Ind.
Eng.Chem. Res. 1987,26, 237-246
237
Modeling of Early Cavity Growth for Underground Coal Gasification Kyun Y. Park and Thomas F. Edgar* Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712
A one-dimensional unsteady-state model has been developed to predict the movement of the cavity wall and drying front during the initial period of coal block gasification (lateral cavity growth). In determining the movement of the cavity wall, linear shrinkage of coal and surface reactions of HzO, 02,and COz with the cavity wall are considered. T h e model predictions have been compared with results from a n experiment where Texas lignite cores were combusted under a variety of conditions which simulate lateral cavity growth. T h e model gives good agreement between computed and experimental results. T h e effects of various physical and chemical parameters on cavity growth are also presented. In underground coal gasification (UCG), coal is converted in situ into fuel gases. A cavity is formed by the conversion of coal, and it grows both outwardly and in the axial direction as gasification proceeds. The mathematical model developed in this work simulates cavity growth in one dimension, i.e., perpendicular to the flow of injected blast gas (Figure 1). Oxygen, steam, and carbon dioxide in the blast gas react with the cavity wall. In addition, steam and carbon dioxide produced in the coal by drying and pyrolysis react with the coal in the region between the cavity wall and the drying front (called “self-gasification”). These chemical reactions remove the coal from the cavity wall. Movement of the cavity wall also occurs by the shrinkage of coal (western US coals shrink during drying and pyrolysis). When the cavity size becomes large, thermomechanical failure of coal becomes a significant factor influencing the cavity growth, especially in the vertical direction. Numerous UCG field tests have been performed during the past 10 years. Only limited field data on cavity growth in a burning coal seam have been obtained, due to the high cost of obtaining such data as well as the difficulty of controlling the operating variables. As a result, a number of laboratory-scale coal block gasification tests have been performed under a three-dimensionalgeometry (Greenfeld, 1980; Thorsness and Hill, 1981; Harloss and Corlett, 1983; Mai et al., 1985). In those experiments, usually a borehole was drilled through the coal block; blast gas was injected into one end of the borehole and product gas withdrawn from the other end. However, even these tests are difficult to interpret because they are three-dimensional tests with the blast gas composition and cavity wall temperature changing with time and along the axis of the borehole. Simpler tests which involve combustion of consolidated coal cores (essentially one-dimensional in nature) have been conducted by Wellborn (1982) and Poon (1985). For these experiments, the operating parameters are more controllable and the modeling is much simpler than with large block or field gasification tests. A one-dimensional unsteady-state model has been developed to predict the movement of the cavity wall and the drying front during the initial period of coal gasification. Such a model is valuable for interpreting cavity growth in laboratory-scale experiments. Massaquoi and Riggs (1983) have developed a model assuming the cavity wall and the drying front move at the same velocity. This assumption is not necessarily valid for the initial period of cavity growth; Mondy and Blottner (1982) reported that 3-4 days may be required before the two fronts move at the same velocity. Thus, in the model presented here, the OSSS-5SS5/S7/2626-0237$01.50/0
cavity wall and the drying front do not necessarily move at the same velocity. In addition, we include linear shrinkage of coal and the reaction of H 2 0 and C02 with the cavity wall, which have not been included in previous models. The model does not take into account the formation of fissures and cracks which may provide a lowresistance path for transport of reactants and products. In addition, the model does not include cavity growth caused by thermomechanical failure of coal, so the model is probably only valid for analyzing lateral cavity growth; thermomechanical failure predominates in vertical cavity growth after the cavity becomes fairly large. In this paper, model predictions are compared with results from an experiment where Texas lignite cores were combusted (Poon, 1984). The effects of various physical and chemical parameters on cavity growth are discussed by using the model.
Model Development and Simulation The system is divided into three zones: wet coal zone, dry coal zone, and ash layer (Figure 1). Unsteady-state energy and mass balances are written for the wet coal zone, the dry coal zone, and the ash layer, respectively. These equations must be solved simultaneously to determine the rates of cavity growth and drying front movement. Details of the governing equations, their boundary conditions, and kinetic equations for the chemical reactions are given in the Appendix. The algorithm for simulation of the model is also described in the Appendix. Results and Discussion Simulation results from the mathematical model have been compared with data obtained from a core combustion test performed by Poon (1985). Figure 2 illustrates the combustion test. The coal core has a dimension of 2.54 cm in diameter and 8.25 cm in length. The blast gas is passed over the top of the core. Combustion proceeds in the direction perpendicular to the flow of the blast gas, which is similar to growth of the sidewall in underground coal gasification. A series of stainless steel rings (2.54-cm diameter and 0.475-cm length for each ring) surrounds the sidewall of the core. These rings prevent the loss of pyrolysis gases through the sidewall and protect the sidewall from reacting with the blast gas, thus maintaining a onedimensional burn. The first ring is removed when the combustion front reaches the bottom of that ring. Then the ash left after combustion is removed, and the blast gas injection point is moved down to the top of the second ring. The remaining rings are removed sequentially as the combustion front propagates downward. The location of 0 1987 American Chemical Society
238 Ind. Eng. Chem. Res. Vol. 26, No. 2, 1987 DRYING FRONT
CAVITY WALL
--
Y) 0
"1 01 0
PYROLYSI
1
,
'
I,.
*
n1 _
I
W E T COAL
0
PARALLEL TO THE BEDOING PLANE
s
PERPENDICULAR TO THE BEODINC PLANE
SOLID L I N E
'
MODEL PREDICTION
e e
I + "
*
11 1 - -
+ ^^
d
il
SELF GASIFICATION
SURFACE R
1
1
Figure 1. Chemical reactions involved in the cavity wall growth.
