
seve ra l expe r imenta l da t a ob ta ined unde r s t eady s t a t e cond i t i ons i n o rde r t o t e s t t he
accu racy o f t h i s mod e l . For vo id f rac t ions be tw een 2 5% and 70% i t ha s been found to
be accura t e enough fo r seve ra l t ypes o f two-phase mix tu re s .
Heat conduct ion in the sol id vesse l wal l and hea t t ransfer be tween the wal l and
th e vessel con ten t s can be a l so t aken in to acco un t . Va r iou s ex t e rna l hea t fluxes a re
a l lowed a long the ax i s f l ow thus , ven t ing t r ans i en t s unde r complex hea t ing o r coo l ing
con d i t i on s can be ana ly sed . Th e two -p ha se f r ic t ion fac to r an d th e loss coe ff ic ien ts du e
to an ab ru p t a re a chan ge in t h e ven t - l i ne a re ca l cu l a t ed in t e rna l ly by th e code . In
add i t i on to t h i s , t h e use r has t he poss ib i li t y t o supp ly ex t e rna l ly d i f feren t h ea t t r ans fe r
coeff ic ients and di f fe rent wal l roughness fac tors in the var ious cont rol volumes.
DEERS i s a gene ra l purpose code which can be used in t he ven t ing o f a l a rge
va r i e ty of sys t em s . How ever , t he use o f a s ing le tw o- ph as e mode l t h ro ug ho ut t he w hole
t ran s i en t r e s t r i c t s t he accuracy of i t s p red ic t ions . A no the r d i s adv an ta ge of t h i s code
i s t h a t i t r equ i re s seve ra l hou rs o f C P U t ime in an o rd ina r y Pe rso na l C om pu te r . B o th
these have been modi f i ed a t t he Jo in t Resea rch Cen t re by conve r t ing and t r ansfe r r ing
t h e c o d e t o m a i n f r a m e c o m p u t e r s a n d b y i n t r o d u c i n g s e v e r a l t w o - p h a s e f l o w m o d e l s
in to the code .
3 .
V e n t i n g E x a m p l e s
T h e p u r p o s e o f t h e e x a m p l e s s h o w n h e r e d e s c r i b e t h e p h e n o m e n a a n d d e m o n s t r a t e t h e
i m p o r t a n c e of s o m e of t h e p a r a m e t e r s r e l a t e d w i t h v e n t i n g . B a s i s of t h e E x a m p l e s a r e
t w o e x p e r i m e n t s c a r r ie d o u t a t t h e M u l t i p h a s e M u l t i c o m p o n e n t ( M PM C ) t e s t f a ci li ty
of t he Jo in t Resea rch Cen t re t oge the r wi th two t e s t ca se s wi th re f r ige ran t R114 which
have been k ind ly con t r ib u te d by Ho echs t AG (8) . T he inp u t cond i t i o ns o f t he s e t e s t s
a re se l ec t ed so a s t o be in l i ne wi th two more depressur i sa t ion expe r iment s r epor t ed in
th e in t e rna t ion a l l i t e ra tu re (18 ,19 ) . T he d imens io ns of t h e vesse l, t h e wo rk ing flu ids,
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t h e s t a r t i n g c o n d i t i o n s , t h e t y p e a n d t h e d i m e n s i o n s o f t h e v e n t - l i n e a r e s u m m a r i s e d
in Table 2.
The same pa rame te r s have been moni to red fo r a l l t he examples p re sen ted be low
however , more emphas i s i s g iven to compar i sons where expe r imenta l da t a a re ava i l ab l e .
T h e p a r a m e t e r s m o n i t o r e d a r e t h e p r e s s u r e , t h e v o i d - fr a c ti o n a n d t h e l i q u i d / v a p o u r
interface in the reac tor vesse l . At the exi t of the vesse l the mass-f lux and the s ta t ic
ex i t -qu a l i t y a re a l so ca l cu l a t ed . Th e l a t t e r i s de f ined a s t h e ra t i o of t h e vapo ur mas s
to the to ta l mass exi t ing the vesse l a t a par t icular t ime s tep. In the f i rs t two examples
wi th a l ong ven t ing p ipe a t t ached a t t he t op o f t he vesse l t he p re ssure h i s to ry a t a
pa r t i cu l a r l oca t ion i s a l so ca l cu l a t ed by the pa r t i c ipa t ing co des .
Not a l l o f t he above ment ioned pa rame te r s cou ld be ca l cu l a t ed fo r each example
d u e t o t h e m o d e l l i n g a s s u m p t i o n s t a k e n b y e a c h c o d e . Fo r e x a m p l e , w i t h t h e SA FI R E
code i t i sn ' t possible to ca lcula te the in terface leve l -swel l in the vesse l due to the
ass um pt io n th a t t he vesse l i s mode l l ed wi th a s ing le nod e . S imi l a r ly , RE L IE F d id
not provide any da ta for the pressure and s ta t ic qual i ty in spec i f ic loca t ions a long the
ven t -p ipe because the whole ven t -p ipe was cons ide red a s a s ing le node .
E x a m p l e
No.
1
2
3
4
5
6
Vessel
V o l u m e
K )
5 0 x l 0
- 3
5 0 x l 0 ~
3
6 . 3 2 X 1 0
- 3
4 .53
1 4 . 6 X 1 0
- 3
105 x l O
- 3
Vessel
D i a m .
( m )
0.40
0.40
0.178
1.19
0.216
0.40
T y p e
of
Vent
L / D = 9 0
L / D = 9 0
Nozzle
B o t t o m
Nozzle
L / D = 7 9
Orifice
L / D = 7 9
Vent
D i a m .
(cm)
2.0
2.0
1.27
5.4
1.9
1.5
1.9
Work ing
Flu id
W a t e r
W a t e r
W a t e r
W a t e r
Freon 114
Freon 114
In i t .
P r e s s u r e
(Pa )
2 . 5 x 1 0
s
2 . 5 X 1 0
5
2 . 9 x 1 0
s
7.2 x 1 0
s
7 . 0 x 1 0
s
8 . 3 x 1 0
s
Ini t .
Void
(%)
2
3 5
2
46
15
15
TABLE 2. The venting examples considered for different vessels and different fluids;
L/D refers to long pipes with the specified Length/Diameter ratio.
