modeling of cavity growth in underground coal
TRANSCRIPT
MODELING OF CAVITY GROWTH IN UNDERGROUND COAL GASIFICATION
by
VIJAY ARVIND SHIRSAT, B. Tech.
A THESIS
IN
CHEMICAL ENGINEERING
Submitted to the Graduate Faculty of Texas Tech University in
Partial Fulfillment of the Requirements for
the Degree of
MASTER OF SCIENCE
IN
CHEMICAL ENGINEERING
Approved
Accepted
May, 1989
/'?V"7
1) ^g ACKNOWLEDGEMENTS
Cv . ^
I am thankful to my mentor. Dr. Jfm Rfggs, without
whose help this work could not have reached its logical
conclusion. I am grateful for the valuable comments and
advice extended me by Dr. R. Rhinehart and Dr. E. Fischer.
I would like to thank Texas Tech for being the
institution it is. My wife, Mai, deserves special thanks
for her constant encouragement.
i f
TABLE OF CONTENTS
PAGE
ACKNOWLEDGEMENTS i i
LIST OF TABLES v
LIST OF FIGURES vii
CHAPTER
I INTRODUCTION 1
1 . 1 Overvlew 1
1.2 Research Rationale 12
1.3 Scope of Thesis 15
II LITERATURE REVIEW 16
2. 1 Cav i ty Geometry 17
2.2 Cavity Growth Mechanisms 18
2.3 Fluid Flow 21
2.4 Heat Transfer 23
2.5 Experimental Verification 24
2.6 Re 1 ated Mode Is 26
2.6.1 Krantz et a 1 28 2.6.2 Schwartz et al 29 2.6.3 Kossack et al 31 2.6.4 Riggs et al 32 2.6.5 Harloff 33 2.6.6 Gibson et al 34 2.6.7 Natarajan et al 34 2.6.8 Grens and Thorsness 36 2.6.9 Yoon et a 1 38 2.6.10 Denn et al 41 2.6.11 Cho and Joseph 42 2.6. 12 Gov i nd and Shah 42
2.7 Field Tests 42
i ii
TABLE OF CONTENTS
PAGE
ACKNOWLEDGEMENTS i i
LIST OF TABLES v
LIST OF FIGURES vi i
CHAPTER
I INTRODUCTION 1
1. 1 Overv iew 1
1.2 Research Rationale 12
1.3 Scope of Thes is 15
II LITERATURE REVIEW 16
2. 1 Cav i ty Geometry 17
2.2 Cavity Growth Mechanisms 18
2.3 Fluid Flow 21
2.4 Heat Transfer 23
2.5 Experimental Verification 24
2.6 Re 1 ated Mode Is 26
2.6.1 Krantz et a 1 28 2.6.2 Schwartz et a 1 29 2.6.3 Kossack et al 31 2.6.4 Riggs et al 32 2.6.5 Harloff 33 2.6.6 Gibson et al 34 2.6.7 Natarajan et al 34 2.6.8 Grens and Thorsness 36 2.6.9 Yoon et a 1 38 2.6.10 Denn et al 41 2.6.11 Cho and Joseph 42 2.6. 12 Gov i nd and Shah 42
2.7 Field Tests 42
i i i
I I I MODELING PROCEDURE 49
3.1 Define the Problem 49
3.2 Identify the Controlling Factors 51
3.2.1 Rubble Pile 57 3.2.2 Gas F1 ow Pattern 58 3.2.3 Gas Composition and
Temperature 58
3.3 Evaluate the Data 59
3.4 Formulate the Model Equations 61
3.5 Implement the Numerical Solution 71
3.6 Val idate the Model 76
3.6.1 Flow Field 76
3.6.2 Material and Energy Balances .. 77
IV RESULTS AND DISCUSSIONS 87
4. 1 Base Case 87 4.1.1 Cy1i ndr i ca1 Coord i nates w i th
a Constant Burn Velocity 96 4.1.2 Cartesian Coordinates (SDB),
Constant Ve1oc i ty 96 4.1.3 Cartesian Coordinates,
Varying Velocity 100
4.2 Sensitivity Studies 100
V CONCLUSIONS AND RECOMMENDATIONS 119
5.1 Conclusions 119
5.2 Recommendat i ons 119
LIST OF REFERENCES 122
APPENDICES
A PROXIMATE ANALYSIS AND DEVOLATILIZATION
DATA FOR ILLINOIS AND WYOMING COALS 127
B FLOW FIELD VERIFICATION 129
C LI ST OF COMPUTER PROGRAMS 133
iv
LIST OF TABLES
TABLES PAGE
3.1 Comparison of Model Results for Gas Composition and Temperature with Thorsness' Results 81
4.1 Pressure, Temperature and Location of Node Points in UCG Cavity for Base Case 88
4.2 Gas Compositions at Node Points in UCG Cav i ty for Base Case 89
4.3 Void Space Temperature, Heating Value and Cavity Diameter vs. Time for Horizontal Bed and Varying Velocity 91
4.4 Void Space Temperature, Heating Value and Cavity Diameter for Horizontal Bed and Constant Ve1oc i ty 97
4.5 Void Space Temperature, Heating Value and Cavity Diameter for SDB and Constant Velocity . 99
4.6 Void Space Temperature, Heating Value and Cavity Diameter for SDB and Varying Velocity .. 101
4.7 Velocity and Heating Value for Varying
Steam/02 Rat i o 103
4.8 Velocity for Varying Radius of CSTR 104
4.9 Heating Value for Varying Radius of CSTR 105
4.10 Velocity for Varying Permeability 107
4.11 Heating Value for Varying Permeability 108
4.12 Velocity for Varying Mass Transfer Resistance . 109
4.13 Heating Value for Varying Mass Transfer
Res i stance 110
4.14 Velocity for Varying Intrinsic Rate 112
4.15 Heating Value for Varying Intrinsic Rate 113
V
4.16 Velocity for Varying Side Wall Burn Temperature 114
4.17 Heating Value for Varying Side Wall Burn Temperature 115
4.18 Velocity for Varying Thermal Conductivity 116
4.19 Heating Value for Varying Thermal
Conductivity 117
4.20 Velocity and Heating Value for Illinois Coal .. 118
A.1 Typ i ca1 Devo1at i1i zat i on Data 128
A.2 Distribution of Components in Coal by Prox{mate Analysis 128
B.l Comparison of Analytical Solution with Finite E1ement Code for Poisson's Equation in Cartes i an Coord i nates 131
B.2 Comparison of Analytical Solution with Finite Element Code for Laplace's Equation in Cylindrical Coordinates 132
vi
LIST OF FIGURES
FIGURES PAGE
1 • 1 Wor 1 d Coa 1 Resources 3
1.2 Energy Consumption by Source 1-86 to 5-86 5
1.3 Various Linking Methods for UCG 8
1.4 UCG in Horizontal Beds 10
1.5 UCG in Steeply Dipping Beds 11
2.1 Lurgi Pressure Gasifier 40
2.2 Shape of Cavity Determined after Postburn Coring at Hanna II, Phase 2 and 3 UCG Site .... 47
2.3 Plan View Showing the Margins of the Hoe Creek 3 Burn Cavity in the Felix 1 and Felix 2 Coa I Seams 48
3.1 Idealized UCG Cavity Geometry 52
3.2 Cavity Configuration 54
3.3 Flow Diagram for UCG Cavity Growth Model 64
3.4 Geometry for UCG Cavity Growth Model 67
3.5 Discretization for Finite Element Code 73
3.6 One-Dimensional Reactor Geometry for Benchmark i ng Purposes 78
4.1 Rate of Cylindrical Cavity Radial Growth 92
4.2 Product Gas Heating Value vs. Time for Horizontal Bed and Varying Velocity 93
4.3 Void Space Temperature vs. Time for Horizontal Bed and Vary i ng Ve I oc i ty 94
4.4 Nodal Side Wall Temperatures vs. Time for Horizontal Bed and Varying Velocity 95
vi i
CHAPTER I
INTRODUCTION
1.1 Overview
America's energy policy has been to promote a balanced
and mixed energy resource system while maintaining public
health, safety, and environmental quality. The premise of
adequate energy at reasonable prices requires the pursuit
of three intertwined objectives: Increasing energy
stability, energy security, and energy strength (1).
The economic cycles of demand and supply, in addition
to political pressures, and production disruptions make any
technological forecastings of energy markets fraught with
uncertainty. Recently oil prices have plummeted from a
$30/bbl to $13/bbl. Though a reliable oil/gas resource
base has been established it would be foolhardy to let this
slump lull us into a sense of false security. Economically
viable and environmentally acceptable alternative sources
of energy must be examined with a view to increasing world
wide supplies.
The three options considered at present are nuclear
energy, solar energy, and coal. Developments have also
been made to exploit wind power, hydroelectric power, and
oil and gas sources.
Many serious accidents to date have proved beyond
doubt that nuclear installations are inherently risky. A
slight mismanagement in plant operation can cause
catastrophic results. Also, the problem of radioactive
waste disposal has not yet been successfully resolved.
Besides, the associated costs in this venture render this a
bad alternative.
As of the present, solar energy does not seem to be
effectively utilized because it does not afford any
I at i tude i n geograph i caI Iocat i on or range of appIi cat i on.
Morever, the capital intensive nature of any project in
this area results in high energy costs.
Coal is one of our most abundant fossil fuels. As
illustrated in Figure 1.1 (2), 25 percent of the world's
recoverable coal resources are located in the United
States. The current U.S. coal reserves are around 6.4
trillion tons. If alI of this coal could be recovered, it
would be sufficient to fuel a 500-MW plant (which can
supply the needs of a city of approximately 150,000
inhabitants) for 1.7 million years (3).
Unfortunately, these coal reserves mostly include
lignite/sub-bituminous coal of low heating value and are
present in thin, steeply dipping seams at a great depth
below the earth's surface. It is economically feasible to
recover only about 0.4 trillion tons (around 6 percent) by
WORLD COAL RESOURCES PERCENT OF TOTAL
(ia9x)
(4.9«)
(6.5X)
(21.0%) (16.6^)
(1 A.9%)
Figure l.l World Coal Resources
existing mining technologies (3). Currently coal amounts
to only 23 percent of our total energy consumption, as
represented in Figure 1.2. Coal consumption in the United
States has been increasing since 1973, but crude oil still
maintains a significant advantage over coal with a lot of
this crude oil being imported (4). Since approximately
2,700 tons of coal are equivalent to 9,000 barrels of crude
oil, it is obvious that with our vast coal reserves, the
United States could significantly reduce oil imports, thus
lowering our increasing trade deficit and increasing the
value of the dollar (5).
Underground coal gasification (UCG) represents one
technique of taking advantage of our nation's enormous coal
reserves. UCG is an insitu process for converting sol id
fuel to gaseous products in the presence of steam and
oxygen. The process has a modest environmental impact and
produces an easily transportable product. The fuels that
can be produced (6) include gasoline, methanol, pipeline
qua Iity gas or medium heating value gas (around 270-600
Btu/Scf) that can serve as a local industrial heating fuel
or for on-site electricity generation. Repeated
demonstrations, in the form of over 20 field tests to date
have established the technical feasibility of the UCG
process. UCG technology allows us to increase our
recoverable coal resources to 1.8 trillion tons (around 30
percent).
(41.8X)
ENERGY CONSUMPTION BY SOURCE JANUARY THROUGH MAY 1986
(5.6X)
(22.5%)
(25.3%)
Figure 1.2 Energy Consumption by Source 1-86 to 5-86
There are numerous advantages to the UCG process. The
modular nature of UCG permits close matching of plant size
to plant market. Besides, it requires reduced capital
investment and process equipment as compared to surface
gasification plants (7). It is not possible, through
conventional mining technologies, to recover the energy
content of coal deposits that are too deep or which occur
in very thin seams. UCG has a distinct advantage over
deep-shaft or strip mining in this regard. It overcomes
problems of ash disposal and coal transport ion besides
eliminating many safety and environmental problems
associated with deep mining.
UCG product costs have been compared to other gas
production methods and indicate that they are comparable to
imported natural gas, about 25 percent lower than slagging
Lurgi gas and 50 percent lower than synthesis gas (7).
Comparison of the cost of electricity produced from several
technologies shows that UCG is relatively more profitable.
If UCG gas is used as pipeline gas, it is estimated that
its cost will be cheaper than gas from conventional sources
such as LNG, and SNG (8).
Some of the potentionaI disadvantages associated with
UCG are the possibility of subsidence and groundwater
contamination. Studies reveal (9) that ash leaching is
responsible for a wide array of ionic and inorganic
species. The major groundwater contaminant is believed to
be phenolic compounds. Besides, there is a possibility of
leakage of toxic gases through a porous overburden and into
the atmosphere.
The technology involved in UCG is relatively simple.
The first step is the selection of a suitable site. The
site must allow economic marketing of the product gas and
be sufficiently far from any major water supply centers.
The overburden should be tested for cave-in possibilities.
The seam should be thick enough to minimize heat losses.
The permeability of the seam in the direction of air flow
must be determined.
Coal seams, as they exist in nature, have inherently
low permeabilities. Morever, recondensation of organics
onto the pore structure further reduces the permeability.
Thus the next step should involve a procedure to enhance
the natural permeability of the coal seam. This is
referred to as linking. The various modes of linking that
have been tried in field tests are directional drilling,
electroI inking, hydraulic fracturing, and reverse combus
tion. These methods are represented in Figure 1.3 (3).
Directional drilling involves drilling a deviated,
curved borehole from the surface through the bottom of the
seam in the vicinity of the injection/production well pair.
Electrolinking involves the passage of an electric current
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between the two wells while hydraulic fracturing involves
the injection of high-pressure water through one of the
wells. Reverse combustion (3) is the most prominent method
used in linking wells. Coal at the bottom of the
production well is ignited and high-pressure air is
injected to sustain the burn- Air injection is now shifted
to the injection weI 1 and the flame front propogates in a
countei—current direction to the air flow towards the
injection well. When the flame reaches the bottom of the
injection well, air injection at high volumetric flow rates
and low pressures effects forward combustion.
Coal seams have two natural configurations; the
horizontal bed (Figure 1.4), and the steeply dipping bed
(SDB) (Figure 1.5). For horizontal seams, vertical
injection and production wells are drilled to the lower
part of the bed. Coal is ignited at the bottom of the
injection well, and the product gas is withdrawn through
highly permeable channels to the production well. In the
case of steeply dipping seams, a primary injection well is
drilled through surrounding strata to the base of the coal
seam, and a production well is drilled through the length
of the coal bed. As gasification proceeds from the base of
the seam, settling of the ash eventually clogs the
injection pipe. Thus, another injection pipe is drilled
into the seam at a higher level, to be used for the later
phases of gasification.
10
Production Well
Injection Well
Overburden
Figure 1.4 UCG in Horizontal Beds
11
To Production Well
Figure 1.5 UCG in Steeply Dipping Beds
12
The nature and properties of the overburden have a
marked impact on the UCG process. Generally, fissured and
siIty claystone, and uncemented sand and soils constitute
the overburden. Structural failure of the overburden can
result in cave-in possibilities. In addition, the influx
of water from the overburden into the underground cavity
affects UCG product gas qua I ities.
1.2 Research Rationale
Coal is ignited at the bottom of the injection well
and the combustion reaction is sustained by the
introduction of a steam/02 mixture. As coal is consumed, a
rubble pile starts to build around the injection well.
Spelling of dried coal within the coal seam and from the
overburden leads to further rubble pile build up. As the
cavity grows in the horizontal and vertical direction, a
time is reached when the diameter of the cavity increases
and the arch supporting the cavity can no longer remain in
place. At this point, when the burn reaches the roof of
the cavity, the heating value of the product gas begins to
dec Iine-
Cavity growth has a marked effect upon the two major
aspects of the UCG process: resource recovery and product
gas heating value. The resource recovery of coal fs
representative of the amount of coal gasified for each
13
injection/production well pair. Economic studies (10)
indicate that the resource recovery is intricately linked
to the economics of the process. In like manner, it is
desirable to maintain the product gas heating value during
the gasification process. Thus, in order to reliably
estimate product gas heating values and coal recovery, a
thorough knowledge of the shape of the cavity during
different stages of gasification is essential.
Some field tests have employed a High Frequency
Electromagnetic (HFEM) absorption technique (11) to
measure the growth of the cavity. This method is generally
used in conjunction with thermocouple responses, material
and energy balances and post-burn coring data. In the HFEM
process a radio frequency transmitting antenna is lowered
down one hole and a receiving antenna down another hole.
The two antennas are moved simultaneously so that they
remain opposite one another (at the same depth) on a line
perpendicular to the seam axis. The intensity of the
signal is different for the overburden, rubble bed, and the
burn zone in the coal seam. Cavity shapes reconstructed
from HFEM, however, may be ambiguous and not altogether
cone I us ive.
Unfortunately, the UCG process is very much like the
classical "black box" since it is very difficult to monitor
what is occurring inside the process. With the aid of
14
highly instrumented field tests, latx)ratory studies, and
theoretical investigations, our understanding of the
behavior of the UCG process has greatly improved. A
variety of physical and chemical factors spanning diverse
fields of knowledge interact in a complicated manner in the
UCG process. Kinetic-transport mechanisms should be
coupled with rock mechanics, tectonic studies, hydrological
and geological factors to afford a realistic insight into
product gas qualities and yields. Such a comprehensive
study is beyond the scope of this thesis. To address the
chemical engineering issues in itself is an involved task.
The flow problem in the cavity is highly coupled with heat
and mass transfer effects. Thus, before developing global
models, controlling mechanisms must be adequately
described. A number of models to date, have utilized
arbitrary assumptions with regard to the control Iing
mechan i sms. In add i t i on, qua I 1tat i ve and quant 1tat 1ve
agreement with field test results is sought, thereby
necessitating the introduction of many adjustable
parameters. Thus, these models have a very limited utility
in cavity growth prediction.
If reliable operational strategies can be formulated,
based on the properties of the coal seam and overburden, it
would aid the process engineer and reduce unforeseen
problems. Keeping in view the costs associated with a
15
single field test which are in the range of $5 million, one
can hardly overemphasize the need for Judicious selection
of a framework of process models to accurately simulate UCG
process conditions. Currently, there Is no comprehensive
cavity growth model that takes into consideration all
associated aspects of UCG and predicts the product gas
qualities along with the cavity growth. Moreover, existing
models have resorted to various arbitrary assumptions as to
the control Iing factors to cavity growth.
1.3 Scope of Thesis
A comprehensive model for UCG of horizontal and
steeply dipping coal seams is developed. The model
predicts the product gas composition and the cavity
dimensions with time. The input parameters considered for
the model are the injection rates, feed compositions,
properties of the overburden, and composition and physical
properties of the coal seam.
A range of coal seams are investigated; and, based
upon product gas qualities, the model can help choose
between various candidate sites. In addition, it affords a
degree of control in predicting cavity growth and allowing
the evaluation of different operating strategies.
CHAPTER II
LITERATURE REVIEW
UCG process modeling can be divided into two general
areas: Cavity growth modeling and product gas quality
modeling. Cavity growth during UCG has long been
recognized as having a major impact upon the economic
viability of the process (12). Over the past decade, there
have been numerous studies conducted on cavity growth and
gas compositions resulting in several proposed models.
Currently, there are no viable UCG models which can be
used a priori to optimize process conditions and yield
reliable site selection criteria. Riggs and Edgar (13)
present a review of cavity growth models. Nine models
proposed from 1975 to 1983 have been compared with respect
to the following model components: Cavity geometry, cavity
growth mechanism, fluid flow, heat/mass transfer, and
experimental verification. Related models like water
Influx, gas composition, and rock mechanics, which can be
interfaced with the main cavity growth model, are also
discussed. The paper is concluded with a proposal on what
is needed for realistic UCG cavity growth modeling
research. Before embarking on a thorough description of
each model, an attempt Is made to summarize some of the
conceptual details presented in this paper.
16
17
2.1 Cavity Geometry
The computational effort involved in any such UCG
model is affected by the geometry chosen to represent the
growing cavity. In the UCG of horizontal seams, the
earlier stages of gasification are well represented by a
cylindrical geometry. However, during the later stages of
gasification, natural constraints of overburden and
underburden cause a rectangular type of geometry to be more
suitable. In this case, the numerical solution has to
account for three spatial dimensions and time. The time
variation is generally handled by the pseudo-steady state
assumption wherein the system simulation is resolved into a
series of steady state solutions.
Backward burn refers to the phenomena where the cavity
grows around the injection well in a direction away from
the production well. Some models try to account for
backward burn by moving the injection point away from the
production well, at a rate determined by field test
estimates. Others identify distinct zones in the coal seam
between the injection and the production wel1.
Some investigators use a vertical cylInder with its
center axis at the injection borehole to simulate cavity
growth in the coal. When the diameter of the cavity
becomes larger than the seam thickness, the cavity cross
section is treated as a rectangle.
18
Some other workers treat cavity growth in the coal
seam by employing a spherical geometry in the vicinity of
the injection well. A series of spherical geometry of
equal solid angles is used to describe the region about the
injection well. The output from this region flows via a
series of concentric cylinders to a char link zone which
connects to the production well.
Some models employing a right circular cylinder
geometry, assume that the link between the cylindrical
cavity and the production weI 1 behaves as a packed bed. In
addition, others try to include downward motion of the
cavity in addition to lateral and vertical growth. Field
test evidence, however, inval1dates the downward growth
assumption.
The models developed by Jennings et al. (14) and
Thorsness et al. (15) were of the more classical finite
difference type, since they were designed to interface with
existing codes for Integrating partial differential
equations. Jennings et al. utilized a finite difference
solution of two-dimensional flow through porous media while
Thorsness et al. used a two-dimensional array of CSTR's.
2.2 Cavity Growth Mechanisms
The principal mechanisms employed in UCG cavity growth
models to date are coal gasification, combustion, drying,
and spa I Iing.
19
The first class of growth mechanisms is Inherently
simple. For a pre-ordained geometry the cavity growth rate
in the coal seam Is directly related to the oxygen
Injection rate. Initially a coal/02 ratio Is assumed based
on field test data or computed based on a gas composition
model. The surface recession rate which is an indicator of
coal consumption is related to the oxygen concentration in
the bulk gas.
The second approach employs a sub-model of a burning
coal surface. Most of these sub-models have reduced
computational effort due to analytical determination of
wall regression rates. Some of the Important aspects
Include location of the combustion front, burn velocity,
and temperature distribution throughout the system. Some
workers assume that the gas and wal1 temperatures are equal
and that all chemical reactions occur at the cavity wall.
Mass transfer effects yield an estimate for the burn rate-
This burn rate in turn affects the energy balance. The
models initially developed do not include any mechanism for
flame extinction. A more detailed numerical sub-model for
the burning coal surface yields knowledge of processes
occurring inside and temperature and pressure
distributions. Massaquoi and Riggs (16) have developed a
one-dimensional model for the burning coal surface which
20
successfully predicts values for the bulk gas oxygen
concentration and temperature which result in flame
ext1 net 1on.
The third type of coal consumption mechanism is
drying-enhanced permeability. Workers in this area use the
degree of drying, pyrolysis and char reactions to determine
the permeability and porosity of the coal. Numerical
Implementation requires a guess of the Initial permeability
distribution. This is a very critical parameter to be
considered in order to obtain realistic model predictions.
Generally a relationship is assumed between the flame front
velocity and the local gas flux. Some models break up the
solid phase into ash, char, dry coal, and wet coal with
correspondingly decreasing permeability values. Jennings et
al. (14) proposed a two-dimensional permeation mechanism
with 1000 node points. Gunn et al. (17) in their one-
dimensional model report a linear relationship between
flame front velocity and gas flux. The permeability of the
node points behind the flame front was assumed to be 10000
times (17) the permeability of the node points ahead of the
flame front. Thorsness et al. (15) also developed a two-
dimensional permeation model but they considered the
following factors:
a) Non1sotherma1 flow through a nonhomogeneous porous
med1a.
b) Unsteady-state material balances on the coal.
21
A finite difference approximation of the conservation
equations was used to solve for the gas flow distribution,
temperature distribution, and variation of the solid phase
composition for the two-dimensional region between the
injection and the production well. At any given point, the
sol id phase and gas phase temperatures are assumed to be
equal. Oxygen transport to the coal was supposed to be
controlled by dispersion, and the dispersion coefficient
was taken to be an adjustable parameter. The solid phase
was considered to be either wet coal, dry coal, char, or
ash. Furthermore, the ash was assumed to have a perme-
ability ten times the dry coal which was assumed to have a
permeability ten times the wet coal.
The final type of mechanism for cavity growth is
drying-induced spalling. Some workers have shown that
spalling of the solid phase enhances the cavity growth
since the heat transfer rate is increased immediately after
the dried coal spalls. Models in this area incorporate
analytical solutions for heat conduction into the solid
phase (rock or coal) along with estimates for structural
failure rates for the overburden.
2.3 Fluid Flow
The fluid flow in a gasification cavity is coupled
very closely to the heat and mass transfer phenomena
occurring in the gas phase next to the reacting coal. The
flow field is complicated by a number of factors:
a) The turbulence introduced by the injection well.
b) The presence of a porous medium as well as an open
channel.
c) The collapse of roof material and coal obstructing the
flow field.
d) The existence of natural convection.
Most simulators, at the onset, assume that there
exists a narrow linkage path of high permeability between
injection and production wells. The flow field can then be
modeled using one of the following assumptions:
a) Plug flow.
b) Plug flow with dispersion (or series of CSTR's).
c) Permeation (Darcy flow).
Riehn and Riggs (18), and Kennedy and Riggs (19) have
investigated the effect of fluid flow in coal cavities.
Most models couple the flow field with a material balance
on the moving flame front or assume a linear relationship
between flame front velocity and the gas flux. Assumption
of variable permeability areas between injection and
production wells is realistic as permeability of points
behind the flame front would be definitely much higher than
those ahead of the flame front. Other models assume that
dispersion controls the flux of oxygen to the flame front.
23
The dispersion coefficient, then, is adjusted to obtain
adequate cavity growth predictions. The plug flow
assumption ceases to be realistic due to channeling of the
flow down the center of the cavity and the formation of
large vortices near the entrance region. Free convection
further complicates matters.
HFEM (11) and post-burn coring data (20) reveal that
the roof collapse during several UCG field tests has been
Incomplete. This implies that the rubble pile does not
reach the cavity roof and that there exists a void space at
the top of the rubble pile during UCG operation. This void
space could provide a highly permeable path allowing the
injected gas to bypass the cavity walls, possibly causing
flame extinction at the cavity walls.
2.4 Heat Transfer
As mentioned ear]\erf the flow field problem Is
Intricately 1 inked to the heat and mass transfer phenomena.
The conservation equations for gas species must be
satisfied. Also the heat losses either by conduction to
unburned coal and overburden, radiation and convection from
the sol id face to the gas or evaporation of the Iiquid
water influx into the cavity must be calculated to yield
accurate values for product gas qualities and heating
values. Most models incorporate simultaneous solution of
24
the gas phase and solid phase material and energy balances.
Some models Include chemical kinetics, along with factors
like free and forced convection, radiation, and solid phase
conduction. More often than not, the resulting equations
are highly coupled and non-11 near, necessitating the use of
an iterative solution scheme. Oxygen is assumed to be
transported to the wall via film diffusion. Maximum
burning coal surface temperatures calculated are in the
order of 1200 K. Still other models use a mass and heat
transfer correlation as used in packed bed models. It is
interesting to note that most of the models are dominated
by permeability effects; where the coal permeability is
increased by increasing the temperature which in turn
causes more flow and correspondingly higher rates of heat
and mass transfer.
2.5 Experimental Verification
Experimental verification of mathematical models for
UCG cavity growth is a difficult and expensive operation.
The scanning capabilities acquired by HFEM tests, and post-
burn coring data are not wholly conclusive. The agreement
between model and experiment can be checked in several
ways:
a) Temperature profile.
b) Coal consumption.
c) Cavity shape.
25
Mathematical models may accurately predict tempera
ture and coal consumption profiles while Introducing a lot
of error in the prediction of cavity shapes. However, even
erroneous results from models have at times provided useful
information. A water influx model, which only considered
permeation, predicted temperature levels far below
observable field test values. This resulted in the use of
different mechanisms, like spelling enhanced drying, in the
study of water Influx. Currently, this model by Krantz et
al. (21) appears to be the best water Influx model.
At times, average parameters determined from a field
test are used in the cavity growth models. The problem
here is that a number based upon the overall process may
actually be the result of a variety of processes occurring
in several different regions of the process. For example,
the coal consumption per unit oxygen injected may be
calculated from field tests and gas composition data. Yet,
the coal consumption in the oxidation zone will be
certainly different than in the reduction and pyrolysis
zones. Therefore, parameters have to be handled with
care.
The critical channel width is the ultimate width
reached for the channel after which point the front
propagates in the downward direction. The cavity does not
grow downward as fast as it grows either vertically or
26
laterally probably due to the build up of ash residue or
slagging of the ash when high oxygen blast concentrations
are used.
Small scale tests may illuminate understanding of
cavity growth mechanisms. The "barrel tests" operated by
Lawrence Livermore National Laboratories (LLNL) have shown
that some coals have anisotropic burning rates presumably
due to structural factors rather than chemical factors.
Few models to date have Incorporated this aspect.
2.6 Related Models
There are several other models which can be Interfaced
with a cavity growth model. Roof collapse affects flow
patterns, and consequently, the coal consumption. Computer
programs for predicting roof collapse or surface subsidence
are in the developmental stages. Recently, some successful
simulations using the finite element have been carried out
for the Hoe Creek 2 test.
Water influx is known to be a critical factor
affecting cavity growth in UCG. Most of the models have
assumed a permeation mechanism for water influx. Krantz et
al. (21) have developed a model which agrees well with
field data. The main source of water Influx comes from
spalling rock. This should be included in a comprehensive
cavity growth model.
27
In general, cavity growth models have not been used to
predict gas composition, since there are simpler methods
available which do not require the solution of complicated
differential equations. UCG cavity growth models should
Incorporate a rubble zone in addition to a channel or
packed bed or the resulting gas compositions are bound to
be in error. The coupling of cavity growth and gas
composition models facilitates handling of parameters like
water influx and spelling.
From the discussions above, it is clear that to
develop a more general UCG cavity growth model that can be
used for site specification and process optimization, an
Integrated program of model development with verification
by accurate data from laboratory and field tests is
required. The controlling factors Identified are roof
collapse, water influx, flow pattern in the cavity, and the
behavior of the burning coal. Effects such as the couplIng
of roof spal1ing and failure with flow patterns, or any
combination thereof, should be quantified.
An accurate description of oxygen transport in the
process Is needed. This should consider the effect of the
rubble pile and the burning coal. The rubble pile could be
characterized by a local size distribution.
Another feature of the main model might include
analysis of roof spalIing given the cavity shape, rubble
28
pile height, temperature distribution in the overburden,
and the mechanical properties of the coal and the
overburden. Also, a burning coal model might be used to
determine the local burn rates and surface temperature and
to predict flame extinction. An assessment of radiation
heat transfer can also be Incorporated. Laboratory studies
should be conducted to study the Influence of each of the
delineated factors and small scale tests should verify the
complete UCG cavity growth model. Finally, a number of
full-scale UCG field tests can be conducted to test the
global model.
Once this is done, the model could be used in the site
selection process. Operational factors like the injection
schedule and the method of linking could be optimized.
These modifications in the process would make UCG a more
efficient and economic means of gasifying coal.
Let us analyze some of the cavity growth models in
deta11.
2.6.1 Krantz et al. (21)
These workers have developed a water-influx model
which Incorporates two principal mechanisms: unsteady-
state radial permeation, and spal1ing-enhanced drying of
the overlying coal and overburden. These mechanisms are
coupled via a cavity growth model. The model predictons
29
follow general trends for the daily average water influx
for the Hanna 2 Phases 2 and 3, Hanna 3, and Hoe Creek 2
UCG field tests, and predict the water Influx for the total
duration of each of these four tests with an average error
of 13.1 percent. The model indicates that the water Influx
per unit mass of coal consumed Increases as the seam
thickness decreases or as the reverse-combustion link is
completed progressively higher In the coal seam.
The Irregular UCG geometry was reduced to that of an
equivalent right circular cylinder having a height and an
equivalent radius which are determined from the coal
consumption, well spacing, and length and height of the
reverse-combustion I ink. Average coal and rock overburden
spal1ing rates were calculated from field test results.
These values were found to be consistent with spalling size
distribution data obtained in the laboratory. In this
manner, the equivalent right circular cylinder as well as
the size of the rubble pile on the floor of the cavity were
predicted as a function of time. This model was used only
to predict the water Influx rates and was compeared with
field test data only on that basis.
2.6.2 Schwartz et al. (22, 23)
This model describes the forward burn process between
two vertical wells linked by a porous link zone which is
30
assumed to be of a certain diameter and permeability. The
blast enters through the injection well with the oxygen
being transported through the reacting walls via the
convection process and ultimately diffusing to the wall
where it chemically reacts with the coal. The cavity then
grows due to the oxidation and reduction reactions which
occur in the reaction zone. At any location the cavity is
assumed to be of cylindrical cross section until the cavity
diameter is equal to the seam thickness. When this occurs,
the model switches to a rectangular cross section. The
roof and floor of the cavity are assumed to be non-reacting
surfaces. The cavity is divided into an hemispherical
region in the vicinity of the injection well and a series
of non-equal diameter cylinders downstream from the
injection welI.
A complex energy balance is included on the side wall
of the UCG cavity. Wall, reaction, and bulk or gas zones
are considered with convective heat transfer between the
wall and gas zones, as welI as wal1 to wall radiation if
the ga;
differences between walI and gas temperatures throughout
the cavity and decreasing temperatures with time.
Convection with or without optically thick radiation
results in much higher temperatures near the injection well
and optically thin radiation within the cavity equilibrates
md gas zones, as welI as wal1 to wall radiation if
IS is optically thin. All variations predict small
31
the temperatures throughout the cavity. The quality of
product gas composition drops with temperature. Model
predictions agree favorably with the Hanna 2, Phase 2 field
test.
2.6.3 Kossack et al. (24)
The model developed is a three-dimensional, four-phase
insitu coal conversion simulator which incorporates fluid
flow, heat transfer, vaporization/condensation, combustion
gasification, pyrolysis, drying, and coal property changes.
The five fluid components considered are water, oxygen,
tar, nitrogen, and a product gas which consists of methane,
carbon monoxide, carbon dioxide, and hydrogen.
The coal seam with overburden and underburden is
divided into N grid blocks, creating a system of 7N
equations in 7N unknowns for the transport equations and a
system of 4N equations and 4N unknowns for the sol Id
balance equations. The two systems are linked in a very
non linear manner by the source/sink terms, the porosity
functions, and the permeability function. The rate of
combustion of oxygen is proportional to the implicit flux
of oxygen into a 'combustion grid block.' The amount of
char consumed, carbon dioxide, and carbon monoxide
produced, and the heat liberated is a function of the
temperature In the combustion grid block.
32
This study found the following:
a) Injection and production over the entire thickness of
the seam will increase recovery.
b) A long link path will Increase recovery.
c) Linking and completing wells at the top of the seam
will lead to reduced recovery.
2.6.4 Riggs et al. (25)
These investigators developed a three-dimensional
model for UCG cavity growth. The model is written in
rectangular coordinates and thus simulates burnout from an
initial 1inkage channel for a horizontal coal seam and
uniform thickness. A plug flow and a pseudo-steady-state
assumption is employed and the various parameters
considered are the coal composition and other physical
properties, water Influx, and seam thickness. The
principal equations include gas species equations and both
sol id and gas phase energy balances. The temperature
profiles are coupled with the reaction rate equations, thus
producing oxidation and reduction zones in the channel.
Convective mass transport coefficients at the coal face
account for dispersive mass transfer effects.
The modeling approach hypothesizes that sweep
efficiency is controlled by the growth of the cavity while
product gas compositions may or may not be dominated by the
33
channel, depending upon the occurrence of a welI-developed
reduction or rubble zone. The model assumes continuous
development in a rectilinear fashion with a series of wells
and predicts gas composition and temperature as a function
of axial distance.
2.6.5 Harloff (26)
The model developed by Harloff accounts for Injected
flow conditions, oxygen content, coal seam thickness, coal
heating value, coal carbon content, and initial link zone
cross sectional area distribution between the injection and
production wells. The model calculates the gas and wall
temperatures, heat losses, and coal consumption as a
function of space and time and thereby predicts cavity
shape.
