Authors:
Wa’il Y. Abu-El-Sha’r;
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.
Keywords:
Framework, Geomembrane, Dusty Gas Model (DGM), Knudsen Diffusion, Equivalent Permeability.