The codes used here do not inc lude a leve l t racking model for the in te rface in the
vesse l be tween the p redominan t ly l i qu id and the p redominan t ly vapour r eg ions . For
t h i s r e a s o n R E L A P u s e s a r a t h e r s i m p l e m o d e l w h i c h a s s u m e s t h a t t h e m i x t u r e l e v e l
ex i s t ed in t he h ighes t vo lume wi th in a ve r t i ca l channe l whe re the l i qu id vo lume f rac t ion
exceeds the va lue of 0 .05 . The exac t loca t ion of the leve l i s then found according to :
au - a
level
H + dh
13
w h e r e
H
i s t he b o t to m e l eva t ion of t he vo lum e iden t i fi ed ,
dh
i s the he ight of th is volume,
a i s th e void f rac t ion ,
OCT,
and a y are the va lues for th e void f rac t ion in th e vo lum e be low
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o r a b o v e r e s p e c t i v e l y . Fo r t h e c o d e s R E L I E F a n d D E E R S t h e l i q u i d / v a p o u r i n t e r f a c e
is a ss um ed t o be a t t h e p l ace w here the vo id f rac t ion g rad ien t ge t s i t s m ax im um va lue
a long the vesse l length .
Di f fe ren t noda l i sa t ion approaches have been fo l lowed in t he va r ious codes wi thou t
a n y a t t e m p t t o o p t i m i s e t h e s iz e a n d / o r t h e n u m b e r of c o n t r o l v o l u m e s u s e d . I n R E L A P
the vesse l is sub d iv ide d in to 10 vo lum es wi th t he ex cep t ion o f Ex am ple - 4 wh ere 12
volumes were used in order to a l low the correc t posi t ion of the discharge l ine , and the
cor rec t vesse l geome t ry . In t he ca ses wi th a l ong ven t -p ipe RELAP used on ly 2 con t ro l
v o l u m e s . I n t h e c a l c u l a t i o n s w i t h t h e t w o SA FI R E s t h e v e n t - l i n e w a s r e p r e s e n t e d w i t h
8 c o n t r o l v o l u m e s ( SA FI R E - 1 ) a n d w i t h 5 0 c o n t r o l v o l u m e s ( SA FI R E - 2 ) . R E L I E F in
a l l th e cases used 100 con t rol volu me s for th e vesse l . As i s a l re ad y show n in Tab le 1
SAFIRE and RELIEF used a s ing le con t ro l vo lume in t he vesse l and in t he ven t - l i ne
re spec t ive ly . In a l l t he ca l cu l a t ions shown he re wi th t he DEERS code the vesse l and
the ven t - l i ne have been mod e l l ed w i th 18 and 15 con t ro l vo lum es re spec t ive ly .
3 .1 .
E X A M P L E - 1 ; T O P V E N T I N G , L OW P R E - R E L I E F V O ID
Th i s is a w a te r b lowdo wn case which ha s been ca r r i ed ou t in t h e Mu l t i -p has e M ul t i -
co m po nen t t e s t fac il it y o f t he J .R .C . I sp ra wi th a long ven t ing p ipe a t t a ch ed a t t h e t o p
of a cyl indr ica l vesse l . In th is example the contents of a near ly ful l vesse l under low
sta r t i ng p re ssure ( com pared to t he am bien t p re ssure ) a re ven ted in a ca t ch t an k . Th e
expe r imenta l da t a ava i l ab l e fo r t h i s exe rc i se a re shown in F ig . l t oge the r wi th o the r
p a r a m e t e r s w h i c h a r e c a l c u l a t e d b y t h e p a r t i c i p a t i n g c o d e s .
The d r iv ing mechan i sm i s t he l imi t ed vapour p roduc t ion in t he vesse l which ho lds
the p re ssure c lose to t he s t a r t i ng va lue whi l e a p redominan t ly l i qu id mix tu re i s expe l l ed
un de r h igh mass- f luxes . Th e who le p rocess m a in t a in s t h e vesse l p re s sure h igh (F ig . l )
for a re la t ive ly longer per iod than in the corresponding case wi th lower in i t ia l f i l l ing
(Ex am ple - 2 ) . Th e p re ssu re osc i l l at i ons wi ll con t inu e un t i l enou gh va po ur has been
produced and the l i qu id -vapour i n t e r face has f a l l en be low the en t rance o f t he ven t - l i ne .
The d i f fe rences be tween the two SAFIRE ca l cu la t ions a re due to t he empi r i ca l
d r i f t - f l u x d i s t r i b u t i o n p a r a m e t e r C
0
for the void f rac t ion and due to the di f fe rent ways
by wh ich the two-ph ase fr i ct ion fac to r i s ca l cu l a t ed in t he ven t - l i ne . In SA FI R E- 1 t he
C
0
has been t ak en a s 1.5 t oge th e r wi th a con s t an t two-p has e f r ic t ion fac to r w he r eas ,
i n S A F I R E - 2 C
0
was equa l t o 1 and th e two -pha se fr i c ti on fac to r ha s been ca l cu l a t ed
in t e rna l ly accord ing to t he loca l cond i t i ons i n each node a long the ven t - l i ne . In bo th
codes the f l ow reg ime in t he vesse l has been a ssumed a s churn tu rbu len t wi th pa r t i a l
l i qu id /v ap ou r d i sengag em ent . Th e flow in t h e ven t ing p ipe has been mode l l ed in
b o t h SA FI R E c a l c u l a t i o n s a s a h o m o g e n e o u s m i x t u r e . D e t a i l s a b o u t t h e tw o ty p e s of
ca l cu l a t ions wi th SAFIRE can be found in (11 ) and (5 ,12 ) r e spec t ive ly .
Al l codes reproduce rea sonab ly we l l t he p re ssure curve ins ide the vesse l wi th a
ra t he r sm oo th pa rabo l i c t yp e o f cu rve . Th e h ighe r mass- f lux p red ic t ed by the code
R E L IE F du r ing the f ir st 6 seconds of t h e t r an s i en t me ans th a t enoug h l iqu id is expe ll ed
from th e vesse l so th a t bulk evap ora t io n wi ll begin ear l ie r th an for th e oth er cod es.
Th is is a l so re f lec ted in th e void -f rac t ion s co m pa riso ns ( Fi g . l ) a t least in th e f irs t few
secon ds o f t he t r ans i e n t . Th ese vo id - f rac t ions i n t he vessel a re t hen t r an s l a t ed in to
h i g h e r e x i t - q u a l i t i e s . C o n t r a r y t o t h i s t h e c a l c u l a t i o n s b y R E L A P a n d D E E R S s h o w a
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EXAMPLE 1 PRESSURE IN THE VESSEL.
LU 1.80
<n 1.60
1.00
l ' ' ' ' l
i
T I M E
(SEC)
EXAM. 1 PRESSURE AT 1.37 m ALONG THE VENT PIPE
FIG. la. Top Venting, 2.5 bar pre-relief pressure , 2% initial void [ or (x) Experiment;
RELAP; SAFIRE-1; SAFIRE-2; RELIEF; DEERS j .
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EXAMPLE 1 MASS - FLUX AT THE EXIT OF THE VESSEL
£
1500.
