Ind. Eng. Chem. Res. 1988,27, 197-203 partial pressures than the Kent-Eisenberg model because of a significant effect due to the reaction of the amine with water in the very lean loading region. This significant effect is explained in the following. For the very lean loading region, i.e., for very low partial pressures of H2S or in the absence of H2S, the equilibrium reaction of the amine with water (water acts as a weak acid, and the reaction is the combination of reactions 7 and 11)becomes relatively important: RNH2
+ HzO + RNH3+ + OH-
(18)
This reaction results in a higher OH- concentration for the very lean loading region than for the other region. This reaction makes the total protonated amine (RNH3+)concentration higher than the stoichiometric concentration of the protonated amine from the reaction of the amine with H2S (eq 16). This forces the reversion of reaction 16 and retards the absorption of H2S according to the Le Chatelier principle. Thus, this gives a higher partial pressure of H2S than that predicted by the simple thermodynamic model, which does not take reaction 18 (i.e., the effect of water) into account. However, the KentEisenberg model takes this reaction into account, resulting in good agreement with the data. The electrode method has first provided data to show this effect due to the reaction of the amine with water and verified the superiority of the Kent-Eisenberg model over the simple thermodynamic model in the lean loading region. Conclusions The electrode method for the measurement of H2SVLE was developed and verified. The new method exhibited advantages over the conventional sparging method in H2S VLE measurements, especially for very lean solutions. This method also provided data, for the first time, to show the effect due to the reaction of amine with water, and this verified the superiority of the Kent-Eisenberg model over the simple thermodynamic model in the lean loading region. Nomenclature a = activity E = electrode potential, V
197
F = Faraday’s constant = 96500 C HHzs= Henry’s law constant for H2S, kPa.L/mol K1 = deprotonation constant of amine, mol/L K = stoichiometric equilibrium constant = dissociation constant of H2S, mol/L K 3 = dissociation constant of HS-, mol/L K , = dissociation constant of water, mo12/L2 P = partial pressure, kPa R = gas constant = 8.314 J/K/mol T = temperature, K y = H2S loading, mol of H2S/mol of MEA Subscript
0 = total concentration Registry No. H2S, 7783-06-4.
Literature Cited Astarita, G.; Savage, D. W.; Bisio, A. Gas Treating With Chemical Soluents; Wiley: New York, 1983. Atwood, K.; Arnold, M. R.; Kindrick, R. C. Ind. Eng. Chem. 1957, 49, 1439. Danckwerts, P. V. Gas-Liquid Reactions; McGraw-Hill: New York,
1970.
Jones, J. H.; Froning, H. R.; Claytor, E. E., Jr. J. Chem. Eng. Data 1959, 4, 85.
Kent, R. L.; Eisenberg, B. Hydrocarbon Process. 1976, Feb, 87. Kohl, A. L.; Riesenfeld, F. C. Gas Purification; Gulf Publishing: Houston, 1979. Lal, D.; Otto, F. D.; Mather, A. E. Can. J. Chem. Eng. 1985,63,681. Leibush, A. G.; Shneerson, A. L. J. Appl. Chem. (USSR) 1950,23, 149. McNeil, K. M.; Danckwerta, P. V. Trans. Inst. Chem. Eng. 1967,45, T32. Muhlbauer, H. G.; Monaghan, P. R. Oil Gas J. 1957,55, 139. The University of Texas a t Austin.
