Modeling and Numerical Analysis for Catalytic Membrane Reactors

Abstract

There has been great interest in membrane reactors over the last decades. The limitation of selectivity and yield of certain products in chemical reactions is an important and not sfficiently solved problem in the field of Chemical Reaction Engineering. One possible way to circumvent this problem is through the use of membrane reactors. Compared to conventional reactors, catalytic membrane reactors have significantly improved performance. In this study the mathematical model employed is based on the coupled convection-diffusion-reaction equations with temperature-dependent reaction coefficients. By using the modified Crank-Nicolson scheme the problem is solved numerically. The numerical approximation is compared to one obtained by the collocation-based pdepe Matlab solver. This renowned Matlab solver fails to compute solutions in the case of large system parameters whereas the modified Crank-Nicolson method copes with the case of large Thiele modulus parameter. The proposed method has unconditional stability and second order of accuracy with respect to both space and time. Since the non-isothermal model has nonlinear power-law kinetics of fractional order, the existence of dead zones is also investigated. The effects of parameters such as reaction order, Peclet number, Thiele modulus on solution profiles are studied. The results show that these parameters influence the appearance of the dead zone in the non-isothermal multi-component reaction. Our parameter studies indicate that there exists a critical value of the Thiele modulus for each component in a consecutive irreversible reaction. Also, the effects of dimensionless Peclet number and Thiele modulus on selectivity, yield of intermediate product and conversion are analyzed. The effect of Peclet number is more significant for small values of Thiele modulus. We also find that, increasing convective flow, the conversion decreases and the increasing Thiele modulus leads to the increase of conversion.