the catalytic combustion of methane over platinum
TRANSCRIPT
THE CATALYTIC COMBUSTION OF METHANE OVER PLATINUM SUPPORTED ON
ALUMINA FIBRES
Chi-wai Lam
B.Sc..(Eng.), M.Sc., D.I.C.
October, 1978
Department of Chemical Engineering and Chemical Technology
Imperial College of Science and Technology
London
A Thesis Submitted for
the Degree of Doctor of Philosophy of the University of London
ABSTRACT
The catalytic combustion of methane over alumina supported
platinum catalysts has been studied. The feasibility of applying
catalysis to energy generation processes has been demonstrated by
oxidizing the fuel in a convective-diffusive type catalytic combus-
tor. The experimental studies covered the measurements of the
combustion kinetics and the performance of the catalytic combustor.
Attention has been focussed on the investigation of the reaction
mechanisms that affect the combustion process. Theoretical models
to describe the performances of the combustor under practical operating
conditions have been developed, which give good agreement with the
experimental results.
The kinetic experiments were carried out using a differential
flow reactor fitted with on-line chromatography. Surface analysis
of catalyst samples was carried out using gas adsorption techniques
and ESCA. An experimental catalytic combustor with embedded
thermocouples was constructed and the performances of the combustor
was studied at different thermal input conditions with methane as
the fuel.
The oxidation of methane on both porous and nonporous alumina
fibre supported platinum catalysts was investigated in detail over
the temperature range of 723 to 923K and at both lean (< 1.0) and
rich (> 2.0) oxygen to methane ratios. The experimental observations
suggested that methane oxidizes on platinum/alumina by two surface
reaction mechanisms, the relative importance of which changes at
temperatures of ca. 813K. Carbonaceous deposition occurs during
methane oxidation as a result of the cracking of methane on the
catalyst surface; this was found to increase with increasing tempera-
ture and decrease with increasing oxygen to methane ratio. The
cracking of methane was shown to be critically enhanced by the low
adsorption strength of oxygen on platinum surface at high temperatures
(above ca. 813K) and by the porous structure of the catalyst. The
production of carbon monoxide was interpreted in terms of the two
reaction mechanisms.
Comparisons between the apparent activation energy of the
oxidation and the desorption energy of oxygen on platinum suggested
that the activation energy is probably dominated by the oxygen-platinum
binding energy. The change in the apparent activation energy above
813K was explained as the effect of thermal compensation, due to the
increased importance of the heat of methane adsorption term at high
temperatures. The thermal instability observed in methane oxidation
was explained by the effect of thermal sensitization originating from
the fast oxidation of hydrogen produced by the dissociative adsorption
of methane, The effects of product inhibition, steam interaction and thermal
sintering were also investigated.
The study on the convective-diffusive type catalytic combustor
using methane as the fuel indicated that, under practical operating
conditions, there is no emission of carbon monoxide or of nitric oxides.
The combustion efficiency has an average value of ca. 95% for the fuel
input conditions studied (0.2 - 0.5 kW). The largest heat transport
component - thermal radiation, was found to be improved as the result
of pushing the hot zone towards the external boundary of the combustor
by increasing the fuel input flowrates.
Theoretical models, based on experimental kinetic data, were
developed to describe the performance of the convective-diffusive cat-
alytic combustor by taking into account heat and mass transport phenomena
occurring inside and at the boundaries of the combustor. As compared
with experimental measurements, the theoretical models successfully pre-
dict the thermal effects which occur during the combustion.
ACKNOWLEDGEMENT
I am grateful for the substantial contributions to this work
by Professor D.L. Trimm, an inspired teacher, enthusiastic researcher
and friend.
I wish to express my appreciation to the following individuals
and organisation :
To Dr. M.H. Stacey of I.C.I. (Mond Division), for his valu-
able discussions, suggestions and assistance in analysing
the catalyst surface as well as in many other ways;
To Professor D.A. Dowden, for his interest and valuable
discussions;
To Dr M.D. Carabine for his assistance at the final stage
of this research;
To my colleagues of the catalysis research laboratory of
the past and present for generating a stimulative and cheer-
ful atmosphere, and to Mr R. Badilla for his advice in using
the apparatus to measure catalyst surface area;
To Imperial Chemical Industries (Mond Division), for the
generous research studentship and financial support on
this research project.
My thanks are also due to my parents for their love and encourage-
ment throughout my education. Finally I have to thank Yau-fu, my wife, without whose support, understanding and prayers this work would not
have been possible.
CONTENTS
CHAPTER
NOMENCLATURE
INTRODUCTION
EXPERIMENTAL
RESULTS
DISCUSSION
CONCLUSIONS
APPENDICES
A-1.
A-2. A-3. A-4. A-5.
Theoretical approach to check the pore diffusion limitation The specific kinetics..
Numerical methods Phys ical properties Computer programs
PAGE
1
5
32
62
162
236
243
243 247 248 255 256
REFERENCES 2.70
1
Nomenclature
parameter in eqs. (A3.15) and (A3.18).
area of the combustor framework (m2)
edge surface area of the combustor (m2)
a radiation emissivity
coefficients of orthogonal polynomials
av external catalyst surface per unit volume of catalyst pad (m 1)
Al - row vector containing internal radiation parameters in Chapter 4
B - parameter in eqs. .(A31,15) and (A3.18)
c molar concentration (ketol m3)
Cpf
-
heat capacity (kJ kmol 1K
1 )
- effective diffusivity for chemical species i (m2sec 1) Deff,i
Di
•
Deff,i'E (m2sec 1 )
Dij binary diffusivity of the ith species in the jth component (m2sec 1)
Dim diffusivity for chemical species i in the mixture (m2sec 1 )
dp catalyst diameter (m)
E activation energy (kJ mol 1 )
F. a radiation distribution function defined as eq. 4.81
Gf - mass flux (kg m-2 sec 1 )
Gm molar flux (kmol m-2 sec-1 )
Grh Grashof number of heat transfer
Grm - Grashof number of mass transfer
g - gravitational acceleration, 9.8 (m sec-2)
H - dimensionless heat transfer group, defined in Table 4.12
h - heat transfer coefficient (kW m-2 K-1 )
AH heat of reaction (kJ kmol 1 )
Af
Aw
ai
2
JD - Chiltern J factor of mass transfer
JH
-
Chiltern J factor of heat transfer
K - dimensionless mass transfer group, defined im Table 4.12
k - lumped solid phase thermoconductivity at the frontal area of the combustor (kW m-1 K -1)
kc solid phase thermoconductivity (kW m-1 K -1)
kf - fluid thermoconductivity (kW m-1 K-1)
ki - kinetic parameters
km - mass transfer coefficient (kmol m'z sec -1)
kr solid phase apparent radiation thermoconductivity (kW m-1 K-1)
L1 thickness of catalyst pad (m)
L2 - dimension of the combustor (m)
M. molecular weight of species i
N number of longitudinal steps or fibre laminations
Nuh Nusselt number of heat transfer
Num Nusselt number of mass transfer
P pressure (atm)
PhX Peclect number of heat transfer in X direction
Pmi - Peclect number of mass transfer for species i in X direction X
Pr - Prandtl number
P(x2) orthogonal polynomial, defined in eq.(A3.6)
Qi - radiant heat flux from ith catalyst lamination (kW m-2)
radiant flux from the combustor to the surrounding (kW m-2)
Re - Reynolds number
Rs - reaction rate (kmol m-2 sec-1)
-rCH4 - reaction rate of methane (kmol kg-1 sec-1)
3
Sc - Schmidt number.
Sh - Sherwood number
St - Stanton number
T - temperature (K)
Tf - fluid phase temperature (K)
Tr - room temperature, 300 (K)
Ts solid phase temperature (K)
U - heat transfer coefficient at the edge of the combustor (kW m-2K-1 )
Wf1 molar fraction of species i in fluid phase
Wi molar fraction of species i in surroundings
Wio - inlet molar fraction of species i
Wsi molar fraction of species i in solid phase
X - dimensionless longitudinal co-ordinate
Y dimensionless lateral co-ordinate
Greek Symbols
a - absorptivity of the fibre lamination
R thermal coefficient of volumetric expansion (K-1 )
y - reflectivity of the fibre lamination
E - force constant in Lennard-Jones potential function
- void fraction
n - effectiveness factor of pore diffusion
e - dimensionless temperature, T/Tr
ei,eff the effective dimensionless temperature of ith fibre lamination
of - fluid viscosity (kg m-1 sec-1 )
✓ - dynamic viscosity (m2 sec-1 )
vi
Pf
pS
pw
- reaction stoichiometry of species i
- fluid density (kg m-3)
- fluid density in surroundings (kg m-3)
fluid density at combustor frontal surface (kg m-3)
4
a - force cons tarkt in Lennard-Jones potential function
Stefan-Boltzmann constant, 1.355x10 -12 (kW m-2 K_4)
transmissivity of the fibre pad
0 - Thiele modulus, defined in Appendix 1
voidage of a single catalyst lamination
Stp collision integral in equation (4.19)
](- molar fraction in Chapter 4
molar percentage in Chapter 3
5
1. Introduction
1.1 General 6
1.1.1 Hydrocarbon oxidation catalysts 6 1.1.2 Catalytic oxidation of hydrocarbons 10 1.1.3 Catalyst supports 15 1.1.4 Catalyst deactivation 15 1.1.5 Modelling of catalytic combustors 17
1.2 The present interests 18
1.2.1 A general survey on methane oxidation 19 1.2.1.1 The gas phase oxidation 1.2.1.2 The effect of homogeneous process on the heterogeneous
catalytic reaction 20 1.2.1.3 The heterogeneous catalytic oxidation 23. 1.2.1.4 Summary of the literature survey 24
1 .2.2 Convective-diffusive type catalyti c combustor 25
1.2.3 The catalytic combustor with premixed air 30
6
1.1. General
In recent years, concern over the problems of air pollution has
led to much scientific research on the modification and improvement of
combustion processes. There are, however, limitations on what can be
achieved by homogeneous combustion. Thus, for example, combustion can
only be carried out within the flammability limits of the fuel, and the
temperature of combustion is always such that nitrogen and oxygen in the
air will combine to produce nitrogen oxides. As a result, interest has
been growing in the concept of catalytic combustion, in which a fuel is
oxidised over a catalyst. Catalytic combustion is efficient, can operate with very lean fuel:air mixtures and the temperature of the
process can be controlled at levels where no direct combination of
nitrogen and oxygen takes place (less than ca. 2000K). Compared with
the ubiquitous flame, the term "catalytic combustion" and "flameless
combustion" are sometimes used interchangeably.
Since the early 1970's, tremendous efforts have been devoted to
catalysis research on auto exhaust emission control (1,2), and the success
of this research has led to the birth of "catalytic muffler". This is
installed in the automotive exhaust system after the engine, in order to
reduce emissions of nitric oxides, carbon monoxide and hydrocarbon (3).
As an extension of this concept, the feasibility of introducing catalyst
into combustion chambers has been widely investigated. The variety of
the applications ranges from domestic heating appliances (4,5) to indust-
rial steam boilers (6) and to automotive and aircraft gas turbine engines
(7,8).
Prior to the successful design of a catalytic combustion system, research is particularly needed to further understanding in the following
areas:
(i) selection of a catalyst that is capable of catalysing
complete oxidation of the fuel and maintaining high
stability under the operating conditions;
(ii) the chemistry of the oxidation process and, in particular,
the chemistry of reactions that could cause deactivation
of the catalyst;
(iii) physical effects that would affect the mass and heat
transport during the operation of the combustor;
(iv) modelling of the chemical and physical phenomena under
practical conditions;
(v) optimal design of the combustor.
This introduction thus aims at providing a background for the
design of a catalytic combustor, including a review of hydrocarbon
combustion catalysis and the modelling of a catalytic combustor. A
literature survey is also given with respect to the oxidation of
methane.
1.1.1. Hydrocarbon oxidation catalysts
Materials found effective as combustion catalysts are, in general,
transition metal oxides and noble metals. One of the most complete
glossaries and guides to the selection of oxidation catalysts was
published in 1946 (9) (Tables 1.1 and 1.2). The initial intention of
the compilation was to review the selective oxidation of hydrocarbon and
the ratings in Tables 1.1 and 1.2 are for the oxidation of hydrocarbons
to some desirable oxygenated hydrocarbons. However, as might be
expected, they are also applicable to combustion or complete oxidation.
It will also be noted that all the catalysts listed are unsupported.
Nevertheless, despite these qualifications, the ratings are consistent with
experience in combustion catalysis (10). A few examples can be added
to this glossary. For example, it has been found that V205 is an
effective hydrocarbon oxidation catalyst (11), and what have been described
as cobalt spinels (12) is another example. These spinels have been
studied for their catalytic activity (13); but there seems to be no
reported use of these materials in combustion processes.
The glossary of catalytic components can be used as a data base for
rough screening of catalysts. Optimization of the catalytic performance
by variations in the preparation,or by specific combinations of several
catalytic components, has been the subject of several studies in the
patent literature. Implementing such optimization requires a knowledge
of the mechanism and kinetics of the reaction, and most of this work has
been directed at partial oxidation; very few studies cover complete
oxidation.
+
GIB
a
TABLE 1.1
Comparative Activity of Some Metals and Oxides
Initial metals and oxides Activity Stability
Platinum +++
Pal 1 adi um ++t-
Manganese +++
Chromic oxide tt Cupric oxidea +
Lead oxide Does not work Nickelous oxide ++ Niobous oxide +
Lanthanic oxide Does not work Molybdic oxide Does not work Yttri c oxi de + Aluminic oxide Does not work Calcium oxide Does not work Magnesium oxide Does not work
a Reduced at high temperature to the inactive form Cu20.
9
TABLE 1.2
Comparative Activity of Binary Oxide Compounds
Initial Oxides Chemical composition of compounds
Activity Stability (usually of the spinel type, with small admixture of oxide)
ZnO + Cr203
ZnO + Cr203
Ni0 + Cr203
Ni0 + Cr203
Mn02+ Cr203
Mn02+ Cr203
Co0 + Cr203
Co0 + Cr203
Hg0 + Cr203
CuO + Cr203
CuO + Cr203
Fe0 + Cr203
Fe0 + Cr203
Mg0 + Cr203
CuO + A1203
Fe0 + A1203
Ni0 + A1203
Mg0 + A1203
ZnO + A1 203
CaO + A1203
Co0 + Fe203
CuO + Fe203
ZnO + Fe203
Mn0 + Fe203
Hg0 + Fe203
Ag20+ Mn02
Cū0 + Mn02
Pb0 + Mn02
BaO + TiO2
Ca0 + TiO2
+ + ZnCr204 + ZnO
++ + ZnCr204
++ + NiCr204 + Ni0
+++ + NKCr204
++ + MnCr204 + Mn0
+++ + MnCr204
++ + CoCr204 + Co0
+++ + CoCr204
++ + HgCr204 + Hg0
++ + CuCr204 + CuO
+++ + CuCr204
++ + FeCr204 + Fe0
+++ + FeCr204
+++ + MgCr204 + Mg0
++ + CuA1204 + CuO
++ + FeAl204 + Fe0
++ + NiA1204 + Ni0
Does not work MgA1204 + Mg0
Does not work -
Does not work - ++ + CoFe204 + Co0 + Fe203
+++ + CuFe204 + CuO + Fe203
+ - ZnFe204 + ZnO + Fe203
+++ + MnFe204 + Mn02+ Fe203
+ HgFe204 + Hg0 + Fe203
++ + nAg20.mMn02
++ + nCoO.MMn02
+ - nPbO.mMn02
Does not work BaTiO3
Does not work CaTiO3
10 1.1.2. Catalytic oxidation of hydrocarbons
Most studies of oxidation reactions have been concerned with the
production of partial oxidation products in useful quantities. Varying
degrees of success have been achieved in this respect, as may be seen
from the general review by Margolis (14), and a more recent review on gas
and liquid phase catalytic oxidation given by Cappelli (15). The ease
with which intermediate products are formed depends on the nature of the
hydrocarbon and on the catalyst used. Unsaturated hydrocarbons may be
oxidized at lower temperatures than saturated hydrocarbons, and the
yields of intermediates produced from the former are usually much greater.
As reported in Table 1.1, platinum and palladium possess the highest activity for complete combustion.
Catalytic oxidation of alkanes (ethane, propane, isobutane, and
butane) was studied by Hiam et.al. (16). They used a platinum filament
as the catalyst and found that the ease of oxidation was ethane < propane:
isobutane . butane. They also concluded that the dissociative adsorption
of the hydrocarbon was the limiting step.
An analysis of complete hydrocarbon oxidation was reported by
Barnard, et.al. (17). They claimed that, for benzene and n-heptane
oxidation over platinum supported silica gel, the rate-controlling step
was the reaction between adsorbed hydrocarbon and adsorbed oxygen.
Cant, et.al. (18) studied the oxidation of propylene and ethylene
over Pt, Pd, Ir, Ru, and Rh supported on silica. In an effort to
interpret their activity data, correlations were presented between the
catalytic activity and the per cent d character of the catalyst and
between the catalytic activity and the atomic radius as shown in Fig. 1.1
and 1.2. More detailed studies designed to establish the nature of inter-
mediates have also been carried out. Oxygen is readily adsorbed on
almost all metals and on many metal oxides (19). Measurements of the
electrical conductivities of some catalysts during their adsorption of
oxygen (20) indicate that negative ions are formed on the surface.
Detailed information has been obtained from desorption measurements and
from studies of the homonuclear oxygen exchange reaction (21, 22) which
show that, in decreasing order of thermal stability, the species 02 , 0
and OZ may all be present on the catalyst surface. In some cases, the
chemisorption of oxygen is accompanied by its dissolution into the bulk
of the catalyst (23).
Pt •
Pd
LOG RATE 12 OLEFIN REACTED,
MOLECULES • SEC" CM" z
II • ETHYLENE OXIDATION
AT 130 'C
• PROPYLENE OXIDATION AT 130 •C
10
Fig. 1.1 Dependence of oxication rate on percentage d character of metal.
I 1 1 44 46 48
? 4-CHARACTER 50
14
13
LOG RATE • 12 OLEFIN REACTED,
MOLECULES SEC-1 CM-2
11
10
Fig. 1.2 . Variation In rate of olefin oxidation with atomic radius of metal.
• ETHYLENE OXIDATION AT 130 'C
• PROPYLENE OXIDATION AT 150 'C
1.32 1.34 1.36
1.38 ATOMIC RADIUS, X
11 •
12
It is clear that oxidation reactions over metals or metal oxides
may involve either adsorbed oxygen or lattice oxygen. It is reasonable
to expect that the oxygen which is least strongly bound to the surface is
that which is most likely to take part in a catalytic reaction, and this
supposition is frequently borne out by experiments (22,24).
A broad investigation of hydrocarbon oxidation catalysts was made
by Morooka and Ozaki (25) by studying the oxidation of propylene over
catalytic components supported on silicon carbide. From their kinetic
data the reaction rate and the order of the reaction with respect to
propylene were correlated with the heat of catalytic oxide formation.
The reaction rate decreases and the order in the hydrocarbon increases
with increasing heat of the metal oxide formation, The authors concluded
that these correlations agree in essence with the work of Sachtler et.al.
(26). The study included two reaction mixtures: (i) L series,
(02)/(C3H6)>1 ( 50:2%), and (ii) H series, (02)/ CC3H6)<1
( 15:15-30°x);
the respective correlations for the reaction at 573K are shown in Figs.
1.3 to 1.6.
Experimental measurements of hydrocarbon adsorption and of
concurrent changes in the electrical conductivity of catalysts show that
the process may or may not involve dissociation of the adsorbate (21).
Non-dissociative adsorption is found to involve the formation of adsorbed
RH+ ions, whereas the dissociative process leads to the formation of
R' and H' groups bound to the surface by largely covalent bonds. The
former process is more usual over metal oxides, and occurs more readily
with unsaturated hydrocarbons than with saturated hydrocarbons. Margolis
has shown (21) that ethane, ethylene and a number of higher hydrocarbons
are adsorbed as RH+ ions both on n-type and p-type catalysts. Hydro-
carbon adsorption on all these catalysts is extremely rapid, and it appears that heats of adsorption decrease as coverage increases. At
higher temperatures, the adsorbed species undergo pyrolysis and/or
oxidation by the surface. Since pyrolysis involves bond fission, it is
possible that the adsorption process becomes dissociative at high
temperatures.
It is generally accepted that saturated hydrocarbons are dis-
sociatively adsorbed on metals (27). At lower temperatures, this
process is more likely to involve the breaking of C-H bonds than of C-C
bonds. Thus two adsorption mechanisms are possible:
- . Pd
• Ag Co . • •
- Cu •Me
Cd • V • Cr
Nie Fe s\ Ci
Tt. 1 I 1
Pt
Cu ti Co
Cd • .Cr
- Ni' F• • •V
I I
.Mn
. C.
Th
Cu
•Ag
Pd
I Pt
V At • C..Y-Cd •
N~•'F. Th •Cr
Mn
Co
1 I 1
-4
-5
-6• LOG V3o0
-7
-8
-0
O 50 100 I50
Fig.1.3 -G HO (k col / O ATOM)
Correlation between the catalytic activity and the heat of forma-ticn .(2Ii4) (L series).
-4
-5 LOG V300-6
—7
-e -9
O 50 100 150 ••51-10 (k col/O ATOM)
Fig• 1.4 Correlation between the catalytic activity and the heat of forma-tion (AHG) (Ii aeries).
0 50 100 ISO -6H0 (k ce1/0 ATOM)
Fig • 1.5 Correlation between the reaction order in propylene (n) and Allo (L series).
I.0
0
-I 0
0.5
n 0
-0.5
O 50 100 ' I50 -AHO ~k Cal/0 ATOM)
Fig. 1.6 Correlation between the reaction order in propylene (n) and AHo at series).
14
RH(g) + 2 * --> R + H * *
RH + H --~ R + H2(g)
At higher temperatures, adsorbed alkyl groups tend to decompose:
(c) CH + 2 * CH + H * 3 **2 *
(d) 2CH C + CH **2 **** 4(g)
where g and * denote the gaseous and adsorbed states respectively.
Unsaturated hydrocarbons tend to be adsorbed by means of it electron
donation to metals as well as to oxides (27). There are, however,
exceptions to this: for example, the adsorption of ethylene on nickel (28)
and on palladium (29) is thought to proceed via the formation of a
1,2-diadsorbed species.
Cullis (30) has reported that ethylene is rapidly and reversibly
adsorbed on a pure silver film; however the process is much slower and
adsorption is much less over the catalyst covered with preadsorbed oxygen.
It appears that not many measurements of this type have been made, but it
is reasonable to anticipate that the hydrocarbon adsorption depends on the
catalyst under the reaction conditions.
Stein et.al (31) has presented some rules for the relative ease
of oxidising hydrocarbons. These general rules are:
Branched chain > straight chain.
Acetylenes > olefins > saturated.
Cn > .... C3>C2>C1
Aliphatic > alicyclic > aromatic.
Because these rules do not account for differences in oxidation
mechanisms over different types of catalysts, their application is con-
sidered in a qualitative sense only.
Evaluating the kinetics of hydrocarbon oxidation over Cu0 catalyst,
Accomazo and Nobe (32) reached the following conclusions, which agree with
Stein's:
(i) Methane is the most difficult hydrocarbon to oxidize, with
acetylene being the least difficult.
(ii) The ease of oxidation increases with carbon number.
(iii) For a given carbon number,, the ease of oxidation increases
with decreasing degree of saturation.
(a)
(b)
1.1.3. Catalyst supports
The role and purpose of the support for the catalytic component in
combustion catalysts have been the subject of some rather unique
technology. As in all heterogeneous catalysis, the support is used to
stabilize the catalytic component, increase the surface area of the
catalyst, and increase the degree of dispersion of the catalyst.
The role of a stabilizer and the increase of the surface area of the
catalyst are most evident with transition metal oxide catalysts. The
role of improved dispersion of the catalytic component is demonstrated
primarily with the noble metal catalysts, where low concentrations of
these expensive components can be used to provide very active catalysts. Solymosi (33) has reviewed the role of the electrical properties of the
support in enhancing the performance of supported catalysts.
There are three principal catalyst configurations commonly used
in catalytic combustors; pellet, monolith, and metallic wire meshes.
Since combustion processes are operated at high temperatures, the
efficiency of the process over pellet catalysts would be affected by
either pore diffusion limitations or by pressure drop across the
combustion chamber. However,monolithic or metallic wire catalysts may
affect the efficiency of the combustor due to decreased surface area, and
explosion may occur due to the low surface to volume ratio of these
configurations.
A new product called "Saffil, Alumina Fibre", was
recently perfected by I.C.I. Mond Division and is something 'of
potential interest in the field of materials which can be used as
supports for catalytic combustion. Two types of alumina Saffil are
manufactured; one has a crystal phase of eta-alumina (porous) while the other has a delta-alumina phase (non-porous). The properties of the
fibres are given in Table 1.3. All the properties which characterize
these Saffil supports, such as high surface area, high voidage (less
pressure impedance), small diameter (less pore diffusion limitation) and
high melting point (over 2200K: maximum working temperature 1673K)
recommend Saffil as a potential support for catalytic combustion.
15 .
1.1.4. Catalyst deactivation
Catalytic deactivation is an area of vital importance in combustion
catalysis. Deactivation can generally be classified as temporary or.
TABLE 1.3
Physical Characteristics of 'Saffil' Fibres*
16
All fibres
Median fibre diameters = 3. um
Fibre lengths > 4. cm
Property Standard
A1 203
HT
A1 203
Surface area, m2/g 150. 2.
Pore volume, ml/g 0.17 0.
Average pore diameter, nm 5.5 0.
True density, g/c.c. 3.0 3.5
Apparent density, g/c.c. 0.096 0.096
Specific heat, J/kg-K
773 - 298K 1025. 1025.
1273 - 298K 1127. 1127.
Thermoconductivity of
fibre blanket, W/m-K 0.048 0.07
Crystal phases eta - A1 203 delta - A1 203
+ mullite
(trace)
Data given by the courtesy of I.C.I.
permanent. Carbon formation due to heavy cracking of hydrocarbon on the•
catalyst active sites could cause a decrease in catalyst activity during
the course of combustion. However, the deactivated catalyst may be.
regenerated by burning the carbonaceous deposit inan Oxidising atmosphere.. Permanent deactivation of supported catalysts can be caused by deposition
of substances such as lead (from leaded fuels) or by sintering or crystal
growth of the catalytic component as a result of its thermal history and/or
oxidation-reduction cycling while in use. The catalytic support can also
lose surface area as a result of thermal and/or hydrothermal (steam)
treatments. If the thermal treatment of the catalyst is severe enough,
a phase transition in supports like alumina can occur.
The effect of the gas atmosphere, at temperatures above 1000K,
on the growth of catalyst particle size was studied by Furhman et.al. with
platinum supported on alumina catalysts (34). The gas atmospheres
investigated include N2, H2, CO, 02, H2O. Their results show that,
under gas phase oxidizing conditions, there is a higher growth rate than
under reducing conditions. They concluded that migration of the metal
atoms is kinetically limited by interphase transfer (reducing conditions)
and by surface diffusion (oxidizing conditions).
1.1.5. Modelling of catalytic combustors
The objective in modelling a catalytic combustor is to predict the
performance of the combustor for a given set of operating variables. A
predictive model must include a sufficient number of chemical and physical
principles to explain all the important observed phenomena, and one must be able to extrapolate into regions where no experimental data extst.
Thus the modelling procedure has two principal stages:'-
(i)
Natural modelling:
(a) Chemical modelling kinetic modelling of the reaction;
(b) physical modelling to describe the transport phenomena occurring in the combustor;
(ii
Mathematical modelling: to describe quantitatively the chemical and physical models.
The modelling stages are inseparably interlinked as it is possible
to generate a natural model of such complexity that its mathematical
representation is either insoluble or impossible.
18
The detailed requirements of a model will vary according to the
application. In general the model may be required to reproduce and
predict one or more of the following features:
(i) Temperature and composition profiles within the combustor.
(ii) The fuel conversion.
(iii) The outlet stream temperature.
(iv) The efficiency of energy transport.
(v) The maximum temperature existing within the combustor.
(vi) The temperature difference between fluid phase and
catalyst particles in the combustor.
All models, however, suffer from the dual (and sometimes mutually exclusive) problems of accuracy and tractability. However, nature has
been provident and some phenomena become unimportant under certain
conditions. For example, film, heat and mass transfer resistance between
the catalyst surface and the fluid phase becomes unimportant as turbulence
develops in the combustor and, when very small catalyst particles are used,
the diffusional limitations within the particle become unimportant.
A detailed description of the theoretical modelling of the
convective-diffusive type combustor is given in Chapter 4.
One factor that did emerge from the modelling was that the model
was very sensitive to the kinetic parameters used and to thermal effects
in the catalyst bed. In response to this sensitivity, careful measurements
of the kinetics of the reaction were undertaken. Time did not allow
detailed measurement of thermal effects in the bed.
1.2. The present interest
The objective of the present study is to demonstrate the feasibility
of applying catalysis to combustor processes and has been divided into
three aspects:-
(i) investigation of the catalytic activity of methane
combustion over platinum supported alumina fibre catalysts;
(ii) measurement of the thermal behaviour of a convective-
diffusive type catalytic combustor using methane as the
fuel and a catalyst as described in (i);
(iii) modelling of the catalytic combustor.
The reasons for the choice of the present system could be
summarized as follows:
19
(i) methane - since this is the most difficult hydrocarbon
to oxidize, an understanding of its combustion
activity would give insight into the activity of
other hydrocarbons.
(ii) platinum - the most active combustion catalyst.
(iii) alumina fibre support - small particle size (less
importance of pore diffusion limitation) and
high void fraction (less pressure impedance)
make it a very suitable support.
convective-diffusive type combustor - this has many
complicated transport phenomena, such as
internal-external thermal radiation, natural
convection effects, axial diffusion, etc.;
modelling of these would give confidence in
the modelling of other types of catalytic
combustor.
1.2.1. A general survey on methane oxidation
This survey is focussed on the kinetics and mechanism which
occur homogeneously and heterogeneously during the catalytic oxidation of
methane.
1.2.1.1. The gas phase oxidation
At sub-atmospheric pressures, the homogeneous oxidation of methane
begins to occur at temperatures above 623K (35). It is a chain reaction,
characterized (36) (in a constant volume system) by an induction period,
followed by a pressure rise stage, during which the reaction rate increases
to a maximum before decreasing again. The major products of the overall
reaction are carbon monoxide, carbon dioxide and water, but small amounts
of formaldehyde, hydrogen peroxide, methanol, hydrogen and ethane may also
be isolated. Formaldehyde is an intermediate under most reaction
conditions (37), but its yield as a percentage of the initial methane
concentration rarely exceeds 3%. The role of hydrogen peroxide depends
much more on the reaction condition (38). Thus it is decomposed by basic
surfaces (e.g. Pb0) and at high temperatures. Carbon monoxide may also
be regarded as an intermediate, the oxidation of which is inhibited both
20
by methane and by formaldehyde (39).
These variations in the behaviour of intermediates are reflected
in the sensitivity of the overall reaction kinetics to experimental
conditions. The trends of observed reaction orders and activation
energies as temperature increases are summarised in Table 1.4.
It has been shown that stoichiometric mixtures of methane and
oxygen react rapidly or even explosively at temperatures above 923K (35).
Table 1.4
General kinetic features of the slow
homogeneous oxidation of methane
Temperature Order in Order in range, K methane oxygen
653-723 2 0.5-1.0
723-823 2-1.5 1.0-1.6
823-923 1.5-0.0 1.6-2.8
Activation energy,. kJ/mole
378
252
168
1.2.1.2. The effect of homogeneous process on the heterogeneous
catalytic reaction
A catalyst of relatively low surface area introduced into a
stoichiometric mixture of methane and oxygen at high temperatures will
provide only a minor alternative route for the homogeneous reaction,
although the surface may serve as a local heat source by which
an explosion can be initiated. Under less severe conditions (for example,
if the reaction mixture contains only a small proportion of methane and
a high surface area catalyst is used) some initiation and propagation steps
may proceed to a certain extent in the gas phase and produce species which
are more readily oxidized at the catalyst surface than in the gas phase.
In addition, recent studies (40) of methane oxidation in the presence of
either silica or alumina surfaces have led to the suggestion of surface
initiated homogeneous reactions. The effect is more significant over
silica surface than over alumina surface, and is only important at
temperatures above ca. 900K. Thus the general effect of these gas-phase
processes will be to increase the apparent rate of the surface reaction.
In view of these effects, if the surface reaction itself is under
investigation, the experimental conditions should be chosen so that the
21
importance of homogeneous processes is negligible. In practice, this
means that the reaction temperature should be kept below 900K.
1.2.1.3. The heterogeneous catalytic oxidation
The main products of the heterogeneous catalytic reaction are
carbon dioxide and water, although small amounts of intermediate products
are formed over some catalysts. The information obtained from the
literature is summarised in Table 1.5.
Stein et.al. (41) have compared the activity of different catalysts
for the complete oxidation of methane. The catalysts which have been
compared include oxides of some of the first-row transition metals as well as palladium, platinum, silver, gold and molybdenum trioxide. Activation
energies of between 67 and 129.6 kJ/mol were measured, and these values
did not vary appreciably with the nature of the support. Pre-exponential
factors were also measured, but are of less interest because the surface
areas of the catalysts were not determined. Comparison of the activities
per weight of the active metal catalysts supported by one type of alumina
indicated the following decreasing order:
Pt>Pd> Cr>Mn >Cu>Ce >Co>Fe>Ni >Ag
The reaction over platinum was first studied in detail by Davies
(42), who measured the heat evolved on the surface of a platinum wire
maintained at the appropriate temperature (473-1173K) in dilute reaction
mixtures. His results indicated that the process involved the reaction
of adsorbed methane with adsorbed oxygen. In a more recent study, using
temperatures between 873 and 1573K, Lintz, et.al. (43) have confirmed
Davies' conclusions with respect to methane oxidation,by showing that the
reaction does not proceed unless the temperature is high enough for methane
to compete effectively with oxygen for adsorption sites. These workers
have also concluded that carbon monoxide, which was formed in increasing
quantities as the temperature was raised, is an intermediate product of the
reaction over this catalyst. At very high temperatures (44) (above ca.
1000K), platinum atoms and surface complexes are vaporised from the
catalyst, so that the mechanism is no longer wholly heterogeneous in
character.
Firth, et.al. (45) studied the catalytic oxidation of methane over
noble metals (Pd, Pt, Rd, Ir) supported on alumina at temperatures below
873K. Their results on complete oxidation indicated that methane may be
adsorbed on two types of active sites, one of which also adsorbs oxygen.
22
TABLE 1.5
Reaction Products of The Heterogeneous Catalytic Oxidation of
Meth ane
Catalyst Support Temperature K
Products Main (trace)
Reference
(a) Metal Catalysts
Platinum 107 Carbon dioxide 46
Water (formic acid)
Pi ati n um Asbes tos 523-873 ditto 47
Platinum 1073 ditto 48
Platinum Asbestos 523-773 ditto 49
Platinum Asbestos 445-973 ditto 50
Platinum Silica gel 473-673 di tto 51
Platinum 423-623 di tto 52
Platinum 473 ditto 53
Palladium Asbestos 523-873 Carbon dioxide 47 Water
Palladium Asbestos 445-973 ditto 50
Palladium Silica gel 473-673 ditto 51'
Palladium Asbestos 473 ditto 54
Palladium Asbestos 723-973 ditto 55
Silver Silica gel 473-673 Carbon dioxide 51 Water (aldehydes )
Silver 773 ditto 56
Copper 773 Carbon dioxide 57 Water (formaldehyde)
Copper Silica gel 473-673 Carbon dioxide 51 Water (acetaldehyde)
Copper Pumice 445-9 73 Carbon dioxide 50 Water
Gol d 423-773 Carbon dioxide 47 Water
Nickel 423-1173 Carbon dioxide 58
(b) Oxide Catalysts
Water, Formaldehyde
Asbestos V205 445-973 Carbon dioxide Water
50
Pumi ce V205 773 ditto 50
Cu0 A sbes tos 523-623 ditto 49, 50, 60
Ni 0 Asbestos 523-773 ditto 49
Ni0 Asbestos 373-623 Carbon dioxide 60
Water, Formaldehyde
23
TABLE 1.5 (Continued)
Catalyst Support Temperature Products
Reference K Main (trace)
Pd0 Asbestos 623-773 Carbon dioxide
49 Water
Ce02 Asbestos 323-773 ditto
49
ZnO Asbestos 623-1273 Carbon dioxide
61 Water, Formaldehyde
Pd0 Asbestos 623-1273 ditto
61
ZnO Asbestos 623-773 Carbon dioxide
49
Water
U & Be - 773-873 Formaldehyde
62 Oxides
(c) Under Conditions for low conversion
Pt(wire) 1023-1123 Hydrogen 63 (hetero-homogeneous mechanism) Carbon monoxide
Cu/CuO 973 ditto 64
Cu/UO2 973 ditto 64
CuMo03 - 973 ditto 64
Pt, pd 973 ditto 65 Au, Ag
24
The activation energies are proportional to the Pauling bond energies
of the oxygen-metal bond. They also reported that the reaction is first
order in methane and zero order in oxygen in the presence of a large excess
of oxygen. No specific reaction rate data were given.
Mezaki and Watson ( 66), in their study of methane oxidation over
platinum supported on alumina, proposed the following mechanism:
CH4(g) + 202(ads.) — ) CO
2 + 2H20
Ahuja and Mathur ( 67) used the initial rate data for the oxid-
ation of methane over palladium to study the reaction mechanism; they
claimed that the most probable mechanism was,
CH4(ads.) + 0
2(ads.)—> CO
2(ads.) + H2O
Trimm, et.al. (68) studied the catalytic activities of palladium
and palladium oxide catalysts below ca. 753K. The complete oxidation of
methane was found to be half order in methane and zero order in oxygen.
A mechanism was proposed for the complete oxidation in which the rate-
determining step appears to be a surface reaction between oxide ions and
dissociatively adsorbed linearly-bound methylene radicals. Weak inhibit-
ing effects due to addition of the reaction products is generally reported
(68,69).
The reaction over silver films was studied at 853K by Enikolopyan,
et.al.( 70). It was found that although, under their experimental cond-
itions the homogeneous reaction was faster than the heterogeneous process,
the latter occurred exclusively in the presence of the catalyst. Further-
more, the small yield (ca.3%) of formaldehyde from the homogeneous react-
ion was completely eliminated by the catalyst.
1.2.1.4. Summary of the literature survey
It has been shown that, while intermediate products are not formed
in large quantities from the heterogeneous oxidation of methane, those that
are produced tend to be associated with particular catalysts. It is there-
fore quite possible that the complete oxidation may proceed by a number of
alternative routes, one of which involves the direct conversion of methane
to carbon dioxide, while others involve the formation of intermediate pro-
ducts which may be either desorbed or oxidized further. Over all the
heterogeneous catalysts so far investigated, reaction routes involving the
25
formation of intermediates are comparatively unimportant and appear to
be of least importance over platinum.