EXAMPLE 1 QUALITY AT THE EXIT OF THE VESSEL
T
I M E
( S E C
FIG. lb. Top Venting, 2.5 bar
pre-relief pressure,
2% initiai void [ or fxj Exp eriment;
RELAP; SAFIRE-1; SAFIRE-2; RELIEF; DEERS
j .
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EXAMPLE 1 NORMALISED LEVEL SWELL IN THE VESSEL
EXAMPLE 1 VOLUMETRIC VOID-FRACTION IN THE VESSEL
0 .45
0 . 4 0
0 . 3 5
0 . 3 0
0 . 2 5
0 . 2 0
0 . 1 5
0 . 1 0
0 .05
0 .00
V /
/
/<
1
-
-
X
;
:
•j
:
:
■
40.0 60.0
T I M E SEC)
FIG. lc . Top Venting 2.5 bar pre-relief pressure, 2% initial void [ or (x ) Experiment;
RELAP; SAFIRE-1; SAFIRE-2; RELIEF; DEERS j .
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421
pe rio d of ma ss-flu x fluctuations w hile th e exit qu ali t y re m ai ns ve ry close to al l- l iquid
f low. During th is per iod the pressure in the vesse l i s mainta ined a t h igh leve ls ; the la t te r
exp la ins to a cer ta in exte nt th e pre ssu re f luctua tions obs erved in th e ven t - l ine . Th e
p h e n o m e n o l o g i c a l d i f f e r e n c e s b e t w e e n t h e R E L I E F , R E L A P a n d t h e D E E R S c o d e s a r e
a lso found in the comparisons of the exi t -qual i t ies ca lcula ted dur ing the f i rs t 40 seconds
wh en the m ass flux i s r a th e r uns t ab l e . Th e two SA F IR E ca l cu la t ions a re s imi l a r t o
t h o s e o f R E L A P.
The exi t -qual i t ies shown in Fig . l a re in l ine wi th the ca lcula t ions for the leve l swel l
wh ich i s a f ic ti tious in te rface be twe en th e pr ed om ina nt l y l iquid an d th e pr ed om in an t ly
vapour regions in the vesse l . For the RELIEF code th is leve l swel l causes th is in te rface
to be ful l contac t wi th the top of the vesse l dur ing the f i rs t 58 seconds of the t ransient .
A simi lar leve l swel l curve i s a l so shown in the same f igure for the RELAP and for
th e DE E R S codes . Th e d i ffe rences be tween thes e codes re f lec t t he va r i a t i o ns of t he
ex i t -qua l i t i e s ca l cu l a t ed a l though i t mus t be a l so t aken in to accoun t t ha t t he l eve l - swe l l
i s ca lc ula ted di f fe rent ly in RE L A P .
3 . 2. EX A M P LE - 2 ; TO P V EN TI N G , LA RG E P RE- RE LI EF V O I D
Th i s is a s imi l a r ca se a s in Exa m ple - 1 bu t a t t he b eg inn ing o f t h e t r ans i en t on ly
6 5 %
o f t he vesse l vo lum e was filled wi th w a te r . Th i s chan ged co mp le t e ly t h e ve n t ing
mechan i sms and the vapour p roduced in t he vesse l was no t su f f i c i en t t o ma in t a in a
high pressure for very long (Fig .2) . For th is reason the pressure curve in the vesse l i s
no t of t h e sam e pa rab o l i c sha pe a s i n F ig . l . Th e am pl i tud e o f t h e p re ssu re osc i l l a t i ons
observed in the corresponding f igures for the previous case a re s igni f icant ly reduced as
is sho wn in Fig .2 and t he pr ess ure in th e vesse l fa ll s ra th er fast in th e f irst 15 seco nds
of the t ransient . Also, the de lay in boi l ing dur ing the f i rs t few seconds of the t ransient
has a much more profound effec t in th is case ra ther than in f i rs t example where the
vessel was pract ical ly ful l .
Al l ca l cu l a t ions ca r r i ed ou t seem to reproduce ra the r we l l t he expe r imenta l da t a
for the pressure in the vesse l . The ca lcula t ions for the pressure in the vent - l ine a re in
good ag reem ent exp e r im enta l va lues a f t e r t he fir st 10 secon ds o f t he t r an s i e n t . In t h i s
e x a m p l e t h e t w o SA FI R E c u r v e s h a v e b e e n c a lc u l a t e d w i t h t h e s a m e i n p u t o p t i o n s a s
t h o s e u s e d i n E x a m p l e - 1 .
T h e p r e s s u r e c u r v e s c o r r e s p o n d i n g t o t h e t w o SA FI R E s a r e s t r o n g l y i n f l u e n c e d
f rom the way the two -phas e fr ic t ion fac to r was ca l cu l a t ed in t he ven t - l i ne . Th i s t o ge t he r
wi th the di f fe rences in the C
0
va lue a re t he ma in rea sons fo r t he va r i a t i ons obse rved
in F ig .2 am on g th e ca l cu l a t ed va lues of t he mass- f lux a t t h e ex i t o f t h e vesse l . W ha t
i s a l so wo r th ob se rv ing f rom the sa me f igure is t h a t t h e pe r iod o f p red ic t ed two -pha se
f low in t he ven t -p ipe i s r a the r shor t .
Al l ca l cu l a t ions p re sen ted in F ig .2 fo r t he ex i t -qua l i t y demons t ra t e t ha t a f t e r a
cer ta in t ime the f low in the vent - l ine becomes a l l -vapour f low unt i l the end of the
t ran s i e n t . Th i s t ime is sho r t e r for R E L A P and longe r for t h e R E L IE F code . In
th e same figure i t is shown t ha t D E E R S s ti l l p red ic t s osc i ll a t i ons for t he ex i t -qu a l i t y
an d th e mass- f lux fo r t he f ir st 30 second s o f t he t r an s i e n t . Co n t r a ry to t he p rev iou s
example , the ca lcula ted leve l swel l does not reach the vesse l top as i s shown in Fig .2 .
T h e R E L I E F a n d t h e D E E R S co d e s , p r e d i c t e d v e n t i n g o f a t w o - p h a s e m i x t u r e d u r i n g
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422
EXAMPLE 2 PRESSURE IN THE VESSEL.
S 2.00
r > 1.60 .
L0
20.0 40.0 60.0 80.0
T I M E (SEC) .
EXAM. 2 PRESSURE AT 1.37 m ALONG THE VENT PIPE
FIG. 2a. Top Venting, 2.5 bar pie-relief pressure, 35% initial void [ or (x) Experiment;
RELAP; SAFIRE-1; SAFIRE-2; RELIEF; DEERS j .
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423
EXAMPLE 2 MASS - FLUX AT THE EXIT OF THE VESSEL
40.0 60.0
T I M E SEC) .
EXAMPLE 2 QUALITY AT THE EXIT OF THE VESSEL
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
t i l l I
T
-.« , .