:~i
i
"0 SO
0 60
0 70
0 80
0 90
1 00
1 1 10
MOLE F R A C T I O N OF O X Y G E N
Figure 3. Comparison of the burning rate between the simulated and the experimental results. VI 0
61
EXPERIMENTAL D A T A
1
MODEL P R E D I C T I O N
1 I I
Blast Gas
1
Figure 2. Reactor for the core combustion test.
the combustion front is identified by measuring the thickness of the ash layer on the coal surface by using a dipstick welded on the blast gas injection tube. The injection tube is movable vertically and can be rotated on its axis. The ash layer is removed by a knife attached to the injection tube. Two thermocouples measure local temperatures. One thermocouple is located 1.9 cm from the top of the core, and the other one is located 3.8 cm below the top thermocouple. More details on the experimental procedure have been described by Poon (1985). Figure 3 shows the effect of oxygen concentration in the bulk gas on the one-dimensional burning rate. Both experimental and simulated results indicate that the burning rate is proportional to the oxygen concentration in the bulk gas, implying that the reaction rate is controlled by the mass-transfer rate of oxygen. The model underestimates the measured burning rate by 10-209'0. The empirical equation used in the model to calculate the oxygen mass-transfer rate is valid only for a fluid approaching a flat plate at a uniform velocity (laminar flow). However, in the test, the blast gas is disturbed by a sudden change in flow direction just before it exits from the injection tube (Figure 2). Hence, the underestimation of the burning rate by the model is probably due to ignoring the turbulence created by the change in flow direction. The reaction temperatures observed in the experiment were relatively
i: 0 '
I00 00
2b0 00
3bO 00
4 b O 00
5 b 0 00
PO0 00
7bC 00
io Figure 4. Effect of the blast gas rate on the burning rate. B L A S T F L O W R A T E . CC/MIN
I
low, ranging from 600 to 900 "C. These temperatures are not high enough for the self-gasification reaction to contribute to the burning rate significantly. Simulation results for higher temperatures are discussed later. Since the overall reaction rate was controlled by the mass-transfer rate, the blast gas flow rate and the thickness of the ash layer on the coal surface can be important factors in determining the burning rate. As shown in Figure 4, the model predicts the trend of the blast gas rate correctly, although it underestimates slightly the absolute burning rate. Figure 5 shows the influence of the ash layer on the burning rate. The burning rate is indicated by the COz concentration in the product gas, which shows a cyclical behavior. The peak rate was observed when the burning front was at the top of a ring (there is no ash layer on the coal surface). The burning rate decreases monotonically as the ash layer builds up; the minimum burning rate (about one-half of the peak rate) is reached just before the ring is removed. The model successfully predicts the cyclical change of the burning rate (Figure 6). The ratio of the peak rate to the minimum rate predicted by the
Ind. Eng. Chem. Res. Vol. 26, No. 2 , 1987 239 0
0
B L A S T GAS R A T E
5150 C C / M I N
MOLE F R A C T I O N OF OXYGEN L
'
F I R S T THERMOCOUPLE
0
0
0 6
SECOND THERMOCOUPLE
l
SOLID L I N E . :
MODEL P R E D I C T I O N
W
+ . I
"0
00
20 00
40 00
60 00
TIME.
80 00
100 00
120 0 0
MIN
Figure 5. Volume percent of COZ in the product gas observed in the core combustion test.
0
0
0
0.00
::
20.00
40.00
80.00
110.00
100.00
120.00
TIME MIN. D R Y I N G FRONT V E L O C I T Y
0
Figure 7. Changes of local temperatures with time.
C A V I T Y WALL V E L O C I T Y
Table I. D a t a for Simulation operating pressure, kPa density of wet coal, g/cm3 water content in coal, wt % ash content in wet coal, wt % pyrolysis data (subbituminous coal) thermal conductivity of wet coal, J/(cm
101.3 1.23 30.0 15.0 Campbell, 1978 37.0 x 10-4
K s)
thermal conductivity of dry coal, J/ (cm
%.OD
20.00
40.00
TIME,
80.00
80.00
100.00
120.00
MIN.
F i g u r e 6. Predicted velocities for the cavity wall and the drying front (mole fraction of oxygen, 0.6; blast gas rate, 5150 cm3/min).
model is approximately the same as that observed in the experiment. Figure 7 shows the transient behavior temperature measurements at 1.9 and 5.7 cm from the top of the core. The discontinuities in the heating rate (or the slope of the temperature change) are due to the intermittent removal of the rings during the combustion test. Removal of a ring changes the reaction rate and subsequently the heating rate. The simulated result is in good agreement with the experimental result. This is in spite of uncertainties in the thermal property data and the estimation of the time-varying heat loss from the sidewall. In fitting the experimental data in Figure 7, the mass-transfer coefficient was adjusted to be 10% higher than the value calculated from the empirical equation (flow past a flat plate). In addition, a constant heat-transfer coefficient was assumed for the heat loss from the wall. The wall heat-transfer coefficient was adjusted so that the maximum temperature observed in the experiment could be matched. In Figure 7, the temperature of the first thermocouple was observed to level off a t about 100 "C for a period of time. This observation supports the assumption in the model that the drying front exists and the drying temperature is 100 "C. We conclude that the model provides good agreement between the simulated and the experimental results.
