Modeling and numerical analysis for cylindrical flow-through catalytic membrane reactor with power-law reaction kinetics: Revealing dead-core phenomena

Cylindrical flow-through catalytic membrane reactors, employing porous membranes impregnated with catalysts, offer enhanced selectivity and yield in chemical reactions. This work focuses on the mathematical modeling and numerical analysis of a cylindrical flow-through catalytic membrane reactor. The proposed reactor model addresses a critical gap in research by incorporating realistic geometries of porous catalytic membranes. This model simulates a series of irreversible reactions following power-law kinetics under non-isothermal conditions within the reactor, formulated using a system of non-linear differential equations to account for mass and heat balances. The paper investigates the occurrence of dead zones within the membrane reactor as a result of rapid reactant depletion, a phenomenon that has not been extensively studied in prior literature for cylindrical membrane reactors. Problems with fractional reaction exponents require efficient numerical solvers since conventional iterative solvers encounter difficulties due to the fact that the power-law reaction term with fractional reaction exponent is not differentiable at the vanishing concentration. A novel time-marching scheme specifically designed for the cylindrical catalytic flow-through membrane reactor is developed and applied for simulations to get valuable insights into dead-core phenomena. The effects of dimensionless process parameters, including Thiele modulus, Peclet numbers, reaction exponent, Prater number, and a membrane geometrical parameter on the concentration and temperature profiles, as well as dead zone formation, are extensively investigated. The simulation results demonstrate that these parameters affect the occurrence of dead zones and their size. Finally, the effect of convective flow on the reactor performance indicators is presented.