:
i i /
H i
/
i l l
I i l U j i / >
■
i l
i
H I ?
i ;
F » |iih * in
t i l l
I K l U
I
1
I I M
O K \
ii y
i
n v
T I M E
( S E C )
FIG.
2b .
Top
Venting,
2.5
bar
pre-relief
pressure,
35%
initiai void
[
or
(x)
Experiment;
RELAP; SAFIRE-1; SAFIRE-2; RELIEF; DEERS j .
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424
EXAMPLE 2 NORMALISED LEVEL SWELL IN THE VESSEL
1.20
i.O 20.0 40.0 EO.O 80 .0
T I M E (SEC) .
EXAMPLE 2 VOLUMETRIC VOID-FRACTION IN THE VESSEL
FIG. 2c. Top Venting, 2.5
bar
pre-relief pressure, 35% initial void [ or (x) E xperiment;
RELAP; SAFIRE-1; SAFIRE-2; RELIEF; DE ERS j .
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425
t he fir st 38 secon ds . Th i s i s p ro bab ly due to t he me tho d u sed in ca l cu l a t ing the m ix tu re
leve l which a l lows the loca l void f rac t ion above th is leve l to be di f fe rent f rom one .
On the o the r ha nd , R E L A P does no t show any con t ac t of t he ca l cu l a t ed in t e r face
w i th the vesse l to p , th er e a re not any mass-f lux f luctua tions th i s t im e an d af te r a
sh or t per io d of mas s-f lux increa se the flux fol lows an expo ne nt ia l dec reas e . Th is is in
agreement wi th t he ca l cu l a t ed ex i t -qua l i t y which i s p rac t i ca l ly one (a l l -vapour f l ow)
du r in g the wh ole t rans ien t . A s for th e void-f rac t ion in th e vesse l , a l l cod es seem to
agree on the shape of the curve ca lcula ted wi th smal l var ia t ions for the f ina l vesse l void
frac t ion.
Th e gene ra l conc lus ion d ra w n f rom th i s exam ple i s t h a t whe n th e vesse l i s no t
ful l , the depressur isa t ion las t s for a shor te r per iod and the vesse l pressure fa l l s ra ther
qu ick ly in t h e beg inn ing o f t he t r an s i en t . Th e vap ou r p ro du c t io n does no t m a in t a in
the in i t ia l pressure in the vesse l , the per iod of two-phase f low in the vent - l ine las t s
sho r t e r and th e ca l cu l a t ed m ass- f lux is sma l l e r t ha n in Ex am pl e -1 . Al so , t h e p re ssu re
his tor ies in the vesse l and in the vent - l ine a re f ree f rom the high f requency osc i l la t ions
found in t he p rev ious example .
3.3.
EXA MPLE-3; TOP VENTING THROUGH A NOZZLE
Th is i s a w ate r b lowd ow n exerc ise carr ied ou t a t th e Th ay er School of En gin eer ing (18)
in a sma l l ve sse l wi th a nozz l e r a the r t han a l ong ven t -p ipe a t t ached a t t he t op o f t he
vesse l . The inpu t cond i t i ons a re s imi l a r t o t hose o f Example -1 thus , we can iden t i fy i f
t he phenomena desc r ibed in t he f i r s t example a re i ndependen t o f t he ven t t ype and o f
th e s ize o f t h e reac to r vesse l. Th e expe r im enta l da t a ava i l ab l e for t h i s exe rc i se a re t h e
pressure his tory a t the bot tom of the vesse l , the f ina l void f rac t ion in the vesse l and
the in terface leve l -swel l da ta measured by an e lec t r ica l c i rcui t be tween the nozz le and
the water in the vesse l .
The expe r imenta l p re ssure i n t he vesse l i s shown wi th the con t inuous l i ne i n
F ig . 3 .
T h e high f requency pre ssu re f luctua tions a re presen t for ab o u t 8 sec ond s an d th e de lay
in boi l ing is of th e sa m e m ag ni tu de as th e f luctua tions in th e pre ssu re cur ve . Sim i lar to
the f i r s t example , bu lk vapour p roduc t ion does no t s t a r t immedia t e ly and the vapour
produced in the vesse l mainta ins the pressure in the vesse l a t re la t ive ly high leve ls .
Th i s l a s t s un t i l enou gh vo id is c rea t e d in t he vessel and du r ing th i s pe r iod th e in t e r face
level is up to the top as is shown in
F i g . 3 .
T h en , th e interf ace level f luctuates up to
the to p o f t he vesse l i nd i ca t ing t ha t t h e ex i t -qua l i t y i s va ry ing d ur in g th i s pe r iod of
instabi l i ty . This a l so a ffec ts the ca lcula ted mass-f lux and the pressure in the vesse l .
A pa r t from the pa rabo l i c sha pe of t h e p re ss ure curve , t he ca l cu l a t ions wi th RE -
L A P a n d D E E R S s h o w n i n F i g . 3 , g ive a be t t e r i ns igh t t o t he phenomena invo lved
by bei ng th e only co de s wh ich ac co un t for th e fluctuations in th e inte rfac e level-swell .
Th es e f luctuat ions a re pr ob ab ly th e resu l t of th e va r ia t ion s obs erved in th e m ass-f lux
and the s t a t i c qua l i t y a t t he ex i t o f t he vesse l . In t he two SAFIRE ca l cu la t ions t he same
equ i l ibr iu m ra t e m ode l i s used to desc r ibe th e f low th ro ug h nozzles . T h e di f fe rences
be tween those ca l cu l a t ions a re due to t he empi r i ca l d r i f t - f l ux d i s t r i bu t ion pa rame te r
C
0
for t he vo id f rac t ion . Co n t r a ry to t he Ex am ples 1 and 2 , t he mass- f luxes ca l cu l a t ed
f r o m SA FI R E 1 a n d 2 a r e c o m p a r a b l e . T h u s , fo r t h e SA FI R E c o d e , t h e m a s s - fl u x is
more sens i t i ve t o t he two-phase f r i c t i on fac to r t han to t he va lue o f C
0
.
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426
EXAMPLE 3 PRESSURE IN THE VESSEL.
UJ 1.50
w 1.00
T I M E (SEC) .
EXAMPLE 3 MASS - FLUX AT THE EXIT OF THE VESSEL
w 6000.
o 5000.
•:-*•--
FIG. 3 a. To p Venting, 2.9 ba r pre-relief pressure, 2% initial void [ Experiment; -
RELAP; SAFIRE-1; SAFIRE-2; RELIEF; DEERS j .
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427
EXAMPLE 3 QUALITY AT THE EXIT OF THE VESSEL
T I M E (SEC)
EXAMPLE 3 NORMALISED LEVEL SWELL IN THE VESSEL
T I M E ( S E C ) .