The model used a retracting injection point in order
to calculate back burn. The prominent assumption here is
that combustion occurs in an open channel. Also, the model
assumed plug flow and arbitrarily adjusted the wall mass
transfer coefficient. Besides, oxidation kinetics were
assumed to be diffusion controlled and porous media
correlations were used to determine the heat transfer
coefficient. A finite element analysis was developed to
determine bulk flow properties inside the UCG cavity. The
effects of area change, compressibility, turbulent wall
34
shear stress, wall heat transfer, and combustion heat input
were considered.
The computer simulation results of cav\ty growth were
compared with actual cavity growth data for the Forestburg
Test, Edmonton, Canada and good agreement trends were
observed. The gas temperatures and oxygen concentrations
were also calculated for axial distance. Initially the
oxygen is consumed fast and the temperature rise is nearly
vertical. As time increases, the fluid velocity decreases
and oxygen transport to the walls being less effective;
the oxygen consumption process is slower. Maximum cavity
temperatures of 1000 K are predicted. The reactor radius
is shown to grow with time in a non-11 near fashion tending
to reach a I 1miting width.
2.6.6 Gibson et al. (27)
These simulators presented a mathematical model of
linked vertical well Insitu coal gasification. The model
consists of a radially expanding cylindrical cavity plus a
half-cylindrical linkage path (which is treated as a series
of continuous isothermal hemi-discs) at the bottom of the
coal seam and includes explicit predictions of ground water
influx from local hydrology.
A negligible temperature difference is assumed for the
gas in the cavity and the wall. The ash residue is assumed
35
to be sufficiently open not to Impede either gas or
radiative heat flow. Heat is assumed to be transferred
radially outward from the cavity wall by an opposed
combination of conduction and convection.
Using time-averaged injection rates and pressures, the
model is compared with the Hanna 2 Phases 1 and 3. The
product gas rates and peak cavity temperatures compare wel1
with the field test data.
2.6.7 Natarajan et al. (28)
The mode1 deve1 oped 1s an equ1 I 1br1um mode 1 for
predicting product gas compositions in UCG. The key
parameters affecting gas compositions are identified as
coal composition, carbonization assay, water influx, steam
injection, coal moisture content, pressure, injection
temperature, and heat losses to the overburden. The model
is based on material and energy balances as well as
thermodynam1c equ111br1um.
The following assumptions are made:
a) The system boundary temperatures, i.e., injection,
production, and ambient coal are specified.
b) Outlet product gas composition is determined primarily
by the water gas shift equilibrium at around 1050 K.
c) Methanation activity is a function of the coal and
mineral type and the hydrogen partial pressure in the
gas phase.
36
d) The injected oxygen is completely consumed and
provides part of the energy to the endothermic
gasification reactions.
e) The coal underground is pyrolyzed prior to
gasification.
The following conclusions are drawn:
a) Increased water Influx leads to a poorer product gas
in terms of heating value, and lowers the production
of gas.
b) Increased strata heat losses also lead to a poorer
product gas In terms of heating value.
c) In the case of pure oxygen or air injection, there is
an optimum water Influx rate.
d) Methane production Is decreased by air injection, due
to the lowering of hydrogen partial pressure.
However, the major methane contribution, over 90
percent is from pyrolysis.
2.6.8 Grens and Thorsness (29)
More recently, these simulators have used a packed bed
model to simulate the region between the injection and
production wells in a UCG process.
Recession rates are controlled by convective heat
transfer from the bed to the walls coupled with the
thermomechanical breakdown of the walls. The recession-
37
rate representation developed characterizes wall breakdown
by either a failure temperature (the critical temperature
at breakdown) or by a thickness of char layer at failure,
and determines rates from a model of heat transfer under
these conditions. The recession rates depend on effective
particle size in the char rubble bed. Wall recession rates
have been calculated for WIDCO, Hoe Creek, and Hanna Coals
for wide ranges of bulk gas temperatures and mass flow
rates. The effective particle diameter and failure
temperature are used as parameters.
Further investigation by Grens and Thorsness (30) has
resulted in a model which incorporates the effect of non
uniform bed properties in the calculation of cavity wall
regression rates. The oxygen-containing injected gas flows
through the low-permeabi1ity ash zone to the high-
permeability wall layer and to the void region. On
reaching the wal1 layer, gas flows proceed along the walI,
and upward to the void regions. For the wall layer, the
flows in the ash bed serve to provide a distributed source
of gas flux along the boundary between the bed and the wall
layer, whose strength varies with position according to the
flow geometry in the bed.
The high temperature zones are thus brought closer to
the wal1, at the edge of the wal1 layer where the oxygen-
containing gas from the ash bed meets, and reacts with, the
38
CO and H2 formed by gasification of char in the wall
layer. Also, the high gas fluxes in the wall layer
provides high heat transfer coefficients to the wall.
These phenomena lead to Increased wall recession rates. In
this model, the wall layer is assumed to offer effectively
no resistance to flow. Heat transfer considerations are
similar to the earlier work by these simulators and gas
flux distributions are derived from packed-bed models such
as that of Thorsness and Kang (31). The predictive
capabilities of the earlier model by Grens and Thorsness
when used in conjunction with different sub-models for
cavity growth in UCG are seen to be enhanced by
Incorporating the features of non-uniform bed properties.
Let us examine some modeling approaches used to
describe moving bed gasifiers. Though developed for
surface gasification facilities, the theoretical concepts
involved are similar to those in UCG.
2.6.9 Yoon et al. (32)
These workers developed a steady-state model of moving
bed coal gasifiers based on kinetics and transport rate
processes, thermodynamic relationships, and mass and energy
balances. The model predictions are in good agreement with
published plant data for the Lurgi gasifier. Optimum feed
ratios are defined for a given coal and for a given mode of
39
operation. The reactor configuration is two-dimensional
(Figure 2.1). Coal Is fed to the top through a lock hopper
and moves downward under gravity, countercurrent to the
rising gas stream. As the coal descends, it is dried and
devolati1ized by the hot gases produced by the gasification
and combustion reactions in the lower section of the
gasifier. A steam/02 mixture is Injected at the bottom and
preheated by the hot ash. The exothermic combustion
reaction provides the heat for the endothermic gasification
and drying reactions. The ash is removed by a rotating
grate and this requires the ash to be dry and soft. The
steam/02 ratio is very important in controlling the
maximum temperature in the reactor; a quantity which
affects the condition of the ash. There is a steep radial
temperature gradient near the walI. The moving bed
gasifier is considered as a combination of an adiabatic
core and a boundary layer. No radial gradients are
considered.
The Yoon et al. model incorporates the following
reactions:
Gasification:
C + H2O = CO + H2
C + CO2 = 2 CO
C+ 2 H2 = CH4.
Combustion:
>-C + O2 = 2 (>- 1) CO + (2 ->)C02.
40
i Feed Coal
Recycle Tar
Driv
Grate Drive
Steam Oxygen
Scrubbing Cooler
Gas
Water Jacket
Figure 2.1 Lurgi Pressure Gasifier
41
^ is a system constant, dependent on reaction conditions,
which determines the primary product distribution of carbon
monoxide and carbon dioxide in the combustion products. ^
is taken to be 1.33. Yoon et al. (32) discuss the
sensitivity of their model results with respect to the
value of A •
Water gas shift:
CO + H2O = CO2 + H2.
Axial mass dispersion is neglected and an appropriate
radiation contribution factor is taken (33). The water gas
reaction is assumed to be at equilibrium. The char/H20,
and the combustion reactions are controlled by their
Intrinsic, as well as mass transfer rates whereas the
char/C02 and the char/H2 reaction rates are intrinsically
controlled. The velocity profile is taken to be axial in
plug flow.
2.6.10 Denn et al. (34)
Later, Denn et al. analyzed the radial effects in
moving-bed coal gasifiers with a two-dimensional reactor
model that predicts the spatial distribution of carbon
conversion, gas composition, and temperature. Effects of
wall heat transfer on the overall performance of moving bed
gasifiers were evaluated.
42
2.6.11 Cho and Joseph (35)
They developed a heterogenous steady-state model for
moving bed coal gasification reactors. Comparisons are
made with plant data on the Westfield gasifier and the
Morgantown Energy Technology Center's gasifier. Parametric
studies indicate that the optimum thermal efficiency is
obtained when the conversion on char is Just complete.
2.6.12 Govind and Shah (36)
These workers developed a mathematical model to
simulate the Texaco downflow entrained-bed pilot-plant
gasifier using coal liquefaction residues and coal-water
slurries as feedstocks. The gasification kinetics describe
different complex reactions occurring in the gasifier and
the hydrodynamics describe the mass, momentum, and energy
balances for solid and gas phases.
2.7 Field Tests
Field tests are very important in parametrization
studies for UCG cavity growth or gas composition models and
in affording us a physical insight into the process. The
Department of Energy (DOE) has sponsored a number of field
projects to determine the feasibility of converting the
nation's vast coal reserves into a clean efficient energy
source \/\a UCG. Due to these DOE sponsored tests a
significant data base of process information (37) has
43
developed covering a range of coal seams (flat
subbituminous, deep flat bituminous, and steeply dipping
subbituminous). Let us examine In brief a few of the field
tests with regard to coal properties, product gas
qualities, and coal consumption patterns.
The Laramie Energy Technology Center, with assistance
from Sandla Laboratories, conducted the Hanna experiments
at a gasification site located in South Central Wyoming
about 2 miles south of the town of Hanna. The Hanna No. 1
coal seam is a 9.1-meter (30 ft) thick aquifer 120 meters
(400 ft) below the surface at the Hanna 1 site.
Sixteen wells were drilled, and, because of the \/ery
low air acceptance rate, some wells were stimulated by
hydraulic fracturing using 130,000 liters of water and
7,000 kg of sand at rates up to 5,000 liters per minute and
pressures up to 3,600 kPa (525 psi). Following this, the
coal was ignited on March 29, 1973. Forward gasification
was maintained until May 30 when reverse conbustion was
initiated with air injection. Forward gasification with
various injection and production wells was carried out
between October 5, 1973, and March 22, 1974.
Hanna 2 was carried out in the Hanna No. 1 coal seam
at a depth of 84 meter (275 ft) below the surface. After
linking, forward gasification began on June 4 lasting till
July 11, 1975. Upon completion of Phase lA, Phase IB was
44
carried out. The experiment consisted of linking and
gasification between the primary injection welI and the
burned out region from Phase lA. The Hanna 2, Phases 2 and
3 utilized a square 60 ft X 60 ft well pattern. The
lateral cavity growth in the experiment varied from 0.15 to
0.46 meters per day, and the vertical cavity growth ranged
from 0.24 to 0.67 meters per day.
The Hanna 3 test was designed primarily to assess the
environmental consequences of UCG. On June 22, the forward
gasification was initiated and the system was shut down on
July 30, 1977.
The Hanna 4 site was located approximately midway
between the Hanna 1 and 2 areas. The depth to the top of
the coal seam was about 100 meters (330 ft) and process
wells were spaced at 30 meters (100 ft).
Besides the Hanna site, the Lawrence Livermore
National Laboratory (LLNL) conducted the Hoe Creek
experiment at a gasification site located In Northeasterm
Wyoming about 20 miles south of the town of Gillette.
The Felix No. 2 seam chosen for the tests lies 40
meters (130 ft) below the surface. The surface Is 7.5
meters (25 ft) thick lying nearly flat and overlaid with 5
meters of fine grained sandstone. Above the sandstone is
the 3-meter (10 ft) thick Felix No. 1 coal seam.
45
The Morgantown Energy Technology Center conducted
Pricetown 1 in the Pittsburg coal seam, at a site near
Pricetown, West Virginia. The swelling bituminous coal is
located 270 meters (900 ft) below the surface with an
average thickness less than 1.8 meters (6 ft).
The first DOE sponsored field test in steeply dipping
coal was performed by the Gulf Research & Development
Company at a site located 8 miles west of the town of
Rawlins in South Central Wyoming. The 18-meter (30 ft)
thick coal seam in the Fort Union Formation was selected
for gasification. The seam is classified subbituminous B
and Iies at a dip of 63 degrees.
On the basis of the Hoe Creek results, a more
extensive series of field experiments was planned to
establish the feasibility of UCG for commercial gas
production under a variety of gasification conditions (38).
This series, known as the large block experiments, was
completed in January 1982. Jointly funded by the DOE and
the Gas Research Institute, the large-block experiments
were carried out at the Washington Irrigation and
Development Company (WIDCO) coal mine near Central la,
Washington, with the cooperation of WIDCO. Originally
conceived as a set of tests in large, isolated blocks of
coal (hence the term large block), the experiments actually
were conducted in adjacent sections of a single exposed
46
coal face. One goal of the large-block experiments was to
provide a better understanding of how the burn cavity grows
and is Influenced by the geology of the site. Another goal
was to explore the feasibility of extending gas production
from a wel1 using the controlled retraction injection point
(CRIP) method. The basic idea of the CRIP technique is to
start a new burn zone in fresh coal by cutting off the
injection pipe at a point upstream of the old cavity and
then reigniting the coal seam.
Figures 2.2 and 2.3 show the top view of the UCG
cavity formed during the Hanna and Hoe Creek tests,
respectively. These cavity shapes were inferred using
post-burn coring, downhole thermocouple strings, and high
frequency electromagnetic monitoring. Some of the general
features observed are the oval cavity shape about the
injection well, as well as a decreasing cavity width moving
from the injection well to the production well.
47
CAVITY BOUNDARY
20
FEET INJECTION WELL PRODUCTION WELL
Figure 2.2 Shape of Cavity Determined after Postburn Coring at Hanna II, Phase 2 and 3 UCG Site
48
Felix #1-K^ . . . . . . .VS
a . V5 ^-i-iill.-io'
Felix # 2 - ^ °
Margins inferred from instruments and rock core
0 20 40 60 80 100ft _: I
After Hill (1981)
Figure 2.3 Plan View Showing the Margins of the Hoe Creek 3 Burn Cavity In the FeMx 1 and Felix 2 Coal Seams
CHAPTER III
MODELING PROCEDURE
Many of the ear I 1er mode 11ng approaches have fa i1ed
to identify the controlling factors for cavity growth and
have taken recourse to arbitrary adjustable parameters in
order to achieve a close agreement with plant data. These
shortcomings have restricted the utilitarian value of such
models. A rigorous riKjdel ing approach is essential in the
development of a realistic model.
The model presented here Is based upon the approach by
Riggs (39). In order to present the details of this model,
the following format will be used:
a. Define the problem
b. Identify the controlling factors
c. Evaluate the data
d. Formulate the model equations
e. Implement the numerical solution procedure
f. Validate the model.
3.1 Define the Problem
The rationale and the scope of the investigation have
already been discussed In the preceding chapters. The
model uses the following data to predict product gas
49
50
compositions, product gas heating values, and cavity
dimensions with time.
a) Coal composition (Proximate analysis &
DevoI at 111zat1on data}
b) Permeability of the coal bed
c) Density and porosity of the virgin coal
d) Pressure drop through the cavity
e) Initial diameter and initial height of the cavity
f) Seam thickness
g) Overburden composition
h) Spalling characteristics of the overburden
i) Injection temperature, rate, and composition
J) Transport properties for the gas and sol id phases
k) Heats of reaction and heat capacities
I) Kinetic parameters.
The model can be used to study the effect of different
sites and injection characteristics in an attempt to
identify the factors that control UCG performance (i.e.,
value of the product gas) to establish realistic site
specification criteria, and to develop economically viable
operational strategies.
The same physicochemical model will be utilized for
UCG of horizontal and steeply dipping beds. The model
developed will be based upon a two-dimensional
51
representation of these processes. The two main components
of the overall model are the flow problem and the material
and energy balances. For both systems, the material and
energy balances will be handled in an identical manner but
for horizontal beds cylindrical coordinates will be
employed In the solution of the flow problem whereas
cartesian coordinates will be used for SDB.
3.2 Identify the Controlling Factors
Before quantifying the mechanisms of the growth
process, some fundamental aspects have to be considered
first. In a study of this sort, a number of idealizations
will, by necessity, have to be made. Primarily, we have to
choose an initial cavity geometry.
A UCG cavity geometry as shown in Figure 3.1 is used
as a basis for studying the cavity growth mechanism. Some
of the general features observed during UCG field tests are
seen to be incorporated in this idealized geometry.
The reactants steam/02 are injected through the
injection well. There are two different modes of gas
injection for UCG cavities: injection at the bottom of the
rubble pile and injection at the top of the cavity. In the
first case, the outlet of the injection well is maintained
at the bottom of the cavity inside the rubble pile. This
52
Top View Side View
Overburden
I Overburden
Figure 3.1 Idealized UCG Cavity Geometry
53
case was found to exist for the recent Tono test which used
the CRIP concept (38) and for the majority of the Raw1ings
test on SDB. It is assumed that the injected gases react
with the coal chunks for a sufficient time; thereby forming
a cavity as shown In Figure 3.2. The model assumes this
mode of injection.
This configuration bears a significant resemblance to
a fixed-bed gasifier. That is, there is a counter-current
contacting between the injected gas and the coal. The
cavity grows around the injection point by spalIIng of the
coal forming the roof of the cavity and by consumption of
the coal on the side walls. As the roof spalls, a rubble
pile is built up in the bottom portion of the cavity. The
injection point will thus be covered with rubblized coal as
the rubble pile grows. Coal pieces, falling from the roof,
are at least partially dried. Once on the rubble pile,
they are contacted with hot gases containing little or no
oxygen; therefore, the remainder of their moisture is
removed and pyrolysis begins. As coal is gasified in the
bed, the bed will settle. That is, there is a downward
flow of the coal pieces in the rubble pile. As the coal
pieces flow further down into the bed, they will be heated
to a higher and higher temperature, resulting in the
removal of their pyrolysis products and the onset of
gasification. The proximate analysis and devoI ati1ization
54
Rock Rock
Figure 3.2 Cavity Configuration
55
data are given in Appendix A. In the gasification zone,
high-temperature gas drives the char/steam and the char/C02
reactions. These reactions will occur largely on or near
the surface of the coal chunks. Eventually, the coal
pieces will reach the bottom of the bed where the
combustion zone is located. Here, the remainder of the
char will be consumed by oxidation, leaving only the ash
beh1nd.
The injected gases (usually a steam/oxygen mixture)
enter the bottom of the bed in the oxidation zone. Here,
the oxygen content of the gas is quickly removed and
replaced by carbon dioxide, producing a high-temperature
gas. As the gas leaves the oxidation zone, it enters the
gasification zone where the thermal energy of the gas
drives the endothermic gasification reactions. As the gas
flows upward, it becomes cooled due to the endothermic
gasification reactions. Before the gas flows upward into
the void space above the coal bed, it passes through the
pyrolysis zone. In the pyrolysis zone, methane, C2's, and
CO are added to the gas which increases its heating value
over what it was from the carbon monoxide and hydrogen
produced in the gasification zone. After the gas enters
the void space above the rubble pile, the majority of its
coal contacting is over since It will have a rather direct
path to the production well; however, it picks up the
56
drying moisture and cools preventing further carbon
reaction. Therefore, the heating value of the gas in the
void space above the rubble pile should remain relatively
unchanged as It flows to the production well. Effects of
continued water gas shift reaction are neglected. The flow
field is not one-dimensional as in a fixed-bed gasifier.
The injected flow moves vertically throughout the bed and
radially toward the cavity walls. Morever, the ash is not
removed from the bed, and the shape of the fixed bed does
not rema1n constant.
Investigations by Yeary (40) Indicate that thermally
driven gasification and settling of the rubble bed are the
two major factors that determine lateral cavity growth.
In the case of thermally driven gasification, thermal
energy from the gas phase Is transported to the altered
coal to drive the endothermic C/H2O and C/CO2 reactions.
The consumption of carbon from the char and the subsequent
mechanical failure of the ash produce a moving boundary.
In the case of settling of the rubble bed there Is a
combination of thermal drying and pyrolysis of the coal on
the side wall followed by the abrasion of the dried coal by
the settling rubble pile. This mechanism is based upon the
fact that the char left after the coal has been dried and
pyrolyzed has a very low structural strength. The rubble
pile settles as the coal is consumed at its bottom. This
57
settling is responsible for the removal of altered coal at
the side wal1.
The following factors should be considered when
determining the conditions for the side wall growth process
Inside a UCG cavity:
a) The rubble pile (size and content) inside the cavity
b) Gas flow pattern inside the cavity
c) Temperature and composition of the gas in the cavity.
3.2.1 Rubble Pile
During the early stages of cavity formation, a coal
rubble pile is formed. The large-block tests conducted by
LLNL established that between 50 percent and 80 percent of
the cavity volume was filled with rubblized coal. As the
cavity grows, the rock overburden is encountered. At this
point, inert rock begins to fall onto the rubble pile by
spa]1ing or perhaps by catastrophic roof col lapse. As the
process continues the rock replaces most of the coal
present in the rubble pile since the coal that is
accessible to combustion and gasification is being
consumed.
During the later stages of the cavity growth process,
the cavity is probably filled to as much as 80 percent of
its volume with "effectively inert" rubble which Is mostly
rubblIzed rock overburden. The permeability of this rubble
pile will have a direct effect upon gas flow through It.
58
The effective permeability of the rubble bed will be
largely determined by the size distribution of the rubble
material.
3.2.2 Gas Flow Pattern
When the injection point is maintained relatively deep
inside the rubble pile, the flow Is controlled by
permeation (Darcy's Law flow) from the injection well
through the rubble bed toward the void gas space above the
rubble bed. The void gas space offers a low flow
resistance path to the production well, and therefore, the
injected flow will preferentially flow through the rubble
bed toward the void space. There will be some radial flow
through the rubble bed toward the cavity walls where
combustion and gasification can occur; the magnitude of
which is to be determined.
3.2.3 Gas Composition and Temperature
In general, the oxygen present in the injected gas
drives the combustion process resulting in the formation of
CO2 and H2O and a significant temperature increase. The
high temperature of the gas drives the gasification and
pyrolysis processes which lower the gas temperature but
add H2f CO, and hydrocarbon (largely CH4) to the gas.
Sulfur compounds like H2S, COS, CS2f and mercaptans are not
mode Ied.
59
Monitoring the gas conditions is extremely important
to the assessment of lateral cavity growth mechanisms since
this will provide Information about the conditions at the
side wall. The relative amounts of the injected gases
reacting with the side wall or flowing directly to the void
zone will depend on the relative pressure drops of the
various paths. The gas space above the rubble pile is
likely to contain a high-temperature, highly turbulent
gas.
Based upon the physical description of the UCG
process, the following factors are identified as control
ling in this process:
a) Injection configuration
b) Lateral growth mechanism of the cavity
c) Roof spalIing and collapse
d) Gas flow pattern through the rubble pile
e) Gasification reaction kinetics
f) Heat and mass transfer effects between the gas and the
rubblized coal.
3.3 Evaluate the Data
The following data are required for the model:
a) Operating conditions
b) Physical properties of coal and gaseous components
c) Permeability of the coal bed
60
d) Reaction kinetics
e) Coal spal1ing rate.
The injection temperature, rate, and composition are
taken directly In accordance with field test settings. An
initial cavity and rubble pile shape is assumed. This
initial condition represents some intermediate condition
(e.g., cavity conditions after 10 days). The geometrical
dimensions of the cavity along with the pressure drop In
the cavity and injection parameters can be estimated fairly
accurately (field test results).
Proximate analysis and devolati1ization data for
Wyoming and Illinois coals are found in a report by Yoon et
al. (33). The pyrolysis yields have been applied to
simulate insitu conditions. These, along with other
physical properties of coal like density and porosity, are
obtained with a high degree of certainty.
There are six gaseous species modeled: 02? CO, CO2•
H2O, H2f and CH4 and the values of the physical properties
such as diffusivities, viscosities, specific heat
capacities, and heats of reaction are taken to be functions
of temperature adapted as such from standard references
(41). The uncertainty associated with these parameters is
reasonably low.
The permeability of the coal bed is a major unknown.
There does not appear to be any experimental data for this
61
parameter. An initial estimate for the permeability is
made based on the Karman-Cozeny equation. The uncertainty
associated with this is of considerable magnitude.
The uncertainty associated with the reaction kinetics
may be around -f/- 300 percent. For benchmarking purposes,
the model is compared with test runs made by Thorsness
(42). These results will be discussed in Section 3.6.2.
The model developed by Thorsness agreed well with UCG plant
data.
Overburden compositions and spalIing rates will depend
on site specifications. Camp (43) has examined different
overburden configurations and his model predicts spalIing
rates which agree with field data. These will be used in
the model. This, however, will only provide an order of
magnitude estimate of the true spalIing rate.
3.4 Formulate the Model Equations
From the analysis of estimates of the cavity shape
for the Hanna, Hoe Creek, and Centralia field tests
(horizontal beds), the cavity can be seen to grow
relatively symmetrically about the injection well from a
plan view. As mentioned earlier, most of the cavity is
occupied by rubblIzed material. The majority of the
pressure drop In the system occurs In the rubble pile.
This in conjunction with the cavity shape in the plan view
62
indicates that the assumption of cylindrical syrrvnetry about
the Injection well is reasonable. For LLNL's CRIP
configuration, the system would be somewhat less symmetric
although this two-dimensional representation should
approximate the general behavior of the system. For this
approximation, the Inertia I effects of the injected flow
are neglected in addition to the rubble zone extending
toward the production well.
The geometry used to model the SDB process is a plane
which is parallel to the face of the overburden and is
completely contained within the coal seam. This geometry
is based upon the following two assumptions:
a) The buoyancy forces in the gas are smalI compared with
the frletional losses as the result of gas flow through the
rubble bed. Darcy's Law can be used to describe the flow
behavior in this system and is given as:
"q' = (-k^)'v'. (P --<gz)
where q is the gas flux vector
k is the permeability of the rubble bed
yUg is the gas viscosity
z represents the vertical direction
X^ gz represents the buoyancy effects
and ^.P the frletional losses.
From field test experience on SDB, V P is about O.l psi/ft
whileV^gz is estimated to be less than 0.001 psl/ft. As a
result, buoyancy effects can be neglected.
63
b) The overburden and underburden do not have a
significant effect upon the behavior of the system. Since
the size of the rubble particles is in the order of inches
and the thickness of the coal seam should be in excess of
10 feet, the flow field should be evenly distributed
between the overburden and the underburden.
The approach used here is to decouple the cavity
growth/coal bed dynamics problem from the problem of
determining the concentration, temperature, and gas flow
distribution through the coal bed. That Is, the
concentration, temperature, and gas flow distribution
through the rubble pile is determined assuming a fixed
cavity shape and coal bed properties.
Since the residence time of the gas in the system is
considerably less than for a coal chunk In the rubble bed,
and since solid/gas systems are generally well described
using the pseudo steady-state assumption; one can assume
that the rubble pile and cavity boundaries remain fixed,
and that the system behaves in a pseudo steady-state
manner. That is, the temperature, pressure, composition
distribution, and geometry throughout the system remain
fixed over a reasonable time step.
Figure 3.3 gives the procedure for the numerical
algorithm. Once the concentration, temperature, and flow
profiles are obtained a step in time is taken during which
64
/ \
>
<
I n i t i a l i z e Problem
>
t Solve Flow Distribution Problem
\ /
Solve Composition and Temperature Profile
\ /
Take Time Step: Calculate New Cavity Geometry Calculate New Bed Properties
and Snape
Figure 3.3 Flow Diagram for UCG Cavity Growth Model
65
the cavity will grow and spal1Ing of the cavity roof will
occur. After a time step is taken a new coal bed problem
will result. Then once again, the concentration,
temperature, and gas flow distribution through the rubble
pile is determined for the new coal bed shape. In this
Euler's time explicit solution manner the growth of the
cavity will be predicted.
Therefore, the first task is to determine the gas flow
distribution, the temperature distribution, and the local
solid-gas reaction rates for the rubble bed and the side
wall. Then based upon these results and an appropriate
time step, the consumption of the coal in the rubble pile
at the side wall can be calculated. In this manner, the
growth of the cavity can be predicted. If several
mechanisms are operating simultaneously affecting lateral
cavity growth and once they are quantified, they can be
interfaced with the model to include their contribution to
the lateral growth of the cavity.
In order to determine the gas flow pattern, the
temperature distribution, and the local coal consumption
rate, the momentum, heat, and mass transfer equations must
be solved simultaneously. This requires an iterative
numerical procedure. The flow distribution problem Is
decoupled from the material and energy balances for
solution purposes. That is, the flow distribution fs
66
determined separately, then those results are used to
perform the material and energy balances. Then the flow
distribution is resolved and so on until convergence is
obtained. The flow distribution is coupled to the material
and energy balances since the local reaction reates
determine the generation term in the flow equation. The
material and energy balances also depend upon the flow
distribution.
For either the horizontal bed or the SDB, the flow
field represents a boundary value problem. That is, the
pressure at the inlet and along the top of the rubble pile
is assumed to be constant. In addition, there is a
symmetry condition in the center, and a no-flow condition
along the cavity floor and side walls (Figure 3.4). Since
there is a generation of moles of gas inside the rubble
pile due to gasification, the following equation represents
a differential mole balance on a point inside the rubble
bed,
V.q = S.
Using Darcy's law this equation can be reduced to,
y2p = -y<^gS/k
where S is the net rate of generation of moles of gas as a
result of gasification and pyrolysis (lb moles/ft - sec).
This is a form of Poisson's equation subject to the
following set of boundary conditions:
67
Constant Pressure Surface V
Gasification Zone
No Flow Condition
Constant Pressure Surface
No Flow Condition
/
•f CSTR Zone
Figure 3.4 Geometry for UCG Cavity Growth Model
68
Pressure at outlet of the injection well = Pi
Pressure In gas void space = PQ
In addition, there is no flow perpendicular to the
side wal1 or perpendicular to the cavity floor: i.e., at
these surfaces, ( P/' n) = 0 , where n is normal to the
surface. Therefore, the above equation, subject to the
boundary conditions, represents a two-dimensional boundary
value problem.
Now consider the material and energy balances for the
bed zone. The oxidation zone will be in a small area near
the outlet of the injection well. This region is assumed
to be of a hemispherical shape about the injection well.
The following reactions are considered to occur in this
zone:
C + 02 = CO2
CO + H2O = CO2 + H2
C + H2O = CO -•• H2.
The first reaction Is assumed to go to completion.
7 Is taken equal to one. An adiabatic flame temperature
calculation is performed to give the maximum outlet
temperature from this region. On the basis of the first
reaction going to completion, the outlet temperature from
this zone is fixed. The value of the equilibrium constant
for the water-gas reaction along with an energy balance
over the region (adiabatic process) yields the degree of
69
the other two reactions and consequently the compositions
of the exit stream. This zone is highly turbulent due to
the flame front near the injection wel1 and the
corresponding high temperatures encountered there.
Consequently, it is very difficult to characterize this
zone. The approach adopted is to model the zone as a
lumped region in which the outlet temperature is fixed.
All the injected oxygen is assumed to be depleted.
In the gasification zone within the coal bed, the
following heterogenous reactions are assumed to be
occurring between solid carbon and gaseous reactants:
C + H2O = CO + H2
C + CO2 = 2C0
C + 2H2 = CH4
CO + H2O = CO2 + H2.
The water-gas shift reaction occurs in the gas phase
and as a surface reaction catalyzed by coal mineral
surfaces. The gasification reactions take place over a
wide temperature range (33), and at various positions the
apparent rate may be controlled by the intrinsic reaction
rate or by pore or bulk film diffusion rates. The intrinsic
reaction rates are assumed to follow mass action laws and
their coefficients follow the Arrhenius Law.
kr,i = kf,0 exp (-Ei/RT).
Values of the kinetic parameters need to be determined from
70
experimental data for the particular coal of interest.
These are obtained from Yoon (33). The bulk film mass
transfer coefficient Is obtained from a 'J-factor'
correlation (44) given as:
kp,i = 2.06/e P CSc-0.092 (p Df/dpRT) 0.575 FQO.AZS;^
where dp is the particle diameter
C Is the void fraction of the coal bed
Sc Is the Schmidt number
Df is the bulk phase diffusivity of the gas
species (1)
FQ is the total molar flux of the gas
T 1s the temperature
and P Is the pressure.
The consumption of the coal particle is assumed to
take place by a shell progressive (SP) mechanism where It
is assumed that the ash retains its structure and remains
on the coal particle to form an ash layer surrounding an
unreacted core. The other possible mechanism is the Ash
Segregation (AS) model where the ash is segregated from the
coal particle, and there is no ash layer between the
combustible fixed carbon and the gaseous reactants (33).
The carbon-steam reaction is assumed to be limited by
the intra-particle diffusion rate of steam as well as the
intrinsic reaction rate (33). The SP model yields:
71
Pvol • (CH20 - CH20,eq) rc/H20 =
^ 6 ^P ~ dpu + ^ ^
rkpdp2 I kp,i dpu^carbo zTo\dp2
Here, CH20,eq s the equilibrium partial pressure of
steam, CH20 is the partial pressure of steam at the
temperature considered, dp is the initial solid particle
diameter, dpu Is the fraction of the particle diameter
which is occupied by unreacted core, Carbo is the initial
concentration of fixed carbon In the particle, kr,i is the
intrinsic reaction rate coefficient for the reaction, kp is
the film mass transfer coefficient, D\ is the effective
diffusivity, and >[ is the effectiveness factor for the
reaction in the core.
For a spherical porous core, ' is given by the
expression (44).
1 = 1//H20 Cl/tanh(3 / H 2 0 ) " 1/3 / H 2 0 ]
where YHZO ^S the Thiele Modulus defined by (44):
7 H20 = clp/6 » sqrt(kr * carbo/Df)
The C/CO2 and the C/H2 reactions are treated in like
manner with their individual intrinsic rates and Thiele
Modu11.
3.5 Implement the Numerical Solution
First, the coal bed is discretized using a number of
node points on the boundaries and in the interior. A
higher density of node points is used in the lower portion
72
of the bed since In this region temperature and
concentrations will be changing more rapidly than in the
upper portion of the bed. In addition, the lower and side
boundaries form a non-uniform geometry; therefore, a finite
element code is required to solve the flow field problem.
A finite element code (45) has been obtained which uses
quadrilateral elements to solve the flow field problem
(Poisson's equation). The input parameters required for
this package are the elemental configuration, nodal
location in the two-dimensional grid, boundary conditions
(pressure values), and the generation term.
Since the permeability of the bed is unknown, the
permeability will be estimated by adjusting its value until
the flow rate into the void space minus the amount
generated is equal to the specified injection rate. Krantz
et al. (21) found that by analyzing the drying-enhanced-
spalIing process, a single parameter could characterize
size distribution of the spalled material. Accordingly,
for this study we will assume a constant bed permeability.
The material and energy balances are appI led to each
node outside the lumped oxidation region in turn starting
with the highest pressure node point. Figure 3.5 depicts
the discretization used for the coal rubble bed. This
ordering is used since the inlet flows to a node point are
used to determine the outlet conditions and temperatures of
73
Figure 3.5 Discretization for Finite Element Code
74
the gas. It has been found that the macroscopic set of
material and energy balance equations (set of non-11 near
algebraic equations) are quite difficult to solve due to
the highly non-11 near effects of temperature; therefore,
the temperature is determined using the regula falsi method
in the following approach. For a fixed temperature, the
material balances are solved, then the energy balance is
evaluated. Next, a new temperature is chosen and the
material balances solved and the energy balance evaluated
until the temperature is found which closes the energy
balance.
As pointed out earller, the material and energy
balances and the flow field must be solved simultaneously;
this requires an iterative solution. First the flow field
is solved using assumed values for the generation terms
throughout the bed. Then the flow distribution is used to
perform the material and energy balances for each node
point. The improved estimates of the generation terms are
used to recalculate the flow field and so on until the
flow, temperature, and concentration distributions converge
to within certain tolerances. Then the reults are used to
determine a new coal bed configuration based upon lateral
growth, roof spalIing, and consumption of coal within the
bed.
75
The model is based on the following assumptions:
a) The flow field near the injection well is not solved.
b) The outlet temperature from the turbulent zone near
the injection well is fixed.
c) There is no pressure drop or a loss in heating value
of the gas from the void space to the production
wel 1 .
d) There exists a pseudo steady-state.
e) The UCG system Is represented in a two-dimensional
manner.
f) The material and energy balances are solved for a
series of CSTR's in the rubble bed.
g) The pyrolysis products and drying moisture are added
to the gas only when it enters the void space.
h) The spalIing rate is constant at 1 ft/day (43).
i) The gas velocity at the side wall is taken to be
constant and proportional to a temperature driving
force.
J) The energy balance at the side wall includes gasifi
cation, convection, conduction, and drying.
k) Thermal conduction is only considered for the side
wall and two columns of node points next to the
boundary.
