Ind. Eng. Chem. Process Des. Dev. 1984, 23, 685-691
665
Effect of Internally Generated Bulk Flow on the Rates of Gas-Solid Reactions. 1 Development of an Approximate Solution
.
Hong Yong Sohn' Departments of MeteHurgy and Metellurgical Engineering and of Fuels Engineering, University of Utah, Salt Lake Clty, Utah 84 1 12
Robert L. Braun Lawrence L i v e r " National Laboratory, L l v e r m e , California 94550
The rate of reaction between a solid and a gas can be substantially slowed when accompanied by an outward bulk flow of a nonreadng gas. Such a gas may be generated by an independent decomposition reaction involving a second solid. The effect of the latter is analyzed theoretically. We have developed a useful approximate method of solution that makes the numerical solutbn of a secondorder differential equatbn unnecessary. The approximate solution is especially useful In the analysis of multiparticle systems with a wide size distribution.
1. Introduction Gas-solid reactions play important roles in many chemical and metallurgical processes. Many recent developments on the subject have been reviewed in the literature (Szekely, et al., 1976; Sohn, 1978,1979,1981; Sohn and Braun, 1980). Because of the heterogeneous nature of gas-solid reactions, the importance of the transport of gaseous species to and from the reaction interface must always be examined. Since in most industrial processes high rates are desired, the reactions are carried out under the conditions in which the chemical kinetics are rapid. Consequently, mass transfer frequently controls the overall rate. Most previous analyses of gas-solid reactions have been based on mass transfer processes for which bulk flow effects are negligible. Notable exceptions are the work of Weekman and Gorring (1965) on the analysis of catalytic reactions in porous catalysts, Saekely (1967) on mass transfer with homogeneous chemical reaction, Natesan and Philbrook f1969) on the diffusion-controlled roasting of sphalerite, Sohn and Sohn (1980) on the reaction of an initially nonporous solid, and Sohn and Bascur (1982) on the reaction of a porous solid. These previous analyses dealt with bulk flow caused by the change in the number of moles of gaseous species upon reaction. No systematic analysis of gas-solid reactions in which there exists an internally generated bulk flow due to a separate reaction has been made, so far as we know. Such a situation arises in a number of industrially important systems. Examples include the combustion and gasification of coal containing volatiles, the carbothermal reduction of metal oxides in a carbon dioxide/monoxidecontaining atmosphere, and the removal of sulfur-containing gases with dolomite. The immediate problem that provided motivation for this work was the analysis of the combustion and gasification by oxygen and steam of oil shale char in a retorted shale block containing carbonate minerals (Braun et al., 1981). The combustion and gasification of char is an important aspect of the combustion retorting of oil shale (Mallon and Braun, 1976; Dockter, 1976; Dockter and Turner, 1978; Soni and Thomson, 1978; Thomson and Soni, 1980; Sohn and Kim, 1980; Burnham et al., 1981; Burnham, 1979a,b,c). A major objective of the work presented in this paper was to systematically evaluate the effect of an internally 0196-4305/84/1123-0685$01.50/0
generated bulk flow on the overall rate of a gas-solid reaction in a single solid particle. A further objective was to obtain an approximate solution to this usually complex problem, which can then be used in the modeling of multiparticle systems. Without such an approximate solution for the single particle problem it is prohibitively difficult to incorporate the bulk flow effect in the overall oil shale retorting process even with a computer of very large capacity. In order to accomplish these objectives we adopted the following approach. We started with a relatively simple specific system involving bulk flow which could be solved exactly. The effect of bulk flow on the overal reaction rate was examined from the solution. An approximate solution method was then developed and tested on the simple system by comparing it with the exact solution. Finally, the approximate method was tested on a more complex case involving the gasification of oil shale char in a shale block with a concurrent generation of carbon dioxide from the decomposition of carbonate minerals. It cannot a priori be expected that an approximate method which works for a specific system will work for a different, more complex system. But we have found that the approximate method we developed works well in much more complex systems. In part 1 we present the development of the approximate solution. The results of applying the approximate method to the gasification of oil shale char will be discussed in 2. 2. The Model System As our model system, we considered a porous solid containing two solids B and F surrounded by gas A. Solid B reacts with gas A and solid F undergoes decomposition producing gas G according to the following A(g) b-B(s) = C(g) d.D(s) (1)
+
+
F(s)-= G(g) + H(s) (2) The intrinsic kinetics of the reaction between gas A and solid B is very fast and thus the overall rate of this reaction is controlled by the diffusion of gas A. As a consequence, there exists a sharp interface between the zones of unreacted solid B and product solid D, as shown in Figure 1.
