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Literature Cited Bruggeman, D. A. G., Ann. Phys., 24, 636 (1935). Crane, R. A., Vachon, R. I., Int. J . Heat Mass Transfer, 20, 711 (1977). Crane, R. A., Vachon, R. I., Khader, M. S.,“Proceedings of the Seventh Symposium on Thermophysical Properties”, 1978. Maxwell, J. C., “A Treake on w i l y and Magnetism”, Vd. 1, p 452, Chrendon, Oxford, 1891.
Meredith, R. E., Tobias, C. W., J . Appl. Phys., 31, 1270 (1960). Rayleigh, Lord, Phil. Mag. J . Sci., 34, 481 (1892). Runge, I . , Z . Tech. Phys., 6, 61 (1925). vanBeek, L, K, H,,Prw,Die,ectr,, , 69 (1967).
Received for review December 8, 1978 Accepted April 26, 1979
Parameter Sensitivity and Kinetics-Free Modeling of Moving Bed Coal Gasifiers Morton M. Denn” and Wen-Ching Yu Department of Chemical Engineering, University of Delaware, Newark, Delaware 1971 1
James Wei Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02 139
A detailed model of a moving bed coal gasifier can provide temperature and composition profiles throughout the reactor, as well as effluent gas composition and temperature. The former are sensitive to certain model inputs, but the latter are insensitive to large variations in the same parameters. Thus, complete model validation requires temperature and composition profiles as well as effluent measurements. The insensitivity of overall model behavior to certain model parameters suggests that a “kinetics-free’’ model would be useful in estimating reactor performance in regions of high carbon conversion. Agreement between the kinetics-free calculation and the detailed model is very good for coals with negligible reactivity to hydrogen.
Introduction
A mathematical model of moving bed coal gasification reactors has been described recently by Yoon et al. (1978). The model, commonly referred to as the University of Delaware (UD) model, employs mass and energy balances, together with information about rates of chemical reactions and physical transport processes. Other models have been published by Amundson and Arri (1978) and Biba et al. (1978); these differ from the UD model in the details of the physical and chemical processes. All models predict temperature and composition profiles in the reactor, as well as effluent compositions and temperatures. The only reliable data available for model validation on pilot and commercial scale gasifiers are effluent gas compositions and temperatures. The UD model predicts effluent properties accurately for both dry ash and slagging moving bed gasifiers (Yoon et al., 1978),and it also predicts that the maximum temperatures are in the feasible operating range; i.e., maxima are below the ash softening temperature for dry ash operation and above the ash melting temperature for slagging operation. Model inputs are taken from independent experiments, but there are uncertainties regarding some parameters. We examine here the sensitivity of the model predictions to these parameters. We find that the detailed temperature and composition profiles in the reactor are sensitive to the parameter values, but the effluent is quite insensitive. These results lead to a “kinetics-free’’ model of gasifier output that can be applied in a region of efficient operation, and they illustrate the need for a more extensive experimental program for complete model validation. Initial Oxidation Product CO/C02 D i s t r i b u t i o n
The initial product distribution of carbon oxidation under the complex conditions in a gasifier is not known. 0019-7874/79/1018-0286$01 .OO/O
Table I. Optimum Feed Conditions Computed by Yoon et al. (1979a) for Lurgi Gasification at 25 atm Pressure with a 700 “ F Blast (Steam + Oxidant) Temperature coal
oxidant
Illinois Illinois Wyoming Wyoming
oxygen air oxygen air
C/O, steam/O, molar molar feed ratio feed ratio 2.98 2.8
3.7 3.28
9.6 6.7 6.8 4.8
This CO/C02 distribution is a model input that cannot be estimated from independent experiments at the present time. Using the initial fractional conversion of C to CO as a model input, the computed maximum temperature is shown in Figure 1 for oxygen-blown gasification of 11linois No. 6 coal in a pressurized Lurgi gasifier with 20-mm diameter coal particles. The final effluent CO/C02 ratio depends also on subsequent attack of C by C 0 2 and HzO, and by the water-gas shift reaction. Feed conditions are given in Table I; these correspond to the optimum conditions computed by Yoon et al. (1979a) for the Illinois coal a t the specified blast temperature. This variation of fractional conversion to CO caused a variation of more than 300 O F in the computed maximum temperature, but no variation in the properties of the gas leaving the reaction zone, which are listed in the first column in Table 11. Effluent calculations for initial CO-C02 distributions of 100% C M % C 0 2 ,50% C0-50% C 0 2 ,and 0% CO-lOO% C 0 2 agree to three significant figures; therefore only one set of figures is listed. Similar results are obtained at the optimal feed conditions listed in columns 3, 5, and 7 of Table I for the air-blown Lurgi gasification of the Illinois coal, and oxygen- and air-blown Lurgi gasification of a high activity Wyoming coal. 0 1979 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 18, No. 3, 1979 287 Table 11. Properties of Gases Leaving t h e Reaction Zone for Conditions Shown in Table I. Calculations Are for Initial 50% CO-50% CO, ; UD Model Calculations Assume a 20-mm Diameter Particle Illinois, 0 , H*O H2