Simulation of Early Cavity Growth Further analyses of cavity growth phenomena have been made by using computer simulation, in order to evaluate the importance of various assumptions in the model. Here we examine several scenarios of cavity growth based on laboratory block gasification tests or large-scale field tests
K s) for T 673 K for T 673 K frequency factor for COz-char reaction, cm3/(g-mol s) frequency factor for HzO-char reaction, cm3/(g-mol s) activation energy for C0,-char reaction, kJ/g-mol activation energy for H,O-char reaction, kJ/g-mol blast gas flow rate, cm3/min bulk gas concn
25.0 x 10-4 25.0 x 10-4
+ 20 x
104(T - 673) 2.0 x 10l2 (Dutta et al., 1977) 2.0 x 10l2 (assumed same as above) 248.1 (Dutta e t al., 1977) 248.1 (assumed same as above) 2500 30% 02, 70% Nz
rather than the core-burning experiment described in the previous section. Such parameter sensitivity tests will allow several conclusions to be drawn regarding the effect of operating conditions on actual underground tests. As a first case, the cavity wall temperature was assumed to be increased at a specified heating rate up to a steady-state temperature. The heating rate was set at 20 "C/min, which corresponds to field measurements obtained in underground coal gasification tests. Other operating data for this simulation are shown in Table I. Figure 8 shows the cavity growth rates without shrinkage and with a linear shrinkage of 25%. During the transient period at which the cavity wall and the drying front move at different velocities, the cavity growth rate with shrinkage is higher than that without shrinkage. However, the gap between the two rates is narrowed as the system approaches a steady state. The two growth rates are expected to merge eventually into one rate at steady state. The shrinkage moves the cavity wall physically but at the same time increases the carbon density. Because the char-gas reaction rates per unit external area are unchanged, the increase of the carbon density then slows down the cavity wall movement. During the initial transient period, the net effect is to enhance the cavity growth rate because the shrinking zone (or dry coal zone) is growing. The shrinking zone will cease to grow when steady state is reached.
240 Ind. Eng. Chem. Res. Vol. 26, No. 2, 1987
0
x
O 'YO
SHRINKAGE 0
SURFACE TEW. 900 DEG. C
A
SURFACE TEW. 1000 DED. C
Q
SURFACE TEW.
1 1 0 0 DEG. C
#
SURFACE T E W .
1 2 0 0 DEG. C
PERCENT
SHRINKACE 2 5 PERCENT
2' 00
1' 00
0
3' 00
4 ' 00
5 ' 00
6 ' 00
:
ga0.00
2.00
1.00
T I M E . HOUR
Figure 8. Effect of the shrinkage on the cavity growth rate.
' 0 2 o
I
5 0
5.00
6.00
Figure 10. Effect of the cavity wall temperature on the cavity wall growth rate (heating rate, 20 OC/min).
C A V I T Y WALL G R O W H RATE. CU/HR
A
4.00
.
0
0
3.00
T I M E , HOUR
0
Ov,
OXYCEN-CHAR REACTION SELF-CASIFICATION REACTION
- 1 Q
w
SURFACE REACTION(CARS0N D I O X I D E - C H A R ) SURFACE REACTION(STEAM-CHAR)
+
J
!i
0 1
70
z ' O k - - z O -
2' 00
3' 00
00
5 00
6 ' 00
T I M E . HOUR
Figure 9. Ratio of the drying front velocity to the cavity wall growth rate.
Thereafter, shrinkage has no incremental effect on the cavity growth rate. The physical movement of the cavity wall due to shrinkage of coal could be neglected in modeling field-scale gasification tests because of the long time scales involved (months). However, the effect of shrinkage should be considered for laboratory-scale experiments in which a significant portion of the test is a t unsteady state. The thermomechanical effect of shrinkage on cavity wall growth is not included in this model for laboratory-scale coal block gasification experiments, although cavity wall crumbling due to thermomechanical effects plays an important role in cavity growth when the cavity becomes large, especially in the vertical direction. Figure 9 shows the transient behavior of the drying front velocity for varying cavity wall growth rates. The cavity wall temperature was assumed to be increased to 1000 "C at a rate of 20 "C/min and thereafter was maintained at that temperature. Simulations were run for three cavity wall growth rates: 1 , 2 , and 3 cm/h. In all cases, the cavity wall growth rate and the drying front velocity approach steady state (ratio of 1.0). However, the time it takes to
f.
3:OO
4:OQ
5100
6100
T I M E , HOUR
Figure 11. Reaction rate with time for a cavity wall temperature of 1000 "C (mole fraction of oxygen, 0.3).
reach steady state depends on the cavity growth rate. For a cavity growth rate higher than 2 cm/h, steady state is reached in 5 h. For a cavity wall growth rate of 1 cm/h, the system is still far away from steady state after 5 h, and the rate of convergence to steady state is reduced as steady state is approached. This is consistent with an estimate by Mondy and Blottner (1982) that steady state for a Wyoming bituminous coal would be reached within 3-4 days for a cavity growth rate of 0.4-0.8 cm/h. Figure 10 shows the effect of the cavity wall temperature on the cavity growth rate. The transient cavity growth rates are different, but the steady-state rates are the same for 900,1OOO, and 1100 OC. However, the steady-state rate for 1200 "C converges to a different steady-state value, apparently, because it has a different flame front location. For the lower temperatures, the flame front is located eventually at the coal surface, though the flame front is temporarily separated from the coal surface. In contrast, for 1200 "C, the flame front is separated from the coal surface and appears never to return to the coal surface.