Since alternative mechanisms would perhaps involve different
forms of adsorbed methane, the observed overall kinetics would be
expected to be a complex function of the various processes. It seems
advisable, in the first instance, to determine the kinetic features of
the reaction. The present work is therefore partly concerned with
kinetic measurements of the oxidation of methane over platinum/alumina
catalysts. As has been shown, the mechanism of the oxidation of methane
over platinum catalyst has not been clearly established. As a result,
it was also intended to make further investigations (by means of
classical kinetic measurements) both of the oxidation of methane itself
and of the further oxidation of possible reaction intermediates.
1.2.2. Convective-diffusive type catalytic combustor
This type of catalytic combustor is in widespread use for domestic
heating purposes, burning either liquid petroleum gas (LPG) or natural
gas (NG) ( 5 ). The standard configuration of the device is shown
schematically in Fig.1.7. The catalyst (usually platinum) is commonly
supported on fibrous materials, such as ceramic wool, asbestos wool,
fibreglass or alumina fibre (Saffil). The catalyst pad is initially
preheated to a threshold temperature (usually ca. 600K) either by an
electric heating element (which is buried in the pad) or by a temporary
pilot flame. If the latter technique is used, an unsteady flame can
be seen to flicker across the surface of the pad. Usually,within about
one or two minutes, the flame is quenched by the catalyst and catalytic
combustion takes over.
The catalytic combustion occurs in a convective-diffusive mode,
where the fuel passes through the catalyst pad by forced convection and
air is supplied from the ambient by molecular diffusion. Under suitable
operating conditions, the combustion process is self-sustaining and the
energy generated is transported to the surroundings by thermal radiation,
convection and conduction loss through the metal framework of the combustor,
with radiation being the highest transport component ( 5 ).
Metal Casing
26
Gas Distributor
Fi brous Catalyst Pad
E--- Fuel Inlet
Electric Heating Element
—Fuel Inlet
Pilot Light
Fig. 1.7 Standard Configuration of the Convective-
Diffusive Catalytic Combustor
27
Two main advantages of this type of device emerge from the
literature ( 4 , 5 , 71 ,72):-
(i) The shape of the combustor can be constructed so that the
pattern of heat transfer is adjustable to suit the application.
(ii) Low emissions of carbon monoxide (less than 10 ppm) and nitric
oxides (less than 0.1 ppm) are observed.
The main disadvantage of the combustor unit is the slippage of
unburnt fuel through the catalyst pad: this effect is more severe with
methane. In assessing the practical importance of the methane slippage,
some orientative calculations are useful. In a room (3x3x3 m3) with poor
ventilation and using an effective thermal load per room volume of 0.06 kW/m3
(which corresponds to a usual value for domestic heating), an average
conversion of the fuel of less than 50% results in the build-up of dangerous
concentration levels of methane (the lower limit of inflammability for methane
in air is approximately 4%) within about 15 hrs.
The efficiency of the combustion is reported ( 4 , 5 ) to be dependent
orifi the choice of the catalyst support. Table 1.6, gives the difference in
maximum methane combustion efficiency over various support materials, all of
which were impregnated with. platinum. It is seen that fibreglass blanket
and alumina Saffil blanket are both efficient catalyst supports for methane
combustion. Because alumina Saffil has a maximum working temperature of
1673K, this support would seem to be most suitable. The influence of
catalyst support on LPG fuels would be expected to be similar to that on
methane, although the combustion efficiency of LPG is somewhat higher.
The combustion efficiency is also reported to be dependent on the
fuel input flowrate ( 4 , 5 ). Fig. 1.8 shows this effect with catalytic
combustors constructed from either fibreglass or alumina Saffil supports,
and using methane as the fuel. It is seen that there exists an optimum
fuel input at which a maximum combustion efficiency can be attained. The
lower flowrate region corresponds to a non-sustaining or low temperature
operation. Higher flowrates result in lower reaction contact times and
decrease combustion efficiencies. Tests at the same thermal load using
propane or butane give rise to a higher combustion efficiency than methane
(72). This higher combustion efficiency is due to the fact that the same
thermal load is reached with a lower fuel flowrate than with methane; as a
consequence, diffusion of oxygen into the catalyst pad is favoured and a
longer reaction contact time is obtained.
TABLE 1.6
Pad material Optimum methane
input, kW/m2
Maximum methane
combustion eff-
iciency, %
Reference'
Tightly packed
asbestos wool
16.0 74.0 5
Ceramic wool
blanket
28.0 86.5 5
Fibreglass
blanket
21.0 95.5
Alumina fibre
blanket (saffil)
23.2 95.5
28
50 40 5 10 20 30
(kW/m2 ) Heat Input
29
In summing up, the fuel slippage through the combustor and the combustion efficiency depends on the following:
(i) support material;
(ii) fuel flowrate;
(iii) oxygen diffusion from ambient atmosphere;
(iv) type of fuel
1.2.3. The catalytic combustor with premixed air
The problem of fuel slippage can be overcome by premixing air or
oxygen with the fuel before the inlet to the combustor. However some less
satisfactory aspects should be considered in connection with this operation
(72) :
(i) For a given power requirement, the fluid flowrate is increased
by the premixed air. As a result, a large part of the energy
released is transferred by convection rather by thermal radiation
which is, in general, preferred for industrial purposes.
The combustion takes place at the inlet face of the combustor.
Owing to the poor thermal conductivity of the support, the
internal temperature of the combustor increases. For the highest
thermal loads, the internal temperature would rise to values
above 1000K, damaging the combustor and probably initiating
homogeneous combustion.
(iii) As a consequence of the above thermal effect, a notable increase
of carbon monoxide content in the flue gases was reported ( 72 ).
An emission of 1000ppm of carbon monoxide was recorded, whereas -
with the operation in which air is supplied by diffusion - the emission was practically negligible.
(iv) An air pumping device and a fuel-air mixer are needed in order
to obtain the required air to fuel ratio.
(v) Adequate precautions must be taken to avoid the risk of explosion
due to ignition of the fuel-air mixture.
As a result of these arguments the diffusive combustor has been more
widely used than the premixed combustor.
31
In the present study, alumina fibre (Saffil) has been used as the
support for platinum in a convective-diffusive type catalytic combustor.
Methane was chosen as the fuel, since this would be expected to give the
minimum combustion efficiency of any hydrocarbon. The study has been
focussed on the dependence of the combustion efficiency on the fuel input
flowrate and on oxygen diffusion from the ambient atmosphere. Experimental
measurements as well as theoretical modelling have been carried out with
the system.
2.
2.1
2.2
Experimental
33
33
Introduction
Materials
2.3 Catalyst preparation 33
2.4 Sample characterisation 36
2.5 Studies of catalytic activity 38 2.5.1 The flow control unit
2.5.2 The microreactor 40 2.5.3 The furnace and temperature control 40 2.5.4 The analysis system 42 2.5.4.1 The chromatographic columns 42 2.5.4.2 GLC calibrations 45 2.5.5 Procedure and experimental techniques 45
2.6 Testing of the catalytic combustor 47 2.6.1 The combustor 47 2.6.2 Temperature measurements 50 2.6.2.1 Thermocouple welding and fixing 52 2.6.2.2 Thermocouple calibration 52 2.6.2.3 Radiant flux measurement 52 2.6.3 Procedure and variables studied 57
Key to figures 59
32
2.1 Introduction
In the present research programme, two main experimental systems
were set up.
A flow system involving a micro-reactor unit was used to study
the activity of platinum/alumina fibre catalysts for the oxidation of
methane and the kineticsof the processes. Included in the system were
means to measure temperature, pressure and to record signals from the
on-line chromatographic detector.
A catalytic combustor unit was constructed and tested, in which temperature profiles were measured by embedded thermocouples on line
with a multi-channel temperature recorder. An infra-red pyrometer was
used to detect the radiant energy flux from the combustor. Gas samples
at the back and front surfaces were extracted and analysed by chromato-
graphy. A gravimetric method was applied to determine the overall and
metallic surface areas of the catalysts.
2.2 Materials
The type,purity, use and suppliers of all chemicals used through-
out the present work are listed in Table 2.1.
In order to remove possible moisture, all the gases were directed
through columns of silica gel before entering the system.
2.3 Catalyst Preparation
The techniques and information for platinum impregnation on the
alumina fibres were kindly provided by I.C.I.(Mond Division).
Impregnation was carried out using a flow system (Fig.2.1) in
which a solution of chloroplatinic acid in ethanol was circulated and
sprayed over the fibre pad. The procedure continued with several rever-
sals of the fibre pad until the solution turned from yellow to colour-
less. This normally took about 30 minutes. The fibre was allowed to
drain by gentle rolling with a heavy bottle to remove surplus alcohol.
The partly drained fibre was allowed to dry in air and in an oven at
363K (nitrogen atmosphere). The dried pad was calcined under nitrogen
33
fibre Pad
CP
Fl g. 2.1. Apparatus for Catalyst Impregnation
35
TABLE 2.1
Purity, Use and Supplier of the Material Used.
Chemicals Purity (%)
or Grade
Use Supplier
Nitrogen >99.9 diluent B.O.C.
Oxygen >99.9 reactant B.O.C.
Methane c.p. reactant B.O.C.
Air catalyst activation B.O.C.
Hydrogen >99.9 Carrier, reactant B.O.C.
Carbon Monoxide 99.8 reactant B.O.C.
Carbon dioxide >99.9 reactant B.O.C.
Formaldehyde identification B.D.H.
Silica gel Column packing Phase Separation,Ltd
Poropak R Column packing Phase Separation,Ltd
Molecular Column packing Phase Separation,Ltd
Sieve, 13x
Alumina fibres Catalyst support I.C.I.
Chloroplātinic acid Catalyst preparation Johnson Matthey
36
in a tubular reactor controlled at 773K for two hours and then under
hydrogen for another two hours at the same temperature.
2.4 Sample Characterisation
Overall surface areas of the catalysts were determined by the
B.E.T. nitrogen adsorption procedure ( 73). The adsorption experiment
was performed in a vacuum microbalance system as shown in Fig.2.2.
A weighed amount of catalyst sample was placed in a silica basket
and degassed at 573K until no further weight loss was detected. The
sample was then isolated from the vacuum pump and cooled at 77K by
liquid nitrogen.Nitrogen was gradually admitted into the system at
increasing pressures and the adsorption equilbrium at each nitrogen
pressure was attained and measured after 5 to 10 minutes.
Pore size distributions were determined using the Pierce treat-
ment( 73). Total pore volume was calculated by applying the Gurvitsch
rule. After the saturation pressure was reached, the desorption isotherm
was obtained by careful partial evacuation of the system.
Carbon monoxide adsorption was used to determine the metallic
surface area in the same gravimetric system. During the experiment the
temperature of the sample was maintained at 195K by a bath containing
a mixture of solid carbon dioxide and methanol. After the saturation
pressure was reached the system was evacuated carefully until no further
loss of weight was detected. The chemically adsorbed amount of carbon
monoxide was then obtained by its final weight after desorption. The
metallic surface area was calculated using the adsorption stoichiometry
of 0.76 (74 ), and the value of 1.25 x 1019 atoms/m2 for the number of
surface atoms per unit surface area of platinum was adopted (75).
Total acidity was obtained by pyridine adsorption using the method
described in reference ( 76 ).
Buoyancy effects at 77K and 195K were assessed by measuring the
weight variation when increasing pressures of nitrogen were admitted
into the system. The corrections were incorporated in the calculations.
CO
MC HMB
PY
<t GS
C
VM
B
TB- CS
MDP
CMP_.._. _
Fig. 2.2 Adsorption Apparatus
CT
2.5 Studies of Catalytic Activity
The catalytic activity of platinum/alumina fibre catalysts for
methane oxidation as well as the kinetics of the process were studied
in this system. The water-gas shift reaction and the methane-steam
reaction were also studied.
The system, represented diagrammatically in Fig.2.3, was designed
and constructed in such a way as to incorporate the flow control,react-
ion and analysis Units.
2.5.1 The flow control unit
The unit is shown in part of Fig.2.3. Gases were supplied from
cylinders, through two-stage pressure regulators to the flow board via
silica gel columns. The flow board consisted of a series of rotameters
(calibrated for each individual gas against soap bubble meters), fine
control needle valves (Edwards model LB2B and Hoke 1300 Series) and open-
ended mercury manometers. A constant flow and reactant mixture were
always obtained by maintaining the readings of the manometers as well.
as those of the rotameters.
Steam was generated in a system consisting of two 500 ml wash-
bottles which were connected in series. The washbottles (Sinta glass)
were fitted with flat sintered glass plates and were immersed in a water
bath which was kept at constant temperature by means of a thermostirrer
(Gallenkamp 2). The temperature was controlled within + 1K over the
whole bath volume. A nitrogen stream, bubbling through water in the
bottles, picked up the vapour and carried it in heated lines to the gas
mixer before going into the reactor. The sintered discs in the bottles
were covered with glass spheres, 5mm in diameter, to minimise flow
fluctuations. The relative amounts of water fed into the reactor could
be controlled by varying either the flow of nitrogen or the temperature
of the water bath.
After passing through the mixer (FT2), the flow was diverted
into two streams. One was admitted into the reactor while the other
was bypassed through a condenser at 273K. The flowrates of the bypassing
stream as well as the reactor exit stream were measured by the bubble
38
CO or CO21
* VENT
WT FT1
t BM
WT
FT2
SSB
MR
VENT
LT
CG
SV BM
VENT
WB
w
Fig.2.3 Apparatus for Catalytic Activity Studies
40
meters. The relative diversion of these two streams was . controlled
by the stainless steel needle valve,NV5. The inlet concentration of
steam could be determined by the weight of water condensation in the
water trap, WT in a fixed time interval. The reactor inlet pressure
was measured by the pressure manometer in which liquid-paraffin oil
with a specific gravity of 0.87 was used.
All the heated lines in the system were either in glass or in
stainless steel. Asbestos paper was wrapped around the lines in order
to have an even temperature distribution and to isolate the metal part
from the nichrome wire. This wire was sheathed in glass cloth tubing
and electrically heated to a temperature of 403-413K by voltage Variacs
The lines were externally insulated with asbestos ropes.
2.5.2 The microreactor
The silica tubular reactor used for the present studies is repre-
sented in Fig.2.4. On the porous sinter disc (porosity "0"), the cat-
alyst fibres were chopped and dispersed evenly among 60 cylindrical
silica pellets in order to establish an isothermal reaction condition.
A thermocouple-well extended down at the centre of the reactor with
the end penetrating into the catalyst bed. The gas space after the
sinter was minimised. In order to detect possible homogeneous reactions
occurringin the gas space, another thermocouple-well was placed in this
gas space to measure any rise in temperature due to homogeneous reaction.
Chromel-alumelthermocouple wires were used,and the temperatures in and
after the catalyst bed were recorded by potentiometers.
The reactor was connected to the gas line with 4mm I.D. ball
joints (S13, Jencons) and mounted in a furnace which was thermally
controlled.
2.5.3 The furnace and temperature control
The furnace was made by winding about 11 metres of nichrome wire
(resistivity 2.77 Wm) around a ceramic tube of size 2.5 cm I.D. and
30 cm long. Since heat loss at both ends was significant, the wind-
ing was made in such a way as to have the spirals closer to each other.
at both ends of the tube. The spirals were fixed in position by
ceramic cement plastering. The leads were sheathed with ceramic rings.
41
2cm
0.3cm
ball joint
cup joint
thermocouple well
porous sinta
I cq
E Fig. 2.4 The Microreactor
42
The tube was then wrapped with asbestos rope and placed inside a box
made of pyrite slabs (23 x 23 x 30 cm3) which was screwed on a handi-
angle framework. The interior space was filled with vermiculite.
The furnace was capable of attaining temperatures up to 1273K. The
temperature was controlled to + 0.5K by a Eurotherm series 070 PID
controller using a chromel-alumel thermocouple as a sensing probe.
This thermocouple was placed in the furnace tube at the same depth as
the catalyst bed. The temperatures monitored by the thermocouples
inside the reactor were sensed by the potentiometers (Croydon Precision
Instruments Type P6). After compensation for the cold junction, the
instruments gave direct readings of temperatures.
The temperature profile along the axis of the furnace at a
temperature setting of 793K is shown in Fig. 2.5, from which it can be
seen that a constant temperature zone (+ 1K) exists over a length of
20 cm of furnace. The reactor was arranged in such a way that the
catalyst bed was always located in that region.
2.5.4. The analysis unit
The analysis of reactants and products was carried out using
on-line gas chromatography. All the lines, the 6-port gas sampling
value and loop as well as the injection port were heated electrically.
The unit was set up to be capable of analysis of gas samples contain-
ing N2, 02, CH4, CO, CO2, H2O and HCHO.
2.5.4.1. The katharometer chromatograph
The chromatographic unit, as shown in Fig 2.6, consisted of a
microkatharometer detector (Servomex MK158) connected with two parallel
columns. For .separation of 02, N2, CH4 and CO, a stainless steel
tubing column ( mm OD, 5.5 m long) filled with Molecular Sieve 13X
(60-80 mesh) was used. The other column, made of the same stainless
steel tubing of 6 m length, was filled with Porapak R (80-100 mesh) to
separate CO2 at 303K, H2O and HCHO at 423K.
The molecular sieve column was immersed in a water bath main-
tained at 293K, while the microkatharometer as well as the Porapak
column were placed inside an air stirred oven (Phase Separation,
chromatograph model LC2) which controlled the temperature within
+ 0.5K. The katharometer was operated at a constant voltage of 6
volts using a hydrogen flow rate of 0.3 cm3 (STP)/sec and its signal
813
803
793
783
a)
V. 773
F ►—a' 763
753
743
733 20 25 30
Depth (cm)
Fig.2.5 Axia( Temperature Prof ite of the Furnace
0 15 10
SG
CG
Fig. 2.6 GLC System
45
was amplified using a Servomex microkatharometer bridge control unit:
the peak area was integrated and recorded using a Vitatron UR 402M
recorder.
In order to have a constant activity for each column, the
columns were frequently reactivated by beina put in an oven at 473K and
passed through nitrogen for a period of time (Molecular sieve column:
48 hrs; Porapak column: 2 hrs).
2.5.4.2. GLC calibration
Calibration of individual gases and liquids was carried out by
injecting a known amount of the gas or liquid onto the chromatograph
using 1 ml disposable Gillette gas-tight syringe and 1pl, 5ul SGE
syringes respectively. When smaller volumes of substance were
required than could be delivered accurately by these syringes, a
mixture of known composition of gas/air or liquid/acetone was prepared
and samples were injected. In order to avoid the non-linear extra-
polation by changing the attenuation of the katharometer control unit,
it was necessary to keep a fixed value of attenuation for an individual
substance whenever its quantitative analysis was required. Calibra-
tion curves were hence obtained from plots of peak area against a known
volume (ml) of substance injected; the peak area was in terms of the
number of counts read off the integrator and corrected for base-
line counts. In the ranges used, all the curves were linear, having
calibration factors equal to the values of the slopes of the curves.
The factors were checked and updated before experimental runs were
begun. However, it was found that these factors changed slightly
after the separation columns were used for a long period. A typical
set of calibration factors is shown in Table 2.2.
2.5.5. Procedure and experimental techniques
A weighed sample of catalyst (normally 0.02-0.06 gm) was chopped
and dispersed in 60 (2 mm x 3 mm) cylindrical silica pellets inside the
reactor. In order to attain good distribution of gas and to preheat
the reaction mixture, a layer of the silica pellets was placed above
the catalyst sample. The system was flushed with nitrogen and the
temperature of the furnace was raised. The catalyst was calcined at
823K with nitrogen for two hours and then reduced with hydrogen at the
same temperature for three hours. Nitrogen was again flushed through
the system, and the temperature was adjusted to the reaction temperature.
TABLE 2.2
Calibration factors and retention time for the GLC analysis
Substance column column
temperature
K
retention
time (min)
attenuation calibration factor
(ml (STP)/counts)
02 molecular sieve 293 0:40 80 3.225 x 10-3
N2 molecular sieve 293 1:10 80 2.965 x 10-3
CH4 molecular sieve 293 1:45 80 3.342 x 10-3
CO molecular sieve 293 2:50 10 2.821 x 10-4
CO2 poropak R 303 2:10 40 1.128 x 10-3
HCHO poropak R 423 1:35 8 1.692 x 10-4
•
H2O poropak R 423 2:15 8 _4
1.895 x 10
47
The reactants were admitted and the reaction started. After steady
state was reached (usually 5-10 minutes as checked by the reaction
temperature) samples were taken at the inlet and outlet of the reactor
for chromatographic analysis. Liquid samples were trapped by the
condenser immersed in an ice bath.
When the concentration of one reactant was varied with the
others remaining constant, the technique was to adjust the inlet
flowrate of the diluent, N2 in order to retain the same reactor inlet
pressure.
When working with steam, the technique used to admit the
reactants was as follows:
The water bath was set at fixed temperatures and the line
heating Variacs were switched on. The carrier gas was then allowed
to bubble through the pick-up system at a fixed flowrate. After
steady pick-up condition was reached, the mixture was admitted to the
inlet line by mixing with the other reactants at the second stage
mixer (FT2, Fig. 2.3). The concentration of steam at the reactor inlet
was measured by its weight condensed in a time interval inside the
condenser at the diverted stream, as shown in Fig. 2.3.
When the run was finished, the reactants were switched off and
the system was flushed with nitrogen.
2.6. Testing of The Catalytic Combustor
The purpose of constructing and testing the catalytic combustor
was to investigate the feasibility of performing a self-sustaining
catalytic combustion of methane in a domestic type appliance, and to
provide adequate information to compare with the results of the
theoretical modelling.
A line diagram of the whole system is represented in Fig. 2.7.
2.6.1. The combustor
The metal framework of the combustor was made of mild steel,
having dimensions as shown in Fig. 2.8. The back casing of the combustor
contained an S-type double-inlet perforated gas distributor; the flowrate of the inlets were controlled independently by two needle valves (Edwards
High Vacuum Ltd.). The distributor was fixed at a position 1 cm away
from the back wall of the casing, with the holes facing the back. In order
to have better gas distribution, the gas coming from the distributor
impinged on the back wall of the casing and bounced through a layer of
STC
GSP i j_ ._Lt. o CC
C} IP
BM
MCTR
0 0 RM
FT
N2
Fig.2.7 The Catalytic Combustor Testing Unit
Gas Distributor (with holes facing at the back )
Fig.2.8 Framework of The. Combustor
50
pure standard alumina fibre before reaching the active catalyst pad.
For initial heating up purposes, an electrical heating element
was buried inside the pure alumina fibre. The element was made by wind-
ing 30 ohms of nichrome wire (2.77 n/m) around five ceramic rods (4:mm OD.,
14 cmclong); the wire was covered by alumina cement. The rods were then
placed inside the alumina fibre so as to span the whole combustor surface
with each rod equidistant from each other. A Eurotherm (series 070) PID
controller was used to control the temperature of the preheating stage
with a sensing thermocouple (chromel-alumel) in the gas gap before the
active catalyst pad. A movable sampling probe, made of 0.8:mm 00 stain-
less steel tubing, was placed in the gas gap in order to extract samples
at the back surface of the catalyst layer for chromatographic analysis.
The catalyst pad was placed in between two stainless steel gauzes
of grid size 5 crosquare, and was held in position by wing screw nuts in
the metal framework. Twelve nuts were used in order to avoid deformation
due to thermal expansion of the metal-work during combustion. In order
to prevent excess compression of the catalyst pad, very thick, pure alumina
fibre was cut into strips. These acted as a gasket through which thermo-
couple leads were directed out and connected to the multi-channel tempera-
ture recorder. The combustor was clamped vertically during the experi-
mental testing.
2.6.2 Temperature measurements
Temperature profiles of the catalytic combustor were measured by
networks of thermocouples which were embedded at various longitudinal
and diagonal positions of the catalyst pad. The temperature readings were
recorded by a multi-channel temperature recorder (Philips, PM8235). The
instrument was able to record temperature readings based on the E.M.F. of Iron-Constantan thermocouple. In the present experiment, chromel-alumel ther-
mocouples were used; calibration of the recorder readings was carried out
using a potentiometer (Croyden Precision Instrument Type P6), as shown
in Fig. 2.9.
773
U,
c
Ū 673
a) ti c 0
a) U) 0 m
ā~ 573
0 U a)
.0
ao
d L
N 473
2 Fig.2.9 Temperature Measurement Calibration
TICK) Measured by 1 Gatovometer 673 773 873 973 273
473 573
2.6.2.1. Thermocouple welding and fixing
Detailed descriptions of the various techniques for thermocouple
welding have been reported by Martz ( 77) and by Corrie ( 78). In the
present work, the technique described by Corrie was adopted. A multiple
junction network was used for the thermocouple assembly with the positive
(chromel) wire acting as a common central wire, and four negative (alumel)
connections welded perpendicular to this. This is represented diagram-
matically in Fig. 2.10. The networks were then placed in a diagonal posit-
ion between layers of the catalytic pad. The sandwiched layers were
finally fixed in position as described in Section 2.6.1.
In the present study, four networks of thermocouples were used.
Two of these were at the back and front surfaces of the catalyst pad and
two were in the pad. The diagonal distances of each junction on an in-
dividual network, with respect to the top right corner position of the
combustor, are given in Table 2.3. The longitudinal distances of each
network were determined by the thickness of the catalyst pad layers.
The thickness of each layer was measured by a thickness milli-gauge meter
(performed atI.C.I.) and each layer was laminated in order to obtain
a uniform thickness. In Table 2.4, the longitudinal distances of the
thermocouple networks are given.
2.6.2.2. The thermocouple calibrations
The junctions of the thermocouple network were calibrated against
a standard chromel-alumel thermocouple using an air furnace. A typical
calibration curve for one junction is shown in Fig. 2.11.
2.6.2.3. Radiant flux measurement
The energy transported, due to radiation from the catalytic combustor,
was measured by an infra-red pyrometer (Land Pyrometer, Type ORF 35/10/6).
The instrument has a working range of target temperatures 273K to 1373K
with the output signal in terms of millivolts. The calibration data were
given by the manufacturer and based on a black body emission. In Table
2.4, the calibration data for black body temperatures versus the pyrometer
output voltages are given. The radiant flux could be calculated by the
Stefan-Boltzmann law,
52
Chrome l
Fig. 2.10 Thermocouple Network
TABLE 2.3
Diagonal positions 6f'the'netw6rk'juntti6ns
Junction no. distance, cm
1 5.4
2 9.9
3 14.0 (centre)
4 27.0
5 32.5
TABLE 2.4
Longitudinal position of the'network
network
A
B
C
D
distance, mm
o 3.0
6.5
10.4
54
\'
L
° 773 -v c ° r.+
673
° ° cr 573
Tem
pe
ratu
re
Ther
moc
oup
le
373 473 573 673 773 873
973
Temperature Read by Thermocouple Junction NO A3 ( K )
TABLE 2.4
Calibration Table for Pyrometer Output The open circuit emf is given for a target emissivity of 1.0
K 0 10 20 30 40 50 60 70 80 90 100
MILLIVOLTS
273 0.000 0.002 0.006 0.010 0.014 0.019 0.025 0.032 0.039 0.048 0.058 373 0.058 0.069 0.081 0.094 0.108 0.123 0.140 0.160 0.181 0.204 0.230 473 0.230 0.258 0.287 0.318 0.351 0.387 0.426 0.469 0.512 0.556 0.602 573 0.602 0.652 0.706 0.763 0.824 0.889 0.957 1.030 1.106 1.187 1.271 673 1.271 1.360 1.453 1.551 1.654 1.762 1.876 1.994 2.117 2.246 2.380 773 2.380 2.520 2.665 2.816 2.973 3.137 3.307 3.483 3.665 3.854 4.050 873 4.050 4.260 4.470 4.690 4.910 5.150 5.390 5.640 5.900 6.170 6.440 973 6.440 6.730 7.020 7.330 7.640 7.960 8.290 8.630 8.980 9.330 9.700
1073 9.700 10.08 10.47 10.87 11.28 11.70 12.14 12.59 13.04 13.51 13.99 1173 13.99 14.48 14.98 15.49 16.01 16.55 17.10 17.66 18.23 18.82 19.42 1273 19.42 20.03 20.66 21.31 21.96 22.64 23.32 24.02 24.74 25.47 26.22 1373 26.22 26.96 27.71 28.48 29.26 30.05 30.86 31.68 32.51 33.35 34.21
Qr a.T44 (2.1)
57
where Qr : radiant fl ux,kWm 2.
Tb : black body temperature in K;
a : the Stefan-Boltzmann constant, 5.669 x 10-11 kWm-2K-4,
The average radiant flux from the catalytic combustor was obtained
by integrating the local radiant flux emitted from the surface element over
the entire surface:
r (2.2)
where the the average radiant flux, kWm-2;
Qr(A): local radian& flux from a surface element having an ' area A, kWm ;
Ah: the entire combustor surface area, m2.
Equation 2.2 could be approximated by
E Qr(Ai) *Ai r
E Ai
where Ai: the area of the ith surface element,m2;
Qr(A.): the radiant flux emitted by the ith surface element,
2 kWm .
2.6.3. Procedure and the variables studied
Before admitting the reactant stream, the catalytic fibre pad was
heated up by a hot flowing stream of nitrogen, heated by passage
through the electrically heated alumina fibre layer. When the temperature
of the catalyst pad reached 773K, the reactant stream was put on line and
the electrical heating element was switched off. The temperature profiles
were then recorded by the multi-channel temperature recorder.
In this experiment, the investigations were focused on the steady
58
State temperature distributions inside the combustor as well as the
combustion efficiencies versus the fuel input powers. Gas samples were
taken at the back and frontal surfaces for chromatographic analysis.
The sampling rate was always less than 0.5% of the gas through-put.
Key to figures
Figure 2.1
CA - chloroplatinic acid solution
CP circulating pump
PF. - perforated funnel
S spray
Figure 2.2
B - barometer
CS - catalyst sample
CT condensation trap
GS gas supply
M - manometer
MB - matching box
MC - microbalance control
MDP mercury diffusion pump
MP - mechanical pump
PY pyridine
R - recorder
TB thermo-bath
VG - vacuum gauge
VM vacuum microbalance
-- - double way taps
°•-- - electric lines
gas lines
single way tap
Figure 2.3
BM bubble meter
CG - carrier gas
F - furnace
FT flame trap
GPC gas purification column
GR gas regulator
LT liquid trap
M manometer
MR microreactor
NV needle valve
59
(continued)
RM rotameter
SSB - steam supply bubbler
SV sample valve
WB - water bath
WT - water trap
WTC - water temperature controller
-{- double way tap
Q - sample injection point
Figure 2.6
BM - bubble.-meter
CG carrier gas
CSV - column selection valve
DC - detecting cell
GR - gas regulator
M - manometer
MK - microkatharometer
MKC microkatharometer controlling unit
MS molecular seive column
PR porapak R column
R - recorder
RC reference cell
RM - rotameter
SG - sample gas
SL sample loop
SV sample valve
-~- - double way tap
Figure 2.7
BM bubble-meter
CC - catalytic combustor
FT - flame trap
GPC - gas purification column
GR - gas regulator
GSP - gas sampling probe
60
(continued)
IP - Infra-red pyrometer
M - manometer
MCTR - multi-channel temperature recorder
R - recorder
RM - rotameter
STC start-up temperature controller
- double way taps
—•--- - electric lines
gas lines
0 - needle valves
thermocouple leads
61
62
3. Results
3.1 Definitions
64
3.2 Preliminary Tests on the Differential Reactor
65
3.2.1 Catalyst activity 65 3.2.2 Reactor isothermicity 65 3.2.3 The effect of gas-solid film diffusion 66
3,2,4 The effect of pore diffusion 66
3.2.5 Homogeneous reactions 68
3.3 Methane Oxidation over Platinum Supported on Porous Alumina 68
Fibre
3.3.1 The catalytic activity of the support 68
3.3.1.1 On the methane oxidation 68
3.3.1.2 On the carbon monoxide oxidation 69
3.3.1.3 Inhibition effects of steam 69 3.3.1.4 Inhibition effect of carbon dioxide - 69
3.3.2 Activity of the supported platinum catalyst 69 3.3.2.1 Effect of temperature 75
3.3.2.2 Effect of oxygen to methane ratio 80
3.3.2.3 The reaction kinetics 80
3.3.2.3.1 The effect'of contact time 63
3.3.2.3.2, The Arrhenius plots 83
3.3.2.3.3 Reaction orders 87
3.3.2.3.4 Product inhibition 91
3.3.2.3.5 Reproducibility check 95
3.3.3
Oxidation of the reaction intermediate-carbon monoxide
95
3.3.3.1
Effects of temperature and (02):(CO) ratio
95
3.3.3.2
Effect of steam addition . 96
3.3.4
Catalyst deactivation
97
3.3.4.1
Effect of steam
97
3.3.4.2
Effect of temperature
99
3.3.4.3
Carbonaceous deposition
102
63
3.4 Methane Oxidation on Platinum Supported on Non-Porous Fibre 103
3.4.1
Catalytic activity of the support
103 3.4.1.1
The kinetics of methane oxidation over the support
103
3.4.2 Catalytic activity of the supported platinum 111
3.4.2.1 Catalyst activity and aging 111
3.4.2.2 The reaction kinetics 114
3.4.2.2.1 The Arrhenius plot 114
3.4.2.2.2 Reaction orders 114
3.4.2.2.3 Product inhibition 119
3.4.2.3 Reproducibility check 120
3.4.3 Oxidation of the reaction intermediate-carbon monoxide 123
3.4.3.1 The reaction kinetics 123
3.4.3.1.1 The Arrhenius plot 123
3.4.3.1.2 The reaction orders 123
3.4.3.2 The effect of catalyst aging 128
3.5 Methane-Steam and Water Gas-Shift Reactions 129
3.5.1 Methane-steam reaction 129
3.5.2 Water gas-shift reaction 130
3.5.2.1 The reaction kinetics 131
3.6 Surface Characterisation 137
3.6.1 Adsorption experiments 157
3.6.1.1 Nitrogen adsorption 137
3.6.1.2 Carbon monoxide adsorption 140
3.6.1.3 Pyridine adsorption 144
3.6.2 ESCA 144
3.7 The Catalytic Combustor 148
3.7.1 Introduction 148
3.7.2 Convective-diffusive catalytic combustor 148
3.7.2.1 The temperature profiles 149
3.7.2.2 Diffusion of air into the pad 155
3.7.2.3 The combustion efficiency 155
3.7.2.4 The heat efficiencies 159
3.7.2.5 Fuel slippage 159
3.7.3 Pre-mixed type catalytic combustor 159
64
3.1 Definitions
1. Conversion: moles of reactant reacted x 100%
moles of reactant fed
2. Yield: moles of product x 100%
moles of methane reacted
3. Contact time: weight of the catalyst in the reactor kgcat-sec
inlet gas molar feed j, kmol
4. Standard feed: A feed of molar composition
15% methane; 30% oxygen and
55% nitrogen as diluent
5. Oxygen diffusion effectiveness factor: The ratio of the actual reaction rate of oxygen
to that which would occur if all the internal
catalyst surface were exposed to the reactant
at the bulk conditions.
6. Combustion efficiency:
moles of fuel consumed x 100%
moles of fuel fed
7. Radiation efficiency:
(energy transmitted by thermal radiation through
the frontal surface of the catalytic combustor)/
(energy released by the consumed fuel) x 100%
8. Convective efficiency:
(energy transmitted by forced convection through
the combustor)/(energy released by the consumed
fuel) x 100%
9. Conduction loss: (energy loss through the metal casing of the
combustor)/(energy released by the consumed fuel)
x 100%
or calculated by energy balance as
100% - radiation efficiency - convection efficiency
65
3.2 Preliminary Tests on the Differential Reactor
Before systemati-c measurements to study the kinetics of the
reaction were started, it was checked that the reaction would take place in
the "kinetic control" region in which the rate of the reaction is not
affected by the internal and external diffusional processes. The
significance of non-isothermicity, catalyst aging and homogeneous
reactions were also checked.
3.2.1 Catalyst activity
The effect of catalyst aging was checked, for both porous and
nonporous Pt/A1203 catalysts, by comparing the activities of methane and
carbon monoxide oxidation processes at different time periods during the
reaction. The reactions were carried out separately using fresh
catalyst samples maintained at 757K and at a contact time of
1378.88 kgcat-sec/kmol, the inlet compositions of reactants were kept
at stoichiometric ratios (15% CH4: 30% 02 and 10% CO: 5% 02 balanced with
N2 as diluent). The gas streams were turned on in the order: diluent,
oxygen, methane or carbon monoxide, and shut down in reverse order. The
activity was defined in terms of the yield of carbon dioxide per mole of
methane or carbon monoxide consumed at the standard condition stated above.
For Pt/A1203 (porous) catalyst, no significant change in either catalytic
activity was observed in the first reaction period of 100 hours. In the
case of the Pt/A1203 (nonporous) catalyst, the activity of carbon monoxide
oxidation was found to decrease after the first reaction period of 40
hours by ca. 65% while the activity of methane oxidation remained
approximately unchanged (Figs. 3.39 and 3.40).
The kinetic results in the present work were obtained during
the time intervals in which the catalysts had the same activities.
3.2.2 Reactor isothermicity
The isothermicity of the reactor was achieved by dispersing the
catalyst with either 40 or 60 silica cylindrical pellets (2 mm x 3 mm).
Using the standard feed conditions*, it was shown that negligible temper-
ature differences(less than ± 1 K)were measured at the inlet, middle and
*The standard feed condition here and in the following sections refers to the standard feed condition stated in section 3.2.1.
66
outlet of the catalyst bed in either case. The reactor is hence con-
sidered isothermal. The steady state temperature of the catalyst bed
was recorded with respect to time and the system was found to be
isothermal to within ± 0.5 K.
3.2.3 The effect of gas-solid film diffusion
The possibility of film diffusional control was investigated using
the method described by Levenspiel (79). The experiments were carried
out at a constant contact time, but at different flow rates of identical
feed composition. Changes in the inlet flow rate to the reactor from 8.5 ml/min to 138.8 ml/min (STP) did not practically affect the conversion
of the reaction. Table 3.1 shows the results of this preliminary test.
3.2.4 The effect of pore diffusion
In order to examine the effect of pore diffusion, the traditional
method is to compare the reaction activity on different catalyst sizes
while keeping the specific surface area constant. However, it is
impossible to apply such tests to the fibre catalyst, since the size of
the fibre could not be altered by grinding.
Alternatively the effect was checked theoretically by applying the
kinetics of methane oxidation at low temperatures (see section 3.3.2.3).
TABLE 3.1
Catalyst Sample
Temperature K
Flow rates ml/min (STP)
Conversion %
P/51 787 18.70 23.6
P/52 787 74.71 23.4
P/53 787 135.90 24.2
P/51 816 19.82 37.0
P/52 816 77.43 36.06
P/53 816 136.05 38.5
The mass equation for diffusion inside the catalyst fibre was
then solved numerically (see Appendix 1) at different temperatures,
bulk concentrations and oxygen to methane ratios. The results are
listed in Table 3.2.