1) Radiation of heat is neglected.
m) Thermal and mass dispersion is neglected.
76
n) The ash resistance to gas flow is non-uniformly set so
as to be higher at the bottom of the bed and lower in
the higher regions,
o) The permeability of the coal bed is constant,
p) The C/H2O, C/CO2. C/H2, and CO/H2O reactions are
assumed to be controlled by intrinsic and mass
transfer rates.
3.6 Validate the Model
A comprehensive model for cavity growth during UCG as
discussed above must confirm to specified verification
procedures in order to reliably establish its validity.
For this to be feasible every component or 'sub-model'
employed in the overal1 modeling strategy must be subject
to consistency checks.
The gas flow and the material and energy balance
subroutines comprise the most important features of the
overal1 model.
3.6.1 FIow Field
A finite element code is employed to solve the two-
dimensional boundary value problem for the pressure
distribution in the coal rubble bed. Details of this code
are given in the modeling section. Analytical solutions
are developed for two cases: a) Poisson's equation in
rectangular coordinates and b) Laplace's equation in
77
cylindrical coordinates. Appendix B gives the necessary
details. A comparison of values for the analytical and
numerical representations is found in Table B.l and Table
8.2. The values of the relative error clearly indicate
that the finite element code accurately represents the
analytical solution. We may then safely extend it to other
flow field situations.
3.6.2 Material and Energy Balances
Thorsness et al. (42) have presented a computer model
for characterizing reacting flows through packed beds. For
verification purposes, one particular aspect of their model
was studied and contrasted with the material and energy
balance subroutine.
A one-dimensional steady-state gasification problem is
examined. The configuration is shown in Figure 3.6. The
specified parameters are the inlet flow. Inlet gas
composition, inlet temperature, and the reactor height and
diameter. This inlet plane can be considered to be the
zone wherein all the oxygen is depleted in a true fixed-bed
gasifier. Temperatures in this region, consequently,
attain peak values. Complexities of pressure variation
through the bed are not considered.
The model developed by Thorsness et al. employs gas
and solid phase mass balances and species conservation
78
CO CO2 H2O H2 CH4
CO CO2 H2O H2 CH4
Figure 3.6 One-Dimensional Reactor Geometry for Benchmarking Purposes
79
equations along with energy conservation equations and
equations for gas and solid phase motions. The partial
differential equations are solved using a Method of Lines
approach wherein the partial differential equations are
discretized in space to yield ordinary differential
equations with time as the dependent variable. A linear
ordinary differential equation solver LSODE is then used to
integrate the system of equations in time to yield the
required results. For solid-particle gas reactions the SP
and AS models are used. There are five heterogenous
reactions considered (C/H2O, C/O2. C/C02» C/H2, CO/H2O)
along with three purely gas-phase reactions (C0/02f H2/02»
CH4/O2). Along with the basic transport properties,
expressions for mass and thermal dispersion are developed
and used.
The material and energy balance subroutine has five
independent equations for five unknowns; namely the mole
fractions of CO, C02» H2O, H2. and CH4. Newton's method is
used to solve the independent variables. The sixth
variable, temperature, is solved by using a secant method
on the energy balance equation. Wall effects are not
considered and dispersion properties are ignored. The only
reactions considered are the water-gas reaction and three
heterogenous reactions (C/C02» C/H2O. and C/2H2). The
equilibrium parameters, activation energies, and
preexponential factors are taken in accordance with their
80
model. At each node point in the bed, gas compositions and
temperatures are obtained by Thorsness et al. Table 3.1
gives a quantitative comparison of the composition and
temperatures obtained by both models. The values of the
relative error clearly indicate the validity of the
material and energy balance formulation. The slight
variation in temperature is attributed to neglecting the
bed conduction in the energy balance.
Let us address the assumptions involved in the model:
a) The area near the injection well is one of intense
turbulence (flame front). It is difficult to
characterize processes occurring in that region and,
for modeling purposes, we consider that region as a
lumped parameter. The pressure in this region is
assumed to be constant. This gives us one boundary
condition for the two-dimensional boundary value
problem which represents the flow field in the bed.
The exit temperatures and compositions from this
region are the only parameters of interest and these
are evaluated independent of the pressure variation.
b) There are two cases considered; one where al1 the
injected oxygen is consumed within the CSTR region and
one when part of the oxygen bypasses through the bed
into the void space. In either case the exothermic
combustion reaction provides the energy for the
81
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vOvOtvj — mr*-cMO^r*>voir>i /^ i r>toiDf*»r^^o<y^o — m — O 0 ^ C 0 ^ ^ ^ * - ' ^ ^ 0 * ^ v D v D v 0 v 0 ^ 0 v D v D v 0 v D ^ ^
"D — — — ; ' ^ ' ^ ^ ' ^ ' ^ ~ ~ " ; ~ ~ " ; ~ " ; ' ^ " t ' ^ O O O O O O O O O O O O O O O O O O O O O
o <_) (ft
^ o v f l O ^ O ^ • ^ O v O < M ^ v O • ^ — C ^ f l O v O i H ' ^ m c v j t v j o j c n m c v i - — - ' O O o ^ o ^ a ^ c ^ a o o o o o o o a o Q O o o a o c v o v O v O v o v o v D v o v D i n m m i r J i o i D m m m i n m m , r t ^ ^ « « ^ — — — — - - — - . - . - « - - — — — — —
O O O O O O O O O O O O O O O O O O O O O
h-
— W v D o a o — c v j c M m - ^ - ^ ^ i n i n i r i i D v O v O v O v O v D
E"". f:':'".': " " ".'". " " " "".'"•'"— " " o o o o o o o o o o o o o o o o o o o o o o o
S r - ' ^ c v j o O ' ^ o i n O ' ^ C D c v j i n o o — m i n r - o o O N O
<n—• — — — — — — —' — — ^ - ^ " ^ - ^ ' ^ ' ^ ' ^ ' ^ ' ^ ' ^ ~ O O O O O O O O O O O O O O O O O O O O O
4j ^ c M c o ' v i n v D i ^ o o a N O — t v j r o ' v i n v o r - c o a N O c — — — —
c 0 1 1
(0 0 a p 0 u in (0
in 4J
D in 0)
o Q: L. 0 M-
(0 4J ^ D (0
% in in 0) c in L 0 JC
ID F -Q:
— Q) "0 0 z: 14-0
c 0 in
M -
t-
r 4J •— 5
(U u D -P (tJ U 0) a E (U
(U 1 -
a E V 0 u c (D
I -
a
82
endothermic gasification reactions. Gasification
reactions require certain base temperatures.
Appropriate temperatures are required to maintain
reasonble gasification reaction rates.
c) As the gas passes upward through the bed from the
injection well to the void space, most of its coal
contacting will be over before it exits the bed.
Nevertheless, there may be some spal1ing rock and coal
which may absorb some energy from the product gas and
reduce the pressure. These spalling effects are
considered in the model but as the gas flows towards
the production wel1 from the void space, these
spalIIng effects are assumed to become negligible and
are neglected. The product gas heating value and
composition does not change significantly from the
void space to the production wel1.
d) The residence time of a coal chunk in the bed is much
higher than the residence time of the gas. Moreover,
solid/gas systems are generally described well using
the pseudo steady-state assumption. Thus, we can
assume that the rubble pile and cavity boundaries
remain fixed and that the temperature, composition,
and pressure distribution remain fixed over a
reasonable time step.
83
e) Most of the cavity is filled with rubblized material.
The majority of the pressure drop in the system is in
the rubble bed. Moreover, the plan view of cavities
formed during field tests indicates that the cavity
grows symmetrically about the injection well. Thus,
the three-dimensional geometry can be considered
effectively by a two-dimensional representation.
f) The coal bed is discretized into a large number of
node points. The residence time of the gas in the
system is in the order of seconds. Thus for a single
node point, it is reasonable to assume that the gas is
well mixed and of uniform temperature and composition.
In addition, the sol id and gas temperatures are
assumed to be the same.
g) It is assumed that there are no pyrolysis products
added to the gas stream in the bed. It is difficult
to know when exactly the pyrolysis reactions start to
occur. Thus the pyrolysis products are added only
when the gas enters the void space. Based on a
pyrolysis temperature it will be relatively easy to
incorporate pyrolysis reactions in the bed itself.
h) Based upon studies by Camp (43), the spalling rate is
taken to be constant. It is difficult to
experimentally determine the rate of overburden
collapse into the underground cavity. This assumption
84
Is reasonable in the light of the wide range of
uncertainties associated with the process.
1) There are two base cases considered; one where the
side wall growth is constant, and one where the gas
ve1oc i ty at the s i de wa11 is proport i ona1 to a
temperature driving force- This temperature driving
force is equal to the difference between the average
temperature in the bottom portion of the cavity at the
side wal1 and a constant temperature. This constant
temperature is the minimum temperature at the side
wall. When wall temperatures fall below this
temperature the velocity is set equal to zero.
Sensitivity studies are conducted with respect to
changes in this parameter.
J) The relative importance of drying, gasification, and
other heat transfer mechanisms is evaluated. In the
general case, all these possible mechanisms are
cons idered.
k) It is relatively easy to incorporate conduction in all
the node points in the bed, but since we are mainly
concerned with side wall growth, this assumption is
reasonable.
1) For thick coal seams there is not an appreciable
distance over which radiation can be important.
Moreover, the mode of injection (at the bottom of the
85
coal seam) precludes the possibility of any radiation
effects in the underground coal bed.
m) The diameter of the coal bed is many orders of
magnitude bigger than the characteristic diameter of a
coal particle. This allows us to neglect dispersion
effects.
n) It has been experimentally observed that an ash layer
accumulates at the bottom of the cavity. Thus, a non
uniform ash distribution is considered through the
bed.
o) The permeability of the coal bed is a major unknown.
There does not seem to be any experimentally observed
value for this parameter. Moreover, changes in this
value affect the numerical stability of the computer
algorithm. Thus, after an initial estimate is made,
the same value of permeability is taken through the
different time steps in the simulation. Sensitivity
studies are also conducted with respect to this
parameter.
p) The C/H2O, C/CO2. C/H2, and the water gas reactions
are assumed to be controlled by kinetic and mass
transfer resistances. Many different studies have
proposed different kinetic schemes. There is no
particular mechanism which is totally representative
of conditions existing in the underground cavity.
86
Nevertheless, sensitivity studies are conducted with
respect to the numerical values for the intrinsic rate
constants and mass transfer coefficient.
CHAPTER IV
RESULTS AND DISCUSSIONS
4.1 Base Case
The base case studied was a horizontal seam gasifica
tion process with a varying side wall burn velocity. The
velocity was assumed to be proportional to a temperature
dr i V1ng force.
Consider an initial cavity geometry (time=0), as shown
in Figure 3.5. The numbers correspond to nodal locations.
Table 4.1 and Table 4.2 give the spatial locations of the
node points along with the pressure, temperature, and
composition values calculated at the initial conditions.
In addition, the following parameters apply to the base
case which is taken to approximate a horizontal bed field
test.
a) Steam/02 ratio = 3.0
b) Radius of hemispherical region = 1.25 ft
c) Permeability of coal bed = 6.4722E-9 ft^
d) Temperature for side wall growth = 2000 R
e) Thermal conductivity of coal bed = 1.071E-4
Btu/ft R sec
f) Coal compositions (Wyoming coal) is as given in
Appendix A
87
88
Table 4.1
Node #
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48
Pressure, Points in
R loc. (ft)
1.250 2.188 3.125 4.063 4.531 5.000 1.210 2.158 3. 105 4.053
4.526 5.000 1.083 2.062 3.041 4.021 4.510 5.000 0.827 1.870
2.913 3.957 4.478 5.000 0.000 1.250 2.500 3.750 4.375 5.000
0.000 1.250 2.500 3.750 4.375 5.000 0,000 1.250 2.500 3.750
4.375 5.000 0.000 1.250 2.500 3.750 4.375 5.000
Temperature and Location of Node UCG Cavity for Base Case
Z loc. (ft)
0.000 0.000 0.000 0.000 0.000 0.000 0.313 0.313 0.313 0.313
0.313 0.313 0.625 0.625 0.625 0.625 0.625 0.625 0.938 0.938
0.938 0.938 0.938 0.938 1 .250 1.250 1 .250 1 .250 1 .250 1 .250
3.625 3.625 3.625 3.625 3.625 3.625 6.713 6.713 6.713 6.713
6.713 6.713 10.000 10.000 10.000 10.000 10.000 10.000
Pressure (atm)
2.500 2.295 2. 180 2. 118 2. 104 2.099 2.500 2.296 2. 179 2. 1 16
2. 102 2.097 2.500 2. 199 2. 176 2.111 2.096 2.091 2.500 2.31 1
2. 179 2. 109 2.093 2.088 2.500 2.358 2. 197 2. 102 2.080 2.073
1 .930 I .93 1 1 .906 1.879 1 .871 1 .868 1.472 1.469 1 .468 1 .466
1 .466 1 .466 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000
Temp (R)
2700.600 2680.609 2667.917 2652.539 2632.528 2425.003 2700-600 2679.869 2667.271 2651.893
2631.984 2424.280 2700.600 2675.973 2663.993 2649.786 2630.689 2421.730 2700.600 2667.503 2651.117 2643.072 2627.489 2418.348 2700.600 2659.801 2644.481 2630.774 2616.078 2406.882
2674.889 2644.030 2626.351 2611.179 2596.377 2338.794 2652.916 2625.550 2608.436 2593.470 2578.877 2260.641 2643.001 2616.909 2600.508 2586.107 2571.566 2229.259
89
Table 4.2 Gas Compositions at Node Points in UCG Cavity for Base Case
Node # Gas Composition CO C02 H20 H2 CH4 (X lOE-6)
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48
0.265 0.281 0.282 0.283 0.285 0.295 0.265 0.281 0.282 0.283
0.285 0.295 0.265 0.282 0.283 0.284 0.285 0.295 0.265 0.282
0.283 0.284 0.285 0.295 0.265 0.283 0.284 0.285 0.286 0.296
0.282 0.284 0.285 0.286 0.287 0.298 0.283 0.285 0.286 0.287
0.288 0.300 0.284 0.286 0.287 0.287 0.288 0.301
0.164 0. 148 0.148 0. 148 0.149 0. 152 0.164 0. 148 0.148 0. 148
0.149 0. 152 0.164 0. 148 0. 148 0. 149 0. 149 0.152 0.164 0. 149
0.148 0.149 0.149 0. 152 0. 164 0. 148 0. 149 0. 149 0. 149 0. 152
0.148 0. 149 0. 149 0. 149 0.149 0. 154 0. 148 0. 149 0. 149 0. 149
0. 149 0. 157 0. 149 0. 149 0. 149 0. 149 0. 149 0. 158
0.357 0.372 0.370 0.367 0.363 0.324 0.357 0.372 0.370 0.366
0.363 0.323 0.357 0.371 0.369 0.366 0.362 0.323 0.357 0.369
0.366 0.365 0.362 0.322 0.357 0.368 0.365 0.362 0.359 0.319
0.371 0.365 0.361 0.358 0.355 0.306 0.366 0.361 0.358 0.355
0.352 0.290 0.365 0.359 0.356 0.353 0.351 0.284
0.213 0. 198 0.200 0.202 0.204 0.229 0.213 0. 198 0.200 0.202
0.204 0.230 0.213 0. 199 0.200 0.202 0.204 0.230 0.213 0.200
0.202 0.203 0,205 0.231 0.213 0.201 0.203 0.204 0.206 0.233 0. 199 0.203 0.205 0.207 0.209 0.242 0.202 0.205 0.207 0.209 0.21 1 0.252 0.203 0-206 0-208 0.210 0.212 0.257
0.000 0.617 1 .603 2.837 4.453
57.056 0.000 0.676 1.657 2.878
4.483 57.131 0.000 0.993 1 .917 3.053 4.600
57.732 0.000 1.669 2.975 3.614 4,870 58.507 0.000 2.293 3.527 4.664 5.878
61.132 1 .053 3.554 5-030 6.326 7.593
79.561 2.748 5.027 6.520 7.852 9.084
101.809 3.494 5.696 7. 155 8.456 9.660
109.442
90
g) Mass transfer resistances are as reported in the
modeling section
h) The intrinsic rates are given as follows (42, 44):
C/H2O = 613 exp (-21137.39/T)
C/CO2 = 0.6 • Rate C/H2O
C/H2 = 0.000836 exp (-8077.504/T)
CO/H2O = 0.2 » p • (0.5 - P/250) » exp (-8.91 +
5553/T) * 2,887,00,000 » exp (-13971/T)
where T is the temperature in K
and P the pressure in atmospheres
i) The height of the rubble bed = 10 ft
j) The diameter of the cavity = 10 ft
k) For the first time step, the lateral velocity is set
equal to 1 ft/day, and at later times the burn rate is
taken to be proportional to a temperature driving
force
V = k • (Tav,t - Tas)
where k = l/(Tav ~ Tas)»
Tav 's the average wall temperature obtained for the
first time step, Tas is the fixed temperature, and
Tav t is the average wall temperature at any time t.
The value of 1 ft/day is taken in accordance with
field test reports (43). Table 4.3 shows the time
variation in void space temperature, wall temperature,
heating value, and cavity diameter for the base case
(Figures 4.1 to 4.4).
91
Table 4.3 Void Space Temperature, Heating Value and Cavity Diameter vs. Time for Horizontal Bed and Varying Velocity
t
day
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
V.S.T.
Rank i ne
2090.077
2082.855
2076.690
2071.250
2066.244
2061.790
2057.612
2053.930
2050.377
2047.387
2044.401
2041.703
2039.188
2037.008
2034.875
H. V.
Btu/scf
263.174
263.130
263.153
263.199
263.248
263.303
263.353
263.403
263.445
263.497
263.533
263.567
263.599
263.634
263.660
vel
ft/day
I .000
0.914
0.842
0.780
0.725
0.678
0.637
. 0.600
0.566
0.536
0.508
0.483
0.458
0.436
0.410
C. D.
ft
12.000
13.829
15-513
17.073
18.523
19.880
21.153
22.353
23.485
24.556
25.572
26.537
27.453
28.325
29.146
92
u •P Q) S It)
3 1 . -T -I
i •2€i H
I •24. H
Q -P
•P i j r - '
I 1 2 -+•••
4J > i 1 '-• H •i-t R) f u -a s J o \ i
4. H
> 10 O
o
_- -H-" . w - T ' "
-a- -B- -G^ - r 5
Time ( d a y )
• / •dor it... •Z' .y rt-y •dt«irn«at^2r
1 Z
_r.1
Figure 4.1 Rate of Cylindrical Cavity Radial Growth
93
i t i S
2€i4.5 -
i'&ti -i
u (0 3 .P
i€k3.5 -.--e-
L — e - ,—e — Q - - - - Q - - —Q- -a-
i i s a -
0) D iH (0 >
Di C
•H
0)
~rf=.'r.- !=i -
2€i2 -
2<51 .5 -
i e i 5 :5
-i r~ 1 1 1 ^
Time (day)
Figure 4.2 Product Gas Heating Value vs. Time for Horizontal Bed and Varying Velocity
94
c •H
c (t)
2 . 1
2.Cr3 - * .
(U M
IT)
(DO
(0 a (0
2.i_ti
2 . 0 / -1
2.i:»5 -
:.L.LC3 -
•a
•.
m TJ
'tL
O > 2 Cul -
'-«... • S -
•2.02 n r 2 2
-r 4
-r s
6 1 ^
1 o —r-1 1 1 2
— T —
1 .3 — I — 1 4. 1 S
Time (day)
Figure 4.3 Void Space Temperature vs. Time for Horizontal Bed and Varying Velocity
95
0)
c •H X c (0
2 . 4 5
.-. 4 i:'....
2.3S -
2.3 1
0) u D
T3
rd U Qi —
rt)._F
''h.. ' ^ .
T3 •H CO
(0 T3 O
2.15 -
2.1 -
2.ce
*-4w.
• - • • - 3
"•a*-.
" " 1 ' - ^ . . " - ^ -
•-?•-_
-r 3 5
1 ^ —r-1 1 1 3 1 5
Time (day)
Figure 4.4 Nodal Side Wall Temperatures vs. Time for Horizontal Bed and Varying Velocity
96
Studies were also conducted for the following
systems.
4.1.1 Cylindrical Coordinates with a Constant Burn Velocity
Table 4.4 shows the results for a constant burn
velocity at the side wall of 1 ft/day for the cylindrical
coordinate case. On comparing Tables 4.3 and 4.4, we see
that nodal side wall temperatures decrease smoothly. For
the base case, the range is from 2425 R to 2075 R but for
this case, the temperature decreases from 2425 to 1975 R.
The void space temperature decreases gradually but falls
off more steeply than for the base case (2090 R to 2015 R
as compared with 2090 R to 2035 R). This is due to the
fact that a greater amount of energy is withdrawn from the
side wall. The cavity diameter increases at a slower rate
with time (12 to 40 ft) as compared with 12 to 29 ft for
the base case. The heating value for both cases is
relatively constant at 263.2 Btu/scf.
4.1.2 Cartesian Coordinates (SDB), Constant Velocity
The Cartesian case study is taken to approximate a
SDB field test. For both the Cartesian coordinates.
97
Table 4.4 Void Space Temperature, Heating Value and Cavity Diameter for Horizontal Bed and Constant Velocity
t
day
1
2
3
4
5
6
7
8
9
10
1 1
12
13
14
15
V.S.T.
Rankine
2090.077
2082.698
2075.702
2068.928
2062.403
2056.096
2050.229
2044.489
2038.898
2033.710
2028.818
2024.596
2020.645
2017.411
2014.390
H.V.
Btu/scf
263.174
263.124
263.131
263.167
263.217
263.275
263.310
263.399
263.443
263.491
263.527
263.568
263.598
263.623
263.640
vel
ft/d
C D .
ft
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
98
constant velocity and Cartesian varying velocity cases,
the height of the bed is taken to be 30 ft with a
consequent 3 ft/day increase. This rate is a
representative estimate as given in field test reports
(37). The initial cavity diameter is 20 ft. A constant
burn velocity of 1 ft/day is assumed. Table 4.5 shows
variations in heating value, void space temperature, nodal
side wall temperatures, and cavity diameter with time.
The heating value drops from 281 Btu/scf but for later
times stays relatively constant at around 277 Btu/scf as
compared to 263.2 Btu/scf for the base case. the nodal
side wall temperatures decrease from 2300 R to 1800 R; a
steep drop compared to a drop from 2425 R to 2100 R for
the base case- The void space temperature drops from
2040 R to 1770 R; a drop of 270 R, compared to 55 R for
the base case- The gas/solid reaction rates are
appreciable even at the top of the bed. Thus due to more
coal contacting, the methane concentration in the product
gas is more for the Cartesian case than for the
cylindrical coordinate case. This component has a
predominant effect on heating value of the product gas
due to its individually high heating value. Consequently,
the heating value is higher than for the cylindrical
system.
99
Table 4.5 Void Space Temperature, Heating Value and Cavity Diameter for SDB and Constant Velocity
t
day
I
2
3
4
5
6
7
8
9
10
1 1
12
13
14
15
V.S.T
Rankine
2039.264
2010.540
1983.503
1958.408
1935.626
1914.094
1894.720
1877.005
1858.391
1842.757
1829.433
1812.175
1794.134
1784.502
1774.737
H.V.
Btu/scf
280.929
280.406
279.972
279.562
279.216
278.887
278.636
278.411
278.096
277.909
277.828
277.471
277.046
277. 112
277. 1 17
vel
ft/d
C D
ft
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
100
4.1.3 Cartesian Coordinates, Varying Velocity
Table 4.6 shows the results for the Cartesian
coordinates case with a varying side burn velocity. The
heating value decreases slightly and remains constant at
279.5 Btu/scf compared to 263.5 Btu/scf for the base case.
The nodal side wall temperatures decrease from 2300 R to
1900 R, which is a steeper drop than the base case. The
void space temperature drops from 2040 R to 1810 R; a drop
of 230 R, compared to a drop of 55 R for the base case.
However, this is not as steep as the temperature drop in
the Cartesian, constant velocity case- This is again due
to the fact that in the constant velocity case a greater
amount of energy is withdrawn leading to a larger
temperature drop.
4.2 Sensitivity Studies
The following parameters were studied with regard to
their effect on product gas heating value and cavity
diameter. These sensitivity studies were performed for the
cylindrical geometry. The system under consideration is
the cylindrical (horizontal coal seam), variable velocity
case.
a) Steam/02 ratio
b) Radius of the hemispherical region
101
Table 4.6 Void Space Temperature, Heating Value and Cavity Diameter for SDB and Varying Velocity
t
day
1
2
3
4
5
6
7
8
9
10
1 1
12
13
14
15
V.S.T.
Rankine
2039.264
2010.177
1984.997
1962.213
1942.018
1922.897
1904.755
1889.525
1873.369
1859.341
1846.798
1835.634
1826.910
1817.020
1808.990
H.V.
Btu/scf
280.929
280.415
280.100
279.896
279.776
279.682
279.626
279.552
279.549
279.530
279.528
279.517
279.507
279.511
279.525
vel
ft/day
1.000
0.913
0.845
0.783
0.727
0.676
0.630
0.587
0.547
0.512
0.477
0.447
0.410
0.398
0.361
C D .
ft
22.000
23.827
25.517
27.083
28.538
29.890
31 . 151
32.325
33.419
34.443
35.397
36.291
37.112
37.907
38.630
102
c) Permeabi1ity of the coal bed
d) Mass transfer resistance
e) Intrinsic kinetics
f) Temperature for evaluating side wall growth
g) Thermal conductivity of the coal bed
h) Coa1 compos i t i on.
The steam/02 rat i o was \/ar i ed from 2. 0 to 3.0. Th i s
parameter was seen to have the most significant effect on
product gas heating value. For a 33 percent drop in
steam/02 ratio, the product gas heating value rises by
about 10 percent, and the burn velocity at the side wall
increases by about 2 percent. Consequently, the cavity
diameter increases by twice this value, i.e., 4 percent.
On a per mole of injected gas basis, there is more oxygen
present. This means that the net driving force for the
endothermic reactions is higher. Thus, the heating value
of the gas leaving the turbulent zone is higher. Table
4.7 shows a relative comparison between values for velocity
and heating value for the base case and perturbations from
the base case.
The diameter of the CSTR zone was increased from 2 ft
to 2.75 ft. A 37 percent increase in diameter resulted in
a decrease in heating value by about 0.04 percent and an
increase in the cavity diameter by 1.5 percent (Table 4.8
and Table 4.9). This is because, for the same height of
103
Table 4.7 Velocity and Heating Value for Varying Steam/02 Ratio
inie
1
2
3
4
5
6
7
8
9
10
A =
Vel
1.000
0.929
0.866
0.810
0.761
0.717
0.678
0.643
0.611
0.581
2.0
Heat Val
290.433
290.366
290.363
290.374
290.395
290.424
290.452
290.481
290.503
290.531
A
Vel
1.000
0.920
0.852
0.792
0.740
0.694
0.654
0.617
0.585
0.554
= 2.5
Heat Val
276.172
276.105
276.113
276.136
276.171
276.205
276.238
276.272
276.306
276.335
A
Vel
1.000
0.914
0.842
0.780
0.725
0.678
0.637
0.600
0.566
0.536
= 3.0
Heat Val
263.174
263.130
263.153
263.199
263.248
263.303
263.353
263.403
263.445
263.497
104
Table 4.8 Velocity for Varying Radius of CSTR
Time
day
1
2
3
4
5
6
7
8
9
10
Rad = 1
Vel
ft/day
1.0000
0.9077
0.8318
0.7687
0.7140
0.6673
0.6259
0.5890
0.5561
0.5257
Rad=1.12
Vel
ft/day
1.0000
0.9112
0.8374
0.7737
0.7196
0.6728
0.6311
0.5940
0.5611
0.5310
Rad=l.25
Vel
ft/day
1.0000
0.9145
0.8422
0.7796
0.7253
0.6783
0.6368
0.5996
0.5662
0.5356
Rad=l.375
Vel
ft/day
I .0000
0.9178
0.8472
0.7856
0.7316
0.6842
0.6424
0.6052
0.5716
0.5410
105
Table 4.9 Heating Value for Varying Radius of CSTR
Time
day
1
2
3
4
5
6
7
8
9
10
Rad=l
H.V.
Btu/scf
263.211
263.176
263.208
263.260
263.307
263.370
263.428
263.473
263.523
263.567
Rad=l.125
H.V.
Btu/scf
263.191
263.143
263.181
263.234
263.283
263.328
263.389
263.430
263.483
263.530
Rad=l.25
H.V.
Btu/scf
263.174
263.130
263.153
263.199
263.248
263.303
263.353
263.403
263.445
263.497
Rad=l.375
H.V.
Btu/scf
263.151
263.103
263.132
263.179
263.217
263.274
263.324
263.375
263.420
263.463
106
bed, the lesser coal contact results in reduced gas
concentrations and lower heating values. Also, side wall
temperatures rise. This results in higher temperature
driving forces and higher resultant cavity diameters.
As the permeability of the coal bed is increased, the
product gas heating value drops whereas the diameter of the
cavity increases. A 50 percent increase in permeability
results in a 19 percent decrease in product gas heating
value and a 3.2 percent increase in cavity diameter (Table
4.10 and Table 4.11). For higher permeability values,
there is a lower temperature drop in the radial direction
resulting in higher side wall burn temperatures and
consequently higher diameters.
There is no appreciable change in product gas heating
value or cavity diameter for changes in the mass transfer
coefficient (Table 4.12 and Table 4.13). The main
resistance is seen to be incorporated in the intrinsic
reaction term. Accordingly, accurate estimations of the
viscosity and diffusivity parameters may not be necessary
good model predictions.
As the intrinsic rate is increased, product gas
heating value increases whereas the cavity diameter drops.
A 50 percent increase in intrinsic rate results in a 0.2
percent increase in heating value and a 3.3 percent
107
Table 4.10 Velocity for Varying Permeability
Time
day
I
2
3
4
5
6
7
8
9
10
Perm=0.8
Velocity
ft/day
1 .000
0.906
0.829
0.763
0.707
0.658
0.615
0.577
0.543
0.512
Perm=0.9
VeIoc i ty
ft/day
1 .000
0.911
0.836
0.772
0.716
0.668
0.626
0.589
0.555
0.525
Perm=l
Ve1oc i ty
ft/day
I .000
0.914
0.842
0.780
0.725
0.678
0.637
0.600
0.566
0.536
Perm=1.1
Velocity
ft/day
1 .000
0.918
0.848
0.787
0.734
0.687
0.646
0.609
0.576
0.546
Perm=l.2
Ve1oc i ty
ft/day
1 .000
0.921
0.853
0.793
0.740
0.695
0.654
0.618
0.585
0.555
108
Table 4.11 Heating Value for Varying Permeability
Time
day
1
2
3
4
5
6
7
8
9
10
Perm=0.8
Heat vaI
Btu/scf
263.588
263.513
263.523
263.575
263.614
263.665
263.712
263.753
263.798
263.845
Perm=0.9
Heat val
Btu/scf
263.365
263.307
263.330
263.368
263.419
263.474
263.522
263.565
263.615
263.653
Perm=1
Heat val
Btu/scf
263.174
263.130
263.153
263.199
263.248
263.303
263.353
263.403
263.445
263.497
Perm=1.I
Heat val
Btu/scf
263.005
262.971
263.001
263.046
263.099
263.152
263.204
263.257
263.302
263.349
Perm=1.2
Heat val
Btu/scf
262.853
262.828
262.864
262.910
262.966
263.018
263.072
263.121
263.170
263.215
109
Table 4.12 Velocity for Varying Mass Tranfer Resistance
mt coef=.8 mt coef=.9 mt coef=lmt coef=l.lmt coef=1.2
Time Velocity Velocity Velocity Velocity Velocity
day ft/day ft/day ft/day ft/day ft/day
1 2
3
4
5
6
7
8
9
0
1 .000 0 . 9 1 4
0 . 8 4 2
0 .780
0 . 7 2 5
0 . 6 7 8
0 . 6 3 7
0 . 5 9 9
0 . 5 5 7
0 . 5 3 6
1.000 0 . 9 1 5
0 .842
0 . 7 7 9
0 . 7 2 5
0 . 6 7 8
0 . 6 3 7
0 . 6 0 0
0 . 5 6 6
0 . 5 3 6
1.000 0 .914
0 .842
0 .780
0 . 7 2 5
0 -678
0 .637
0 .600
0 .566
0 . 5 3 6
1 .000 0 .914
0 .842
0 . 7 7 9
0 .725
0 .678
0 .637
0 .600
0 .566
0 .536
1 .000 0 .914
0 .842
0 .780
0 .725
0 .678
0 .637
0 .600
0 .566
0 .536
110
Table 4.13 Heating Value for Varying Mass Tranfer Resistance
mt coef=.8 mt coef=.9 mt coef=lmt coef=l.lmt coef=1.2
Time Heat val Heat val Heat val Heat val Heat val
day Btu/scf Btu/scf Btu/scf Btu/scf Btu/scf
1
2
3
4
5
6
7
8
9
10
263.
263.
263.
263.
263.
263.
263.
263.
263.
263.
. 175
. 130
. 156
.201 '
.250
.305
.361
.406
.450
.495
263.
162.
263.
263.
263,
263.
263,
263.
263.
263.
. 176
. 129
. 152
. 195
.249
.303
.358
.401
.451
.494
263.
263.
263.
263.
263,
263,
263,
263.
263,
263,
. 174
. 130
.153
. 199
,248
.303
,353
,403
,445
.497
263.
263.
263.
263.
263.
263.
263.
263.
263.
263.
. 172
. 128
. 151
. 198
.249
.300
.349
,404
,443
,485
263.
263.
263.
263.
263.
263.
263.
263,
263.
263.
. 169
. 120
. 150
. 194
.246
.296
.354
.407
,443
,490
111
decrease in cavity diameter (Table 4.14 and Table 4.15).
The higher reaction rates near the top of the bed result in
higher gas concentrations and temperatures thereby
increasing heating values. However, there is a greater
drop radially which causes lower side wall burn
temperatures. Thus, the driving force for burn propagation
is smaller and the resultant cavity diameter is reduced.
An increase in the fixed side walI temperature causes
the cavity diameter to decrease. There is no significant
effect on product gas heating value (Table 4.16 and Table
4.17). The burn velocity is given as a temperature driving
force; the difference between the average wall temperature
and a set temperature. As the value of this fixed
temperature increases, the difference reduces thereby
lowering the growth velocity.
Product gas heating values and cavity diameter are
seen to be relatively insensitive to the thermal
conductivity of the coal bed (Table 4.18 and Table 4.19).
Changes in coal composition result in no appreciable
change in product gas heating value and cavity diameter.
Nevertheless, Illinois coal yields slightly higher heating
values (Table 4.20).
