Nonlinear sorption kinetics and surface diffusion effects on gas transport in low-permeability formations
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In coals and shales, gas transport and storage are important for accurate prediction of production rates and for the consideration of subsurface greenhouse gas sequestration. They involve coupled fluid phenomena in porous medium including viscous flow, diffusive mass transport and adsorption. Standard approach to describe gas-matrix interactions is deterministic and neglects the effects of local spatial heterogeneities. Using an upscaling approach based on small perturbation theory, the authors have previously investigated the influence of small-scale heterogeneities in matrix porosity on Darcy flow and Fickian-type pore diffusion in the presence of linear non-equilibrium gas adsorption (Fathi and Akkutlu, 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 the gas behavior 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, i.e., surface (or solid) diffusion. In this paper, we incorporate the sorption nonlinearity and surface diffusion into their formulation and apply the same upscaling approach. Gas sorption involves the so-called Langmuir kinetics, which reduces 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. Whereras, the surface diffusion, although commonly ignored by the industry, brings an intricate nature to the gas release dynamics. Through macro-transport effect of the heterogeneity, it increases the ultimate gas recovery and, through the macro-kinetics effect of the heterogeneity, it decreases the time needed to reach the ultimate recovery significantly. As the consequence of these effects, it is shown that the gas-matrix system does not reach the equilibrium adsorption limit during any stage of the gas release. Copyright 2009, Society of Petroleum Engineers.
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Proceedings - SPE Annual Technical Conference and Exhibition
