Title: Finite Element Methods in Simulating the Separation of a Gas Mixture induced by a Membrane
Presenter: Dr. Robert DeJaco
Abstract: Ardent Process Technologies (previously known as Compact Membrane Systems) is a start-up company located in New Castle, DE. As we seek to commercialize membrane technologies we have developed for (i) separation of propane from propylene and (ii) capture of carbon dioxide from point sources, we are developing mathematical models and numerical simulation schemes to provide our customers with accurate cost estimates, obtain intuition on phenomena occurring inside our products, and control our processes as they operate continuously in the field.

In this talk, I will present a mathematical model for separation of propane from propylene with a membrane. The membrane allows propylene to diffuse much faster through it than propane,
leading to a separation. I will then utilize an expanded mixed finite element method [1,2] to
discretize nonlinear partial-differential equations describing the total mass balance and
momentum balance on each side of the membrane, and use a streamline—diffusion method for
the equations describing conservation of propylene mass. After presenting an iterative approach for solving the nonlinear and coupled equations, I will present some numerical experiments to estimate convergence rates. I will conclude with some visualizations of the solutions and a summary of future directions.

1. Z. Chen, Expanded Mixed Finite Element Methods for Linear Second-Order Elliptic
Problems, I, ESIAM: Mathematical Modelling and Numerical Analysis, 32: 479—499,
1998.

2. Z. Chen, Expanded Mixed Finite Element Methods for Quasilinear Second-Order Elliptic
Problems, II, ESIAM: Mathematical Modelling and Numerical Analysis, 32: 501—520,
1998.