co co
2
CH, T, " F H,/CO
T,
"F
Wyoming, 0,
Illinois, air
Wyoming, air
UD
KF
UD
KF
UD
KF
UD
KF
0.680 0.315 0.092 0.218 0.002 1441 3.43 2072
0.679 0.321 0.091 0.219 0 1437 3.52 2004
0.619 0.37 6 0.156 0.262 0.002 1482 2.42 2082
0.614 0.386 0.152 0.266 0 1452 2.55 1977
0.485 0.451 0.218 0.295 0.032 1383 2.07 2361
0.453 0.547 0.247 0.297 0 1320 2.21 2362
0.428 0.525 0.332 0.328 0.025 1403 1.57 2100
0.406 0.594 0.356 0.328 0 1353 1.67 2191
2200 I
I
I
,
f l
,
----100
I 800
'
0
1
I
05
I O
F r a c t i o n o l Conversion t o
CO
0
Figure 1. Maximum temperature computed with UD model for Lurgi gasification of 20-mm diameter Illinois No. 6 coal as a function of initial oxidation CO/C02 distribution. Feed conditions are given in Table
I.
%
c"
2500
L
2000
C
h
I
2
3
4
5
6
mm diameter
7
8
9
IO
Distance above G r a t e l f t i
Figure 3. Composition profiles computed with UD model for Lurgi gasification of Illinois No. 6 coal with 3-mm and 100-mm particles, 50% initial conversion to CO, and feed conditions in Table I.
"Kinetics-Free"Model The insensitivity of the product gas composition and temperature to large variations in both oxidation selectivity and particle size suggest that the overall performance of the gasifier in the region of efficient carbon utilization is determined solely by stoichiometric and thermodynamic constraints. Yoon et al. (1979b) have shown that such constraints limit the feasible operating region on a triangular diagram of carbon, oxygen, and steam feed ratios, and they have further shown that the usual operating points for a dry ash gasifier do not correspond to lines of thermodynamic equilibrium. Exit gas concentrations and temperature can be estimated without detailed consideration of kinetics using only the following assumptions. (i) Carbon conversion is given. (In practice, this may limit application to operating regions in which carbon conversion may be taken as complete.) (ii) All feed oxygen is consumed. (iii) The water-gas shift reaction is at equilibrium. These assumptions are sufficient to fix the gas concentrations and temperature above the gasification zone, but prior to devolatilization and drying. The exit gas temperature and composition is then determined by including the devolatilization products and coal drying as reported by Yoon et al. (1978). The detailed calculation steps are as follows, starting from the reactor bottom with known exit carbon composition. (i) Combustion utilizes all feed oxygen. The composition above the combustion zone is fixed by the distribution of oxidation products between CO and COz, and the temperature is computed from the adiabatic temperature rise. (Heat losses may be included if the region near the reactor wall is to be accounted for, but an adiabatic analysis is adequate for a reactor like a Lurgi gasifier with a 3 to 4 m diameter. All calculations reported here are adiabatic.) (ii) Water-gas shift equilibrium is established adiabatically above the combustion zone. The temperature computed here is a very rough estimate of the maximum
I/ 1 5 0
IC
10 0
-- 3 -100
0
I
2
3
4
5
6
m m diameter m m diameter
7
8
9
IO
Distance above Grote ( f t )
Figure 2. Temperature profiles computed with UD model for Lurgi gasification of Illinois No. 6 coal with 3-mm and 100-mm particles, 50% initial conversion to CO, and feed conditions in Table I.
Particle Size The UD model uses a single mean particle size as an input. Because the oxidation reactions are expected to become mass-transfer limited in the region of the maximum temperature, the particle size should significantly affect the model predictions. Results of two calculations using Illinois No. 6 coal with the feed conditions in Table I and an initial CO/C02 ratio of unity are shown in Figures 2 and 3. The 3-mm particle size represents the limit of negligible mass transfer resistance and intrinsic kinetic control, while the 100-mm particle represents an extreme case of diffusion limitation. The sharp combustion front is considerably broadened by the mass transfer limitation, and the maximum temperature is reduced by nearly 300 OF,but the gaseous effluent compositions and temperature at the top of the reaction zone (before devolatilization and drying) are nearly unchanged. Evidently the overall performance under these feed conditions is insensitive to the details of the physicochemical processes involved in the reactions.