112
Table 4.14 Velocity for Varying Intrinsic Rate
me
ly
1
2
3
4
5
6
7
8
9
10
Rate=.8
Ve1oc i ty
ft/day
1 .000
0.922
0.855
0.796
0.745
0.700
0.659
0.623
0.591
0.561
Rate=.9
VeIoc i ty
ft/day
1 .000
0.918
0.848
0.788
0.735
0-688
0.648
0.611
0.578
0.548
Rate=1
Velocity
ft/day
1.000
0.914
0.842
0.780
0.725
0.678
0.637
0.600
0.566
0.536
Rate=l.1
Ve1oc i ty
ft/day
1.000
0.91 1
0.837
0.772
0.717
0.669
0.627
0.589
0.555
0.525
Rate=l.2
Velocity
ft/day
1 .000
0.908
0.831
0.765
0.709
0.660
0.618
0.579
0.546
0.515
113
Table 4.15 Heating Value for Varying Intrinsic Rate
Time
day
1
2
3
4
5
6
7
8
9
10
Rate=.8
Heat va1
Btu/scf
262.903
262.843
262.868
262.906
262.950
263.005
263.054
263.094
263.142
263.179
Rate=.9
Heat val
Btu/scf
263.037
262.992
263.013
263.062
263.109
263.161
263.206
263.255
263.303
263.340
Rate=1
Heat val
Btu/scf
263.174
263.130
263.153
263.199
263.248
263.303
263.353
263.403
263.445
263.497
Rate=1.1
Heat val
Btu/scf
263.293
263.250
263.281
263.322
263.383
263.433
263.480
263.535
263.584
263.628
Rate=l.2
Heat val
Btu/scf
263.408
263.368
263.397
263.450
263.504
2636.560
263.604
263.655
263.706
263.752
1 14
Table 4.16 Velocity for Varying Side Wall Burn Temperature
Ta = 1800 Ta = 1900 Ta = 2000 Ta = 2100 Ta = 2200
Time Velocity Velocity Velocity Velocity Velocity
day ft/day ft/day ft/day ft/day ft/day
1
2
3
4
5
6
7
8
9
10
1 . 0 0 0
0 . 9 4 2
0 . 8 9 1
0 . 8 4 6
0 . 8 0 6
0 . 7 7 1
0 . 7 3 9
0 . 7 1 0
0 . 6 8 4
0 6 5 9
1 . 0 0 0
0 . 9 3 1
0 . 8 7 1
0 . 8 1 9
0 . 7 7 3
0 . 7 3 2
0 . 6 9 6
0 . 6 6 4
0 . 6 3 4
0 . 6 0 7
1 . 0 0 0
0 . 9 1 4
0 . 8 4 2
0 . 7 8 0
0 . 7 2 5
0 . 6 7 8
0 . 6 3 7
0 . 6 0 0
0 . 5 6 6
0 . 5 3 6
1 . 0 0 0
0 . 8 8 8
0 . 7 9 7
0 . 7 1 9
0 . 6 5 4
0 . 5 9 8
0 . 5 4 9
0 . 5 0 7
0 . 4 6 9
0 . 4 3 6
I . 0 0 0
0 . 8 3 6
0 . 7 1 4
0 . 6 1 5
0 . 5 3 3
0 . 4 6 7
0 . 4 1 1
0 . 3 6 4
0 . 3 2 3
0 . 2 8 8
115
Table 4.17 Heating Value for Varying Side Wall Burn Temperature
Time
day
1
2
3
4
5
6
7
8
9
10
Ta = 1800
Heat val
Btu/scf
263.174
263.130
263.150
263.196
263.240
263.300
263.346
263.399
263.449
263.496
Ta = 1900
Heat vaI
Btu/scf
263.174
263.130
263.152
263.194
263.248
263.301
263.354
263.408
263.449
263.492
Ta = 2000
Heat va1
Btu/scf
263.174
263.130
263.153
263.199
263.248
263.303
263.353
263.403
263.445
263.497
Ta = 2100
Heat va1
Btu/scf
263.174
263.130
263.158
263.203
263.253
263.309
263.350
263.397
263.444
263.478
Ta = 2200
Heat val
Btu/scf
263.174
263.130
263.173
263.219
263.273
263.321
263.357
263.398
263.437
263.466
1 16
Table 4.18 Velocity for Varying Thermal Conductivity
Thcon=.8 Thcon=.9 Thcon=l Thcon=1.1 Thcon=1.2
Time Velocity Velocity Velocity Velocity Velocity
day ft/day ft/day ft/day ft/day ft/day
1
2
3
4
5
6
7
8
9
10
1.000
0 . 9 1 5
0 . 8 4 2
0 . 7 8 0
0 . 7 2 5
0 . 6 7 8
0 .637
0 . 6 0 0
0 . 5 6 6
0 . 5 3 6
1.000
0 . 9 1 5
0 .842
0 . 7 8 0
0 . 7 2 5
0 . 6 7 8
0 .637
0 . 6 0 0
0 .566
0 . 5 3 6
1 .000 0 .914
0 .842
0 .780
0 .725
0 .678
0 .637
0 .600
0 .566
0 .536
1 .000 0 .914
0 .842
0 .780
0 . 7 2 5
0 .678
0 .637
0 .600
0 .557
0 .536
1 .000 0 .914
0 .842
0 .780
0 .725
0 .672
0 .637
0 .600
0 .566
0 .536
1 17
Table 4.19 Heating Value for Varying Thermal Conductivity
Time
day
1
2
3
4
5
6
7
8
9
10
Thcon=0.8
Heat vaI
Btu/scf
263.173
263.124
263.155
263.195
263.252
263.297
263.355
263.399
263.444
263.491
Thcon=0.9
Heat val
Btu/scf
263.170
263.122
263.154
263.197
263.247
263.295
263.359
263.400
263.450
263.489
Thcon=1
Heat val
Btu/scf
263.174
263.130
263.153
263.199
263.248
263.303
263.352
263.403
263.445
263.497
Thcon=l.1
Heat val
Btu/scf
263.171
263.132
263.152
263.198
263.251
263.306
263.358
263.401
263.449
263.492
Thcon=l.2
Heat val
Btu/scf
263.173
263.128
263.155
263.196
263.260
263.302
263.355
263.406
263.453
263.490
118
Table 4.20 Velocity and Heating Value for 111i no i s Coa1
me
1
2
3
4
5
6
7
8
9
10
V.S.temp
2090.90
2082.77
2076.74
2071.41
2066.34
2061.85
2057.68
2053.91
2050.55
2047.37
Heat val
263.2356
263.1677
263.1870
263.2300
263.2740
263.3200
263.3730
263.4180
263.4680
263.5100
Ve1oc i ty
1.000000
0.914280
0.841950'
0.779400
0.725180
0.678090
0-636630
0.599000
0.566100
0.535400
CHAPTER V
CONCLUSIONS AND RECOMMENDATIONS
5.1 Conclusions
A comprehensive model has been developed to predict
cavity growth and product gas heating value with time for
both horizontal coal seams and SDB.
The simulation agrees well with field test results.
Sensitivity studies conducted on the model indicate that
the most important parameter affecting model results is the
steam/02 ratio. Other parameters that have an intermediate
effect on model performance are the permeabi1ity of the
coal bed, intrinsic reaction rates, diameter of the CSTR
region, and the value of the fixed side wall temperature.
The mass transfer coefficient and the thermal conductivity
of the coal bed are found to have a negligible effect upon
the model results.
5.2 Recommendations
The following recommendations could enhance the range
of app1i cat i on for the mode 1:
a) The model should keep track of the spatial coal compo
sition, i.e., what happens to the coal as it falls
1 19
120
through the rubble bed. The coal composition will
influence the reaction rates, temperatures, and gas
compositions at nodal points through the bed. This
will affect cavity growth.
b) The model should incorporate spatial variations in
permeability. This is an unknown parameter but it has
a predominant effect upon the flow field.
c) Changes in product gas heating value should be
monitored for later times when rock can spall into the
rubble bed. Spalling of rock can reduce product gas
temperatures and heating values considerably.
Besides, the moisture content in the spalling rock can
influence product gas compositions.
d) The model currently considers the addition of pyrol
ysis products only in the void space; the contribution
of additional pyrolysis products in the top regions of
the bed could be incorporated without any trouble.
e) The model should characterize the size distribution of
the coal in the bed. This parameter will influence
the exit compositions and temperatures.
f) The hemispherical region should be modeled with
respect to its turbulent mixing and heat transfer
characteristics. The exit gases from this zone pass
through the coal bed and into the void space. Thus
the temperature and composition of the gases from this
121
zone determine the product gas quality and composi
tion. Since this is a zone of very high temperature,
it is difficult to characterize processes occuring
therein.
LIST OF REFERENCES
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2. World Coal Study, "Bridge to the Future: Report of World Coal Study," Ballinger Publishing Co., Cambridge, MA, 247 p. (1980).
3. Krantz, W. B., and Gunn, R. D., "Underground Coal Gasification: The State of the Art," AIChE Symposium Series. Vol. 79, pp. 1-3 (1983).
4. Monthly Energy Review, Energy Information Administration, Part 6, Coal, Department of Energy, pp. 67-70 (May, 1986).
5. Per I and, R. K., and Daniel, J. H., "Industry's Role in Exporting UCG Technology," Proceedings of the 10th Annua 1 UCG Sympos i um, Williamsburg, VA, pp. 7-10 (1984).
6. Stephens, D. R., Thorsness, C B., Hill, R. W., and Thompson, D. S., "Underground Coal Gasification: UCG is Technically Feasible," Chemical Engineering Progress, pp. 39-40 (February, 1984).
7. Burwel1, E. L. "Underground Coal Gasification: Potential of Underground Coal Gasification," Chemi ca1 Engineering Progress, pp. 35-38 (February, 1984).
8. Massaquoi, J. G. M., "Combustion in Underground Coal Conversion," PhD Dissertation, West Virginia University, Morgantown, WV (1981).
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10. Massay, N. A., Gladzer, B. H., and Edgar, T. F., "Estimated Costs of Methanol, Hydrogen, and Syngas from In-Situ Gasification of Texas Lignite," Proceedings of the 7th Annual UCG Symposium, Fallen Leaf Lake, CA, pp. 545-561 (1981).
122
123
11. Thorsness, C B., and Creighton, J. R., "Review of Underground Coal Gasification Field Experiments at Hoe Creek," AIChE Symposium Series, Vol. 79, pp. 17-18 (1983) .
12. Shirsat, V. A., and Riggs, J. B., "UCG Cavity Growth Model," Proceedings of the 12th Annual UCG Symposium, Saarbrucken, Germany, pp. 297-304 (1986).
13. Riggs, J. B., and Edgar, T. F., "Sweep Efficiency Models for Underground Coal Gasification: A Critical Assessment," AIChE Svmoos i um Ser i es. Vol. 79, pp. 108-120 (1983).
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15. Thorsness, C B., Rosza, R. B., and Wong, R., "Two-Dimensional Modeling of In-Situ Coal Gasification, "Proceedings of the 3rd Annual UCG Symposium, Fallen Leaf Lake, CA, pp. 160-165 (1977).
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20. Yangberg, A. D., and Sinks, D. J., "Postburn Core Drilling Results from Hoe Creek 3," Proceedings of the 7th Annual UCG Symposium, Fallen Leaf Lake, CA, pp. 18-28 (1981).
21. Krantz, W. B., Camp, D., W., and Gunn, R. D-, "A Water Influx Model for UCG," Proceedings of the 6th Annual UCG Symposium, Shangri-La, OK, pp. 21-26 (1980).
124
22. Schwartz, S. H., Eddy, T. L., Mehta, K. H., Lutz, S. A., and Binaie-Kondolsjy» M., "Cavity Growth Mechanisms in UCG with Side Wall Burn Gasification," presented at the 53rd Annua I-Fa 11 Technical Conference and Exhibition of the Society of Petroleum Engineers of AI ME, Houston, TX (October, 1978).
23. Schwartz, S. H., Eddy, T. L., and Nielson, G. E., "A Simple UCG Cavity Model with Complex Energy Balance," Proceedings of the 6th Annual UCG Symposium, Shangri-La, OK, pp. 69-70 (1980).
24. Kossack, C A., "Development and Application of a Three-Dimensional In-Situ Coal Conversion Simulator," Proceedings of the 6th Annual UCG Symposium. Shangri-La, OK, pp. 84-96 (1980).
25. Riggs, J. B., Edgar, T. F., and Johnson, C M., "Development of Three-Dimensional Simulator for Cavity Growth During Underground Coal Gasification," Proceedings of the 5th Annual UCG Symposium, Alexandria, VA, pp. 245-252 (1979).
26. Harloff, G. J., "A Two-Dimensional Model of Underground Coal Gasification Cavity Growth with Application to the Canadian Forestburg," Proceedings of the 5th Annual UCG Symposium, Fallen Leaf Lake, CA, pp. 213-227 (1981).
27. Gibson, M. A., Pennington, R. E., and Wheeler, J. A., "Mathematical Modeling of Linked Vertical Well In Situ Coal Gasification," Proceedings of the 6th Annual UCG Symposium, Shangri-La, OK, pp. 1-14 (1980).
28. Natarajan, R., Edgar, T. F., and Savins, G. J., "Equilibrium Model for UCG," Proceedings of the 6th Annual UCG Symposium, Shangri-La, OK, pp. 15-20 (1980) .
29. Grens, E. A., and Thorsness, C B., "Wall Recession Rates in Cavity Growth Modeling," Proceedings of the 10th Annual UCG Symposium, Williamsburg, VA, pp. 448-461 (1984).
30. Grens, E. A., and Thorsness, C B., "The Effect of Non-Uniform Bed Properties on Cavity Wall Recession," Proceedings of the 11th Annual UCG Symposium, Denver, CO, pp. 413-423 (1985).
125
31. Thorsness, C B., and Kang, S. W., "A Method-Of-Lines Approach to Solution of Packed-Bed Flow Problems Related to Underground Coal Gasification Processes," Proceedings of the 10th Annual UCG Symposium, Williamsburg, VA, pp. 333-348 (1984).
32. Yoon, H., Wei, J., and Denn, M., "A Model for Moving Bed Gasification Reactions," AIChE Journal, Vol. 24, No. 5, pp. 885-902 (1978).
33. Yoon, H., Wei, J., and Denn, M. M., "Modeling and Analysis of Moving Bed Coal Gasifiers," EPRI AF-590, Project 986-1, TPS pp. 76-653 (November, 1977).
34. Denn, M. M., Wei, J., Yu, W. C , and Cwikllnski, R. , "Detailed Simulation of a Moving-Bed Gasifier." EPRI Report AP-2576 (1982).
35. Cho, Y. S., and Joseph, B., "Experimental and Modeling Studies in Moving Bed Coal Gasification," American Chemical Society, pp. 56-60 (1981).
36. Govind, R., and Shah, J., "Modeling and Simulation of an Entrained Flow Coal Gasifier," AIChE Journal, Vol. 30, No. 1, pp. 79-92 (January, 1984).
37. Cena, R. J., Thorsness, C B., and Ott, L. L., "Underground Coal Gasification Data Base," UCID-19169 Rev. 1 (November, 1982).
38. Stephens, D. R., Thorsness, C B., Hi 11, R. W., and Thompson, D. S., "Underground Coal Gasification: UCG is Technically Feasible," Chemical Engineering Progress, pp. 43-44 (February, 1984).
39. Riggs, J. B., "Assessment of Lateral Cavity Growth Mechanisms," Proceedings of the 9th Annual UCG Symposium, Bloomlngdale, IL, pp. 227-236 (1983).
40. Yeary, D. L., "Experimental Study of Lateral Cavity Growth Mechanisms in Underground Coal Gasification," MS Thesis, Texas Tech University, Lubbock, TX (1987).
41. Re id, C R., Prausnitz, J. M., and Sherwood, T. K.. The Properties of Gases and Liquids, McGraw Hill (1977).
42. Thorsness, C B., Private Communication, Lawrence Livermore National Laboratories, CA (1986).
126
43. Camp, D. W., "A Model of Water Influx for UCG," MS Thesis, University of Colorado, Boulder, CO (1980).
44. Thorsness, C B., and Kang, S. W., "A General-Purpose, Packed-Bed Model for Analysis of Underground Coal Gasification Processes," LLNL Report UCID-2073 1 (April, 1986).
45- Sani, B., Private Communication, Dept. of Chemical Engineering, University of Colorado, Boulder, CO (1985).
APPENDIX A
PROXIMATE ANALYSIS AND DEVOLATILIZATION
DATA FOR ILLINOIS AND WYOMING COALS
127
128
Tab 1e A.1 Typ i ca1 DevoI at iIi zat i on Data
Fractional Distribution of Volatiles (weight percent)
tar, oil plus phenol 207. chemical water 237. coal gas 57%
Distribution of Coal Gas (7.v/v)
CH4 H2 CO C02
other (hydrocarbon. H2S, N2)
50.3 13. 1 20.6 6. 1 9.9
Table A.2 Distribution of Components in Coal by Proximate Analysis
I I 1i no i s Coa1 Wyom i ng Coa1
Moiture 10.23 17.06 Ash 9.10 5.80 Fixed Carbon 45.97 43.20 Volatile Matter 34.70 33.94
APPENDIX B
FLOW FIELD VERIFICATION
129
130
The results from the finite element code are compared
with the analytical solution for the following cases:
a) Poisson's equation, Cartesian coordinates
b) Laplace's equation, cylindrical coordinates.
Table B.l and Table 8.2 show a comparison between the
analytical and numerical solution for the two cases. It is
seen that the finite element code agrees well with the
analytical solution. Other cases were tested and checked.
The two main components of the numerical algorithm are the
finite element code (solving the pressure field) and the
material and energy balance solver. The generation terms
are obtained from the material and energy balance
subroutine. In Poisson's equation, the generation term is
1. For Laplace's equation, the generation term is 0.
Thus, the finite element code can be extended for
situations with varying generation terms.
131
Table B.1 Comparison of Analytical Solution with Finite Element Code for Poisson's Equation in Cartesian Coordinates
int
1
2
3
4
5
6
7
8
9
10
1 1
12
13
14
15
16
X
0.0000
0.3333
0.6667
1.0000
0.0000
0.3333
0.6667
1.0000
0.0000
0.3333
0.6667
1.0000
0.0000
0.3333
0.6667
1.0000
y
0.0000
0.0000
0.0000
0.0000
0.3333
0.3333
0.3333
0.3333
0.6667
0.6667
0-6667
0.6667
1.0000
1.0000
1.0000
1.0000
P model
0.0000
0.0000
0.0000
0.0000
0.0000
-0.1206
-0.1206
0.0000
0.0000
-0.1206
-0. 1206
0.0000
0.0000
0.0000
0.0000
0.0000
P ana 1yt
0.0000
0.0000
0.0000
0.0000
0.0000
-0.1207
-0.1207
0.0000
0.0000
-0.1207
-0.1207
0.0000
0.0000
• 0.0000
0.0000
0.0000
132
Table B.2 Comparison of Analytical Solution with Finite Element Code for Laplace's Equation in CyIindrica1 Coordinates
int
1
2
3
4
5
6
7
8
9
10
1 1
12
13
14
15
16
17
18
19
20
21
22
23
24
25
r
1.000
1.250
1.500
1 .750
2.000
1 .000
1.250
1.500
1 .750
2.000
1 .000
1.250
1.500
1 .750
2.000
1.000
1.250
1.500
1 .750
2.000
1.000
1.250
1.500
1 .750
2.000
z
0.000
0.000
0.000
0.000
0.000
0.250
0.250
0.250
0.250
0.250
0.500
0.500
0.500
0.500
0.500
0.750
0.750
0.750
0.750
0.750
1 .000
1 .000
1 .000
1 .000
1 .000
P model
0.0000
0.3219
0.5850
0.8074
1.0000
0.0000
0.3219
0.5850
0.8074
1.0000
0.0000
0.3219
0.5850
0.8074
1.0000
0.0000
0.3219
0.5850
0.8074
I.0000
0.0000
0.3219
0.5850
0.8074
1.0000
P analyti
0.0000
0.3219
0.5849
0.8072
1.0000
0.0000
0.3219
0.5849
0.8072
1.0000
0.0000
0.3219
0.5849
0.8072
1.0000
0.0000
0.3219
0.5849
0.8072
1.0000
0.0000
0.3219
0.5849
0.8072
1.0000
APPENDIX C
LIST OF COMPUTER PROGRAMS
133
134
c C UCG CIAVITY GROWTH MODEL: VIJAY A. SHIRSAT C C THIS PROGRAM YIELDS A PREDICTIVE ESTIMATE OF THE LATERAL GROWTH C OF THE CAVITY FORMED DURING UNDERGROUND COAL GASIFICATION. THE C UNDERSTANDING OF THIS PHENOMENON IS ESSENTIAL IN ORDER TO MAXIMIZE C THE RESOURCE RECOVERY OF COAL. C THE INPUT PARAMETERS FOR THE MODEL ARE THE FEED RATE OF THE GAS C MIXTURE INJECTED INTO THE COAL BED, THE MOLAR RATIO OF OXYGEN TO C STEAM IN THE FEED, INJECTION TEMPERATURE AND PRESSURE. BASED ON C THIS, THE PROGRAM LOCALIZES A COMBUSTION ZONE WHEREIN CONSTANT C PRESSURE PREVAILS. THE EQUILIBRIUM PARAMETERS FOR THE VARIOUS C PEACTIONS OCCURING HEREIN DETERMINE THE EXIT TEMPERATURE AND C COMPOSITION OF GAS FROM THE COMBUSTION ZONE. IN ADDITION, AN C ADIABATIC FLAME TEMPERATURE CJOiCULATION YIELDS THE MAXIMUM POSSIBLE C TEMPERATURE. C SIMULTANEOUSLY, THE LAPLACE'S EQUATION IS SOLVED INITIALLY TO YIELD C THE PRESSURE DISTRIBUTION THROUGH THE RUBBLE BED (THE INITIAL DIMEN-C SIONS OF WHICH ARE ASSUMED). THE BED IS DISCRETIZED INTO A NUMBER OF C NODE POINTS FOR NUMERICAL PURPOSES. ALSO, THE EFFECTIVE VOLUME OCC-C UPIED BY A PARTICULAR GRID POINT IN ADDITION TO THE FLOW AREA BETWEEN C ONE POINT AND ANOTHER IS CALCULATED AND UTILIZED IN DETERMINING THE C TEMPERATURES AND COMPOSITIONS OF THE GAS THROUGH THE BED. PERMEABI-C LITY VARIATIONS CJ^ BE MADE BY EQUATING THE FLOW THROUGH THE VOID C SPACE TO THE INJECTION FLOW FOR THE CASE OF NO GENERATION (LAPLACE'S C EQUATION). AFTER THIS IS ACCOMPLISHED, AN ITERATIVE PROCEDURE IS C ADOPTED WHICH INVOLVES PASSING THE APPROPRIATE GENERATION TERMS TO C THE PRESSURE DISTRIBUTION PROBLEM YIELDING VARIOUS FORMS OF POISSON'S C EQUATION. THE RESULTANT PRESSURE VARIATION YIELDS A NEW SET OF GENE-C RATION TERMS WHICH IS PASSED BACK AND THE WHOLE PROCESS IS REPEATED C UNTIL CONVERGENCE IS OBTAINED. NEXT, A TIME STEP IS TAKEN DURING C WHICH A CERTAIN AMOUNT OF COAL SPALLS FROM THE ROOF AND IS CONSUMED C AT THE SIDE WALL. THESE SPALLING RATES ARE TAKEN FROM FIELD TEST C DATA. IN ADDITION, THE LOCAL PROPERTIES OF THE BED WILL VARY. THE C SPALLING OF THE COAL AND THE VOLUME OF THE COAL CONSUMED IN THE C RUBBLE BED WILL YIELD A NEW HEIGHT OF THE BED IN THE TIME STEP C CONSIDERED (WHICH SHOULD BE LARGE ENOUGH TO FACILITATE THE NUMERICAL C PROCEDURES EMPLOYED). CONSEQUENTLY, A DISCRETIZATION YIELDS A NEW C GRID FOR WHICH THE OVERALL PROCESS IS REPEATED. IN THIS MANNER, THE C GROWTH OF THE CAVITY IS PREDICTED AND THE PRODUCT GAS HEATING VALUES C AND COMPOSITIONS ARE CALCULATED. C
c c C INITIALIZATION SECTION C c c
COMMON /MY/ VI (128) COMMON /ONE/ CSTCO,CSTC02,CSTH2,CSTH20,CSTCH4 COMMON /POINT/ NNP,NX,NE COMMON /PTBAL/ INPT COMMON /DISTAN/ DIS(50,50) COMMON /ARE/ AREA(50,50) COMMON /VOLUM/ VOLUME(50) COMMON /SIX/ AC02,BC02,CC02,AH2,BH2,CH2,ACH4,BCH4,CCH4 COMMON /SEVEN/ ACO,BCO,CCO,AH20,BH20,CH20 COMMON /NODE/ Nl(70),N2(70),N3(70),N4(70) COMMON /TWO/ XCOUT(50),XH2OUT(50),XCO2OT(50),XH2UT(50),XCH4OT(50) 1,TOUT(50),XTOT(50) COMMON /THREE/ BIGG(128,2),PR(128,2),ISUM COMMON /PRE/ APR COMMON /FINl/ TAD,FRSCON,SECCON COMMON /GENER/ GENR(50) COMMON /MORE/ GENSUM COMMON /PARM/ RATEl,RATE2,RATE3,VOL,RATE4
135
COMMON /CONS/ CARCON COMMON /CB/ CARGAS COMMON /NET/ TOTVOL,VERTSP,TIMEFR COMMON /NETT/ ITIME COMMON /COUNT/ ILL COMMON /MOLFLW/ FIVEl(50),XTOTIN(50),Q(50,50) COMMON /PERMEA/ PERM,PERNEW COMMON /INJECT/ MATINJ COMMON /FACTAR/ PACT(50) COMMON /HEAT/ HIN,HOUT,RTERM COMMON /FECDTA/ TC(4 8),COORD(182,2) COMMON /FECDTl/ IE (52,9),IP(128,2) COMMON /DENSE/ DENCOL COMMON /VCY/ BIGBRO COMMON /CHECK/ DELHI,THC0N,DELT2,VEL0CY,FRCIN,DELHVP COMMON /CHEK/ DELH2,DELH3,DELH4 COMMON /HCHEK/ HINCO,HINC02,HINH20,HINH2,HINCH4 COMMON /HCHECK/ H0TC0,H0TC02,H0TH20,H0TH2,H0TCH4 COMMON /VCK/ VELCON COMMON /RCHEK/ DEri,DEF2,DEF3,DEF4,DEF1A,DEF1B,DEF1C,DEF4A COMMON /RCHEC/ DEF2A,DEF2B,DEF2C,DEF3A,DEF3B,DEF3C,DEF4B COMMON /RCHECl/ ETA2,DIAPRT,DIAUNR,CARBO,RINT2,AMTC0F,DIFFUE COMMON /RCaffiC2/ WASHO,BEE,AONE,BONE,QU,QUT,SONE,STWO,STWOR COMMON /RCHEC3/ BTWO,BTWOR COMMON /PARG/ FRACIN(2) DIMENSION X(5),FX(5),T(3),A(6,6),XINC(5),FN(3)
C C DATA INPUT SECTION C C
DATA PNCO,PNC02,PNH20,PNH2,PNCH4,PNVM,PNCHAR/0.206, 1.061, .1706,.131,.503,.3394, .49/ DATA TREF,TBPOIT,HLV/536.4,671.4,18036./ DATA C0LHCA,C0LHCB,C0LHCC/.2, .00088, .0015/ DATA CPC01,CPC021,CPH201,CPH21,CPCH41/7.75,12.25,9.52,7.2,15.7/ DATA CPC02,CPC022,CPH202,CPH22,CPCH42/7.72,12.22,9.5,7.1,15.6/ DATA CPCO3,CPCO23,CPH2O3,CPH23,CPCH43/7.7,12.2,8.75,7.05,15.5/ TPYROL-2200. TEEl-100. TEE2-(TPYROL-4 60.-32.)-5./9 .
C C THE FOLLOWING CALCULATES THE HEAT CAPACITY OF COAL FOR THREE C DIFFERENT REGIMES IN THE CAVITY. THE DENSITY OF COAL, THE C VOID SPACE AREA, THE TIME STEP TAKEN FOR CAVITY GROWTH AND THE C SPALLING RATE IS SET. AN INITIAL PERMEABILITY ESTIMATE IS BASED C UPON THE KARMAN-COZENY EQUATION. C
CPCOLl-12.• (COLHCA+COLHCB*(TEE1+TEE2)/2.+COLHCC«PNVM) TEEAMB-25. CPCOL2-12.•(COLHCA+COLHCB*(TEEAMB+TEEl)/2.+PNVM-COLHCC) CPC0L3-12.•(COLHCA+COLHCB*(TEE2+10.)+COLHCC*PNVM) DENCOL-1.35 DENCOL-DENCOL*30.48**3/454.*PNCHAR TIMEFR-24.*3600. VERTSP-3. VELO-VERTSP/TIMEFR VODARE-10.*10. MATINJ-1 ICOUNT-1 PERM-6.47221E-9 FRACIN(l)-0.6 DO 400 1-1,50 GENR(I)-0.
4 00 CONTINUE DO 500 1-1,50 PACT(I)-0.0
136
500 CONTINUE 1000 ITIME-1
TOTVOL-0. CARGAS-0.
C C ITIME IS THE COUNTER FOR THE TIME STEP (1 DAY) AND ILL IS THE C COUNTER TO CHECK FOR CONVERGENCE OF THE FLOW FIELD. C
DO 399 ITIME-1,15 C DO 300 ILL«1,3
ILL-1 32 CARBON-0.
CARB-0. CALL FLOW CJILL AFT TOTX-CSTCO+CSTC02+CSTH2+CSTH20+CSTCH4 WRITE(6,195) TAD,FRSCON,SECCON,CARCON
195 FORMAT(5X,'ADIABATIC FLAME TEMPERATURE- ',E15.7,//,5X, 1'CONVERSION IN C-H20 REACTION- ',E15.7,//,5X, 1'CONVERSION IN WATER GAS REACTION- ',E15.7,//,5X, 1'CARBON CONSUMED IN COMBUSTION ZONE- ',E15.7) CALL ORDER
C SOME INITIAL ESTIMATES OF THE MOLE FRACTIONS OF THE FIVE SPECIES C (CO, C02, H20, H2, CH4) ARE GIVEN WHIC:H ARE LATER MODIFIED TO GET C THE FINAL MOLE FRACTIONS. C
X(l)-0.2887529 X(2)-0.16164 X(3)-0.30397 X(4)-0.2456 X(5)-0.7E-8 N-5 ERLIM-l.E-4 DO 401 1-1,50 GENR(I)-0.0
401 CONTINUE GENSUM-0. NYY-NNP-NX DO 78 9 M0-1,NYY
C C L REFERS TO THE NODE POINT AND APR TO THE PRESSURE. A VARYING C ASH RESISTANCE CAN BE SET THROUGH THE BED. C
L-IFIX(PR(M0,1)) APR-PR(MO,2) IF(ILL.EQ.3) GO TO 1032 GO TO 1033
1032 WRITE (6,91) L,APR 91 F0RMAT(5X,//,5X,'NODE POINT « IS- ',12,4X,'PRESSURE IS- ',E15.7)
C1033 WRITE(6,1211) COORD(L,1),COORD(L,2) C1211 FORMAT(5X,'X- ' ,E15.7,2X, 'Y- ',E15.7) C1033 IF(COORD(L,2).GE.1.0) GO TO 800 C GO TO 801 C 800 FRACIN(l)-0.2 C GO TO 802 C 801 IF(COORD(L,2).GE.0.5) FRACIN(1)-0.4 C IF((C00RD(L,2).GE.0.0).AND.(C00RD(L,2).LT.0.5)) FRACIN(1)-0.7 C IF(COORD(L,2).LT.0.0) WRITE(6,6000) C6000 FORMAT(' ERROR, COORD(L,2) LESS THAN 0.0') C IF(COORD(L,2).LT.0.0) STOP 1033 FRACIN(2)-l.O-FRACIN(l)
C C INITIAL ESTIMATES ARE GIVEN FOR THE TEMPERATURE, THE SIXTH PARAMETER C WHICH IS ESTIMATED BY THE SECANT ROUTINE. THIS REQUIRES TWO ESTIM-C ATES, NAMELY, THE LOWER AND UPPER BOUND. THE TRUE TEMPERATURE VALUE
137
C LIES IN BETWEEN. C
TLOW-1800. IF(ILL.GT.l) GO TO 300 IF(MO.EQ.l) GO TO 1210 IF(COORD(L,1).EQ.O.) GO TO 1201 GO TO 1202
1201 JEE-L-NX JEEP-JEE-1 DIFFT-(TOUT(JEEP)-TOUT(JEE))*DIS(JEE,JEEP)/DIS(L,L-NX-1) TLOW-TOUT(JZEP)-DIFrT-50. v /*- «* A; GO TO 1210
1202 DO 1203 1-1,3 LA-(NX+l)*I+2 IF((L.EQ.2).OR.(L.EQ.LA)) GO TO 1204
1203 CONTINUE GO TO 1205
1204 JEE-L+NX+1 JEEP-JEE-1 DIFFT- (TOUT (JEEP) -TOUT (JEE) ) *DIS (JEE, JEEP) /DIS (L, L-1) TLOW-TOUT(JEE)-DIFFT-50. GO TO 1210
1205 DO 1206 1-5,7 LA-(NX+l)*I+2 IF(L.EQ.LA) GO TO 1207
1206 CONTINUE GO TO 1208
1207 DIFFT-TOUT(L-NX-1)-400. TLOW-DIFFT-50. GO TO 1210
1208 DIFFT-(TOUT(L-2)-TOUT(L-1))-DIS(L-1,L-2)/DIS(L, L-1) TLOW-TOUT(L-1)-DIFFT-400,
999 FORMAT(5X,'TLOW- ',E15.7) GO TO 1210
300 TLOW-TOUT(L)-200. 1210 KW-1
T(KW)-TLOW CALL NEWTON (N, X, FX, ERLIM, XINC, A, FN, KW, T, L) ALOW-FN(l) TUPP-TLOW+30.
15 KW-2 T(KW)-TUPP CALL NEWTON (N, X, FX, ERLIM, XINC, A, FN, KW, T, L) UPP-FN(2) IF(ALOW*UPP.GT.0.0) GO TO 57
112 TMID-TUPP-(UPP*(TUPP-TLOW)/(UPP-ALOW) ) KW-3 T (KW) -TMID IF(ABS((TMID-TUPP)/TMID).LE.l.E-5) GO TO 36 IF(ABS((TMID-TLOW)/TMID).LE.l.E-5) GO TO 36 CALL NEWTON (N, X, FX, ERLIM, XINC, A, FN, KW, T, L) AMID-FN(3) IF((UPP*AMID).GT.0.0) GO TO 96 TLOW-TMID ALOW-AMID GO TO 112
96 TUPP-TMID UPP-AMID GO TO 112
57 TUPP-TUPP+10.0 GO TO 15
C C THIS IS THE FINAL CALL TO THE NEWTON ROUTINE WHICH GIVES US THE C CONVERGED VALUES FOR THE GAS COMPOSITIONS AT THE TEMPERATURE WHICH C WAS DETERMINED FROM THE SECANT ROUTINE. C
138
36 CALL NEWTON (N,X,FX, ERLIM, XINC, A, FN, KW,T,L) XC0UT(L)-X(1) XC020T(L)-X(2) XH20UT(L)-X(3) XH2UT(L)-X(4) XCH40T(L)-X(5) T0UT(L)-T(3) IF(ILL.EQ.3) GO TO 1098 GO TO 1099
1098 WRITE(6,197) 197 FORMAT(5X,/,5X,'MATERIAL AND ENERGY BALANCES HAVE CONVERGED')
WRITE(6,198) XCOUT(L),XC020T(L),XH20UT(L),XH2UT(L),XCH40T(L) 1,T0UT(L)
198 F0RMAT(5X,(5(2X,E15.7)),/,5X,'TEMPERATURE OUT- ',E15.7) WRITE(6,902) L,N1(L),N2(L),N3(L),N4(L),AREA(L,N1(L)), 1AREA(L,N2(L)) , AREA(L,N3 (L) ) , AREA(L,N4 (L) ) , VOLUME (L)
902 F0RMAT(5X,(5(2X,I2)),/,5X,(5(2X,E15.7))) WRITE (6,901) FIVEl (L),XTOTIN(L),FN(KW)
901 FORMAT(5X,'FLOW OUT- ',E15.7,2X,'FLOW IN- ',E15.7,2X, I'FN- ',E15.7)
1099 GENSUM-GENSUM+GENR(L) CARGAS-CARGAS+ (RATE1+RATE1+RATE3) *12 . "VOLUME (L) TOTCAR-TIMEFR* (CARGAS+CARCON) TOTVOL-TOTCAR/DENCOL/2.•0.5 RTOTY-RATEl+RATE2-RATE3 RSIDE-GENR(L)/RTOTY IF(ILL.EQ.3) GO TO 1114 GO TO 1115
1114 WRITE (6,1112) RTOTY,RSIDE 1112 FORMAT(5X,'NET GENERATION- ',E15.7,/,5X,'RSIDE- ',E15.7)
WRITE (6,1113) HIN,HOUT,RTERM,DIFFT 1113 FORMAT(5X,'HIN- ',E15.7,2X,'HOUT- ',E15.7,2X,
I'HEAT GEN- ',E15.7,2X,'DEF- ',E15.7) WRITE(6,9993) GENSUM,GENR(L),CARGAS,VOLUME(L),RTOTY
9993 FORMAT(5X,'GENSUM- ',E15.7,2X,'CONTR GEUR' ',E15.7,/,5X, I'CARGAS- ' ,E15. 7, 2X,'VOLUME (D- ' , E15 . 7, 2X, ' NET GENER- ',E15.7) WRITE(6,1111) RATEl,RATE2,RATE3,RATE4
1111 FORMAT(5X,'RATES',2X,(4(2X,E15.7))) 6015 FORMAT(5X,'WASHO- ',E15.7,2X,'B- ',E15.7,2X,'Al- ',E15.7,/,
15X,'B1- ',E15.7,2X,'Q- ',E15.7,2X,'QT- ',E15.7./,5X,'SI- ',E 11S.7,2X,'S2- ',E15.7,2X,'S2R- ',E15.7,/,5X,'B2- ',E15.7,2X, l'B2R- ',E15.7)
6014 FORMAT(5X,'MC- ',E15.7,2X,'DP- ',E15.7,2X,'DUP- ',E15.7,/,5X, I'ETA- ',E15.7,2X,'RK2- ',E15.7,2X,'DIFF- ',E15.7,/,5X, I'CARBO- ',E15.7)
6011 FORMAT(5X,'RTl- ',E15.7,2X,'RT2- ',E15.7,2X, ' R3- ',E15.7,/, 15X,'R4- ',E15.7,2X,'RIA- ',E15.7,2X,'RIB- ',E15.7,/,5X,'RIC- ',E 115.7,2X,'R2A- ',E15.7,2X,'R2B- ',E15.7,/,5X,'R2C- ',E15.7,2X, l'R3A- ',E15.7,2X,'R3B- ',E15.7,/,5X,'R3C- ',E15.7,2X,'R4A- ',E 115.7, 2X, 'R4B- ',E15.7)
602 FORMAT(5X,'DELHI- ',E15.7,2X,'DELH2- ',E15.7,2X,'DELH3- ',E15.7 1,/,5X,'DELH4- ',E15.7,2X,'V0L- ',E15.7,2X,'THCON- ',E15.7,/,5X, l'D2- ',E15.7,2X,'VCY- ',E15.7,2X,'DENC- ',E15.7,/,5X, I'FRCI- ',E15.7,2X,'TIM- ',E15.7,2X,'DVP- ',E15.7,/,5X, I'AREA- ',E15.7,2X,'DIS- ',E15.7) WRITE(6,603) HINCO,HINC02,HINH20,HINH2,HINCH4 WRITE(6,6 0 4) HOTCO,H0TC02,H0TH2 0,H0TH2,HOTCH 4
603 FORMAT(5X,'HC0- ',E15.7,2X,'HC02- ',E15.7,2X,'HWAT- ',E15.7 1,/,5X,'HH2- ',E15.7,2X,'HCH4- ',E15.7)
604 FORMAT(5X,'H0C0- ',E15.7,2X,'H0C02- ',E15.7,2X,'HOWAT- ',E15.7 1,/,5X,'H0H2- ',E15.7,2X,'H0CH4- ',E15.7)
1115 IF(L.EQ.NNP) GO TO 790 789 CONTINUE
790 ILL-ILL+1 IF(ILL.GE.4) GO TO 405 GO TO 32
139
39 IF(IC0UNT.EQ.3) GO TO 405 FACTOR-0. NXPLl-NX+1 QSUM-0.
C C A CORRECTION FOR THE PERMEABILITY IS MADE BASED ON GENERATION.