Ind. Eng. Chem. Res. Vol. 26, No. 2, 1987 241
t
N 0
0
OXYCEN-CHAR R E A C T I O N
A
SELF-GASIFICATION REACTION
6
SURFACE REACTION(CAR0ON
g
-1
WATER CONTENT I N COAL
DIOXIDE-CHAR)
SURFACE REACTION(STEAU-CHAR)
0
10. PERCENT
A
20. PERCENT
E
30. PERCENT
0.0w
I-
6 =0
$EO
01
-0:OO
XI
- ,
1.00
2:OO
3:OO
4:OO
5:OO
6:OO
1100
00.00 '
2:OO
T I M E . HOUR
3100
4:OO
5:OO
6:OO
T I M E , HOUR
Figure 14. Effect of the water content on the cavity wall growth rate. 0 N
WATER CONTENT : 30, PERCENT
n. 0-
0
X
1.
C A V I T Y WALL T E M P . . D E C . C
0
10. PERCENT
A
20.
g
30. PERCENT
0
vi
-'h 1
PERCENT
900. 1000
7
00.00
0 0
"0 00
1
1 00
2 00
3 00
4 00
5 00
8 00
T I M E . HOUR
F i g u r e 13. Effect of water content on the cavity wall temperature (bulk gas temperature, lo00 "C; mole fraction of oxygen, 0.1; heating rate, 20 OC/min).
The individual reaction rates for the reaction of oxygen with the cavity wall, the self-gasification reaction, the reaction of C 0 2with the cavity wall, and the reaction of H 2 0 with the cavity wall are shown for 1000 and 1100 "C, respectively, in Figures 11 and 12. In Figure 12, the oxygen-char reaction disappears after 1h when all the oxygen transferred to the cavity wall is consumed by combustion of the volatile gases (the flame front is separated from the cavity wall). The oxygen-char reaction reappears in 2.5 h as the pyrolysis and drying fronts move farther from the cavity wall (the flame front is returned to the cavity wall). This behavior of the location of the flame front has been visually observed in core combustion tests (Poon, 1985). The cavity wall temperature will change the proportion of the individual reaction rates, but the overall rate is not affected as long as the flame front is located a t the cavity wall (Park, 1985). Figure 13 shows the effect of the coal moisture content on the coal surface temperature (or cavity wall tempera-
00
2.00
3 . 00
4.00
5 . 00
Z 00
6.
T I M E . HOUR
Figure 15. Mole fraction of H20in the gases emerging from the cavity wall.
ture). The water content was varied from 10% to 30%. The bulk gas temperature was increased to 1000 "C at a rate of 20 "C/min. The surface temperature decreased as the moisture content was increased. The resulting effect on the cavity growth rate is shown in Figure 14. During the first hour of simulation, the cavity growth rate was lower for a larger water content. If the surface temperature reached a sufficiently high temperature, however, the situation was reversed. The higher moisture content gave a higher cavity growth rate, implying that the availability of water in the coal, rather than the reaction temperature, controls the self-gasification reaction rate. Figure 15 shows that the water vapor generated at the drying front is completely reacted by the self-gasification reaction for a coal surface temperature higher than 1000 "C. This indicates that, above 1000 "C, the rate of water vapor generation a t the drying front controls the self-gasification reaction rate. If the coal surface temperature is not high enough for the steam-char reaction to occur significantly, the water content in the coal may have little effect on the cavity growth rate. This behavior was observed in the core
242 Ind. Eng. Chem. Res. Vol. 26, No. 2, 1987
-'
c YI
I.
....cE j:
C A V I T Y WALL TEUP OXYGEN C O W
0
0 '
A
O 2
%
0 3
1000
OEG
C
I N THE BULK GAS
and property data 1
Solve the energy balance equation ( 2 ) f o r the wet coal zone I
W I-
&1 $ :i
"L Solve the energy balance equations, ( 2 ) and ( I l ) , for the wet and dry coal zones simultaneouslv
0
u +
%
UYI
- 1
t 01
m l N
OO 0 0
0 15
0 30
MOLE F R A C T
0 45
0 60
0 75
OF S T E A M
Figure 16. Effect of the steam concentration on the cavity growth rate for a cavity wall temperature of 1000 O C .
1,
See-I Fig. 19
I
\
Calculate the cavity wall growth rate
I 1
1
Estimate the temperaturedependent properties
u)
C A V I T Y WALL TEUP OXYGEN CONC
:-I ---vb$ 0
1100
DEG
C
I N THE BULK GAS
0
O 1
A
0 2
y
o s
Time e Time limit
i
no STOP
1
Figure 18. Flow diagram for numerical solution 1.
-4
on the effect on the surface reaction of HzO and COz with the cavity wall on the cavity growth rate. In the laboratory-scale coal block gasification test by Lawrence Livermore Laboratory (Shannon et al., 1980), a steam-oxygen mixture (2.4:l)as the blast gave a higher lateral cavity growth rate than air as the blast. This may be the only experimental evidence to support the simulation result for the influence of steam concentration.
