While introducing a liquid sweep into the permeate side of a polymeric membrane (the lower pressure side to which gas permeates) can improve the ability of a membrane to separate a gas mixture [1,2], numerical simulations of the two-phase flow are challenging. The system of partial-differential equations is highly coupled and nonlinear and becomes degenerate near the inlet boundary of pure liquid. To address the nonlinearities, we first discretize the variational form of the problem with piecewise linear functions on an unstructured mesh of rectangles and solve the equations with Newton’s method using a line search. To obtain a solution that conserves mass, we then post-process the local flowrates into the lowest-order Raviart-Thomas space [3]. A mesh refinement analysis indicates reasonable convergence rates compared to analytical rates for linear problems. A comparison to experiments allows the utility of simulations to be further assessed.
References:
1. Loprete, K. E. (Compact Membrane Systems Inc. dba Ardent Process Technologies). Method for Humidifying Facilitated-Transport Membranes. US 17/276,639. 2021.
2. Majumdar, S. (Compact Membrane Systems Inc. dba Ardent Process Technologies). Humidification and Selective Permeation Module. US 17/772,247. 2022.
3. Raviart, P. A.; Thomas, J. M. A Mixed Finite Element Method for 2nd Order Elliptic Problems. Mathematical Aspects of Finite Element Methods, 1977.
