To obtain a quantitative description of the underlying flow, we consider a flat cell filled with an anisotropic porous spacer. A polymeric membrane is placed on top of the spacer and gas permeates through as liquid water flows through the cell. To model the system, we adapt work found elsewhere [3], using the van Genuchten relations for the dependence of the capillary pressure on saturation (volume fraction of liquid) and the relative mobility of each phase. While numerical simulations are challenging due to the nonlinearities present in the problem and the degeneracy associated with the inlet boundary of pure liquid, we overcome this challenge by separating the calculations into two parts. 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 flow-rates into the lowest-order Raviart-Thomas space. A mesh refinement analysis indicates reasonable convergence rates compared to analytical rates for linear problems. We perform experiments through the cell and utilize them to obtain the permeability matrix of each phase flowing through the anisotropic spacer (a porous medium) and assess the validity of numerical simulations.
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. Bear, J. Modeling Phenomena of Flow and Transport in Porous Media. Springer International Publishing AG, Switzerland. 2018.