The rate of diffusion of gas A into the solid and hence the rate of reaction between gas A and solid B will be 0 1984 American Chemical Society
888
Id.Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 XA
= 0 at r = rc
(8)
and X A = XAO a t r = ro (9) Here, we have assumed a fast, irreversible reaction between A and B and neglected the external mass transfer effect. From stoichiometry, the rate of consumption of solid B can be related to the flux of gas A, which can be evaluated from eq 5, as follows
QdAj(
After appropriate substitutions and rewriting in dimensionless form, eq 10 becomes - dtc/dtt
Reaction interface
Figure 1. A schematic representation of the model system.
affected by the outward bulk flow of gas G. We shall analyze a system in which the diffusion of gaseous species is in the ordinary molecular regime and the solid has a sufficiently high permeability so that the total pressure is uniform throughout the system. Retorted oil shale is one such example and is analyzed in detail in part 2. For a spherical particle, the mass balance equation for gas A in the layer of solid product D is d ,($N,J =0 (3) Assuming the applicability of a constant pseudobinary effective diffusivity of gas A (Bird et al., 1960), the flux NA can be expressed as
(4)
Noting that for one mole of A reacted one mole of C is produced, eq 4 can be rewritten as
= [exp(-P2)/61/h[eXp(-P2t,2) vc exp(-P2)1 - t,28T'/2[erf(P) - erf(@?1,)1)(11)
in which t c
= r/ro
and
We see that the effect of internally generated bulk flow is represented by a single factor j3. We further note that when /3 = 0, eq 11 reduces to the familiar case of diffusion-controlled reaction between A and B according to eq 1, namely (Sohn and Szekely, 1972; Szekely et al., 1976) 1/6 dtt tc(l- 7,) Integration of eq 11 with the initial condition
--dtC
-
vc = 1 at t+= 0 (5) Since our major objective here is to develop a relatively simple approximate method for incorporating the effect of bulk flow, we shall consider the c q e of uniform volumetric generation of gas G. This will be approximated if the characteristic time for the reaction of B is relatively short compared with that for the consumption of solid F. The approximate method developed below, however, has been found to apply even for the case in which the rate of generation of gas G varies with time. The relationship between NGa t any r and the rate of generation of G is
in which uG is the uniform rate of generation of G in mol/(m3 9). Substituting eq 5 in eq 3 together with eq 6 and solving for xA, we obtain for constant De
in which C , and C2 are the constants of integration to be evaluated from the boundary conditions. In this case we will use the following boundary conditions
(12)
(15)
(16)
gives qc as a function of tt, from which the conversion of B is obtained using the following relationship x=1-7:
(17)
3. Approximate Method In the relatively simple system used above, the rate of reaction could be expressed in analytical form given by eq 11. We need to develop an approximate solution method for other more complex systems which are not amenable to analytical solutions and must therefore be solved by a numerical method. As stated earlier, a simplified solution method would especially be advantageous for the analysis of multiparticle systems. We first define a parameter representing the relative importance of the internally generated bulk flow. This parameter must be so defined that its numerical value can be computed from the known system conditions. It must be sufficiently flexible so that it can be defied for systems in which the rate of the internally generated bulk flow varies with time, and also for those in which both diffusion and chemical kinetics affect the overall rate. We thought a " a b l e choice was the relative importance of the bulk flow and the inward diffusive capacity, expressed as molar fluxes at the external surface. Thus, we define the following ratio R [{(molar flux of internally generated gas) X (xAo)]/[inward diffusive flux of gas A, assuming chemical reaction is fast, in the absence of internally generated bulk flow]], (18)
Ind. Eng. Chem. Process Des. Dev., Vol. 23,No. 4, 1984
687
*O*l
Approximate solution
1
\ i L
0.2 -*
p2 = 1
c
0.0 0.02
1
f
-I
\
0.1
sphere
o.2
10
R, ratio
0.4
0
Figure 2. Correction factor (6) vs. ratio (R).
