# Mathematical modelling of gas separation and storage using advanced materials

2009

## Degree Name

Doctor of Philosophy

## Department

School of Mathematics and Applied Statistics

## Abstract

Clean, sustainable and cost-efficient fuel alternatives are expected to replace conventional fossil fuel combustion systems as environmental and economic pressures rise. Alternative fuel candidates include synthetic gas, purified natural gas and hydrogen gas. The realization of an alternative fuel-based economy hinges on the efficient separation and storage of gases, for applications such as pollutant capture, synthetic fuel production, fuel purification and fuel storage. Membranes and adsorbents are materials characterized by an internal network of angstrom and nano-sized pores which are designed to separate and store gases, respectively. This thesis is concerned with the development of simple mathematical models to explain and predict gas transport and adsorption properties within advanced materials. Such models will guide the tailoring of porosity to optimize the desired properties. This thesis makes contributions to the following three areas:

• Gas separation Firstly, a new model that determines the transport properties of a gas within individual pores is presented. The model considers the interactions of the gas with the surface of the pore to characterize the various transport regimes within pores of different size, shape and composition. This is an entirely new approach to understanding and interpreting the various diffusion regimes known to occur within gas separation membranes. The new model can be used to determine the optimal pore characteristics that maximize the separation of gas mixtures. Secondly, a new empirical relationship between gas diffusion and the membrane free volume is introduced which is found to accurately describe known diffusion behaviour for a range of polymer membranes. This leads to a new method for determining the amount of free volume necessary to achieve a desired gas diffusion rate.

• Gas storage Based upon fundamental thermodynamic principles, a new model for gas storage within adsorbents is presented. The model incorporates the interactions between the gas and the internal surface area of the adsorbent, and proves to be an accurate and fast method for predicting storage performance within adsorbents of varying porosities. This novel approach can be used to determine the pore characteristics necessary to store the maximum amount of gas under the required operating conditions.

• Physical aging A new physical aging model based on the mechanism of vacancy diffusion is derived that accurately matches existing aging data. Using this model and the existing theory the mechanisms of physical aging are examined, particularly for thin polymer films. Specifically, the new approach provides new insights into the physical aging mechanisms responsible for polymer densification and can be used as a tool to predict the polymer’s performance over time.

Finally, the new mathematical models that are presented here provide considerable insight into complex physical processes, and will serve to accelerate the development of alternative energy technologies by providing simple guidelines for material design.

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Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.