FIG. 3b. Top Venting, 2.9 bar pre-reJief pressure, 2% initial void [ Exper imen t ;
RELAP; SAFIRE-1; SAFIRE-2; RELIEF; DEERS ,
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428
The exi t -qual i t ies shown in Fig .3 a re in l ine wi th the ca lcula t ions for the in terface
leve l swel l . T he leve l-swell ca lcula ted by th e RE L IE F cod e (Fig .3) i s in ful l co nta c t
w i th th e top of th e vesse l du r in g the f irs t 18 seco nd s. A fter th i s per iod th is in te rface
level fa ll s be low the top of th e vesse l an d a l l -vapo ur f low st a r t s . T he co rre sp on din g
i n t e r f a c e c a l c u l a t i o n s f r o m t h e c o d e s R E L A P, R E L I E F a n d D E E R S a r e s h o w n i n t h e
same f igure and a re i n good agreement wi th t he expe r imenta l da t a .
3 .4 . E X A M P L E - 4 ; B O T T O M V E N T I N G
This i s a bot tom vent ing exerc ise carr ied out in the la rge vesse l of Genera l Elec t r ic
(19 ) .
Th is vesse l i s 1 .19 m in dia m ete r , 4 .07 m in he ight and th e ven t ing nozzle
has been p l aced 0 .7 m f rom the bo t tom of t he vesse l . The the s t a r t i ng p re ssure was
72 ba r t hus , t he capab i l i t i e s of t he codes a re t e s t ed und e r h igh ope ra t ing p re ssu re s
tog e the r wi th t he i r ab i l it i e s for sca l ing up from l abo ra to ry s i ze vesse ls . Th e pa ram e te r s
measured in t h i s example a re shown in F ig .4 . These pa rame te r s a re t he p re ssure and
the l iquid/vapour in te rface in the vesse l , as wel l as the mass-f lux and the s ta t ic qual i ty
at the exit of the vessel .
As i s shown in Fig .4 , the pressure in the vesse l decreases s lowly dur ing the f i rs t 20
seconds of the t ransient th is i s then fol lowed by a per iod of rapid pressure reduct ion
un t i l a new s t a t e of equ i l i b r ium is r eache d . Du r ing th e f ir s t 20 secon ds the v apo ur
produced in t he vesse l ho lds up the p re ssure i n t he vesse l whi l s t a p redominan t ly
l iquid mix tu re i s expel led f rom th e vesse l . Th is i s conf i rme d a lso by th e low exi t -
qua l i t y dur in g th e f ir s t 16 seconds of t he t r ans i en t u n t i l t h e l i q u id /va po ur i n t e r face
reaches t he ven t ing nozz l e . Then , two-phase mix tu re i s expe l l ed f rom the vesse l and
dur ing th is per iod the pressure in the vesse l fa l l s rapidly .
In t he two SA F IR E ca l cu la t ion s t he rad i a l va r i a t i on o f t h e vo id f rac t ion was
d e a c t i v a t e d (C
0
— 1) and a churn turbulent f low regime in the vesse l has been assumed
wi th no pa r t i a l l i qu id /v apo ur d i seng agem ent . Th e qua l i t y a t t he en t ran ce o f t he ven t in g
nozzle in both codes i s assumed to be the average qual i ty of the vesse l . However , in
SAFIRE-1 the Equ i l i b r ium ra t e mode l has been employed fo r t he two-phase nozz l e f l ow
w h e r e a s , i n SA FI R E - 2 t h e H o m o g e n e o u s E q u i l i b r i u m M o d e l ( H E M ) . T h e d i f f e r e n c e s i n
the f low model a re not very s igni f icant for the pressure and the mass-f lux but a f fec ted
th e ca lc ula ted exi t -q ual i t ies espec ia l ly c lose to th e end of th e t ra ns ien t . I t m us t be
po in t ed ou t t ha t i n SAFIRE the pos i t i on o f t he ven t ing nozz l e can be on ly p l aced
at th e bo t t o m of th e vesse l (due to the fac t th a t the vesse l i s mo del led w i th a s ingle
con t ro l vo lum e) . The re fo re in S A F IR E the t r ans i en t i s t e r m ina ted w i th 100% vo id in
the vesse l . This was not the case for the other codes which discre t i sed the vesse l wi th
seve ra l con t ro l vo lumes .
B e t t e r r e p r e s e n t a t i o n h a s b e e n a c h i e v e d w i t h t h e R E L I E F a n d R E L A P c o d e s
which model led the vesse l wi th severa l nodes. In fac t the shape of the pressure curve
ca l cu la t e d by RE L A P i s ve ry s imi l a r t o t he Ex pe r im ent a l cu rve even wi th a sma l l n um
ber of nodes in the vesse l . Close to the end of the t ransient , due to l iquid ent ra inment
in t he ven t t he measured mass- f lux i s h ighe r t han the va lue p red ic t ed by RELIEF and
RELAP. These sma l l d i f fe rences i n t he mass- f lux a re t r ans l a t ed in to l a rge dev ia t ions
f rom the measured ex i t -qua l i t i e s due to two-d imens iona l e f fec t s which cou ld no t be
t a k e n i n t o a c c o u n t i n o n e - d i m e n s i o n a l c o d e s . T h e c a l c u l a t i o n s w i t h t h e D E E R S c o d e
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429
EXAMPLE 4 PRESSURE IN THE VESSEL.
>
■
■
i
£
50.0
EXAMPLE 4 MASS - FLUX AT THE EXIT OF THE VESSEL
35000 .
1
J
1 5 0 0 0 .
FIG.
4a. Bottom
Venting 72
bar
6
initial void [ or (x) Experiment;
SAFIRE-1; SAFIRE-2; RELIEF; DEERS j .
RELAP;
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430
EXAMPLE 4 STATIC QUALITY AT THE EXIT OF THE VESSEL
EXAMPLE 4 NORMALISED LEVEL SWELL IN THE VESSEL
0. so
0 .4 0
0 .3 0
0 .2 0
0 .10
0 .00
: \
-
-
•
—\
\
\ \
i . . .
\
\
NN.
~\
j
J
i
L _
. . . i . .
-
•
:
-
i i i i i i
T I M E (SE C )
FIG. 4b. Bottom Venting, 72 bar, 46% initial void [ or (x) Experiment;
SAFIRE-1; SAFIRE-2; RELIEF; DEERS j .
RELAP;
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431
a re a l so in exce l len t ag re em ent wi th t he exp e r im enta l d a t a for t h e ex i t -qua l i t y . Th e
shape o f t he o the r cu rves i s r ep roduced equa l ly we l l howeve r wi th some s ign i f i can t
differences for the vessel pressure and for the interface level swell . These differences
are due to the in terface s l ip coeff ic ient used in the ca lcula t ions. The va lue sui table for
non-foamy l iquids has been se lec ted which was the same as in a l l the other top vent ing
cases wi th no a t t empt t o op t imi se i t fo r bo t tom ven t ing .