O ' / "
0'
0 00
0' 15
0'30
MOLE F R A C T
0 45
0 60
0 75
OF S T E A M
Figure 17. Effect of the steam concentration on the cavity growth rate for a cavity wall temperature of 1100 "C.
combustion test (Poon, 1985). Thus, the moisture content may have a negative or positive effect on the cavity growth rate depending on the cavity wall temperature, which in turn is determined by the operating conditions and the properties of the coal. The cavity wall temperature is probably most affected by flow rate of the blast gas and oxygen concentration in the blast gas. Figures 16 and 17 show the effect of steam concentration in the bulk gas on the cavity growth rate with oxygen mole fractions of 0.1 and 0.3 for 1000 and 1100 "C, respectively. The ash layer thickness is assumed to be zero. For a cavity wall temperature of 1000 "C, the steam concentration has no effect on the cavity growth rate (Figure 16). However, for a cavity wall temperature of 1100 "C, the steam concentration is shown to have a significant effect on the cavity growth rate for an oxygen mole fraction lower than 0.2 (Figure 17). For an oxygen mole fraction of 0.3, a higher cavity wall temperature is required for the steam concentration in the bulk gas to affect the overall cavity growth rate. Very little experimental data are available
Conclusions The mathematical model developed in this work has been shown to give good agreement between simulated and experimental results for coal combustion. The effects of various physical and chemical parameters on cavity growth have been discussed by using the model. The conclusions drawn from this work are as follows. (1)The cavity growth rate is determined by the rate of oxygen transfer to the cavity wall from the bulk gas stream if the flame front is located at the cavity wall. If the flame front is separated from the cavity wall, the cavity growth rate is determined by the self-gasification reaction and the surface reactions of H 2 0 and CO, with the cavity wall. (2)At cavity wall temperatures higher than lo00 "C, the surface reactions of H20 and COzwith the cavity wall are fast enough to be a significant contribution to the cavity growth rate. (3) The physical movement of the cavity wall due to shrinkage by drying and pyrolysis should be considered for a small-scale test in which the transient state is important. However, the shrinkage effect can be neglected for a large-scale field test in which the transient period is negligible compared to the steady-state period. (4)The presence of an ash layer on the cavity wall provides a significant resistance to mass transport of the reactants to the cavity wall. (5) The water content in a given coal may have a negative or positive effect on the cavity growth rate depending
Ind. Eng. Chem. Res. Vol. 26, No. 2, 1987 243
I
I
X, = conversion
'IA''
Calculate the cavity growth rate by shrinkage(V ) sh
z =
I
location, cm
Greek Symbols arJ= stoichiometric coefficient for component i in the jth vr
= 0
I
self-gasification reaction = initial porosity of micropores in char = density, g/cm3
cB0
p
Superscripts 0 = initial
Calculate the self-gasifica-
d = drying p = pyrolysis s = self-gasification Calculate the oxygen transfer
Subscripts a = ash b = bulk
1
c = cavity wall d = dry coal or drying front eq = equivalent 1 = component i sh = shrinkage r = reaction t = total v = volatiles
Calculate the oxygen requirement(Nr ) for combustion of the volatiles
b
R1 and R
R1=O
Calculate V
from
equation (18)
9
V c= V +r V s h
1.
Appendix. Mathematical Model Development and Numerical Solution The model equations for the wet coal zone, the dry coal zone, and the ash layer are given below. Wet Coal Zone. Energy Balance. The drying front location changes with time; hence, it is more convenient to use the substantial derivative defined as
'IB'
Figure 19. Flow diagram for numerical solution 2.
on the cavity wall temperature, which is determined by the operating conditions and the properties of the coal.
Nomenclature C = concentration, g-mol/cm3 C = specific heat, J/(g K) = average molar specific heat, J/(g-mol K) DLe= effective diffusivity of component i, cm2/s E = activation energy, J/g-mol H = heat-transfer coefficient, J/(cm2 s K) (AH), = heat of vaporization of water, J/g (AH); = heat of reaction of the self-gasification of component i, J/g-mol k = thermal conductivity, J/(cm s K) K, = reaction rate constant for the gas-solid reaction, (g-mol 9)
L = linear fraction shrinkage of coal mi, = instantaneous mass of component i volatilized per unit mass of dry coal by the jth subreaction M , = instantaneous mass of component i volatilized per unit mass of dry coal M , = molecular weight, g/q-mol N = molar flux, g-mol/(cm s) R = reaction rate, g-mol/(cm3s) R1 = reaction rate for the oxygen-cavity wall reaction, gmol/(cm2 s) R2 = reaction rate for the self-gasification reaction, g-mol/(cm2 S)
R3 = reaction rate for the surface reaction of H20 and C 0 2 with the cavity wall, g-mol/(cm2s) S = reaction surface area, cm2/cm3 t = time, s T = temperature, K V = linear velocity, cm/s W = weight fraction on wet coal basis X = molar fraction
where v d is the velocity of the drying front. The determination of v d is described later. Assuming the thermal conductivity of wet coal is constant, the energy balance equation for the wet coal zone is DT kw a2T aT -=-+ vd (2)
Dt
P,(C,,)
dz2
az
with boundary conditions a t z = z d (drying front)
T = T, atz=a
T = T, where T , is the drying front temperature. Removal of water contained in the coal is assumed to occur entirely a t the drying front. The drying front temperature (T,) is assumed to be 100 "C. Dry Coal Zone. Mass Balance. In the dry coal zone, pyrolysis and gasification reactions occur. C 0 2 , CO, H2, CHI, C2H6,and tars are produced by the pyrolysis reactions, which can be treated as first-order decomposition reactions. By use of kinetics data for western coals developed by Campbell (1978), the overall pyrolysis reaction rate for component i can be represented by a sum of the contributions of each subreaction
where Rip is the pyrolysis rate of component i, M iis the instantaneous mass of component i devolatilized per unit mass of coal, mijois the total mass of component i for the j t h subreaction, mij is the instantaneous mass of compo-