For the model system described in the previous section, substituting eq 6 and 10 together with eq 15 in eq 18, we get R = 2p2(1/qC- 1)
1.2
1.6
Figure 3. Comparison between the approximate and the exact solutions for constant B2 (diffusion control; sphere).
(19)
The effect of internally generated bulk flow on the overall reaction rate within the solid will depend on this ratio R. The greater the ratio R, the larger the inhibiting effect of the internally generated bulk flow. We now express the actual overall rate, as follows, in terms of the overall rate in the absence of the internally generated bulk flow, which may include the chemical reaction term if important actual rate = (correction factor, G)(overall rate in the absence of internally generated bulk flow) (20) The expression for the overall rate in the absence of internally generated bulk flow will depend on the reaction system and conditions. Closed-form expressions, both exact and approximate, for many gas-solid reactions have been derived by Sohn and co-workers (Szekely et al., 1976; Sohn, 1978,1981; Sohn and Braun, 1980; Sohn and Sohn, 1980; Sohn and Bascur, 1982). For the model system described above, it is represented by eq 15. The correction factor in eq 20 is a function of R and will have a value between 0 and 1. A systematic, statistical approach could not be defined for determining the correction factor. Therefore, we relied on visual comparisons. By comparing the conversion-vs.-time relationships obtained from integrating eq 11 and 15, we have determined by simple examination that the following relationship gives the best approximate solutions for a wide range of /3 values 6 = 1 - exp(-1.3 R4.37);for R < 0.4 = 0.85 - exp(-1.8/R); for 0.4 I R = 10R-2.5;for 6.9 IR
0.8
tt, dimensionless time
-Exact solution
- - - Approximate solution p* = 3 sphere
1.0
0
2.0
3.0
4.0
Figure 4. Comparison between the approximate and the exact solutions for constant p2 (diffusion control; sphere). 1
0.8
m
-051
-
0.6
solution --- Exact Approximate solution
c
.-E
E
8
X-
0.4 -
I
p2 =
lo
sphere
< 6.9
4. Test of the Approximate Method In this section we present a number of cases in which the exact solution is compared with the approximate solution obtained by integrating eq 20. Case 1. Comparison for the Model System Discussed in Section 2 from Which Eq 21 Was Derived. Figures 3-5 show the comparison for p2 = 1, 3, and 10, respectively. Overall, the agreement is quite satisfactory, especially when the reaction rate is substantial, namely during the initial period. At higher conversion when the rate slows down, the agreement becomes less satisfactory.
-
I
1 1
(21)
Figure 2 shows a plot of the correction factor 6 as a function of R.
6.0
5.0
tt , dimensionless time
0.0 0
5
10 15 20 25 30 35 40 45 50 ti, dimensionless time
Figure 5. Comparison between the approxipate and the exact solutions for constant @ (diffusion control; sphere).
This region, however, is of less importance due to the slow reaction rate. For a smaller value of p2 (a lower rate of internally generated bulk flow), calculations show that the agreement becomes much better. An attempt to use p2 = 100 brings a numerical difficulty in eq 11. I t is expected that the agreement will be less satisfactory for very large values of p2. However, such a case would be of little practical interest, because the reaction rate would be extremely slow
688
Ind. Eng. Chem. Process Des. Dev., Val. 23,No. 4, 1984
where :a
a
'5e 0.4
---
Exact solution Approximate solution
p2 = 10 {sin [(tt + 0.5)n/211
x
sphere
= kr0/6D,
This definition of a,2 has been used before [1,2,5] for a shrinking-core system. In terms of u,2 thus defined, the criteria for the asymptotic regimes of chemical control and pore-diffusion control are given by a," < 0.1 and u," > 10, respectively, for a tolerance of about 10% error and by a," < 0.01 and u,2 > 100, respectively, for a tolerance of about 1% error. In the absence of the internally generated bulk flow, eq 24 reduces to -dsc/dtt = l/[l/u,"
0 0.0 0.5
1.0 1.5 2.0 2.5 tt , dimensionlesr time
3.0
3.5
3.0
l 3.5
1.o
0.9 0.8
E
3
0.7 0.6
5
'i: 0.5
e8
0.4
0
'0-
0.3
0.2
0.0 o 0.0 0.5
. 1.0
1.5
2.0
2.5
t', dimensionless time
Figure 6. (a) Comparison between the approximate and the exact solutions for variable f12 (diffusion control; sphere); (b) variation of 6 with time for the case of part a above.