* Exxon Research and Engineering Company. Gary T. Rochelle,*’ Philip C. Tsengt W. S. Winston Ho? David W. Savage* Department of Chemical Engineering The University of Texas ut Austin Austin, Texas 78712 and Exxon Research and Engineering Company Annandale, New Jersey 08801 Received for review June 1, 1987 Accepted September 24, 1987
Extinction Phenomena in Countercurrent Packed-Bed Coal Gasifiers: A Simple Model for Gas Production and Char Conversion Rates Global carbon conversion and gas production in a countercurrent moving-bed char gasifier is shown t o be determined solely by conditions under which the endothermic carbon gasification reactions are extinguished, in the limit of the large activation energy typical of these reactions. A simplified reaction scheme is employed in which gasification agents C 0 2 and H 2 0 and products CO and H2 are lumped intosingle pseudospecies to develop a simple analytical model for conversion in the gasifier in terms of the asymptotic extinction temperature of the gasification reaction. T h e assumption of water gas shift equilibrium at this temperature then allows a calculation of detailed product gas composition leaving the reaction zone of the gasifier. The derivation is shown to be valid for chars of sufficiently high reactivity. Model results are compared with those of more comprehensive numerical calculations. Numerical modeling of moving-bed (countercurrent) coal gasifiers such as the Lurgi type has shown that peak temperatures and other derived quantities for the active combustion zone are very sensitive to model assumptions and to parameter values which are generally not wellknown (cf. Arri and Amundson (1978); Yoon et al. (1978)). However, overall conversion rates and effluent gas com0888~5885/88/2627-0197$01.50/0
positions have proven to be remarkably insensitive to model details. These observations led Denn et al. (1979) to formulate a simplified “kinetics-free” model for a onedimensional packed-bed gasifier based on material balances with a specified carbon conversion rate, which employed the assumption of water gas shift reaction equilibrium to calculate the produced gas rate and composition. 0 1988 American Chemical Society
198 Ind. Eng. Chem. Res., Vol. 27, No. 1, 1988 ~~,a,ilicatio"-i-~,:.b:ygiis-l
/-COmbustio"
-
-4
z-
+ x
Figure 1. Schematic of temperature and gas-phase species concentrations in a one-dimensional countercurrent packed-bed char gasifier.
The insensitivity of gas production rates and compositions on mass transfer and kinetic details for these systems, in light of the wide range of reported kinetic constants for the participating reactions in the gasifier, lends appeal to the concept of a kinetics-free modeling approach. However, it is well-known that the gas-solid reactions occurring in the gasifier are typically far from equilibrium. This implies control by a rate process. It is the purpose of this work to identify the controlling factors determining carbon conversion in the gasifier and to develop a simple model to estimate the optimum feed rate of char to the gasifier as well as product gas flows and compositions. Below, we show that to leading order, global gasifier conversion is controlled solely by kinetic extinction of the highly activated endothermic gasification reactions, and even though reported values of the inetic constants for these reactions are widely variable for a given coal type, in general calculated results for extinction temperatures and conversion rates are not. The formulation extends ideas from the theory of activation energy asymptotics applied to ignition and extinction phenomena in gas-solid combustion of single particles, developed in early works by Libby and Blake (1979), Libby (1980), Kassoy and Libby (1982), and others, to endothermic gasification reactions in packed beds and provides a concise explanation for the global behavior of the gasifier. An idealized analytical model has been developed based on these concepts which has been incorporated in simulations describing the dynamics of cavity growth during underground coal gasification (Britten and Thorsness, 1985; Thorsness and Britten, 1986).
Model Formulation We consider a one-dimensional, adiabatic, packed-bed gasifier in which gas containing oxygen, steam, and perhaps nitrogen flows upward in the positive z direction, contacting solid char, consisting of carbon and ash, which is settling countercurrently in the negative z direction at a rate which will be calculated. Temperature and gas species profiles in the gasifier are sketched qualitatively in Figure 1. Steady operation is assumed, that is, the temperature and concentration profiles in the reactor do not change in the stationary frame of reference. Where oxygen contacts carbon, a thin, intense zone of gas-solid and gas-phase combustion develops. We will not attempt to resolve this zone but demand that no carbon passes through it and that no oxygen passes through the opposite end. Downstream from this zone, a relatively broader gasification zone of decreasing temperature exists, wherein carbon is removed