DO 402 1-1,6 LPY-NNP-2.*NX+(NX-I) Q(LPY,N2(LPY))-FIVEl(LPY)/AREA(LPY,N2(LPY) ) QSUM-QSUM+Q(LPY,N2(LPY)) FACTOR-FACTOR+PACT(LPY)
402 CONTINUE PERNEW-(GENSUM+TOTX)"PERM/FACTOR PERM-PERNEW WRITE (6, 419) NXPLl, NX, FACTOR, GENSUM, TOTX, PERM if??SJ7i^^;'^4%''"'2X''N3«" M2,2X,'FACTOR- ' ,E15 . 7,/, 5X, I'GENSUM- ',E15.7,2X,'T0TX- ',E15.7,2X,'PERM- ',E15.7) MATINJ-2 / -- / DO 403 L-1,NNP GENR(L)-GENR(L)*PERM/PERNEW
403 CONTINUE ICOUNT-ICOUNT+1 GO TO 1000
405 FLSUM-0.0 COI-0. CO2I-0. H2OI-0. H2I-0. CH4I-0. TEMI-0. DO 407 1-1,6 LPY-NNP-(NX+1)+I
C C THE TEMPERATURES AND GAS COMPOSITIONS AT THE TOP OF THE BED ARE C CALCULATED AND BASED ON SPALLING RATES, A MATERIAL AND ENERGY C BALANCE IS PERFORMED TO OBTAIN COMPOSITIONS AND HEATING VALUES OF C GAS FROM THE VOID SPACE C
COI-COI+XCOUT(LPY)*FIVE1(LPY) C02I-C02I+XC020T(LPY)"FIVEl(LPY) H20I-H20I+XH20UT(LPY)-FIVEl(LPY) H2I-H2I+XH2UT(LPY)"FIVEl(LPY) CH4I-CH4I+XCH40T(LPY)*FIVE1(LPY) TEMI-TEMI+TOUT(LPY)•FIVEl(LPY) FLSUM-FLSUM+FIVEl(LPY) WRITE(6,414) C0I,C02I,H20I,H2I,CH4I,FLSUM,TEMI
414 F0RMAT(2X,(7(2X,E15.7))) 4 07 CONTINUE
COBED-COI C02BED-C02I H20BED-H20I H2BED-H2I CH4BED-CH4I TBED-TEMI/FLSUM TPYROL-TBED-30. WRITE(6,412) COBED,C02BED,H20BED,H2BED,CH4BED,FLSUM, TBED
412 FORMAT(2X,(7(2X,£15.7))) CONT1»COBED*CPC01+C02BED*CPC021+H20BED*CPH201+H2BED*CPH21 1+CH4BED^CPCH41 CONT2-COBED*CPC02+C02BED^CPC022+H20BED*CPH202+H2BED*CPH22 1+CH4BED*CPCH42 CONT3-PNCO*CPC03+PNC02*CPC023+PNH2*CPH23+PNCH4*CPCH43 TERMl-(TBED-TREF)*C0NT1 TERM2-(TREF-4 60.)•C0NT2 TERM12-VELO*VODARE*DENCOL*1.25*0.5/12.
140
TERM3-CONT3*PNVM^(TPYROL-460.)•TERM12 TERM4-CPC0L1*(1.-PNH20)*TERM12*(TPYROL-TBPOIT) TERM5-TERM12*CPC0L2*(TBPOIT-TREF) TERM6-HLV*PNH20*TERM12 TERM7-TERM12*(TBPOIT-460.)*PNH20*CPH203 TERM8-TERM12^PNCHAR^CTCOL3*(TPYROL-460.) RIGHT-TERM1+TERM2+TERM3+TERM4+TERM5+TERM6+TERM7+TERM8 TERM9-C0NT3•PNVM^TERMl2 TERMl0-TERM12•PNH20«CPH203 TERMl1-PNCHAR*CPC0L3 *TERM12 ALEFT-TERM9+TERM10+TERM11+CONT2 TVOD SP-RIGHT/ALEFT C0VD-C0BED+TERM12*PNC0*PNVM C02VD-C02BED+TERMl2 * PNC02 *PNVM H20VD-H20BED+TERM12•PNH20 K2VD«H2BED+TERM12*PNH2*PNVM CH4VD-CH4BED+TERM12•PNCH4 *PNVM WRITE(6,411) C0VD,C02VD,H2OVD,H2VD,CH4VD,TVODSP
411 FORMAT(5X,'VOID CO- ',E15.7,2X,'VOID C02- ',E15.7,/,5X, I'VOID H20- ',E15.7,2X,'VOID H2- ',E15.7,/,5X,'VOID CH4- ', 1E15.7,2X,'TEMP VOID SPACE- ',E15.7) GASUM-C0VD+C02VD+H2VD+CH4VD HVLCO-COVD/GASUM*28.^4348.0285 HVLH2-H2VD/GASUM-122970.6 HVLCH4-CH4VD/GASUM-16.*23940. HVLGAS-(HVLCO+HVLH2+HVLCH4)/359. WRITE(6,513) HVLGAS,HVLC0,HVLH2,HVLCH4
513 F0RMAT(5X,(4(2X,E15.7))) BIGBRO-(TOUT(6)+TOUT(12)+T0UT(18)+TOUT(24)+TOUT(30) )/5 . IF(ITIME.EQ.l) TAV-(TOUT(6)+TOUT(12)+TOUT(18)+TOUT(24)+TOUT(30) ) /5 WRITE(6,514) BIGBRO,TAV,VELCON
C C THE SIDE WALL GROWTH IS ASSUMED TO BE DEPENDENT ON GASIFICATION AND C THE VELOCITY IS TAKEN AS A DIFFERENCE BETWEEN THE AVERAGE SIDE WALL C TEMPERATURE AND A FIXED TEMPERATURE. C
IF(ITIME.EQ.l) VELCON-1./(TAV-2000.) 514 FORMAT(5X,'AVE TEMP- ',E15.7,2X,'1ST TIME AV TEMP- ',E15.7,/,
15X,'VELCON (K-D- ',E15.7) 399 CONTINUE
STOP END SUBROUTINE AFT
C C THIS ROUTINE UTILIZES THE INLET TEMPERATURE, COMPOSITION, AND C EQUILIBRIUM PARAMETERS ALONG WITH HEAT CAPACITY, HEAT OF REACTION C DATA TO CALCULATE THE MAXIMUM ADIABATIC FLAME TEMPERATURE, CONVER-C SION IN THE WATER GAS AND C/C02 REACTIONS THEREBY YIELDING THE OUT-C LET TEMPERATURE AND COMPOSITION OF GAS FROM THE COMBUSTION ZONE. C THE OXYGEN INJECTED IS ASSUMED TO BE DEPLETED. C
COMMON /ONE/ CSTCO,CSTC02,CSTH2,CSTH20,CSTCH4 COMMON /SIX/ AC02,BC02,CC02,AH2,BH2,CH2,ACH4,BCH4,CCH4 COMMON /SEVEN/ ACO,BCO,CCO,AH20,BH20,CH20 COMMON /TEMPER/ TC COMMON /FINl/ TAD,FRSCON,SECCON COMMON /CONS/ CARCON CARCON-0.0 TAD-2800.0 ITMAX-50 EPS-l.OE-5 DELTAH—94 051.0 X-0.0232126 A-3.0 ACH4-3.381 BCH4-10.03E-3
141
C C H 4 — 1 . 3 2 7 E - 6 A C O 2 - 1 0 . 5 7 B C 0 2 - 2 . 1 / ( 1 . 8 * 1 0 0 0 . ) C C O 2 - ( 2 . 0 6 * 1 . 8 ^ 1 . 8 * 1 . 0 E 5 ) A H 2 - 6 . 5 2 B H 2 - 0 . 7 8 / ( 1 . 8 * 1 0 0 0 . ) CH2— ( 1 . 8 ^ 1 . 8^0 . 1 2 E + 5 ) A C O - 6 . 7 9 B C O - 0 . 9 8 / ( 1 . 8 ^ 1 0 0 0 . 0 ) C C O - 3 5 6 4 0 . 0 A 0 2 - 7 . 1 6 B 0 2 - 1 . 0 / 1 8 0 0 . 0 CO2-129600.0 AH20-7.3 BH20-2.46/1800.0 CH2O-0.0 TBASE-537.0 TINLET-720.6 RGSCAL-1.987 HTWATG—9837.0 HTCSTM-31382.0 TC-2700.6 TERM3-A*X*(AH20*(TBASE-TINLET)+BH20/2.0*(TBASE**2-TINLET**2)) TERM4-X*(A02*(TBASE-TINLET)+B02/2.0*(TBASE**2-TINLET**2) 1+C02*(1.0/TBASE-l.0/TINLET)) C0NST-DELTAH*1.8*X+TERM3+TERM4-(X*AC02*TBASE) -1(X*BC02/2.0*TBASE**2)-(X-CC02/TBASE)-(A*X^AH20^TBASE) 1-(A*X*BH20/2.0*TBASE**2) ONE-X*AC02+A*X*AH20 TWO-X*BC02/2.0+A*X*BH2O/2.0 THREE-X*CC02 DO 4 ITER-1,ITMAX TNUM-(ONE*TAD+TWO*TAD*TAD+THREE/TAD+CONST) TDEN-(ONE+2.0*TWO*TAD-THREE/(TAD*TAD)) DELTAT-TNUM/TDEN TAD-TAD-DELTAT IF(ABS(DELTAT/TAD).GT.EPS) GO TO 4 GO TO 66
4 CONTINUE 66 WRITE(6,111) TAD
111 FORMAT(5X,'AD TEMP- ',E15.7) EQLK-0.0265*EXP(7860.0/(RGSCAL-1500.0)) REACHT-X*(A02*(TBASE-TINLET)+B02/2.0*(TBASE**2-TINLET**2) 1+C02*(1.0/TBASE-l.0/TINLET))+A*X*(AH20*(TBASE-TINLET)+BH20/2.0 1*(TBASE**2-TINLET**2))+DELTAH*1.8*X WATERH-(AH20* (TC-TBASE)+BH20/2.0*(TC**2-TBASE**2) ) COH-(ACO* (TC-TBASE)+BCO/2.0*(TC**2-TBASE**2)+CCO* 1 (1.0/TC-l.O/TBASE)) C02H-(AC02*(TC-TBASE)+BC02/2.0*(TC**2-TBASE**2)+CC02* 1(1.0/TC-l.O/TBASE)) H2H-(AH2*(TC-TBASE)+BH2/2.0*(TC**2-TBASE**2)+CH2* 1(1.0/TC-l.O/TBASE))
DEN0M-HTWATG«1.8-WATERH-COH+C02H+H2H C0ND1-REACHT+A*X*WATERH+X*C02H C0ND2-HTCSTM*1.8-WATERH+COH+H2H THIRD-(EQLK-1.0)•C0ND1**2/DEN0M**2+EQLK*A*X*C0ND1/DEN0M+X"
ICONDl/DENOM F I R S T — 1 . 0*EQLK+ (C0ND2) * * 2 * (EQLK-1. 0) / (DEN0M»*2) +C0ND2/DEN0M SECOND-2.*C0ND1*C0ND2*(EQLK-1.)/DENOM*«2+EQLK*A*X*COND2/DENOM
1+EQLK*A*X+C0ND1/DEN0M-X+X*C0ND2/DEN0M F I R S T - - 1 . 0 * F I R S T SECOND—1. 0*SECOND THIRD—1. 0*THIRD FRSCON-(-1.0*SECOND+SQRT(SECOND**2-4.0*FIRST*THIRD))/(2.0-FIRST) SECC0N--1.0/DENOM*(FRSC0N*C0ND2+C0ND1) CSTCO-FRSCON-SECCON
142
CSTC02-SECC0N+X CSTH20-A*X-FRSCON-SECCON CSTH2-FRSC0N+SECC0N CSTCH4-0.0 CARCON-(X+A*X*(1.-FRSCON))*12. RETURN END SUBROUTINE ORDER
C C THIS SUBROUTINE USES THE PRESSURE DISTRIBUTION FROM FLOW AND ARR-C ANGES THE NODE POINTS WITH THEIR CORRESPONDING PRESSURES IN ORDER C OF DECREASING PRESSURE EXCLUDING THE CONSTANT PRESSURE (CSTR) NODES. C AN ORDERED ARRAY PR IS OBTAINED SEQUENTIALLY. C
COMMON /MY/ VI (128) COMMON /THREE/ BIGG(128,2),PR(128,2) , ISUM COMMON /ONE/ CSTCO,CSTC02,CSTH2,CSTH20,CSTCH4 COMMON /TWO/ XCOUT(50),XH2OUT(50),XCO2OT(50),XH2UT(50),XCH4OT(50) 1,TOUT(50),XTOT(50) COMMON /MOLFLW/ FIVEl(50),XTOTIN(50) COMMON /TEMPER/ TC COMMON /POINT/ NNP,NX,NE COMMON /PTBAL/ INPT DIMENSION USA(128,2) ZT-26. DO 19 I-1,NNP BIGG(1,1)-FLOAT(I) BIGG(I,2)-VI(I)
19 CONTINUE ISUM-0 DO 36 I-1,NNP
444 FORMAT(5X,'NODE POINT • I S - ' ,E15.7,5X,'PRESSURE IS - ' , E 1 5 . 7 ) ISUM-IStJM+1
36 CONTINUE ISUMA-ISUM-1
2 DO 31 I-1,ISUMA 33 DO 32 L-I,ISUM
IF(BIGG(I,2).LT.BIGG(L,2)) GO TO 66 IF(L.EQ.ISUM) GO TO 31
. GO TO 32 66 USA(I,1)-BIGG(1,1)
USA(I,2)-BIGG(I,2) BIGG(I,1)-BIGG(L,1) BIGG(I,2)-BIGG(L,2) BIGG(L,1)-USA(I,1) BIGG(L,2)-USA(I,2)
32 CONTINUE 31 CONTINUE 771 FORMAT(5X,/,5X,'FOLLOWING IS THE ORDERED ( HIGHEST TO LOWEST )
IPRESSURE ARRAY') ICOUNT-0 DO 800 I-1,ISUM IF(I.EQ.6) GO TO 801 II-BIGG(I,1) XTOT(II)-CSTCO+CSTC02+CSTH20+CSTH2+CSTCH4 XCOUT(II)-CSTCO/XTOT(II) XH20UT(II)-CSTH20/XT0T(II) XC020T(II)-CSTC02/XT0T(II) XH2UT(II)-CSTH2/XT0T(II) XCH40T(II)-CSTCH4/XTOT(II) TOUT(II)-2700.6
111 FoSi-r^Xr^POIN"* IS- ', 12,/,5X,'MOLES OF CO OUT- ',E15_7 /,5X, I'MOLES OF C02 OUT - '^E15.7,/,5X,'MOLES OF H20 OUT- ',E15 7 / 5X, I'MOLES OF H2 OUT- ',E15.7,/,5X,'MOLES OF CH4 OUT - ,E15 7,/,5X, 1'OUTLET TEMP OF CSTR- ',E15.7,/,5X,'TOTAL MOLES OUT- ',E15.7)
143
c c c c c c c c
ICOUNT-ICOUNT+1 800 CONTINUE 801 I-ICOUNT+1
INPT-ISUM-ICOUNT-NX-1 IW-ISUM-NX DO 802 J-I,NNP IPT-J-ICOUNT PR(IPT,1)-BIGG(J, 1) PR(IPT,2)-BIGG(J,2)
: WRITE(6,113) PR(1PT,1) ,PR(IPT,2) 113 FORMAT(5X,'PRESSURE ARRAY - ',2E15.7) 802 CONTINUE
RETURN END SUBROUTINE NEWTON (N, X, FX, ERLIM, XINC, A, FN, KW, T, L)
THIS ROUTINE CALLS THE MATERIAL AND ENERGY BALANCE PROGRAM AND PASSES NEW MOLE FRACTIONS TO THE LINEAR EQUATION SOLVER WHICH YIELDS INCREMENTS IN MOLAR VALUES DEPENDING ON THE JACOBIAN GENERATED. IF THE INCREMENTAL VALUES SATISFY THE CONVERGENCE CRITERION THE FINAL MOLAR VALUES ARE PASSED TO MAIN WHERE A SECANT SEARCH METHOD IS USED TO ISOLATE THE CORRECT VALUE OF TEMPERATURE.
COMMON /TWO/ XCOUT(50) ,XH2OUT(50) ,XCO2OT(50) ,XH2UT(50) ,XCH4OT(50) 1,TOUT(50),XTOT(50) COMMON /THREE/ BIGG(128,2),PR(12e,2) , ISUM COMMON /SIX/ AC02,BC02,CC02,AH2,BH2,CH2,ACH4,BCH4,CCH4 COMMON /SEVEN/ ACO,BCO,CCO,AH20,BH20, CH20 COMMON /NODE/ Nl(70),N2(70),N3(70),N4(70) COMMON /PRE/ APR COMMON /GENER/ GENR(50) COMMON /PERMEA/ PERM,PERNEW COMMON /INJECT/ MATINJ COMMON /FACTAR/ PACT(50) COMMON /DISTAN/ DIS(50,50) COMMON /ARE/ AREA(50,50) COMMON /VOLUM/ VOLUME(50) COMMON /PARM/ RATEl,RATE2,RATE3,VOL,RATE4 COMMON /POINT/ NNP,NX,NE COMMON /COUNT/ ILL COMMON /MOLFLW/ FIVEl (50),XTOTIN(50),Q(50,50) COMMON /HEAT/ HIN,HOUT,RTERM COMMON /NET/ TOTVOL,VERTSP,TIMEFR COMMON /DENSE/ DENCOL COMMON /CHECK/ DELHI,THCON,DELT2,VEL0CY,FRCIN, DELHVP COMMON /CHEK/ DELH2,DELH3,DELH4 COMMON /HCHEK/ HINCO,HINC02,HINH20,HINH2, HINCH4 COMMON /NETT/ ITIME COMMON /HCHECK/ HOTCO,H0TC02,H0TH20,H0TH2, H0TCH4 COMMON /VCY/ BIGBRO COMMON /VCK/ VELCON COMMON /RCHEK/ DEF1,DEF2,DEF3,DEF4,DEF1A,DEF1B,DEF1C,DEF4A COMMON /RCHEC/ DEF2A,DEF2B,DEF2C,DEF3A,DEF3B,DEF3C,DEF4B COMMON /RCHECl/ ETA2,DIAPRT,DIAUNR,CARBO,RINT2,AMTC0F,DIFFUE COMMON /RCHEC2/ WASHO,BEE,AONE,BONE,QU,QUT,SONE,STWO,STWOR COMMON /RCHEC3/ BTWO,BTWOR COMMON /FECDTA/ TC(4 8),COORD(182,2) COMMON /FECDTl/ IE (52,9),IP (128,2) COMMON /PARG/ FRACIN(2) DIMENSION A(6,6) ,X(5) ,FX(5) ,XINC (5) , T (3) ,FN(3) SUM-0.0 ITEN-1
1 CALL SOLVE(X,FX,KW,T,FN,L) CALL DER(N,X,FX,KW,T,FN,L,A) DETER-SIMUL(5,A,XINC,l.E-5,0,6) DO 333 I-1,N
144
A L P H A - l . 0 X ( I ) - X ( I ) + A L P H A * X I N C ( I )
3 3 3 CONTINUE DO 10 I - 1 , N I F ( A B S ( X I N C ( I ) / X ( I ) ) .GE.ERLIM) GO TO 1 X R A T - X I N C ( I ) / X ( I )
10 CONTINUE ITEN-ITEN+1 RETURN END SUBROUTINE SOLVE(X,FX,KW,T,FN,L)
C c C THIS SUBROUTINE EVALUATES THE MATERIAL AND ENERGY BALANCES FOR C THE NODE POINTS IN THE ( IVITY. PREEXPONENTIAL FACTORS, INTRINSIC C RATE CONSTANTS, HEATS OF REACTION VALUES, ALONG WITH THE POROSITY C AND DIAMETER VALUES OF THE COAL PARTICLE (REACTED AND UNREACTED) , C AND THE DIFFUSIVITY AND VISCOSITY TERMS YIELD VALUES FOR THE C RATES OF THE FOUR REACTIONS CONSIDERED IN THE BED. THE FLOW TERMS C ARE EVALUATED BY DARCY'S LAW. IN ORDER TO DO THIS, WE HAVE TO C IDENTIFY A NODE POINT BY ITS NEAREST NEIGHBOR AND NOTE IF IT HAS C FLOW TO OR FROM ANY OF ITS NEAREST NEIGHBORS. THIS CRITERION IS C DETERMINED BY THE PRESSURE AT EACH NODE POINT AND THE FLOW IS TAKEN C TO BE FROM THE HIGHEST PRESSURE POINT TO THE LOWEST PRESSURE POINT C (THESE POINT (S) BEING THE ONES ON THE TOP OF THE BED, VOID SPACE) . C FIVE EQUATIONS BASED ON THE MOLE FRACTIONS OF THE COMPONENTS ARE C EVALUATED AND A SIXTH EQUATION FOR TEMPERATURE IS GOT BY THE C GENERATION TERMS AT THE VARIOUS NODE POINTS. THESE EQUATIONS ARE C SOLVED BY THE NEWTON AND SECANT METHODS TO YIELD COMPOSITION AND C TEMPERATURE VALUES THROUGHOUT THE RUBBLE BED. C C
COMMON /TWO/ XCOUT(50),XH2OUT(50),XCO2OT(50),XH2UT(50),XCH4OT(50) 1,TOUT(50),XTOT(50) COMMON /THREE/ BIGG(128,2),PR(128, 2) , ISUM COMMON /SIX/ AC02,BC02,CC02,AH2,BH2,CH2,ACH4,BCH4,CCH4 COMMON /SEVEN/ ACO,BCO,CCO,AH20,BH20,CH20 COMMON /PRE/ APR COMMON /GENER/ GENR(50) COMMON /NODE/ Nl(70),N2(70),N3(70),N4(70) COMMON /DISTAN/ DIS (50,50) COMMON /ARE/ AREA(50,50) COMMON /VOLUM/ VOLUME(50) COMMON /PARM/ RATE1,RATE2,RATE3, VOL, RATE4 COMMON /POINT/ NNP,NX,NE COMMON /PERMEA/ PERM,PERNEW COMMON /INJECT/ MATINJ COMMON /FACTAR/ PACT(50) COMMON /COUNT/ ILL COMMON /MOLFLW/ FIVEl(50),XTOTIN(50),Q(50,50) COMMON /HEAT/ HIN,HOUT,RTERM COMMON /NET/ TOTVOL,VERTSP,TIMEFR COMMON /DENSE/ DENCOL COMMON /CHECK/ DELHI,THCON,DELT2,VEL0CY,FRCIN, DELHVP COMMON /CHEK/ DELH2,DELH3,DELH4 COMMON /HCHEK/ HINCO,HINC02,HINH20,HINH2,HINCH4 COMMON /NETT/ ITIME COMMON /HCHECK/ HOTCO,H0TC02,H0TH20,H0TH2,H0TCH4 COMMON /VCY/ BIGBRO COMMON /VCK/ VELCON COMMON /RCHEK/ DEFl,DEF2,DEF3,DEF4,DEFIA,DEFIB,DEFIC,DEF4A COMMON /RCHEC/ DEF2A,DEF2B,DEF2C,DEF3A,DEF3B,DEF3C,DEF4B COMMON /RCHECl/ ETA2,DIAPRT,DIAUNR,CARBO,RINT2,AMTCOF,DIFFUE COMMON /RCHEC2/ WASHO,BEE,AONE,BONE,QU,QUT,SONE,STWO, STWOR COMMON /RCHEC3/ BTWO,BTWOR COMMON /FECDTA/ TC(48).COORD(182,2)
145
COMMON /FECDTl/ IE (52,9),IP (128,2) COMMON /PARG/ FRACIN(2) DIMENSION XCO(50,50),XCO2(50,50), 1XH20(50,50) ,XCH4(50,50) ,XH2(50,50) l,X(5),FX(5),T(3),FN(3),TE(3),RHOI(2)
C C THESE DIAMETER VALUES WERE CONSIDERED FOR THE BENCHMARKING PROCEDURE C TO CHECK THE MATERIAL AND ENERGY BALANCE PROGRAM AGAINST RUNS MADE BY C THORSNESS OF LLNL. C C DATA DIAP/8.432,8.441,8.45,8.458,8.465,8.472,8.479,8.485,8.491, C 18.4 96,8.501,8.506,8.512,8.523,8.545,8.592,8.68,8.816,8.991, C 19.176,9.351/ C DATA DIAU/7.918,7.933,7.947,7.96,7.972,7.984,7.994,8.004, C 18.013,8.021,8.029,8.037,8.047,8.064,8.1,8.175,8.311,8.522, C 18.787,9.061,9.314/
DATA PI,CONVDS,TIME,TREF/3.14,62.4 1,86400.,536.4/ DATA GASCT,RIDEAL,EPSEXT,EPSTOT,ARBG/10.73,8.314,0.52,0.76, 110.73/ DATA PRCON1,PRCON2/68097.456, 14.7/ DATA EPSIN,DIAPIN,EPSl,EPS2/0.5,9.435E-3,0.5, 0.5/ DATA ACTV1,ACTV2,ACTV3,ACTV4/-17500.,-17500.,-8025.,-13971./ DATA ACT1,ACT2,ACT3,ACT4/-20150.,-16310.,10982., 3920./ DELHl-74194.2 DELH2-56487.6 DELH3-39337.2 DELH4-16542. DELHVP-1000. DELTl-1.5 VELOCY-1.0
C V E L C O N - 1 . / 2 0 0 . I F ( I T I M E . G T . l ) VELOCY-VELCON*(BIGBRO-2000.)
C VELOCY-VELCON*(BIGBRO-2000.) R H O K D - I O O O . R H O I ( 2 ) - 1 0 0 0 . V I S C 1 - 4 . E - 6 V I S C 2 - 2 . 9 3 E - 8 TE (KW) - ( (T (KW) - 4 6 0 . - 3 2 . ) "5 . / 9 . ) + 2 7 3 . 0 VIST-VISC1+VISC2*TE (KW) DELFA-2 . •AC0-AC02 DELFB-2 .*BC0-BC02 DELFC-2.•CC0-CC02 DELSA-AC0+AH2-AH20 DELSB-BC0+BH2-BH20 DELSC-CC0+CH2-CH20 DELTA-ACH4-2. •AH2 DELTB-BCH4-2.*BH2 DELHI-DELHI+DELFA*(T(KW)-TREF)+(T(KW)••2-TREF**2)/2.-DELFB 1+(1./T(KW)-1./TREF)-DELFC DELH2-DELH2+DELSA*(T(KW)-TREF)+(T(KW)•*2-TREF**2)/2.-DELSB 1+(1./T(KW)-1./TREF)"DELSC DELH3—DELH3+DELTA*(T(KW)-TREF)+(T(KW)••2-TREF«*2)/2.-DELTB 1+CCH4/3.*(T(KW)••3-TREF**3)-2.*CH2*(1./T(KW)-1./TREF) DELH3—1.0*DELH3 DELEA-AC02+AH2-AC0-AH20 DELEB-BC02+BH2-BCO-BH20 DELEC-CC02+CH2-CC0-CH20 DELH4—DELH4+DELEA*(T(KW)-TREF)+DELEB/2.•(T(KW)••2-TREF-*2) * IDELEC*(1./T(KW)-1./TREF) DELH4 —1.0*DELH4
C C NON-UNIFORM RESISTANCES CAN BE SET THROUGH THE BED. C C FRACIN(1)-0.7 C IF (COORD (L, 2) .GE. 1.0) GO TO 800
146
C GO TO 801 C 800 FRACIN(l)-0.2 C GO TO 802 C 801 IF(COORD(L,2).GE.0.5) FRACIN(1)-0.4 C IF((COORD(L,2).GE.0.0).AND.(COORD(L,2).LT.0.5)) FRACIN(1)-0.7 C FRACIN(2)-l.O-FRACIN(l)
IF(MATINJ.EQ.2) PERM-PERNEW LPLl-L+1 LMNl-L-1 LMNX-L-NX-1 JACK-0
C C THE THERMAL CONDUCTIVITY AND VOID FRACTIONS ARE DETERMINED C LATER REACTED AND UNREACTED PARTICLE DIAMETERS ARE OBTAINED C
THCON-2. 4*1000.-.3048/(4.18*252. "3600.-LB) FRCIN-0.7 WASHO-FRACIN(l) BEE-FRACIN(l)/FRACIN(2) AONE-WASHO*RHOI(2)/RHOI(1) BONE-(l.O-EPSIN)/(1.0-EPSEXT) QU-((1.O+BEE)*1350.*0.49/2.*FRACIN(2))/(RHOI(2)•(1.O-EPSIN)) DO 600 1-1,10 J-(NX+1)*I IF(L.EQ.J) GO TO 601
600 CONTINUE GO TO 603
601 QU-((1.O+BEE)-1350.*0.49*FRCIN)/(RHOI(2)*(1.O-EPSIN)) 603 QUT-QU**0.33334
SONE-1.0-(1.0-AONE)*BONE*QU S TWO-AONE/SONE STWOR-STWO**0.3334 BTWO-BONE*QU BTWOR-BTWO*0.3334 DlAPRT-DIAPIN•STWOR DIAUNR-DIA?RT*BTWOR PVOL-6.*(1.-EPSEXT)/3.14/DIAPRT**3 PF-APR*(0.5-APR/250.)
C C ARRHENIUS RATE CONSTANTS ARE GIVEN. C
P R E X P l - 2 . 44E-3*RIDEJVL PREXP2-4 .07E-3*RIDEAL PREXP3-8 .26E-9*RIDEAL P R E X P 4 - 2 . 8 8 7 E S * 1 0 0 0 . * 0 . 2 * E X P ( - 8 . 9 1 + 5 5 5 3 . 0 / T E ( K W ) ) " P F AK10-1 .24E14 / (RIDEAL-TE(KW)) A K 2 0 - 3 . 1 4 E 1 2 / (RIDEAL*TE(KW)) AK30-1.45E-11*RIDEAL*TE(KW) A K 4 0 - 0 . 0 2 6 5 IF(ILL.GT.1) DELTl-TOUT(L)-TOUT(LPLl) DELT2-T0UT(LMNl)-T(KW)
C CALL VISCIT(X,APR,T,KW,VISCOS) VIS-VIST*0.3048/(.454*18.) CONCTL-APR*!.01325E5/(RIDEAL-TE(KW)) VOL-VOLUME(L) Z-PRC0N1*PRC0N2 ONE-0.0 TWO-0.0 THREE-0.0 FOUR-0.0 FIVE-0.0
C C THE PROCESS IS STARTED TO DETERMINE NODAL NEIGHBORS OF A NOCE POINT C BASED ON THE 5 PRESSURE VALUES (4 NEIGHBORS). FLOW OCCURS FRCM A C POINT OF HIGH PRESSURE TO LOW PRESSURE. VALUES BASED ON DARCY'S LAW C ARE CALCULATED.
147
DO 40 M-1,ISUM IF(IFIX(BIGG(M, D ) .EQ.Nl(L)) GO TO 39
40 CONTINUE 39 C«BIGG(M,2)
DO 41 M-1,ISUM IF(IFIX(BIGG(M, D ) .EQ.N2(L)) GO TO 38
41 CONTINUE 38 D-BIGG(M,2)
IF(N3(L) .EQ.49) GO TO 50 DO 42 M-1,ISUM IF(IFIX(BIGG(M, D ) .EQ.N3(L)) 60 TO 37
42 CONTINUE 37 E-BIGG(M,2) 13 IF(N4(L) .EQ.50) GO TO 51
DO 43 M-1,ISUM IF(IF1X(BIGG(M, D ) .EQ.N4(L))G0 TO 36
43 CONTINUE 36 F-BIGG(M,2)
GO TO 61 50 Q(N3(L) ,L)-0.
XC0(N3(L) ,L)-0. XC02(N3(L),L)-0. XH2(N3(L) ,L)-0. XCH4(N3(L) ,L)-0. XH20(N3(L) ,L)-0. T3—1. Q(L,N3(L))-0. XC0(L,N3(L) )-0. XC02(L,N3(L) )-0. XH2(L,N3(L) )-0. XCH4(L,N3(L) )-0. XH2O(L,N3(L))-0. GO TO 13
51 Q(N4(L) ,L)-0. XC0(N4(L) ,L)-0. XC02(N4(L) ,L)-0. XH20(N4(L) ,L)-0. XK2(N4(L) ,L)-0. XCH4(N4(L) ,L)-0. T4-1. Q(L,N4(L))-0. XC0(L,N4 (L) )-0. XC02(L,N4(L))-0. XH2O(L,N4(L))-0. XH2(L,N4(L))-0. XCH4(L,N4(L))-0.
61 IF(C.GT.APR) GO TO 71 Q(N1(L) ,L)-0. XC0(N1(L) ,L)-0. XC02(Nl(L),L)-0. XH2(N1(L) ,L)-0. XCH4(Nl(L),L)-0. XH20(N1(L) ,L)-0. XCOUT(Nl(L))-0. XC020T (Nl(L))-0. XH20UT(Nl(L))-0. XH2UT(N1(L) )-0.
Q a^Nl (Ln^--i"o*PERM-Z*APR* (C-APR) / (VIS*GASCT*T (KW) 1«DIS(L,N1(L))) ONE-Q(L,Nl(L))*AREA(L,Nl(L)) Tl-1.