as long as the internally generated bulk flow lasts. This motivated us to study the case in which the rate of internal bulk flow varies with time, the results of which are discussed below. Case 2. Systems in Which p2 Varies with Time. In this test B2 was arbitrarily varied with time according to the following B2 = K1(sin[(tt + O . ~ ) T / K ~ ] ~ ~ (22) Figures 6 and 7 show the comparison for the cases of K1 = 10 and K2 = 2 and K1 = 10 and K2 = 1, respectively. It can be seen that the agreement is very good even when the correction factor varies from unity to almost zero. Case 3. Overall Rate Controlled by Chemical Reaction and Pore Diffusion. The above two cases involved systems rate-contxolled by pore diffusion only. The approximate method through the use of the ratio R and the correction factor 6 developed in section 3 was also tested for a shrinking-core system in which the overall reaction rate is controlled by both chemical reaction and pore diffusion. The mathematical formulation for the exact solution for this case closely parallels that given in section 2 except that eq 8 is replaced by -NA = kCTxAat r = rc (23) The rate of reaction, eq 11, now becomes
+ -ds,/dtt = [exp(-D2) /61 /lexp(-B2v?) / s,[exp(-B2v?) - vc exp(-B2)1 - v,28r1/%rf(B) - erf(BvJl1 (24)
(25)
+ 6vC(1- qc)l
(26)
Even in the case where chemical reaction affects the overall rate, best results are obtained with the ratio R defined as in eq 18 using the denominator based on diffusional capacity of the system. The approximate solution is obtained by using eq 26 in eq 20, with the correction factor 6 obtained by eq 21 with R obtained from eq 19. Figure 8 shows the comparison between the exact and approximate solutions for P2 = 3. The agreement is good even for the small value of u,2 = 0.01 used here. For larger u,2 the agreement is better. We mentioned earlier that a value of u,2 = 0.01 normally means that the reaction is almost exclusively controlled by the chemical reaction rate. This is not necessarily true when there is an internally generated bulk flow. Rather, the presence of bulk flow can cause a substantial pore-diffusion limitation even when u,2 = 0.01. This can be seen in Figure 8 from the significant difference between the exact solution and the solution in absence of internally generated bulk flow. Two other tests with internally generated bulk flow in ~ the mixed-control regime were made, again using u," = 0.01 to provide a severe test of the approximate solutions. Figure 9 shows the comparison when p2 = 10 and Figure 10 shows the comparison when p2 varies with time according to eq 22 with K1= 10 and K 2 = 100. Again, the agreement is better for larger a,". 5. Discussion The approximate method discussed above has been developed using a model system for which the exact solution is possible. The reaction of a porous solid is in general not amenable to analytical solution and thus must be solved numerically. A gas-solid reaction accompanied by an internally generated bulk flow can be analyzed exactly by writing appropriate governing equations, which are typically differential equations of two-point boundary value type. When the internal bulk flow is large the equations can become quite stiff, introducing numerical difficulties. Furthermore, when a multiparticle system is analyzed, the exact description requires the numerical solution of a second-order differential equation for an individual particle a t every time step and position plus the integration for conversion. The computational advantages of using the approximate solution developed above are considerable. It is much greater in the analysis of a multiparticle system with a wide size-distribution, in which the temperature and concentration of the bulk gas may vary with time and/or position. It is anticipated that the approximate method will also work for a porous solid by using approximate closed-form solutions obtained previously, as mentioned in section 3, in lieu of eq 11 or 26. This is discussed in part 2. The performance of the approximate solution is quite satisfactory in most cases. Deviation from the exact solution may become considerable at high conversions, when
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 1.0
-
I
,
1.0
I
I
-
x
0.2
1
0.0 0.0
2
I
I
1.o
I
I
I
I
iI
1
I
m
.-6
0.0
I
3.0
2.0
I
;--L-J--
889
2000
0
tt , dimensionlesstime
4000 6000 8000 tt , dimensionlesstime
1000
Figure 9. Comparison between the approximate and the exact solutions for constant p2 (mixed control; sphere).