TABLE 3.2
Temp. K - Bulk. Composition (molar fraction)
Catalyst centre Composition
(molar fraction)
Oxygen Diffusion
Effectiveness
Factor
02 CH4 02 CH4
723 0.4 0.2 0.4 0.2 1.0
723 0.3 0.3 0.3 0.3 1.0
723 0.1 0.2 0.1 0.2 1.0
723 0.05 0.2 0.05 0.2 1.0
823 0.4 0.2 0.4 0.2 1.0
823 0.3 0.3 0.3 0.2 1.0
823 0.1 0.2 0.1 0.2 1.0
823 0.05 0.2 0.05 0.2 1.0
923 0.4 0.2 0.387 0.196 0.99
923 0.3 0.3 0.285 0.295 0.99
923 0.1 0.2 0.095 0.198 0.99
923 0.05 0.2 0.0472 0.199 0.99
1023 0.4 0.2 0.2924 0.164 0.96
1023 0.3 0.3 0.185 0.259 0.92
1023 0.1 0.2 0.0629 0.187 0.96
1023 0.05 0.2 0.0286 0.1924 0.96
The result shows that diffusional effect would become signifi-
cant at temperatures above 973K.
67
3.2.5 Homogeneous reactions
A standard feed of reactants was directed into an empty reactor
in order to find out whether the gas phase reaction could be important
or not. In the case of methane oxidation (Table 3.3), the oxidation
process starts at temperatures of ca. 903K with carbon monoxide as the
major product.
TABLE 3.3
Effect of homogeneous reaction
CH4 15.42
02 in 23.30
Temperature K
Conversion
911
930
951
16.5
52.0
74.0
3.3 Methane Oxidation over Platinum Supported on Porous Alumina Fibre
3.3.1 The catal tic activity of the su.port
Experiments were carried out to investigate the catalytic
activity of the porous alumina fibre for methane oxidation. The results
given in the following sections show that the pure fibre does catalyse
the oxidation process to a certain extent. _.
3.3.1.1 On the methane oxidation
The reactivity of the porous alumina fibre over the temperature
range of ca. 773-873K was studied and the results have been plotted in
69
Fig. 3.1. The reactor outlet analysis shows that carbon dioxide
was produced predominantly across the whole temperature range, even in
the temperature region where the outlet concentration of oxygen was
depleted below that of the methane. No traces of carbon monoxide
or other oxidation intermediates were observed and overall oxidation
of methane was always achieved. The Arrhenius plot of the oxidation
process on the porous fibre is given in Fig. 3.2, which shows an
apparent activation energy of 67.68 kJ/mole.
3.3.1.2 On the carbon monoxide oxidation
The reactivity of carbon monoxide oxidation over the porous
fibre was studied. In Fig. 3.3 the conversion of carbon monoxide
was plotted against the reaction temperature. The result shows that
the conversion exhibits a maximum value of 82% at a temperature of ca.
803K.
3.3.1.3 Inhibition effects of steam
The effects of steam addition to the oxidation of methane and
carbon monoxide on the porous alumina fibre at different temperatures
were studied. The results given in Fig. 3.4 show that the methane
oxidation over the porous alumina fibre is inhibited by steam at both
793K and 833K. The carbon monoxide oxidation process, as shown in
Fig. 3.5, is inhibited significantly by steam at 790K while no such
effect is observed at 840K.
3.3.1.4 Inhibition effects of carbon dioxide
The effects of carbon dioxide addition on the methane and carbon
monoxide oxidation at different temperatures were studied. As
shown in Figs. 3.6 and 3.7, there is practically no influence by the
additive on both oxidation processes.
3.3.2 Activity of the supported platinum catalyst
In order to construct a reaction model for the methane oxidation
over Pt/A1203 catalyst, the oxidation process was investigated inten-
sively under various conditions. The products of the reaction were shown
Com
positio
n
20
30
70
%(CH4)in= 21.8
% (02 )in= 25.0
Contact Time =1075.7 kgcat-sec kmot
L -- C H4
0-02
0--0O2
10
773
I ,V 793 813 833 853 873 893 913
Temperature ( K ) Fig. 3.1
O E
Catalyst : Pure Porous Alumina Fibre
al0~ CO2~in- \25.0~
Fig. 3.2
! t i
1Ō4
1 Ō5 1.35 1.40 1.45 1.50 1.55 1.60 1.65
1 X101 [ mole RgT kJ
Contact Time = 2283.3 kgcat-sec kmol
773 853 723 823
100
90
80
70
60 0
*(7 L d c 50 0 U
Catalyst : Pure Standand Al203 Saff ii O U 40
30
20
10
0 693
72
Temperature ( K
20 CH
4 C
onve
rsio
n
10
C 2 /i
l
10
Fig. 3.5
1
20 0
30
73
0_833 1.c % (C 2 In `25.0 )
Inlet Contact Time = 3007.3 kg cat-sec kmol
ins-793K %(CH4)n (20.6
Inlet Contact Time = 3007.3 kgcat-see k mot
10 20 30 % H2O
Fig. 3.4
100
90
0--790 K 15.43 NI k23.72
Inlet ContactTime= 2339.9 kgcat-sec kmol
% C
O C
onve
rsio
n
17.10 50 — -840 K %(C°
n \ 22.77 )
Inlet Contact Time = 2339.9 _k cat-sec kmol
30
40
30 %(H2O)in
0_631 K % 1.0 } n = `24.8 J
Inlet Contac Time = 3068.3kgcat- sPc kmol
0 U C
A-793 K % CO24/In=`24.5 .\
Inlet Contact Time=3068.3 kgcat-set kmol
0
30
.20
0
0 U
70
74
0 10 20 30 %(C 02) in
Fig. 3.6
90
0 0
c 80 7.6 0
_ 0-790 K % k CO2 /In- \ 23.7
Inlet Contact Time = 2346.5 g cat -sec kmol
A-840 K %~CO2/in 22.8
Inlet Contact Time= 2346.5 kgcat- sec kmol
A
A
60 0
10 20
30 %(CO2)in
Fig. 3.7
75
to be carbon dioxide, carbon monoxide and water. Traces of formal-
dehyde were found only when the catalyst was previously treated at
high temperatures in an environment of steam. The kinetics of the
reaction were investigated and the activation energy was measured.
The following results were obtained using the differential
reactor packed with Pt/A1203 porous fibre catalyst.
3.3.2.1 Effect of temperature
The effect of the reaction temperature on the oxidation process
was investigated in order to provide product distribution spectra as
a function of reaction temperature. The temperature was varied between
733 and 883K, and a constant contact'time of 1331.6 kgcat-sec/kmol was
always maintained by adjusting the inlet flow rates of the reactant
mixture (26.7% CH4, 27.8% 02) with respect to the changes of reaction
temperature. In Fig. 3.8, it would seem that the reaction begins at
a temperature of ca. 743K and leads to the predominant production of
carbon dioxide up to ca. 813K; carbon monoxide appears at ca. 813K.
A self-acceleration phenomenon was observed when an attempt was
made to raise the reaction temperature from 818K to ca. 828K. The
reaction temperature increased drastically to ca. 853K and was accom-
panied by the appearance of ca. 6% carbon monoxide measured at the
outlet stream from the reactor' arid by complete consumption of oxygen.
However, such a phenomenon was not observed when the reaction was carried
out under oxygen rich conditions. In Fig. 3.9, the result shows that,
under oxygen rich conditions(02:CH4 ratio is higher than the stoichio-
metry of the overall reaction), carbon dioxide production predominates
throughout the temperature range of ca. 773 to 923K.
It is also interesting to note that a hysteresis effect of the
reactor outlet composition of carbon monoxide versus reaction temperature
was observed during the methane oxidation process. As the experimental
results given in Fig. 3.10 show, the reaction ran away to ca. 853K and
was accompanied by an exit level of carbon monoxide of ca. 6% as a result
of a slight perturbation of temperature above ca. 823K. After the
high temperature was reached, the temperature was decreased but the carbon
monoxide exit composition maintained the constant level before it dropped
back drastically to ca. 0.8% at a temperature of ca. 813K. This effect
could be reproduced with different catalyst samples.
An unstable feature was also observed when the methane stream
30 C H4 02 /in C 27.7
Contact Time =1377.17 kg cat-sec kmot
cr 20
0 .N 0 A. E 0 U
0
76
733
783
833 873
Fig. 3.8 Temp. ( K )
Catalyst Sample: 0.4wt % Pt /A1203 ( Porous )
Contact Time = 1370 kgcat-sec
0-CH4 0- 02 ~--0O2 0-00
kmol
% (CO2 )in = (40.8)
30 c 0 Fig. 3.9 •N 0
E
8 0 ō 20
'
773 823 873 923
Temp. (K)
18
7
0
U
8
0 () 773 823 Temp. ( K ) 873
0 Forward
a Backward
0/°~CFi4~in- ~2 7.8
Contact Time =1350.54 ka cat-sec kmole
°0(H O2
~in- (29.00 9.21
Contact Time= 830.8 kg cat-sec kmol
0-- Forward
0— Backward
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0 0 I _I I I I I
783 793 803 813 823 833 843 853 863 873 Temp. (K)
0
Fig. 3.11
773
80
was switched on before the oxygen stream (with steady state compositions
of 26.7% CH4 and 27.8% 02), after flushing the reactor with nitrogen
at 773K. The temperature of the catalyst bed ran away to ca. 843K and
ca. 6% carbon monoxide was detected in the reactor outlet stream.
However, under the same•conditions, when oxygen was switched on first
the reaction proceeded smoothly with a temperature rise less than 5K
and only carbon dioxide was detected in the product stream.
Experiments were also carried out at low 02/CH4 ratio in order
to investigate the mechanism of carbon monoxide formation. An inlet
mixture of 9.2% 0 and 29% CH4 was admitted over the catalyst. In
Fig. 3.11 the ratio of formation of carbon monoxide tocthat of carbon
dioxide is plotted as a function of the reaction temperature at a
contact time of 830.8 kgcat-sec/kmol. Carbon monoxide only appears
above temperatures of ca. 813K.
3.3.2.2 Effect of oxygen to methane ratio
As a result of the observation that carbon monoxide appears at
high temperatures and low oxygen concentrations, experiments were per-
formed to show the importance of the oxygen to methane ratio on the
formations of carbon oxides at the temperature which favours the
oxidation process to carbon monoxide.
The result in Fig. 3.12 gives the dependencies of carbon oxides
formation vs. the composition of inlet oxygen at 830K. It was shown
that, at the fixed methane composition, carbon dioxide increases with
increase in oxygen composition (02/CH4 above 1.13), at the expense of
carbon monoxide. In Fig. 3.13 the dependencies of carbon oxides
formation on the methane composition at 830K are given; these increased
simultaneously up to 15% CH4 (02/CH4 = 0.75). With further increase in
the methane composition (02/CH4 < 0.75) the outlet concentration of carbon
dioxide decreased while that of carbon monoxide was maintained at a nearly
constant level.
3.3.2.3 The reaction kinetics
The following series of experiments were designed to investigate
the kinetics of the oxidation process on Pt/A1203 (porous). The
experimental data were obtained under such conditions that the degree of
[ 02] [CH41
3.0
90 50
100 0 0.5 1.0 1.5 2.0 2.5 3.5
60
40 0
[ CR 1= 20
Temp. = 830K
Contact Time = 1300.1 kg cat-sec
40
c, 30 °
N~ a.
20
• 80 a)
N 0 0 70
60
Fig. 3.12 50 10
10 20 30 40 50%
[ 02 ~
6 7 0 '0 0
1.0 3.0 2.0 [ 02]
4.0
0— c o2 0—co
0 O U
[ 02}1= 11.25
Temp.= 830K •
Contact Time=1304.04 kg cat -sec kmol
Fig. 3.13
0
10 20 30 40 %[CH4l in
83
conversion depends linearly on the contact time and, as a result, initial
rate interpretations can be applied.
3.3.2.3.1 The effect of contact time
In this experiment, two catalyst samples of 0.4 wt % Pt on A1203
were used, and the contact time varied between 594.16 to 3564.94 kgcat-
sec/kmol at constant inlet compositions. The relationship between
the conversion and the contact time was studied at three temperatures
(787, 815, 844K). The results are shown in Figs. 3.14 and 3.15; the
ranges in which the conversion is linearly dependent on contact time
are summarized in Table 3.4.
TABLE 3.4
Temp, K
Range of linear relationship
Conversion % Contact time, kgcat-sec/kmol
787 0 - 30 0 - 2098.63
815 0 - 52 0 - 2079.68
844 0 - 60 0 - 1385.00
3.3.2.3.2 The Arrhenius plots
In order to investigate the thermal dependence of the reaction
rate, initial rate data were obtained at various temperatures with a
constant oxygen and methane concentration. By plotting loge(-ro) as
a function of 1/R .T (mole/kJ) (Fig. 3.16), the values of the apparent
activation energies were obtained. It is shown that the oxidation
process has an apparent activation energy of 187.06 kJ/mole up to ca.
803K but that a lower activation energy is observed at higher temperatures.
Con
vers
ion
50
40
kgcat-sec .10-2
5 10 15 20 25 30 35 40 45 kmol
60
70
30
80
10
20
0 0
Temp.= 844 K
% ( OZ)in- 1286105)
p--Temp.= 815 K
% 02 )in \ 25.8
0'— Temp.= 786 K
02 in ~25.4
Fig. 3.14
0 5 10 15 20 25 30
Con
vers
ion
40
70
60
50
30 U
20
10
0
n— Temp.= 844 K (cH4(16.2
0 2 , n 26.4 i
0---Temp. - 815 K
% (CH4O "n " 23.7 /
a--- Temp.= 788 K
%(C =( HO 13.15 O
2 in 23.00 J
Fig. 3.15
kg cat-sec x10-2 kmol
873 848 1Ō4
Temp. ( K ) 798 773 823
% (co" ),,,=(3 ..90) Catalyst : Sample A
0--Catalyst : Sample B
°~0 (CH4)in - C18.20J
4--Catalyst : Sample C
°0 C O2 / in \ 203.602 J
Fig. 3.16
U
1.40 1.45 1.50 1.55 1.60 1.65 1.70 —x101 mot
FT kJ
The frequency factors, k0, at different temperatures were deter-
mined by the Arrhenius equation,
- r0 = k0 exp (-E/RT) f ((CH410, (02)0)
(3.1)
where f ((CH4)o, (02
)0) is a functional dependence on methane and
oxygen concentrations which can be simplified to
f = [DX . (02)0 (3.2)
Measurement of the reaction orders, m and n,is reported below.
3.3.2.3.3 Reaction orders
The reaction order with respect to each reactant was determined by
keeping the initial concentration of the other reactant constant and by
varying the initial concentration of the reactant concerned. The
logarithmic plots of the initial rate versus the reactant concentration
are given in Figs. 3.17 to 3.20. Since, as shown in Fig. 3.16, there
is a change in the activation energy at ca. 803K, the reaction orders of
individual reactantsat both low ( < 803K) and high ( > 803K) temperatures
were obtained from the slopes of such plots and are summarized in
Table 3.5.
TABLE 3.5
- r0 = k0 exp (-E/RT) CCH4) o (02) o
T,K m n
789 1.0 0.75
817 1.0 1.0
Once the reaction orders had been determined, the characteristic
87
10
ō E
U
ū U DI
0.67
v • 02!CH4
%(CH4)= 18.75
Temp.= 789 K !< 02 / C H4 >l
2.21 0.73
101 %(02)in
rat ecc ICH4Im
m= slope= 1.0
%(021= 31
Temp. = 789 K
%(CH 1in 102
4
10
88
101
5 tn 0 x
2.22
Fig. 3.17
1 02
rate oc [ 02 In
ri= slope = 0.75
Fig. 3.18
1 2 5 4 3
89
10
in 5 0 x
1 10 20 30 40 50 60 60 100
%(CH4/in
1 1 10 • 100
10
%( 02) in
1000 0 100 200 300 400 500 600 700 800 900
[ CH4 l0 [ 0210
15
O E
0 L
5
0
91
rate constants at different temperatures could be obtained from the
slopes of the plots (Fig. 3.21) of the initial rate versus the reactant
concentration elevated to the respective order, i.e.
k = ro/ (CH41 o (02):13 (3.3)
Since
k = ko exp (-E/RT) 3.4)
The frequency factor ko could also be calculated at both low
(<803K) and high (>803K) temperatures. The values are tabulated in
Table 3.6.
TABLE 3.6
Temp
K
k ko
(kmoi/kcat-sec)
789 1.4150 x 10-7
3.438 x 105
817 1.5879 x 10-7
5.025 x 10-2
Values of ko should be corrected for surface area, the measurement
of which is reported in section 3.6. Specific kinetic data are
given in Appendix 2.
3.3.2.3.4 Product inhibition
The effects of the reaction products on the reaction rate were
studied. In these experiments, the reaction products (carbon dioxide,
steam and carbon monoxide) were fed into the system at the same time as
oxygen and methane at both low ( < 803K) and high ( > 803K) temperatures.
The results are plotted in Figs. 3.22-3.26.
o'
A
Temp.= 791 K
(C . jj 02H4
)in = C2123.
8065)
Fig. 3. 22
I I I t t III! I I• I I I t l l
10 100 % (CO2)in
t-6 1
Temp.= 816 K
%\ 02 Iin' (18.72)
Fig. 3.23
I 1 I I I I 1 1 1 t I I I 1 1 1
0
166
•
10 100 (CO2 )in
92
O E
93
106 I 1 I I I I 10 100
1 10 100
% ( H20 )in
166 i I t i t i I
Temp.= 848 K
% ( 029in -(21)
Fig. 3. 25
% ( H20)in
a ~ a N
rn
10-S—
Temp.= 789 K
O ll (CH (r17 ll
02 fin - l 21
Fig. 3. 24
s ~V
104
E
10
Temp.= 791 K
%\02 4/in ~ 24.1 i
Fig. 3.26
% (CO)in I I I 1 1
10
95
The results indicated that neither the addition of carbon dioxide
nor that of steam showed significant inhibition effects at both low and
high temperatures, as shown in Figs. 3.22-3.25. Slight negative
effects of carbon monoxide addition were observed at 791K, (Fig. 3.26)
and the logarithmic plot shows a negative order of 0.4 up to 5% addition.
Further increase in the concentration of carbon monoxide in the feed
stream became difficult because of thermal instability. . The same
difficulty occurred when the effect of carbon monoxide addition was
studied at higher temperatures.
3.3.2.3.5 Reproducibility check
Three sets of experimental data obtained from the study of the
kinetics of the methane oxidation process on three catalyst samples have
been compared. The Arrhenius plots in Fig. 3.16 show that the acti-
vation energies within the temperature range of 753-843K are reproducible.
3.3.3 Oxidation of the reaction intermediate - carbon monoxide
The results (Figs. 3.8-3.13) show that carbon monoxide appears
above reaction temperatures of ca. 813K where the depletion rate of oxygen
is faster than that of methane and the oxygen to methane ratio is lower
than unity. Experiments were designed to examine whether the oxidation
of the intermediate is the limiting step in the reaction process.
3.3.3.1 Effects of temperature and (021:( ) rati o
Carbon monoxide oxidation over the Pt/A1203 catalyst was studied.
The results in Table 3.7 show that complete conversion of carbon monoxide
was achieved at a reaction temperature of 749 and 837K when the concen-
tration of oxygen was sufficient (> the stoichiometric ratio). The
experiments in which the oxygen concentration was below the stoichiometric
amount indicated that, at reaction temperatures of 789 and 858K, oxygen
was completely consumed in the oxidation process.
96
TABLE 3.7
Temp K
Contact time kgcat-sec
reactor inlet molar fraction(*) CO 02
reactor inlet molar fraction(*) CO 0
2 CO2 kmol
749 553.04 0.048 0.165 - 0.142 0.0489
837 465.62 0.228 0.127 - 0.017 0.2561
798 648.54 0.264 0.065 0.170 - 0.1150
798 654.43 0.345 0.060 0.258 - 0.1124
858 666.68 0.345 0.060 0.260 - 0.1108
(*) Balanced with nitrogen
The indications obtained from these experiments can be compared
with the results of methane oxidation over the same catalyst and show
that, at both low and high temperatures, the rate of carbon monoxide
oxidation on Pt/A1203 catalyst is faster than that of methane oxidation
if the oxygen concentration level is kept higher than stoichiometric.
Since, at low 02/CH4 ratio (methane oxidation), complete consumption of
oxygen was also observed, comparison of the reaction rates between two
oxidation processes could not indicate that carbon monoxide oxidation is
still faster than;methane oxidation when the oxygen concentration is
insufficient.
3.3.3.2 Effect of steam addition
The effect of steam on the oxidation of carbon monoxide over the
Pt/A1203 catalyst was studied at various temperatures. The experi-
mental results which are tabulated in Table 3.8 show that in all cases
(even when the ratio of (H20)/L021 and (H20)/(CO) are 4.6 and 5.7
respectively) complete conversion of carbon monoxide was always achieved.
97 TABLE 3.8
Temp K
Reactor (*) inlet composition
Contact time
kgcat-sec
Conversion
CO 02 H2O kmol
721 18.44 23.80 0 909.85 100
720 18.73 23.66 17.29 898.92 100
839 20.38 25.28 0 1025.11 100
838 20.38 24.99 21.44 1016.03 100
842 5.88 7.34 33.42 753.73 100
(*) balanced with nitrogen
3.3.4 Catalyst deactivation
A series of experiments was designed to investigate the possible
factors which can affect the deactivation of the Pt/A1203 catalyst used in
the methane oxidation process.
3.3.4.1 Effect of steam
A sample of 0.0456 gm of the Pt/A1203 catalyst was treated in an
atmosphere of 18% H2O over the temperature range of ca. 1023K for 61 hours.
The catalytic activity of the sample was then studied over the temperature
range of ca. 783 to 873K for the methane oxidation process. The reaction
product spectra are given in Fig. 3.27. The results show that the treated
catalyst promotes carbon monoxide formation as compared with the previous
experiments (Fig. 3.8), in which carbon monoxide formation only occurs when
oxygen concentration is insufficient and at temperatures of about ca. 813K.
An almost constant amount of formaldehyde (ca. 2%) was also detected in the
product mixture over the same temperature range (Fig. 3.27). The activity
of this sample for carbon monoxide oxidation was also studied by introducing
an inlet mixture of C0:02 = 6.5:21% into the reactor over the temperature
range 688 to 906K; no reaction was observed, but traces of carbon
dioxide were found at the outlet of the reactor at 906K as a result of
homogeneous reaction.
c: 0 ~
(/)
0 0-E 0 u en en 0
CD ~ '-
0
~ 0
30~--------------------------------------~--~
20
10
0/0 (C'HL.). = (22 .0 ) 02 In 26. 9
Inlet Contact Time= 406.15 kg cat-sec kmol
0- 0 2
(J-- CHI. O-co Q-HCHO
D-G02
o ----~~------~--------------~------------~ 773 823 873
Temperature (K) Fig. 3.27
0.0456 gm (0.4 wt % Pt) Standard Al203 Soffit, after
Treatment at 923 ~ Temp.~ 1088 K for 6: 30 hrs.' in the
Atmosphere of 18.12 % H20 and 8 0/0 CHI.
923
99
3.3.4.2 Effect of temperature
The possibility of catalyst sintering effect due to high temper-
ature treatment was examined. A sample of 0.0457 gm of the Pt/A1203
catalyst was treated in an atmosphere of flowing nitrogen at 1068K for
6i hours. The activity of the catalyst was studied before and after the
treatment. The results are given in Table 3.9.
There is no decrease in catalytic activity of the sample after the
high temperature treatment. In order to compare with the results given
in Fig. 3.27, an inlet mixture of 21.8% CH4 and 28% 02 was admitted to the
reactor at an inlet contact time of 1134.45 kgcat-sec/kmol, and the
catalytic activity of the thermally treated - sample was studied over the
temperature range of ca. 783 to 873K. The product spectra are given in
Fig. 3.28. In contrast with the results given in Fig. 3.27, carbon
monoxide only appeared at high temperature where the oxygen to methane
ratio was below unity. The Arrhenius plot of the reactivity of methane
oxidation over the treated sample (Fig. 3.29) shows a change in activation
energy at a temperature of ca. 810K, which coincides with the results of
the catalysts without thermal pre-treatment. The activity of the sample
on carbon monoxide oxidation was also studied with an inlet composition of
7:21% (C0:02); complete conversion was always attained at the temperature
range of ca. 683 to 858K.
TABLE 3.9
Before treatment After treatment
Temp K
% inlet CH4
4 2
reaction rate
kmol/kgcat-sec
Temp K
% inlet CH4 4 2
reaction rate
kmol/kgcat-sec
796
821
21.3 27.5
21.4 28.2
4.2650x10-5
8.1546x10-5
795
820
21.8 2.8
22.1 2.8
4.4243x10-5
8.3402x10-5
823 873 923
Reactor Temp. ( K )
100
Inlet %( 02 ) ~ 27.94
Inlet Contact Time= 1134.45 kgcat-sec kmol
Fig. 3.28
0.0457 gm ( 0.4 wt % Pt) Standard A1203 Saff i l , after
Treatment at 1068 K for 6:30 hrs in the Atmosphere
of N2
Temp. K ) 873 848 823 798 773
1.35 1.45 1.55 1.65
Fig .3.29 RT x 101 mol / kJ
0,0457 gm (0.4wt%Pt) Standard A1203 Saffil , after
Treatment at 1068 K for 6 : 30 hrs in the Atmosphere of N2
101
3.3.4.3 Carbonaceous deposition
It is thermodynamically feasible that carbonaceous residue can
be deposited over the catalyst: under either reducing or oxidizing conditions.
This will block the catalytic sites for the complete oxidation of methane
and finally poison the whole catalyst. Experiments were performed to
investigate such effects.
A sample of 0.0465 gm of the Pt/A1203 catalyst was treated in an
atmosphere of 23.3% CH4 (balanced with nitrogen) at 823K for 62 hours.
The activity of the catalyst was studied before and after the treatment.
The results are given in Table 3.10. A slight decrease in catalytic
activity (ca. 10%) for methane oxidation was observed during the first
15 minutes after admitting the reactant mixture. There was no obvious
decrease in catalytic activity after one hour (see Table 3.10). Carbon
monoxide oxidation over the sample was then studied at 709K and 841K. In
both cases, complete conversion was attained.
TABLE 3.10
1 Before treatment After treatment
Temp % inlet * Reaction rate Period after Temp % inlet * Reaction rate K
CH4 02 kmol/kgcat-sec treatment hr
K CH4 02 kmol/kgcat-sec
793 19.5 26.5 3.20x10-5 . < 4 793 19.5 26.5 2.93x10-5
> 1 793 19.5 26.5 3.20x10-5
841 18.8 26.2 8.04x105 <1 841 18.8 26.2 8.00x10-5
* balanced with nitrogen
A experiment was carried out to study the possibility of carbon-
aceous deposition on the catalyst surface under high temperature and low
oxygen level conditions. An inlet mixture of 21.33% CH4 and 8.74% 02
was passed over a sample of the catalyst at 838K for 32 hours. After
that the reactants were switched off and the reactor was flushed with
nitrogen, and 31.6% 02 was fed into the system. Neither carbon monoxide
nor carbon dioxide was observed in the outlet stream of the reactor. The
102'
103
activity of the treated catalyst for the carbon monoxide oxidation was
later checked by admitting an inlet mixture of 26.7% 02 and 18.95% CO;
complete conversion of carbon monoxide was again obtained. However, if
a carbonaceous film did exist at such conditions, it should be in
a very thin layer such that it would oxidise very quickly in the absence of
methane. Unless sufficient carbon is deposited, neither carbon monoxide
nor carbon dioxide would be observed. Nevertheless, the effect of
carbonaceous deposition in the process of methane oxidation was demonstrated
by the gas adsorption experiment as reported in section 3.6.1.2.
3.4 Methane Oxidation on Platinum Supported on Nonporous Alumina Fibre
3.4.1 Catalytic activity of the support
Experiments were carried out to investigate the catalytic activity
of the low surface area alumina fibre for methane oxidation.
A sample of pure alumina fibre was used with a reactant mixture of
14.23% CH4 and 21.30% 02 at a constant contact time of•2269.32 kgcat-sec/mol.
Fig. 3.30 shows the results of the methane conversion as a function of
reaction temperature. The pure alumina fibre produced a conversion
varying from 15% at 783K up to ca. 55% at 873K. The product stream
analysis shows that carbon monoxide was the main product across the temper-
ature range studied, with a yield of ca. 70%. A small yield of formal-
dehyde (ca. 1%) was detected in the outlet stream across the temperature
range. It was also observed that the percentage yield of carbon monoxide
exhibited a maximum of ca. 75% at ca. 823K, further increase in temperature
decreasing the yield.
The study of carbon monoxide oxidation over the pure alumina showed
that the conversion of carbon monoxide was practically zero below ca. 793K,
further increase of temperature resulting in a slight conversion (Fig. 3.31).
3.4.1.1 The kinetics of methane oxidation over the support
The Arrhenius plot of the process of methane oxidation (Fig. 3.32)
gives an apparent activation energy of 63.95 kJ/mole.
The logarithmic plots of the initial reaction rate versus the
reactant concentrations at 789K and 831K are given in Figs. 3.33 - 3.36,
and the reaction orders are summarised in Table 3.11.
773 783 793 803 813 823 833 843 853 863 873 Temp. (K )
Con
vers
ion
40
80
70
60
50 ō o 0
40 -< CD a
30
20
10
0
80
70
60
50
L 30
a
20
10
0
Temp. (K )
0 v
Conv
ers i
on
(C002)in -1 24.37
Contact Time= 2319.55 1ca~ -sec kmol
Catalyst : Pure HT Alt
Fig. 3. 31
798 773 848 823 873
• • •
1.40 1.45 1.50 1.55 1.60
1 X 10 mol / kJ RT
10 5 1.35
0
10 4
(CHL) 02~in
.23)
Catalyst : Pure HT Alt 03
Fig. 3.32
_ EA = 63.95 k J kmol • • •
•
107
100
0—CO Yield -CH4 Conversion
104
10
► 10
Catalyst : (Pure) Nonporous Al2 03
Temp.= 789K % (02)in= 23.54
Fig. 3.33
► ► i i i i i i I I i i I 1 1 1 1
10 100 %(CH4)in
Catalyst : (Pure) Nonporous A1203
Temp. = 789K
% (CH4)in = 21.18
t ilt
Fig. 3.34
1
100
108
0—CO Yield -CH4 Conversion
104
- rec 102)1.36
105
10 %(02)in
100
10
•zst
109
100
0--CO Yield
CH4 Conversion I I I l u i i I I I I I lilt
-r ce (CI )1
105
Catalyst : (Rire) Nonporous A 12 03
Temp. = 831 K
'Yo (02)in=20.68
Fig. 3.35
I I i t i l I i I I l l l l
1 10 100 %(CH4)in
104
106
10
0—CO Yield
n— CH4 Conversion
1 10 100
110
100
10
% ( 02)in
•■•• -•••• • y•-•.• -• •
1 1 1 1 1 1 1 f I
-roc 102 )1.36
Catalyst : (Pure) NonporousAl203
Temp. 830K
0/9 (CH4 )in= 13.65
Fig. 3.36
It ill I I I I It I I 156
a U
165
111
TABLE 3.11
Catalyst: pure nonporous alumina fibre
Temp Reaction order K
CH4 02
789 1.0 1.36
831 1.0 1.36
3.4.2 Catalytic activity of the supported platinum
3.4.2.1 Catalyst activity and aging
The activities of the fresh and aged (after 40 hours use) catalysts
were studied at 801K and 842K; methane conversion was plotted as a
function of contact time (Figs. 3.37 and 3.78). With a fresh
catalyst, at both low and high temperatures, carbon dioxide was the
predominant product and the percentage yield of carbon monoxide was zero.
With an aged catalyst (Figs. 3.39 and 3.40) carbon monoxide appeared to be
predominant at low contact times up to a yield of 70% and 20% (801K and
841K respectively). Carbon monoxide diminished when the contact time was
increased. Traces of formaldehyde (ca. 0.5 - 1.0%) were detected at
low contact times with the aged catalysts at both temperatures. The
absolute reaction rates of methane oxidation over both fresh and aged
catalysts were calculated and are tabulated in Table 3.12.
TABLE 3.12
CH4 i 02
Catalyst condition I
Temp
K
Rate
kmol/kgcat-secx105
Decrease in activity
fresh 801 1.76 -
aged 801 1.65 6.25
fresh 841 3.53 -
aged 841 3.14 11.0
O—CH4 Conversion
- A--CO Yield
Catalyst Sample: Fresh 2.35wt % Pt/HT AI203
Temp.= 802 K
%(OH )in - \22.38)
Fig. 3.37
70
60
50
40
30
20
10
0 0
70
60
50
40
d
30
20
10
0 0
1.0 2.0 3.0 4.0 5.0 6.0
Contact Time kgcat-sec X 1Ō 3 kmaI
Fig. 3.38
4.0 5.0 6.0 kg cat-sec x 10-3
kmol
0--CH4 Conversion
£ —00 Yield
1.0
2.0 3.0
Contact Time
7.0
7.0
Catalyst Sample : Fresh 2.35 wt % Pt/ HT A1203
Temp.= 843K
024 llJin=
11 \23.08!
112
( 14.33) \ 21.42/ CCH4 ~ 02 i
n- CH4 Conversion 0-- CO Yield
Catalyst Sample 2.35wt % Pt / HT A1203 (used over 40 hrs )
Temp.= 801 K
Fig. 3.39
1.0 2.0 3.0 4.0 5.0 6.0 7.0
x 10 3 Contact Time "cat -sec kmol
£--CH4 Conversion
0—CO Yield
Catalyst Sample: 2.35wt% Pt/HT A1203 (used over 40 hrs )
Temp. = 841 K
02 /in = (13
21.65).93
21.65/
Fig. 3.40
1.0 2.0 3.0 4.0 5.0 6.0 7.0 Contact Time — ca es-- .163
80
70
60
50
40
30
20
10
80
70
60
50
40
30
20
10
113
A slight decrease in reaction rate due to catalyst aging was
observed, and the percentage losses in activity were 6.25% and 11.0% at 801
and 841K respectively.
3.4.2.2 The reaction kinetics
The results given in Figs. 3.37 and 3.38 show that the conversion
of methane is linearly dependent on contact time up to 35% at 802K and
47% at 843K. The experimental data hereafter were reported at such
conditions that the degree of conversion would lie in the region where
initial rate interpretation could be applied.
3.4.2.2.1 The Arrhenius plot
Initial rate data were obtained at various temperatures with cons-
tant oxygen and methane concentrations. The values of the apparent
activation energies were obtained from the slope of the plot of loge(-ro)
as a function of 1/RT, mole/kJ (Fig. 3.41). As with the case of
Pt/A1203 (porous), the oxidation process on this catalyst also shows a
break in apparent activation energy at ca. 823K. The values of the
apparent activation energies are 166.66 kJ/mole and 75.54 kJ/mole at low
and high temperatures respectively.
The rate constants at different reaction temperatures were
evaluated after the reaction orders were determined.
3.4.2.2.2 Reaction orders
The reaction orders with respect to each reactant were determined
for the corresponding temperature regions where the process has different
apparent activation energies, in a similar way as described in section
3.3.2.3.3. The logarithmic plots of the initial rate versus the reactant
concentration are given in Figs. 3.42 and 3.43. The reaction orders of
individual reactants at both low.(< 823K) and high (> 823K) temperatures
were obtained from the slopes of such plots and are summarised in Table 3.13.
1.60 1.65
1 X 10 m°1 RT kJ
1.40 1.45 1.50 1.55
115
ō E
Temp. ( K )
873 848 823 798 10_4
748
n= 0.7
—roc [CH4)6
0— Catalyst Sample 2.35wt% Pt/ HTAI203
Temp.= 835 K
% ( 02 )in = 22.55
~- Catalyst Sample 235wt% Pt/ HTAl203
Temp.= 801 K
%(02)in= 23.0
Fig. 3.42
106
( 02 / CH4 ) in
4.0 3.0 2.0 1.5 1.0 0.75 0.45
1 10
10i0
% (CH4)in
116
1Ō4
(02/CH4)in 0.53 0.76 1.0 2.0 2.4
117
-r ec [02]fl
0-- Catalyst Sample : 2.35wt% Pt / HTA (203
Temp. = 833 K
( CH4 )i n= 15.73
nj-- Catalyst Sample 2.35wt % Pt/ HT Al203
Temp. =801K
%(CH4)in=15.13
106 1 10 100
% ( 02) in
6
LO 0 x
Fig. 3.44
[CH4]0 [0210
0 100 200 300 400 500 600 700 800 900 1000 1100
119
TABLE 3.13
- ro = ko exp (-E/RT) (CH4) (02) 110
Temp K
m n
801 1.0 1.0
835 1.0 1.0
The characteristic rate constants at different temperatures
could be obtained as described in section 3.3.2.3.3. The plots of the
initial rate, ro, versus (CH4Im (02V ō are given in Fig. 3.44. The
values of the rate constants, k, and the frequency factor, ko, were
calculated and are listed in Table 3.14.
TABLE 3.14
Temp k l ko
K (kmol/kgcat-sec)
801 4.0753x10-8 3.086x103
835 9.812x10-8
5.282x10-3
Values for k and ko are given with respect to the weight of the catalyst
and should be corrected for active surface area, the measurement of which
is reported in section 3..6. Specific kinetic data are given in Appendix 2.
3.4.2.2.3 Product inhibition
The effects of the addition of the main products on the reaction
rate were studied. In these experiments, varied amounts of carbon
dioxide, steam or carbon monoxide were fed into the reactor in a mixture
120
of constant concentrations of oxygen and methane. The initial reaction
rate of methane was plotted as a function of percentage additions at
both low.(< 823K) and high (> 823K) temperatures.
The results in Figs. 3.45 to 3.47 indicate that there was practically
no inhibitive effect due to the addition of carbon oxides or steam on the
initial rate measured at both temperatures.
3.4.2.3 Reproducibility check
Two sets of experimental data obtained from the study of the kinetics
of the methane oxidation process on two catalyst samples have been compared.
The Arrhenius plots (Fig. 3.48) show that the apparent activation energies
within the temperature range studied have good reproducibility. The
absolute magnitudes of the initial rates on different samples were also
compared, and the results show good agreement (Table 3.15).