T h e v e n t i n g m e c h a n i s m n o t i c e d f ro m t h i s b o t t o m v e n t i n g e x a m p l e is t h a t t h e
va po ur p rod uced d ur in g the f ir s t pa r t of t he t r ans i en t ca nn o t ea si ly e scap e f rom t he
vent . This process las t s unt i l the leve l swel l in the vesse l drops s igni f icant ly and unt i l
two-phase f low s t a r t s . Then the change o f t he f l ow reg ime c rea t e s a sha rp reduc t ion o f
the pressure in the vesse l . In rea l i ty th is change i s not so sharp due to two—dimensional
effec ts . B et te r repre se nta t io n i s achieved wh en th e vesse l i s ana lyse d wi t h severa l node s.
3.5.
EXAMPLE-5; TOP VENTING, SMALL VESSEL
Th i s exam ple i s a dep re ssu r i sa t ion exe rc ise which has been ca r r i ed o u t a t Ho echs t
wi th re fr igerant R114 as the working f lu id . The vent ing pipe inc ludes an or i f ice which
has been p l aced 0.70 m from the ex it o f t h e vesse l. Th e pa ra m e te r s me asu red du r ing
th i s example a re shown in F i g . 5 . For reas ons of s im pl ic i ty only one ca lc ula t i on f rom
S A F IR E i s p re sen ted he re . Th i s ca l cu l a t ion has been ca r r i ed ou t w i th churn tu r bu len t
f low, pa r t i a l l i qu id /vapour d i sengagement , and wi th t he d r i f t - f l ux d i s t r i bu t ion pa ram
e t e r C
0
equa l t o 1. Th e or if ice p l a t e wa s neg lec t ed in SA F IR E and t he d i am e te r of t he
ven t ing p ipe was t aken a s 1 .9 cm. RELAP and DEERS have mode l l ed the o r i f i ce by
su i t ab ly ad jus t ing the f l ow a rea be tween two con t ro l vo lumes used fo r t he ven t -p ipe .
In t h e R E L IE F code the d i scha rge f low-ra te mo de l has been ad jus t ed acc ord ing to t h e
phys i ca l p rop e r t i e s of t he re f r ige ran t R114 . H ea t - t r an sfe r p he no m en a f rom the vessel
wa l l have been t aken in to accoun t i n RELAP.
W h a t i s s ign if i can t ly d i ffe ren t i n th i s examp le in comp ar i son w i th Ex am ple -2 ,
i s th a t th e de lay in boi l ing dur i ng th e f i rs t second wh ich does no t seem to affec t th e
pre ss ure curve so much a s i n t he o the r ven t ing ca ses . Th e p red ic t ions wi th t h e R E L IE F
code a re i n exce l l en t ag reem ent wi th t he m easu red va lues . As is shown in
F i g . 5 ,
all
codes seem to ove rpred ic t t he mass- f lux even though the ca l cu l a t ed qua l i t i e s a t t he
exi t of th e vesse l a re in re la t ive ly good agr eem en t wi th m ea su red v a lues . I t sho uld be
m ent io ned he re t h a t bo th the mass- f lux an d the s t a t i c ven t -qua l i t y have been m easu red
1.5 m downst ream from the exi t of the vesse l .
The s ta t ic qual i ty for re f r igerant R114 seems to fa l l rapidly to low values (c lose
to a l l - l iquid f low) fol lowed soon af te rwards wi th a sharp increase to a l l -vapour vent ing.
T h e e x i t - q u a l i t i e s c a l c u l a t e d b y t h e R E L I E F a n d t h e D E E R S c o d e s s h o w e d t h a t a l l -
va po ur flow ha s been even tua l ly achieved af te r th e f i rs t 30 seco nds . T he ca lcu la t io ns for
th e void-f rac t ion in th e vesse l (Fig .5) re f lec t the dif fe rences be tw een t he ca lcu la ted and
measured mass- f luxes so the ac tua l vo ids a re much lower t han the ca l cu l a t ed va lues .
3.6. EXAMPLE-6; TOP VENTING, LARGE VESSEL
In the p re sen t ven t ing exa mp le the d im ens ions o f t he cy l indr i ca l ve sse l has been nea r ly
do ub led so th a t th e vesse l vo lum e is now 105 l i t res inste ad of th e 14.6 l i t res used in
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432
EXAMPLE 5 PRESSURE IN THE VESSEL.
UJ 4.00
<n 3.00
■
2.
00
'.
K
\ \*
: \ V
\ V \
\
\
\ \ x
: \ \
N
^ x
\ \ \
\ \ \
N
: \ \ >
\ ^
; \ \
\
T » i i ? I i i i i 1 i
•
X *
0
s
\
X
x
^ , \ * x
~^C^-
x
*
5T.
]
•
■
.
;
-
■
■
X w
- * » < x
10.0
20.0
30.0
10
T I M E SEC .
EXAMPLE 5 MASS - FLUX AT THE EXIT OF THE VESSEL
'■
\
m
h
\
\ \
f c £
f
x
x x
x
«
:
X
*
x
- > - ^ x X X
• • ■ 1 ' - ' ^
X
. . 1
^ x ^ T x
;
-
■
■
■
;
;
20 . 0
T I M E I SEC)
FIG. 5a . Top Venting-, 7 bar pre-relief pressure, 15% initial void [ or (x) Experiment;
RELAP; SAFIRE; RELIEF; DEERS j .
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433
EXAMPLE 5 QUALITY AT THE EXIT OF THE VESSEL
EXAMPLE 5 VOLUMETRIC VOID-FRACTION IN THE VESSEL
'
0 . 0 2 0 . 0
T I M E
FIG. 5b. Top
Venting,
7 bar pie-relief pressure, 15% initial void [ or (x) Experiment;
RELAP; SAFIRE; RELIEF; DEER S }.
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434
EXAMPLE 6 PRESSURE IN THE VESSEL.
» 3.00
— J — I — I — I — T — J —
0.00 L .
0.0
_ 1_
10.0 20.0 30.0
T I M E SEC) .
EXAMPLE 6 MASS - FLUX AT THE EXIT OF THE VESSEL
- / ••. -
• ; \
: / \
i
\
LI V N
:
«
\
x
N
1
\
\
\
I \ \ x ■
■ >
N l
^ • ^ ^ ■ . - . . :
j t V *
K,
* »%
w
«„ ■
„ [ ^ H
2 0 . 0 30 . 0
T I M E
I
SEC)
.
FIG. 6a . Top Venting, 8.3 ba r pre-relief pressure, 15% initial void [
or (x) Experiment;
RELAP; SAFIRE; RELIEF; DEERS j .