sphere
0.0
tt, dimensionless time
100
50
0
Figure 7. (a) Comparison between the approximate and the exact solutions for variable b2 (diffusion control; sphere); (b) variation of 6 with time for the case of part a above.
150
200 250
300 350 400
tt , dimensionlesstime
Figure 10. Comparison between the approximate and the exact solutions for variable b2 (mixed control; sphere).
1.o
-
0.8 m
0 -
-- -. --
0.6
Exact solution Approximatesolution Solution in absence of internally generated bulk flow
.-s
r
z
8
0.4
X'
p2=3 0; = 0.01 sphere
0.2
0
I
I
100
200
I
-
-
overall rate. This is an important result because it proves the general applicability of the approximate solution method. The approximate method was further applied to a slab geometry with a diffusion-controlled reaction. The exact rate corresponding to eq 11 for a slab of finite thickness 2r0reacting from both surfaces with negligible end effects is dqc - P exp(- P2)/r1I2 (27) dtf erf(P) - erf(Psc) Definitions of the parameters remain the same if the following generalized expressions are used --
-
I 300
FPVP
qc I -r
400
2FpbDe C' *xO ( & ) t
Figure 8. Comparison between the approximate and the exact solutions for constant @* (mixed control; sphere).
a strong internally generated bulk flow persists during the entire reaction period. If strong bulk flow is present only during a part of the main gas-solid reaction, the approximate solution gives a good representation of the exact solution as can be seen from the cases in which P2 is varied with time. The approximate method obtained, based on the analysis of a diffusion-controlled gas-solid reaction, was also seen to be satisfactory when chemical kinetics affect the
(28)
AP
tt, dimensionless time
tt
2
(29)
I
PB
and 2 p2 I
uG
2FPecT
FPvP
(A,)
where Fpis the shape fador (= 1or 3 for a slab or a sphere, respectively) and we note that FpVp/A is the half thickness for a slab and the radius for a spkere.
690
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 l.OI
1
’
I
I
‘/&q
I
41 0.8
0.6
2
“
R
p2 = 3
x
0.4
-I-
Exact solution --- Approximate solution
p2 = 10(sin
slab
-1
P
10.00.0I
0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
I
tt , dimensionless time
~~
0.8
t
m
c
.-
E
E
0.4
0
x 0.2
/ *
I*-/ /’
- - -Approximate
1
pz
solution
= 10
slab
t 0.0
0
10
20
30
40
50
+ 0.5)~l)’
I
1 .o
1
.
i 1
I
2.0
I 3.0
i
tt , dimensionless time
Figure 11. Comparison between the approximate and the exact solutions for constant f12 (diffusion control; slab). ”O
[(tt
slab
0.2
60
70
t t , dimensionless time
Figure 12. Comparison between the approximate and the exact solutions for constant f12 (diffusion control; slab).