TABLE 3.15
Reproducibility check
Condition: CH 15.8 024 .E - 21.3
Temp K
Catalyst
Reproducibility
±
Reaction rate kmol/kgcat-secx105
PH1 PH2
783 0.660 0.685 3.7
793 1.02 0.971 4.8
803 1.41 1.302 7.7
813 1.93 1.834 5.0
823 2.60 2.49 4.2
833 3.05 2.78 8.9
843 3.42 3.10 9.4
853 3.86 3.49 9.6
10
0~
a
$(L
0-Catalyst Sample: 3-Catalyst Saw(ei 235wt%Pt/HTA1203 2.3Swt%Pt/HTA1203
Temp.= 833 K Temp.= 798 K
S'\ 02 /1n' (11:2) %(CO2 )in=(2313)
Fig. 3.65
1 I I 1 1 1, 1
10 100 'GtCO2) jn
121
0
Catalyst Sample : 2.35wt %Pt/HT A1203
0-Temp.= 833K
•/. /11 87) \
\0122/in`Is22
8-Temp.= 799K
H4 16.10 p2 )in ' ~22.201
1D i 1 1 1 11, 1 1
1 10 V= (COtin
Fig, 3.46
1 1 ( I 1 1
103
Catalyst Sample : 2.35 wt % Pt / H T A1203
Ū a Y
10
O-Temp,* 833 K
%(CO26 ~in' 121;
a-Tem
p
p.. 796 K
• '/= (0y )1n=(21.01)
Fig. 3,47
1 a-1~_ui._L I-. 1._s,_ 10
% (ii-,O) in 150
Temp. l K ) 873 848 823 798 773
1Ō4
Catalyst : 0.235wt % Pt /HTAl203
~-- Sample PH 1
%~ 02 )in-~21. 0/ 0— Sample PH 2
( 024/in -( a 21.31J 10 6
0 E
1.60 1.65
1 x 101 mol kJ RT
1.35 1.55 1.50 1.45 1.40
122
3.4.3 Oxidation of the reaction intermediate carbon monoxide..
The results described in the previous sections show that methane
oxidation over aged catalyts or over the pure alumina support generated
mainly carbon monoxide. In this section, results obtained for the
reactivity of carbon monoxide over a fresh sample of the Pt/A1203
catalyst are described, and the kinetics of carbon monoxide oxidation
over the supported platinum catalyst are given.
3.4.3.1 The reaction kinetics
The contact time was varied from 1437.62 kgcat-sec/ketol -
2799.57 kgcat-sec/kmol by changing the flow rate at a constant composition
over the Pt/A1203 catalyst (Fig. 3.49). For the range of con-
ditions studied the plot of the conversion versus the contact time was lin-
ear, and the initial rate approximation could be applied to evaluate the
experimental data.
3.4.3.1.1 The Arrhenius plot
The apparent activation energy of carbon monoxide oxidation over
the fresh Pt/A1203 catalyst was obtained from the Arrhenius plot given in
Fig. 3.50, and had a value of 45.98 kJ/mole over the temperature range of
ca. 723 to 853K.
3.4.3.1.2 The reaction orders
The reaction orders with respect to the reactants were determined in
a similar way to that described in section 3.3.2.3.3. The logarithmic
plots of the initial rate against the concentration of the reactant
concerned are given in Figs. 3.51 and 3.52, and the reaction orders are
summarised in Table 3.16.
It was shown that the order with respect to carbon monoxide is
unity over the concentration range studied. At low oxygen concentration
(below stoichiometric ratio), the order in oxygen is unity, while at excess
concentrations(above stoichiometric ratio) the order is zero.
The rate constants at different temperatures were calculated for
high oxygen concentration levels and the values were plotted against
123
Catalyst Sample: 2.35 wt% Pt/ HTA 1203
Temp. = 853K
\0D.tn ( \231.14
2 4
Contact Ti me
6 kg cat-sec km'
0
0 10
% C
O .
Conv
ersio
n
100
90
80
70
60
50
40
30
20
10
0 1V
Temp. (K) 873 848 823 798 773
10-4 748
124
1.40 1.45 1.50 1.55 1 .60 1.65
1 x 101 mat RT kJ
%( 02)= 24.4
Inlet Contact Time=
1990.6 kg cat -sec kmo
Temp.= 799 K
r
1 02)in = 24.4
Catalyst : 2.35wt%Pt/ HT AI203
Temp.= 799 K
Fig. 3.51
O U
Conv
ers i
on
100
.0.1
10
1
4
125
1
10
100 ( CO ) in
10 100 % ( 026
Catalyst: 2.35wt%Pt/HTAl203
Temp. = 800 K
% (CO)in= 19.84
126
x
X -0
m
C:)
x106 The Rate Constant k r/CO , kmolkgcat-sec
N
128
exp (-E/RT) in Fig. 3.53. The frequency factor (2.033 x 10-3 kmol/
kgcat-sec) was obtained from the slope of the plot.
TABLE 3.16
Reaction order of carbon monoxide oxidation
rate a [Al n
Species Concentration of IAI %
Reaction order n
[021/(CO) range
CO (2.1 - 21.) 1.0 (11.6 - 1.16)
02 (5.0 - 13.0) 1.0 (0.25 - 0.65)
02 (13.0 - 40.0) 0.0 (0.65 - 2.0)
3.4.3.2 The effect of catalyst aging
The activities of a fresh and used (40 hours) catalyst sample
were compared. A significant decrease in reaction rate was observed
(Table 3.17), with the used catalyst.
TABLE 3.17
Condition: CO 120.0 02 - 24.4
ICatalyst 1 Temp 1 Reaction rate 5
I Condition
1 K I kmol/kgcat-sec x 10
fresh 800 4.60
aged 800 1.70
3.5 Methane-Steam and Water-Shift Reactions
The experimental results described in the previous section were
intended to investigate methane oxidation over Pt/A1203 catalyst.
However, the questions of whether methane could directly react with steam
or whether carbon monoxide (the reaction intermediate) could interact
with steam over the catalyst was not clarified. Therefore, in the
following sections, the interactions of steam with methane and carbon
monoxide in the absence of oxygen (i.e. (02)/(CH41 = 0) are described.
3.5.1 Methane-steam reaction
An attempt was made to study the activity of the methane-steam
process over platinum supported on high surface area alumina fibre.
Although the thermodynamic calculations indicate that the equilibrium
constant, Kp, favours the reaction above temperatures of ca. 903K
(Table 3.18), no reaction was observed on two catalyst samples (0.0456 gm
and 0.2642 gm 0.4 wt % Pt/A1203) over the temperature intervals of 712 -
1088K at concentrations of 21% CH4 and 22% H20.
TABLE 3.18
CH4 + H2O = CO + 3H2
I Temp.(K)lEquilibrium constant, Kp (atm2)
713 5.4 x 10-4
773 9.89 x 10-3
873 5.18 x 10-1
973 12.01
1073 155.11
129
3.5.2 Water gas-shift reaction
The calculation of equilibrium conversions for the reaction:
CO + H2O = CO2 + H2
over the temperature range of 773 to 881K is given in Table 3.19.
TABLE 3.19
Condition: CO
13.58 H2O
23.26
Temperature K
% equilibrium conversion
773 91.6
817 80.0
838 79.5
860 76.5
881 76.43
The values in Table 3.19 indicate that the reaction is highly
feasible and could happen as a side reaction during the process of methane
oxidation. Therefore experiments were designed to investigate the
kinetics of the shift reaction over the catalyst (0.4 wt % Pt/A1203) which
was used in the oxidation process of methane.
130
131
3.5.2.1 The reaction kinetics
The dependence of carbon monoxide conversion on contact time
was studied. In Fig. 3.54 the result shows that the reaction has an
initial rate characteristic up to 24% conversion. The experimental
results reported hereafter were carried out under such conditions that
the conversion of carbon monoxide was below 20%'in order that initial rate
interpretation could be applied.
The Arrhenius plot, Fig. 3.55, (ca. 673 - 873K) gives an apparent
activation energy of 38.95 kJ/mole.
The initial rate dependence on carbon monoxide, steam, carbon
dioxide and hydrogen is given in Figs. 3.56 to 3.59. The reaction
orders are summarised in Table 3.20.
TABLE 3.20
Reaction Dependences on Shift Reaction
CO + H2O = CO2 + H2
r a (A) n
Species A
'Concentration range [A) %
'Reaction order n
[H201/(C01 range
CO (4,23) 0.447 (6,1)
H2O (12,36) 0.366 (0.66,2.1)
CO2 (2,12) 0.0 1.85
H2 (0,10) -0.232 1.30
(10,24) -0.734 1.30
30 Catalyst : 0.4 wt% Pt / Al2 03 ( Porous )
Temp. = 817 K
20
CO
% C
onv
ers i
on
10
0 0 2 6 8 10 12 14 16
Contact Time , kg cat- sec /kmol x 103 18
1.85 1.80 1.75 1.70 1.65 1.40 1.45 1.50 1.55 1.60
ō E
0 U L
Temp. ( K ) 873 848 823 798 773 748 723 698
10 5 661
100 w 10 %(CO)in
w %A
16
Temp.= 815 K
%\C0'in - 13.2)
-r co I CO2)n
n= 0
Fig. 3.58
106 1 10 100
% (CO2)in
10 5
Temp.= K(17. 86
C0\in= ,.13.70~
O E ii
slope= -0.236
0 U
10-6
slope= - 0.734
t\ Fig. 3.59
i $ I i b I I I I i I$
1 10 100 % (N2 )in
137
The addition of hydrogen showed that the gas has a strong in-
hibiting effect on the reaction, which became stronger when the hydrogen
concentration level was higher than the steam concentration in the
reactor. The addition of carbon dioxide did not exhibit conspicuous
inhibitory effects.
3.6 Surface Characterisation
3.6.1 Adsorption experiments
3.6.1.1 Nitrogen adsorption
Surface areas of the catalyst samples were determined by nitrogen
adsorption. at 77K. Typical isotherms are shown in Figs. 3.60 to 3.62, from
which values of the surface area and total pore volume of the samples were
calculated. The results are listed in Table 3.21.
There was no significant difference in surface areas of the samples
before and after reaction. The sample which had been treated in the atmosphere
of steam at 1073K for 6/ hours was found to have lost its pore structure
completely.
TABLE 3.21
Nitrogen Adsorption
BET Pore Average pore Sample History surface volume diameter
area, m2/gm ml/gm nm
Pt/A1,0, fresh 115.5
(pr us)
Pt/A1 0 used as catalyst 106.2 (pb r3bus) for methane
oxidation
Pt/A1 0 treated in steam
5.04 (port us) at 1073K for
62 hrs
Pt/A1,0.2 fresh
2.84 (nbnorous)
Pt/Al 0 used as catalyst
2.49 (nbnOorous)for methane
oxidation
0.26 4.93
0.22 4.50
0 1.5 0.5 . to
1.4 0 0.2 0.4 0.5 0.8 1.0 1.2
P/ Pot m
P/ Pat m
5.0
4.0
Sample: 0.514 gm Reacted 0.4 Pt %/A1203 (Porous)
4— Adsorption 0— Desorption
0— Sample : 0.625gm 0.4 Pt% / A(203 ( Porous) Treated with 1120 at 1073K
for 71/2 hrs
0 71
Fig. 3.61
1.0
138
Fig. 3.60
0— Desorption
0-- Adsorption
Sample : 0.1159 gm Standard A1203
-c w .c S-o (/)
"0 « N
Z
0\ E
0.15
0.10
o o 0.2 0.4
Sample: 0.1363gm HT A1203
Surface Area = 2.84 m2/ gram
Fig.3.62
0.6 0.8 1.0
PI Patm
139
1.2
3.6.1.2. Carbon monoxide adsorption
The active sites on the catalyst surface were determined by carbon monoxide
adsorption at 196K (75 ). The adsorption isotherms for the catalyst samples
are represented in Figs. 3.63 and 3.64. The amount adsorbed at vacuum condition
for the corresponding sample is given in Table 3.22.
The results show that pure porous alumina has the ability to adsorb carbon monoxide to an extent of about 38% of that of platinum/alumina(porous) catalyst.
The sample of the platinum/alumina(porous), after treatment in steam for 6i hrs,
showed a weak ability to adsorb carbon monoxide.
TABLE 3.22
CO adsorption
140
Sample Structure History CO molecules adsorbed/gm
x 10-19
CO molecules adsorbed per BET Surface
x 10-17
m2)
A1203 porous
Pt/A1203 porous
Pt/A1 203 porous
Pt/A1 203
A1203 nonporous
Pt/A1203 nonporous
Pt/A1203 nonporous
Pt/A1 203 nonporous
Pt/A1203 nonporous
reduced in H2 at 793K
reduced in H2 at793K
used as catalyst 4.526 for methane oxi-dation 80 hrs
treated in steam 0.22 at 1073K for 62 hrs
reduced in H2 at 793K
reduced in H2 at 673K for hr
treated at 873K for 4 hrs
used as catalyst 1.57 for methane oxi-dation<40 hrs
used as catalyst 0.55 for methane oxi-dation> 40hrs
porous before
1.752
4.641
0.316
6.293
0.68
1.52
4.02
3.92
221.6
27.32
63.05
22.1
20
Alumina (Porous)
Q— Fresh, Pt/A[203
A—Used for Methane Oxidation Pt / A1203
0— Pure A1203
f--Treated in Steam at 1073 K for 2 hrs Fig. 3. 63
0 100 200 300 400 500 600 700 800
141
Pressure of CO ( torr)
Alumina ( Nonporous )
14.2
7, 0
ū 6.0
°' 5.0 ō
-10 .ā 4.0 1 0
I 3.0 0 a)
2.0 0
1.0
0
Q--- Fresh Pt / AI203
0-- Used as Catalyst for CH4 Oxidat i on<40 hrs
A-Treated at 873K for 10 hrs
0—Used as Catalyst for CH4 Oxidation> 40 hrs
2-- Pure A1203
Fig. 3.64
0 10 20 30 40 50
60 70
Pressure of CO
( torr
143
A series of experiments was carried out to examine the possibility of
deposition of carbonaceous residues during the course of methane oxidation.
A sample of platinum supported on porous alumina was suspended from the
microbalance in environments of different oxygen to methane concentration
ratios at two temperature conditions (773 and 853 K), until no change of
weight was observed. The system was then evacuated to 10- `torr and cooled to
195K before carbon monoxide adsorption was performed. It was shown that the
amounts of carbon monoxide adsorbed were found to decrease after the treat-
ments (table 3.23). In between each run, the surface area of the catalyst was
restored by oxidation (oxygen)-evacuation (vacuum)-reduction (hydrogen) procedure. The results show that the catalyst, after exposure in an atmos-
phere of methane, lost active surface area to about 74% at 773K and
92% at 853K.
No similar experiment was performed over platinum supported on nonporous
alumina catalyst, since it was anticipated that the result would be obscured
by the thermal sintering of platinum (see Table 3.22).
TABLE 3.23
Effect of carbonaceous deposit on the active surface area of a
platinum/alumina (porous) catalyst
Reaction pressure = 1 atmosphere
CO uptake at "clean" catalyst = 4.6x1019 molecules/gm
Reaction temperature
K
Oxygen to methane
ratio
Carbon monoxide uptake after
reaction. molecules/am x 10-19
773 2.0 4.22
773 1.0 4.20
773 0.5 3.87
773 0.0 2.40
833 2.0 3.71
833 1.0 2.53
833 0.5 1.56
833 0.0 1.43
144
The results on the nonporous alumina samples indicated that tremendous
sintering of platinum (nearly 10 fold)occurred when the sampleswere treated
at 873K for 4 hours. The catalyst sample which had been used in kinetic
experiments over 40 hours adsorbed 65% less carbon monoxide than the sample
which was used less than 40 hours (table 3.22).
3.6.1.3. Pyridine adsorption
The acidities of the supports were determined by pyridine adsorption at 293K., The isotherms for two kinds of alumina fibre are represented in Fig.3.65. The amount of pyridine adsorbed at vacuum condition is given in
Table 3.24.
The results show that the surface concentration of acidic site of the
nonporous support (represented by pyridine adsorbed per surface area of sample)
is about 10 times that of the porous support.
TABLE 3.24
Pyridine adsorption
Sample Number of molecules adsorbed Number of molecules adsorbed per gm of sample per surface area of sample
x 10-20 x 10-18
Porous 1.75 1.52 alumina
Nonporous 0.4 14.1 alumina
3.6.2. ESCA
Electron spectroscopy for chemical analysis has been used to study the
surface changes of the catalyst samples after methane oxidation (performed at
I.C.I., Mond Division). The instrument was an AEI ES2008B electron spectrometer.
The sample, under examination, was bombarded with achromatic Mg Ka X-rays,
whose main spectral line is at 1254 eV.
145
70
0— Pure Porous Alumina
— Pure Nonporous Alumina
40
30
20
Fig. 3. 65
Mol
ecu l
es A
dsor
bed
0 0 2 4 6 8 10 12 14
Pressure of Pyridine ( torr)
TABLE 3.25
Sample Peak Height Intensities x 104 c.p.s. % Atomic
Code Cls 015 Al2p Si2p Pt4d C 0 Al Si Pt
P-1 5.94 18.2 1.52 2.91 - 33 42 10 15
P-2 1.26 21.5 4.38 0.67 (<) 0.15 10 55 31 4 (<) 0.3
P-3 1.13 21.4 4.35 0.43 (<) 0.15 7 58 32 3 (<) 0.3
NP-1 4.68 14.6 0.80 2.80 33 42 6 19
NP-2 8.90 38.7 7.11 1.22 0.42 26 47 23 3.5 0.5
NP-3 9.10 45.9 1.82 6.90 0.26 24 51 5.5 18.5 0.1
(Pt4f)
* The (<) refers to the minimum level that could be measured above the background noise
using 0ls as the reference level with A1203 as substrate.
0'
147
The surface analysis is given in Table 3.25; and the results are expressed
both as peak height intensities x 104 c/s, and approximate atomic percentages.
The nature and history of the samples are described in Table 3.26.
TABLE 3.26
Sample
Nature of sample
code
P-1
porous alumina
P-2
0.4 wt% Pt impregnated
on porous alumina
P-3 0.4 wt% Pt impregnated
on porous alumina
nonporous alumina
2.3 wt% Pt impregnated
on nonporous alumina,
2.3 wt% Pt impregnated
on nonporous alumina
History of sample
used as a catalyst for methane oxidation
used as a catalyst for methane
oxidation at ca. 773-873 K for
80 hrs.
used as a catalyst for methane
oxidation at (02)/(CH4) < 0.5
and ca. 843 K for 6 hrs.
used as a catalyst for methane
oxidation
used as a catalyst for methane
oxidation for 25 hrs.
used as a catalyst for methane
oxidation for 50 hrs.
NP-1
NP-2
NP-3
148
3.7 The Catalytic Combustor
3.7.1 Introduction
The experimental catalytic combustor was constructed and tested using a methane-oxygen mixture. In order to obtain sufficient information to compare with the theoretical models, temperatures at various longitudinal as well as diagonal positions of the combustor were measured by sandwiched layers of thermocouples. The catalytic effect of the thermocouple on the methane oxidation process was checked by putting an equivalent length of chromel/alumel thermocouple wires into an empty differential reactor and flowing methane and oxygen at the standard feed condition (as stated in section 3.2.1). No conversion of methane was observed and hence the measured temperature profiles were not affected by the nature of the thermocouple wires.
The catalytic fibre pad was initially heated by a hot flowing stream of nitrogen. The gas stream was passed through a pure alumina fibre pad, inside which an electrical heating element was buried; the gas was heated and evenly distributed in this pad. When the temperature of the catalytic pad inlet reached 723K, the fuel stream was put on line and the electrical heating element was then switched off. The reaction was self-sustained, and, on reaching equilibrium, the signal detected by the thermocouple at each position was recorded by the multi-channel temperature recorder. After the steady state had been reached, gas samples were extracted within a millimeter of the front surface of the pad and from the gas space at the inlet. In order not to disturb the flow pattern, the sampling rate was always less than 0.5% of the gas throughput. Chroma- tographic analysis indicated that there was no CO or NOx emission. The radiative heat flux from the combustor was measured by an infra-red pyrometer and the temperature distribution on the front surface was detected by the allocated thermocouple. In daylight there was practically no visible sign of combustion but in darkened conditions (and especially with high reactant flow rates), a dull red glow could be seen emanating from the layers of fibre just below the surface of the pad.
3.7.2 Convective-diffusive catalytic combustor
In this case, methane was passed through the catalytic pad by
forced convection while the oxygen was supplied from ambient air, which
penetrated through the layers by the diffusive mode. At the conditions
studied, neither carbon monoxide nor nitric oxides were detected at the
front surface of the combustor.
3.7.2.1 The temperature profiles
Temperatures were measured at longitudinal and diagonal positions of
the combustor. Fig. 3.66 shows the longitudinal temperature distri-
bution at the centre position of the catalytic pad. The experimental
results for various input methane flow rates were also plotted on the
same graph. As shown in the figure, at each flow rate condition a hot
zone was observed inside the pad, which moved towards the outer surface
as the input methane flow rate was increased. At the lowest flow rate,
the hot zone was just at the back surface of the catalytic pad with a
temperature as much as 200K (approx.) above that of the front surface.
It was also found that, at the highest flow rate, the temperature distri-
bution was much smoother and the maximum temperature was only about 40K
higher than that at the front surface (Fig. 3.66). In Fig. 3.67 the
maximum temperature observed in the pad was plotted against the input
methane flow rate, and it is seen that the lower the flow rate the higher
the maximum temperature. However, if the flow rate was lower than ca.
6 ml/sec the reaction was no longer self-sustained and the heater was then
extinguished.
The lateral temperature profiles were measured by the thermocouples
which were fixed at the diagonal positions in four planes parallel to the sur-
faces of the combustor. In Figs. 3.68, 3.69 and 3.70 (various input
methane flow rates) the temperature profiles on different planes were plotted
against the diagonal positions. The centre of the heater appeared to have
the highest temperature, and the regions of the pad near the edge were cooled
down due to the conduction loss through the metal framework and the back
casing. With the highest flow rate, the lateral distribution became more
smooth and less different from other planes.
149
Outer Surface of the Heater
973 ml /sec
symbol (28K)
Q 12.05
Q 10.18
7.87
Q 6.20
Fig. 3.66
10 Depth of Heater ( mm )
0 5
> Direction of Flow
150
151
923
ci
°^ 873 a) s c a
v L a)
E a I-
E 823
E
773
6 7 8 9 10 11 12 13
Fuel Input ml /sec (298K )
9731
873
~ 773
Q) L-
.3 673 o S-Q) 0-E ~ 573
473
Flowrate = 12.05 ml/sec ( 298 K )
373~1 ------------~----------~------------~----------~--~ o 5 10 15 20
Diagonal Distance (cm
Distance from
Inlet (mm)
0- 0.0·
(J-- 3.0
0- 6.5
0- 10.35
Fi g. 3.68
.... \on f\)
Symbol :
Distance from , Inlet (mm)
0 0 0 0 0.0 3.0 6.5 10.35
0 5 10 15 20
973
873
Y 773
a)
673 L a CQ
a) I— 573
473
373
Diagonal Distance ( cm )
973
873
Distance from
Inlet (mm)
773 a)
a L
673 a)
573
o-- 10.35
Fig. 3.70
473
w U'
0 20 (cm)
Diagonal Distance ( Upper Right Corner to Lower Left Corner )
5
10
15
3.7.2.2 Diffusion of air into the pad
The oxygen supply to the combustion process is due to the mole-
cular diffusion of ambient air against the bulk flow of the fuel. The
diffusional rate is thus affected by the bulk flow rate: the higher the
bulk flow rate, the less air could penetrate into the catalytic pad.
In Fig. 3.71 the concentration probe analysis shows that, at the inlet
surface, the composition of nitrogen which diffused through the pad
decreased with increasing bulk flow rate. Extrapolation of the result
to zero bulk flow rate indicated that - at zero bulk flow conditions -
the composition of nitrogen at the back surface of the heater is 79%.
This shows that the pad is highly porous and that the basic resistance to
the air penetration into the pad is due to the opposite motion of the
bulk flow. Increase in the power input (increase in fuel input) would
also increase the rate of oxygen consumption and hence decrease the oxygen
level inside the pad. Fig. 3.72 shows the oxygen analysis at the back
of the pad; at a fuel input of 7.9 ml/sec, the oxygen level was 3.3%.
According to the results in Fig. 3.71, for no reaction the oxygen level
expected to be present at the back of the bed as a result of diffusion is
16.7%. Hence it is easy to show that almost 80% of the oxygen was
consumed before the end of its diffusional path. The percentage of
oxygen consumed was plotted against the fuel input and the results are
given in Fig. 3.72; this shows that the oxygen consumption rate increased
with increasing fuel input.
The analysis of the nitrogen distribution at the frontal surface is
given in Fig. 3.73. With the smooth profiles of nitrogen distribution,
the results indicated that the ambient air could evenly diffuse to the
front face of the heater. The nitrogen composition was a little less
than in unvitiated air, since it was diluted by the combustion products.
With the range of fuel input flow rate studied (6.25 - 12.05 ml/sec), the
nitrogen composition at the surface decreased from ca. 78% to ca. 70% as
the flow rate was increased.
3.7.2.3 The combustion efficiency
The methane combustion efficiency of the process was defined as
the amount of fuel burned per amount of fuel input. In Fig. 3.74, the
combustion efficiency was plotted as a function of the fuel input. The
combustion process had an average efficiency of ca.95% at the flow rate
155
C
C C
()( B
6Z) =as/l
w
% N2 at the Back of Pad 1~ N Q1 O O O O
04.
A
C
IA ID CD
% Oxygen At The Back Of Pad W A UI 01 V CO
co tn V1 O O p
loos oy, 6uiyor,aa oaojag pawnsuo3 uo64xO % O O
90
Fuet Inft ow ml /sec (298 K
ō O
6.25
Q 7.87
10.18
Q 12.05
Fig. 3.73
50 0 10 20
Diagonal Distance (cm
Fig. 3. 74
Power kw x 10
158
35
40 25
30 20 100
95
E 0 U
85
80 6 7 8 9 10 11 12 13
Fuel Input ( ml/sec) (298 K )
159
range studied; however the efficiency decreased about 3% as the fuel
input was doubled from 6m1/sec to 12 ml/sec.
3.7.2.4 The heat efficiencies
The energy generated from the catalytic combustion process is
transported by means of radiation, convection and conduction loss through
the metal casing of the combustor. • The heat efficiency of each transport
component was computed as the energy transmitted by the component con-
cerned relative to the energy released by the fuel that was consumed.
In Fig. 3.75, as the fuel input was doubled from 6 ml/sec to 12 ml/sec,
it was shown that the radiation and convection efficiencies increased
from ca. 50% to 70% and 10% to 20% respectively. The conduction loss
through the metal casing of the combustor (calculated by energy balance)
was eliminated when the radiation and convection efficiencies were improved.
3.7.2.5 Fuel slippage
As described in the previous sections, increase of the fuel input
results in better temperature profiles, more efficient radiation and
convection transports, accompanied by less conduction loss. However,
as shown in Fig. 3.76, the higher the fuel input, the higher the amount
of unburnt fuel which can slip through the catalytic pad. At an input
methane flow rate of 12 ml/sec, the slippage of unburnt fuel was up to
0.9 ml/sec.
3.7.3 Pre-mixed type catalytic combustor
An attempt was made to inject a pre-mixed oxygen and methane mixture in-
to the catalytic combustor. The experiment was unsuccessful because of a
severe explosion, involving a backward propagating flame starting inside
the pure alumina fibre immediately after the reactants were switched on.
As a result of current safety rules, no further experiments were attempted.
75
U
C
W
4- 50 4- w
25
0
40 20 100
6 7 8 9 10 11 12 13 14
0—Radiation Transport
n---Convection Transport
0—Conduction Loss
Power kW x 102 25 30 35
160
Fuel Input . ml/ sec (2981
35 30 25 1.0
0.4
0.2 Fig. 3.76
Power kW x 102
8 9 10 11 12
Fuel Input ml/sec (298 K )
161
162
4. Discussion
4.1 General 164
4.2 Chemical Aspects for the Catalytic Oxidation of Methane 166
4.2.1 The catalytic activities of the alumina supports 166
4.2.2 Platinum supported on porous alumina 171
4.2.2.1 Formation of carbon monoxide 171 4.2.2.2 Formation of carbonaceous deposits 173
4.2.2.3 Kinetics and mechanism of the reaction 175 4.2.2.4 The reaction stability 185 4.2.2.5 Catalyst deactivation 186
4.2.2.6 Methane-steam and water-gas shift reactions 187
4.2.3 Platinum supported on nonporous alumina 192
4.2.3.1 Kinetics of the reaction 192
4.2.3.2 The reaction stability 197
4.2.3.3 Effect of catalyst ageing 197
4.2.4 Effect of supports on the platinum/alumina catalysts 198
4.3 Physical and Mathematical Models for the Air Diffusive Type 199
Catalytic Combustor
4.3.1 Introduction 199
4.3.2 Mass and heat transport 199
4.3.2.1 Mass transport through the combustor 200
4.3.2.2 Mass and heat transport at the fluid-fibre interface 200
4.3.2.3 Intraparticle heat and mass transfer 203
4.3.2.4 Model of the internal radiation 203
4.3.2.5 Heat and mass transport by natural convection 209
4.3.3 Mathematical modelling for the catalytic combustor 210
4.3.3.1 General description of model 210
4.3.3.2 Simplified models 212
163
4.3.4 Evaluation of radiation efficiency 216
4.3.5 Steady state results 217
4.3.5.1 Comparison with experimental results 217 4.3.5.2 Parametric sensitivities 219
4.3.5.2.1 Effect of fuel input flowrate 219
4.3.5.2.2 Effect of pad thickness 228
4.3.5.2.3 Effect of void fraction 231
4.3.5.2.4 Perturbation on lumped thermoconductivity 251
164
4.1. General
The objective of the present study has been to study the catalytic
combustion of methane over platinum/alumina catalysts. The feasibility
of applying catalysis to energy generation processes has been demonstrated
by oxidizing the fuel through a convective-diffusive type catalytic
combustor which can be used as an option for domestic heating purposes.
The experimental results have been compared with the predictions of a
mathematical model.
In general, the catalytic combustion process is a combination of
catalysis and transport phenomena; and the performance of the combustor
is affected by the chemical and physical factors governing the oxidation. In order to obtain a detailed description of and to model the combustor
performance, the course of this investigation has been divided into
three parts: (1) measurement of the kinetics of methane oxidation, from
which attempts have been made to indicate the chemical factors that
affect the process; (ii) measurement of the thermal behaviour of the
combustor at practical conditions; (iii) applying the results obtained
in the kinetic experiments and simulating the heat and mass transport
processes; physical and mathematical models have been set up to compare
with the experimental observations. Studies of parametric sensitivity
based on the theoretical models have also been made.
During the course of these studies the following phenomena were
observed:-
(I) Kinetic Measurements
(1) The pure alumina supports catalyse the oxidation of
methane. With the high surface area alumina (porous),
carbon dioxide is the only carbon compound in the product
stream. With the low surface area alumina (nonporous),
the product stream contains mixtures of carbon oxides.
(2) Carbon monoxide oxidizes on the pure porous alumina with
a maximum conversion of ca. 80% at a reaction temperature
of ca. 800K; while carbon monoxide only slightly oxidizes
on the pure nonporous alumina.
(3) Surface analysis shows that, on both pure alumina supports
used to oxidise methane, some coverage of carbonaceous
residue exists.
165
(4) Overall oxidation of methane is always attained with
platinum/alumina catalysts provided the process is
operated at suitable conditions. The conditions under
which carbon monoxide appears in the reactor product
stream are:
(a) high reaction temperature ( >ca. 823K) and low
oxygen to methane ratio (<2, the reaction stoichiometry);
(b) if the catalyst was pre-treated in steam at high
temperature, 1070K;
(c) after catalyst aging due to usage over long periods.
(5). Kinetic studies on methane oxidation over platinum/
alumina catalysts reveal that:
(a) the activation energy changes (decreasing in mag-
nitude) at the reaction temperature of ca. 813K;
(b) the reaction order with respect to oxygen concentration
also changes in the range of reaction temperature corres-
ponding to the change of the apparent activation energy;
(c) the reaction is not significantly inhibited by the
major products of oxidation.
(6) In oxygen free environments, methane does not react with
steam in the temperature range of ca. 600-1000K over
platinum/alumina catalysts. A study of the water gas-
shift reaction over the same catalyst shows that carbon
dioxide and hydrogen are the products of the reaction, and
the reaction is inhibited by hydrogen.
(7) The reaction temperature ran away when methane was
admitted to the reactor before oxygen, over a catalyst
supported on the porous alumina. No such effect was
observed when the operation was reversed, nor over the
catalyst supported on nonporous alumina.
(8) Carbon monoxide quickly oxidizes on the platinum/alumina
catalysts in the absence of methane. Substantial loss in
carbon monoxide oxidation activity was observed after
using the nonporous catalyst for 40 hours.
166
(II) Measurement of the combustor performance
(1) For each fuel input flowrate condition, a hot zone was
observed inside the catalytic pad.
(2) The hot zone moved towards the outer surface as the input
fuel flowrate was increased.
(3) The temperature profiles were smoother at higher flowrates.
(4) The higher the bulk flowrate, the less air could penetrate
into the catalytic combustor.
(5) Increase in the fuel input increased the rate of oxygen
consumption and hence decreased the oxygen concentration
inside the combustor.
(6) The ambient air could evenly diffuse to the outer surface
of the combustor. The nitrogen composition at the outer
surface was slightly less than in unvitiated air, as a
result of mixing effects•
(7) As the input flowrate increased, the amount of unburnt fuel
slipping through the combustor also increased.
(8) In the range of flowrate studied, the heat efficiency due to
radiation transfer increased with increasing flowrate.
(9) Neither carbon monoxide nor nitric oxides emission was
detected at the outer surface of the combustor.
4.2. Chemical Aspects for the Catalytic Oxidation of Methane
In the following sections, the discussion will be focussed on the
facts observed in the kinetic study. The chemical factors that affect the
activity of the reaction are discussed mechanistically. The effect of
mass and heat transfer processes are also examined.
4.2.1. The catalytic activities of the alumina supports
The experimental results show that the pure alumina supports are
not catalytically inert to the methane oxidation process. The product
spectra of methane oxidation (Figs. 3.1 and 3.2) show that the porous
alumina catalyses the reaction to produce carbon dioxide while the non-
porous alumina favours selectivity to carbon monoxide.
167
The catalytic activity of the alumina supports could be attributed to
the surface acidity of the materials. Pyridine titration experiments
(Fig. 3.65, and Table 3.24) indicate that both alumina fibres adsorb the
basic reagent while the nonporous fibre possesses a higher surface concen-
tration of acidic site (expressed by pyridine molecules adsorbed per sur-
face area of sample). The occurrence of acidity could be due to the
existence of surface silica-alumina, as shown by ESCA (electron spectro-
scopy for chemical analysis) (Table 3.25). In concurrence with pyridine
titration experiments, the ESCA result shows that the nonporous alumina
fibre exhibited Si2p signal with a peak intensity higher than that of
porous alumina.
Taylor et,al, ( 80) believed that chemical interaction between a carbon atom of a hydrocarbon with catalyst acid sites would necessitate
the breaking of a carbon-hydrogen bond prior to the formation of a
carbonium ion. Their experiments on exchange reaction between methane
and deuteromethanes over silica-alumina showed that the reaction occurs at
618K, a temperature considerably lower than that at which methane oxidation
takes place. This would mean that, in the methane oxidation process,
carbon-hydrogen bonds are quite easily broken and adsorption of the
carbonaceous species would occur at the acidic centres. The samples (both
porous and nonporous alumina), after use for the methane oxidation, were
examined by ESCA; the results were compared and interpreted qualitatively.
The analysis showed existence of carbonaceous deposits (Table 3.25).
Alkhazov, et.al. ( 81), in their work on the oxidative dehydro-
genation of ethylbenzene on alumina catalysts also reported that the
hydrocarbon, being adsorbed on the most acidic centres of the catalyst
surface and reacting with oxygen strongly bonded with the surface, under-
goes oxidative transformation with formation of oxidation carbonaceous deposits. These deposits are strongly retained on the catalyst surface.
The residues can interact with weakly adsorbed oxygen or with oxygen
from the gas phase (by an impact mechanism) to oxidize further to carbon
oxides.
These concepts are applied in the present approach to suggest a
reaction mechanism for methane oxidation over acidic alumina catalysts.
The mechanism suggested involves the following steps:
(i) adsorption of methane on the acidic centres;
(ii) oxidation of the adsorbed carbonaceous species by adsorbed oxygen
or by oxygen in the gas phase.
168
However, the experimental results show that the selectivity of
methane oxidation and the reactivity of carbon monoxide over the two types -
of. alumina supports are different. The nonporous alumina favours the
formation of carbon monoxide and is less active for the oxidation of
carbon monoxide, while the porous alumina catalyses both methane and carbon
monoxide oxidation to form carbon dioxide. The difference in the cata-
lytic behaviour may be due to the following effects:
(1) surface initiated homogeneous reaction
(ii) pore diffusion
(iii) nature of the surface acidity
Methane oxidation over either silica or alumina surfaces can lead to
a hetero-homogeneous process as reported by Russian workers ( 40 ).
They discovered that the amount of homogeneous reaction (which is surface
initiated) over silica surfaces is much higher than that over alumina
surfaces, and that the materials themselves could catalyse the reaction
heterogeneously. They also reported that, over silica, methane oxidizes
to carbon oxides and formaldehyde, while it oxidises completely over
alumina. A part of their results is extracted in Table 4.1.
TABLE 4.1 *
Temperature = 873K, 02:CH4 = 1:2
Catalyst Oxygen %
Conversion %
Homogeneous contribution
5'102
5 1.0 30
20 4.0 18
A1203 5 6.7 12
20 21.0 5
* From reference ( 40) .
169
According to their data, alumina favours homogeneous reactions less than silica, and increases in oxygen concentration in the system would also reduce the homogeneous effect. As a result, the effect should be small in the present system. In agreement with this, experiments on the silica reactor containing silica pellets (at the standard feed condition) showed that methane could only be oxidized above 900K (Section 3.2). In view of these observations, even if the homogeneous effect existed, its influence on the overall conversion should not be significant within the ranges of feed conditions ([02)/[CH4] >1) and temperature (< 873K).
The difference in the reaction selectivity may be affected by pore diffusion. The alumina with the porous structure could capture the
reaction intermediate (carbon monoxide) for a longer period inside the
pores and overall oxidation to carbon dioxide would be favoured. In agreement with this, experiments on the nonporous alumina support in-dicated that the selectivity of carbon monoxide decreases with increasing catalyst contact time.
The difference in catalytic behaviour between the two types of alumina could also be caused by the fact that the surface acidity of the nonporous alumina is higher than that of porous alumina. The influence of catalyst surface acidity on hydrocarbon oxidation is directly reflected in the selectivity of oxidation intermediates ( 81 , 82 ). Acidic alumina, possessing higher surface concentrations of acidic sites, would be expected to (and does)favour incomplete oxidation. In addition, compari- son of the oxidation activities of methane over the two types of alumina (Fig. 4.1) shows that the nonporous alumina (which has higher concentra- tion of acidic centre) had a higher specific activity. This would pro- bably indicate that the nature of the acidic centre on the surface of these two alumina fibres may be different and would affect the reaction
mechanism of the oxidation process to different extents. The nature of the acidic centres could not be differentiated by the pyridine adsorption experiment.