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temperature in the reactor. (Steps i and ii can, of course, be combined.) (iii) The remaining carbon is converted by reaction with steam and C02. Reaction with hydrogen is not considered because of the slow rate of the methanation reaction. The composition above the gasification zone is fixed by the distribution between carbon reaction with steam and C02, and the temperature is computed from the adiabatic temperature decrease. (Heat losses may be included.) In practice only the steam reaction is needed, since water-gas shift equilibrium will be established and the COz reaction is not independent. (iv) Water-gas shift equilibrium is established adiabatically above the gasification zone. This is the composition and temperature at which product gas leaves the reaction zone of the gasifier. (Steps iii and iv can also be combined.) The final gas temperature and composition is fixed by the overall mass and energy balances and the water-gas shift equilibrium, together with the requirements of complete oxygen and carbon utilization. Thus, the effluent properties are independent of the initial oxidation CO/COz split and particle size. Indeed, if an estimate of the maximum temperature is not required, the complete calculation can be carried out in one step. Model Results Results of the kinetics-free (KF) model are also shown in Table I1 for the four coal and oxidant combinations in Table I. The calculations are for an initial CO/CO2 ratio of unity. The calculations for the Illinois coal using the KF model are very close to those of the detailed UD model for both air and oxygen blasts; the differences between the two model calculations undoubtedly are a result in part of the use of different numerical procedures. There are more discrepancies between the UD and KF models for the Wyoming coal. The Wyoming coal is a high activity coal, and the kinetic parameters used in the UD model result in a significantly higher degree of methane formation than for the low activity Illinois coal. Methane formation is not included in the kinetics-free calculation. For the Wyoming oxygen and air cases, the differences in gaseous compositions can be accounted for by 0.032 and 0.025 mole conversion by the reaction 3H2 + CO CH4 H20. Conclusions The magnitude and location of the maximum reactor temperature are important process variables for operation of a moving bed gasifier (Yoon et al., 1979a), and the details of internal reactor profiles are very sensitive to
-
+
certain model parameters. The relative insensitivity of effluent properties to these same model parameters shows clearly that the use of effluent measurements alone for model validation is inadequate. A better understanding of combustion kinetics under the environmental conditions characteristic of a pressurized gasifier is particularly needed. One of the primary uses of a mathematical model is to define efficient operating regions. The UD model can be used to compute feed and processing conditions that will lead to essentially complete carbon conversion in the adiabatic core of the reactor. Such conditions will lie along a line on the C-O2-H20 triangular diagram (Yoon et al., 1979b). Selection of an operating point along that line is based on the allowable maximum temperature, and that choice must be made conservatively with the present uncertainty over the magnitude of the maximum. The kinetics-free calculation described here provides a rapid means for estimating overall gasifier performance under conditions of efficient carbon utilization, with the best accuracy for coals that have negligible hydrogen reactivity under gasifier conditions. Of course, it is easy to develop a second kinetics-free calculation (KF2) based on carbon-hydrogen reaction to methane fast enough to reach equilibrium. A detailed model calculation such as that from the UD model is required to determine an appropriate set of feed conditions. The loci of optimal feed conditions computed by Yoon et al. (1979b) for oxygengasified Illinois and Wyoming coals are both straight lines with essentially the same slope over most of the feasible region for dry ash gasification on the triangular diagram. Thus, a single operating point as calibration is sufficient to allow KF calculations to determine the effect of feed variations on the effluent.
Acknowledgment This work was supported by the Electric Power Research Institute. The paper was presented at the EPRI Workshop on Coal Gasification Reactor Modeling, Asilomar Conference Grounds, Pacific Grove, Calif., June 21-23, 1978.
Literature Cited Amundson, N. R., Arri, L. E., AIChE J . , 24, 87 (1978). Biba, V., Macak, J., Kbse, E., Malecha, J., I d . Eng. Chem. RocessDes. Dev., 17, 92 (1978). Yoon, H., Wei, J., Denn, M. M.. AIChE J., 24, 885 (1978). Yoon, H., Wei, J., Denn, M. M., Chem. Eng. Sci., 34, 231 (1979a). Yoon, H., Wei, J., Denn, M. M., Ind. Eng. Chem. Process Des. Dev., 10, 306 (197913).
Received for review March 6, 1979 Accepted April 5 , 1979