The capacity of the system for inward diffusion (or the rate of diffusion-controlled reaction) in the absence of bulk flow to be used in the denominator of eq 18 in a slab is --dsc - -1/2 (31) dtt 1 - sc This equation is equivalent to eq 15 for a sphere. The flux of gas G (internally generated bulk flow) at the external surface in this case is NG = rOuG (32) In terms of eq 28 through 32, eq 18 becomes R = 2p2(1 - qc) (33) The approximate solution is obtained by integrating eq 20 together with eq 31 and 6 computed from eq 21 with eq 33. In Figures 11,12, and 13 the approximate solution thus obtained is compared with the exact solution obtained by integrating eq 27. While the agreement is reasonable, it can be improved (especially for large b2) by obtaining a new relationship between 6 and R for a slab geometry. We note, however, that sphere is the most often encountered geometry in practice. In the examples used in this paper, gas G has been assumed to be generated uniformly in the solid. In order for the reaction between gas A and solid B to take place, gas A must diffuse past the external surface of the solid. It is, therefore, expected that the approximate method developed in this work will be valid even when the internal
Figure 13. Comparison between the approximate and the exact solutions for variable @* (diffusion control; slab).
generation of gas G varies with radial position, because this method is based on the relative importance of the bulk flow and diffusion at the external surface. Acknowledgment This work was performed under the auspices of the U S . Department of Energy by the Lawrence Livermore National Laboratory under Contract No. W-7405-ENG-48. Nomenclature A, = external surface area of the solid b = number of moles of solid B reacted per unit mole of the gaseous reactant CT = total molar concentration of gas De = effective diffusivity of gaseous reactant in the porous solid F, = solid shape factor (equal to 1, 2, and 3 for a slab, an infinite cylinder, and a sphere, respectively) k = reaction-rate constant K,, K 2 = constants in eq 22 N = molar flux of gaseous species r = distance from the center of symmetry in the solid R = parameter for the relative importance of the internally generated bulk flow and the inward diffusion, at the external surface of the solid; defined by eq 18 t = time tt = dimensionless time defined by eq 29 UG = molar rate of generation of gas G per unit volume V, = volume of the solid xA = mole fraction of gas A X = fractional conversion of solid B Greek Symbols (3* = dimensionless rate of internal generation of bulk flow defined by eq 30 b = correction factor for the effect of bulk flow defined by eq 21 qc
= dimensionless radius of the unreacted core
pB = molar concentration of solid B :a = gas-solid reaction modulus defined
by eq 25
Subscrip.ts A = gas A B = solid B c = unreacted core G = gas G i = species i 0 = external surface Literature Cited Bird, R. E.: Stewart, W. E.; Lightfoot, E. N. “Transport Phenomena”; Wiley: New York, 1960; p 571. Braun, R. L.; Mallon, R. 0.;Sohn, H. Y. 14th Oil Shale Symposium Proceedings, Colorado School of Mines Press: Golden, CO, 1981: p 289.
Ind. Eng. Chem. Process Des. Dev. 1984, 23, 691-696
89 1
Sohn, H. Y.; Braun, R. L. Chem. Eng. Sci. 1980. 35, 1825. Sohn, H. Y.; Klm, S. K. Ind. Eng. Chem. Process Des. Dev. 1980. 19, 550. Sohn, H. Y.; Sohn, H.J. Ind. Eng. Chem. Process Des. Dev. 1980, 79,
Burnham, A. K. Fuel 19790,58, 285. Burnham, A. K. Fuel 1979b,58, 713. Burnham, A. K. Fuel 1 9 7 9 ~58, 719. Burnham, A. K.; Crawford, P. C.; Carley, J. F. ”Heats of Combustion of Retorted and Burnt Colorado Oil Shale”; Lawrence Lhrermore National Laboratory Rept. UCRL-86470,Livermore, CA, 1981. DocMer, L. AICMSymp. Ser. 1978, 72(155), 24. Dockter, L.; Turner, T. F. I n Sltu 1978. 2 , 197. Mallon. R. G.;Braun, R. L. Colored0 School Mnes Quart. 1978, 77(4),309. Nfitesan, K.; Philbrook, W. 0. Trans. T M S - A I M 1989,245, 2243. Sohn, H. Y. Met. Trans. B 1978,9B, 89. Sohn, H. Y. “Rate Processes of Extractive Metallurgy“; Sohn, H. Y.; Wadsworth, M. E., Ed.; Plenum: New York, 1979;p 1. Sohn, H. Y. “Metailurglcal Treatises”; Tien, J. K.; Elliott, J. F., Ed.; The Metallurgical Society of AIME Warrendale, PA, 1981; p 23. Sohn, H. Y.; Bascur, 0. A. I d . Eng. Chem. Prmes.9 D e s . Dev. 1982,27, 658.
