Dynamic Mathematical Modeling of an Isothermal Three-Phase Reactor: Model Development and Validation
Publication: Journal of Environmental Engineering
Volume 129, Issue 7
Abstract
A catalytic reactor model (CatReac) that describes the transport and series reactions of compounds in a three-phase fixed-bed catalytic reactor is developed for the purpose of describing the volatile assembly reactor system within the potable water processor on-board the International Space Station. CatReac includes these mechanisms: advective flow, axial dispersion, gas-to-liquid and liquid-to-solid mass transport, intraparticle mass transport with pore and surface diffusion, and series reactions of multiple compounds. A dimensional analysis of CatReac revealed the following seven dimensionless groups may be used to determine the controlling transport and/or reaction mechanisms: (1) the Peclet number is the ratio of the advective to the dispersive transport; (2) the Stanton number is the ratio of the external mass transfer rate to the advective rate; (3) the Damköhler number compares the reaction rate to the advective transport rate; (4) the surface diffusion ratio equals the rate of transport by surface diffusion divided by the rate of transport by advection; (5) the pore diffusion modulus is the ratio of the rate of transport by pore diffusion to the rate of transport by advection; (6) the ratio of the gas to liquid advective rates; and, (7) the Biot numbers for surface and pore diffusion compare the external mass transfer rate to the intraparticle mass transfer rate. These dimensionless numbers are used to evaluate the impacts of the different mechanisms on the overall performance of the reactor. The numerical solution using orthogonal collocation was validated for a wide range of controlling mechanisms by comparing model simulations with several analytical solutions: (1) Gas-to-Liquid mass transfer controlling the overall mass transfer-reaction mechanisms, for a wide range of Pe number values; (2) Liquid-phase dispersion controlling the overall process; (3) Liquid-to-solid mass transfer resistance controlling the overall mass transfer-reaction process; (4) Reactions in series with two possibilities (4a): No intraparticle mass transfer resistance, and (4b): Significant intraparticle mass transfer resistance; (5) Langmuir isotherm (5a): single compound, no mass transfer resistance, and (5b): multicomponent competitive adsorption without mass transfer resistance; (6) Unsteady state operation: Plug flow with mass transfer and no reaction. These validations systematically examine all the mechanisms that are included in the general model and examine the model limitations based on the controlling mechanisms.
Get full access to this article
View all available purchase options and get full access to this article.
References
Audeves, D. (1998). “Dynamic mathematical modeling of an isothermal three-phase catalytic reactor.” PhD dissertation, Michigan Technological Univ., Houghton, Mich.
Barker, P. E., England, K., and Vlachogiannis, G.(1983). “Mathematical model for the fractionation of dextran on a semi-continuous counter-current simulated moving bed chromatograph.” Chem. Eng. Res. Des., 61(4), 241–247.
Crittenden, J. C., Hutzler, N. J., Geyer, D. G., Oravitz, J. L., and Friedman, G.(1986). “Transport of organic compounds with saturated groundwater flow: Model development and parameter sensitivity.” Water Resour. Res., 22(3), 271–284.
Danckwerts, P. V.(1953). “Continuous flow systems: Distribution of residence times.” Chem. Eng. Sci., 2(1), 1–13.
Finlayson, B. A. (1980). Nonlinear analysis in chemical engineering, McGraw–Hill, New York.
Fogler, H. S. (1992). Elements of chemical reaction engineering, 2nd Ed., Prentice–Hall, Upper Saddle River, N.J.
Gear, C. W. (1971). Numerical initial value problems in ordinary differential equations, Prentice–Hall, Upper Saddle River, N.J.
Hashimoto, I., Deshpande, K. B., and Thomas, H. C.(1964). “Peclet numbers and retardation factors for ion exchange columns.” Ind. Eng. Chem. Fundam., 3(3), 213–218.
Hinshelwood, C. N. (1933). The kinetics of chemical change in gaseous systems, 3rd Ed., Oxford, London.
Rosen, J. B.(1954). “General numerical solutions for solid diffusion in fixed beds.” Ind. Eng. Chem., 46(8), 1590–1594.
Rosendall, B., and Finlayson, B. A.(1995). “Transport effects in packed-bed oxidation reactors.” Comput. Chem. Eng., 19(11), 1207–1218.
Stuber, F., Wilhelm, A. M., and Delmas, H.(1996). “Modelling of three phase catalytic upflow reactor: A significant chemical determination of liquid-solid and gas-liquid mass transfer coefficients.” Chem. Eng. Sci., 51(10), 2161–2167.
Szukiewicz, M., Kaczmarski, K., and Petrus, R.(1998). “Modelling of fixed-bed reactor: Two models of industrial reactor for selective hydrogenation of acetylene.” Chem. Eng. Sci., 53(1), 149–155.
Tonkovich, A. L., Carr, R. W., and Aris, R.(1993). “Enhanced yields from methane oxidative coupling by means of a separative chemical reactor.” Science, 262(5131), 221–223.
Tsai, G.-J., and Tsao, G. T.(1991). “Dynamic response of an isothermal three-phase slurry reactor. I. The PM-PM-HS/ID model. Analytical solutions for continuous and semi-batch operations.” Chem. Eng. Sci., 46(3), 889–900.
Viswanathan, S., and Aris, R.(1974a). “Countercurrent moving bed chromatographic reactors.” Adv. Chem. Ser., 133(13), 191–204.
Viswanathan, S., and Aris, R.(1974b). “An analysis of the countercurrent moving bed reactor.” SIAM-AMS Proc., 8, 99–124.
Warna, J., and Salmi, T.(1996). “Dynamic modelling of catalytic three phase reactors.” Comput. Chem. Eng., 20(1), 39–47.
Yang, J. (2001). “Optimization and application of a three-phase isothermal catalytic model.” PhD dissertation, Michigan Technological Univ., Houghton, Mich.
Information & Authors
Information
Published In
Journal of Environmental Engineering
Volume 129 • Issue 7 • July 2003
Pages: 586 - 594
Copyright
Copyright © 2003 American Society of Civil Engineers.
History
Received: Jun 4, 2001
Accepted: Sep 13, 2002
Published online: Jun 13, 2003
Published in print: Jul 2003
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.