62 IF(D.EQ.APR) GO TO 701 ir(D.GT.APR) GO TO 72 Q(N2(L) ,L)-0.
148
XCO(N2'L),L)»0. XC02 (N2 (L) , L) -0 . XH2(N2(L),L)-0. XCH4(N2(L),L)-0. XH20(N2(L),L)-0. XCOUT (N2(L))-0. XC020T(N2(L))-0. XH20UT(N2(L))-0. XH2UT(N2(L))-0. XCH40T(N2(L))-0. Q (L, N2 (L) ) — 1 . 0*PERM*Z*APR* (D-APR) / (VIS*GASCT*T (KW) 1*DIS(L,N2(L))) TWO-Q(L,N2(L))»AREA(L,N2(L)) T2-1. GO TO 63
63 IF(N3(L).EQ.49.) GO TO 64 IF(E.GT.APR) GO TO 73 Q(N3(L) ,L)-0. XCO(N3(L),L)-0. XCO2(N3(L),L)-0. XH2(N3(L),L)-0. XCH4(N3(L),L)-0. XH20(N3(L) ,L)-0. XCOUT(N3(L))-0. XC020T(N3(L))-0. XH20UT(N3(L))-0. XH2UT(N3(L))-0. XCH40T(N3(L))-0. TOTM3-0.0 Q (L, N3 (L) ) — 1 . 0*PEPM*Z*APR* (E-APR) / (VTS*GASCT*T (KW) 1«DIS(L,N3(L))) THREE-Q(L,N3(L))*ARZA(L,N3(L)) T3-1. GO TO 64
64 IF(N4(L).EQ.50) GO TO 100 ir(F.GT.APR) GO TO 74 Q(N4(L) ,L)-0. XC0(N4 (L) ,L)-0. XC02(N4 (L) ,L)-0. XH2(N4(L) ,L)-0. XCH4(N4(L),L)-0. XH20(N4(L) ,L)-0. XCOUT(N4(L))-0. XC020T(N4(L))-0. XH20UT(N4(L))-0. XH2UT(N4(L) )-0. XCH40T(N4(L))-0. Q (L, N4 (L) ) — 1 . 0*PERM*Z*APR* (F-APR) / (VIS*GASCT*T (KW) 1«DIS(L,N4(L) )) FOUR-Q(L,N4(L))*AREA(L,N4(L)) T4-1. GO TO 100
71 Tl-TOUT(Nl(L)) Q(N1(L) ,L)—1.0*PERM*Z*C* (APR-C) / (VIS*GASCT*T1*DIS (L, Nl (L) ) ) TEMPOR-XCOUT(Nl(L)) XCO(Nl(L),L)-TEMPOR TEMP0R-XH20UT(Nl(L)) XH20(Nl(L),L)-TEMPOR TEMP0R-XC020T(Nl(L)) XC02(Nl(L),L)-TEMPOR TEMP0R-XH2UT(Nl(L)) XH2(Nl(L),L)-TEMPOR TEMP0R-XCH40T(Nl(L)) XCH4(Nl(L),L)-TEMPOR ONE-0.0 GO TO 62
149
72 T2-T0UT(N2(L)) Q (N2 (L) , L) — 1 . 0*PERM*Z*D* (APR-D) / (VTS*GASCT*T2*DIS (L, N2 (L) ) ) TEMPOR-XCOUT (N2 (L) ) XCO(N2(L),L)-TEMPOR TEMP0R-XC020T(N2(L)) XC02(N2(L),L)-TEMPOR TEMP0R-XH20UT(N2(L)) XH20(N2(L),L)-TEMPOR TEMP0R-XH2UT(N2(L)) XH2(N2(L),L)-TEMPOR TEMP0R-XCH40T(N2(L)) XCH4(N2(L),L)-TEMPOR TWO-0.0 GO TO 63
73 T3-T0UT(N3(L)) Q (N3 (L) , L) — 1 . 0*PERM*Z*E* (APR-E) / (VIS*GASCT*T3*DIS (L, N3 (L) ) ) TEMPOR-XCOUT(N3(L)) XCO(N3(L),L)-TEMPOR TEMP0R-XC020T(N3(L)) XC02(N3(L),L)-TEMPOR TEMP0R-XH20UT(N3(L)) XH20(N3(L),L)-TEMPOR TEMP0R-XH2UT(N3(L)) XH2(N3(L),L)-TEMPOR TEMP0R-XCH40T(N3(L)) XCH4(N3(L),L)-TEMPOR THREE-0.0 GO TO 64
74 T4-T0UT(N4(L)) Q(N4 (L) ,L)—1.0*PERM*Z*F* (APR-F) / (VTS*GASCT*T4*DIS (L,N4 (L) ) ) TEMPOR-XCOUT(N4(L)) XCO(N4(L),L)-TEMPOR TEMP0R-XC020T(N4(L)) XC02(N4(L),L)-TEMPOR TEMP0R-XCH40T(N4(L)) XCH4(N4(L),L)-TEMPOR TEMP0R-XH2UT(N4(L)) XH2(N4(L),L)-TEMPOR TEMP0R-XH20UT(N4(L)) XH20(N4(L),L)-TEMPOR FOUR-0.0 GO TO 100
701 Q(N2(L) ,L)-0. Q(N3(L),L)-0. Q(N4(L) ,L)-0. XC0(N2(L) ,L)-0. XC0(N3(L) ,L)-0. XC0(N4 (L) ,L)-0. XC02(N2(L) ,L)-0. XC02(N3(L) ,L)-0. XC02(N4(L) ,L)-0. XH20(N2(L) ,L)-0. XH20(N3(L) ,L)-0. XH20(N4(L) ,L)-0. XH2(N2(L) ,L)-0. XH2(N3(L) ,L)-0. XH2(N4(L) ,L)-0. XCH4(N2(L) ,L)-0. XCH4(N3(L) ,L)-0. XCH4(N4(L) ,L)-0. T2-1. T3-1. T4-1.
100 QTOT-Q (Nl (L) , L) +Q (N2 (L) , L) +Q (N3 (L) , L) +Q (N4 (L) , L)
C TOTAL OUTPUTS AND INPUTS TO A NODE POINT ARE DETERMINED AND THE
150
C MATERIAL AND ENERGY BALANCE EQUATIONS ARE FORMULATED,
•AREA(N1(L),L) *AREA(N2(L) , L) *AREA(N3(L),L) •AREA (N4 (L) , L) L) *AREA (Nl (L) , L) L)*AREA(N2(L),L) L)*AREA(N3(L),L) L)-AREA (N4 (L) ,L) L)*AREA(N1(L),L) L) *AREA (N2 (L) , L) L) *AREA (N3 (L) , L) L)"AREA(N4(L),L) L)*AREA(Nl(L),L) L)*AREA(N2(L),L) L)•AREA(N3(L),L) L)^AR£A(N4 (L) , L) •AREA(N1(L) ,L) •AREA(N2(L) , L) •AREA(N3(L) ,L) *AREA(N4(L) ,L)
CONl-XCO(Nl(L),L)•Q(Nl(L),L) C0N2-XC0(N2(L),L)*Q(N2(L),L) C0N3-XC0(N3(L),L)•Q(N3(L) , L) C0N4-XC0(N4(L),L)*Q(N4(L),L) C02N1-XC02(Nl(L),L)"Q(Nl(L) C02N2-XC02(N2(L),L)-Q(N2(L) C02N3-XC02(N3(L),L)•Q(N3(L) C02N4-XC02(N4(L),L)*Q(N4(L) CH4N1-XCH4(Nl(L),L)-Q(Nl(L) CH4N2-XCH4(N2(L),L)*Q(N2(L) CH4N3-XCH4(N3(L),L)•Q(N3(L) C H 4 N 4 - X C H 4 ( N 4 ( L ) , L ) - Q ( N 4 ( L ) H 2 0 N 1 - X H 2 0 ( N l ( L ) , L ) • Q ( N l ( L ) H 2 0 N 2 - X H 2 0 ( N 2 ( L ) , L ) • Q ( N 2 ( L ) H 2 0 N 3 - X H 2 0 ( N 3 ( L ) , L ) * Q ( N 3 ( L ) H 2 0 N 4 - X H 2 0 ( N 4 ( L ) , L ) - Q ( N 4 ( L ) H 2 N 1 - X H 2 ( N l ( L ) , L ) • Q ( N l ( L ) , L) H 2 N 2 - X H 2 ( N 2 ( L ) , L ) - Q ( N 2 ( L ) , L ) H 2 N 3 - X H 2 ( N 3 ( L ) , L ) * Q ( N 3 ( L ) , L) H 2 N 4 - X H 2 ( N 4 ( L ) , L ) - Q ( N 4 ( L ) , L ) XCOIN-CON1+CON2+CON3+CON4 XC02IN-C02N1+C02N2+C02N3+C02N4 XH20IN-H20N1+H20N2+H20N3+H20N4 XCH4IN-CH4N1+CH4N2 +CH4N3+CH4N4 XH2IN-H2N1+H2N2+H2N3 +H2N4 XTOTIN(L)-XC0IN+XC02IN+XH20IN+XH2IN+XCH4IN FIVE-ONE+TWO+THREE+FOUR HINCO-ACO*(CONl*Tl+CON2*T2+CON3*T3+CON4*T4)+BCO/2.*
1(CONl*T1^^2+CON2*T2^^2+CON3»T3^^2+CON4*T4*^2)+CCO^ 1 (CON1/T1+CON2/T2+CON3/T3+CON4/T4)-(CON1+CON2+CON3+CON4)• 1(CCO/TREF+ACO^TREF+BCO/2.•TREF^^2)
HINC02-AC02^(C02N1*T1+C02N2*T2+C02N3^T3+C02N4^T4)+BC02/2 .* 1 (C02N1*T1**2+C02N2*T2^^2+C02N3^T3^*2+C02N4^T4"«2)+CC02* 1 (C02N1/T1+C02N2/T2+C02N3/T3+C02N4/T4) - (C02N1+C02N2+C02N3+C02N4) 1^(CC02/TREF+AC02^TREF+BC02/2 . •TREF**2)
HINCH4-ACH4*(CH4N1*T1+CH4N2*T2+CH4N3*T3+CH4N4*T4)+BCH4/2.• 1 (CH4Nl*Tl**2+CH4N2*T2*^2+CH4N3^T3*«2+CH4N4^T4«*2)+CCH4/3 .« 1 (CH4N1^T1**3+CH4N2*T2**3+CH4N3*T3**3+CH4N4^T4**3)-(CH4N1+CH4N2 + 1CH4N3+CH4N4) * (CCH4/3 . *TREF**3+ACH4*TREF+BCH4/2 . •TREF«*2)
HINH20-AH20* (H2ONl«Tl+H2ON2"T2+H20N3*T3+H2ON4»T4)+BH20/2 . • 1 (H20N1«T1**2+H20N2*T2^«2+H20N3^T3^^2+H20N4*T4**2)+CH20* 1 (H20N1/T1+H20N2/T2+H20N3/T3+H20N4/T4) - (H20N1+H20N2+H20N3+H20N4) 1*(CH20/TREF+AH20*TREF+BH20/2.*TREF**2)
HINH2-AH2* (H2N1*T1+H2N2*T2+H2N3*T3+H2N4*T4) +BH2/2 . • 1 (H2N1*T1«^2+H2N2^T2"^2+H2N3^T3**2+H2N4*T4*^2)+CH2* 1 (H2N1/T1+H2N2/T2+H2N3/T3+H2N4/T4)- (H2N1+H2N2+H2N3+H2N4) * 1(CH2/TREF+AH2*TREF+BH2/2.*TREF**2)
HIN-HINCH4+HINH2+HINH20+HINC0+HINC02 C C SIDE WALL GROWTH I S BASED ON GASIFICATION AND AN ENERGY BALANCE C I S ADDED FOR NODAL POINTS ON THE SIDE WALL. C
DO 901 1-1,8 JACK-(NX-1)+(NX+1)*(I-l) IF(L.EQ.JACK) GO TO 902 GO TO 901
902 HIN-HIN-THCON*AR£A(L,LPLl)•DELT1/DIS(L, LPLl) GO TO 903
901 CONTINUE 903 DO 904 1-1,8
JACK-NX+(NX+1)•(I-1) IF(L.EQ.JACK) GO TO 905 GO TO 904
905 HIN-HIN-THC0N*AREA(L,LPL1)-DELTl/DIS(L,LPLl)+THCON"
151
1AREA(L, LMNl) •DELT2/DIS (LMNl, L) GO TO 906
904 CONTINUE 906 DO 907 1-1,8
JACK-(NX+1)+(NX+1)*(I-l) IF(L.EQ.JACK) GO TO 908 GO TO 907
908 HIN-HIN+THC0N*AREA(L,LMN1)*DELT2/DIS(LMN1,L)-VELOCY*DENCOL*FRCIN 1*AREA(L,LMNl)/(24.^3600.)•(0.1023^DELHVP+0.4597«DELH2/18.)
907 CONTINUE SCNO-0.6 DIFF-VTST/(18./lOOO.*SCNO*CONCTL)
C APR-APR*1.01325E5 FLTRM-QTOT*454./.3048**2
C C THE MASS TRANSFER AND INTRINSIC RATE PARAMETERS ARE CALCULATED. C
AMTC0F-RIDEAL^2.13^TE(KW)*FLTRM/(EPSEXT«APR*1.01325E5)* 1(APR*1.01325E5*DIFF/(DIAUNR*RIDEAL*TE(KW)-FLTRM))**0.575 RINT1-PREXP1*EXP(ACTVl/TE(KW))*TE(KW) RINT2-PREXP2*EXP(ACTV2/TE(KW))•TE(KW) RINT3-PREXP3*EXP(ACTV3/TE(KW))-TE(KW) RINT4-PREXP4^EXP(ACTV4/TE(KW)) DirFUE-DIFF*0.5**2 CARBO-700/0.012 PHIl-SQRT(RINTl*CARBO/DirFUE)"DIAUNR/6. PHI2-SQRT(RINT2*CARB0/DIFFUE)"DIAUNR/e. PHI3-SQRT(RINT3*CARB0/DIFFUE)*DIAUNR/6. PHI4-10. E T A l - 1 . / P H I l * ( 1 . / ( T A N K ( 3 . * P H I 1 ) ) - 1 . / ( 3 . * P H I 1 ) ) E T A 2 - 1 . / P H I 2 * ( 1 . / ( T A N H ( 3 . * P H I 2 ) ) - 1 . / ( 3 . • P H I 2 ) ) E T A 3 - 1 . / P H I 3 ^ ( 1 . / ( T A N H ( 3 . * P H I 3 ) ) - 1 . / ( 3 . • P H I 3 ) ) E T A 4 - 1 . / P H I 4 * ( 1 . / ( T A N H ( 3 . " P H I 4 ) ) - 1 . / ( 3 . " P H I 4 ) )
C C EQUILIBRIUM PARAMETER VALUES ARE CALCULATED AND EQUILIBRIUM C COMPOSITIONS ARE CONSEQUENTLY OBTAINED. C
AK1-AK10*EXP(ACTl/TE(KW)) AK2-AK20*EXP(ACT2/TE(KW)) AK3-AK30*EXP(ACT3/TE(KW)) AK4-AK40*EXP(ACT4/TE(KW)) CC02EQ-X(1)*"2/AK1*(APR*1.01325E5/RIDEAL/TE(KW) ) *«2 CH20EQ-X(1)*X(4)/AK2"(APR"1.01325E5/RIDEAL/TE(KW))•*2 CH2EQ-SQRT(ABS(X(5))*APR"1.01325E5/(AK3"RIDEAL"TE(KW))) CCOEQ-APR"1.01325E5*X(2)"X(4)/(AK4"X(3)"RIDEAL-TE(KW)"EPSTOT) IF(CCOEQ.GT.CONCTL) CCOEQ-CONCTL RATEl-PVOL"(APR*1.01325E5*X(2)/RIDEAL/TE(KW)-CC02EQ)/ 1(1./(PI*AMTCOF*DIAPRT**2)+6./(ETA1«RINT1"DIAUNR*"3"CARB0"PI)+ 1(DIAPRT-DIAUNR)/(2.•PI"DIFFUE"DIAPRT"*2)) RATE2-PV0L"(APR"1.01325E5"X(3)"EPSTOT/RIDEAL/TE(KW)-CH20EQ)/ 1(1./(PI*AMTCOF*DIAPRT*"2)+6./(ETA2*RINT2*DIAUNR*"3*CARBO"PI) + 1(DIAPRT-DIAUNR)/(2.*PI"DIFFUE"DIAPRT""2) ) RATE3-PV0L"(APR*1.01325E5"X(4)/RIDEAL/TE(KW)-CH2EQ)/ 1(1./(PI"AMTC0F"DIAPRT**2)+6./(ETA3*RINT3*DIAUNR**3*CARBO"PI)+ 1(DIAPRT-DIAUNR)/(2.•PI*DIFFUE*DIAPRT-*2)) RATE4-PV0L*(APR*1.01325E5*X(1)/RIDEAL/TE(KW)-CCOEQ)/ 1(1./(PI*AMTCOF*DIAPRT**2)+6./(ETA4"RINT4*DIAPRT"*3-1000."PI) ) RATEl-RATEl".3048""3/454. RATE2-RATE2".3048""3/454. RATE3-RATE3".3048""3/454. RATE4-RATE4".3048""3/454. FIVEl(L)-XTOTIN(L)+VOL"(RATE1+RATE2-RATES) DEFl-(1./(PI"AMTC0F"DIAPRT""2)+6./(ETA1*RINT1*DIAUNR"«3" 1CARB0"PI)+(DIAPRT-DIAUNR)/(2."PI"DIFFUE-0IAPRT"«2)) DEF2-(1./(PI"AMTC0F*DIAPRT*"2)+6./(ETA2*RINT2*D:AUNR-"3" 1CARB0*PI) +(DIAPRT-DIAUNR)/(2.•P:*DIFFUE"DIAPRT«-2) )
152
DEr3- (1. / (PI*AMTC0F*DIAPRT^^2) +6 . / (ETA3«RINT3^DIAUNR**3* 1CARB0*PI) + (DIAPRT-DIAUNR) / (2 . •PI*DIFFUE*DIAPRT**2) ) DEF4-(1./(PI*AMTC0F»DIAPRT*^2)+6./(ETA4^RINT4^DIAPRT*^3* 11000.*PI)) DEFlA-1./(PI*AMTC0F^D1APRT^«2) DEFlB-6. / (ETA1^RINT1^DIAUNR**3*CARB0*PI) DEFIC- (DIAPRT-DIAUNR) / (2 . •PI*DIFFUE"DIAPRT**2) DEF2A-1./(PI*AMTC0F*DIAPRT""2) DEF2B-6. / (ETA2*RINT2*DIAUNR""3*CARBO"PI) DEF2C- (DIAPRT-DIAUNR) / (2 . •PI^DIFFUE^DIAPRT^^2) DEF3A-1./(PI*AMTC0F*DIAPRT*^2) DEF3B-6. / (ETA3*RINT3*DIAUNR^*3*CARBO*PI) DEF3C- (DIAPRT-DIAUNR) / (2 . *PI*DIFFUE*DIAPRT**2) DEF4A-1./(PI*AMTC0r^DIAPRT""2) DEF4B-6./ (ETA4*RINT4"DIAPRT^«3^1000.•PI) HOTCO-FIVEl(L)"X(1)•(ACO^(T (KW)-TREF)+BC0/2.*(T(KW)**2-TREF*"2 1)+CC0*(1./T(KW)-1./TREF)) H0TC02-FrVEl (L) "X (2) • (AC02" (T (KW) -TREF) +BC02/2 . * (T (KW) **2-1TREF"*2)+CC02*(1./T(KW)-1./TREF) ) H0TH20-FIVE1 (L) *X (3) • (AH20* (T (KW) -TREF) +BH20/2 . • (T (KW) **2-1TREF**2)+CH20*(1./T(KW)-1./TREF) ) H0TH2-FIVE1 (L) "X (4) * (AH2* (T (KW) -TREF) +BH2/2 . * (T (KW) ••2-TREF** 12)+CH2*(1./T(KW)-1./TREF) ) H0TCH4-nVEl (L)*X(5) • (ACH4* (T (KW)-TREF)+BCH4/2 . • (T (KW) *"2-lTREF"«2)+CCH4/3." (T(KW) "*3-TREr""3) ) HOUT-HOTCO+HOTC02+HOTH20+HOTH2+HOTCH4 RTERM-2. "RATE3"DELH3-RATE1"DELH1-RATE2"DELH2+RATE4"DELH4 FX (1) -XCO IN-FIVEl (L) "X (1) + (2 . "RATE1+RATE2-RATE4) "VOL FX(2)-XC02IN-FIVE1 (L)"X (2)+VOL"(RATE4-RATE1) F X ( 3 ) - X C H 4 I N - F I V E 1 (L)"X(5)+RATE3*V0L FX(4) -XH20IN-FIVE1(L)"X(3) -VOL"(RATE2+RATE4) F X ( 5 ) - 1 . 0 - ( A B S ( X ( 1 ) ) + A B S ( X ( 2 ) ) + A B S ( X ( 3 ) )+ABS (X (4) )+ABS (X (5) ) ) FN (KW) -HIN-HOUT+VOL"RTERM POT-1.01325E5 C O N V - 0 . 3 0 4 8 " " 3 / 4 5 4 . Z I P - 0 . 0 0 1 G E N R ( L ) — 1 . " (RATE1+RATE2-RATE3) "ZIP"VIS"ARBG*T (KW) / (EPSTOT*APR
1 " 1 4 . 7 " P E R M * 3 2 . 1 7 ) I F ( L . G E . ( N N P - 2 . " N X - 1 ) ) PACT(L) - (APR-D)"AREA(L,N2(L) )
1*14 . 7 * A P R * 3 2 . 1 7 / ( 1 0 . 7 3 * T ( K W ) * V I S * D I S ( L , N 2 ( L ) ) ) RETURN END SUBROUTINE DER(N,X,FX,KW,T,FN,L ,A)
C C THIS ROUTINE CALCULATES THE PARTIAL DERIVATIVES OF THE FUNCTIONS C WITH RESPECT TO THE INDEPENDENT VARIABLES. A(I,J) REPRESENTS THE C PARITAL OF THE I'TH FUNCTION WITH RESPECT TO THE J'TH VARIABLE. C VALUES OF N AND X(I) ARE SUPPLIED TO DER BY NEWTON . C
DIMENSION A(6,6) ,X(5) ,FX(5) ,XNEW (5) , FXNEW (5) ,DUMMY(5) , 1T(3) ,FN(3) Hl-O.OOOl H2-0.0001 H3-0.0001 H4-0.0001 H5-2.E-5 DUMMY (1)-X(1)+H1 XNEW(l)-DUMMY(1) DUMMY(2)-X(2) XNEW(2)-DUMMY(2) DUMMY(3)-X(3) XNEW(3)-DUMMY(3) DUMMY(4)-X(4) XNEW(4)-DUMMY(4) DUMMY(5)-X(5) XNEW(5)-DUMMY(5)
153
N-5
CALL SOLVE (XNEW, FXNEW, KW,T, FN, L) DO 1 I-1,N DO 1 J-1,N
1 A(l,J)-0. A(1,1)-(FXNEW(1)-FX(1))/(XNEW(1)-X(1)) A 2,1)-(FXNEW(2)-FX(2))/(XNEW(1)-X(1) A 3,1)-(FXNEW(3)-FX(3))/(XNEW(1)-X(1)) A(4,1) - (FXNEW(4)-FX (4) ) / (XNEW(l)-X(l) ) XNEW(1)-XNEW(1)-H1 XNEW(2)-XNEW(2)+H2 CALL SOLVE(XNEW,FXNEW,KW,T,FN,L) A(1,2)-(FXNEW(1)-FX(1))/(XNEW(2)-X(2)) A (2, 2) - (FXNEW (2)-FX (2))/(XNEW (2)-X (2)) A(3,2)-(FXNEW(3)-FX(3))/(XNEW(2)-X(2)) A (4, 2) - (FXNEW (4)-FX (4) ) / (XNEW (2)-X (2) ) XNEW(2)-XNEW(2)-H2 XNEW(3)-XNEW(3)+H3 CALL SOLVE (XNEW, FXNEW, KW,T, FN, L) A(l,3)-(FXNEW(l)-FX(1))/(XNEW(3)-X(3)) A(2,3)-(FXNEW(2)-FX(2))/(XNEW(3)-X(3)) A(3,3)-(FXNEW(3)-FX(3))/(XNEW(3)-X(3)) A (4, 3) - (FXNEW (4)-FX (4))/(XNEW (3)-X (3)) XNEW(3)-XNEW(3)-H3 XNEW(4)-XNEW(4)+H4 CALL SOLVE(XNEW,FXNEW,KW,T,FN,L) A(1,4)-(FXNEW(1)-FX(1))/(XNEW(4)-X(4)) A (2, 4) - (FXNEW (2)-FX (2))/(XNEW (4)-X (4)) A(3,4)-(FXNEW(3)-FX(3))/(XNEW(4)-X(4)) A(4,4)-(FXNEW(4)-FX(4) ) / (XNEW(4)-X(4) ) XNEW(4)-XNEW(4)-H4 XNEW(5)-XNEW(5)+H5 CALL SOLVE(XNEW,FXNEW,KW,T,FN,L) A(1,5)-(FXNEW(1)-FX(1))/(XNEW(5)-X(5)) A(2,5)-(FXNEW(2)-FX(2))/ (XNEW (5)-X(5)) A(3,5)-(FXNEW(3)-FX(3))/(XNEW(5)-X(5)) A(4, 5) - (FXNEW (4) -FX (4) ) / (XNEW (5) -X (5) ) A(5,l)—1.0 A(5,2)—1.0 A(5,3)—1.0 A(5,4)—1.0 A(5,5)—1.0 A(l,6)—FX(1) A(2,6)—FX(2) A(3,6)—FX(3) A(4,6)—FX(4) A(5,6)—FX(5) RETURN END FUNCTION SIMUL(N,A,XP,EPS,INDIC,NRC)
C •••••••*•••«»••»••*••••**••« ABSTRACT ••••••••••••••••••••••••••••-. C THIS SOLVES THE SYSTEM OF LINEAR EQUATIONS GENERATED BY A GAUSSIAN-C ELIMINATION WITH PARTIAL PIVOTING METHOD. C •*•••*»•••«*••«•«••••••• INPUT DESCRIPTION ••••••••••••••••••••••••-C THE FUNCTION REQUIRES THE VALUES OF A (I, J) AND N. ALSO THE VALUES C OF X(I)'S WHICH HAVE TO BE MODIFIED ALONG WITH THE ERROR CRITERION C ARE PASSED. C •*••••«••••**••*••«••• OUTPUT DESCRIPTION •••••••••••••••«•••••••••-C THIS OUTPUTS THE REQUISITE INCREMENTS IN X(I)'S AND THE UPDATED C VALUES OF THE INDEPENDANT VARIABLES ARE PASSED BACK TO NEWTON C TILL THE CONVERGENCE CRITERION HAS BEEN SATISFIED.
DIMENSION IR0W(6) , JC0L(6) , J0RD(6) ,Y(6) ,A(NRC,NRC) , XP (N) MAX-N+1
C BEGIN ELIMINATION PROCEDURE 5 DETER -1.
DO 18 K-1,N
154
KMl-K-l C SEARCH FOR THE PIVOT ELEMENT
PIVOT-0. DO 11 I-1,N DO 11 J-1,N
^ ? ? ^ l^^.^^^ ^^^^ ARRAYS FOR INVALID PIVOT SUBSCRIPTS l£^(K.EQ.l) (30 TO 9 DO 8 ISCAN-1,KM1 DO 8 JSCAN-1,KM1 IF(I.EQ.IROW(ISCAN)) GO TO 11 ir(J.EQ.JCOL(JSCAN)) GO TO 11
8 CONTINUE 9 IF(ABS(A(I,J)) .LE.ABS(PIVOT)) GO TO 11
P1V0T-A(I,J) IROW (K) -I JCOL(K)-J
11 CONTINUE C ENSURE THAT SELECTED PIVOT IS LARGER THAN EPS
IF(ABS(PIVOT).GT.EPS) GO TO 13 SIMUL-0. RETURN
C UPDATE THE DETERMINANT VALUE 13 IROWK-IROW(K)
JCOLK-JCOL(K) DETER-DETER*P IVOT
C NORMALIZE PIVOT ELEMENTS DO 14 J-1,MAX
14 AdROWK, J)-A(IROWK, J)/PIVOT C CARRY OUT ELIMINATION AND DEVELOP INVERSE
A(IROWK,JCOLK)-1./PIVOT DO 18 I-1,N AIJCK-A(I,JCOLK) IF(I.EQ.IROWK) GO TO 18 A (I, JCOLK) —Al JCK/PIVOT DO 17 J-1,MAX
17 IF(J.NE.JCOLK) A(I, J)-A(I, J)-AIJCK*A(IROWK, J) 18 CONTINUE
C ORDER SOLUTIONS IF ANY AND CREATE JORD ARRAY DO 20 I-1,N IROWI-IROW(I) JCOLI-JCOL(I) JORD(IROWI)-JCOLI
20 IF(INDIC.GE.O) XP(JCOLI)-A(IROWI,MAX) C ADJUST SIGN OF DETERMINANT
INTCH-0 NMl-N-1 DO 22 I-1,NM1 IPl-I+1 DO 22 J-IP1,N IF (JORD (J) .GE. JORD (I)) GO TO 22 JTEMP-JORD(J) JORD (J)-JORD (I) JORD(I)-JTEMP INTCH-INTCH+1
22 CONTINUE IF ( (INTCH/2*2 .) .NE. INTCH) DETER—DETER
C IF INDIC IS POSITIVE RETURN WITH RESULTS IF(INDIC.LE.O) GO TO 26 SIMUL-DETER RETURN
C IF INDIC IS NEGATIVE/0 UNSCRAMBLE THE INVERSE C FIRST BY ROWS 2 6 DO 28 J-1,N
DO 27 I-1,N IROWI-IROW(I) JCOLI-JCOL(I)
155
27 Y(JCOLI)-A(IROWI,J) DO 28 I-1,N
28 A(1,J)-Y(I) C THEN BY COLUMNS
DO 30 1-1,N DO 29 J-1,N IROWJ-IROW(J) JCOLJ-JCOL(J)
29 Y(IROWJ)-A(I,JCOLJ) DO 30 J-1,N
30 A(I,J)-Y(J) C RETURN FOR INDIC NEGATIVE OR 0
SIMUL-DETER RETURN END SUBROUTINE FLOW
C C THIS ROUTINE IS A FINITE ELEMENT CODE USED TO SOLVE FOR THE PRE-C SSURE FIELD THROUGH THE CAVITY. C c C PROGRAM FINITEl(DIN,TAPE5-DIN,DOUT,TAPE6-DOUT,OUTPUT,TAPEl-OUTPUT) C THIS CODE USES QUADRILATERAL FINITE ELEMENTS TO SOLVE THE PROBLEM C DU/DT+V«DEL(U)-DEL(KDEL(U))-LAMBDA*U-F ,IN OMEGA C KDU/DN+BETA*(U-UO)-Q ,ON OMEGA C AA(.,.) AND AM(.,.) HAVE DIMENSION .GE. NVNP BY (ML+MU+1) C PA(.,.) HAS DIMENSION .GE. NVNP BY (2*ML+MU+1) C"""«""""FIRST DIMENSION OF PA MUST BE NDEN .GE. NVNP"""""""""*"" C**"*****NDEN' IS ENTERED BY PARAMETER STATEMENT****"""""""""""""" C V(.),U(.),IP1 (.) HAVE DIMENSION .GE. NVNP C UI(.),VI(.) HAVE DIMENSION .GE. NNP C NTRAN .EQ. 0 FOR STEADY STATE C NTRAN .EQ. 1 FOR CONSISTENT MASS TRANSIENT C NTRAN .EQ. 2 FOR LUMPED MASS TRANSIENT C NMETH .EQ. 1 FOR VARIABLE STEP TRAPEZOID C NMETH .EQ. 2 FOR CONSTANT STEP INTEGRATOR C GAM - INTEGRATION METHOD PARAMETER C - 0, FOR EXPLICIT EULER (WITH ASSOCIATED STABILITY LIMIT) C - 0.5, FOR TRAPEZOID RULE (IMPLICIT) C - 1.0, FOR IMPLICIT EULER C NDF .EQ. NUMBER OF DEGREES OF FREEDOM IN BASIS SET C NE .EQ. NUMBER OF ELEMENTS C NCN .EQ. CONSTANT NODES C NNP .EQ. TOTAL NUMBER OF NODES C NAXI .EQ. 0 FOR CARTESIAN FORMULATION C NAXI .EQ. 1 FOR AXISYMMETRIC FORMULATION C - FOR AXISYMMETRIC CASEr X-R AND Y-Z C NGAU DETERMINES ORDER OF GAUSSIAN INTEGRATION C NGAU-1 ]1 BY 1 GAUSS QUADRATURE C NGAU-2 ]2 BY 2 GAUSS QUADRATURE C NGAU-3 ]3 BY 3 GAUSS QUADRATURE C NGAU-4 ]4 BY 4 GAUSS QUADRATURE C DELT .EQ. THE INITIAL GUESS OF TIME STEP SIZE C NVNP- NNP-NCN .EQ. VARIABLE NODES C D(.,.) HAS DIMENSION NNP BY 2 C EPSMAX .EQ. A DESIRED UPPER BOUND ON TIME INTEGRATION TRUNCATION ERROR C DELTP .EQ.THE TIME INCREMENT BETWEEN PRINT OUT C IPRMAT .EQ. THE NUMBER OF ELEMENTS FOR WHICH ELEMENT MATRICES ARE TO BE C PRINTED C IPGMAT .EQ. 0 IF NO GLOBAL MATRICE PRINT IS DESIRED C .EQ. 1 IF GLOBAL MATICE PRINT IS DESIRED C TI (TF) .EQ. THE INITIAL (FINAL) TIME VALUE
REAL IX,IXC,IYC COMMON /BIG/ AA( 80,37),AM( 80,37) COMMON /PI/ V( 80),IP1( 80),B( 80),UI(128),U( 80),D( 80,2) COMMON /P2/ ML, ML2,MU,.MLM,MLL, NCN, NBDl, DELT, DELTP, EPSMAX,
156
'??»$^0N^s;'(^uS)''''^"''''°''''^°^'°''^'°^'°'^»'"^^ COMMON /MORE/ GENSUM COMMON /NODE/ Nl(70),N2(70),N3(70),N4(70) COMMON /DISTAN/ D1S(50,50) COMMON /ARE/ AREA(50,50) COMMON /VOLUM/ VOLUME(50) COMMON /POINT/ NNP,NX,NE COMMON /NET/ TOTVOL,VERTSP,TIMEFR COMMON /NETT/ ITIME COMMON /CONS/ CARCON COMMON /CB/ CARGAS COMMON /FECDTA/ TC(48),COORD(182,2) COMMON /FECDTl/ IE (52,9),IP(128,2) COMMON /COUNT/ ILL COMMON /GENER/ GENR(50) COMMON /VCY/ BIGBRO DIMENSION PA(80,55) DATA NDEN/80/ IF(ILL.EQ.l) GO TO 1901
C ir((ILL.EQ.3).AND.(ITIME.EQ.l)) GO TO 1901 GO TO 1902
1901 CALL NODAL 1902 NDF-4
NGAU-4 MU-7 ML-7 NTRAN-0 NMETH-2 NAXI-0 IPRMAT-0 IPGMAT-0 ALAM-0.0 IF(NTRAN .EQ. 0)GO TO 2257 IF(NMETH .NE. 1)G0 TO 2256 READ(5,150)TI,TF,DELT,DELTP,EPSMAX GO TO 2257
2256 READ(5,150)TI,TF,DELT,DELTP,GAM 2257 NVNP-NNP-NtN
NBDL-1 MLM-ML+1 ML2-ML+2 MLL-MLM+MU DO 5 I-l,NVNP B(I)-0.0 DO 5 J-1,MLL AM(I, J)-0.0
5 AA(I,J)-0.0 C INPUT GLOBAL COORDINATES OF NODE I )COORDINATES ARE ORDERED IN C INCREASING NODE NUMBER] COORD(1,1) .EQ.. X-COORDINATE OF NODE I , C COORD(I,2) .EQ. Y-COORDINATE OF NODE I C INPUT GLOBAL NODE NUMBERS IN ELEMENT I] NODES ARE TRAVERSED IN A C COUNTERCLOCKWISE DIRECTION AROUND ELEMENT. C COUNTERCLOCKWISE DIRECTION AROUND ELEMENT(CORNER NODES FIRST THEN C MIDSIDE NODES IN THE CASE OF QUADRATIC BASIS SET). C INPUT NODE TYPE] IP (I,1) .EQ. 0 IF U IS SPECIFIED AT BOUNDARY NODE I] C IP (1,1) .EQ. 1 IF NODE I IS AN INTERIOR NODE] IP (1,1) .EQ. 2 IF THE C FLUX IS ZERO AT BOUNDARY NODE I] IP (1,1) .EQ. 3 IF THE GENERAL FLUX C BOUNDARY CONDITION APPLIES AT BOUNDARY NODE I. C DETERMINATION OF THE NUMBER OF SPECIFIED BOUNDARY NODES ABOVE ACTIVE NODE I C INPUT OF U VALUES AT SPECIFIED BOUNDARY NODES. THE ELEMENTS OF TC(. ) C ARE ORDERED IN INCREASING GLOBAL NODE NUMBER
lP(l,2)-0 IF(IP(1,1) .EQ. 0)IP(1,2)-1 DO 62 1-2, NNP IP(I,2)-IP(I-1,2)
157
IF(IP(I,1) .EQ. 0)IP(I,2)-IP(I,2)+1 62 CONTINUE
DO 2 M»1,NE C CONSTRUCT ELEMENT MATRICES
CALL MAKE (NAXI,NDF,NGAU,M,NTRAN) C CONSTRUCTION OF GLOBAL CAPACITY AND DISSIPATION MATRICES AND FORCE VECTOR
DO 523 K-1,NDF 1»IE(M,K) 11-IP(I,2) IF (IP (1,1) .EQ. 0)GO TO 524 I2-I-I1 B(I2)-B(I2)-CE(K)
524 DO 523 L-1,NDF J-IE(M,L) IF(IP(J,1) .EQ. 0)GO TO 523 J1-IP(J,2) J2-J-J1 IF (IP (1,1) .EQ. 0)GO TO 522 K1-J2-I2 K2-K1+MLM IF(K2 .LT. 1 .OR. Kl .GT. MU)GO TO 523 AA(12,K2)-AA (12,K2)+AE(K,L)+ALAM"BE(K,L) AM(I2,K2)-AM(I2,K2)+BE(K,L) GO TO 523
522 B(J2)-B(J2)-(AE(L,K)+ALAM"BE(L,K))"TC(II) 523 CONTINUE 2 CONTINUE
IF(IPGMAT .EQ. 0)GO TO 589 WRITE(6,601) WRITE(6,502)((AA(I,J),J-1,MLL),I-l,NVNP) WRITE(6,602) WRITE(6,502) ((AM(I,J),J-1,MLL),1-1,NVNP) WRITE (6, 603) WRITE(6,502) (B (I),I-l,NVNP)
589 CONTINUE C INPUT OF INITIAL CONDITIONS
IF(NTRAN .NE. 0) READ (5, 300 "JI (I) , I-l, NVNP) IF(NMETH .NE. 1)G0 TO 225; IF(NTRAN .EQ. 1)WRITE(6,?Q2)EPSMAX IF(NTRAN .EQ. 2)WRITE(6,903)EPSMAX
2258 CONTINUE C TIME INTEGRATION
IF(NTRAN .EQ. 0)GO TO 2259 IF{NMETH .EQ. 1)CALL TRAP(NDEN,NVNP,TI,TF,PA,lER) IF(NMETH .EQ. 2)CALL CSTEP(NDEN,NVNP,NTRAN,GAM,TI,TF,PA,lER) IF(IER .NE. 0)GO TO 9998 GO TO 1000
C CALCULATION OF STEADY STATE SOLUTION 2259 DO 82 I-l,NVNP
DO 82 J-1,MLL PA(I,J)-AA(I,J)
82 CONTINUE CALL DECB(NDEN,NVNP,ML,MU,PA,IP1,IER) IF(IER .EQ. 0)GO TO 98 WRITE(6,700)lER GO TO 1000
98 DO 20 I-l,NVNP 20 U(I)-B(I)
CALL SOLB(NDEN,NVNP,ML,MU,PA,U, IPl) WRITE(6,901)
C RECONSTRUCTION AND OUTPUT OF FULL NODAL SOLUTION VECTOR NA-1 DO 107 I-l,NNP IF(IP(I,1) .EQ. 0)GO TO 108 I1-I-IP(I,2) VI(I)-U(I1)
158
GO TO 107 108 VI(I)«TC(NA)
NA-NA+1 107 CONTINUE
WRITE(6,500) (VI (I),I-l,NNP) 99 CONTINUE
GO TO 1000 9998 WRITE(6,700)lER 1000 CONTINUE 100 FORMAT(1215,FIO.5) 150 FORMAT(4F10.5,E10.3) 200 FORMAT(315,2F10.7) 202 FORMAT(414) 203 FORMAT(FIO.7) 204 FORMAT(15X,2F10.7) 300 FORMAT(5E15.8) 400 FORMAT(3E15.8) 500 FORMAT(6(3X,E15.8)) 502 FORMAT(7(2X,E15.8)) 600 FORMAT(/) 601 FORMAT(20X,37HAA(I,J):7(2X,E15.8) rSUMMED ON I FIRST) 602 FORMAT(20X,37HAM(I,J):7(2X,E15.8):SUMMED ON I FIRST) 603 FORMAT(20X,16HB(I):7(2X,E15.8)) 700 FORMAT(1OX,12,16HTH PIVOT IS ZERO) 901 FORMAT(4 6X,21HSTEADY STATE SOLUTION) 902 FORMAT(33X,25HC0NSISTENT MASS TRANSIENT,lOH(EPS"UMAX-,ElO.3,IH)) 903 FORMAT(35X,21HLUMPED MASS TRANSIENT,lOH(EPS"UMAX-,ElO.3,IH))
2002 FORMAT(50X,20HEXECUTION STARTED AT,4X,A10) 2003 FORMAT(49X,21HEXECUTION FINISHED AT,4X,A10) 2345 FORMAT(II)
RETURN END SUBROUTINE MAKE(NAXI,NDF,NGAU,M,NTRAN)
C FF(X,Y) IS THE HEAT SOURCE FUNCTION AND MUST BE SUPPLIED HERE C FKl IS THE X-DIFFUSIVITY FUNCTION AND MUST BE SUPPLIED AS A FUNCTION C FK2 IS THE Y-DIFFUSPVITY FUNCTION AND MUST BE SUPPLIED AS A FUNCTION C V1(X,Y) IS THE X-COMPONENT OF VELOCITY VECTOR AND MUST BE SUPPLIED HERE C V2(X,Y) IS THE Y-COMPONENT OF VELOCITY VECTOR AND MUST BE SUPPLIED HERE
COMMON /BIG/ AA( 80,37),AM( 80,37) COMMON /PI/ V( 80),IP1( 80),B( 80),UI(128),U( 80),D(80,2) COMMON /P2/ ML,ML2,MU,MLM,MLL,NCN,NBDL,DELT,DELTP,EPSMAX, 1AE(9,9) ,BE(9,9) ,CE(9) , BETA (30, 3) , TO (30, 3) . Q (30, 3) , IPRMAT COMMON /MY/ VI (128) COMMON /MORE/ GENSUM COMMON /GENER/ GENR(50) COMMON /FECDTA/ TC(48),COORD(182,2) COMMON /FECDTl/ IE (52,9),IP(128,2) DIMENSION P(4,4) ,W(4,4) ,DBAA(9,2) ,BAA(9) ,DMAP(2,2) ,DELBA(9,2) DIMENSION BA(9,4,4),DBA(9,2,4,4) ,DE(9)
C DIMENSION FF(48,48) REAL JAC,JACl,LI,L2,JACI,JAC2 DATA P/0.0,0.57735026918963,0.77459666924148,0.86113631159405, 0.0, 1-.57735026918963,-.77459666924148,-.86113631159405,0.0,0.0,0.0, 20.339981043584 86,0.0,0.0,0.0,-0.339981043584 8 6/ DATA W/2.0,1.0,0.55555555555556,0.34785484513745, 1.0, 1.0, 10.55555555555556,0.34785484513745,0.0,0.0,0.88888888888889, 20.6521451548 6255,0.0,0.0,0.0,0.6521451548 6255/ FKl (X,Y)-1.0 FK2(X,Y)-1.0 VI (X,Y)-0.0 V2(X,Y)-0.0 FF(X,Y)-0.
