Mass Transport of Adsorbed-Phase in Stochastic Porous Medium with Fluctuating Porosity Field and Nonlinear Gas Adsorption Kinetics
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Using an upscaling approach based on small perturbation theory, the authors have previously investigated the influence of local heterogeneities in matrix porosity on Darcy flow and Fickian-type pore diffusion in the presence of linear non-equilibrium gas adsorption Fathi and Akkutlu, J. Transp. Porous Med. 80, 281-3044 (2009). They identified non-trivial macro-transport and -kinetics effects of the heterogeneity which significantly retard gas release from the matrix and influence the ultimate gas recovery adversely. The work was a unique fundamental approach for our understanding of gas production and sequestration in unconventional reservoirs; however, it was simplified and did not consider (i) the presence of nonlinear sorption kinetics and (ii) a transport mechanism for the adsorbed phase. In this article, we incorporate the nonlinearity and surface diffusion effects of the adsorbed-phase into their formulation and apply the same upscaling approach to further study the heterogeneity effects. Gas sorption involves the so-called Langmuir kinetics, which is reduced to the well-known Langmuir isotherm in the equilibrium limit. It is found that the nonlinearity participates into both macro-transport and -kinetics, promoting primarily the surface diffusion effects. Whereas surface diffusion, although commonly ignored during modeling subsurface phenomena, brings an intricate nature to the gas release dynamics. Through macro-transport effect of the heterogeneity, it increases ultimate gas recovery and, through the macro-kinetics effect of the heterogeneity, it significantly decreases the time needed to reach the ultimate recovery. As the consequence of these effects, it is shown that the gas-matrix system practically does not reach the equilibrium adsorption limit during any stage of the matrix gas release. 2011 Springer Science+Business Media B.V.
