Cell-element simulations to optimize the performance of osmotic processes in porous membranes

We present a new module of the software tool PoreChem for 3D simulations of osmotic processes at the cell-element scale. We consider the most general fully coupled model (see e.g., Sagiv and Semiat (2011)) in 3D to evaluate the impact on the membrane performance of both internal and external concentration polarization, which occurs in a cell-element for different operational conditions. The model consists of the Navier–Stokes–Brinkman system to describe the free fluid flow and the flow within the membrane with selective and support layers, a convection–diffusion equation to describe the solute transport, and nonlinear interface conditions to fully couple these equations. First, we briefly describe the mathematical model and discuss the discretization of the continuous model, the iterative solution, and the software implementation. Then, we present the analytical and numerical validation of the simulation tool. Next, we perform and discuss numerical simulations for a case study. The case study concerns the design of a cell element for the forward osmosis experiments. Using the developed software tool we qualitatively and quantitatively investigate the performance of a cell element that we designed for laboratory experiments of forward osmosis, and discuss the differences between the numerical solutions obtained with the full 3D and reduced 2D models. Finally, we demonstrate how the software enables investigating membrane heterogeneities.