(548e) Effective Medium Theory for the Transport of Fluid Mixtures Through Porous Media

The transport of fluids in the narrow confined pore spaces
disordered materials with complex pore topologies is central to many emerging
technologies for gas separation and storage, as well as in nanofluidics.
Optimizing
the performance of such technologies requires a deep understanding of how the
flow of these mixtures is affected by the topology of the pore space,
particularly its pore size distribution and pore connectivity. While there
exist accurate techniques such as the hybrid effective medium-correlated random
walk theory for the estimation of the effective diffusivity characterizing the
transport of single fluids through porous materials, equivalent approaches for
the case of fluid mixtures are yet to be developed.  Existing alternatives for multi-component
systems rely on computationally intensive solution of the pore network
equations, or ad hoc adaptations of
the single fluid theories which are useful for a limited variety of systems. We
present here a hybrid Effective Medium-Correlated Random Walk Theory for the
calculation of the matrix of effective transport coefficients of fluid mixtures
diffusing through porous materials. The theory is suitable for those systems in
which component fluxes at the single pore level can be related to the chemical potential
gradients of the different species through linear flux laws, and corresponds to
a generalization of the classical single fluid effective medium theory for the
analysis of random resistor networks. Comparison with simulation of the
diffusion of binary CO₂/H₂S and ternary CO₂/H₂S/C₃H₈
gas mixtures in membranes modeled as large networks of randomly oriented pores
with both continuous and discrete pore size distributions demonstrates the
power of the theory, which was tested using the well known generalized
Maxwell-Stefan model for surface diffusion at the single pore level.