244
Ind. Eng. Chem. Res. Vol. 26, No. 2, 1987
nent i for the j t h subreaction devolatilized per unit mass of coal, and W is the number of peaks. Tsang and Edgar (1983) used a similar pyrolysis kinetics model in modeling block pyrolysis. As shown in Figure 1, the water vapor generated at the drying front and the pyrolysis gases move toward the cavity wall in the direction opposite to the movement of cavity wall and drying front. Thus, the gases must ultimately pass through the hot char zone; water vapor and some of the pyrolysis gases react with the char before they flow into the cavity. This phenomenon is called self-gasification. The major self-gasification reactions occurring in the dry coal zone are HzO + C r? CO + H2 (4) co2 + c 2 2 c o (5) where C represents char. In determining the removal rate of char by reactions 4 and 5, the following empirical equation was used rather than a Langmuir-Hinshelwood type of rate equation (Dutta et al., 1977)
coal zone is neglected (Park, 1984). Energy Balance. Conduction from the cavity wall toward the wet coal zone, convection by water vapor and pyrolysis gases in the direction opposite to conduction, and heat of reaction by self-gasification constitute the key terms in the energy balance equation in the dry coal zone. By use of the substantial derivative as was used for the wet coal zone, the energy balance in the dry coal zone is formulated as
where V is the linear velocity of the moving coordinate with boundary conditions at z = z d (drying front)
T = T, at z = zc (cavity wall) -h d -
x,
PCO - Pc = ___
PCO
-
(7)
Pa
where X, is the conversion, S is the reaction surface area, p, is the instantaneous density of char, p: is the initial density of char, and pa is the density of ash. The water-gas shift reaction does not remove char directly but changes the mole fractions of HzO, C02, CO, and Hz. However, the effect of changes in H2 and CO mole fractions on the char removal rate cannot be explicitly handled in the rate equation chosen here. The effect of the water-gas shift reaction on the char removal rate is assumed to be included implicitly in the empirical coefficients in the rate equation. The removal of char by C 0 2 is negligible compared to that by H 2 0 for most operating conditions in underground coal gasification processes. Reaction orders for C02-char and H,O-char reactions are both assumed to be unity a t atmospheric pressure (Dutta et al., 1977; Sundaresan and Amundson, 1980). The reaction surface area, S , is not constant but changes with conversion. The ratio of instantaneous reaction surface area to initial reaction surface area, S/P, is calculated from the reaction model presented by Tseng (1982)
where es0 is the initial porosity of micropores in the char. From eq 3-6, the mass balance in the dry coal zone is given by
where N ; is the molar flux of component i, (Mw)L is the molecular weight of component i, and aLjis the stoichiometric coefficient for component i in the j t h self-gasification reaction. For mass transfer in the gas-char reactions, the pseudo-steady-state assumption applies (Bischoff, 1963). The concentration of reactant gas i which is required to calculate the self-gasification reaction rate (R,s) is calculated from
In eq 10, the diffusion effect on the flow through the dry
dT = Heq [ ( Tb)eq dz
-
where (TI,),, is the equivalent bulk gas temperature and Heqis the equivalent heat-transfer coefficient. When the cavity wall boundary interfaces with the bulk gas stream with no ash layer located in between and no radiation heat loss is considered, Hq becomes the ordinary heat-transfer coefficient and (Tb),, becomes the bulk gas temperature. However, the boundary condition is not that simple when an ash layer exists between the cavity wall and the bulk gas stream and radiation loss is included. Hq and (Tb)eqthus represent equivalent values. The radiation heat loss and the heat of reaction, which are nonlinear with respect to temperature, are linearized by using Heq, Ash Layer. The ash layer is located between the cavity wall and the bulk gas stream. Ash is left after the coal is reacted. The thickness of the ash layer is assumed to have a finite upper limit, which is a user-specified parameter. In laboratory-scale coal block gasification of Texas lignite coal, Mai et al. (1985) observed an ash layer thickness of about 1.2 cm. Mass Balance. Oxygen in the bulk gas stream diffuses through the ash layer toward the cavity wall. Volatile gases flow countercurrent to the diffusion of oxygen. Oxygen is preferentially consumed for the combustion of the gaseous species leaving the cavity wall. Here the gas-phase oxidation reactions are assumed to be much faster than other competing reactions, such as the oxygen-char reaction, and they are assumed to occur at a sharp flame front. The location of the flame front is determined by using the approach of Arri and Amundson (1978) and Massaquoi and Riggs (1981). The molar flux of a gas component through the ash layer is modeled by
The values for Dr (effective diffusivity) are assumed to be the same for all the components but hydrogen. For hydrogen, the effective diffusivity is set at 3 times larger than that of the other components. C 0 2 and H20 produced by combustion, which are present in the bulk gas stream, can also react with the cavity wall (hereafter called the surface gasification reaction with the cavity wall). Energy Balance. A pseudo-steady-state energy balance is employed in the ash layer. The temperature of the ash layer is around 1000 "C, and the thermal conductivity is
Ind. Eng. Chem. Res. Vol. 26, No. 2, 1987 245 much higher than that of coal, due to the temperature effect and due to the high porosity of ash (Chlew and Glandt, 1983). The steady-state energy balance in the ash layer is d2T dT 12, - + [-NtC, + p,(C ) V I - = 0 (13) dz2 p a dz where Nt is the molar flux of gases passing into the cavity, Cp is the average specific heat, and V, is the linear velocity of the cavity wall movement with boundary conditions a t z = z, (ash edge) dT -12, - = H(Tb - T,) + u(-T,~+ CfkTk4) dz a t z = z, (cavity wall) T = T,
Determination of Front Velocities. The drying front velocity is determined from the heat flux equation given by
