# Assessment and Discussion of the Steady-State Determination in Zeolite Composite Membranes for Multi-Component Diffusion

## TL;DR

This paper introduces a new method to determine steady states in zeolite composite membranes for multi-component gas diffusion.

## Contribution

The study proposes an alternative model for zeolite diffusion that avoids the need for a complex thermodynamic matrix.

## Key findings

- The method is applicable to membranes with any support orientation relative to the zeolite film.
- The role of the support in separation can be neglected under certain conditions.
- Using the dusty gas model or viscous flow in the microporous support yields different results.

## Abstract

A versatile, clear, and accurate method for determining the steady states of multi-component diffusion through composite membranes is presented in this study. This method can be used for simulating and designing membranes with any support orientation with respect to the zeolite film. In the mathematical model of the membrane, it was assumed that mass transport in the zeolite layer occurs by surface diffusion in accordance with the generalized Maxwell–Stefan model. Diffusion in the macroporous support was described by the dusty gas model (DGM). An alternative model of diffusion in the zeolite was proposed to the universally accepted model, which uses a matrix of thermodynamic factors Γ. Thus, the difficulty of analytically determining this matrix for more complex adsorption equilibria was eliminated. This article is dedicated to methodological and cognitive aspects. The practical features of the method are illustrated using two gas mixtures as examples, namely {H2, CO2} and {H2, n-C4H10}. The roles of zeolite and support in the separation of these mixtures are discussed. It was demonstrated under what circumstances the presence of the support can be neglected in the steady-state analysis of the membrane. The effect of the alternative application of the dusty gas model or viscous flow only in the microporous support was discussed.