by reaction with carbon dioxide and steam. If the gasifier is operated under optimal conditions, there exists an extended region of relatively constant temperature at the downstream end of the gasification zone, in which no significant reactions occur. This constant temperature is the effective extinction temperature of the endothermic gas-solid reactions under the prevailing conditions, since the progress of this highly activated reaction removes heat from the gas stream until it is too cold to continue in the presence of O(1) amounts of reactants in concentrations removed from thermodynamic equilibrium. Generally, this extinction temperature is still high enough that sensible heat from the product gas is more than sufficient to dry and pyrolyze the incoming coal feed further downstream; thus the gasification zone is insulated from downstream end effects. The pressure throughout the reaction zones is assumed constant, constant average values for solid and gas heat capacities are used, and local thermal equilibrium between the phases is assumed. In the interest of discerning leading order effects, the following simplified reaction system is employed. We assume that H 2 0 and COz and H2 and CO can be lumped into the same pseudocomponents, such that we have effectively four gas-phase species in the combustion-gasification zone, oxygen (A), gasification agent (B = C 0 2 + HzO),gasification product (P = Hz+ CO), and inert (I), which react according to the scheme A+C-B (1) B+C-2P (2) 2P A 2B (3) This is justified in part by the observation that stoichiometrically the C02-C and HzO-C reactions are identical and further by the commonly made assumption that the water gas shift reaction HzO + CO C02 + H2 (4) is in equilibrium, and thus the relative concentrations of H 2 0 and COz can adjust instantaneously to the local thermal environment. The rates of the C02-C and HzO-C reactions are quite similar, although the rate of the latter reaction is held to be greater (Walker et al., 1959; Ergun and Mentser, 1965). Yoon et al. (1978) employed the criterion of Ergun and Mentser (1965) and used rco2+c= O . ~ I - ~ , ~while + ~ , Arri and Amundson (1978) did not consider the C 0 2 + C reaction directly. Wen and Chuang (1979),modeling entrainment coal gasifiers, considered the rates to be identical. We do the same and define a weighted average heat of reaction for (2) based on the injected gas composition:
+
YH20f qH,O+C
-
y02f qCO2+C
(5)
q2 = y02f
YH20f
(Symbols are defined in the Nomenclature section). In this formulation, stoichiometry demands that q 3 = q1 + q 2 , where the reaction heats are defined as absolute values at 298 K. It should be noted here that whether oxygen initially reacts to form CO or COPhas no bearing on the global results as long as the bookkeeping is done correctly. We consider here complete conversion to COz in one step. The reverse rate of the gasification reaction 2 is not considered, since it is rarely of importance for typical gasifier conditions. Also, the hydrogasification reaction 2Hz + C CH,, which for many situations does not occur to a significant extent, is not considered since it would destroy the symmetry of the simplified reaction scheme above. Before the dimensionless equations describing the gasifier operation are introduced, it is helpful to discuss the
-
Ind. Eng. Chem. Res., Vol. 27, No. 1, 1988 199 bed characteristics leading to the scale factors for nondimensionalization. We consider the combustion/gasification zones to be uninfluenced by either upstream or downstream end effects, such that axial boundaries on the reaction zones can be taken as fa. The solid settling velocity varies as a function of position in the bed in a fashion dependent on the composition and packing behavior of the solid being removed by reaction. We assume that the overall bed density is constant, although incorporation of this as a function of carbon conversion is straightforward. The maximum solid settling velocity us, (to be calculated) occurs a t the downstream end of the gasification zone, and we use this as a scale factor to nondimensionalize the solid velocity: u, = u,*/u,,
(6)
The superscript * denotes a dimensional quantity. The gas flux is made dimensionless with its upstream feed value, the fraction of carbon remaining in the solid phase is scaled with its feed value, length is made dimensionless with a scale z,, and the temperature is normalized with its values at either end of the carbon conversion zone: Fg= Fg*/Fgf Xc = Wc/Wco z = z*/z,
T=- T* - Tf