The f i s t term in the numerator is the heat conduction into the drying front, and the second term is the heat loss into the wet coal zone; the difference is the heat available for vaporizing water. The velocity at the cavity wall is determined by the rate of removal of coal by chemical reactions and physical movement of the cavity wall due to shrinkage of coal (15) vc = VI + v s h where V, is the cavity wall moving velocity, VI is the cavity wall moving velocity contributed by chemical reactions, and v s h is the cavity wall moving velocity contributed by shrinkage of coal. Shrinkage of coal is caused by drying and pyrolysis. The overall shrinkage is the sum of the two effects
+ vshp
(16) where v s h d is the contribution by drying and v s h p is the contribution by pyrolysis. Vshdis determined by the linear fractional shrinkage (Lsd) multiplied by the drying front velocity ( v d ) . For western coals, Ld is known to be about 0.1. Due to the lack of data on pyrolysis shrinkage, in this work the amount of shrinkage is assumed to be proportional to the conversion of the pyrolysis reaction, since the shrinkage is caused by collapse of molecular structure of coal due to the pyrolysis reaction. By mathematical manipulation in several steps (Park, 19841, the equation to determine v s h p is vsh
=
Vshd
where W: is the total fraction of volatiles contained in the coal and L,, is the linear fractional shrinkage of coal a t complete removal of volatiles. The velocity of the cavity wall movement contributed by chemical reactions is determined by the chemical reaction rates and density of the coal char. The chemical reactions involved in the cavity wall movement are the reaction of oxygen with the cavity wall, the surface reactions of H 2 0 and C 0 2 with the cavity wall, and the selfgasification reactions. The amount of oxygen which reacts with the cavity wall (R,) is determined by subtracting the stoichiometric requirement for the volatiles combustion
from the total rate of oxygen transfer from the bulk gas stream toward the cavity wall. R1 is zero if the flame front is separated from the cavity wall; oxygen is depleted by the combustion of volatiles before it reaches the cavity wall. The self-gasification reaction rate (R,) is calculated from eq 6. An empirical equation is used to calculate the rate (R3)of the surface reaction of H20 and C02with the cavity wall. This equation is based on fitting simulation data obtained from solving numerically a one-dimensional convection-diffusion problem involving C02and H20. See Park (1984) for more details. The overall contribution by chemical reactions to the cavity wall moving velocity is therefore determined as
(Rl
VI =
+ R2 + R3)(Mw), pcO(1- Wa)
(18)
where W , is the weight fraction of ash in char and (Mw)c is the molecular weight of char. Numerical Solution. The energy balance equations, (2) and ( l l ) , for the wet coal zone and the dry coal zone are solved by using backward finite difference. In the wet coal zone, grid points are not uniformly spaced but were more densely located near the drying front. Heat transfer in the wet coal zone is modeled as a semiinfinite medium. One boundary is at the drying front, and the other boundary is located a sufficient distance from the drying front so that the teniperature gradient can be neglected at the boundary. The nonuniformly spaced grid points move at the velocity of the drying front movement, and the distance between the two boundaries is maintained constant. However, in the dry coal zone, uniformly spaced grid points with varying grid spacing are used. The velocity of each grid point in the dry coal zone, which is required to solve the energy balance equation, is determined by linear interpolation as V,n - V, V, v, = v( dn -- 1) i+ (19) (n - 1) ~
where i is the sequential number of a grid point and n is the total number of grid points. The numerical procedure was used by Murray and Landis (1959) to solve phase change problems. It was also used by Tsang and Edgar (1983) to solve mass and energy balances for a block pyrolysis experiment. Flow diagrams for the numerical simulation procedure are shown in Figures 18 and 19. Before the cavity wall temperature reaches the drying temperature, T,, eq 2 is solved with the derivative boundary condition at the cavity wall. After the cavity wall temperature reaches T,, the derivative boundary condition is replaced by a constant value of T,. The drying front velocity is calculated from eq 14. Before the cavity wall temperature reaches the ignition temperature, the cavity wall moves only by shrinkage of coal. After the cavity wall temperature reaches the ignition temperature, the reaction of oxygen with the cavity wall and the combustion of the volatiles emerging from the cavity wall become significant. The cavity wall movement is controlled by the oxygen reaction with the cavity wall and shrinkage of coal. Until the cavity wall temperature reaches 670 "C,H20 and C 0 2 reactions with char are not considered. If the cavity wall temperature is higher than 670 "C,the cavity wall moving velocity is determined by the sum of the reaction of oxygen with the cavity wall, the self-gasification reaction, the surface reaction of H 2 0 and C 0 2 with the cavity wall, and shrinkage of coal. Details on determining these reaction rates are described elsewhere (Park, 1984). This time step is controlled so that the distance between the drying front
Ind. Eng. Chem. Res. 1987, 26, 246-254
246
and the cavity wall does not change by more than 5% of the previous distance. However, an upper limit for the time step is provided. L i t e r a t u r e Cited Arri, L. E.; Amundson, N. R. AIChE J . 1978, 24(1), 72. Bischoff, K. B. Chem. Eng. Sci. 1963, 18, 711. Campbell, J. H. Fuel 1978,57, 217. Chlew, Y. C.; Glandt, E. D. Ind. Eng. Chem. Fundam. 1983, 22(3), 276. Dutta, S.; Wen Y.; Belt, R. J. Ind. Eng. Chem. Process Des. Deu. 1977, 16(1), 20. Greenfeld, M. Presented a t the Proceedings of the 6th Underground Coal Conversion Symposium, Afton, OK, July 1980, p IV-70. Harloff, G. J.; Corlett, R. C. Analysis of Results of Laboratory Simulation of Underground Coal Gasification, Presented at the ASME/JSME Thermal Engineering Joint Conference, Honolulu, HI, March 1983. Mai, M. C.; Park, K. Y.; Edgar, T. F. In Situ 1985, 9(2), 119.
