A generalized numerical framework for solving cocurrent and counter-current membrane models for gas separation

Membrane separation has become a panacea for various scientific and engineering problems, including water treatment, gas separation, purification, hemodialysis, and drug delivery. Modeling and simulation of such systems are necessary for the design, analysis, and optimization of membrane separation processes. Despite numerous studies, an efficient numerical solution of such systems is an open problem, especially when speed and reliability matter. In this study, a generalized numerical framework for solving cocurrent and counter-current membrane models is proposed, which hinges on a straightforward and reliable Gauss-Seidel method with successive over-relaxation. The results confirm the speed and reliability of the proposed algorithm, while it is validated by the experimental data for the separation of a mixture of CH(4) and CO(2), as well as a mixture of He, CO(2), N(2), and CH(4). The permeate outlet pressure estimation error can be reduced to any value as low as ∼10(−14)%, while the computational time on a personal laptop is not more than 4.5 s. This algorithm can be readily implemented in various programming languages and commercial software applications.