Ind. Eng. Chem. Fundam. 1980, 19, 325-326
325
CORRESPONDENCE Comments on "Parameter Sensitivity and Kinetics-Free Modeling of Moving Bed Coal Gasifiers"
Sir: The conclusions of Denn et al. (1979) regarding the kinetics-free modeling of gasifiers are based on the results obtained from their model of a moving bed coal gasifier (Yoon et al., 1978). However, the same inferences can also be derived from the theory of linear equations without resorting to detailed calculations by a rigorous model. In the model of Yoon et al., the transport equations are solved by a finite difference method with appropriate boundary conditions and stoichiometric and thermodynamic constraints. The following chemical reactions were included in the model C HzO e CO + H2 (1)
+ c + COZ * 2co C + 2H2 CHI
c+0 2
-
2(X - 1)CO + (2 - X)CO,
(2) (3) (4)
X is a system constant which determines the primary product distribution of CO and COS in the combustion products. It can be obtained by combining the following combustion reactions c + 0 2 c02 (44 2co (4b) 2c + 0 2
--
Alternately, reactions 4a and 4b result from substitution of X = 1 and X = 2, respectively, in eq 4. The fiial results of the analysis for mass and energy flow across the gasification zone boundaries depend only on the boundary conditions and constraints specified by a user of the model, including the assumption of water gas shift equilibrium, and the extent of conversion of coal components. Parameters such as transport properties and reaction kinetics only affect the reaction path in the gasifier. For example, the temperature profile in the gasifier depends on these parameters. Equations 1to 4 represent a set of independent reactions for the coal gasification system under consideration here. Any other set of independent reactions will yield the same results for mass and energy flow across the system boundaries (Balzhiser et al., 1972), and this was observed by Denn et al. when they varied the value of X in eq 4 to
Sir: The comments by Jagota are generally consistent with the conclusions of Denn et al. (1979). We do not agree, however, that the same inferences can be derived from the theory of linear equations without resorting to detailed calculations by a rigorous model. Contrary to Jagota's assertion, the user of a detailed moving bed reactor model is not free to specify the extent of conversion of coal components; this value is obtained from solution of a boundary value problem. The conclusions regarding "kinetics-free" modeling are therefore applicable only when it is known a priori that: (1) feed conditions are such that the combustion reaction will ignite; (2) there is sufficient gasifier residence time above 0 196-43 13/80/ 1019-032590 1.OOlO
yield different distributions of CO and COPin the primary combustion products. A variation in the value of X does not result in a new independent equation. For example, the following sets of algebraic equations result in the same solution, Le., x = 1,y = 1, irrespective of the value of A. set 1 x+y=2 2n+y=3 set 2
(1 + 2h)x
+ (1 + h)y = 2 + 3X 2x+y=3
The first equation of set 2 is a combination of the equations in set l, and therefore not an independent equation. The kinetics-free models do not require detailed analysis and calculations which are associated with more rigorous models, such as that of Yoon et al. However, the kinetics-free models only yield results for material and energy flow across the system boundaries. Such models are generally useful for feasibility studies. But rigorous models may be required for equipment design. It is worth mentioning here that Gumz (1950) has illustrated the application of kinetics-free models for coal gasifiers and blast furnaces. More recently, kinetics-free models of several coal gasifiers have been included in the Materials-Process-Product Method's computer program for feasibility studies of coal conversion processes (Roig et al., 1978, 1979), which has been developed by IR&T Corporation, McLean, Va., for the U.S. Department of Energy. Literature Cited Baizhiser, R. E., Samueis, M. R., Eiiiassen, J. D., "Chemical Engineering Thermodynamics", Prentice-Hall, New York, 1972. Denn, M. M., Yu, W. C., Wei, J., I d . f n g . Chem. Fundam., 18, 286 (1979). Gumz, W., "Gas Producers and Blast Furnaces: Theory and Methods of Calculation", Wiiey, New York, 1950. Roig, R. W., Jagota, A. K., Soni, D. S., Leggett, N., "Materials-Rocess-Product Analysis of Coal Process Technology", Final Report for Project Phase 11, U.S. Dept. of Energy, HCPIT2027-01 (Sept 1976). Roig, R. W., Jagota, A. K., Soni, D.S., "Materiais-Process-Roduct Analysis of Coal Process Techndogy", Final Report for Prow Phase 111 (in preparation), U.S. Dept. of Energy, Contract No. ET-764-01-2872 (1979). Yoon, PI.,Wel, J., Denn, M.M.,AIChEJ., 24, 885 (1978).
Mobil Research and Development Corporation Princeton, New Jersey 08540
Ani1 K.Jagota
the combustion zone to allow attack by steam and COzto utilize all of the fixed carbon that is not oxidized, so that the exit carbon can be taken to be approximately zero; and (3) the kinetics of hydrogen attack on carbon to form methane are sufficiently slow to neglect this reaction. Only plant operating data or the output from a detailed model can specify operating conditions where these requirements are true. A "kinetics-free" calculation can then be used to study system sensitivity in the neighborhood of such operating conditions. It is useful to note here that "kinetics-free'' calculations can be carried out in several ways, as long as four constraints are imposed on the compositions leaving the re@ 1980 American Chemical Society