(7) Tex - Tf where Tf is the gas feed temperature and Texis the unknown extinction temperature of the gasification reaction. The natural macroscopic length scale z, changes across the zone of maximum temperature, since different terms dominate in the species and energy balance equations in different zones. We will define and employ the length scale for the gasification zone in the following analysis. Since zero-gradient boundary conditions are taken a t fa and the combustion zone is not resolved, this scale can be used to represent the entire region. Due to the stoichiometry of the reaction scheme, it is convenient to develop the gas balance equations in molar units. In the axial ( z ) coordinate centered a t the point where the oxygen concentration goes to zero, the dimensionless carbon balance is
Dimensionless boundary conditions for the dependent variables are d Yi z + -m T = dT/dz = - = 0 (i = A, B) dz U, = -w, Fg = 1 Yi = Yif 2-m
T=l dT/dz=O dYi/dz = 0 (i = B, P)
uS=-1 (14)
We now proceed to develop expressions for the unknowns in the system. First, we can immediately combine (10) and (12) to describe the dimensionless gas flux as a function of the produced combustible gas fraction: 2 Fg= 2 - Yp Next, (8), ( l l ) , and (12) can be combined to eliminate the reaction terms and integrated across the reaction zones to arrive at an expression for the downstream solid velocity in terms of the product gas fraction:
Equations 11, 12, and 13 can be combined in a similar fashion and use can be made of the relation between reaction heats based on the reaction stoichiometry to give an equation relating Ypmto the extinction temperature Tex:
c, wco
(Tex -
Tf)Cg
A relation for Texis needed to complete the development. This can be obtained by a local analysis of the equation describing the disappearance of species B in the gasification zone. Here, O2 is not present and (2) is the only reaction of importance. Given that the reaction rate may be controlled either kinetically or by various diffusional resistances, the dimensionless balance equation for species B can be written
where where kd(T,P,d,,X,) is the sum of the diffusive rate constants: is a dimensionless solid flux. The total molar gas balance is
The independent gas-phase species balances are
(19)
(i.e., for transport internal to the char particle (i) and through the gas film (f) and/or ash layer (a) surrounding the particle), and kk(Xc,T,P)is the intrinsic kinetic rate constant which we assume is described by Arrhenius kinetics f i s t order in molar reactant concentrations and with a large activation temperature:
In the limit of a large activation temperature for the intrinsic kinetics, the transition from diffusional to kinetic rate control occurs abruptly over a small decrease in temperature. For most of the gasification zone, k d > 1, so (34) can be recast into the form of (20) with suitably modified A and T,to calculate effective extinction temperatures in the presence
of a rate-inhibiting product. It should be noted that as long as O(1) quantities of reactants steam and carbon dioxide exist throughout the gasification zone, as is typical for gasifier operation, these results are largely independent of the reaction order with respect to YB. The error involved with neglect of the heat effect of the water gas shift reaction has been discussed. There is another potential for error due to the assumption of local equilibrium for this reaction. This assumption has been used in many studies to calculate detailed product gas compositions but may not always be strictly valid at temperatures characterizing the downstream end of the gasification zone. The error introduced by this assumption manifests itself mainly in the distribution of carbon-containing species in the product gas; total carbon conversion is only slightly affected due to the small heat effect of this reaction. Cho and Joseph (1981) used kinetic expressions for the forward and reverse rates of this reaction to show that a change of over 3 orders of magnitude in the overall rate constant for this reaction changed the carbon conversion rate by only about 5%)while changing the ratio H,/CO in the product gas by about 30%. Yoon et al. (1978) also studied the effect of the error made by this assumption on gas compositions and determined it to be small. Conclusions Conversion of a reactive char in a countercurrent packed-bed gasifier has been shown to be determined largely by the temperature at which kinetic extinction of the endothermic carbon gasification reactions occurs, a condition that can be quantified in terms of the large activation temperature of the reactions. The relative insensitivity of calculated asymptotic extinction temperatures, and therefore conversion rates, to a wide range of effects has been demonstrated. Kinetic parameter insensitivity arises from a compensation effect in which a change in activation temperature is offset by a like change in preexponential factor. Thus, model predictions which use widely varying kinetic parameter values taken from the literature give similar results. An analytical model has been developed based on a simplified reaction scheme and an extinction temperature of the endothermic gasification reaction to give estimates of carbon conversion and gas production rates valid for chars of sufficient reactivity such that an abrupt change from kinetic to diffusional gasification rate control occurs over a relatively small temperature change. Calculated results compare favorably with results of comprehensive numerical models describing gasification of such coals, and sources of discrepancy between the models have been identified. Acknowledgment