Massaquoi, J. G. M.; Riggs, J. B. AIChE J . 1983, 29(6), 975. Mondy, L. A.; Blottner, F. G. Presented a t the Proceedings of the 8th Underground Coal Conversion Symposium. Keystone, CO, Aug 1982; p 1. Murray, W. D.; Landis, F. J . Heat Transfer 1959 ( M a y ) 106. Park, K. Y. Ph.D. Dissertation, University of Texas, Austin, 1984. Poon, S. S. M. S. Thesis, University of Texas, Austin, 1985. Shannon, M. J.; Thorsness, C. B.; Hill, R. W. Report UCRL-84584, June 1980; Lawrence Livermore Laboratories. Sundaresan, S.; Amundson, N. R. Ind. Eng. Chem. Fundam. 1980, 19(4), 351. Thorsness, C. B.; Hill, R. W. Presented at the Proceedings of the 7th Underground Coal Conversion Symposium, Fallen Leaf Lake. CA. Sept 1981; p 331. Tsang, T. H. T.; Edgar, T. F. In Situ 1983, 7(3), 237. Tseng, H. P. Ph.D. Dissertation, University of Texas, Austin, 1982. Wellborn, T. A. M.S. Thesis, University of Texas, Austin, 1982.
Received for reuieu January 14, 1985 Accepted June 24, 1986
Effect of Nonuniform Distribution of Solid Reactant on Fluid-Solid Reactions. 2. Porous Solids H o n g Yong S o h n * a n d Yong-Nian Xia Department of Metallurgy and Metallurgical Engineering, University of Utah, Salt Lake City, Utah 84112-1183
T h e grain model for fluid-solid reactions is extended t o the solids with nonuniform distribution of the solid reactant. T h e nonuniform distribution can have a substantial effect on the conversion-vs.-time relationship as well as the time for complete reaction when pore diffusion affects the overall rate. In general, a monotonically increasing distribution of the solid reactant will accelerate the overall rate, and a monotonically decreasing one will delay the process, when compared with the case of the uniform distribution. T h e law of additive reaction times previously proposed for fluid-solid reactions involving uniform distribution is shown to yield a useful approximate solution even for the reaction of a porous solid with nonuniform distributions of the solid reactant. In part 1 (Sohn and Xia, 1986), we discussed the reaction of an initially nonporous solid with a nonuniform distribution of solid reactant. Although the case of a nonporous solid covers a lot of practical situations, a porous solid with nonuniform distribution of solid reactant is also often encountered. A pellet in which particles of pure, dense solid reactant are distributed in a porous matrix of an inert solid or a pellet into which the particles are compacted with nonuniform compactness is an example of this situation. In chemical and metallurgical systems, the sinters and agglomerates, some ores, and the active absorbents deposited in an inert carrier are some of the actual examples. There has been a great deal of work treating the subject of fluid-solid reactions of porous solids with uniform distribution of solid reactant (Sohn, 1979, 1981; Sohn and Szekely, 1972; Szekely and Evans, 1970, 1971a,b; Szekely et al., 1976). However, as we have pointed out in part 1 (Sohn and Xia, 1986), only in certain circumstances can we treat the problem with the theory for uniform distribution with acceptable accuracy. In view of this, a systematic analysis of the problem is necessary in order to obtain more accurate information. In the following, a grain model with a nonuniform distribution of solid reactant is developed, which is based on the grain model mainly described in Sohn and Szekely (1972) and Szekely et al. (1976). We will emphasize the model formulation and general observations for an arbitrary form of the distribution function, as well as some numerical results for certain specific distributions. We will also present the results of applying the law of additive
reaction times previously proposed for solids with uniform distribution of the solid reactant (Sohn, 1978, 1981). This law gives an approximate closed-form solution for the conversion-vs.-time relationship. It will be shown in this paper that the relatively simple approximate solution gives a satisfactory representation of the reaction of solids with nonuniform distribution of the solid reactants. During the preparation of this paper, Ramachandran and Dudukovic (1984) published a paper on a similar problem. There is, however, a substantial difference in the model formulation between the two studies. We will discuss this difference in the following section. Model Formulation The physical model under consideration is sketched in Figure 1. The essential feature of the physical structure is that the pellet consists of two parts: one is the small, dense grains of the solid reactant, and the other is either the void which is actually the interstices among the grains or the inert solid with porosity in which the grains are nonuniformly dispersed. The grains are assumed to have identical shapes and sizes. Both the pellet and the grains can have one of the three basic shapes: flat plates, long cylinders, and spheres. The fluid-solid reaction under consideration is
A,, + W
S ,
=
c,,,+ dD,,,
with intrinsic kinetics
0SSS-SSS5/S~/2626-0246$O1.50/0 0 1987 American Chemical Society
(1)