To summarise, the oxidation of methane on the supports is consistent with a reaction mechanism involving carbonaceous intermediates. The differing selectivities observed may result from differences in pore structure or in surface acidities between the two supports.
mo l/(
acid
ic sit
e)-
sec
1.40 1.45 1.50 1.55 1.60
RT x 101 mol/kJ
170
Q-- Nonporous Al203
Porous A1203
%(p24)in -(21.3 /
Assumption
Acidic Site Pyridine MoleculeAdsorbed = 1 . 1
Fig. 4. 1
171
4.2.2. Platinum supported on porous alumina
4.2.2.1. Formation of carbon monoxide
The product composition spectra, described in Figs.3.8, 3.9 show
that the reaction temperature critically affects the product distribution
when the effective oxygen to methane ratio is lower than the overall
oxidation stoichiometry ((02)/ (CH4,<2). In the temperature range studied
(ca. 753 to 873K), carbon dioxide and carbon monoxide are the only products
of the reaction, and the selectivity to carbon monoxide increases with increa-
sing temperature when the oxygen to methane ratio inside the system is lower
than unity. The appearance of carbon monoxide at such conditions may be due
to the following reasons:
(i) insufficient oxygen is present in the system. If the oxidation of
carbon monoxide were rate limiting, competition with methane for
oxygen would allow the reaction intermediate to pass through the
reactor;
pore diffusion limitations. The carbon monoxide formed by methane
oxidation at the external surface of the catalyst does not have suf-
ficient time to react.;
(iii) the carbon monoxide produced is kept away from the active surface
at high temperatures (above ca. 813K) when the oxygen to methane ratio
is lower than unity.
The possibility of carbon monoxide oxidation being the rate limiting
step was examined by measuring the oxidation reactivity of carbon monoxide
on the platinum/alumina catalyst under various conditions of reaction temper-
ature and oxygen concentrations (Tables 3.7, 3.8). The results were compared
with those obtained from the methane oxidation experiments •(over the same cat-
alyst). Since complete conversions were always achieved with carbon monoxide
oxidation, it is unlikely that the appearance of carbon monoxide is due to
its slow reaction rate during methane oxidation. Addition of steam to the
reaction system did not obviously inhibit the oxidation of carbon monoxide
in the range of reaction temperature ca. 673 to 873K (even when the ratios of
PH20) / [02) and [H20]/(CO) were as high as 4.6 and 5.7 respectively) . Neither
was the oxidation inhibited by the addition of carbon dioxide.
Nicholas,et.al. (83) reported the kinetics of carbon monoxide oxidation
over a platinum-porous glass fibre supported catalyst across a temperature range
of 728 to 888K. The initial rates of carbon monoxide oxidation, from their
kinetic data under various conditions of temperature and oxygen concentration
are compared with the initial rates of methane oxidation obtained in the present
investigation (Table 4.2). Assuming that Nicholas' catalyst has the same
specific surface of platinum as the
172
TABLE 4.2
Temp.
K
Oxygen Composition
%
* CO Oxidation CH4 Oxidation CO
Composition
%
-rC0
kmol
CH4 Composition
%
-rCH
4 kmo1 kg - sec kg - sec
773 20 10 1.203x10-1 10 1.853x10-3
813 20 10 I.404x10-1 10 7.764x10-3
853 20 10 1.612x10-1 10 9.037x10-3
773 10 10 5.730x10-2 10 1.102x10-3
813 10 10 6.687x10-2 10 1.938x10-3
853 10 10 7.678x10-2 10 3.520x10-3
773 5 10 2.729x10-2 10 4.293x10-4
813 5 10 3.185x10-2 10 7.550x10-4
853 5 10 3.700x10-2 10 1.371x10-3
* Kinetics obtained from reference (83 ).
173
present catalyst, the initial rate of carbon monoxide oxidation is at
least an order of magnitude faster than that of methane.
To sum up the above, oxidation of carbon monoxide could not be
the limiting step in the process of methane oxidation over a platinum
catalyst. However, the presence of carbon monoxide in the product stream
could be due to inhibition on the catalyst surface, which was due to neither
adsorbed water nor carbon dioxide.
The problem of pore diffusion is unlikely to affect the appear-
ance of carbon monoxide because if there is diffusional limitation in
methane oxidation, then the same phenomenon should be observed in carbon
monoxide oxidation experiments. Complete conversions of carbon monoxide were always achieved with the porous catalyst.
On the basis of the product distribution spectra (Figs. 3.8 and
3.9)) the concentration ratio of oxygen to methane effectively present in
the reactor could influence the reaction mechanism. Thus, from Fig. 3.8,
the effective oxygen to methane ratio (approximated by the average between
the inlet and outlet compositions) in the temperature range of ca. 733 to
813K has changed from ca. 1.0 to 0.8 with the predominance of carbon di- oxide. Carbon monoxide appears above 813K when the ratio is lower than
0.8. One could suggest that methane oxidizes on the platinum/alumina
catalyst to produce only carbon dioxide up to ca. 813K, when the effect-
ive oxygen to methane ratio is above 0.8. The reaction gives carbon mon-
oxide, possibly by another mechanism, at temperatures above ca. 813K and
with the effective oxygen to methane ratio below ca. 0.8; the carbon mon-
oxide formed does not oxidise further at high temperatures.
4.2.2.2. Formation of carbonaceous deposit
Studies of carbon monoxide adsorption of the catalyst sample after
treatments at various conditions for methane oxidation suggested the exist-
ence of carbonaceous deposit on the catalyst surface (Table 3.23). The
deposition was found to increase with increasing temperature and decrease
with increasing oxygen to methane ratio. Thus, the sample, after use as
catalyst at 853K when the oxygen to methane ratio was lower than unity,
was found to have over 40% of its active sites occupied. If these pb-
servations are fitted with the product distribution spectra obtained
from the kinetic studies of methane oxidation, it can be suggested that
the deposition of carbonaceous residues on the catalyst surface has the
effect of blocking the selectivity for carbon dioxide production.
174
Formation of the carbonaceous deposit could be initiated by adsorp-
tion followed by decomposition of methane on the catalyst surface. The
chemisorption of methane is known to be dissociative, and the possible
mechanism is ( 84):
CH + 2 * ----~ CH + H 4 * 3
CH + 2 * —~- CH + H * 3 **2
CH + 2 * --> Cu + H **2 *** *
CH +2 * C +H *** **** *
4H 2H2 + 4 *
The sign (*) denotes an active site.
Those adsorbed species occupying more than two active sites (such
as CH2, CH, C) are believed to be strongly bonded, and they are collectively
named as carbonaceous deposits. It is likely, however, that the carbon-
aceous deposit is most strongly chemisorbed on the "bridge sites" as bridge-
bonded methylene radicals (84) and that oxidation involves primarily the
reaction of less stable linearly-bonded radicals with surface adsorbed
oxygen or oxygen in the gas phase ( 81 , 85) . Binke and Petersen (86) ,
in their work on the hydrogenolysis of cyclopropane over alumoplatinum
catalyst, suggested that coke formation begins on the alumina and then
encroaches on the platinum islands. The residual activity is explained
by the inability of the carbon particles to cover completely the platinum
atoms having a low coordination number.
Using the data obtained from carbon monoxide adsorption studies on
"clean" catalyst (Table 3.23), the quantity of surface platinum atoms is
calculated as 6.133 x 1019 atoms/gm (taking the adsorption stoichiometry
as 0.76 ( 74)). Assuming that 50% of the surface is covered with mono-
layer carbonaceous deposit and that the kinetic expression given by Weisz
et.al. (87 ) is valid, the burning rate of the carbonaceous deposit on the
surface can be calculated:-
where
-rc = k•P02,C c (4.1)
the rate constant, k = 1.9 x 108 exp (18923 /RT) sec 1.
atm 1,
Cc is the moles of carbon present per gm of catalyst,
Po2 is the pressure of oxygen, atm.
175
The burning rate, at 823K and PO 2 = 0.1 atm, is 1.0 x 10-7 mole/sec-gm.
Compared with methane oxidation, the burning rate of the carbon-
aceous deposit is much slower than the oxidation rate of methane. There-
fore, the catalyst would only be able to provide a portion of its active
surface for methane oxidation under conditions where simultaneous carbon-
aceous deposition occurs. However, the time required to regenerate the
active surface in 30% oxygen and at 793K is
tb = J do 20 min. rc
This time approximately agrees with the experimental result,
reported in Table 3.10, that the catalyst, after exposure in an atmosphere
of methane at 823K, was found to decrease its activity for methane oxida-
tion at 793K for only the first 15 min after admitting the reactant
mixture into the reactor.
4.2.2.3. Kinetics and mechanism of the reaction
Measurements of the kinetics of the oxidation reaction in the
temperature range ca. 723 to 873K shows a change in the apparent activation
energy at about 813K giving a value of 187.06 kJ/mole over the lower
temperature range and 86.02 kJ/mole in the higher temperature range.
The effect of pore diffusion limitation on the shift of the apparent
activation energy could not be examined by conventional methods (checking
the activity by varying the particle size). Alternatively, the effect was
checked theoretically by assuming that the kinetics in the low temperature
region (below 813K) is intrinsic. However, as shown in Table 3.2, the
calculation indicates that the effect of pore diffusion limitation should
not be significant if the chemical kinetics of the reaction were retained
in the high temperature region.
Homogeneous oxidation of methane could be initiated by silica
(reactor wall) or alumina (supports) ( 40) (See section 4.2); however, it
should not be significant at temperatures below ca. 873K. Another
related work on methane oxidation over nickel/ceramic catalyst ( 88)
demonstrated the presence of heterogeneously initiated homogeneous reaction
at temperatures only above ca. 1073K. As a result, the following dis-
cussion on the kinetic observations and the mechanistic explanations must
be related to the surface phenomena.
The reaction orders were measured at two temperatures which were
bounded in the regions of the two different apparent activation energies.
(4.2)
176
The initial rate relationships observed were:-
a at 786K,
and
at 817K, -d(CH4)/dt « (CH4). (02)
in the range of {021 / (CH4J from 0.75 to 2.2.
These rate expressions suggest that the rate determining steps of the
reaction, in both low and high temperature regions, are the interactions
between the reactants. However, because the reaction orders with respect
to oxygen concentration are different, the features of interaction could
not be the same in both temperature regions.
The rate expressions obtained in the present study show some
differences from expressions found in the literature (45,68). In particular,
the oxygen dependence has been generally reported to be zero-order. The
difference could be due to the fact that the P revious works were not
carried out at low oxygen to methane ratios (usually (02]/(CH4) » 2) when
determining the order to oxygen. Certainly, the order with respect to
oxygen should be zero when oxygen concentration is in excess.
The 1st and ith order dependence on methane and oxygen concentration
suggest that, at low temperatures, gas phase or weakly adsorbed methane
reacts with oxygen which may be both diatomically and monoatomically
adsorbed. In the temperature range of ca. '673 to 873K, oxygen adsorbs on
platinum surface to form more than one adsorbed state ( 89 , 90 , 91 , 92 ).
Ion-Ion emission mass spectra have shown the most likely chemisorbed states
for oxygen on platinum are Pt0 and Pt02 (91 ). Oxygen isotopic exchange
( 91) showed that oxygen adsorption is dissociative so that, even in the
form of Pt02, a platinum atom is shared by two atoms of oxygen from two
different molecules. However, it is natural to expect that adsorbed
oxygen molecules would enter as a whole into Pt02. The positive constant
order dependence on methane concentration at low temperature in the range
of oxygen to methane ratio, 0.75 < [021 /(CH4I < 2.2, would imply either
that methane is not adsorbed on the catalyst surface or that the catalyst
surface consists of two types of site, one of which slightly adsorbs
methane while the other adsorbs oxygen.
The kinetic data, obtained in the low temperature range, were thus
fitted with various possible Langmuir-Hinshelwood kinetic models (Table 4.3)
by nonlinear regression (Powell's conjugated method) (93). Among the
tested models, the dual site model, which shows the best fit to the
experimental data (see Fig. 4.2), has a mathematical expression:
-d [CH4) /dt a (CH41. (02)
177
_ k1 (CH4).[o2) + k4 CH4).(02) r CH4 - {1 + k2(02)i} {1 + k3 (02}} (4.3)
The expression describes the interaction between the gaseous methane
and surface oxygen which is adsorbed monoatomically and diatomically on
two different sites.
At 793K
k3 = 1.735 x 10-2
k4 = 4.510 x 10-4 , kmol/kgcat-sec
).= molar fraction of species
It is interesting to note that the ratio k4/k1 has a value of 0.25.
This would mean that the reaction probability for the monoatomically
adsorbed oxygen is four times higher than that for the diatomically
adsorbed oxygen. This is possibly due to the fact that the maximum
oxygen surface coverage corresponds to a Pt0 structure, in agreement with
the result reported by other investigators ( 91 , 94 , 95 , 96 ) .
The apparent activation energy in the low temperature region
(ca. 723 to 813K) has a magnitude of 187.06 kJ/mole which is well in agree-
ment with the value of 200 kJ/mole reported by Firth et.al. ( 45) in the
temperature region between 690K and 783K. The desorption energy of
oxygen on platinum at 800K was reported as 177.65 kJ/mole (92). In view
of the strength of the desorption energy, it is likely that the activation
energy for the reaction would be dominated by this oxygen-platinum binding
energy.
The first order dependence on oxygen concentration at high tempera-
tures indicates that the adsorbed state of oxygen on platinum is no longer
rich in the monoatomically adsorbed structure. The disappearance of the Pt0
adsorbed state could be due to the result of carbonaceous deposits at high
temperatures. On palladium catalysts, it was suggested ( 68) that carbon,
formed during the oxidation of methane, is deposited selectively on high
energy bridge-bonded sites. In the platinum catalyst, the bridge-bonded
sites are likely to be those neighbouring platinum surface atoms which
adsorb oxygen monoatomically.
As distinct from low temperatures (below ca. 813K), methane
exhibits a higher adsorption ability and competes for surface sites with
oxygen. There could be two reasons for this: (i) the cracking rate of
methane is higher at high temperatures, as shown by the carbon monoxide
adsorption experiments (Table 3.23) (the higher the temperature, the higher the
kl = 1.810 x 10-7 , kmol/kgcat-sec
k2 = 7.34 x 10-3
TABLE 4.3
Matrix of Surface Reaction Models (a)
Models CH4 02 CO2 H2O Site
1 1 1 0 0 1 *
2 1 1 0 0 2
3 1 2 0 0 1 *
4 1 2 0 0 2 * *
5 1 1 ,2 0 0 3 * *
6 0 1 ,2 0 0 2
(a) 0 : gaseous state 1 : unimolecular adsorption state 2 : dissociative adsorption state * : different catalytic site
Site 1,2, and 3 : single, dual and triple site respectively
178
10
0 0 10 20 3 0 40
40
30
180
amount of carbonaceous deposit); and (ii) the sticking probability (defined
as the ratio of the rate of adsorption to the collision rate with the
surface) of oxygen on platinum surface dramatically decreases at tempera-
tures above ca. 823K, as reported by Nishiyama and Wise (92 )whose result
is duplicated in Fig. 4.3:
700 81-3 900 ,Tro Temp. I K I
Fig. 4.3 Variation in sticking probability of oxygen with platinum
surface temperature (From reference (92))
The appearance of carbon monoxide above ca. 813K at low oxygen to
methane ratio (102)/(OH
4) <1) (see Fig. 3.8) would thus be explained in
terms of shifting the reaction mechanism. At temperatures below ca. 813K,
oxygen could be easily adsorbed on the surface and the reaction between
the strongly adsorbed oxygen and either weakly adsorbed methane or gaseous
methane produces carbon dioxide. At temperatures above ca. 813K, oxygen
is less strongly adsorbed while methane is easily adsorbed on the surface;
as a result, the interaction of strongly chemisorbed methane radicals with
gaseous oxygen and weakly chemisorbed oxygen gives carbon oxides. Further
oxidation of carbon monoxide is inhibited by the high coverage of carbon-
aceous deposit and methyl radical on the catalyst surface. Furthermore,
carbon monoxide could also be produced as a result of reaction between
carbon dioxide and carbon deposit on the surface (97),
CO2
C = 2C0
181
The experimental results, (Figs. 3.12 and 3.13) suggest that the
adsorption of methane and oxygen at high temperatures is competitive in
nature. The higher the oxygen concentration (or the higher the (021
/(CH4) )
the higher the surface coverage of oxygen and the higher the carbon
dioxide production (Fig. 3.12). Increase in methane concentration (or
decrease in (02) /(CH4)) would increase production of both carbon oxides
simultaneously. Further increase in methane concentration (1021/[CH4J< 0.75)
would result in full surface coverage of methane and thus favour carbon
monoxide production at the expense of.carbon dioxide.
The experimental results obtained at 830K were fitted with
Languir-Hinshelwood kinetic models (Table 4.4) by nonlinear regression
(Powell's conjugated method) ( 93). Among the tested models, the
reaction model which invokes qualitatively the concept of simultaneously
occurring surface and gaseous impact mechanism shows the best fit to the
experimental data (see Fig. 4.2). The model has a mathematical
expression: fr
-r kl {CH4).{02) + k41CH4)'~02) CH4 {1 + k2(CH4) + k3(02)}2 {1 + k2 (CH4)+ k3(021}
(4.4)
At 830K the parameters, with a standard deviation (in methane conversion)
of + 3.27% (below the allowable range of experimental error + 5%) are:
kl = 3.138 x 10-3 kmol/kgcat-sec
k2 = 6.669
k3 = 4.337 x 10-3
k4 = 2.639 x 10-4 kmol/kgcat-sec
Assuming that at high temperatures the adsorbed state of oxygen has
a Pt02 structure, the first term of eq. (4.4) describes the interaction
between adsorbed methane and diatomically adsorbed oxygen; through this
mechanism the product selectivity is dominated by carbon dioxide. If
k2(CH4) is predominant in the denominator (at low [02)/(CH4)), eq. (4.4)
reduces to r11
-rCH
= k21021 + k4 • (02)2 (4.5) 4 k2 ~ CH4 ) k2
At constant oxygen concentration, the first term diminishes with
increasing methane concentration and thus describes the negative tendency
observed for the selectivity for carbon dioxide, with respect to high
TABLE 4.4
Matrix of Surface Reaction Models (a)
Model CH4 02 CO2 CO H2O Site
1 1 1 *
0 0 0 1 2 1 1 0 0 0 2 3 1 0 0 0 . 0 1 4 1 1,0 0 0 0 1
(a) 0 : gaseous state 1 : unimolecular adsorption state * : different catalytic site
Site 1 and 2 : single, dual site respectively
182
183
methane concentratiop ([02] /(CH4) <0.75).
The second term of eq.(4.4) describes the interaction between adsorbed
methane and gaseous oxygen at high temperature; through this impact mechanism
the product selectivity is dominated by carbon monoxide. The ratio of the
first and second terms of eq.(4.4) reflects, then, the relative rate of
methane oxidation through these two mechanisms; the ratio being
= k4 .11 + k2 (CH4J+ k3(02]}. [02J -1
rs k1
If k2(CH4)/k3(02)is large, then eq.(4.4) reduces to
= k4 .11 + k2 [C1-1411. [02) - rs k1
(4.6)
(4.7)
Eq.(4.7) shows that the relative importance of the gaseous impact
reaction path decreases with increasing oxygen concentration, and thus
describes the negative tendency, observed on the selectivity for carbon
monoxide, with respect to increasing oxygen concentration.
Since the reaction at high temperatures (above ca. 813K) is sugg-
ested to involve significant chemisorption of methane, the activation
energy for the surface reaction at high temperatures is related to the
heat of adsorption of methane,
E2 = E1 + Rad
(4.8)
where E2 is the apparent activation energy of the reaction above
813K;
E1 is the true activation energy of the reaction and could
be approximated as the activation energy at low temperatures;
Qad is the heat of adsorption of methane.
The chemisorption of methane is dissociative ( 84) and, in view
of the strength of the hydrogen-to-oxygen bond, it is most likely that
the hydrogen atom formed in this dissociation will be bonded to adsorbed
oxygen.
184
In this case,
- 4ad = EPt-C + E0-H - EC-H (4.9)
A value of the carbon-to-platinum bond was given as 29 kJ/mole
( 98), and the strengths of oxygen-to-hydrogen and carbon-to-hydrogen
bonds are given as 492 and 435 kJ/mole (99) respectively. Hence, from
eq.(4.9), the heat of adsorption of methane is calculated as -86 kJ/mole.
Therefore the apparent activation energy of the reaction at high temp-
eratures, E2 is approximated by eq.(4.8),
E2 = 187.1 - 86 = 101.1 kJ/mole
The value has a similar magnitude as the observed apparent act-
ivation energy (86.02 kJ/mole) in the kinetic experiments. The dis-
crepancy may be due to the weaker platinum-oxygen binding energy at high
temperatures. However, the model rationally explains the change of the
apparent activation energy.
In order to sum up the above discussion, the nature of the rate
determining step in the process of methane oxidation over the platinum/
alumina catalyst is summarized in Table 4.5.
TABLE 4.5
Possible mechanism of methane oxidation.
Temperature [02J/[CH41
state at reaction
product oxygen methane
<813 0.5 - 2.2 monoatomically and diatonically adsorbed
gaseous or weakly adsorbed
CO2
>813 075 - 2.2 diatomically adsorbed
strongly adsorbed and carbonaceous deposit
CO2 (main)
CO
>813 <0.75 .
weakly adsorbed or gaseous phase
strongly adsorbed
CO (main) CO2
185
Product addition experiments showed that the oxidation products
(CO2' CO and H20) do not inhibit the reaction, except that addition of
carbon monoxide over ca. 10% was found to result in thermal instability.
These observations indicate that the desorption of the reaction products
are not rate determining in the oxidation process. Firth, et.al. (100)
observed that steam strongly inhibits methanol oxidation over platinum
wire catalyst but there is no significant influence on the reaction over
platinum on a - or y - alumina carrier. They interpreted the phenomenon
in terms of alumina being able to act as a sink to remove some of the
adsorbed water or hydroxyl groups from the surface of platinum, so that
the metal surface is always available for the oxidation process.
Especially in steam reforming processes, the catalytic activity of
alumina has been reported and a role of the carrier for steam adsorp-
tion has been suggested elsewhere (101).
4.2.2.4. The reaction stability
The thermal effects observed in the experiments are listed as
follows:
(i) The reaction temperature ran away from ca. 820K to ca. 853K (at
a contact time of 1400 kgcat-sec/kmol) when the reactant mixture con-
tained low oxygen to methane ratios ((02]/(CH4] ca. 1.0). No such
phenomenon was observed with high oxygen to methane ratios.
(ii) The reaction temperature ran away from 773K to ca. 853K at a
contact time of 1400 kgcat-sec/kmol when the methane stream was admitted
into the reactor before the oxygen stream. No such phenomenon was
observed when oxygen was switched on first.
Before attempting to interpret the phenomena by chemical reasons,
one must anticipate that the thermal instability may be due to the
inter-intraphase temperature gradients which could cause an exothermic
reaction to run away. Since the fibre catalyst has a diameter of
micrometric order, it could be expected that the fibre itself
was isothermal. The fluid-solid temperature gradient was checked by
utilizing the energy balance,
Q = h•Sg•OT (4.10)
where
Q is the power released due to the oxidation reaction,
W/gm-cat;
h is the fluid-solid interphase heat transfer
coefficient, W/m2;
186
Sg is the specific surface area of the catalyst and
has a value of 120 m2/gm;
AT is the temperature gradient at the solid-fluid
interphase, K.
With the conditions used in the experiments (Fig. 3.8) the
power, Q, generated due to the reaction is 80.2 W/gm-cat; and the
heat transfer coefficient is calculated (102) as 28.5 W/m2 (see sec.
4.3.2.2.). The temperature gradient, AT is then predicted by eq.(4.10),
AT = Q/h•Sg = 0.02K (4.11)
It was thus shown that the temperature difference between gas
phase and catalyst bulk was minute, and that the system was virtually
isothermal.
The limits of flammability for methane-oxygen-nitrogen mixtures
have been reported in the range of (02)/(CH4) from 1.5 to 4.0 under
similar conditions (103). Utilizing this criteria, it is unlikely
that the thermal instability observed was due to the flammability
characteristics of the mixture.
It would seem that the instability is caused by significant
adsorption of methane (which occurs above ca. 813K when oxygen is
present) or preadsorption of methane (which occurs in oxygen free condi-
tions even at a temperature of 773K (see Table 3.23)). Chemisorption
of methane is dissociative and results in the formation of adsorbed
hydrogen radicals or desorbed gaseous hydrogen molecules. Therefore
one would anticipate that the thermal instability was sensitized by
the presence of hydrogen and its subsequent fast oxidation causes the
reaction to run away. Similar effects were observed by Dongworth
et.al. (71).
4.2.2.5. Catalyst deactivation
Experimental study of methane oxidation over the catalyst
sample which had been heated (ca. 1073K) in an inert atmosphere
(Figs. 3.28 and 3.29) shows that there is no major change in the
activity as a result of heat treatment alone (Table 3.9), but that
heat treatment in the presence of steam (Fig. 3.27) does have some
effect. Carbon monoxide is seen to be produced from methane oxidation
even at high oxygen levels. Passage of carbon monoxide and oxygen
over the same catalyst showed that the steam treated catalyst did not
oxidize carbon monoxide.
187
The BET and carbon monoxide adsorption experiments on the steam
treated catalyst sample show tremendous loss in the gas up-take. This
would mean that steam treatment at elevated temperatures could result
in pore collapse and thus the platinum particles would be buried .inside
the alumina. The residual activity for methane oxidation could be
interpreted in a similar way as the nonporous catalyst (see Section
4.2.3.).
Carbonaceous deposit on the catalyst surface did not show sig-
nificant irreversible deactivation. It would be expected that films
of carbonaceous deposit should be oxidized easily in an oxygen rich
condition.
4.2.2.6. Methane-steam and water gas-shift reactions
The experimental work on the methane-steam and water gas shift
reactions was intended to clarify the possibility of the direct inter-
action between the reactant (methane) or the reaction intermediate
(carbon monoxide) and the major product (steam). However, the data
obtained in water gas shift reaction are sufficient_to allow the
investigation of details of the reaction and the characteristics of the
catalyst.
The calculation of equilibrium constants for the methane re-
forming process over the temperature range used are listed below:
TABLE 4.6
CH4 + H2O = CO + 3H2
Temp. (K) Kp (atm2)
713 5.4 x 10-4
773 9.89 x 10-3
873 5.1768 x 10-1
973 12.012
1073 155.1089
Although the equilibrium constant at temperatures above ca. 873K
favours the conversion of methane, the experimental observations show
that there is no conspicuous conversion over the temperature interval
of 712-1088K. This could be due to either (a) platinum/alumina
Temperature (K)
reactor inlet molar fraction
% experimental(*)
% equilibrium conversion conversion
188
catalyst not catalysing the reaction, or (b) sintering effects leading
to blockage of the catalytic sites for the reaction at temperatures
above ca. 873K. In view of the steam effect on the platinum/alumina
catalyst (Section 4.2.2.5), sintering of the support appears to be the
most possible reason.
The study of the shift reaction over the platinum/alumina
catalyst gives an apparent activation energy of 38.96 kJ/mole. The
small dependence of the reaction rate on the temperature is possibly
due to the following three reasons:
(a) the rate of the forward reaction may nearly equal the rate of
the backward reaction;
(b) interfacial mass transfer limitations;
(c) inhibition by reaction products at high conversions;
The calculation of equilibrium conversions at higher temperatures are
listed below:
TABLE 4.7
H20 CO
817 0.2326 0.1397 12.93 80.0
838 0.2326 0.1328 14.13 79.5
860 0.2326 0.1385 15.40 76.9
881 0.2326 0.1320 13.00 76.43
(*) inlet contact time = 4704 kg-cat-sec/kgmol.
The above data show that, although there is a tendency to
decreasing conversion with increasing temperature, the potential towards
the equilibrium level is still high enough to allow the reaction to
proceed. Therefore the first possibility can be deleted. An increase
in conversion with decreasing reactor inlet flowrate (Fig. 3.54) would
indicate that interfacial mass transfer limitation is not important,
therefore the second possibility is also negligible. An inhibitive
effect was observed (Fig. 3.59) when hydrogen was introduced to the
reactor. It is interesting to note that hydrogen strongly inhibits the
reaction when its concentration level reaches the inlet concentration
of steam to the reactor. This could be the result of competitive
adsorption between steam and hydrogen on the catalytic sites. Carbon
dioxide does not exhibit conspicuous inhibition to the shift reaction
(Fig. 3.58).
189
However, according to the data obtained On the shift reaction,
the conversion of carbon monoxide due to direct interaction with
steam is negligible with reference to the product spectra of methane
oxidation observed in the temperature range of ca. 773 to 873K.
An attempt was made to fit the experimental data numerically
with 24 kinetic models based on the Langmuir-Hinsheiwood theory. The
mechanistic bases of the models are summarized in Table 4.8. A
computer program was set up by applying Powell's optimization technique
( 93) to search the minimum of a function in a multiple parameter
space. The objective function is to minimize the discrepancy
between the estimated and observed conversions of carbon monoxide in
the shift reaction, which is
m S(K) = E (a - &)
i=1
2 (4.12)
where K : the vector of parameters
m : number of experimental points
a : observed conversion of carbon monoxide
a estimated conversion of carbon monoxide, which
is function of K.
Among the 24 kinetic models, model No. 18 has the best fit to the
32 experimental data points (see Fig. 4.4). The kinetic model has
the mathematical expression:
kl [CO).fH2OJ -rC0 =
{1 + k2[C0]}'{1 + k3[H20) +
k (CO2).[H2]
k5 {1 + k3[H20]2 + k4(H2)21 2
at 814K,
where - rC0 : reaction rate of CO, kmol/kgcat-sec
k1 : 0.1854 kmol/kgcat-sec
k2 :12.3908
k3 :36.7107
k4 :48.8071
k5 : 1.3228
): molar fraction of species
(4.13)
TABLE 4.8
CO + H2O = CO2 + H2
Matrix of Surface Reaction Models(a)
Models CO H90 CO2 H2 Site Direction of reaction
1 1 1 0 0 1 —4 2 1 1 0 0 1
3 1 1* 0 0 2 -->
4 1 7 0 0 2 c—~--
5 1 1 1 1 1 ---30
6 1 1 1 1 1 ___N. _
7 1 1* 1 1* 2 ---.
8 1 1" 1 11 2 --~ tramp
9 1 2 1 2 1 ---1), 10 1 2 1 2 1 --..
11 1 1 0 1 1 ----->
12 1 1 0 1 1 --_N.
13 1 1* 0 1* 2 —b
14 1 1 * 0 1 * 2 —;„.
15 1 2 0 2 1 --j
16 1 2 0 2 1 —.1,
17 1 2* 0 2* 2
18 1 . 2* 0 2* 2 -..! ---
19 2 2* 0 2* 2
20 2 2* 0 2* 2 --s c-
21 2 2 0 2 1 ........
22 2 2 0 2 1 —~ 23 0 2 0 2 1 --~ 24 1 0 0 0 1 -s
(a)
0: gaseous state
1: unimolecular adsorption state
2: dissociative adsorption state
3t: different catalytic site
Site 1: only one kind of catalytic site on the catalyst surface
Site 2: two different kinds of active sites on the surface
--- : irreversible reaction
. reversible reaction
190
40
30 Con
vers
ion
0 0 10 20 30 40
192
According to the Langmuir-Hinshelwood theory, the rate deter-
mining step of the shift reaction is thus a reversible surface reaction.
The forward path involves the interaction between two different sites.
One kind of site unimolecularly adsorbs carbon monoxide, while the
other kind of site dissociatively adsorbs steam and hydrogen. In
the backward path, carbon dioxide in the gaseous state interacts with
hydrogen adsorbed on one kind of catalytic site. Some opposite
views are reflected in the literature (104) which object to the use
of kinetic models to describe a reaction mechanism, because the sur-
face heterogeneities were ignored in the derivation of the theory and
because it is difficult to rule out reaction mechanisms based on
experimental kinetic experiments. However, as demonstrated by
Boudart (105, 106), the Langmuir-Hinshelwood kinetic rate expressions
will still lead to rate functions which are qualitatively correct. Shchibrya, et.al. (107) proposed a kinetic expression for the
shift reaction over Cu : Zn : Cr catalyst, which has a mathematical
form of:
-y = k1 .PH 2
O
PCO . k . P + P 2 H2O CO2
m •
PCO2' H
2 k3'PH20'P
CO
• (4.14)
The above expression has also been tested against the present experi-
mental data. The parameters which give a standard deviation of
0.0408 are listed below:
m = 0.6504
kl = 0.0016099 kmol/kgcat-sec
k2 = 554.048
k3 = 0.13047
pi = molar fraction of species i (subject to total pressure = 1 atm).
4.2.3. Platinum supported on nonporous alumina
4.2.3.1. Kinetics of the reaction
Measurements of the kinetics of the oxidation reaction in the
temperature range ca. 770 to 873K show a change in the apparent
activation energy at about 823K, giving a value of 166.66 kJ/mole
over the lower temperature range and 75.54 kJ/mole in the higher
temperature range.
193
These observations give support to the previous discussion on
the porous catalyst, in which the change of the apparent activation
energy was interpreted in terms of the adsorption ability_ of oxygen
decreasing significantly at temperatures above ca. 813K, thus allowing
methane to chemisorb on the surface. As a result, the same explanation
was applied to interpret the magnitude (91.1 kJ/mol) of the change of the
apparent activation energy over the nonporous catalyst.
The reaction orders were measured at two temperatures, which
were bounded by the regions of the two different apparent activation
energies. The initial rate relationships. observed were :-
at 801K,
and
1 at 833K, - d (CH4]/dt °` [CH41 402)
As distinct from the observation on the porous catalyst, the
reaction rate at low temperature has a first order dependence on.
oxygen concentration. This may indicate that the adsorbed state of
oxygen on platinum is present as Pt02. In the light of Carberry's
work (108), small platinum crystallites exhibit a strong tenacity for
oxygen to yield PtO, from which the adsorbed oxygen atom (entity 0) is
difficult to extract; platinum particles with large crystallite size
exhibit less tenacity for oxygen and the adsorbed oxygen (perhaps in
the form of Pt02) is easier to react. The platinum particle sizes
on both porous and nonporous support were calculated and compared by
utilizing the carbon monoxide adsorption data. On the assumption
of spherical particles, the platinum particle on the nonporous alumina
is about twenty times larger than that on the porous alumina. This
difference in the supported platinum may be reflected in the type of.
oxygen adsorption (108).
The apparent activation energy over the nonporous catalyst in
the low temperature region (below ca. 813K) is less than that over
the porous catalyst at the same temperature range (by a magnitude of
20.4 kJ/mole). As discussed in Section 4.2.2.3, the activation
energy of the oxidation reaction could be dominated by the oxygen-
platinum binding energy; therefore the lower activation energy could
be due to weaker bonding of oxygen over platinum as the result of the
larger particle size.
The experimental results (Fig. 3.42) show that the reaction
d (CH4) /dt œ [CH41102)
194
order with respect to methane concentration decreases from 1.0 to 0.7
if the oxygen to methane ratio is lower than unity in the high tem-
perature region. A shift of the reaction mechanism at high
temperatures (above ca. 823K) due to significant chemisorption of
methane is again suggested.
However, as distinct from the porous catalyst, no trace of
carbon monoxide was observed at high temperatures with a catalyst used
for less than a period of 40 hours (Figs 3.37 and 3.38). Since the
formation of carbon monoxide over platinum/alumina (porous) catalyst
was attributed to the effect of strong adsorption and cracking of
methane at high temperatures, the reasons for the non-reproducibility
over platinum/alumina (nonporous) could be as follows: (i) By analogy with oxygen adsorption ability, the large platinum
particle on the nonporous alumina would provide weaker bonding
for methane; as a result, the mechanism involving high surface
coverage of methane (to favour carbon monoxide formation)would
be less important.
(ii) It is known that, in the catalytic process of hydrocarbon
cracking, there exists a threshold residence time (or an
induction period) before strong adsorption of the hydrocarbon
or the carbonaceous deposition occurs (109). The existence
of the threshold residence time was explained (109) in terms
of the carbonaceous deposition requiring the formation of a
reaction intermediate which initiates the cracking process.
In view of this concept, the porous catalyst could be suggested
to be able to capture methane inside the pore for a longer
period, compared with the short residence time of methane over
the nonporous catalyst. As a result, the mechanism,involving
high surface coverage of methane would not occur over the non-
porous catalyst.
The experimental data obtained at 835K were fitted with single
site and dual site models (Table 4.9). Among the tested models, the
Langmuir-Hinshelwood single site reaction model, which shows the best
fit to the experimental data (see Fig. 4.2), has a mathematical
expression:
k1 (CH4).{021
rCH4
{1 + k2 [CH4] + k3(021 (4.15)
The parameters, with a standard deviation (in methane conversion)
of 2.67% (below the allowable range of experimental error + 5%), are:
195
k1 = 9.357 x 10-4 kmol/kgcat-sec
k2 = 7.9412 x 10-2
k3 = 4.1977 x 10-1
The kinetic study of carbon monoxide oxidation (Figs. 3.49 to
3.53) over the platinum/alumina (nonporous) catalyst (used less than
40 hours) allows some interpretation of the reaction path of methane
oxidation over the same catalyst. If the methane oxidation occurs
through a consecutive scheme (i.e. CH4
4.0 2 CO - 02 CO2.), then the
concentration of carbon monoxide which should appear in the reactor
product stream is ( 79 ) ,
(COI = (CH410 (1 (3)
k2 /k
1 + - 1
1 - k2/k
1
where (CH4)0 is the initial concentration of methane;
a is the conversion of methane;
k1, k2 are the rate constants of methane and carbon monoxide
oxidations respectively.
Utilizing the conditions in Figs. 3.37 and 3.38, the concen-
tration of carbon monoxide is calculated from eq. (4.16) and listed
in Table 4.10. According to the calculations, a concentration of
carbon monoxide of ca. 3.5% should be present in the reactor product
stream if the oxidation of methane occurred through the consecutive
path. However, the experimental results show that, at both high and
low temperatures, no carbon monoxide was observed. This suggests that
the oxidation of methane could either occur through
(i) a concurrent scheme
+ 0 C0
(a)
(4.16)
+ 02 CH4
2 V
(b) CO2
with high selectivity through path (b)
or (ii) a direct single reaction
0 CH4 -- 2 CO
2
TABLE 4.9
Matrix of Surface Reaction Models(a)
Models CH4 02 CO2 H2O Site.
1 0 1 0 0 1
2 1 0 0 2
3 1 1 0 0 1
(a)
0 : gaseous state 1 : unimolecular adsorption state * : different catalytic site
Site 1 and 2 : single and dual site respectively
TABLE 4.10
Temp k2/kl methane conversion (eq.4.16) calculated observed
K % [CO) % (C01
802 2.00 30.0 3.30 0
843 1.81 30.0 3.45 0
196
197
4.2.3.2. The reaction stability
The reaction instability phenomena observed in the system of
platinum/alumina (porous) catalyst, were not observed with the platinum/
alumina (nonporous) catalyst. The reaction instability, as discussed
in Section 4.2.2.4, was believed to be the effect of the presence of
hydrogen produced by fast cracking of methane over the catalyst sur-
face. In view of this concept, the cracking ability of the nonporous
catalyst is comparably less than that of the porous catalyst. It is
perhaps due to the results of shorter "induction" residence times for
methane or to a weaker adsorption for methane over the larger platinum
particles.
