Framework for Estimating Vapor Transport Parameters through Intact Geomembranes by the Dusty Gas Model (DGM)

Abstract

A framework based on the Dusty Gas Model (DGM) for estimating gas/vapor transport parameters through geomembranes has been suggested to address the limitation in the commonly used method for the analysis of Water Vapor Transmission (WVT) tests which is based on Fick’s first law of diffusion. Currently, it is assumed that gas or vapor transport through geomembranes occurs via molecular diffusion and thus Fick’s law of diffusion is suitable for carrying out the analysis. The main limitation, however, stems from the fact that geomembranes have extremely low permeability, varying from 10-12 to 10-15 cm/sec, that renders other gas transport flux mechanisms such as Knudsen diffusion significant and in many cases is more important than molecular diffusion. This indicates that Knudsen diffusion dominates the gas transport mechanisms through geomembranes and that the adequacy of Fick’s law to model gas transport through geomembranes is questioned. The DGM, on the other hand, incorporates Knudsen diffusion, as well as: viscous flow, bulk diffusion (nonequimolar and molecular diffusion), surface diffusion and thermal diffusion. Analysis of reported measurements of Water Vapor Transmission (WVT) test using the suggested framework resulted in estimates of the Knudsen diffusion coefficient, rather than the effective molecular diffusion coefficient that is commonly obtained when applying Fick’s law. The obtained Knudsen diffusion coefficients are then used to estimate the average pore radius of the geomembranes. For the sake of contrasting the two methods, the reported WVT results were also analyzed based on the commonly used method, and the results were used to estimate the porosity of the geomembranes. The estimated value of the porosity is unreasonable and supports the argument presented in this study which states that Knudsen diffusion is the dominant mechanism for transport through geomembranes and not molecular diffusion. Finally, a new set of geomembrane parameters, permeance and permeability is introduced. The newly defined parameters are theoretically rigorous since they are based on the dominant mechanism and assume no equivalence of isobaric and non-isobaric systems.