Simulation of gas separation using partial element stage cut modeling of hollow fiber membrane modules

On the Maximum Obtainable Purity and Resultant Maximum Useful Membrane Selectivity of a Membrane Separator

Design considerations concerning the maximum purity of a membrane separator, and the resultant maximum effective selectivity of the membranes were explored by modeling a binary gas membrane separator (pressure-driven permeance) using a dimensionless form. Although the maximum purity has an analytical solution at the limit of zero recovery or stage cut, this solution over-predicts the obtained purity as the recovery is increased. Furthermore, at combinations of high recovery, low feed mole fraction, and low pressure ratio, the maximum purity becomes independent of selectivity above some critical selectivity. As a consequence of this purity limitation, a maximum selectivity is defined at which further increases in selectivity will result in less than a 1% change in the final purity. An equation is obtained that specifies the region in which a limiting purity is less than unity (indicating the existence of a limiting selectivity); operating at less than the limiting pressure ratio results in a purity limitation less than unity. This regime becomes larger and more significant as the inlet mole fraction decreases (e.g., inlet feed mole fraction of 10% and pressure ratio of 100 results in a maximum useful membrane selectivity of only 130 at 95% recovery). These results suggest that membrane research should focus on increasing permeance rather than selectivity for low-concentration separations. The results found herein can be used to set benchmarks for membrane development in various gas separation applications.

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 CH4 and CO2, as well as a mixture of He, CO2, N2, and CH4. 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.