Dynamic Mathematical Modeling of an Isothermal Three-Phase Reactor: Model Development and Validation

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.