This work was performed under the auspices of the 1J.S. Department of Energy by Lawrence Livermore National Laboratory under Contract W-7405-Eng-48. Nomenclature A = Arrhenius preexponential factor, l/(Pa.s) A = oxygen B = gasification agent (=COz + HzO) C = heat capacity D, = effective diffusion coefficient in ash layer D, = effective diffusion coefficient in char particle DeEf= effective mass dispersion coefficient I), = molecular diffusion coefficient d = initial particle diameter f l = gas flux Zf = dimensionless solid flux defined by (9)
Ind. Eng. Chem. Res., Vol. 27, No. 1, 1988 203 f = functional dependence of gasification rate on extent of
carbon conversion I = inert k , = ash layer mass-transfer rate, mol/(m3.s) k d = diffusive rate constant, mol/(m3.s) kf = film mass-transfer rate, mol/(m3.s) ki = intraparticle mass-transfer rate, mol/ (m3-s) kk = kinetic rate constant, mol/(m3-s) I t , = mass-transfer rate coefficient, mol/ (m2.s) A4 = atomic weight P = gasification product (H2 and CO) P = pressure qi = heat of reaction i ri = rate of reaction i T = temperature T , = activation temperature T,, = extinction temperatore us = solid velocity wi = weight fraction of species i in original coal Wi = weight fraction of species i in char X , = fraction original carbon Yi= mole fraction of gas i z = axial coordinate zs = length scale of gasification zone Greek Symbols
b = inverse of dimensionless activation energy for gasification
reaction = measure of reaction Damkohler number q = effectiveness factor A = reaction Damkohler number X = bed thermal conductivity p = density @ = Thiele modulus 6
4b= bed external porosity
= porosity of ash layer 4c = porosity of char particle
@a
Subscripts
b = bed c = carbon f = feed conditions g = gas s = solid -co = upstream end of gasification zone 03 = downstream end of gasification zone Superscripts
* = dimensional variable
-
= average or characteristic value
Appendix. Estimation of Solid Physical Properties This appendix outlines a method for estimating internal porosities and intrinsic densities of coal char particles based on proximate analysis data, which is felt intuitively reasonable providing effects of swelling or shrinkage upon drying and devolatilization can be neglected. Assuming that the original coal particle is essentially nonporous, the porosity created by drying is @d = w w P c / P w (35)
where pc is the density of the original coal and pw the density of water. The porosities of the fully pyrolyzed char and the ash are, respectively,
f#)c
= (1 - ffI,\l
-
(36)
Given the external porosity of the char bed density is
@b,
the solid
and the carbon fraction in the char is
w,,= wc + Wa WC
(39)
Literature Cited Agarwal, A. K.; Sears, J. T. Ind. Eng. Chem. Process Des. Dev. 1980, 19, 364-371. Aris, R. The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts; Clarendon: Oxford, 1975; Vol. 1, Chapter 3. Arri, L. E.; Amundson, N. R. AIChE J. 1978,24, 87-101. Boudart, M. Kinetics of Chemical Processes; Prentice-Hall: Englewood Cliffs, NJ, 1968; pp 179-182. Britten, J. A.; Thorsness, C. B. Proc. 11th Underground Coal Gasification Symposium, 1985, US.DOE Report DOE/METC-85/ 6028 365-380. Cho, Y. S.; Joseph, B. Ind. Eng. Chem. Process Des. Dev. 1981,20, 314-318. Denn, M. M.; Yu, W.-C.; Wei, J. Ind. Eng. Chem. Fundam. 1979,18, 286-288. Dutta, S.; Wen, C. Y.; Belt, R. J. Ind. Eng. Chem. Process Des. Dev. 1977,16, 20-30. Ergun, S.; Mentser, M. Chem. Phys. Carbon 1965, 1, 203-263. Gibson, M. A.; Euker, C. A,, presented at the AIChE Symp. on Laboratory Reactors, Los Angeles, 1975. Gupta, A. S.; Thodos, G. AIChE J. 1963,9, 751-754. Johnson, J. L. Am. Chem. SOC.Ado. Chem. Ser. 1974,131,145-178. Kassoy, D. R.; Libby, P. A. Combust. Flame 1982,48, 287-301. Libby, P. A.; Blake, T. R. Combust. Flame 1979,36, 139-169. Libby, P. A. Combust. Flame 1980, 38, 285-300. Sears, J. T.; Muraldihara, H. S.; Wen, C. Y. Ind. Eng. Chem. Process Des. Deu. 1980, 19, 358-364. Smith, J. M. Chem. Engineering Kinetics, 3rd ed.; McGraw-Hill, New York, 1981; pp 462-468. Thorsness, C. B.; Britten, J. A. Proc. 12th Underground Coal Gasification Symposium, 1986;, U.S. DOE Report DOE/FE/60922-H1 239-251. W-lker, P. L., Jr.; Rusinko, F.; Austin, L. G. Ado. Catal. 1959, 2, I 33-22 1. Wen, C. Y.; Wang, S. C. Ind. Eng. Chem. 1970,62, 30-51. Wen, C. Y.; Chuang, T. 2. Ind. Eng. Chem. Process Des. Deu. 1979, 18, 684-695. Yoon, H.; Wei, J.; Denn, M. M. AIChE J. 1978, 24, 885-903. Yoon, H.; Wei, J.; Denn, M. M. Chem. Eng. Sci. 1979,34, 231-237.
Jerald A. Britten Chemistry and Materials Science Department Lawrence Liuermore National Laboratory Livermore, California 94550 Received for review October 10, 1986 Accepted October 7, 1987