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435
EXAMPLE 6 QUALITY AT THE EXIT OF THE VESSEL
EXAMPLE 6 VOLUMETRIC VOID-FRACTION IN THE VESSEL
a 0.30
FIG. 6b. Top Venting, 8.3 bar pre-relief pressure, 15% initial void [ or (x) Experiment;
RELAP; SAFIRE; RELIEF; DEERS j .
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436
t h e p rev ious examp le . Th e d im ens ion s o f t he ven t ing p ipe which is aga in a t t ach ed a t
the top o f t he vesse l a re t he same a s i n Example -5 . However , con t ra ry to t he p rev ious
example no o r i f i ce was p re sen t and the s t a r t i ng p re ssure was now 8 .3 i ns t ead o f 7 ba r .
The expe r imenta l da t a ava i l ab l e f rom Hoechs t AG a re t he p re ssure i n t he vesse l ,
th e mas s-f lux and th e qua l i ty 1 .5 m from the exi t of th e vesse l (Fig .6) . T hu s, the
measurements must be inf luenced both by the change in the s ize of the vesse l as wel l as
f rom th e chan ge in the typ e of ven t used . T h e sh ap e of th e pre ssu re curv e in th e vessel
sho wn in Fig .6 , i s s igni f icant ly di ffe rent f rom th e co rre sp on din g case in F i g . 5 . T h e
t rans i en t now l a s t s much longe r due to t he l a rge r amount o f l i qu id in i t i a l l y con ta ined
in the vesse l . The pressure does not fa l l as fast as in the previous example and the in i t ia l
de l ay in bo i l i ng wi th t he p re ssure r ecove ry a f t e rwards no t a s l a rge a s i n Example -5 o r
a s in s i m i la r w a t e r d e p r e s s u r i s a t i o n s . T e m p e r a t u r e m e a s u r e m e n t s b e f o re t h e o p e n i n g
of t he va lve has conf i rmed tha t t he l i qu id was a t sa tu ra t ion a t 74 °C . The pe r iod ove r
which th is de lay in boi l ing takes place i s mu ch longer th a n in th e smal le r vesse ls . Th is
i s probably due to the la rger amount of l iquid conta ined in the vesse l pr ior to in i t ia t ion
of t he t r ans i e n t . T he bes t ag re em ent in t he p re ssure curve i s p red ic t e d by R E L IE F
after the first 10 seconds.
S imi l a r t o t he p rev ious example on ly one SAFIRE ca l cu la t ion i s p re sen ted in
Fig.6 wi th the same input opt ions for the f low regime in the vesse l and in the vent - l ine .
Hea t - t r ansfe r phenomena f rom the vesse l wa l l have been a l so t aken in to accoun t i n t he
c a l c u l a t i o n s b y R E L A P.
For a l l codes the mass-f lux ca lcula ted a t the exi t of the vesse l i s much lower than
the ac tu a l va lues me asur ed 1.5 m dow ns t rea m in the ven t - l i ne . Th e ca l cu l a t ion s f rom
R E L I E F a r e in c lo s er a g r e e m e n t w i t h t h e e x p e r i m e n t a l d a t a sh o w n in F i g .6 . T h e
maximum va lue o f t he mass- f lux measured in t h i s exe rc i se i s s l i gh t ly l ower t han the
corresponding va lue in Fig .5 when an or i f ice was reducing the f low area of the vent -
pipe by 38%. These di f fe rences in the mass-f lux are expected to be a lso present in the
ex i t -qua l i t y . Th i s is no t t he case tho ug h a s i s shown in F ig .6 . Th e exp e r im enta l d a t a
in t h i s f i gure cor re spond to t he s t a t i c -qua l i t y measured 1 .5 m downs t ream in the ven t -
l ine and could be compared wi th the ca lcula ted qual i ty a t the exi t of the vesse l only
wh en th e li qu id en t ra ined in t he ven t - l i ne is a ssu me d n o t t o evap ora t e i n t h i s l eng th .
The ex i t -qua l i t i e s ca l cu l a t ed wi th t he SAFIRE and the DEERS codes a re i n exce l l en t
a g r e e m e n t w i t h t h e e x p e r i m e n t a l v a l u e s w i t h t h e c o r r e s p o n d i n g R E L A P c a l c u l a t io n s
a l so rea sonab ly c lose . A compar i son be tween the ex i t -qua l i t i e s measured in Examples
5 and 6 show s th a t t he qua l i t y of t he mix tu r e is abov e 50% an d a l l -vapo ur - f lo w s t a r t s
l a t e r t han when the re was an o r i f i ce (F ig .5 ) . In t he l a t t e r ca se t he ex i t -qua l i t y ge t s
close to al l- l iquid flow but for a shorter period of t ime.
T h i s e x a m p l e d e m o n s t r a t e d t h a t t h e e v a p o r a t i o n p r o c e s s d e p e n d s o n t h e s i z e o f
th e vesse l even if th e in i t ia l void-f rac t ion i s th e sa m e. O n th e oth er h an d, th e size of the
ven t employed changes the dura t ion o f t he two-phase re l ea se a s we l l a s t he compos i t i on
of t he two phase mix tu re . These two pa rame te r s migh t have cance l l i ng e f fec t s which
cannot be easi ly ident i f ied when only the pressure in the vesse l i s moni tored.
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4 . C o n c l u s i o n s
The p re sen t work focuses on the phenomenology o f t he depre ssur i sa t ion o f r eac to r
vessel s t h r ou gh s ix exp e r im enta l exam ples pe r fo rmed in d i ffe ren t t e s t f ac i li t ie s . The se
examples have been ana lysed in o rde r t o demons t ra t e t he impor t ance o f t he geome t r i ca l
a n d o p e r a t io n a l p a r a m e t e r s .
The depressur isa t ion processes depend on the s ize of the vesse l and on the s ize of
the vent used. For example , the leve l swel l osc i l la t ions observed in smal l reac tor vesse ls
does no t necessa r i l y mean tha t t hey wi l l r ema in the same when the d imens ions o f t he
vesse l and the ven t - l i ne a re i nc reased . Al so , t he pos i t i on o f t he ven t can cause changes
i n t h e d e p r e s s u r i s a t i o n p r o c e s s e s . T h u s , d u r i n g b o t t o m v e n t i n g , t h e l i q u i d d i s c h a r g e
causes a r a the r sma l l depre ssur i sa t ion ra t e dur ing the f i r s t seconds o f t he t r ans i en t ;
th is ra te i s s igni f icant ly in creased la te r whe n two-p has e f low sta r t s .