50 DO 5 I-l,NDF CE(I)-0.0 DO 5 J-1,NDF BE(I,J)-0.0
159
5 AE(I,J)-0.0 Z GAUSSIAN INTEGRATION
DO 100 120-1,NGAU DO 100 J20«1,NGAU IF(M .GT. 1)G0 TO 31 Ll-P(NGAU,120) L2-P(NGAU, J20)
C GENERATE AND STORE DERIVATIVES OF BASIS FNCS. AT GAUSS POINTS C GENERATE AND STORE BASIS FNCS. AT GAUSS POINTS
CALL BASIS(LI,L2,NDF,BAA,DBAA) DO 32 IJ-1,NDF BA(IJ,I20, J20)-BAA(IJ) DO 32 IK-1,2
32 DBA(IJ,IK,I20,J20)-DBAA(IJ,IK) 31 X-0.0
Y-0.0 DO 30 I-l,NDF KA-IE(M,I) X-X+COORD(KA,1)"BA(1,120, J20)
30 Y-Y+COORD(KA,2)"BA(I,I20,J20) FF1-FF(X,Y) FFB-0.0 DO 308 I-l,NDF KA-IE(M, I) FFB-FFB+GENR(KA)"BA(1,120, J20)
308 CONTINUE C DERIVATIVES OF COORDINATE MAPPING
DO 71 K3-l,2 DO 71 K2-l,2 DMAP(K2,K3)-0.0 DO 71 K1-1,NDF
71 DMAP(K2IK3)-DMAP(K2,K3)+COORD(KA,K2)"DBA(K1,K3,I20, J20)
C CALCULATION OF AREA JACOBIAN JAC-DMAP (1, 1) "DMAP (2,2) -DMAP (1,2) "DMAP (2,1) JACI-l.O/JAC JAC2-(X**NAXI)*JAC
C GRADIENT OPERATOR DELBAdl, 1)-JACI* (DMAP (2,2) *DBA (II, 1, 120, J20) -DMAP (2, 1) "
6^S^Ul'JwA?S-\-DMAP (1,2) "DBAdl, 1,120, J20)+DMAP (1,1)"
C CONSTRUCTION^OF'BULK^CONTRIBUTIONS TO ELEMENT MATRICES
?E(l}-CEa)^rFB"JAC2"BA(1,120, J20)"W (NGAU, 120) "W (NGAU, J20)
^ (j^ ,f'h^^Tx T*r9« /irri IX. ^ "DELBAd. 1) "DELBA(J, 1) +FK2 (X, Y) IDELBAl
J)-AE (I, J) +JAC2" (FKl (X, Y) "DELBAd, 1) "DELBA(J, 1) +FK2 (X, Y) -._-.^d,27-DELBA(J,2) + (Vl(X,Y)"DELBA(J,l)+V2(X,Y)"DELBA(J,2))" -Jwa T T20 J20n "W(N<aiU,J20) "W (NGAU, 120) .,„. . S(i:"-BEd;j)+JAC2"^(i;i20,J20)"BA(J,I20,J20)"W(NGAU,l20)" 81 1W(NGAU, J20)
100 CONTINUE KB-2 IF(NDF .EQ. 8)KB-3 DO 21 K-1,4 KA-IE(M,K) IF(IP(KA, 1) .LT. 3) GO TO 21 READ(5,201) (Q (NBDL, I) ,1-1/KB) IF(IP(KA,1) .NE. 4)G0 TO 278 READ(5,201)(BETA(NBDL,I),1-1/KB) READ(5,201)(TO(NBDL,I),1-1,KB)
278 NBDL-NBDL+1 C GAUSSIAN INTEGRATION
DO 7 120-1,NGAU GO TO (8, 9,10,11) ,K
160
8 L2—1, Ll-P(NGAU,120) GO TO 12
9 Ll-1. L2-P(NGAU,120) GO TO 12
10 L2-1. Ll-P(NGAU,120) GO TO 12
11 LI—1. L2-P(NGAU,120)
C GENERATE BASIS FNCS. AT GAUSS POINTS C GENERATE DERIVATIVES OF BASIS FNCS. AT GAUSS POINTS
12 CALL BASIS(LI,L2,NDF,BAA,DBAA) C GENERATE DERIVATIVES OF COORDINATE MAPPING
DO 14 Ka-1,2 DO 14 K2-l,2 DMAP(K2,K3)-0.0 DO 14 K1-1,NDF KA-IE(M,K1)
14 DMA? (K2,K3)-DMAP (K2,K3)+COORD(KA,K2) "DBAA(K1,K3) C CALCULATION OF LINE JACOBIAN
19 GO TO (15,16,15,16),K 15 JACl-SQRT(DMAP(1,1)"*2+DMAP(2,1)••2)
GO TO 17 16 JACl-SQRT(DMAP(2,2)••2+DMAP(1,2)^^2) 17 CONTINUE
C INTERPOLATION OF BETA, Q, AND TO ON BDRY. KK-K+1 IF(KK .EQ. 5)KK-1 KKK-K+4 Ql-Q(NBDL,1)•BAA(K)+Q(NBDL,2)•BAA(KK) IF (NDF .EQ. 4) GO TO 35 Ql-Ql+Q(NBDL,3)•BAA(KKK)
35 IF(IP(KA,1) .EQ. 3)G0 TO 36 BET-BETA(NBDL,1)•BAA(K)+BETA(NBDL,2)•BAA(KK) TOl-TO(NBDL,1)•BAA(K)+TO(NBDL,2)•BAA(KK) IF (NDF .EQ. 4)GO TO 19 BET-BET+BETA(NBDL,3)"BAA(KKK) TOl-TOl+TO(NBDL,3)•BAA(KKK)
C CONSTRUCTION OF BDRY. CONTRIBUTIONS TO ELEMENT MATRICES MURDA - K+1
36 DO 18 I-K,MURDA K4-I IF(I .EQ. 5)K4-1 IF(IP(KA, 1) .NE. 3)G0 TO 37 CE(K4)-CE(K4)-Q1"BAA(K4)"JAC1"W (NGAU, 120) IF(I .GT. K)GO TO 18 IF (NDF .GE. 9)CE(KKK)-CE(KKK)-Q1"BAA(KKK) "JAC1"W(NGAU, 120) GO TO 18
37 CE(K4)-CE(K4)- (Q1+BET"T01)"BAA(K4)"JAC1"W(NGAU, 120) IFd .GT. K)GO TO 27 IF (NDF .GE. 9)CE(KKK)-CE(KKK)-(Q1+BET"T01)"BAA(KKK)"JAC1" IW(NGAU,120) IF(NDF .GE. 9)AE(KKK,KKK)-AE(KKK,KKK)+BET"BAA(KKK)"BAA(KKK)" 1JAC1"W(NGAU,120)
27 DO 28 J-K,MURDA K5-J IF(J .EQ. 5)K5-1 AE(K4,K5)-AE(K4,K5)+BET"BAA(K4) "BAA(K5) " JACl"W (NGAU, 120) IF(J .GT. K)GO TO 28 IF(NDF .EQ. 4)GO TO 28 AE(K4,KKK)-AE(K4,KKK)+BET"BAA(K4)"BAA(KKK)"JACl"W(NGAU, 120) AE (KKK, K4)-AE (K4, KKK)
28 CONTINUE 18 CONTINUE
161
7 CONTINUE 21 CONTINUE
IF(M .GT. IPRMAT) GO TO 9987 WRITE(6,9003) WRITE(6,9001) WRITE(6,9000) ( (AE(I, J) , J-1,NDF) ,I-1,NDF) WRITE(6,9003) WRITE(6,9002) WRITE(6,9000)(CE(I),I-1,NDF) WRITE(6,9003)
9000 FORMAT(4(2X,E15.8)) 9001 FORMAT(20X,37HAE(I,J):4(2X,E15.8):SUMMED ON I FIRST) 9002 FORMAT(20X,17HCE(I):4(2X,E15.8)) 9003 FORMAT(/) 9987 IF(NTRAN .NE. 2)GO TO 22
S-0.0 DO 101 I-l,NDF DE(I)-BE(I,I) DO 101 J-1,NDF
101 S-S+BE(I,J) T-0.0 DO 102 I-l,NDF
102 T-T+DEd) DO 103 I-l,NDF DO 103 J-1,NDF
103 BE(I,J)-0.0 DO 104 I-l,NDF
104 BE(I,I)-S"DE(I)/T 22 CONTINUE
IF (M .GT. IPRMAT) GO TO 23 WRITE(6,9004) WRITE(6,9000) ((BE(I,J),J-1,NDF),1-1,NDF)
9004 FORMAT(20X,37HBE(I,J):4(2X,E15.8):SUMMED ON I FIRST) WRITE(6,9003)
201 FORMAT(3F10.7) 23 CONTINUE
RETURN END SUBROUTINE BASIS(LI,L2,NDF,BA,DBA) REAL L1,L2
LINEAR AND QUADRATIC APPROXIMATION ON QUADRILATERALS DIMENSION BA(9) ,DBA(9,2) ,S(9) ,T(9) DATA S /-l.,l.,l.,-l.,0.,l.,0.,-l.,0./ DATA T /-l.,-l.,l.,l.,-l.,0.,l.,0.,0./
LINEAR BASIS FNCS. BASL (X, Y, XI, Y D -0 . 25^ (1. +X-XI) • (1. +Y^YI) DEAL (X, Y, XI, Y D -0 .25"XI" (1. +Y"YI)
: SERENDIPITY QUADRATIC FNCS. BASQC(X,Y,XI,YD-0.25"(1.+XI^X)•(1.+YI*Y)*(XI"X+YI"Y-1.) DBAQC(X,Y,XI,YI)-0.25"(1.+YI"Y)"(XI"YI"Y+2."X"XI"XI) BASQM(X, Y, XI, Y D -0 . 5" ( (1. -X"X) " (1. +YI"Y) "YI"YI+ (1. +XI"X) " (1. -Y"Y) 1XI"XI) DBAQM (X, Y, XI, Y D — X " (1. +Y*YI) •YI-YI + O . 5^ (1. -Y"Y) "XI"XI"XI
; LAGRANGE QUADRATIC BASIS FNCS. BASLC (X, Y, XI, Y D -0 . 25" (XI+X) " (YI+Y) "X"Y DBALC (X, Y, XI, Y D -0 . 25* (XI+2 . "X) " (YI+Y) "Y BASLM(X,Y,XI,YD-0.5"(X"(XI+X)"(1.-Y"Y)"XI"XI+Y"(YI+Y) "(1. 1-X"X)"YI"YI) DBALM(X,Y,XI,YD-0.5"(XI+2."X)"(1.-Y"Y)"XI^XI-X^Y^(YI+Y) l^YI^YI BASLO(X,Y)-(1.-Y^Y)•(1.-X^X) DBALO (X, Y) — 2 . •X^ (1. -Y^Y)
: LINEAR IF(NDF .NE. 4) GO TO 1 DO 5 1-1,4 BA(I)-BASL(L1,L2,S(I) ,T(I))
162
DBA (1,1)-DEAL (L1,L2,S(I),T(I)) 5 DBA(I,2)-DBAL(L2,L1,T(I),S(I)) RETURN
1 IF (NDF .NE. 8) GO TO 2 C QUADRATIC SERENDIPTY
DO 6 1-1,4 BA(D-BASQC(L1,L2,S(I),T(I)) DBA(I,1)-DBAQC(L1,L2,S(I),T(I))
6 DBA(I,2)-DBAQC(L2,Ll,T(I),Sd)) DO 7 1-5,8 BA(I)-BASQM(L1,L2,S(1),T(I)) DBA (1,1)-DBAQM (LI, L2,S(I) ,T(D)
7 DBA(I,2)-DBAQM(L2,L1,T(I) ,S(I)) RETURN
2 DO 8 1-1,4 BA(I)-BASLC (LI,L2,S(I) ,T(I) ) DBA(1,1)-DBALC(LI,L2,S(I) ,T(I))
8 DBA(I,2)-DBALC(L2,L1,T(I),S(I)) DO 9 1-5,8 BA(I)-BASLM(L1,L2,S(I) ,T(I)) DBA(1,1)-DBALM(LI,L2,S(I),T(I))
9 DBA(1,2)-DBALM(L2,LI,T(I) ,S(I)) BA(9)-BASLO(LI, L2) DBA(9,1)-DBAL0(L1,L2) DBA(9,2)-DBALO(L2,LI) RETURN END SUBROUTINE DECB (NDIM, N,ML,MU, B, IP, lER) DIMENSION B(NDIM,1),IP(N)
C LU DECOMPOSITION OF BAND MATRIX A. . L^U - P^A , WHERE P IS A C PERMUTATION MATRIX, L IS A UNIT LOWER TRIANGULAR MATRIX, AND U IS AN C UPPER TRIANGULAR MATRIX C N - ORDER OF MATRIX C B - N BY (2^ML+MU+1) ARRAY CONTAINING THE MATRIX A ON INPUT C AND ITS FACTORED FORM ON OUTPUT. C ON INPUT, B(I,K) (1 .LE. N) CONTAINS THE K-TH DIAGONAL OF A, OR C Ad, J) IS STORED IN B (I, J-I+ML+1) . C ON OUTPUT, B CONTAINS THE L AND U FACTORS, WITH U IN COLUMNS 1 TO ML+MU+1, C AND L IN COLUMNS ML+MU+2 TO 2«ML+MU+1. C ML,MU- WIDTHS OF THE LOWER AND UPPER PARTS OF THE BAND, NOT C COUNTING THE MAIN DIAGONAL. TOTAL BANDWIDTH IS ML+MU+1. C NDIM - THE FIRST DIMENSION (COLUMN LENGTH) OF THE ARRAY B. C NDIM MUST BE .GE. N. C IP - ARRAY OF LENGTH N CONTAINING PIVOT INFORMATION. C lER - ERROR INDICATOR. C - 0 IF NO ERRORS C - K IF THE K-TH PIVOT CHOSEN WAS ZERO (A IS SINGULAR). C THE INPUT ARGUMENTS ARE NDIM, N, ML, MU, B. C THE OUTPUT ARGUMENTS ARE B, IP, lER.
IER-0 IF (N .EQ. 1) GO TO 92 LL-ML+MU+1 Nl-N-1 IF (ML .EQ. 0) GO TO 32 DO 30 I-l,ML II-MU+I K-ML+l-I DO 10 J-1,II
10 Bd, J)-B(I, J+K) K-II+1 DO 20 J-K,LL
20 B(I,J)-0.0 30 CONTINUE 32 LR-ML
DO 90 NR-1,N1 NP-NR+1
163
I F ( L R . N E . N)LR-LR+1 MX-NR XM-ABS(B(NR, D ) IF (ML . E Q . 0)GO TO 42 DO 40 I - N P , L R I F ( A B S ( B ( 1 , 1 ) ) . L E . XM)GO TO 40 MX-1 X M - A B S ( B ( I , 1 ) )
40 CONTINUE 42 I P ( N R ) - M X
IF(MX . E Q , NR)GO TO 60 DO 50 I - 1 , L L XX-B(NR, I ) B(NR, I ) - B ( M X , I )
5 0 B ( M X , I ) - X X 60 XM-B(NR, 1)
IF(XM . E Q . 0 . 0 ) G O TO 100 B ( N R , 1 ) - 1 . / X M I F (ML . E Q . 0)GO TO 90 XM—B(NR, 1) KK-MINO(N-NR,LL-1) DO 80 I - N P , L R J - L L + I - N R X X - B ( I , 1 ) •XM B(NR, J ) - X X DO 70 I I - 1 , K K
70 B ( I , I I ) - B ( I , I I + 1)+XX"B(NR, I I + l ) 80 B ( I , L L ) - 0 . 0 90 CONTINUE 92 NR-N
I F ( B ( N , 1 ) . E Q . 0 . ) G O TO 100 B ( N , 1 ) - 1 . / B ( N , 1 ) RETURN
100 lER-NR RETURN END SUBROUTINE SOLB (NDIM, N,ML,MU, B, Y, IP)
C THE FOLLOWING CARD IS FOR OPTIMIZED COMPILATION UNDER CHAT. DIMENSION B(NDIM,1),Y(N),IP(N)
C SOLUTION OF A"X - C GIVEN LU DECOMPOSITION OF A FROM DECB. C Y - RIGHT-HAND VECTOR C, OF LENGTH N, ON INPUT, C - SOLUTION VECTOR X ON OUTPUT. C ALL THE ARGUMENTS ARE INPUT ARGUMENTS. C THE OUTPUT ARGUMENT IS Y.
IF(N .EQ. 1)G0 TO 60 Nl-N-1 LL-ML+MU+1 IF(ML .EQ. 0)GO TO 32 DO 30 NR-1,N1 IF(IP(NR) .EQ. NR)GO TO 10 J-IP (NR) XX-Y(NR) Y(NR)-Y(J) Y(J)-XX
10 KK-MINO(N-NR,ML) DO 20 I-1,KK
20 Y(NR+I)-Y(NR+I)+Y(NR)"B(NR,LL+I) 30 CONTINUE 32 LL-LL-1
Y(N)-Y(N) "B(N,1) KK-0 DO 50 NB-1,N1 NR-N-NB IF(KK .NE. LL)KK-KK+1 DP-0.0 IF (LL .EQ. 0)GO TO 50
164
DO 40 I-1,KK 40 DP-DP+B(NR, I+1)*Y(NR+I) 50 Y(NR)-(Y(NR)-DP)"B(NR, 1)
RETURN 60 Y(1)-Y(1)*B(1,1)
RETURN END SUBROUTINE TRAP (NDEN,NNP, TI, TF,PA, lER)
TRAPEZOID INTEGRATOR WITH ERROR CONTROL DIMENSION ID (2),PA(NDEN,1) COMMON /BIG/ AA( 80,37),AM( 80,37) COMMON /PI/ V( 80),IP1( 80),B( 80),UI(128),U( 80),D(80,2) COMMON /P2/ ML,ML2,MU,MLM,MLL,NCN,NBDL, DELT, DELTP, EPSMAX, 1AE(9,9),BE(9,9),CE(9),BETA(30,3),T0(30,3),Q(30,3) , IPRMAT COMMON /MY/ VT(128) COMMON /FEC:DTA/ TC (48) ,COORD (182,2) COMMON /FECDTl/ IE (52,9),IP(128,2) NTN-NNP+NCN TIPT-TI+DELTP IF(TIPT .GE. TF)TIPT-TF
SPECIFIED TRUNCATION ERROR SQUARED EPS-NNP^(6.•EPSMAX)""2 TH-1.0/6.0 NSTEP-0 M-0 M3-0
70 M2-1 TIME-TI IF(M3 .GT. 0)GO TO 90 WRITE(6,800)TI,DELT
OUTPUT OF INITIAL SPECIFIED NODAL VALUES OF U RECONSTRUCTION AND OUTPUT OF FULL NODAL SOLUTION VECTOR
NA-1 DO 120 I-1,NTN IF(IP(I,1) .EQ. 0)GO TO 121 I1-I-IP(I,2) VI (I)-UI(Il) GO TO 120
121 VI(I)-TC(NA) NA-NA+1
120 CONTINUE WRITE(6,500) (VI (I),I-1,NTN) WRITE(6,600)
GENERATING FIRST TWO TIME STEPS FOR PREDICTOR-CORRECTOR DO 82 I-l,NNP VI(I)-UI(I) DO 82 J-1,MLL
82 PAd, J)-AM(I, J) CALL DECB(NDEN,NNP,ML,MU,PA,IPl, lER) IF(lER .EQ. 0)GO TO 90 RETURN
90 CONTINUE DO 76 I-l,NNP AB-0.0 DO 78 J-1,NNP K-J-I+MLM IF(K .LE. 0 .OR. K .GT. MLL)GO TO 78 AB-AB+AA(I,K)-UI(J)
7 8 CONTINUE IF(M2 .EQ. 1 .AND. M3 .EQ. 0) V (I)—AB+B(I)
76 U(I)-(-AB+B(I))«DELT IF(M2 .EQ. 2)GO TO 94 IF(M3 .EQ. 1)G0 TO 31 CALL SOLB (NDEN,NNP,ML,MU, PA, V, IPl) DO 80 I-l,NNP
80 D(I,1)-V(I)^DELT
165
62 IF(M3 .EQ. 0)GO TO 91 31 DO 61 I - l ,NNP 61 D ( I , 1 ) - T R ^ D ( I , 1 ) 91 DO 93 I - l ,NNP
DO 93 J-1,MLL 93 P A d , J ) - A M d , J ) + .5^DELT«AA(I,J)
CALL DECB(NDEN,NNP,ML,MU,PA,IPl,lER) I F d E R .EQ. 0)GO TO 94 RETURN
94 CALL SOLB(NDEN,NNP,ML,MU,PA,U,IPl) IF(M2 .EQ. 2)GO TO 100 DO 98 I-l,NNP D(I,2)-2.^U(I)-D(I,1)
98 UI(I)-U(I)+UI(I) TIME-TIME+DELT NSTEP-NSTEP+1 M2-2 GO TO 90
100 E-0.0 COMPUTATION OF LOCAL TRUNCATION ERROR
DO 101 I-l,NNP 101 E-E+(U(I)-1.5"D(I,2) + .5»D(I,1))^*2 CHECK TO SEE IF STEP SIZE SHOULD BE CHANGED
IF(E .GT. EPS) GO TO 97 TIME-TIME+DELT NSTEP-NSTEP+1 DO 104 I-l,NNP UI(I)-U(I)+UI(I)
104 D(I,1)-2.^U(I)-D(I,2) ID(1)-1 ID(2)-2 BEO-1.5 BEl—.5 IF(TIME .GE. TIPT)GO TO 1050 GO TO 85
CHANGE IN STEP SIZE AND START OVER 97 TR-.8*(EPS/E)••TH
DELT-TR^DELT M3-1 DO 103 I-l,NNP
103 UI d)-VI(I) GO TO 70
105 DO 92 I-l,NNP DO 92 J-1,MLL
92 PAd, J)-AM(I, J)+.5^DELT«AA(I, J) CALL DECB(NDEN,NNP,ML,MU,PA,IPl,lER) IFdER .EQ. 0)GO TO 85 RETURN
85 CONTINUE TR-1.0
GENERATION OF SOLUTION AFTER FIRST TWO STEPS DO 56 I-1,NI^ AB-0.0 DO 55 J-1,NNP K-J-I+MLM IF(K .LE. 0 .OR. K .GT. MLL)GO TO 55 AB-AB+AA(I,K)•UI(J)
55 CONTINUE 56 U(I)-(-AB+B(I))^DELT
CJILL SOLB (NDEN, NNP, ML,MU, PA, U, IPl) E-0.0
COMPUTATION OF LOCAL TRUNCATION ERROR DO 87 I-l,NNP
87 E-E+(U(I)-BE0^D(I,ID(1) ) -BEl-D (I, ID (2) ) )""2 EPS-9."NNP"((TR+1.0)«EPSMAX/TR)""2
ABOVE STATEMENT ACCOUNTS FOR EFFECT OF STEP CHANGE ON
166
C THE LOCAL TRUNCATION ERROR C CHECK TO SEE IF STEP SIZE SHOULD BE CHANGED
IF(E .LE. EPS) GO TO 109 C CHANGE IN STEP SIZE
TR-.8*(EPS/E)«"TH BE0-1.0+.5*TR BEl-l.O-BEO DO 42 I-l,NNP D(I,1)-TR"D(I,1)
42 D(I,2)-TR^D(I,2) DELT-TR^DELT 60 TO 105
C CHANGE IN STEP SIZE 109 M-M+1
BEO-1.5 BEl—.5 MA-ID(2) ID (2)-ID (1) ID(1)-MA TIME-TIME+DELT NSTEP-NSTEP+1 DO 83 I-l,NNP UI(I)-U(D+UI(I)
83 D(I,MA)-2.^U(I)-D(I,ID(2)) IF(TIME .GE. TIPT)GO TO 1050 IF(M .GE. 4)GO TO 102 GO TO 85
102 TR-.8^(EPS/E)^^TH C CHECK TO SEE IF TIME STEP INCREASE IS LARGE ENOUGH
IF(TR .LT. 1.5)GO TO 85 BE0-1.0+.5^TR BEl-l.O-BEO DELT-TR^DELT DO 43 I-l,NNP D(I,1)-TR^D(I,1)
43 D(I,2)-TR^Dd,2) M-0 GO TO 105
C INTERPOLATION OF SOLUTION AT SPECIFIED TIME VALUE 1050 T20-(TIME-TIPT)/DELT
AL—T20* (l.-.5^T20) BL—.5^(T20^*2) DO 1051 I-l,NNP
1051 U(I)-UI(I)+AL^D(I,ID(1))+BL«D(I,ID(2)) EE-SQRT(E) WRITE(6,801)EE,TIPT,DELT
C RECONSTRUCTION AND OUTPUT OF FULL NODAL SOLUTION VECTOR NA-1 DO 122 I-1,NTN IF(IP(I,1) .EQ. 0)GO TO 123 I1-I-IP(I,2) VI(I)-U(I1) GO TO 122
123 VI(I)-TC(NA) NA-NA+1
122 CONTINUE WRITE(6,500)(VI(I),I-1,NTN) WRITE(6,450)TIPT, (U(I) ,1-1,NNP) WRITE(6,600)
802 FORMAT(38X,28HTOTAL NUMBER OF TIME STEPS -,I5) 801 FORMAT(27X,13H(TIME ERROR -,ElO.3,IH),2X,6HTIME -,F10.5,2X,
17H(DELT -,E10.3,1H)) 800 FORMAT(51X,6HTIME -,FIO.5,2X,7H(DELT -,E10.3,1H)) 600 FORMAT(/) 500 FORMAT(6(3X,E15.8)) 450 FORMAT(6E13.6)
167
IF(ABS(TIPT-TF) .LE. 1.0E-06)GO TO 1052 TIPT-TIPT+DELTP 1F(TIPT .GE. TF)TIPT-TF IF(TIME .GE. TIPT)GO TO 1050 1F(M .GE. 4)GO TO 102 GO TO 85
1052 WRITE(6,600) WRITE(6,802)NSTEP RETtJRN END SUBROUTINE CSTEP(NDEN,NVNP,NTRAN,GAM,TI,TF,PA,lER)
C CONSTANT STEP SIZE TIME INTEGRATOR C NOTE (1) FIRST OR SECOND ORDER C (2) LINEAR INTERPOLATION USED AT PRINT TIMES
C GAM - INTEGRATION METHOD PARAMETER C - 0, FOR EXPLICIT EULER (WITH ASSOCIATED STABILITY LIMIT) C - 0.5, FOR TRAPEZOID RULE (IMPLICIT) C - 1.0, FOR IMPLICIT EULER
C lER - ERROR FLAG, 0 IF INTEGRATION IS SUCESSFUL AND 1 OTHERWISE C NSTEP - NO. OF TIME STEPS NEEDED TO REACH TIME -TF C NTRAN - 1 FOR CONSISTENT MASS C NTRAN - 2 FOR LUMPED MASS
C PUT COMMON BLOCKS FROM MAIN IN HERE COMMON /BIG/ AA( 80,37),AM( 80,37) COMMON /PI/ V( 80),IP1( 80),B( 80),UI(128),U( 80),D( 80,2) COMMON /P2/ ML,ML2,MU,MLM,MLL,NCN,NBDL,DELT,DELTP,EPSMAX, 1AE(9, 9) ,BE(9,9) ,CE(9) ,BETA(30, 3) , TO (30, 3) , Q (30, 3) , IPRMAT COMMON /MY/ VT(128) COMMON /FECDTA/ TC(48),COORD(182,2) COMMON /FECDTl/ IE(52,9),IP(128,2)
DIMENSION PA(NDEN, 1) C ZERO UNASSIGNED VARIABLES
IER-0 C INITIALIZE MISCELLANEOUS PARAMETERS
NTN-NVNP+NCN METH-0 NSTEP-0 TIME-TI IER-0 TIPT-TI WRITE(6,801)TI
C OUTPUT OF INITIAL SPECIFIED NODAL VALUES OF U C RECONSTRUCTION AND OUTPUT OF FULL NODAL SOLUTION VECTOR
NA-1 DO 120 I-1,NTN IF (IP(I,1) .EQ. 0) GO TO 121 I1-I-IP(I,2) VI(I)-UI(I1) GO TO 120
121 VI(I)-TC(NA) NA-NA+I
120 CONTINUE WRITE(6,800) (VI(J),J-1,NTN) WRITE(6,802) TIPT-TI+DELTP IF (TIPT .GE. TF) TIPT-TF
C USE DIFFERENT (MORE EFFICIENT) ALGORITHM IF USING C EXPLICIT EULER ON LUMPED MASS SCHEME
IF ((NTRAN .NE. 1) .AND. (GAM .EQ.O.)) GO TO 84 C DECOMPOSE MATRIX ONCE AND FOR ALL
DO 92 I-l,NVNP DO 92 J-1,MLL
168
PAd,J)-AM(I,J)+GAM^DELT^AA(I,J) 92 CONTINUE
CALL DECB(NDEN,NVNP,ML,MU,PA,IP1,IER) IF (lER .NE. 0) GO TO 1999
C INCORPORATE DELT PERMANENTLY INTO RHS WHERE EQUATION OF INTEREST IS «^ «.. AM*(U(N+1)-U(N)/DELT —AA*U (N) + B DO 82 I-l,NVNP B(I)-B(I)*DELT DO 81 J-1,MLL AA(I,J)-AAd,J)"DELT
81 CONTINUE 82 CONTINUE
GO TO 85 84 CONTINUE
METH-1 C LOOP 199/200 ONLY DONE FOR LUMPED MASS EXPLICIT EULER
DO 200 I-l,NVNP AB-DELT/AM(I,MLM) 3(I)-B(I)*AB DO 199 J-1,MLL AAd, J)-AA(I, J)*AB
199 CONTINUE 200 CONTINUE 85 CONTINUE
C GENERATION OF SOLUTION DO 55 I-l,NVNP U(I)-0.0 DO 56 J-1,NVNP K-J-I+MLM IF (K .LE. 0 .OR. K .GT. MLL) GO TO 56 U(I)-U(I)-AA(I,K)«UI(J)
56 CONTINUE U(I)-U(I)+B(I)
55 CONTINUE IF (METH .EQ. 1) GO TO 57 CALL SOLB(NDEN,NVNP,ML,MU,PA, U, IPl)
57 TIME-TIME+DELT NSTEP-NSTEP+1 DO 83 I-l,NVNP D(I,1)-UI(I) UI(I)-U(I)+UI(I)
83 CONTINUE IF (TIME .GE. TIPT) GO TO 1050 GO TO 85
C LINEAR INTERPOLATION OF SOLUTION AT SPECIFIED TIME VALUE C INTERP. FORM— U (PRINT)-U (OLD)-r (T (PRINT)-T (OLD) )/DELT" (U (NEW)-U (OLD) ) 1050 T20-((TIME-DELT)-TIPT)/DELT
DO 1051 I-l,NVNP 1051 U(I)-D(I,1)+T20"U(I)
WRITE(6,801) TIPT C RECONSTRUCTION AND OUTPUT OF FULL NODAL SOLUTION VECTOR
NA-1 DO 122 I-1,NTN IF (IP (1,1) .EQ. 0) GO TO 123 I1-I-IP(I,2) VI(I)-U(I1) GO TO 122
123 V1(I)-TC(NA) NA-NA+1
122 CONTINUE WRITE(6,800) (VI (J),J-1,NTN) WRITE(6,802) IF(ABS(TIPT-TF) .LE. l.OE-06) GO TO 1052 TIPT-TIPT+DELTP IF(TIPT .GE. TF) TIPT-TF IF(TIME .GE. TIPT) GO TO 1050
169
GO TO 85 1999 CONTINUE
C FORMAT STATEMENTS
802 FORMAT(/)
iSsI wS??5^°'''"'^^''^'' ^ ° ^ " ^^°--- ^^^^ ABORTED.,//) RETURN END SUBROUTINE NODAL
C
r l^^rlr^l^J^^ ROUTINE WHICH ASSIGNS NODE NUMBERS, NEIGHBORS, S ^.-^S^^^°*^^ ^0 ^ ^ NODE POINTS IN THE RUBBLE BED. NODAL COORD-H , ^ H! AREAS, VOLUMES, ELEMENTAL CONFIGURATIONS, AND DISTANCES ^ ^ H^^° ^°^ SOLVING THE PRESSURE FIELD AND THE MATERIAL AND C ENERGY BALANCES AT EACH NODE POINT C