4.2.3.3. Effect of catalyst aging
Experimental results show that the platinum/alumina (nonporous)
catalyst used for methane oxidation over 40 hours exhibits differences
in the selectivity for carbon monoxide formation (Figs. 3.39, 3.40).
The effect may be due to three reasons:
(1) sintering of platinum particles causes sequential loss in
platinum surface area or in catalytic activity;
(ii) influence of the acidic support;
(iii) catalyst poisoning.
The results of the carbon monoxide adsorption study (Table 3.22)
of the sample used for the methane oxidation over 40 hours show a three-
fold loss in the gas up-take in comparison with the sample used less
than 40 hours. These observations support reason (i) stated above.
ESCA results (Table 3.25) on the samples of platinum impreg-nated catalyst show that the silica surface content decreased from
19% to 3.5% after the impregnation; however, the silica surface content
18.5% was recovered when the sample was used for methane oxidation over
50 hours. In view of these results, the reappearance of the surface
silica could be responsible for the selectivity to carbon monoxide, with
the gas being produced in a way similar to the reaction on pure alumina.
Further oxidation of the carbon monoxide would be depressed due to loss
of platinum surface area.
Catalyst poisoning is unlikely to cause the observed effect.
Oxidation of residual carbonaceous deposits had little effect on the
observed selectivity.
198
4.2.4. Effect of the supports on the platinum/alumina catalysts
The two alumina supports used in the present study have a physical structure which is either porous or nonporous. It has been
shown that pore diffusion limitations would not occur over the porous
catalyst in the range of conditions used in the process of methane
oxidation. As has been discussed in Section 4.2.1, the catalytic
activities of the pure supportswere attributed to the surface acidity
due to the presence of surface aluminosilicate.
The ESCA results (Table 3.25) show that impregnation with
platinum of both supports decreased the surface content of silica
considerably. Since the support catalytic activity was considered to be due to the effect of the presence of surface silica, one could
anticipate that substantial disappearance of the surface silica
content would result in considerable loss in support influence on the
process of methane oxidation. It was also observed that the platinum/
alumina (porous) catalyst did not exhibit significant changes in
surface silica content (as well as the reaction activity) after use
for methane oxidation over 100 hours, while the surface silica content
of the platinum/alumina (nonporous) catalyst was almost recovered
(and accompanied by increasing carbon monoxide) after use for methane
oxidation over 50 hours. The increase in selectivity to carbon
monoxide could thus be related to the reappearance of the surface
acidity.
The total surface area and porosity of a support are the chief
factors affecting sintering of the supported catalyst particles ( 75).
The carbon monoxide and nitrogen adsorption measurements (Table 3.22)
on the catalyst samples demonstrated the effect on metal and total surface areas respectively of various treatments.
199
4.3. Physical and Mathematical Models for the Air Diffusive Type
Catalytic Combustor
4.3.1. Introduction
Detailed considerations of physical phenomena are necessary when
setting up models to describe the behaviour of a catalytic combustor.
However the transport phenomena occurringin a fixed bed reactor are complex
and models accounting for all the phenomena would result in computational
intractability.
In this section, the processes of mass and heat transport occurring
in the catalytic combustor are discussed. The literature survey on the
empirical correlations for the interfacial mass and heat transfer are
summarised and their uncertainty due to extrapolation is discussed. An
internal radiation model to describe the solid-solid thermal interactions
is derived. By combining the necessary physics, a set of mathematical
models is formulated to describe the performance of the air diffusive type
catalytic combustor. An integration model to evaluate the amount of
energy released by thermal radiation to the surroundings is also given.
4.3.2. Mass and heat transport
The combustion occurs with a series of parallel and consecutive
transport phenomena which involve :
(a) convection-diffusion of flow through the catalyst layers
(b) mass transport of reactants from the ambient fluid to the active
surface (inter-particle and intra-particle diffusions)
(c) energy transport through,
(i) forced convection at fluid-solid interface
(ii) solid-solid conduction
(iii) solid-solid radiation
(iv) natural convection
(v) radiation to the surroundings
Energy transport by (iii) is particularly important when a high
void fraction catalyst packing is used.
200
(d) mass diffusion at the frontal surface of the heater enhanced by the
buoyancy effect due to natural convection
4.3.2.1. Mass transport through the combustor
' Mass transport through the catalytic pad occurs by combined
convection and diffusion. The convective flow results from the bulk motion
of the fluid and the diffusive flow can be described by Fick's law of diffusion.
The molar flux of the ith component can be represented by
Gi = Wfi Gm - c Deff,i a Wfi (4.17)
Due to the low bulk flowrates (as generally used in the practical combustor) and
high void fraction (greater than 0.9) of the catalytic pad, it is possible to
approximate the effective diffusion coefficient by molecular diffusivity.
The theory of diffusion in multicomponent mixtures is complex (110), but
it has been found possible to deal with the problem in an approximate manner by
employing a diffusion coefficient Dim for speciesi in a mixture of n components
1 n W.
Deff,i "6 = (1-Wi) JEl D 1J
j$i i = 1„n ,n (4.18)
Dij is the binary diffusion coefficient of the ith species in the jth component,
and can be estimated by the Lennard-Jones expression
Dij _ 0.001858 T3/2 ICI +Mj )/Ivti It I 1/2
P o ie SD
(4.19)
where T is the absolute temperature (K); Mi, Mj are the molecular weights of
the two species; P is the total pressure (atm), QD is the "collision integral",
a function of KT/eij (110); c, a are the force constants in the Lennard-Jones
potential function; and K is the Boltzmann constant.
4.3.2.2. Mass and heat transport at the fluid-fibre interface
The shape of the catalyst influences the hydrodynamic flow surrounding
it, and the flow, in turn, influences rates of transport processes normal to
201
the surface. Hydrodynamic flow normal to an infinite cylinder may be
taken as representative of the flow past a single fibre of a high void
fraction pad. The actual flow is, of course, perturbed by the presence of
adjacent fibres, and the magnitude of the perturbation increases with
decreasing void fraction. The infinite cylinder assumption may be satisfied
with I.C.I. Saffil pads, where the fibres have a ratio of length to diameter
approximately equal to 104, and the pad has a void fraction greater than 0.9.
Dimensional analysis (112) suggests the following as the basis for
empirical correlations for the mass and heat transfer processes:
The Chilton J factors
JD - . km Sc2"3 = f (Re) f
JH - C .G Pr2/3 = f (Re) pf f
(4.20)
(4.21)
McAdams (113) has presented the J factor of heat transfer for the flow across an
infinite cylinder as a function of Reynolds number, and the relation can be
correlated as
JH = Nu•Re-1 • Pr-1/3 = 0.5305•Re-0.49
0.1 < Re < 100 (4.22)
By analogy (112) the mass transfer correlation can be obtained
Sh•Re-1 • Sc -1"3 = 0.5305•Re-0.49
The dimensionless groups are defined as:
d .~ P
f hdp
Re = u f Nu - ---- f
k •d Sh Sc uf
fD C
pf uf Pr = k
f
(4.23)
202
Morgan (102) proposed heat transfer correlations for-crossflow forced
convection over cylinders in air, and which are given in Table 4.11.
It.was suggested that the infinite cylinder approximation Would result
in overestimating the heat tracsfēr coefficient'for a multiple gauze system.
Similarly it would be•sūrmised that the application to the fibre pad may
result in the same uncertainty.
TABLE 4.11
Re Nu = a.(Re)b
From To a b
70_4
4x10-3
9x10-2
1
35
4x10-3
9x10-2
1
35
5x103
0.437
0.565
0.800
0.795
0.583
0.0895
0.136
0.280
0.384
0.471
It is possible to assume the fibre pad is composed of a series of screens
or stacked screens (two or three screens in series), and that each screen is
a network of infinite cylinders normal to the direction of flow. Satterfield
and Cortez (115) correlated the mass transfer coefficient for a screen catalyst
and they also found that the mass transfer coefficients for stacked screen
matrices were slightly lower than those for single screens. The difference
was believed to result from the effects of fluid separation, the interactions
between screens and the uneven void fraction of the stock; however, the
difference was found to be insignificant.
Their correlation is:
where
Jp,cb
= 0.865 • Re-0.648
G .d Re i = u-
(4.24)
where is the voidage of a single screen. In their experiment, they had a
mean Reynolds number of 1.9.
203
Shah and Roberts (116) present their correlations for mass transfer
of stacks of one to five screens, which is
JO,
~ = 0.751•Re-0.56
Re < 135 (4.25)
Coppage and London (114) presented their experimental results on heat
transfer of stacked screens, and their data was correlated by Satterfield
and Cortez (115) to give,
JH,cp
= 0.731•Re 0.644 Re < 103 (4.26)
The value of $ can be assumed equal to the void fraction of the fibre pad,
since it is reported by I.C.I. that the void fraction of the pad is very evenly
distributed. Equations 4.25 and 4.26 are applied in present work to evaluate
the convective mass and heat transfer coefficients of fluid-fibre interfaces.
It should be borne in mind that linear extrapolation of the literature
correlations to a range of lower Reynolds numbers may introduce uncertainty,
since it was pointed out by McAdam (113) that, as the Reynolds number decreases,
the slope of the correlating line for the J factors increases.
4.3.2.3. Intraparticle heat and mass transfer
It is generally accepted that, in heterogeneous catalysis, the solid
phase can be considered isothermal (111), and the major resistance of heat
transport resides in the fluid film around the particle.
To account for the pore diffusion inside the fibre catalyst, the effective-
ness factor, rfi, is introduced, which is defined as the ratio of the actual
reaction rate to that which would occur if all of the surface throughout the
inside of the catalyst particle were exposed to reactants at the same conditions
as those existing at the outside surface of the particle. The quantitative
analysis of the effectiveness factor is given in Appendix 1. A computer
program has been written to calculate the effectiveness factor and is given
in Appendix 5.
4.3.2.4. Model of the internal radiation
The radiation model presented here considers a bed of fibres to be
represented by a number of parallel fibre laminations with arbitrary spacing
between successive laminations. A set of such laminations is considered with
index 1 to N inclusive. The medium contained between neighbouring laminations
ith (i+l)th
3
(i-1)th
204
(representing the gas phase) is assumed to be a perfect. transmitter. Each lamination is considered grey and is partially transparent, having a transmissivity T, and absorptivity a, and reflectivity y, with
T +a+y =1 (4.27)
The fraction T may. be thought of as representing the effective void fraction (if it is even throughout the bed) through which radiant energy will transmit without absorption and reflection. The sum of a + y may be thought of as the
partial fraction of area occupied by the solid phase which is opaque to radiant transfer, and the fibre absorbs and reflects energy as a grey body; in other _ words, the values of a and y are constant.
The laminations are bounded by two boundary thermal sources or sinks with indices zero and N+1, and at the absolute temperatures To and Tn+l respectively. For this model, the problem of interest is to evaluate the steady unidimensional heat transfer rate of internal radiation through the fibre laminations. From this model approximation, the long range interactions caused by internal transmission and reflection between the successive laminations can be simplified to a Fourier type heat conduction problem by introducing a local radiation conductivity. This is represented in Fig. 4.5, where i and i+ are denoted as the indices for the back and frontal surfaces of the ith lamination. The arrows represent the paths of thermal radiation.
Fig. 4.5
205
Considering an mth lamination with m < i (that is to say the mth lamination
is situated at the back of the ith lamination), and considering the ith
lamination to be the energy source, the fraction of radiation energy transmitted
from the i surface to the m+ surface (- and + denote the indices for the back
and frontal surfaces) is
T(i-m-1)
• i > m (4.28)
After the energy has reached m+, a fraction of energy is absorbed by the mth
lamination, while a fraction is reflected back to the ith lamination; therefore
the fraction of energy reflected to i is
—m-1) •y•
T i > m
• i > m (4.29)
The reflected energy is then reflected from i to m+ after reaching i-, and
the fraction of energy reflected to ni+ due to the "first" internal reflection is
y.T . y,T(i-m-1) r i >
= y .T3(i-m-1)
• i > m (4.30)
Therefore, by a series of internal reflections, the total fraction of energy
transmitted from i to m+ (i > m), when the ith lamination is treated as an
energy source, is
T(i-m-1) + 2~ 3(i-m-1) + 4,T5(i-m-1) + ___ y
= T(1—m-1)r1+y2T2(i —m-1) + y4T4(i—m-1) + ---- 3
i —m-1 1 1 _Y2T2(i-m-1)
where y2T2(i-m-1)
< 1 and i > m.
(4.31)
Similarly, when i < m, the total fraction of energy transmitted from i+ to
m is
i < m 9
m — i -1 1 T( ).[
1-y2T2(m-i-1)
(4.32)
206
Taking a reference mth lamination, and considering energy to be transferred
to the lamination from the sources at the left and right hand sides, the
total energy from the left hand side sources is
m-1 T(m-i-1). 1
i=0 [1y_
2 2(m-1-1)I'Q+iT (4.33)
and the energy transmitted through the mth lamination, when sources are at
the left hand side, is
m-1T(m-i) 1 +
2 2(m-i-1)]."9 i=0 1-Y T (4.34)
where Q = a•a.(T.)4, is the radiant heat flux from the "+" surface of ith
lamination, and
a: emissivity
a: Stefan-Boltzmann Constant
Ti: the temperature at the "+" surface of ith lamination.
The energy radiates by the mth lamination from the positive side is:
Q+ m
(4.35)
Similarly the total energy transmitted from the sources at the right hand side
is
(4.36)
where "-" denotes the condition at the negative side of the lamination.
Consider Fig. 4.6
m+h gl(m)
g 2(m) l
N+l T(i-m-1) 1 -
1_ 2T2(i-m-1),.Qi i=m+1 t Y
Fig. 4.6
at steady state, the nett-flux across each lamination should be identical, i.e.
and
Sm =
(m-1) gl(m-1) - g2 2
m-1 T (m-i) E '~
N+1 (i-m-i), — T
i=m+l
= gl(m) - g (m)
1 m N
1
2 2(m-i-1),
- am
+
Qi + QM
, Qi
207
(4.37)
(4.38)
1 -y T
1 2 T2(i-m-1)J
1-y
1 m N
If the whole fibre pad is divided into very thin laminations such that the
conditions at the negative and positive sides of each lamination are the same,
then
Qi = Qt = Q. = a•a•T4
(4.39)
When the fibre laminations are bounded by two thermal sinks then
Qo = QN+1 = 0
It will be more compact to introduce vector notation to eq. (4.38 ), then
m= 1 sl = A1 •Q ti ti
m= i si = Ai•Q ti ti
m= N Si
= AN'Q ti ti
(4.40)
where Ai is a lxN row vector, Q is a Nxl column vector and si is scalar.
Since
61 = - si= - N = s therefore
= SJ= A • Q % ti ti ti
where Al
J is a Nxl unit vector,and A = ti ti
AN NxN
(4.41)
(4.42)
4aaiZTm
kr,m Bm Bm+1 (4.48)
The heat flux vector Q can be obtained as 1
Q = SA-1 •J if IAI# 0 ti ti ti ti (4.43)
208
or
6B = Q ti )
(4.44)
where B - A-1'J ti ti ti
therefore,
6B1 = a'6•T~
SBm = a•a• Tm
SBN = a•Q• TN
(4.45)
After algebraic manipulation of eq. ( 4.45), the net radiant flux across each
lamination at steady state can be obtained as,
4 4
S = ao(Tm - Tm+1)
.
if Tm ~ Tm+l , eq. (4. 46) can be reduced to
4aaT3(Tm - Tm+l) S =
Bm _Bm+1
4aaTm•AZ Tm+1 - Tm or = —
Bm _ Bm+l
AZ (4.47)
where AZ is the spacing between mth and (m+1)th laminations.
Eq. ( 4.47) is analogous to Fourier law of thermal conduction in the direction
perpendicular to the surfaces of fibre laminations, having the local radiation
conductivity,
Bm - Bm+l (4.46)
where Bm is a parameter in terms of m, y and T.
Eq. ( 4.48) decouples the "long-range" interaction, where the local heat flux
depends on the temperatures far away from the point under consideration, and
results in the flux which depends only on local temperature gradient. Hill and
209
Wilhelm (117) pointed out that the use of radiation conductivity to decouple
the integral effect caused by internal radiation in semi—transparent material
may result in an inaccuracy of a range from 5 to 25 %; the smaller value
applying for large heat flux. Vortmeyer (118) also showed that the error
might be up to 20 % when steep temperature gradients occur.
In the present work, eq. ( 4.48) is applied to evaluate the internal
radiation contribution to the energy transport through the catalytic combustor.
A computer program (given in Appendix 5) is set up to calculate the local
radiation conductivity in order to collaborate with the combustor model which
is presented in section 4.3.3.
4.3.2.5. Heat and mass transport by natural convection
A fraction of the energy generated in the combustion process is lost to
the surroundings due to natural convection at the frontal surface edges,
metal frame work and casing of the heater. However, it is difficult to assess
the amount of the loss, because of the irregular heater structural surfaces,
(see Fig.2.8). Nevertheless it is possible to estimate the heat loss by
applying the flat plate correlation of natural convection.
The Nusselt number of natural convection from .a vertical plate is given
by Bird, Stewart and Lightfoot (112),
Nuh = 0.517•(Grh•Pr)1/4 (4.49)
where Grh is the Grashof number of heat transfer
Grh E
gRL2• At/v2
Eq. ( 4.49) can be applied to evaluate the amount of heat loss due to natural
convection.
By similarity, the mass transfer parameter at the frontal surface of
the heater due to natural convection (119) is
Num = 0.517•(Grm•S c)1/4 (4.50)
where Grm is the Grashof number of mass transfer
P Grm = gL2/v2•(ps - 1 )
w
Eq. ( 4.50) can be applied to evaluate the mass transfer at the frontal surface
of the heater due to the buoyancy force generated by the difference in density
210
at the external boundary of the heater.
Equations ( 4.49) and ( 4.50) are used in the present work to formulate
the boundary conditions for the mathematical model in simulating the performance
of the combustor.
4.3.3. Mathematical modelling for the catalytic combustor
Having discussed the heat and mass transfer processes that would occur
during the catalytic combustion in the preceding sections, in this section a
set of mathematical equations is developed to enable the consideration of all
the phenomena in a convenient fashion.
Cartesian coordinates are chosen in order to simulate the practical system.
4.3.3.1. General description of model
The following considerations and assumptions are made in establishing
the mathematical model.
Considerations:
(1) Mass transport in the fluid phase is caused by bulk flow and molecular
diffusion.
(2) Solid phase heat transport is caused by conduction and radiation.
(3) Heat loss is due to natural convection at the edges of the combustor.
(4) Fluid-solid interfacial heat and mass transfer resistance exist.
(5) Intra-particle mass transfer resistance exists.
(6) Heat and mass transport at the frontal surface of the heater is enhanced
by buoyancy force.
(7) Steady state operation exists.
Assumptions:
(1) Planar symmetry.
(2) Negligible pressure drop across the bed.
(3) Physical properties of the fluid are constant throughout the bed.
(4) Intra-particle heat transfer resistance is negligible.
(5) Molar flowrate is laterally uniform and constant across the bed.
211
Mass balance on component i:
(i) Fluid phase:
aW aW a W
ax (D ec axe) + āy (Dec
ayl) - Gm axe km•av(Wfi-Wsi) = 0
(ii) Solid phase:
km.av(Wfi Wsi) + vi•Rs(Ws,T5).n = 0
Energy balance:
(1) Fluid phase:
aTf -G
m' Cp' ax + h•av(Ts-Tf) = 0
(ii) Solid phase:
(4.51)
(4.52)
(4.53)
āx (kc+kr) axs + ey a h•a v(Ts-Tf) +(-H)R(Ws,TS)q = 0 ( J
{(kc+kr)
(4.54)
The dimensionless form of these equations can be obtained by introducing the normalized variables I = x/L1 , T = y/L2, 0 = T/Tr whence:
a 1 aWfi + a 1 aWfi aWfi _ K W -W = 0 ag
(Pmix a$ ) aT
(Pm1 ay )
ax ( fi si) (4.55)
K(Wfi - Wsi) + Rs.(Ws,o) = 0 (4.56)
(4.57)
a (Ph aeS) + a (P1 aes) - H(05-0f) + Rs(Ws,6s) = 0
a X ax, aT aY (4.58)
where Rsi = vi•Rs(Ws,Ts)9 Ll/Gm
Rs = (-AH)Rs(Ws,Ts),1 L1 /GmCpTr
9 = 9(S,Ws,es)
"f- + H(es - ef) = 0 ax
212
The definitions of the dimensionless groups are given in Table 4.12.
The above equations can be solved to generate concentration and temperature
profiles for suitable boundary conditions. However, the full solution of
these equations requires a complicated numerical procedure. An alternative
and more pragmatic approach has been adopted to simplify the problem. When
the dimensionless groups of film mass and heat transfer have magnitudes much grea-
ter than unity (K, and H »1)(120), for finite reaction rate and temperature
gradients the differences of concentration and temperature across the fluid-
solid film should be insignificant (i.e. the quantities Wfi Wsi and of. -
(3s vanish). The mass and heat transfer parameters at practical operating
conditions of the catalytic combustor are calculated and their values are
listed in Table 4.13. The calculation shows that the parameters R and H have values much greater than unity (order of 108), and hence the film concentration
and film temperature gradients are negligible. The two phase model (eqs. 4.55
to 4.58) can thus be reduced to a one phase model.
4.3.3.2. Simplified models
Two dimensional-one phase model can be obtained by setting Wsi = Wfi = Wi
and es = of = e (Eqns. 4.55 to 4.58), then mass equation:
a- - ( Pml
aWi
) + a_ (pml W. - W.
+ R.(W,e) = 0 aX i- aX aY ~y aY aR ti
energy equation
aX
- (
Ph- aX ) + Y
ay (Ph- aY) - X + Rs(W,e) = 0
X -
where i = 1, ----,N-1 (N = number of mass components) and
n-1 WN = 1 - E W.
1=1
(4.59)
(4.60)
4.61)-
For the process of methane combustion,five mass components (N2, CH4, 02,
CO2 and H20) are involved. Thus it is necessary to solve a set of five
simultaneous differential equations (four mass equations and one energy
equation). By choosing the mass component vector as:
u3
TABLE 4.12
Symbol Definition Description
Pmi_ L1Gm/DiC Peclect numbers of mass transfer X
Pm.- L2G m/L1DiC for ith species Y
K km av Li/Gm Dimensionless parameters for film
mass transfer
H h a vLl/GmCp Dimensionless parameters for film
heat transfer
Ph _ L1 GmCp/(kc + kr) Peclect numbers for heat transfer
X Ph_ L2GmCp/L1 (kc + kr) Peclect numbers for heat transfer
Y
TABLE 4.13
Temperature
K
Fuel Flowrate
ml/sec (STP)
K H
673 9 6.06x107 1.00x108
873 9 6.62x107 1.01x108
673 5 8.42x107 1.46x108
873 5 9.19x107 1.50x108
j = 4,5 (4.66)
i = 1,2,3 (4.67)
j = 4,5 (4.68)
• W1
W2
W3
W4 W5
WN 2 WCH4 W02
CO2 Wu 2n,
and taking advantage of the stoichiometry between the reaction products
(CO2 and H20),
WCO2 vCO2
WH2O vH2O (4.62)
then the mass vector W is reduced so that only three independent mass variables and the compositions of CO and H20 are
(WN 2' WCH4° and W )need to be solved, p CO2 2
calculated by mass balance. In making the above simplification, an assumption
has been made that there is no separation of CO2 and H2O 'inside the combustor.
The boundary conditions for eqns.4.59 and 4.60 are;-
aWi aWi
aY aY Y=0
0<X 1:
Y=1
=0 i = 1,2,3 (4.63)
3 W. = (1-lE1 W.) vj/(v4+v5)
0, Y s l: at X = 0,
aWi
eX = Pm. (W. - W.
j = 4,5
i = 1,2,3
(4.64)
(4.65)
3 W. = (1- E W.) vj/(v4+v5)
i=1
at X= 1,
awi
- aX
— NumX (W.-174,) mix Wi
Wj = (1 - E Wi )vj/(v4+v) i=1
215
0.< X< 1: aY
Y=0
=0
(4.69)
ae
aY = NuhY(e - 1)
Y=1 (4.70)
0 .< Y .< 1: ae
aX X=0
= Ph (e-1) x
(4.71)
ax x=1
= Y(e4-1) + Nuh_(e-1) - Rh_e X X
(4.72)
where
Numx = Num• L1/L2 (Dimensionless group of natural
convective mass transfer)
k Af Nuh_ = Nuh • -A- r- (Dimensionless groups of natural convective
Y w heat transfer)
L1 k Nuh_ = Nuh
a a Tr L1
Y k
(Dimensionless group of thermal
radiation)
The two dimensional-one phase model, developed above, constitutes a
set of four coupled parabolic partial differential equations. A computational
technique of combined finite difference - orthogonal collocation methods is
applied to the solution of this set of equations. A brief description of the
technique is given in Appendix 3.
When heat loss at the edges of the. heater is negligible (Nuh_ « 1), the two
dimensional model can be reduced to a one dimensional model. Y Then the
mass equation becomes:-
d 1 dWi dWi
d(Pi dx
) dx } R1(W,a) = 0
3 W. = (1- E W.) v./ (v4+v5)
1=1
i = 1,2,3
j = 3,4
(4.73)
(4.74)
216
The energy equation becomes:-
(pn de) _ de - St(e-1) + Rs(W,e) = 0
dX dX dX (4.75)
The boundary conditions are:
dW at X = 0 -
Pmi (Wi Wio) dX
i = 1,2,3, (4.76)
at X- 1
de
dX Ph (0- 1)
dWi
dX Num- (W.-Wi) - PmiWi
- dX = y(e4-1 ) + Nuh-(e-1
(4.77)
i = 1,2,3 (4.78)
- Ph e (4.79) X
where 4•U•L1
t - L2 Gm Cp
The one dimensional-one-phase model constitutes a set of four coupled
ordinary differential equations. A finite difference method is applied to.
the solution of this set of equations. A brief description of the difference
simulation is given in Appendix 3.
4.3.4. Evaluation of radiation efficiency
The radiation efficiency of the catalytic combustion is defined as the
amount of energy transported by thermal radiation to the surroundings per
amount of energy given out by fuel consumption due to combustion.
The radiation heat flux from the heater to the surroundings is:-
4 i=l 4
R= a aT E F.e. r i=N 1 'eff
(4.80)
where eieff
• the effective dimensionless temperature of ith fibre lamination
for the one dimensional model eieff
e. for the two dimensional model
e. = jo
ei
dY 1eff
Fi: the distribution function governs the quantity of energy emitted by radi-
ation from ith lamination to the surroundings, and can be defined as:
217
F. = (1-0e11-i
N: number of laminations (Nth lamination is the frontal lamination),
c: the void fraction of the fibre pad;.
and
i=1 i=1
E F = E (1-e)eN-i = 1 i=N i=N
(4.81)
(4.82)
By substituting Fi into eq.( 4.80), the radiation heat flux from the heater
is
4.3.5. Steady state results
In the following section, the solutions of the mathematical models are
given and compared with experimental data which were previously described in
chapter three. Parametric sensitivities on flowrate, pad thickness, void
fraction and perturbation on thermoconductivity are also studied.
4.3.5.1. Comparison with experimental results
The experimental results presented in chapter three are compared with
the calculations, based on the theoretical models, in Table 4.14. The models
predict that (as was indicated by experiment) the reaction zone becomes wider
and the hot spot moves towards the external surface of the combustor with in-
creasing fuel input flow rate. The models also predict the same effects of
slippage and radiation efficiency on changing the fuel input. The discrepancy
between the experimental and model results could be improved by modifying the
heat transfer parameters, particularly the buoyancy effect of the boundary.
This would, however, be an unsound approach, since the fluid mechanics
involved would be complicated.
R = a a Tr (1-0 AE1 cN-i e.
i=N eff
TABLE 4.14 _
by radiation
Bed thickness = 1.04 cm
ATmax: Tmax - Tout R: the efficiency of energy transported
Fuel input Experimental 1-Dimensional model 2-Dimensional model
ml/min
(S.T.P.)
Slippage ATmax Tout m1/min (STP) Tpos K
R Slippage ATmax Tout K ml/min (STP) Tpos
R Slippage ATc,max Tc,out
ml/min (STP) Tins K
R
0/0
288.0 47.2 299.0 37.5 304.0
374.5 13.2 595.0 10.2 591.0 11.3 597.0 38.4
0.0 0.091 0.091
243.0 289.6 298.0
477.0 18.6 653.0 61.0 14.7 607.4 47.3 15.8 616.0 48.3
0.31 0.273 0.340
146.0 181.9 183.0
614.7 30.3 735.0 66.3 26.6 702.1 54.8 27.3 704.2 57.6
0.48 0.455 0.41
37.0 62.0 70.7
727.8 48.4 780.0 70.0 44.0 754.0 56.4 45.8 757.1 59.0
0.55 0.520 0.50
219
The differences between the 1-dimensional and 2-dimensional models are
not significant, because the heat loss at the edges of the combustor has a
less important effect on the temperature profiles. Figures 4.7 and 4.8 show
that the lateral temperature profiles of the 2-dimensional model are practically
flat; a drop of temperature only occurs near the edges. The central temperature
profiles measured by experiments are plotted in Fig. 4.9 with the results of
the 1-dimensional model. The comparisons show that the 1-dimensional model
predicts successfully the hot region of the combustor.
4.3.5.2. Parametric sensitivities
Having discussed the validity of the theoretical models, the parametric
sensitivities to the operating variables such as fuel input flowrate, pad
thickness, void fraction and perturbation on thermoconductivity are studied in
the following sections. In order to reduce complexity, the study is based on
the one dimensional model.
4.3.5.2.1. Effect of fuel input flowrate
Results presented in Fig. 4.9 indicate that, with increasing fuel input,
the reaction zone becomes wider and the maximum temperature rise is less. The
effect of the flowrate on the concentration profiles can be seen from the
results of two typical flowrate conditions, as shown in Figs. 4.10 and 4.11.
At the lower flowrate condition, the diffusion of oxygen is easy and the
[02] : (CH41 ratio within about 80 % of the reactor bed is higher than the
overall reaction stoichiometry (= 2). At the higher fuel input, the diffusion
of oxygen becomes difficult and about 70 % of the reactor bed the [02) : 1CH40
ratio has a value lower than the stoichiometry.
In Fig.'4.12, the effects of fuel flowrate on the fuel conversion and
the radiation efficiency are given. The conversion decreases monotonically
with increasing fuel input flowrate; the dependence could be explained in terms
of lower contact time, less oxygen concentration and lower process temperatures.
It is also shown that the radiation efficiency exhibits a maximum at the flow-
rate range of ca. 700 ml/min (STP). As demonstrated in Figs. 4.13 and 4.14,
the contribution of each fibre.lamination to the total radiation heat flux from
the heater (as defined in eq. ( 4.80), shows that the zone that can "see" the
surroundings with less obstruction is about a fraction of 0.3 of the total
catalytic pad thickness, and this fraction lies near the external.
boundary of the combustor. As a result, the radiation efficiency does not
-depend on the temperatures within the rest of the pad, and it can only be
0.0 220
0.5 1.0 edge
300 0.0
centre
Fig. 4.7
Dimensionless Bed Thickness
800
700
600
500
400
0.5 1.0 edge
Fig. 4.8 0.0 centre
Dimensionless Bed Thickness
0.0
Fuel Input = 662.3 ml/min (STP)
Pad Thickness= 1.0 cm 1.0 1000
221
222
0.0 0.5
1.0 Dimensionless Bed Thickness
Catalytic Bed Thickness : 1.04cm
Flowrate Theoretical Exptd. ml/min STP) Curve Symbol I
340.8
433.7
559.6
662.3
Fig. 4.9
a ❑
O 0
950
0.4
900 Fuel Input :
433.7mI/min ( STP I
Catalytic Pad Thickness : 1.04cm
700
Fig. 4.10
600
223
0.0 0.5 .1.0
Dimensionless Bed Thickness
Input Fuel: 652.3 ml/min
( STP )
Catalytic Bed Thickness* 1.04cm
Fig. 4.11
UO
UOD
Jd J
Dp
N
600 0
04
1 800
P
E a H
700
0
0.5
1.0
Dimensionless Bed Thickness
1200 400 600 800 1000
Fuel Input ml/min ( STP )
uo!s
Janu
o3 la
nj %
95
90
80
60
C a, U
w C O
.46
40
20
100
85
D D1 D2 0.3 0.4
28 Input Fuel : 433.7 mVmin
( STP )
Pad Thickness 1.04 cm
16
0
24
20
J/cm
2 /so
c x
1.03
External Surface
F--Direction of Flow
Dimensionless Pad Thickness
20 .4D 60 80 100
Number of Lamination
Fig. 4.13
Dimensionless Pad Thickness
36 0.1 Q2 0.3 0.4
Fuel Input : •662.3 ml/min 32 (STP
Pad Thickness : 1.04 cm
28
24
20
16
12
J /c
m2/s
ec
x 10
3
Emis
sion
D
istri
butio
n ,
External Surface
Direction of Flow
0 20 40 60 80 100
Number of Lamination
Fig. 4.14
228
improved when the temperature near the external surface can be increased.
The positive dependence of the radiation efficiency on the fuel input could
be explained as that, at such range of fuel input flowrate (less than 700 ml/
min STP), the increase of flowrate results in a higher radiation zone tempera-
ture and hence increases the efficiency of energy transported by radiation.
Further increases of the input flowrate (above 700 ml/min STP) cause the
efficiency to become inversely dependent on flowrate, because the process
temperature is reduced due to shorter contact time for reaction and lower
oxygen concentration inside the combustor.
4.3.5.2.2. Effect of pad thickness
The results presented in Figs.4.15 and 4.16 represent the temperature
and concentration profiles occurring in the combustor with a pad thickness of
2 cm. By comparing the profiles in Figs. 4.10, 4.11, 4.15 and 4.16, it can
be seen that the thicker the pad the better the thermal insulation and this
results in higher process temperatures. With the fuel input at 433.8 ml/min
(STP), the peak temperature inside the pad increases 27 K when the pad thickness
is doubled from 1 cm; with the flowrate at 662.3 ml/min (SIP), the difference
in peak temperature is 9 K.
By comparing the concentration profiles presented in Figs. 4.10, 4.11,
4.15 and 4.16, it can be seen that the efficient [02] : [CH4l ratio within the
combustor with a thicker catalytic pad has a lower value.
The effect of pad thickness on the operating characteristics of the
catalytic combustor are summarized in Table 4.15.
TABLE 4.15
Effects of pad thickness
Fuel input
ml/min (STP)
Pad thickness
cm
Tmax K
% pad thickness
with 02/CH4 2
433.8 1.0 897 83
433.8 2.0 924 40
662.3 1.0 817 34
662.3 2.0 826 17
500 0 1..0 0.5
900
Inputflowrate of Fuel : 433.7m1/min( STP)
0.5 Catalytic Pad Thickness :
2.0 cm
0.4
0.3 3 0 -I 0
0.2 ō.
800
600
0.1
Fig. 4.15
Dimensionless Bed Thickness
Fig. 4.16
230
Input Fuel: 662.3m1/min(STP
Pad Thickness : 2.0 cm
0.0 0.5
Dimensionless Bed Thickness
231
Fig. 4.17 represents the temperature profiles of various pad thicknesses. The results show that a big jump in the process temperature occurs when the catalytic pad is increased to 4 cm thick.
4.3.5.2.3. Effect of void fraction
The effects of void fraction are represented by the results given in Figs. 4.18 and 4.19.
The results (curves A, C in Fig. 4.18) show that the heat transfer processes could be improved by close packing (low void fraction). Although the temperature distribution inside the combustor could be smoothed by lowering
the pad void fraction, the air diffusion into the catalyst could, at the same time, be inhibited. As shown in Fig. 4.19, the (02J:(CH4) ratio inside the
combustor decreases as the pad void fraction decreases. Insufficient amounts of oxygen inside the combustor would consequently affect the conversion of the fuel, as indicated by curve B in Fig. 4.18.
4.3.5.2.4. Perturbation on lumped thermoconductivity
The thermal behaviour of the catalytic combustor is affected by thermal conduction through the catalyst as well as by radiation. As was described in Section 4.3.2.4., the internal radiation can be simplified to a Fourier type conduction by introducing a local apparent thermoconductivity. The energy transport can thus be described by lumping the effects of conduction and radiation in terms of a lumped thermoconductivity. In this section, the effect due to mis-estimating the thermoconductivity is studied.
In Fig. 4.20, the results represent the temperature profiles with various perturbations in the estimated lumped thermoconductivity. By comparing curves a and b, it can be shown that a 50% overestimation of the thermo-conductivity would result in underpredicting the peak temperature by 30K. Another implication that can be drawn is that the temperature distribution could be improved by using a packing material with high thermoconductivity.
1200
1100
232
0
0.5 1.0
Dimensionless Bed Thickness
Input Fuel Ftowrate: 559.4 mVmin( STP
Curves Pad Thicknesstcm)
a 0.5
5 1.0 2.0
d 3.0
e 4.0
Fig. 4.17
233
Void Fraction Fig. 4. 18
A 300
200
100
0
254
Input Fuel 559.4m1/min( STP )
Pad Thickness : 1.0cm
Void Curve Fraction
b
0.8
0.7
0.6 c s U
0
d 0.5
e 0.4
Fig. 4.19
Dimensionless Pad Thickness
235
Tem
pera
ture
Input Fuel Flowrate 559.4 ml/min ( STP )
900 Pad Thickness: 1.04im
Curve
Perturbation on Lumped Thermo- Conductivity, k
a 0.5
b 1.0 ( base
c 2.0
d 5.0
e 50.0
Fig. 4. 20
Dimensionless Pad Thickness
236
5. Conclusions
1. The catalytic activities of catalyst supports for methane
oxidation vary with the surface acidity due to the existence
of surface silica-alumina. The difference in the product
selectivity between the two types of alumina supports (porous
and nonporous) may result from: (1) the effect of pore diffu
sion,which allows the reaction intermediate (carbon monoxide)
to be captured for a longer period inside the porous catalyst
resulting in overall oxidation to carbon dioxide, (ii) the
difference in concentration of surface acidity. The nonporous
alumina, which possesses higher surface concentrations of acidic sites, favours incomplete oxidation.
2. The oxidation of methane on the alumina supports is consistent
with a reaction mechanism involving: (i) adsorption of methane
on the acidic centres; (ii) oxidation of the adsorbed carbon-
aceous intermediates by adsorbed oxygen or by oxygen in the
gas phase.
3. Over platinum/alumina (porous) catalyst, carbon dioxide is the
only product of methane oxidation at temperatures less than
ca. 813K; the appearance of carbon monoxide in the product
stream at the higher reaction temperatures depends on the
oxygen to methane ratio present in the system. Lower ratios
(below ca. 0.8) favour higher selectivity to carbon monoxide.
