Avoidance of Dead-Zone Formation in Flow-through Catalytic Membrane Reactor

Nonlinear convection-diffusion-reaction equations play a vital role in chemical reactor engineering, particularly with the growing interest in the use of catalytic membrane reactors that require innovative numerical schemes. In this paper, a model is studied for a single reaction characterized by power-law kinetics that involves fractional reaction exponent. To address the challenge of dead-zone formation in a membrane with distributed catalyst due to the fractional reaction exponent, a suitable time-marching scheme is employed to solve the two-point nonlinear boundary value problem. A bisection algorithm is developed to effectively compute the necessary membrane velocity to suppress formation of dead zones. The effects of the Thiele modulus and reaction exponent on length of dead zone and its suppression are investigated. Through both analytical and numerical approaches, we provide valuable insights into the mechanisms underlying dead-zone formation and its mitigation strategies. These findings are useful for optimal design of membrane reactors and their operation.