COMMON /BIG/ AA( 80,37),AM( 80,37) COMMON /PI/ V( 80),IP1( 80),B( 80),UI(128),U( 80),D( 80,2) COMMON /P2/ ML,ML2,MU,MLM,MLL, NCN,NBDL, DELT, DELTP, EPSMAX, lAE(9,9),BE(9,9),CE (9),BETA (30,3),TO(30,3),Q(30,3) COMMON /MY/ VK128) COMMON /MORE/ GENSUM COMMON /NODE/ Nl(70),N2(70),N3(70) ,N4(70) COMMON /DISTAN/ DIS(50,50) COMMON /ARE/ AREA(50,50) COMMON /VOLUM/ VOLUME(50) COMMON /POINT/ NNP,NX,NE COMMON /NET/ TOTVOL,VERTSP,TIMEFR COMMON /NETT/ ITIME COMMON /CONS/ CARCON COMMON /CB/ CARGAS COMMON /FECDTA/ TC(4 8),COORD(182,2) COMMON /FECDTl/ IE(52,9),IP(128,2) COMMON /COUNT/ ILL COMMON /VCY/ BIGBRO COMMON /VCK/ VELCON DIMENSION PA (80, 55) , DUMMY (50, 2) ,DELY"(20) ,BRO(20) , DEE (20) DATA NDEN/80/ DATA IX,DELYLT,DELYBG,PI,IXC/0,2.0,5.0,3.14, 1/ DATA PR1,PR2/1.0,2.5/ DATA ICODE/2/ DENCOL-100."(0.304 8""3)/.454 WID-1.0 BR0(l)-5. DEE (1)-10. IZ-ITIME-1
C C BASED ON LATERAL GROWTH (SIDE WALL), NEW DIMENSIONS ARE OBTAINED. C ALSO, BASED ON VERTICAL SPALLING, A NEW HEIGHT FOR THE BED IS C OBTAINED FOR LATER TIME STEPS. C
IFdTIME.GT.l) GO TO 4 GO TO 5
4 BRO (ITIME) -BRO (IZ) + (BIGBRO-2000 . ) "VELCON C DEE(ITIME)-DEE(IZ)+(VERTSP/(24."3600.)"TIMEFR"BRO(ITIME)"WID-C ITOTVOL)/(BRO(ITIME)"WID)
WRITE (6,7777) TOTVOL,TIMEFR,VERTSP,BRO(ITIME) ,WID 7777 FORMAT(5X,'VOL- ',E15.7,2X,'TIM- ',E15.7,2X,'SP- ',E15.7,2X,
I'BRO- ',E15.7,2X,'WID- ',E15.7) DEE(ITIME)-DEE(IZ)
C IFdCODE.NE.l) DEE (ITIME)-DEE (IZ) +(VERTSP/(24. "3600.) "BRO C 1(ITIME)""2"PI*TIMEFR-T0TV0L)/(PI"BRO(ITIME) ""2) C WRITE(6,6) DEE(ITIME),ITIME 6 FORMAT(5X,'DEE- ',E15.7,5X,'TIME- ',12)
170
R - 1 . 2 5 NCN-1 NX-5 LJ-1 LL-0
C THE PROCEDURE IS STARTED TO ASSIGN NODE LOCATIONS AND COORDINATES, C
COORD(1,1)-R COORD(1,2)-0.0 IP(l,l)-0 TC(1)-PR2 Nl(l)-2 N2(1)-1+NX+1 N3(l)-0 N4(l)-0
72 FORMAT(5X,'LJ- ',I2,5X,'TC- ',E15.7) : WRITE(6,71) IXC,COORD(1,1),COORD(1,2),IP(1,1)
YOLD-R ICTR-1 ILK-1 NNP-1 Y-0.0 MLK-1 YP-0.0 MINX-NX-1 DO 300 ICTR-1,MINX YP-Y+R/4. IF(MLK.GT.l) GO TO 676 LB-NX-1 DO 206 I-l,LB WY-0. IFd.EQ.LB) GO TO 3001 GO TO 3002
3001 COORD(NX,1)-(BRO(ITIME)-R)/(2."(NX-1))+COORD(1,1) COORD(NX,2)-WY IP (NX, 1)-2
; WRITE(6,71) NX,COORD(NX,1),COORD(NX,2),IP(NX,1) NXPLl-NX+1 COORD(NXPLl,1)-BRO(ITIME) COORD(NXPLl,2)-WY IP(NXPLl,1)-2
; WRITE(6,71) NXPL1,C00RD(NXPLl,1),COORD(NXPLl,2),IP(NXPLl, 1) IAND-IAND+1 GO TO 3003
3002 EXX-(BRO(ITIME)-R)"I/(NX-1)+R IAND-I+1 COORD(lAND,1)-EXX C00RD(IAND,2)-WY
3003 IP(IAND,l)-2 IB-I+1 IBB-I+2 IFd.EQ.LB) GO TO 41 GO TO 42
41 Nl(IBB)-IB N2(I3B)-IBB+NX+1 N3(IBB)-0 N4(IBB)-O
; WRITE(6,76) IBB,N1(IBB),N2(IBB),N3(IBB),N4(IBB) 42 Nl (IB)-IB+1
N2 (IB)-IB+NX+1 N3(IB)-I N4(IB)-0
: WRITE (6, 71) lAND, COORD (lAND, 1) , COORD (lAND, 2) , IP (IAND,1) : WRITE(6,76) IB,NldB) ,N2(IB) ,N3(IB) ,N4(IB) 20 6 CONTINUE
171
676 1AND-ICTR*NX+ICTR+1 COORD(lAND,1)-SQRT(R**2-YP**2) COORD (LAND, 2)-YP IP(IAND,1)«0 N1(IAND)-IAND+1 N2(lAND)-IAND+NX+1 N3(LAND)-IAND-NX-1 N4 (lAND)-O NCN-NCN+1 LJ-LJ+1 TC(LJ)-PR2
C Sg?l!|;?|! J5^i^J;j^)'N2(IAND),N3(IAND),N4(IAND)
^ NKNX-I'^^' ^^^ND, COORD (IAND,1), COORD (LAND, 2), IP ( LAND, 1) DO 1332 I-1,NN ECH-BRO(ITIME) IF(I.EQ.NN) GO TO 3004 GO TO 3005
3004 INX-IAND+1
C00RD(lSc;2)-S^^"^°^^^^"^"^"^^^^^^'^^'^>'**=°°"^<^^^'^> I P d N X , 1 ) - 1
C WRITE ( 6 , 71 ) INX,COORD(INX, 1 ) , COORD (INX, 2 ) , I P d N X , 1)
COORD(INXP,1)-ECH C 0 0 R D ( I N X P , 2 ) - Y P I P (INXP, 1 ) - 2 N l ( I N X P ) - I N X N2(INXP)-INXP+NX+1 N 3 ( I N X P ) - I N X P - N X - 1 N4 dNXP)-0
C WRITE(6,71) INXP,COORD(INXP,1),COORD(INXP,2),IP(INXP,:) C W?.ITE(6,76) INXP,N1(INXP) ,N2(INXP) ,N3(INXP),N4 (INXP)
IAND-IAND+1 GO TO 3006
3005 Z.\1-(ECH-SQRT(R*"2-YP*"2) ) /NN"I C '".•~.ITE(6, 991) ECH,YP,NN,EX1,I 991 -CRMAT(5X,'H- ',E15.7,3X,'YP/YN- ',E15.7,3X,'NN- ',I2,/,5X,
I'EXl- ',E15.7,3X,'I- ',12) IAND-IAND+1 COORD(lAND,1)-EX1+SQRT(R""2-YP""2) COORD(lAND,2)-YP
3006 IP(IAND,1)-1 IB-IAND+1 Nl (lAND)-IAND-l N2 (IAND)-IAND+1 N3(lAND)-IAND-NX-1 N4 (lAND)-IAND+NX+1 IFd.EQ.NN) GO TO 12 GO TO 1332
12 N1(IB)-IAND N2(IB)-IB+NX+1 N3(IB)-IB-NX-1 N4 (IB)-O
C 13 WRITE(6,76) lAND, Nl (lAND) ,N2 (lAND) ,N3 (lAND) , N4 (lAND) C WRITE (6,71) IAND,C00RD(IAND,1),C00RD(IAND,2),IP(lAND,1) 1332 CONTINUE
Y-YP MLK-MLK+1
300 CONTINUE DO 59 11-1,20 DELY(II)-DELYBG-(DELYBG-DELYLT)/DEE(ITIME)"(DEE(ITIME)-YOLD) YNEW-YOLD+DELY(II) IF(YNEW.GT.DEE(ITIME)) GO TO 18 GO TO 19
172
18 YNEW-DEE(ITIME)
'' llS^Sri^^lJScJJ^ * " • M2,/,5X,'1ST NEAREST NEIGHBOR- ',12,/,
"/:5^!^4?f5^^^^°£o;:'^^2r''^^ ^^^ ^ ^ ' ^ ''" '' i'??^i'^E!?^?!/!5jf:i;:^?;/^r'—- ''--^'/'=x/ 19 IAND-NX*(ICTR+l)+l+dCTR+l)
COORD(LAND,1)-0.0 COORD(LAND,2)-YNEW IF(YNEW.EQ.DEE(ITIME)) GO TO 20 IP(IAND,l)-2 Nl(IAND)-IAND+1 N2(LAND)-IAND+NX+1 N3(lAND)-IAND-NX-1 N4 (lAND)-O GO TO 202
20 IP(IAND,l)-0 Nl(lAND)-IAND-NX-1 N2(IAND)-IAND+1 N3(lAND)-O N4(lAND)-O NCN-NCN+1 LJ-LJ+1 TC (LJ) -PRl
C WRITE(6,72) LJ,TC(LJ) C202 WRITE (6, 76) IAND,N1 (lAND) ,N2 (LAND) ,N3 (lAND) ,N4 (lAND) C WRITE(6,71) LAND,COORD(LAND,1),COORD(lAND,2),IP(LAND,1) 202 NN-NX-1
DO 332 I-1,NN ECH-BRO(ITIME) IFd.EQ.NN) GO TO 3007 GO TO 3008
3007 INX-IAND+1 COORD (INX, 1) -COORD (LAND, 1) +ECH/ (2 . * (NX-1) ) COORD(INX,2)-YNEW IP(INX,1)-1
C WRITE(6,71) INX,COORD(INX,1),COORD(INX,2) , IP(INX, 1) INXP-INX+1 COORD(INXP,1)-ECH COORD(INXP,2)-YNEW IP(INXP,l)-2 Nl(INXP)-INX N2(INXP)-INXP+NX+1 N3(INXP)-INXP-NX-1 N4(INXP)-O IF(YNEW.EQ.DEE(ITIME)) GO TO 3010 GO TO 3011
3010 Nl(INXP)-INXP-NX-1 N2(INXP)-INX N3(INXP)-0 IP(INXP,l)-0
C3011 WRITE(6,76) INXP, Nl (INXP) ,N2 (INXP) ,N3 (INXP) , N4 (INXP) C WRITE(6,71) INXP,COORD(INXP,1),COORD(INXP,2),IP(INXP,1) 3011 IAND-IAND+1
IF(YNEW.EQ.DEE(ITIME) ) IP(INXP,l)-0 IP(INXP,1)-2 GO TO 3009
3008 EX1-ECH/NN*I C WRITE(6,991) ECH,YNEW,NN,EXl, I
IAND-IAND+1 COORD(lAND,1)-EXl COORD(lAND,2)-YNEW
3009 IF(YNEW.NE.DEE(ITIME)) GO TO 43 IP(IAND,l)-0 GO TO 44
43 IP(IAND,1)-1
173
IB-IAND+l N1(IAND)-IAND-1 N2(IAND)-IAND+1 N3(lAND)-IAND-NX-1 N4(LAND)-IAND+NX+1 IF(I.NE.NN) GO TO 332 N1(IB)-IAND N2(IB)-IB+NX+1 N3(IB)-IB-NX-1 N4dB)-0 GO TO 332
44 NCN-NCN+1 LJ-LJ+1 TC(LJ)-PRl Nl(lAND)-IAND-NX-1 N2(IAND)-IAND+1 N3(IAND)-IAND-1 N4(lAND)-O IB-IAND+1 IFd.EQ.NN) GO TO 91 GO TO 332
91 N1(IB)-IB-NX-1 N2 (IB)-IAND N3(IB)-0 N4(IB)-0 LJ-LJ+1 TC (LJ) -PRl IP(IB,l)-0
C WRITE(6,76) IB,N1(IB),N2(IB),N3(IB) ,N4(IB) C 92 WRITE(6,72) LJ,TC(LJ) C 45 WRITE(6,76) IAND,N1(lAND),N2(lAND),N3(lAND),N4(lAND) C WRITE (6, 71) LAND, COORD (lAND, 1) , COORD (LAND, 2) , IP (LAND, 1) 332 CONTINUE
ICTR-ICTR+1 ILK-ILK+1 YOLD-YNEW IF(YNEW.GE.DEE (ITIME)) GO TO 30
5 9 CONTINUE 30 ICTMAX-ICTR
DO 301 ICTR-1,ICTMAX L-LL+1 MCC-NX*ICTR DO 301 J-L,MCC IE(J,1)-J+ICTR-1 IE(J,2)-IE(J,1)+1 IE(J,3)-IE(J,2)+NX+1 IE(J,4)-IE(J,3)-1 LL-NX"ICTR
C WRITE(6,69) IE (J, 1) , IE (J, 2) , IE (J, 3) , IE (J, 4) 69 FORMAT(4(5X,12) )
301 CONTINUE NNP- (ICTR+1)*(NX+1) NCN-NCN+1 NE—ICTR*NX
C WRITE(6,70) ICTR,NNP,NE,LJ 70 FORMAT(5X,'CTR- ',12,/,5X,'•NODE POINTS- ',I2,/,5X,
l'# ELEMENTS- ',I2,/,5X,'# CONST NODES- ',12) DO 330 1-1,50 DO 329 J-1,50 AREA(I,J)-0.0 DISd, J)-0.0
32 9 CONTINUE VOLUME(I)-0.0
330 CONTINUE
C BASED ON SPATIAL COORDINATES, THE DISTANCES BETWEEN THE NODE POINTS
174
C IS OBTAINED. C
DO 326 J0S-1,NNP DIS(J0S,N1(JOS))-SQRT((COORD(JOS,1)-COORD(Nl(JOS) , 1))"*2+ 1(COORD(JOS,2)-COORD(Nl(JOS),2))"»2) DIS(J0S,N2(JOS))-SQRT((COORD(JOS,1)-COORD(N2(JOS),1))**2+ 1 (COORD (JOS, 2) -COORD (N2 (JOS) , 2) ) **2) IF(N3(JOS).EQ.O) GO TO 326 DIS(J0S,N3(JOS))-SQRT((COORD(JOS,1)-COORD(N3(JOS),1))**2+ 1 (COORD (JOS, 2)-COORD (N3( JOS) ,2) ) **2) IF (N4 (JOS) .EQ.O) GO TO 326 DIS(J0S,N4(JOS))-SQRT((COORD(JOS,1)-COORD(N4(JOS),1))""2+ 1(COORD(JOS,2)-COORD(N4(JOS),2))""2)
326 CONTINUE DO 327 J-1,NNP IF(N3(J) .EQ.O) N3(J)-49 IF (N4 (J) .EQ.O) N4(J)-50
C WRITE (6,328) J,DIS(J,N1(J)),DIS(J,N2(J)) , DIS(J,N3(J) ) , C 1DIS(J,N4(J) ) 328 FORMAT(5X,'POINT # IS- ',12,/,5X,'DISl- ',E15.7,2X,'DIS2- '
1E15.7,2X,'DIS3- ',E15.7,2X,'DIS4- ',E15.7) 327 CONTINUE
IFdCODE.EQ.l) GO TO 941 GO TO 992
941 DO 50 I-l,NX C c C THE FLOW AREA BETWEEN THE NODE POINTS IS OBTAINED. C ALSO, THE EFFECTIVE VOLUME OCCUPIED BY EACH NODE IS CALCULATED, C c
AREA(I,N1 (I) )-(COORD(I,2)+COORD(I+NX+l,2) ) 12. AREA(N1(I) ,I)-AREA(I,N1(I))
50 CONTINUE C WRITE(6,7010) AREA(1,2),AREA(2,1),AR£A(2,3),AREA(3,2) C WRITE(6,7010) AREA(3,4),AREA(4,3),AREA(4,5),AREA(5,4) 7010 F0RMAT(4(3X,E15.7))
NXPLl-NX+1 DO 53 I-l,NXPLl IFd.EQ.l) GO TO 51 GO TO 52
51 IAJAY-1 GO TO 54
52 IAJAY-I-1 54 IF(I.EQ.NXPLl) GO TO 56
GO TO 57 56 lAKAY-NXPLl
GO TO 58 57 IAKAY-I+1 58 VOLUME (I) - (COORD (lAKAY, 1) -COORD (lAJAY, 1) ) /2 . "AREA(I,N1 (I) ) 53 CONTINUE
ICCL-(IAND+1)/NXPLl DEPTH-1.0 ICLMNl-ICCL-1
C WRITE(6,999) ICCL,ICLMN1 999 FORMAT(5X,'ICCL- ',12,3X,'ICLMNl- ',12)
DO 29 J-1,ICLMNl ZDIL-J"(NX+1)+1 ZEIL-ZDIL+1 ZFIL-ZDIL+NX+1-2 ZLIL-ZFIL+1 ZGIL-ZDIL+NX+1 ZHIL-ZDIL-NX-1 JZEIL-IFIX(ZEIL) JZFIL-IFIX(ZFIL) JZDIL-IFIX(ZDIL)
175
J2HIL-IF1X(ZHIL) J2GIL-IF1X(2GIL) JZLIL-IFIX(ZLIL) ZNIL-COORD(JZEIL,1)/2. ZKIL- (COORD (J2L1L, 1) -COORD (JZFIL, 1) ) /2. DO 321 JJ-J2E1L, JZFIL IF(J.EQ.ICLMNl) J2GIL-JJ ZIIL-(COORD(JJ+1,1)-COORD(JJ-l,l))/2. ZOIL-(COORD(JZGIL,2)-COORD(JZHIL, 2) ) /2 . IF(J.EQ.ICLMNl) GO TO 801 AREA(JJ,N2(JJ))-ZOIL AREA(JJ,N3(JJ))-ZIIL AREA (JJ, N4 (JJ) ) -ZIIL AREA (N2 (JJ) , JJ) -AREA (JJ, N2 (JJ) ) AREA (N3 (JJ) , JJ) -AREA (JJ, N3 (JJ) ) AREA(N4(JJ),JJ)-AREA(JJ,N4(JJ)) VOLUME(JJ)-ZOIL"ZIIL GO TO 321
801 AREA(JJ,N2(JJ))-DEPTH"ZIIL AREA(N2(JJ),JJ)-AREA(JJ,N2(JJ)) VOLUME(JJ)-AREA(JJ,N2(JJ))"ZOIL
321 CONTINUE IF(J.EQ.ICLMNl) GO TO 802 VOLUME(JZDIL)-ZOIL*ZNIL VOLUME(JZLIL)-ZOIL*ZKIL AREA(JZDIL,Nl(JZDIL))-ZOIL AREA(JZDIL,N2(JZDIL))-ZNIL AREA(JZDIL,N3(JZDIL))-ZNIL AREA(JZLIL,N2(JZLIL))-ZKIL AREA(JZLIL,N3(JZLIL))-ZKIL AREA(Nl(JZDIL),JZDIL)-AREA(JZDIL,Nl(JZDIL)) AREA(N2(JZDIL),JZDIL)-AREA(JZDIL,N2(JZDIL)) AREA (N3 (JZDIL) , JZDIL) -AREIA (JZDIL, N3 (JZDIL) ) AREA (N2 (JZLIL) , JZLIL) -AREA (JZLIL, N2 (JZLIL) ) AREA(N3(JZLIL),JZLIL)-AREA(JZLIL,N3(JZLIL)) GO TO 29
802 AREA(JZDIL,N2(JZDIL))-DEPTH^ZNIL AREA(N2(JZDIL),JZDIL)-AREA(JZDIL,N2(JZDIL)) VOLUME(JZDIL)-AREA(JZDIL,N2(JZDIL))•ZOIL VOLUME(JZLIL)-ZOIL^AREA(JZLIL,JZFIL)
29 CONTINUE GO TO 993
992 DO 500 I-l,NX AREA(I,N1(I))-(COORD(I,1)+C00RD(1+1,1))/2.^2."PI" 1(COORD(I,2)+COORD(I+NX+1,2))/2. AREA(N1(I) ,I)-AREA(I,N1(I) )
500 CONTINUE ; WRITE(6,7010) AREA(1,2),AREA(2,1),AREA(2,3),AREA(3,2) ; WRITE(6,7010) AREA(3,4) ,AREA(4,3) ,AREA(4,5) ,AREA(5,4)
NXPLl-NX+1 ICCL-(IAND+1)/NXPLl ICLMNl-ICCL-1 DO 290 J-1,ICLMNl ZDIL-J"(NX+1)+1 2EIL-ZDIL+1 ZFIL-ZDIL+NX-1 ZLIL-ZFIL+1 ZGIL-ZDIL+NX+1 ZHIL-ZDIL-NX-1 JZEIL-IFIX(ZEIL) JZDIL-IFIX(ZDIL) JZFIL-IFIX(ZFIL) JZHIL-IFIX(ZHIL) JZGIL-IFIX(ZGIL) JZLIL-IFIX(ZLIL) ZNIL-((COORD(JZDIL,1)+COORD(JZDIL+1,1))/2.)""2-
176
1(COORD(JZDIL,1))•*2 DO 421 JJ-J2EIL,JZFIL ZPIL-(COORD(JJ,1)+C0ORD(JJ+1,1))/2. ZOIL- (COORD (JJ-1,1) +C0ORD (JJ, 1) ) /2 . IF(J.EQ.ICLMNl) JZGIL-JJ ZIIL-(COORD(JZGIL,2)-COORD(JZHIL,2))/2. ZMIL-PI"(ZPIL^^2-ZOIL^*2) IF(J.EQ.ICLMNl) GO TO 5004 AREA (JJ,N2 (JJ) ) -ZIIL^2. •PI^ZPIL AREA (JJ, N3 (JJ) )-ZMIL AREA (JJ, N4 (JJ) ) -ZMIL AREA (N2 (JJ) , JJ) -AREA (JJ,N2 (JJ) ) AREA (N3 (JJ) , JJ) -AREA (JJ, N3 (JJ) ) AREA(N4(JJ) ,JJ)-AREA(JJ,N4(JJ)) VOLUME (JJ)-AREA (JJ,N3 (JJ) ) •ZIIL GO TO 421
5004 AREA(JJ,N2 (JJ) )-2 . •PI^ZPIL^ZIIL AREA(N2(JJ) , JJ)-AREA(JJ,N2(JJ)) VOLUME(JJ)-ZIIL*ZMIL
421 CONTINUE
IF(J.EQ.ICLMNl) GO TO 5001 AREA (JZDIL,Nl(JZDIL))-2.•PI^ZIIL^(COORD(JZDIL,1)+C00RD( lJZDIL+l,l))/2. AREA(JZDIL,N2(JZDIL))-PI^ZNIL AREA(JZDIL,N3(JZDIL))-PI^ZNIL VOLUME(JZDIL)-AREA(JZDIL,N2(JZDIL))"ZIIL AREA (JZLIL,N2(JZLIL))-PI"(COORD(JZLIL,1)••2-((COORD(JZLIL 1,1)+COORD(JZFIL,1))/2.)^^2) AREA(JZLIL,N3(JZLIL))-PI^(COORD(JZLIL,1)""2-((COORD(JZLIL 1,1)+COORD(JZFIL,1))/2.)""2) VOLUME(JZLIL)-AREA(JZLIL,N2(JZLIL))"ZIIL AREA (Nl(JZDIL),JZDIL)-AREA(JZDIL,Nl(JZDIL)) AREA (N2(JZDIL),JZDIL)-AREA(JZDIL,N2(JZDIL)) AREA (N3(JZDIL),JZDIL)-AREA(JZDIL,N3(JZDIL)) AREA (N2 (JZLIL) , JZLIL) -AREA (JZLIL, N2 (JZLIL) ) AREA(N3(JZLIL),JZLIL)-AREA(JZLIL,N3(JZLIL)) IF(J.NE.l) GO TO 290 DO 5002 JI-1,6 VOLUME (JI) -AREA(JI,N2 (JI) ) "COORD (J+NX+1, 2) /2 .
5002 CONTINUE GO TO 290
5001 AREA(JZDIL,N2(JZDIL))-2."PI"ZIIL"(COORD(JZDIL, 1) +COORD 1(JZDIL+1,l))/2. AREA (N2(JZDIL),JZDIL)-AREA(JZDIL,N2(JZDIL)) VOLUME(JZDIL)-ZNIL"PI"ZIIL VOLUME(JZLIL)-PI"ZIIL"(COORD(JZLIL,1)""2-((COORD (JZLIL l,l)+COORD(JZFIL,l))/2.)""2)
290 CONTINUE 993 JABB-IAND-NX-1
lANDPl-IAND+1 C WRITE(6,191) JABB,ICCL,LAND 191 FORMAT(3(3X,12))
C WRITE(6,7010) VOLUME(1),VOLUME(2),VOLUME(3) , VOLUME(4) DO 324 JJ-1,IANDP1 IF(N3(JJ) .EQ.O) N3(JJ)-4 9 IF(N4(JJ) .EQ.O) N4(JJ)-50
C WRITE(6,325) JJ, AREA(JJ,N1(JJ)),AREA(JJ,N2(JJ)),AREA(JJ,N3(JJ)) C 1, AREA (JJ,N4(JJ)), VOLUME (JJ),N1(JJ) ,N2(JJ) ,N3(JJ) ,N4(JJ) 325 FORMAT(5X,'POINT • IS- ',12,/,5X,'AREAl- ',E15.7,2X,'AREA2- ',
1E15.7,2X,'AREA3- ',E15.7,2X,'AREA4- ',E15.7,/,5X, I'VOLUME- ',E15.7,/,5X,'N1- ',I2,3X,'N2- ',I2,3X,'N3- ',12 1,3X,'N4- ',12)
324 CONTINUE DO 340 I-l,NNP DUMMY(I,1)-COORD(I,1) D UMMY(1,2)-COORD(1,2)
177
C WRITE(6,971) I,DUMMY(I,1),DUMMY(I,2) C971 FORMAT(5X,'I- ',12,/,5X,'DUMMYl- ',E15.7,4X,'DUMMY2- ',E15.7) 340 CONTINUE
RETURN END SUBROUTINE VISCIT(X,APR,T,KW,VTSCOS)
C c C THIS ROUTINE UTILIZES STANDARD PARAMETER VALUES (MOLECULAR WEIGHTS, C AND OTHER CONSTANTS TO OBTAIN VISCOSITY OF GAS COMPONENTS, AND C CONSEQUENTLY AN AVERAGE VISCOSITY. REDUCED VOLUME, SATURATED PRE-C SSURES, ETC. ARE USED (SHERWOOD & REID). C
DIMENSION T(3) ,X(5) ,C02VSC(5) ,C0VSC(6) ,H2VSC(5) ,CH4VSC(6) , LAK(4),BJ(5,6) ,A1(7) DATA CO2VSC/-8.095191E-1,6.0395329E-2,-2.824853E-5,9.843776 lE-9 -1.47315277E-12/ DATA COVSC/-5.24575E-l,7.9606E-2,-7.82295E-5,6.2821488E-8, 1-2.83747E-11,5.317831E-15/ DATA H2VSC/2.72941,2.3224377E-2,-7.6287854E-6,2.92585E-9, 1—5 2869938E—13/ DATA CH4VSC/2.968267E-l,3.711201E-2,1.218298E-5,-7.02426E-8, 17.543269E-11,-2.7237166E-14/ DATA AK/0.0181583,0.0177624,0.0105287,-0.0036744/ DATA TCR,AS,BS,CS,R,VCR/647.3,0.426776E2,-0.38927E4,-0.9486 154E1,4.61631E-4,3.147E-3/ DATA Al/4.0El,5.27993E-2,3.75928E-3,2.2E-2,-3.741378,-4.783 1828E-3,1.592343E-5/ DATA AMWC02,AMWCO,AMWH2,AMWCH4,AMWH20,FACTOR/44.,2e.,2. , 116.,18.,0.67197E-6/ ^ ^ ^ DATA BJ/0.501938,0.235622,-0.274637,0.145831,-0.027049, 10.162888,0.78 9393,-0.743539,0.263129,-0.025303, 1-0.130356,0.673665,-0.959456,0.347247,-0.026776, 10.907919,1.207552,-0.687343,0.213486,-0.08229, 1-0.551119,0.067067,-0.49708 9,0.100754,0.060225, 10.146543,-0 .084337,0.195286,-0.032932,-0.02026/
C WRITE(6,612) APR, KW, T (KW) ,X (1) ,X (2) , X (3) , X (4) , X (5) C 612 FORMAT(5X,'PRE- ',E15.7,3X,'KW- ''^2'/'5X,'T- ',E15.7 / X, C I'Xl- ',E15.7,3X,'X2- ',E15.7,3X,'X3- ',E15.7,3X,'X4- ',E15.7, C 1/,5X,'X5- ',E15.7)
TEMP-((T(KW)-492.)"5./9.)+273.0 PRESS-APR"14.7"6.895E-3 SUM-0.0 DO 10 1-1,5 SUM-SUM+C02VSC(I)"TEMP""(I-l)
10 CONTINUE VTSC02-SUM"FACTOR/AMWC02 SUM-0.0 DO 11 1-1,6 SUM-SUM+COVSC(I)*TEMP**(I-l)
11 CONTINUE VISCO-SUM*FACTOR/AMWCO SUM-0.0 DO 12 1-1,5 SUM-SUM+H2VSC(I)"TEMP""(I-l)
12 CONTINUE VISH2-SUM"FACTOR/AMWH2 SUM-0.0 DO 13 1-1,6 SUM-SUM+CH4VSC(I)"TEMP""(I-l)
13 CONTINUE VISCH4-SUM"FACTOR/AMWCH4 TSAT-AS+(BS/(ALOG(PRESS)+CS)) SUM-0.0 DO 1 K-1,3
178
N - K - l SUM-SUM+ (Al (K+4) * (TSAT**N) )
1 CONTINUE , ! ^ ? ^ (R"TEMP/PRESS) - A l (2) *EXP (-A1 (3) *TEMP) + ( 1 . 0 / ( 1 0 . "PRESS) ) 1" (Al (4 ) -EXP (SUM) ) "EXP ( (TSAT-TEMP) / A l (1) ) REDUT2-TEMP/TCR S U M - 0 . 0 DO 1 9 I L - 1 , 4 K - I L - 1
19 SUM-AK(IL)*( (1 .0 /REDUT2)*«K)+SUM ETAO-SQRT (REDUT2) * ( 1 . 0/SUM) - 1 . OE-6 REOSW-SPVOL/VCR S U M l - 0 . 0 DO 7 I N - 1 , 6 DO 8 I M - 1 , 5 M-IM-1 N - I N - 1
8 SUM1-SUM1+BJ(IM, IN) * ( ( 1 . 0 /REDUT2-1. 0) **N) " ( ( 1 . 0 / R E D S W - l . 0) ""M) 7 CONTINUE
SUM2- ( 1 . 0 /REDSW) "SUMl VISCV-ETAO"EXP(SUM2) VI SH20-VTSCV*FACT0R/AMWH20 VISCOS-(X(1)"VISCO+X ( 2 ) * V I S C 0 2 + X ( 3 ) • V I S H 2 0 +
IX (4) »VISH2+X(5.) •VISCH4) C AMEMWT-(X(1) •AMWC02+X(2)^AMWC0+X(3)^AMWH20+X(4)^AMWH2+X(5)-AM C 1 W C H 4 ) / ( X ( 1 ) + X ( 2 ) + X ( 3 ) + X ( 4 ) + X ( 5 ) ) C WRITE ( 6 , 78 ) VTSC02, VISCO, V1SH2, VISCH4, VTSH20 C78 FORMAT(5X, 'C02- ' , E 1 5 . 7 , / , 5 X , ' C O - ' , E 1 5 . 7 , / , 5 X , ' H 2 - ' , E Z 1 1 5 . 7 , / , 5 X , ' C a 4 - ' , E 1 5 . 7 , / , 5 X , ' W A T E R - ' , E 1 5 . 7 ) C WRITE(6 ,79) VTSCO,VISCOS,AMEMWT C79 FORMAT (SX, 'VISCOSITY AT MOLE FRACTIONS AND TEMPERATURE- ' , E 1 5 . 7 C 1 , / , 5 X , ' V I S C O S I T Y LBS/SEC F T 2 - ' , E 1 5 . 7 , / , 5 X , ' A V E R A G E MOL WT- ' , E C 1 1 5 . 7 ) C DEBUG INIT
RETURN END
/ / G O . S Y S I N DD • / /
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