4. Because of the micro-size (of the order of a micron) of the fibre catalyst, pore diffusion does not affect significantly
the reaction rate for methane oxidation or carbon monoxide
oxidation over the platinum/alumina (porous) catalyst. The
negligible effect of pore diffusion could be seen from the
small values of the Thiele modulus (<, 1.) at the reaction
conditions.
5. The reaction rate of carbon monoxide oxidation over platinum/
alumina catalysts is faster than that of methane oxidation.
6. Over platinum/alumina (porous) catalyst, deposition of carbon-
aceous residues occurs during methane oxidation, particularly
237
at conditions of high temperature (above ca. 813K) and low
oxygen to methane ratio (below ca. 0.8). The deposition
increases with increasing temperature and decreases with
increasing oxygen to methane ratio. The carbonaceous
deposit is most likely to be strongly chemisorbed on the
"bridge sites" as bonded methylene radicals; the oxidation
rate of these is much slower than the oxidation rate of
methane. As a result, at conditions favourable to carbon-
aceous deposition, the residual catalytic activity for methane
oxidation is probably due to the reaction of less stable
linearly adsorbed methyl radicals with gaseous oxygen or with
surface adsorbed oxygen.
7. In the presence of oxygen, the cracking or the adsorption of
methane on the catalyst surface is highly significant at high
temperatures (above ca. 813K), and is enhanced by the large
decrease in the oxygen sticking ability for chemisorption on platinum surface at temperatures above ca. 813K.
8. The kinetic studies indicate that the most probable oxygen
chemisorbed states on the platinum surface are Pt0 (bridge site)
and Pt02 (linear site); the former corresponds to maximum
coverage at temperatures below 813K.
9. Over platinum/alumina catalysts, methane oxidizes by two mech-
anisms, shifting from one to another at temperatures of ca.
813K. At temperatures below ca. 813K, the reaction between
strongly adsorbed oxygen and either weakly adsorbed methane
or gaseous methane to produce carbon dioxide is the rate deter-
mining step. At temperatures above ca. 813K, the rate deter-
mining step is probably the interaction of strongly chemisorbed
methane with gaseous oxygen and weakly chemisorbed oxygen;
carbon oxides are the products of the reaction.
10. Further oxidation of carbon monoxide at high temperatures is
inhibited by the high coverage of carbonaceous deposit and of
methyl radicals on the catalyst surface. The appearance of
carbon monoxide could also result from the gasification of the
carbonaceous residues by carbon dioxide.
238
11. The desorption energy of oxygen on platinum surface has a
similar magnitude as the apparent activation energy observed
in the methane oxidation process, and the activation energy
for the reaction is probably dominated by the oxygen-platinum
binding energy.
12. The kinetic studies of the methane oxidation have shown a shift
in the apparent activation energy to lower values above ca.
813K. The change is explained as the effect of thermal com-
pensation by the heat of adsorption of methane.
13. The methane oxidation reaction is not inhibited by the addition of the reaction products, such as carbon oxides and steam.
14. Thermal instability occurs in the process of methane oxidation
when significant adsorption or preadsorption of methane takes
place over platinum/alumina catalysts. The effect is believed
to be sensitized by the presence of hydrogen, produced by dis-
sociative adsorption of methane. The subsequent fast oxida-
tion of hydrogen causes the reaction system to run away.
15. Thermal treatment (up to ca. 1073K), on the platinum/alumina
(porous) catalyst in an inert atmosphere does not cause major
loss in the catalyst activity for methane oxidation. Steam
treatment of the catalyst at elevated temperatures results in
pore collapse. As a result, the platinum particles could be
buried inside the alumina and substantial loss of catalytic
sites could result.
16. Carbonaceous deposits on the catalyst surface (as the result of
cracking of methane) did not cause irreversible deactivation.
It would be expected that films of carbonaceous deposit should
be oxidized easily in an oxygen rich atmosphere.
17. Over platinum/alumina catalyst, methane-steam reactions are not
catalysed in oxygen free environments, but the same catalyst catalyses the water gas shift reaction.
18. Kinetic studies of the water gas shift reaction indicates that
239
the reaction is inhibited by hydrogen. Based on the Langmuir-
Hinshelwood theory, the best-fit kinetic model shows that the
catalyst surface possesses two kinds of active site; one
adsorbs carbon monoxide while the other competitively adsorbs
hydrogen and water. The rate determining step of the shift
reaction is a reversible surface reaction. In the forward
path, interaction between adsorbed carbon monoxide and water
is involved while,in the backward path,the interaction is.
between gaseous carbon dioxide and adsorbed hydrogen.
19. The reaction orders in oxygen for methane oxidation over platinum
supported on porous and nonporous catalysts are distinctly different. Over the former catalyst, the oxygen adsorbed
state is believed to be a mixture of Pt0 and Pt02, while it is
present as Pt02 over the latter. The difference is interpreted
in terms of different oxygen adsorption strengths . over different
sizes of platinum crystallites deposited on these two supports.
20. The cracking of methane over the nonporous platinum/alumina
catalyst is comparatively less than that over the porous
catalyst. The effect may be the result of shorter "induction"
residence times for methane over the nonporous catalyst or of
a weaker adsorption strength for methane over the larger
platinum particles.
21. As the result of the loss in platinum surface area and the
recovery of silica surface content after long periods of use
(> ca. 40 hrs.) for methane oxidation, the selectivity of carbon
monoxide production over the aged nonporous catalyst increases
with decreasing reaction contact time.
22. Experimental study has been performed to investigate the thermal
behaviour of the convective-diffusive type catalytic combustor.
The temperature profiles, measured by embedded thermocouples,
indicate the existence of a hot zone which moves towards the
combustor frontal surface as the fuel input is increased. At
the lowest flowrate at which the combustion could be self-
sustained, the hot zone was just at the back surface of the
catalytic pad, with a temperature as much as 200K (approx.)
above that of the frontal surface. Smooth temperature distri-
240
butions with smaller maximum temperatures could be achieved with higher fuel input flowrates.
23. The energy generated by the combustion process is delivered by thermal radiation, convection and conduction loss through the metal casing. Thermal radiation is the largest transport component.
24. The convective-diffusive type combustion process has an average methane combustion efficiency (or methane conversion) of ca. 95%. The efficiency decreased about 3% as the fuel input doubled from the minimum self-sustained flowrate (6 ml/sec); the effect was attributed to the shorter reaction contact time and to the difficulty of ai r diffusion at hi gher flowrates.
25. The energy transport by radiation and convection components was found to increase with increasing fuel input flowrate throughout the experimental range.
26. In the convective-diffusive catalytic combustor, the oxygen supply to the combustion process was due to molecular diffusion of ambient air against the bulk flow of the fuel. The higher the bulk flowrate, the less air could penetrate into the cata- lytic pad. Increase in the fuel input (up to 12 ml/sec (STP)) increased the consumption rate of oxygen as the result of the wider reaction zone.
27. No emission of carbon monoxide or nitric oxides was detected at the operating conditions of the convective-diffusive catalytic combustor.
28. The analysis of nitrogen distribution at the frontal surface showed smooth mass profiles which would indicate that the flow patterns inside the combustor were uniform and that ambient air could evenly diffuse to the frontal surface of the combustor.
29. Fuel slippage from the convective-diffusive catalytic combustor
241
increases with increasing fuel input flowrate, as the result of less reaction contact time and of air diffusion difficulties.
30. An attempt to inject pre-mixed oxygen and methane mixture was unsuccessful because of a severe explosion, involving a back-ward propagating flame ignited at the inlet section of the catalyst layer.
31. Theoretical models were developed based on the experimental kinetic data to describe the performance of the convective-diffusive catalytic combustor by taking into account the heat and mass transport phenomena occurring inside and at the
boundaries of the combustor.
32. As compared with the experimental measurements, the theoretical models successfully predict the thermal effects which occur in the convective-diffusive catalytic combustor. Improvement of the discrepancy between the experimental and theoretical results would involve modification of heat transfer parameters, and particularly the internal radiation parameters and the buoyancy effects at the boundary.
33. The one dimensional-one phase model was found to be sufficient.
to predict the performance of the combustor. This. results from the fact that (i) the high mass and heat:: transfer_ coefficients are enhanced by the small diameter of the fibre catalyst, .(ii) the heat loss at the edges of the combustor is less important as compared
with the energy transport by radiation and convection components.
34. The calculated mass profiles showed that, under efficient air diffusion conditions, only the inlet section of the catalyst layer is responsible for the major combustion (over 50% conversion): the rest of the catalyst pad acts as a thermal insulant to keep the temperature in the reaction zone sufficiently high to sustain combustion.
35. It has been shown that only about 30% of the total catalyst pad thickness is responsible for the thermal transport by radiation; this fraction lies near the external boundary of the combustor.
242
As a result, the radiation efficiency does not depend on the
temperatures within the rest of the pad, and efficiency can only
be improved when the temperature near the external surface can
be increased. This could be done by increasing the fuel input.
36. The calculations based on the theoretical modelling showed that
thicker catalyst pads would result in higher thermal insulation
and in higher temperature at the inlet section. Consequently
it could be expected that catalyst deactivation would occur at
such conditions of high temperatures and steam (produced by
reaction) abundant environments. The catalyst deactivation
effect was not included in the present theoretical modelling.
study.
37. Theoretical calculations showed that the heat transfer processes
could be improved by close packing (low void fraction pad).
However, lower void fraction catalyst pads would result in
poorer diffusion of air into the combustor.
243
Appendix 1
Theoretical approach to check the pore diffusion limitation
The oxidation of methane over platinum/alumina (porous) fibre catalyst was checked for the possibility of pore diffusion limitation at high temperature by utilizing the kinetic data obtained at low temp- erature region (> 813K) as the intrinsic kinetic information.. The mass equations were solved by taking the assumption that single fibre catalyst was isothermal under the operating conditions and could be treated as an infinite cylinder. This was based on the very small diameter to length ratio and effectively high dispersion of platinum
particles on, the support.
The mass equations:
(A1.1) Deff,i •c• r~ār(rdri ))=vi .pb.kT.yl 475 i =1,2
where Deff,i : the effective pore diffusivity of species i, m2/sec yi : molar fraction of species i
=1 methane i
=2 oxygen c : the bulk gas concentration, kmol/m3 i: the reaction stoichiometry of species i
kT: the reaction rate constant at temperature T, 1.087x109exp(-2250l.26/T) kmol/kg-sec
T : reaction temperature,K
Pb: catalyst bulk density, 96kg/m3
The boundary conditions :
dri =0 at r=0
at r= Ro
i = 1,2
244
The dimensionless form of eq.A1.1 :
(A1.2) 2 0 ~75
d ( dE') ~..yl .y2
, i =1,2
The boundary conditions :
dpi = 0
yi = .Y- lo
at =0
at =1
i = 1,2
where E E r/Ro
v4 .pb.kT
Deff,i'C • Ro
Ro is the fibre diameter, 5.5pm
Egs.A1.2 were solved, at various bulk conditions, by finite diff- erence method. The differential equations were approximated by a forward- backward difference scheme as described in Section A3.3.1. The resulting equations are :
41) - y(2) = 0
(A1.3) yin-l) - (2+l/n)4n) + (1+l/n)yin+1) _ h2.F(n) , n =2,N
y(Nfi1) = Yio
where N is the number of integration steps h is the step size (h=l/N)
Eqs. A1.3 can be expressed in matrix form :
(Al .4) A . Y. = Bi i = 1 ,2 Bi is the source term and where the coupling of species 1 and 2 occurs.
_ 2 . (dyi/dE) 1 (A1.7) ni =
y ,y0.75
10 20
Evaluations of the effectiveness factors were performed at various
245
Eq. A1.4 can be solved by a self-iterative scheme (121), which is :
(A1.5) A.y'M+1) =B7M) i=1,2
where M denotes the number of iterations.
The updated profiles were obtained by the Gaussian elimination method
(122). The procedure was found to be fast convergent; and . one iteration
required about 20ms of the central processor time of a CDC 6400 computer.
The accuracy was checked by repeating the procedure while halving the step
size.
The effectiveness factor of species i, ni, over the catalyst was
defined as :
(A1.6) - 21TRo•0eff,i.c.(dri )r= Ro
0•75 rrRo2.vi.Ab.kT•yIC 20
or
bulk conditions and the data are given in Table 3.2.
The effective pore diffusivity Deff
was approximated by the Knudsen
diffusivity for the very small pore diameter (= 5.5nm) of the catalyst
(111). For species i, the expression is:
(A1.8) Deff,i
= 5.335x10-7 T/Mi m2/sec
where T is the temperature in K
Mi is the molecular weight for species i.
The quantity, (I), is called the Thiele modulus, . the smaller
values of which indicate the less significance of the pore diffusion
limitation. The values of the Thiele modulus were calculated at various
temperature conditions. The results, listed in Table A1.1, show that,
in the temperature range from 800 to 1000K, the Thiele modulus for both
methane and oxygen is very much less than unity (< 10-4). With such
small values of the Thiele modulus, one would expect that the pore diff-
usion limitation should be practically absent with the fibre catalyst.
TABLE A1.1
Temp. 0CH4 002
800 5.6940x10-6 9.5760x10^6 850 1.3221x10-5 2.2235x10-5 900 2.7980x105 4.7056x10-5 950 5.4760x10^5 9.2145x10-5 1000 -4 1.0000x10 1.6818x10-4
246
247
Appendix 2
The Specific kinetics
The amounts of active sites on both porous and nonporous platinum/alumina catalysts were measured by carbon monoxide adsorption. The kinetic data of methane oxidation over the catalysts (Table 3.6 and 3.14) are thus correlated with the adsorption data (Table 3.22) for active surface area. The results are given in Table A2.1.
TABLE A2.1
Catalyst Temp.
K ko
kmol/kgcat-sec kos
kmol/m2 (Pt)-sec
Pt/A1203 789 3.438x105 70.375
(porous) 817 5.025x10-2 1.029x10-5
Pt/A1203* 801 3.086x103 1.867
(nonporous) . 835 5.282x10-3 3.196x10-6
.* ' The specific rate is based on the adsorption data measured with the
sample used for methane oxidation less than 40hrs.
Two assumptions have been made in the correlation of kinetics which are : (i) the adsorption stoichiometry of carbon monoxide over platinum is taken as 0.76 (74); (ii) the number of surface atoms per unit area of the metal can be approximated as 1.25x1019 atoms/m2 ( 75). In correlating the specific kinetics for the nonporous catalyst, the result has been affected by the uncertainty due to the platinum sintering.
Appendix 3
Numerical Methods
A3.1. Finite Difference Approximation
In any finite difference method, the region of integration is divided into a set of grid elements. The differential equations, and, where applicable, their boundary conditions, are approximated and sat-isfied at each of the points by difference equations for the values of the dependent variables at that point and at some, or all, of its neigbours.
The difference approximations for the first and second order derivatives are :
(A3.1) y'(x) = (y(x+h)-y(x)1 /h ,(two-point forward formula)
(A3.2) y'(x) = (y(x)-y(x-h)}/h ,(two-point backward formula)
(A3.3) y'(x) = (y(x+h)-y(x-h))/(2h) ,(two-point central formula)
(A3.4) y "(x) = (y(x+h)-2y(x)+y(x-h))/h2 ,(three-point central formula)
where h is the size of the grid.
A3.2. Orthogonal Collocation
Orthogonal collocation is one of the family of weighted residual methods in which an approximate solution is sought by requiring the "residual", obtained by substituting an approximating polynomial into the original differential equation, to be zero at some specified points. In orthogonal collocation method, the collocation points are taken as the roots to the approximating polynomial. The choice of the latter, however, is largely a matter of numerical experience. For boundary value problems, Villadsen et.al. (122) employed orthogonal polynomials as the trial functions to satisfy the boundary conditions as well as the roots to the polynomials giving the collocation points.
For a two dimensional problem, one can either apply the orthogonal collocation across the whole integration field in both directions,or divide the integration range in one direction into a series of finite elements over which the method is applied separately to obtain the profile in the other direction. The latter approach has been applied to calcu-
late the profiles of the two dimensional combustor model.
249
The solution can be derived in terms of the values of the var-
iables at the collocation points, rather than as functions of the poly- nomial coefficients. The whole problem is thus reduced to a simple matrix problem. Accurate quadrature formulas are also available to enable the abstraction of integrated properties, and the polynomials are easily generalized to planar, cylindrical, or spherical geometries, as well as to a wide variety of boundary conditions. A detailed review on this method was given by Fi nl ayson (123) .
For problems with symmetrical property, a possible choice of trial function for the solution is :
N (A3.5) y(x) =y(1 ) + (1-x2)1Ela.Pi-1(x2)
and the orthogonal polynomials, Pi(x2) are defined by :
(A3.6)
where Sc
i w( x2) P.
J( x2 )P.(x2)xf-ldx = C1 61 j = 1,2,....,i-1
ai : the coefficients of the trial function w(x2): the weighting function
Ci : some constant N : number of interior collocation points
bi j - 1 1 j
=0 1,j
= 1 planar geometry f = 2 cylindrical geometry
= 3 spheri cal geometry
Eq. A3.5 can be expressed as N+1
2i-2 y(x) = E aix
i=1
Differentiating this and evaluating the expressions at the collocation points:
(A3.7) y NElxJ
i-2 ai
il
(A3.8)
(A3.9)
N+1
axlx = iEl(2i-2)x
~i-3 ai J
250
ā2
J
N+1
xlx = E(2i-2)(2i-3)x i-, l ai
Expressing the above in matrix form :
(A3.10) Y = Q . A
K(Y) (A3.11) = G . A
(A3,12) h2CYi= it 'A
where Y and A are vectors of y(xp and ai respectively.
Q. = xji-2 Ji
G. = (2i-2)x~i-3 Ji
Hsi = (2i-2)(2i-3)x~i-4
Eliminating A gives :
(A3.13) x(Y) ā = G . 4 1
= U . Y
(A3.14) āxz(Y) = H . n-1. Y = V . Y
Thus the derivatives are expressed in terms of the values of the
function at the collocation points. The roots of polynomials can be
deduced by successive application of Graeffe's root squaring (121) and
Newton's methods. For polynominals up to the sixth order, tables of
the roots are presented by Finlayson (123). It has been suggested (123)
that, for low-order approximations, one should choose to define the
weighting factor w as 1-x2, whereas for faster convergence, to define the
factor as unity.
251
A3.3. Application to combustor models
A3.3.1. One Dimensional Model
A finite difference method was used to solve the set of mass and
energy equations. The equations have a general form of :
(A3.15)
Where
E x(A ) +Bdx
+Cy+R =0 ax
R is the source term;
A is a function of y;
B and C are constant.
Boundary conditions:
dx x=c1 = G(y) or x=1
where G is some function of y.
The region of integration is divided into N grids. Eq. A3.15
can be approximated and satisfied by the difference equations given in
Section A3.1 at each grid point. For unconditionally stable and unique
numerical solution (124), a forward-backward technique is used by app-
roximating y" with the central formula (eq.A3.4), and y' with the back-
ward formula when B/A < 0 or with forward formula when B/A> 0. The local
values of A are calculated at each grid point. The gradients at the
lower and upper bounds are approximated by forward and backward diff-
erence formulas respectively. The resulting set of difference equat-
ions can be expressed in matrix form as :
(A3.16) F(Y) - P.Y - Q(Y) = 0.
where P is the characteristic matrix ((N+1)x(N+1)) with tri-
diagonal structure;
g. is a (N+1)-dimensional column vector which is usually
a nonlinear function of Y, and where the coupling of
the dependent variables occur.
252
The set of nonlinear algebraic equations (eq.A3,16) can be solved by the generalized Newton-Iterative method (124). The algorithm for the solution is :
(A3.17)
where
y(n+l) = yin)_ ikāy. i(Y3n+1),Yin))rl. fi(yfn+l),Ysn))
i
Viand Y2 are compartments of Y, containing elements yk with k< i and k. i respectively; fi is the ith element of F; n denotes the nth iteration.
It has been suggested that the iteration factor, wi should be chosen in the range (0,2) (124). Choices of wi higher than unity
can increase the convergence rate appreciably. However the higher values of wi would also result in numerical instability. In the present problem with a nonlinear boundary condition (due to radiation effect at the external boundary of the combustor), it was found that stable solutions and reasonably fast convergence rates would be acquired if the chosen values of the iteration factor were small (wis 1) in the regions where the grad-ient was steep (external boundary), and large (1< w1< 2) in the regions where the gradient was smooth.
The convergence and accuracy of the solutions generated by iterat-ions were verified by direct substitution into the system of eq. A3.16, and repeating the iteration procedure while halving the size of the grid. When the calculation was based on the experimental conditions, the dimen-sionless temperature profile measured was used as the initial profile to start the iteration procedure. Other calculations were started with the initial profiles at similar conditions. On a CDC 6400 computer, one it-
eration of the calculation procedure requires 2ms of the central processor time.
A3.3.2. Two Dimensional model
A combined finite difference - orthogonal collocation method was used to solve the set of mass and energy equations. The equations have
253
a general form of :
āx(A āx) + āy(B ay) + Cāe + R = 0
R is the source term; A and B are functions of e; C is a constant.
The boundary conditions in the longitudinal direction, x, are similar to those for the one dimensional model. The present problem has symmetric properties; and the boundary conditions at the upper bound in the lateral direction have a form of :
(A3.19) 1y=l= G(0)
where G is some function of 0. As with the one dimensional model, the region of integration
was divided into N regular grids in the longitudinal direction, and the derivatives of this direction were approximated by finite different formulas as in the case for the one dimensional model. The region of in integration in the lateral direction was divided at the collocation points, and the second order derivative was replaced by the formula given in eq. A3.4. The resulting equations have a form :
N+1 A3.20) Pjk . oj + a E V..e. + Qjk 0
1=1
for k=1,M+1 j = 2,N
where N is number of internal collocation points M is number of longitudinal grids P jk is the characteristic row vector,(lx(M+l)J, containing the informations at the kth longitudinal grid of the jth lateral collocation point.
of is the column vector,[(M+1)xl), containing the values of the dependent variable in longitudinaldirection at the jth lateral collocation point a is a constant Vii etc. are elements of the collocation matrix, V
(A3.18)
where
254
denotes the value of 0 at grid point i,k 8i,k Qjk is the source term at the grid point j,k.
Eq.(A3.19) is replaced to : N+1
(A3.21) 1.E1
UN+l,i'ei,k G(eN+l,k)
The problem was solved by the same trial and error procedure (generalized Newton-Iterative method) as described in Section A3.3.1. The numerical method was tested for convergence using the polynomials with weighting functions w=1 and w=1-x2 . Finalyson (123) suggested
that the polynomial of the first type was more efficient in solving boundary value problems with steep gradient at y=1, because the roots of the polynomial would be concentrated at the boundary. The alter- native polynomial normally gave more accurate results. It was found that the numerical methods converged to a definite solution, independ- ent of the type of orthogonal polynomial used. The results were generally obtained with N=5 and w=1.
k = 1 ,M+1
255
Appendix 4
Physical properties
The physical properties are assumed to be constant and have
these values (125):
Fluid heat capacity, Cpf = 29.26 kJ/kmol-K
Fluid thermoconductivity, kf = 3.902x10-5 kW/m-K
Fluid viscosity, of = 2.3x10-5 kg/s-m
Fluid Prandtl number, Pr = 0.73
Solid phase emissivity, a = 0.45
256
Appendix 5
Computer Programs
The service routines
Name Function
MTP subroutine to calculate the mass transfer parameters
HTP subroutine to calculate the heat transfer parameters
THERK subroutine to calculate the solid phase lumped thermo- conductivities
TRIDI subroutine to solve the set of linear equations with tridiagonal matrix structure
RATE subroutine to calculate the reaction rates
ORTHO subroutine to calculate the collocation matrics
RADCON subprogram to calculate the internal radiation parameters
DIFFUSE subprogram to calculate the mass distributions within the porous catalyst and to calculate the effectiveness factors of the catalyst
MINV library routine to perform matrix inversion
REAFIT subprogram to perform parameter fitting procedure utilizing the library routine VA04A
VA04A library routine to perform nonlinear regression with Powell's conjugated method
CALCFX subroutine to calculate the objective function to be minimized
RKUTT subroutine to perform Runge-Kutta integration
YGRD subroutine containing the set of ordinary differential equations to be integrated by RKUTT
MODEL subroutine containing the reaction model
— HTRAN ST
HEAT
SIZE
GO
VOID
THICK
— HEATER
BARK
RADK
COND
PEM MTRAN
STOI(I)
THETA(N) TEMPA —
R
X(M,N) REACT
Xl (M,N)
Tl(N)
TR
BDE N
E
GRH
List of variables for combustor models 257
Common Definition Equivalent in Block Text
thermal Peclet number
dimensionless group of thermal radiation
Computer Variable
PEH•
GAMA
Ph
Y
Stanton number St
heat of reaction -AH
dimension of the combustor L2
fluid molar flux Gm
void fraction es
pad thickness L1
dimenionless lumped (kc+ kr)/kc solid phase the rmo-conducti vi ties
internal radiation parameter
mass Peclet number Pm
stoichiometry of species i vi
dimensionless temperature e profile
dimensionless reaction rate -
composition profiles wi
iterated composition profiles
iterated dimensionless temperature profile
room temperature Tr
catalyst bulk density pb
activation energy E
Grashof number of heat Grh transfer
(Continued)
NUHX Nusselt number of heat transfer
GRD Grashof number of mass transfer
NUMX Nusselt number of mass Num transfer
DP fibre diameter Dp
SIMA Stefan-Boltzmann constant a
EMIS emissivity e
EFF radiation efficiency
TRAD radiation heat flux from R the combustor
ARAD(I) radiation distribution Fi function at ith lamination
NPT number of collocation points
NSTEP number of regular grids
258
IACCv1
parameter calculations at each steps for: mass transfer heat transfer mass and heat sources
IACC-4)
halve long-itudinal step size
> crī ten a
criteria (convergent)
yes
no
halve longitudinal step' size
accurac•
yes
test resid
solutions for the new temperature and mass profiles
Logic diagram for the combustor models coding 259
enter
two dimensional
one dimensional
• set laternal collocation points
finite difference simulation
finite difference-orthogonal collo-cation simulation
inlet conditions combustor specifications physical parameters set longitudinal step size internal radiation parameters-(calculated externally)
initial temperature and mass profiles
print results
Cf.;
260
PROGRAM (lF13 (INPUT,ODTPUT,nATAI,COMP,TAPE5=INPl TAF'E6=0UIPUT, £TAFE7=DATA1 , Tl1PE8=CO "iP )
. C THIS PRoGRA:'M IC TO cOLVE A ONE DI%AENSIONAL O6E PHASE HUDEL or
C A DIFFUSIVE CATALYTIC HEATER BY FINITE DIFFERO CE ANALYSIS
C UNITS ARE IN C.G.S.SYSTEM, REAL NUHX, NUMX DIMENSION) H (100) , EFFCH4 (100 ) DIr'E_NSI1)N E3ARG(100),X(5,1(1n),TFIETA(100),A4100),P(100),C(100),.
*D(1 00),DIS(100),PEM(5,100),STUI(5),GARK(100),V(100), *DAE'(5),G(100),T1(100),X1(5,1U0),BG(1U0),RADK(1UU),R(10U) DIMENSION) X0(5) DIN.LNSION BARK(100) DIt"EIiSIOEJ ARAD(300) CO^'.MON/EFFECT/EFFC)I4 ' COMMON/HI RAN/PEII, DAH, GAp.1A, ST, NEAT, RU COE'MON/iiEATER/SIZE,GO,VOID,THICK CO1' MON/COND/BARK, RADK COrJ oN/rITRAI J /PEr-1, DAM, STOI Co11NON/TE'9PA/THFTA COI;MUN/REACT/R,X,X1,T1,NI CON'r1ON/PERTUR/PER
C DEFINE IIUF'IBFR OF THr INTEGRATION STEP
WRITE(6,12) 12 FORMAT (1X „1HUMr3ER OF LONGITUDINAL STEP, I3a))
READ(5,13)NSTEP 13 FOH MT (I3 )
C THE SPECIFICATION OF THE HEATER AND THE .INPUT DATA WR1TE(6,14)
14 FORr1lAT (1X, 5)GAS MOLAR FLOWRATE, MOLE/SEC, F 12. s3N ) READ(5,15) 601
15 FOhi'?AT (F12. ) WRITL(6,.16)
16 FORH T(1X,a)CATALTiC PAD THTCKNESS,CH,F10.6n1) READ(5,17) THICK
17 FOhNAT(F10.(') SIZL=6.*2.54 WRITE (6,21. )
21 FOkh`;AT (l. , J ? NLET TEMPERATURE, K, F7.6h) ) REAL)(5,22)TIN
22 FOFiiAT(F7.3) STUI(1)=—l. ST01(2)=-2, STOI(6)=1, ST01(4)=2. STUI(5)=0. G01=6Ul/SIZE:/STZE
C INITIAL GUESS POR THE FUEL,OXYGEN AND TEMPERATURE PPUFILLS---- CALL TGUESS (TEICTA, NSTEP, STEP ) WRITE(6,24)
24 FOkNAT(1X,;ITUE ITERATION FACTOEZ,W,F7.30) DO 23 I=1,NSTEP,5
23 REAU(5,26)(c!(I),J=T,I+4) 26 FOhl"AT (5F10.5 )
WRITL(6,25) 25 FOR AT(lX, )CQNVERGENCE CRITERIA,F7.3@)
REEftL) (5 , 2.2) C imm. I T WRITLx(6,18)
18 FORMA I (1X, j)i.!IJt"1 EIER oF ITERATIONS, IS0J ) ,EAU(5,19)NIOIT
19 FORMAT(I5)
VOID=0.93 DO 101 1=1,NSTEP+1 BA1G(I)=1. X(1,I)=0.2*(1.-STEP*FLOf%T(ī-1)) X(2,11=0.2 X(3,I)=0. X(4,1)=0. X(5,1)=0.6
101 CONTINUE C
REACTION PARAMFTERS
TR=300. HER1 =191759. BDEN=0.093 f3DEN=BDE.W*(1.-VOID)/0.07 RO=BOEN*3.438E+05
C READ TN INTEfRNAL RAnIATīON PARAMETERS DO 400 I=1, NSTEp, 5 READ(7,401)(RADK(J),J=I,I+4)
400 CONTINUE 401 FORMAT(5L20.14)
C- ITERATION FOR THE PROFILES IU=0 DO 500 ITz1,N0IT
DFLUX=O.- G0=G01 - CALL MTP (NSTEP )
C CALCULATION FOR THE CATALYST EFFECTIVENESS FACTOR,EFFCH4 CALL DIFF USE (NSTEP ) DO 2000 1=2,5
2000 DFLUX=DFLUX+(X(I,2)-X(I,11)/STEP/PEM(I,1) XO(1)=1./(DFLUX+1.) DO 2001 1=2,5 • DFLUXI=(X(I,2)-X(I,1))/STEP/PEM(I,1)
2001 X0(I)=OFLUXII/(DFLUX+1.) G0=G01/X0 (1 ) DO 501 IJ=1,NSTEP+1 DO 502 J=1,2
502 IF(X(J,IJ).LE_.0.)X(J+IJ),1.E-05 501 CONTINUE
N1=1 CALL TIIERK(N,TFP) CALL RATL (I,;STEP ) CALL HTP l r';STEP )
C - - - - TEPLr;ATORE EQUATION TA=1 . +PEF+*STF:P*r3ARG (1) /BARI< (1 ) TB=PLI(*STEF'+PARG (1) *TIr,I/RARK (1) /TR P=THE.TA (1 ) * TA-THETA (2) -TB T1(1)=TI1[TIA(1)- , (1)*P/TA DO 102 1=2,HSTEP BARK(I)=LARK(I-1) IF (THETA (I) *TR. GT.41 7.) GO TO j E=4471U. GO TO 2
1 E=20560. 2 CONTINuE
TC=1. +PEN B iRG (I) *sTEP/I ARK (1 ) • TD=2.+PEM*BAPG (I) *STEP/RARK (I) +PEI I*ST*STEI'*STEP/BARK (I ) TE=STEP*STEI'*PEI I*ST/BARK (I ) TF=STEP*STEP*PEH*DAI1/BARK (I ) P=1C*Ti(I-1)-TD*THETA(I)+TPETA(I+1)+TE+TF*IZ(1)
260-1
261 ()=-TCA+TF*R(I)*E/1.987/TR/THET[\(I)**2 T1(I)=THETA(I)-w(I)*P/0
102 CONTINUE P=11 (,JSTEP) -GAMA*STEP* (THETA (NSTEP+1) **4-1.) /BARK (NSTEP )
C HEAT TRANSFER AT TNE FRONTAL SURFACE BY BUOYANCY EFFECT COND=1.672E-04 COI'JD=COND*(1.-VOID)/0.07 DE('°=28.82/B2. 05/THETA (IJSTEP+1) /TR BETA=1.-/THETA (NSTEP+1) /TR DELTAT=(THCTA(NSTEp+1)-1.)*TR VIS=0.00023 GK=9.334E-05 PR=0.73 GRH=SIZE**3*DEN*DEN*981..*1 ETA/VIS/V1S*DELTAT C1=0.517 NUHX=C1*(GRIItPR)**n.25*THICK/SIZL*GK/CONU/(3ARK(NSTLP) P=THETA(NSTEP+1)-P+I\IUHX€(THETA(NSTEP+1)-1.)*STEP -PEH/BARK(NSIEP) 4;
£1ILLTA ( NSTEP+1) *STEP
()=1.+4. *GAMA*STEP*THETA ( NSTEP+1 )**3/BARK ( (`NSTEP) +NUI iX*STEP-0Et I/ FiARK f (PISTEP) *STEP T1INSTEP+1)=THETA(NSTEP+1)-W*P/(,)
C FUEL EOUATION CALL MTP(NSTEP) B(1)=-1.-STLP*PEM(111)*BARG(1) C(1)=1. D(1)=-STEP*PEM(1,1)*X0(1) NI=2 CALL RATE(NSTEP) DO 103 I=2, NSTEP A(I)=1.+STEP*PEMi(1,I)*BARG(I)/2. - E3 (1) =-2. +DA ~'i (1) *PEm (1. I) *STE('*STEP*R (I) /X (1, I ) C (I) =1 . -PEM (1 , I) *STEP*BARG (I) /2. D(I)=0.
103 CONTINUE C ASS TRANSFER AT THE FRONTAL SURFACE BY BUOYANCY EFFECT
DE(4R=28. b2/82. 05/TR VISK=VIS/DEN GRL=y81.*SILE**3*(r)ENR/nEN-1.)/VISK/VISK SC=0.65 NUI4'X=C1 * (GRU*SC) **0.25*THICK/SIZE A(J\STEP+1)=1. B (NS rEp+1) =-1 . -r1UMX*STEP+PEMI (1 ,NSTEP+1) *STLP C(NSTEP+1)=U. IJ(NSTEP+1)=1). CALL TRIDI(A.B.C•D,V.I'JSTEP) DO 2U1 I=1,+'.ISTEP+1
201 X1(11i)=V(I) C OXYGEN EOHi1TTON
U3( 1 )=-1.-STEP*PEN(2,1)*jARG(1) D(1)=-STEP*PE_If(2,1)*XU(2) NI=3 CALL RATE(NSTEP) DO 104 I=2,t STEP IF(THETA( I)*TR.GT.817.) GO TO 3 URL=0.75 GO Tu 4
3 ORD=1. 4 CONTINUE
A(I)=1.+PE!J(2,I)*STEP*BARG(I)/2. B(I)=-2.
e0)=B/I f[l4#(2)*P[M(2,7)*3T[P*6T[P*SRU/X(2"I)*R(I) C(I)=1°~PEM(2^I)*STEP*BARG(I)/2° D(I)=-DAF,(2)*P[P:(2~I)*STLP*STEP*(1°-011p)+R(I) 261-1 .
I04 CONTINUE AIHST[p+1)=1° 2(NSTEP+1)=-]°~AUOx*ST[P+PFM(21NST[P+1)*6[L!`
D(N8TEP+1)=-NUM%*0~21*STEP CALL TkIUI(4^B,C10,V.NSTEp) 00 202 I=1.NST[P+1
202 X1(2vI)=V(I) C - HITROG[N EQUATION
8(1)=-1°-PEm(5"1)*RxRG(1)*ST[p 0(1)=-ST[P*PEN(5,1)*X0(5) DO I07 I=2"h8T[P A(I)=1^+PEM(51I)*8TEP*B8RG(I)/?° C(I)=1.-P[M(5vI)*STEP*B8KG(I)/2^
107 D(I)=-UAM(5)*P[M(5^I)*STEP*STEp*K(I) A(hsTEP+l)=l° B(HSTEP+1)=-1°-UUMX*STEn+PEM(5"N8T[P+1)STEP O(NST[P+1)=-NUMX*0~79*STEp CALL TRIDI(4,B°C°D"VvNST[P) DO 205 l=1vWSTEP+1
205 X1(51I)=V(T) C~ CALCbLATIOQ OF CARB0H DIOXIDE E STEAM CWPUSITIUNS
DO 800 I=2"WUTEP+1 %X=1.~X1(1^I)~%1(2°I)~X1(50) X1(3.I)=XX/3°
800 x1(4,I)=X%*2°/3° DO 701 T=1~N6T[P+1 DO 702 Jc3.4 IF(%1(J11)~LT°0°)X2(J.T)=0°
702 CONTINUE 701 CONTINUE
[ CUmpfiRE WITH THE PR[VI0US ITERATl0N PROFILES DO 112 I=1"0ST[P+1 ' ` TDJF=THET8(I)-T1(I) IF(AR5(T0IF)°5T^CRIT*A8s(T1(I))} GO TO 1lb FDIF=X(l^I1~X1(l'I) IF.(488(FbIF),5T°CRYT *ARS<x1(1"T)))60To ll5 U0lF=X(2,I)-Xl(21I)
112 JF(A88(DDIF).GT°CRIT*ABS(X1(2.I))) G& TO 115 6O TO 116
115 DO 117 I=1,N3TEP+1 00 118 J=1°5
118 X(J^I)=xl(J.I) G(I)=8AH61I)
117 THETA(I)=T1(1) 500 CONTINUE 116 DD 119 I=1,H5TEP+1,9+IU
IF(I~EQ~10)lU=1 DIS(l)=FLUAT(I~1)*STEP J=T1(I)*TR G6=G(l)*6U
119 NRITE(6"120)DIS(I)°T^(Xl(J,I),J=115).66 120 FOHMxT(F5^511X"7E18~3)
WRITE(6,505)IT 503 FORMAT(1%°@mUMBFR OF ITFR8TI0HS
DO 121 I=1^NST[P+1 121 WRIT[(8"122) (Xl(J,I),J=1^2)"Tl(l) 122 FOR#AT(2E10°3^F10°6)
262
C CALCULATION OF THE cA )TATIf):r CFF1CILNCY DP=3.E—U4 SIMA=1.355E-12 Et 1 S=[ .47 r•JPL=IFIX(T(r1CK*(1.—VOID)/DP) LPD=IFIX(STEP*(].—VU1D)/OP) IN=i STEP+1 I=1 TRH(:)=0. DO 901 J=1,0PL IGhron=J-1 ABLTA=(1.—VoILJ)*VOIU4*ICit / IF(J.GT.LPow-1) GO TO 902 Go To 903
902 IN=IiJ-1 1=1+1
903 TA\1E=tTl(IN)+T1(IN-1))/2.*TR ARVD (J) =ARETA*TAVE**4'i<STi'iA Efj.IS TRAD=TRAD+Ar<AD (J ) IF(TRJ\c).GT.ARAr(J)/.001.)GU TG 9u4
901 CONTINUE 904 EFF^TRAD/ (Gol—G0*X1. (1, r-isTEP+1)) /i(E=AT
'JF1TE (6,905)EFF,TRAD 905. FO('MAT (1X, ai<ADI11TIOi-J EFF ICTE i'CY---- Ft. • 51 ( ~: T OT);L Ei)`,u A T TOL
£ FLUX,Ci L/(SO.Cp.)/.SEC----6s,F8.q) ) t RITE(6,906)
906 FOkMiT(1X,c)TE(E RADTATInn Er ISSTON DISTKP'>UITfN.)) DO 9U7 I=1,J WRITE(6,908)I,AnI►L)(I)
907 CO('JTINUE 908 F0WtM T(1X,I3,2X,F9.5)
STOF' END
SUbROOTINE TE(ERK (NSTEP ) DIME!NNNSION,: RADK (100 ) DIh•EHS10N Bi\RK(100),THETA(1 00 )
C0r° N,r)IJ/CCI•JD/BARK , kADK COr`:r=1(1N/TE1'IPA/ T HETi-\. Coi°,14ON/H} ATER/5TZE,GU,NrID,THIgi: CoRM0N/PEJ TUP/PER CK=1.672E-04 CK=CK*(1.—Vū10)/U.07 DO 1 I=1 , NST Er' BAkK (I)=RADK (I) * (THETA (T) *300. )
1 COI:TINUE RETURN END
SUBROUTINE HTP(!;STEP) C01 '1UfJ/F4TRAN/PEN,DAH.GAptA.ST,i)EAT,1 U COt'iMUPJ/HEATEF?/SIZE, G0, VOID, TH ICK CP=7. COI'JD=1.672E-04 COND=CONV*(1.-VOID)/0.07 PEH=THICK*CP*GO/COND DAti=THICK*HEAT*R.0/300./GO/CP' EM 1s=0.45 [1P=3. E-04 PN=THICK/FLOAT(NSTEP)*(1•-VOID)/OP GO;A=1.355E-12*EMIC*300 • **3*THICK/CU1ii)
C CALCULATION OF FREE HEAT CONVLCTION H=20.32 0EN=9.417E-04 BEI A=2 •6b1E-03 v1S=0.00023 GK=9.334E-05 PR=0.73
C=0.517 GR=H**3*DEN*DEN*9B1.*BETA/VIS/VIS*100 AF=(H-2.54)*2.54*4.*2. AW=SIZE*THICK*q.