237. Sohn, H. Y.; Szekely, J. Can. J . Chem. Eng. 1972, 50, 874. Soni, Y.; Thomson, W. J. “1 lth Oil Shale Symposium Roceedlngs”; Colorado School of Mines Press, Qolden; CO, 1978; p 384. Szekely, J.; Evans, J. W.; Sohn, H. Y. “Gas-SolM Reactions”; Academic Press: New York. 1978. Szekely, J. Chem. Eng. Scl. 1987,22, 777. Thomson, W. J.; Sonl, Y. In Sku 1980,4 , 61. Weekman, V. W.; Gorring, R. L. J . Catal. 1965. 4,260.
Received for review August 6 , 1982 Reuised manuscript received October 17, 1983 Accepted November 9, 1983
Effect of Internally Generated Bulk Flow on the Rates of Gas-Solid Reactions. 2. Multiple Gas-Solid Reactions during the Gasification of Char in an Oil Shale Block Hong Yong Sohn’ h p r t m e n t s of Metellurgy and Metallurgical Engineering and of Fuels Engineering, University of Uteh, Salt Lake City, U a h 84 7 72
Robert L. Braun Lawrence Livermore Netional Lahatoty, L i v e r m e , California 94550
The approximate solution method for correcting for the effect of internally generated bulk flow developed in part 1 is applied to the gasification of oil shale char which involves a number of gas-solld reactions. The method was developed based on a rather simple gas-solid reaction system, but it Is shown to work quite well for a complex system. A method for extending the application to an even more involved system Is discussed.
1. Introduction In the combustion retorting of oil shale, a major portion of the energy required for kerogen pyrolysis is supplied by the combustion of char (the residual organic carbon and hydrogen from the pyrolysis) and oil vapor. The air injected may be diluted by steam and recycle gas. An ideal retorting process would maximize the combustion of char so as to minimize the combustion of oil. Thus, the gasification and combustion of char are important aspects of the combustion retorting. Since in many retorting processes oil shale pieces are larger than 1cm, the char reactions are strongly influenced by the diffusion of gaseous species within the solid. The reaction of char is primarily with 02,C02, and H20. Decomposition of carbonate minerals is an important source of C02and hence this decomposition must be considered in analyzing char reactions. The reaction of char with O2 and COz in blocks has been described previously (Mallon and Braun, 1976). In this paper we describe the mathematical analysis of the simultaneous reaction of char with H 2 0 and COPin blocks. The experimental aspects of studying this reaction have been described in considerable detail elsewhere (Braun et al., 1981). This paper will emphasize the mathematical analysis using a mathematical model based, as far as possible, on fundamental principles. The equations involved are quite complex and require the numerical solution of differential equations. Thus, another major em0196-4305/84/1123-0691$01.50/0
phasis in this paper is the application of the approximate method developed in part 1(Sohn and Braun, 1984) to the analysis of this system. 2. Mathematical Model 2.1. Background. At sufficiently high temperature (>500 “C)under which the gasification and combustion of oil shale char take place at substantial rates, major reactions involved are (1)the evolution of H2 from char, (2) the decomposition of carbonate minerals, (3) the reaction of char with 02,C02and H20,and (4) the water gas shift reaction. Figure 1 schematically shows these various reactions. The experiments, performed as a part of the overall study (Braun et al., 1981),focused on the reaction of char in gas mixtures containing H 2 0 and COP This situation is encountered in the retorting process immediately following kerogen decomposition before the oxygen front reaches the region. Furthermore, the analysis of this simpler reaction system in the absence of O2provides a better opportunity to test the model for the char-H20 reaction. The analysis of this reaction system, even in the absence of 02,is complicated due to the fact that a net bulk flow of gas is generated inside the block. Steam must diffuse into the solid against this bulk flow to react with char. Previous studies on simpler gas-olid reaction systems were referenced in part 1. Our modeling philosophy was to formulate a predictive model based on fundamental principles. This would allow 0
1984 American Chemical Society