Compar i sons be tween d i f fe ren t t op-ven t ing examples ca r r i ed ou t wi th a nea r ly
ful l vesse l an d whe n the vesse l wa s ha l f -e mp ty revea led tw o di f fe rent de pre ssu r isa t ion
proc esses dep en din g on th e in i t ia l f il lings. T he f i rs t pro cess occu rs in an a lm os t full
vesse l du r ing th e f irs t seconds o f t h e t r an s i en t and i s cha r ac t e r i se d by va po ur p ro du c t ion
tog e th e r wi th an expu l s ion o f a p red om inan t ly l iqu id m ix tu r e un de r va ry ing m ass-
fluxes. In t he second p rocess a p red om inan t ly va pou r mix tu re is expe l l ed wi th l a rge r
dep ressu r i sa t ion ra t e t ha n in t h e f irs t p rocess .
The cha rac t e r i s t i c de l ay in bo i l i ng which occurs dur ing the top ven t ing ca ses a f t e r
the ven t ing va lve has been opened , i s p rac t i ca l ly shadowed by the p re ssure osc i l l a t i ons
w he n th e vesse l has been in i t ia l ly full . Di fferences in th e im po rta nc e of th e de lay
in boi l ing have been a lso observed in the la rger vesse ls even wi th s imi lar pre-re l ie f
cond i t i ons . These d i f fe rences have been a t t r i bu ted to t he l a rge mass o f l i qu id con ta ined
in the large size vessels.
Four very di f fe rent numerica l codes have been used for the theore t ica l ca lcula t ions.
These codes have been e i the r one -d imens iona l i n t he vesse l (RELIEF) o r i n t he ven t -
l i ne (SAFIRE) o r bo th in t he vesse l and in t he ven t - l i ne (RELAP & DEERS) . I t ha s
been ev iden t i n a ll t he exam ples t h a t for rea l i st i c r epre se n ta t io n o f t h e t h e h ydr od y-
namic p rocesses , a t l e a s t t he vesse l shou ld be mode l l ed wi th seve ra l con t ro l vo lumes .
B e t t e r r ep re se n ta t io n o f t he pa r am e te r s r e fe r r ing to t h e ven t - l i ne has been ach ieved
f rom one -d imens iona l ca l cu l a t ions which , i n add i t i on to t he vesse l , d i sc re t i sed a l so the
ven t - l i ne i n t he ax i a l d i rec t ion . Th i s unfor tuna te ly i nc reases t he computa t iona l t ime
and t he com plex i ty o f t h e code . Th us , t he answer t o t h e d i l e m ma of emp loy ing a
d e t a i l e d o n e - d i m e n s i o n a l c o d e w h i c h u s e s g r e a t e r c o m p u t a t i o n a l t i m e , a g a i n s t t h e u s e
of a f a st and s im ple code wi th a ce r t a in n um ber o f a ss um pt i on s , li es on how acc ura t e
o n e n e e d s t o r e p r e s e n t t h e p h e n o m e n a o c c u r r i n g d u r i n g a n e m e r g e n c y
relief.
Al t hou gh good repre s en ta t ion o f t he depre s sur i sa t ion p rocesses in t he vessel has
been ach ieved wi th t he one -d imens iona l ca l cu l a t ions shown he re , t he use o f t he same
two-phase f low model for the vesse l as wel l as for the vent - l ine and for the whole range
of void fract ions from 0 (al l l iquid flow) to 1 (al l vapour flow) may not always be a
good approach . The re su l t s i n t he bo t tom ven t ing example a s we l l a s fo r f l u ids o the r
t h a n w a t e r d e m o n s t r a t e d t h a t a m o r e p h e n o n o m e n o l o g i c a l r e p r e s e n t a t i o n o f t h e f lo w
migh t be necessa ry . Unfor tuna te ly , t he se mode l s have the d i sadvan tage o f i n t roduc ing
emp i r i ca l pa ram e te r s which then requ i re a ce r t a in degree o f t un in g . Eve n tua l ly , t h i s
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438
makes the numer i ca l mode ] use r -dependan t and the ove ra l l p red ic t ive capab i l i t i e s o f
the code wi l l a lways rema in doub t fu l .
F ina l ly , f rom the examples shown he re i t c an be conc luded tha t by measur ing on ly
the p re ssure and the rema in ing mass i n t he vesse l , no t a l l o f t he occur r ing phenomena
can be iden ti f ied . Th e mass- f lux and th e ven t - l i ne qua l i t y d i sclose som e im po r t a n t
in fo rma t ion wheneve r a de t a i l ed unde rs t and ing o f t he depre ssur i sa t ion p rocesses i s
necessary . This de ta i led understanding seems to be necessary for sca l ing to la rger s ize
un i t s and for an accu ra t e i npu t ( source t e rm ) to p rob lem s o f a tm osp he r i c d i sp e r s ion .
ACKNO WLEDGEMENTS
T he au th or t h an ks M essr s . A.B enuzz i , S .Duf fi eld, G.F ranche l lo , G.Fr i z , H.S taed tke
a n d K .B e l l w h o p r o v i d e d t h e c a l c u l a t i o n s w i t h R E L A P, SA FI R E a n d R E L I E F a n d
con t r ibu ted s ign i f i can t ly t o t he eva lua t ions o f t he p re sen t examples .
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u
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11 Benuzz i A, " SA FI R E Ca lcu la t ion Resu l t s o f t he Vesse l B low dow n B enc hm ark
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19 H e w i t t G .F . , " Ph y s i c a l B e n c h m a r k E x e r c i s es , E x p e r i m e n t a l d a t a s e t s f or ev a l u a
t i on of mo de l l i ng m e th od s " , Ha rwe l l La bor a to r y , Ju n e 1986 .
void f rac t ion
dynamic v i scos i ty (Pa s )
dens i ty (Kg m
- 3
)
surface tension (N m
_ 1
)
S u b / S u p e r s c r i p t
v a p o u r p h a s e
dr i f t quan t i t y
No de be low cur ren t no de
l iquid phase
M a x i m u m v a l u e
0 .4 eqn . [ l l ]
0 . 3 e q n . j l l ]
N o d e a b o v e c u r r e n t n o d e
two phase
A
d
D
dh
f
H
9
J
Re
C/oo
U pool
U
X
N o m e n c l a t u r e
interf ace sl ip coefficient (m
5
K g
- 1
s
- 2
)
d i a m e t e r ( m )
Cont ro l vo lume he igh t (m)
fr ic t ion fac tor (m)
E leva t ion f rom vesse l bo t tom (m)
grav i t a t i ona l acce l e ra t ion (m s
- 2
)
drift flux (m s
_ 1
)
R e y n o l d s n u m b e r
bu bb le r i se ve loc i ty (m s
_ 1
)
bub b le ve loc i ty eq n . [ l l ] (m s
- 1
)
aver age ve loc i ty (m s
_ 1
)
qual i ty
a
p
a
9
J
L
t
M
m
n
U
2p
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