.FHTR:=C*GK*(6R*PE)**0.25/1J*AF/Aw ST=4.*FHTR*THICK{/SIZE/GO/CP RETURN END
THE HEATE:ī i! l
262-1
SUBROUTINE TRIDI lA,f3;c,[?,V,hdSTEP} THIS SUBROUTINE Ic TO SOLVE A SET OF LINEAR LOUATIO, WITH A TRIDIAGONAL STR[1CTuriE
DI tiEt'1SIOP A(50(1)0B(500),C(500),U(500),V(51)0)4HL1A(bti0),i;;.', rt(t;t:) BETA(1)=B(1) GAf lit;(1)=O(1)/F FTA(1) 00 1 I=2,NSTEP+1 BETA(I)=B(I)-A(T)*C(1-1)/f ETA(.I-1)
1 GAVMF{ (I) =D (I) /Fj[TA (1) -A ( I) *GAA;f"iA (I --1) /BL 1 /'. (I ) V ((\KS1 EP+1) =GAiJ:i4A (NSTEP+1 )
_.I=NSTEP J=NSTEP+1
2 V (1) =GAMk:A (I) -C (I) *V (J) ,BETA ( 1 I=1-1 - J=J-J. IF(I.EU.0) Gn Tn 3 GO TO 2
3 RE1 URN END
SUBROUT I NE TP (NSTFP ) REAL KTE(6),KE(C)1,KTE12(6),•1(6) DIr'.EI'ISIOH PEP (5,100), U)Itf'`(5),STUI(5),EK(6).0NIE"6A(c_o fsa. *TNETA(100).S12(6),TT(100) COi i1LiON/TEMPA/T1 IETA COf•' RON/MTRAH/PE°1:, DI , STOI COr':f1ON/HEATER/SI ZE.6O, VOID, TF-SICK DDLN=0.093 RO=BUEN*3.438E+05 00 1 1=1,5
1 DAP'.(I)=STOI (I) *THIr K*RO/GO ASSUhIIJG ALL THE SPECIES U frFt)SE IN AItt DO 100 1=1 , ItSTEP+1
100 THLT/a (I) =THLTA (I) *300. m( 1 )=16. V(2)=32. 14(3)=44. m(41=18. M(5)=28. m(6)=28.84 EK(1)=1486
EK(2)=106.7 EK(3)=195.2 EK(4)=2QC.1 EK(5)=71.4 EK(6)=78.6 DO 2 1=1.6
2 KE(I)=1./EK(I) SImA(1)=3.758 SIFA(2)=3.467' SIMA(3)=3.941 SIMA(4)=2.641 SIPA(5)=3.79R -S1 1 A(6)=3.711 DO. 3 I_1.NSTEP+1 DO 4 J=1,6
4 KTE(J)_KE(J)*T)iETII(I) DO 5 J=1,5 KTE12(J)=SQc(-f (KTE(6)*KTE(J) ) S12(J),(SIt»IA(J)+SIMA(6) )/2.. IF(KTE12(J).GT.2.) GOT0 6 • IF(KTE12(J).GE.1.40) GOTO 7 A=1.439 F3=-0.4996 GO TO 201)
7 A=1.40156 • 8=-0.38447 GO TO 200
6 IE(KTE12(J).GT.4.2) GOTO 8 A=1.3011 . 8=-0.2820.7 GO TO 200
8 4=1.1117 E3=-0.17202
200 OMEG/(J)=A*KTE12(J1**Fi AA=0.001658*THETA(T)**1.5 E3f3=SoRTWI(J)+m(6))/M(J)/M(6) ) CC=S12(J)**2*OMEGA(J) C=1 . /82. 05/T!-IETA (I ) D12=AA*BF /CC*C
5 PEM (J, I)=THICK*GO/n12/VOID 3 CONT 11JUE
DO 500 I=1,NSTEP+1 500 THETA(I)=THETA(I)/300.
RE1 Ur N • - END
Z63
! ),
SUBROUTINE DATE (FISTEP) 263-1 DIENSIOF EFFCH4 (100 ) DIl"EFJSION P(100),X(5,101I),X1( S,IFJO).THETA(100).1l 1 t! l) C0kMUN/REACT/R, X , X1 , T1, g•,11 COMON/TEIfPA/T((ETA CO F-'h ON/EFFECT/EFFCH4 00 100 I=1,tSTEP+1 DO 200 J=1,2 IF(X(J,I).LF.0.)X(J,I)=1.E-05
200 TF(X1(J.I).LE.0.)X1(J.T)=1.E-0=; 100 CONTINUE
R0=3.438E+05 IF(NI.EQ.1) GOTO 1 IF (IJI . E0.3) GOTO 2 IF(1•J1.E0.4) GOTO 6 DO 10 I=1 , IJSTEP+1 T=T1(I)*300. IF(T.GT.817.) GOTO 3 R (1)=3.438E+05/EXP (4471n. /1 .987/T) *X (1 . T) *X (2, J ) **O.7`.)- ;1 2.2 7c, GO TO 10
3 R(I)=1.140E-02/EXP(20560./l•yli7/1)*X1(1,1)*X(2,1)*5244u.741-. 10 cO 1TINuE
GO TO 20 2 UO 11 I=1,NSTEP+1
T=11(I)*300. IF(T.GT.817.) GOTO 4 R(1)=3.438E+05/EXP(44710./1.`87/T)*X.1(1..1)*Y.(2,1)**0.75 316%. 7 GO TO 11
4 R (1 )=1.140E-02/FXPI 20560. /1 , 987/T) *X1 (1 , 1) *X (2 1 1) *524t30 . 746 11 CONTINUE -
GO TO 20 1 00 12 I=1,NSTEP+1
T=T,IETA(I)*300. IF(T.GT.817.) Go Tn 5 R(I)=3.438E+05/EXP(44710./1.967/1)*X(1,1)*X(-2,.t)**0.7±~* 41:„ GO TO 12
5 R(I)=1.140L-C12/EXp(20560./1.937/T)*X1(J.,I)*X(?,1)*52L“io.7rr_ 12 COOTINUE
GO TO 20 6 00 13 I=1 , NSTEO+1
T=T1(1)*300, IF (T.GT.817.) Go TO 7 R(1)=3.438E05/EXP(44710./1.987/1')*X1 (10)*X1 (2.1)*T0.7` t-31h, .
GO TO 13 7 R(1)=1.140E-02/FXP(20560./1.987/f)*X1(1,1)*X(2, I)*524hl).7-Ib 13 CONTINUE 20 DO 30 T=1,NSTEP+1 30 R(1)=R(I)/RO*EFFCH4(I)
RETURN
END-
I)
PROGRAM 02P1 (II:;PUT, OUTPHT, n/ A1, COi.'iP, T APE-=INPUT, T APE t~=';N1r jT t
*TAPE7=DATA1, TAPE8=C04'P ) REAL 1UUHX UMENSION )((2,100),THET1 (100),P,ARF (1L ),MJ'( 4),:: (4,q),:(t11;0),
*DIS(100)c(I (2,101)),T(5,100),T1(IU0), I l (-:H;1)e(C(4,4-),X:;(q), *01(4,4),NI(N,4) DI1 EIJSION RADK (100 ) DIMENSION F(6,100) DIhMENSION AH/\D(300) DIDE1')SION D(100,4) DIMENSION V(5,20)
C TwO [_•IMEIJSIONAL M0DEL TO CALCULATE I L TEMPERATURE
C BY CO MBINED METHODS OF OF-TI-IUGOHAL. Crii_L.°LCATiON ANN (=TNIIL C ūIFFERENCE
CONMOI1/HTRAH/PEH,DAN,GA` AIST,HE)iT,RU COmMUN/HEATER/SIZE,Gu,VOID, THICK COMMON/COND/RARK, RADK COMI4UN/REACT/R,x,x7,11, .i1
COC'+ i ON/TE MPA/THETA COM 40N/MATR I C /AA . BR , XO COl MON/PT /CPT . NSTEP=99 STEP=1./FLOAT(NSTEP)
C READ IN THE CONCENTRATION AND THE TEMPERATURE PNUF i LES EHICH
C WERE CALCULATED PRE=VIOUSLY FROM THE ONE DIMENSIONAL MODEL
C (PROGRAM DF11) £ THE TEMPERATURE PROFILE wILL BE USED AS THE
C INITIAL GUESS FOR THE ITERATION OF THE TEMPERATURE DISTRIBUT-
ION IN THE PRESENT AODEL DO 10 I=1,NSTEP+1 READ(8,1)(X(U,I),J=1,2),T1(
1 FORMAT(2E10.3,F10.6) X1(1,I)=X(11I)
10 X1(21I)=X(21I) SET IN THE rMATR1CS FOR ORTHOGONAL COLLUL/ 1ION
WRITE(6,600) 600 FORMAT (1X, C1NUj :I;ER OF COLLOCATION POINTS, 11 ? )
READ (5, 6(A) NPT 601 FORMAT(I1)
CALL ORTHO C
READ IN THE INTERAL RADIATION PLARM TERS
DO 20 I=1,50,5 20 READ(7,21) (HADK(J),J=I,T+4)
DO 50) 1=1,30 30 RADK (69+I) =HA(JK (I+2U )
DO 4() I=21,69 4) RADK (I) =h ANR (2:) ) 21 FORMAT (5E20. 14) .
C REACTION PARAMETERS TR=3U0. HEAT=191759. BDEN=0.093 R0=UIEN*3.438E+05
C HEATER SPECIFICATION AND INPUT DATA
V0ID=0.93 THICK=1.04' SIZE=6.*2.54 WRITE(6957)
57 FORMAT(1X,WFUEL INPUT FLOwRA7E.mULE/SCC,r12.10@)
READ(5,56)G01 58 FORMAT(F12.10)
264-1
G01_G01/SIZE/SIZE 4RITE(6,50)
50 FORMAT(1X,,DGAS MOLAR FLUX,E10.3,MOLE/(CM)2/SECT) READ(5,51)G0
51 FOkMAT(E10.3) C INITIAL GUESS OF THE RADIAL PROFILES
DO 800 IP=2,NPT+2 DO 801 IJ=1,F'JSTEP+1
801 T(IP,IJ)=T1(IJ) 600 CONTINUE
WRITE(6156) 56 FORMAT(1X,@THE ITERATION FACTOR,w,F7',3n1)
READ(5,52)W 52 FORMAT(F7.3)
WRITE(6153) 53 FORMAT (1X, DTHE CONVERGENCE CRITERIA,F7.3U )
READ(5,52)CRIT WRITE(6,54)
54 FORmAT (1X, ā1NUMBER OF ITERATION, I30 ) REAO(5,55)NOIT
55 FORMAT(I3) WRITE(61500)
500 FOF<MNT(1X,ā1LATERNAL THERMAL CONDUCTIVITY,CAL/CM-SEC—C,F12.9(11) REAO(5,400)ACOId
400 FORMAT(F12.9) CP=7.
.AAAA=ACON*THICK/CP/GO/SIZE/SIZE*4. - C ITERATION FOR THE PROFILES
CALL HTP(NSTEP) DO 100 IT=1,NOIT DO 98 I=1,NSTEP+1 00 99 IP=1,NPT+1 IO=IP+1
99 TI(I0,I)=T(IO,I) 98 CONTINUE
DO 110 I1'=1,NPT IO=IP+1 00 111 I=1, NSTEP+1
111 THETA(I)=T(IO,I) N I =1 CALL THERK (NSTEP ) CALL RATE(NSTEP) TA=1.+PEH*STEP/BARK(1) TB=PEH*STEP/BARK(1) P=THETA(1)*TA—THETA(2)—TB T1(1)=THETA(1)—W*P/TA DO 112 I=2,1'F5TEP BARK(I)=BARK(I-1) IF(THETA(I)*TR.GT.017.)G0 TO 113 E=44710. GO TO 114
113 E=20560. 114 CONTINUE
TC=1.+PEH*STEP/BARK(I) TD=2.+PEH*STEP/BARK(I) TE=STEP*STEP*PEH*DAH/BARK(I) ALFA=AAAA*PEH*STEP*STEP/BARK(I) TF=O. DO 115 IB=1,NPT+1 I0=1E3+1
'265
115 TF=ALFA*BF3(IP,Ip)*T(IO,I)+TF P=TC*T1(I-1)-TD*THETA(I)+THETA(I+1)+TF4TE*it(1) Q=-TO+ALFA*BL3 (IP. IP)+TE*R (I) *E/1.987/TR/THETA (I) **2 T1(I)=THETA(I)-W*P/0
112 CONTINUE C HEAT TRANFER AT THE .FRONTAL SURFACE BY RUOYANCY EFFECT
COND=1.672E-04 DEN=28.82/82.05/THETA(NSTEP+1)/TR BETA=1./THETA(NSTEP+1)/TR DELTAT=(THETA(NSTEP+1)-1.)*TES VIS=0.00023 GK=9.334E_05 PIA=0.73 C=U.517 GRH=SIZE**3*DEI.J*UEN*981 .*BETA/VIS/V1S*DEL I AT NUHX=C* (GRH*PR) **0.25*THICK/SIZE*(,K/COPD/B RK (jISTEP ) P=THETIt (NSTEP+1) -T1 (NSTE P) +GNMA*STEP (THLTA (i 7STLP+1) 4 --1 .) /ti)3i,;,s l i J
£STEP)+fJUHX* (THETA (NSTEP+1) -1. 1 *Sl- EN-PEH/f /:RK i P.tsTEP) *Ti !E J (":E i Lv+I ) £*STEP 0=1 .+4. *GAM *STEP*Tf-1E_TA (NSTEP+1) **6/[3)iRK (I•;STLP) +I UHX*S"! I;I'-PE=l.IRK
£ (NSTEP) *STEP T1(NSTEP+1)=THEETA(NSTEP+1)-W*P/O 00 116 I=1 . HSTEP+1 I0=1P+1 DELTAT=100.
116 T(IO,I)=T1(I) 110 CONTINUE •
DO 117 I=11NSTCP+1 C CALCULATION OF THE HEAT TRANSFER PAPAkLTE_PS AT THE HLATE_F EUI,L C (FREE CoNVECT I ON )
H=8.*2.54 BETA=1 . /373. OEN=28.82/82.05/373. VIS=0.00023 GK=0.0226*0.00413 GR=H**3*(_ PR=0.73. C=0.517 FEITK=C*GI: AW=SIZE*T AF=(H-2.5 PP=0. 81=+FHTR*AF/AW*SI Z[/2. /ACOri DO 118 J=1 , I'iPT IO=J+1
11L PP=PP+AA(NPT+1,J)*T(IO,I) P=NI-PP O=AA(NPT+1,I PT+1)+Bl.
117 T (NPT+2, I) =F'/O - DO 200 IFT=2,NPT+2 DO 119 I=1 , IJSTEP+1 ABT=ABs(T(IPT,I)-TI(IPT,l) )
119 IF(ABT.GT.CRIT*T(IPT,I))GO TO 100 200 CONTINUL
GO TO 120 100 CONTINUE 120 CONTINUE
NIP=NPT+1 DO 121 IG=11NPT+1 DO 122 IP=1.NPT+1
EN*DEH*981•*BETA*DEL.Ti1T/VIS/VIS
*(Gii*PR)**0.25/H HICK*' . 4)*2.54*4.*2.
0Q(I0.IP)=X0(I0)**( 2*IP-2). _121 CONTINUE - 265-1 -
"CALL 14INV(QI,QO,O11NIP)
. DO 123 I=1,I,iSTEP+1 T(1,I)=0. 00 124. IJ=1,NPT+1
124 T(1,I)=T(111)+0I(1,Id)*T(IJ+11I) .125 CONTINUE
C EVALUATION OF THE RESIDUES AT THE CflLLUCATIuf•; PUF;iP;
DO 1000 IK=1,NPT DO 1001 J=1,fJSTEP+1
1001 THLT,t(J)=T(IK+1,J) CALL THERK(NSTEP) CALL FATL (NSTEP ) TA=1.+PEH*STEP/BARK(1) TB=PEH*STEP/RARK (1 ) F(1K,1)=THETA(1)*TA-THETA(2)-Th IP=IK+1
.
DO 1002 JK=2,NSTEP BARK (dK) =BARK (JK-1 ) TC=1.+PEH*STEP/RARK(JK) TD=2.+PEI-I*STEP/P3ARK (JK ) TE=STEP*STEP*PEH*OAH/(3AftK(JK)
.ALF I AAAA*PEI I*STEP STEP/kARK (J{< ) TF=0. 00 1003 IE3=1,NPT+1 10=413+1
1003 TF=ALFA*EB(IK,IB)*T(1O,JK)+TF=
1002 F(1K,JK)=TC:*T(IP,UK-1)-TO*T(1P,JK)+T(TP,JK+1.)+TF-+-1 E.*( t (,JK )
F(IK,NSTLP+1)=T(IP,PJSTEP+1)-T(IPINSTEP)+LIA0A*STE_P*(i t:l.l'tt iJ4- ) .
£4-1.)/BAP.K(NSTFP) 1000 CONTINUE
IU=O WRITE(6,700)(XO(J),J=1,PJPT)
700 FOFCMAT (1X, ā)TI(E VALUE OF THE COLLOCATION POINTS c7,l i
00 125 I=1, NSTEP+1, 9+1U IF(I.EQ.1U)IU=1 DIS(I)=FLOAT(I-1)/FLOAT(LJSTEP) DO 300 J=1,IIPT+2
300 V(J,I)=T(J,1)*TR 125 WRITE(6v127)f)IS(I),(V(J,I),J=1,IJPT+2).Gi) 127 FORNIAT (F5.3, 1X, 5E10. 5, / (6X,'+E10. 3) )
WRITE(61128)IT 128 FORMAT (1 X, @HUPf(3ER OF ITERATIONS
WRITE(6,701) 701 FORMJ T (1X, @ 1HE VALUE OF THE RESIDUES AT DIE COLLYCA I ION PO i t IOJS i„
f)
IZ-O DO 702 I =1 , HSTEP+1 , 9+I7_ IF(1.EO.10)IZ=1
702 WRITE(6,703) (F(J,I),J=7 ,iJ('T) 703 FORMAT (8E 10 .3 )
• STOP END
266 SUEROUTINE ORTHO
C THIS SU5ROUTIHE IS TO CALCULATE THE l;t+ I f ICS FUii T;UI i LCHN I i_
C (OF ORTHOGONAL COLLOCATION (;ITH 1'IF UfiOLF UF IIIL ORTHoG L
C PULYI OH Ij;L UP TO 6TH AHD WElG ITI 1G fALT('k .LO, 1-X.r:*2 DIREivSIO A(4,4),G(4,4),0(4,q),01(q,q),C(4,Hj),D(41L;), Xi)('i),` 14,:, )
COhuIU;ON/MATRiC/i\,I ,XU _- - COP'I ON/P1 /h1PT 1F(NPT.EC;..6)GO TO 1 IF(NPT.EO.5)GO TO 2 IF(NPT.EC.4)G0 TO 3 IE-fFilPT.E(;.3)G0 TO 4 IF(NPT.EL.2)GO TO 5 XO(1)=0.4472135955 GO TO 6
5 X0(1)=0.2852315165 XO(2)=0.7650553239
GO TO 6 4 X0(1)=0.2092992179
X0(2)=0.5917001814 XO(6)=0.8717401485 GO TO 6
3 XO(1)=0.1652789577 XO(2)=0.477924949E X0(3)=0.7387738651 X0(4)=0.9195339082 GO TO 6
2 XO(1)=0.1365529329 X0(2)=0.3995309410 X0(3)=0.6328761530 X0(4)=0.0192793216 X0(5)=0.9448992722 GO TO 6
1 X0(1) =0.1163318h89
X0(2)=0.3427240133 XO(3)=0.5506394029 XO(4)=0.728l665991
X0(5)=0.8678010538- X0(6)=0.9599350453 N=NPT+1
XO(N)=1. 00 100 J =1 , H DO 101 I=1,r, Q(J,I)=X0(J)**(2*I-2)
C(J,1)=FLOAT(2*I-2)*A0(J)*=(2*E-5)
101 0(J,I)=FLOAT(2*I-2)*FLOAT(2*I-6)*XO(J)**(2*I-4 )
100 CONTINUE CALL i"IINV(S, ,O1,U
DO 200 I=1,11 DO 201 J=1,:,.i A(1,J)=0. B(I,J)=0. DO 202 K=1 , i A(1,J)=A(I,J)+C(I,K)*S(K,J)
202 B(1,J)=B(I,J)+D(I,K)*S(K,J) 201 CONTINUE 201 CONTINUE
WRITE(5i10l' f'T 10 FORM T (1X,;lftul'` ER OF COLLOCAT I ;I i'_JIi- f ': , 12 )
RET U1- N END
PRGG~M ~TFFU~E<IUpUT^0UTpUTvTkPL5~IHnUTvT,^n[6~(vjT~o ~} 266-1 i<
C
EVALUATION OF THE CATALYST EFFECTIVENESS FALT0|`
THE KINETIC INEO8ftrI0D3 UDTAlUE0 IN LU1. T[p()Lk,T /
AS8UF[0 AS THE INTkTN3IC KINETIC nA7m "/'.` THL
LIMITATION IS CHECKED TU[URE[TlCALLY THIS PRU6RWn Is i,IU0JLIFD 5O AS To SU/VL As A 3Uu/(Hi THE [OMt:iUSTDR MODEL .v!HEN CALCULATION u| lN[ LOCAL. r[,LL!]YL NESS FACTOR IS K[QVIKED IHIS PROGRIO IS MOOIFlrD SO AS TO LINK .1T|/ THE L,r^ox|uH m0D[L WHEN CALCUL8TJUN OF THE LOCAL [F ~[CTIVEWE5t, f- o[/u'' is
REQUIRED DI ENSI0^ [H4(500)^02(5nU)"AC||//(5
£°U(500),A82(500)^Ro2(50O),[O2( ~0u ~
REACTION CONDITIONS
NS7[P=4O [H4(1)=°2 O2(1)=°2 DO 300 ITEMP=1"10 T=673°+FL0AT(lT[Mp)*50,
TEPP=T-273° WRITE(6°301)T[MP
301 FOHM8T(5X.iliT[MP[QATUk[°C 03"F8.3*//) C
PHYSICAL DATA
R=°0Ul VOIO="45
PRAU=2°5E-07 C=1°/82^05/T CH4(1)=[H4(1)*C
02(1)=02(1)*C DKCH4=9700°*pRAD*SnHT(T/16.) DKO2=UKCH4*SORT(0°5) RK=387100°*EXP(~44710°/1^987/l)*3°*100°*^1,74 EDCU4=DKCH44-VOIn [D02=UKO2*VOID HK=KN/C**1"74 THI1=|{*R*RK/EDOH4 THI2=R*R*nK*2°/[D02 A0=°7* H=~1°/FLUXT(NSTEP)
~ INITIAL ESTIMATION OF OXYGEN PROFILE
DO 100 N=2^|/8T[P+1 02(N)=-02(1)*FL08T(QSTFp+1-H)*/{
100 COGTlN.E
[ I@TTTA[EV0LUTTOH OF M[T|/A!|L PROFILE AcH4(1)=o° 80H4(1)=l° CCH4(1)=0°
DO 101 N=2^i|ST[P ACH4<Q>=1°-.5/FLOAT(N-I) BCH4(H)=-2°-T}iI1*i|*H*02(H)
101 C[h4(N)=1°+°5/FLO4T(H-1) ACU4(NST[p+1)=1~
BCh4(NsT[P+1)=-1. CCH4(NST[P+1)=0° O[H4(1)=Of4(1)
DO 1»2 N=2,|/STLP+1 202. DCH4(0)=0.
CALL TRI[IO^[H4,13[H41CCn4"nCH4^0/4^|iSTEP/ C
INITIAL [VALUATION nF nXYG[W PH0FTLE
AO2(1)=U°
~ C C C ~ C C C C
/`)^eCH4('ino)'CCh4(7m),//Ll-'g itl'`" } )1 DOX2(50o) .Y[/!4 ( 5Li, ) , `/ 02<'-:0u>
(302(1)=1. CO2(1)-0. DOX2(1)=02(1 ). - DO 104 N=2,l'STEP A02(N)=1.-.5/FLOAT(N-1) 802(N)=-2. CO2 (i'J) =1 .+. w/FLoAT (I'I-1 ) IF(02(H).LE.0. )02 (N)=0.0001
104 00X2(N)=THI2*H*H*CH4(N)*O2(Ii)**iii A02 (I JSTEF'+1) =1. B02 (NSTEP+1) =-1 . CO2 (IISTEP+1) =0. DOX2(NSTEP+1)=0. CALL TRIDI(A02,(32,CO2100X2i02.lJSTEP)
C
ITERACTION FOR THE PROFILES 00 105 ITER=1,20
C i"IETHANE EO(IATInH C MATRIX DATA UPDATE
DO 106 N=2,iJSTEP BCli4 (N) =-2 . IF(02(N).LE.O.)02(N)=0.n001
106 OCH4(N)=THI1*H*H=CH4(N)*02(N)**A11 CALL TRIDI(ACI141)iC144.CCF44,0CH4,VC!(4INSTEP)
C OXYGEN EQUATION C DATA UPDATE
DO 107 N=2,NSTEP IF(02(N).LE.O.)02(N)=0.0001
1.07 DOX2 (N) =THI2*11*H*VCH4 (N) *02 (N) **AA CALL TRIDI(AO2.[102,CO2.(10X2,V02,NSTEP)
111 DO 112 N=1,I'ISTEP+1 CH4 (IJ)=VCI14(N) -
112 02(N)=V02(FJ) 105 CONTINuE
G02=THI2*C114 ( 1)*02(1)**AA-(02(2)-02(1))/H/ii • GCH4=THI1 *CH4 (1) *02 (1) *r-AA- (CH4 (2) -CH4 (1)) /I1/H GO2=G02/1: GCH4=GCH4 /R Z=2./R/Iln/CH4(1)/02(1)**AA EFFCH4=Z*EDCH4*GCH4 EFF02=Z*ED02*G02/2. WRITE(6.201) EFFCH4,EFF02
109 00 110 N=1 . NSTEP+1 - RATIU=02(N)/CH4(H) •DIS,-FLO/1T (riSTEP+1-N) *H CH4 (NJ) =Ch4 (N) /C 02(N)=02(N)/C
110 rlRITE(6,200)0IS,CH4(N),02(N).KAT1O 200 F0khAT(4F15.4) •300 CONTINUE 201 FORMIT(//,5X.alEFFCii4=6),F12.4,4X,i1EFFU2=uu,F12.4,//)
STOP END
267
t 267-1 ~,
PROGRAM RADCON(INPUT,OUTPUT,VOIDb,TAPE5=INi'lJT,TI PL.i;=OHT ;>. i , 1 .. F 7 *=VOID5)
C THIS PROGRAM IS TO CALCULATE THL C RADIATION CONDUCTIVITIES
DI (' Ei''iSIOIJ A(50,50)03(51),RADK(5u),C(5(J,5u) DIN ErJSION D(50.50)- SI',A=1.355E-12 THICK=1.04 AA=0.45 N=50 VOID=0.93 OP=3.E-04 E=THICK/FLOAT(N) PNE*(1 . -VOIC)) /DP T=VOID**}rfi AA=(1.-T)*AA R=1.-AA-T A(1,1)=1. DO 101 I=2,N
101 A(1,I)=-T**(I-2)/(1.-R**2*T*4 (2*(I-2)) ) DO 11)2 M=210-1 AW1M)=1. DO 103 I=1, i"-1
103 A(N,I)=T**(ir-I)/(1.-R**2*T**(2* ty1i-I-1) )) DO 104 I=M+1,N
104 A(P,I)=-T**(I-f ' 1)/(1.-R**2*1**(2*(I-n-1))) 102 CONTINUE
A(NtN)=1. DO 105 i=1.0-1
105 A(N.I)=T**( i•1-I)/(1.-iZ**2*T**(2=(N-I-1))) CALL MINV(D,A,C,N.) DO 106 i =1,Ai B(M)=0. DO 107 J=1,i',i
107 B(R)=B(P)+D(is,J) 106 CONTINUE
B(N+1)=0. 00 108 ( =1,i'J
100 RADK (M) =4 . *AA*SIMA*E/ (P (fi) -f3 (i +1.) ) D0 110 M=1,i'J,5 WRITE(6,109) (RADK(J),J=4)
110 WR1TL(7,109) (RADK(J),J=M,V+4) 109 FOkiviAT(5F20.14)
STOP END
268
PROGRAM REAFIT(II'!PUT,OUTPUT,DATAITAPE5=INPUT,TAPE6=(t!.1 Ti'i ! , I Ai'L.-L= *DATA)
C EXPERIMENTAL DATA FITTING
DIMENSION AK(10),AQ1100),B0(1U(,),Cu(1(10),iJu(1hst),F0(1 ~ :
F(100),CONVA(100),FAO(1t?0),E(in),w(130) DII EWSION EA(100) DII'ENSION ESTCOH(100) DImENSIOW AAK (10 ) EXTERNAL CALCFX CO MON/IIB DA ī A/A0,80,C0,00,FA01cONvI,, IE.XP COMMON/OUTDA/ESTCON COI° moN/PARAM/AAI< ,
C READ IN EXPERIr1ANTAL DATA
NEXP-32 DO 100 I=1,IIEXP READ(8,1)A0(I),30(I),CU(1),1)0(I),Fli(1),A(J),F(I) IF(C0(I).ED.0.)CO(I)=.1F-20 .IF(DU(I).EU.0.) D0(I)=.1E-20
1 FORMAT(7F10.8) FO(I)=F0(I)/60./1000.
F(I)=F(I)/60./1000, FAQ(I)=FO(I)*A0(I)• FA(I)=F(I)*A(I) CONVA(I)=(FAO(I)—FA.(I))/FAO(I) :IF(CONVA(I).LT.0.)CONVA(I)=0.
100 CONTINUE C INITIAL ESTIMATIONS FOR THE RATE CONSTw.: TS----------
WRITE(6,1000) • 1000 FORMAT(1X,FIPLEASE STATE NO. OF PARAMETERSnr)
READ(512000)NPARA 2000 FORMAT(I2)
WRITE(6,3003) 3000 FORN1AT(1X,61PLEASE FILL IN INITIAL ESTIM/1TL5 OF THE_ PiaRtiHL i i_;t:, T
DO 400 I=1,IPARA 400 READ(5,4000)AK(I) 4000 FORMAT(F19.6)
C SETTING OF CRITERIA WRITE(6,5000)
5000. FORMAT t 1X, niPLEASE SET IN ESCALE hIJD E (I) J • READ(5,4000)ESCALE
READ(5,4000)EK - DO 200 I=1,iiPARA E(I)=EK
200 CONTINUE IPRINT=0 ICON=1 WRITE.(6,600t; )
6000 FORMAT( lx,.:!PLEASE SET IN MAXFUl4 AND MAXI1cv0 READ(5,7000)r AXFUN READ(5,7000)mAXFIT
7000 FORmAT (I3 ) N3I'J=HPARA* (IJPARA+3 )
C OPTIP IZATIOr.I OF THE SUrft OF THE St iAFE- LPPogS OF THE WRITE(614)
4 FORM/\T(//,16X,c7STA1.I )ARD DEUII'TIONct, // ) C OVERALL CONVERSION
CALL VA04A( AK.E,NPAKA,SU?'iS(>> ,EScALE,IF'!;1 1J,lfiiii,MAXF 1 I ,ChL; t ',,,'
*,MAXFUN) WRITE(6,3)
3 FORMAT(//,16X,ōESTii4ATE\) VALUE0,4X,iilo SERVEU VALIJL(.,//)
DO 300 I=1,NdEXP 300 WRITE(6,2)ESTCON(I),CONVA(I) 2 FORMAT(10X,F15.6,5X ,F15.6)
WRITE(615)(AAK(I),I=1,NPAI: A) 5 FORMAT(/,10X,@VALUE OF THE PARAMETERS ,Nl 12.b)
• STOP •
END
SUBROUTINE CALCFX(NP(\RA,l\K,SUMSQ) 268-1 DIMENSION AK(10),A0(100),B0(100),C0(10O),UU(10U),F0(100),COVn(i'!t
*) DIMENSION YO(1),Y(1),YG(1),YH(1),AAK(10) DIMENSION ESTCO:J (100 ) COMMON/OUTDA/ESTCON COP MON/I1JDATA/A7,B(I,CU,fU,r0,CL'Ii\li,Il(=XP COMMUN/INEXP/I , ;CAT CORMON/PA!tit /AAK EXTERNAL YGRD DO 200 I=1,NPARA
200 AAK(I)=AK(I) WCAT=U.2h42 H=1 NGRID=10 H=1`./FLOAT(! GRID) SUkS0=O. RUNGE-KUTTA INTEGRATION FOR THE CONVEkSIO:I
00.100 I=1. HEXP YD(1)=0. X=0. UO 101 I N TEG=1, f•JGR I O
101 CALL RKUTT(X,H,fiTOIY,YG,Y}{,1GR0)
SUmSQ=SUmSO+ (Y (1) -CONVA (I)) **2 ESTCON(I)=Y(1)
100 CONTINUE AN=FLOAt(NEXP)-1. DEV1A=SQRT(SUMS(/AN) WRITE(6,2)DEVIA •
2 FORMAT(10X,F15.6). RETURN END SUBROUTINE YGRD(X,N,Y,YG,MOOEL) REAL Y(N),YG(N) DIMENSIO1NJ AK. (10),A0(100),E30(1()U),CU(1UU),UU(10 ),Fi,ti( if) 0),C:,;:ViL *0) COf' MON/INDATA/A0IBOICOI00IFAOICONVA9WEXP COf MON/INEXP/I,L CAT COMMON/PART /AK EXTERNAL MODEL IF(Y(1).GT.1.)Y(1)=1. IF(Y(1).LT.0.)Y(1)=0. ALFA=Y(1)*AU(I) CO=A0(I)-ALFA H20=B0(I)-ALFA CO2=CU(I)+ALFA H2=00(I)+ALFA T=b14, EA=931.72 REACTION MODEL EQUATION
FFAO=FAU(I) CALL MODEL (AK,EA,T,CO.IA20,CO2,H2,WCA7,FFNU,YG) RETURN
269
SUBROUTINE RKUTT(X.H,N,YD,YIYG,YHIYGRU) C RUNGL KU1TA INTEGRATION ROUTINE C*-********* :******'************************9*******4* ~ * d. 4 , r , _
C AR(GUMENT LIST DEFINITIONS C X= INDEPENDENT VARIABLE C H= CURRENT INTEGRATION INTERVAL C N= NUMBER OF DIFFERENTIAL f ūOATIU!'JS C YD= DEPENDENT VARIABLES IN DOJALL PRLCISIO i C Y= WORKING SPACE ALSO ALSO DEPENDENT VAR1i\ LLS l.'i Si;t.;i? C ON EXIT FRO14 THIS SUBBROUTINE 6U1 **NUT** UN LHit-:Y C YG= THE DERIVATIVES OF Y WITH RESPECT TO X C YH= WORKING SPACE C YGRD (X, N, Y, YG i NAME AWIJ ARGUVENTS OF THE SUFi',NUt U-iL 1J i -s C DERIVATIVES OF THE DEPENDENT vARIABLES Y willi RLSF L1 C************* '** ** **** ********i ******a;=f=*** ** *w*** t' k ~:1'x o. 4 ,t .$ a . r r C THE FOLLOWING T !O TYPE STATE :•iENTS ARE VERY Ii,;i'OKTil;: I C NOTE THEM CAREFULLY
REAL X,H,Y(N),YG(N),YH(IJ) ********************************* : ***** :********** ****4: ,-; 4M
OIh'+ENSIOW YD(N)
DO 1J=1,N 1 Y(J)=YD(J) CALL YGRO(X,N,Y,YG) 002 J=1 ,N YG(J)=YG(J)*H
2 YH(J)=YG(J) X=X+0.5*FI 004I=1,2 D03J=1,N •
3 Y(J)=YD(J)+.5*YG(J) CALL YGRD(X,N,Y,YG) 004J=1,N YG(J)=YG(J)*H
4 YH(J)=YH(J)+2.*YG(J) X=X+0.5*H 005J=1,W
5 Y(J)=YD(J)+YG(J)• CALL YGRO(X,N,Y,YG) DO6J=1,N YH(J)=(Yh(J)+H*YG(J))/h. YD(J)=YD(J)+YH(J)
6 Y(J)=YD(J) RETURN END
• ,•
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