Molecular diffusion is an important mechanism for hydrocarbons moving from pores to pores and from pores to hydraulic fractures in unconventional shale production. The diffusion coefficient is also an essential parameter in two-dimensional (2D) NMR map interpretations. However, molecular diffusion in the micro- and nanometer scale pore network of the unconventional shale rock remains poorly understood. The objective of this work is to link the restricted diffusion coefficient to the pore scale characteristics of shale gas media. A random walk algorithm is implemented to investigate the effects of pore-throat ratio (ratio of pore body radius to pore throat radius), length ratio (ratio of throat length to pore radius), pore shape and topology. It is concluded that, at an equal surface-to-volume ratio, the diffusion coefficient increases in pores with higher angularity. The effects of pore-throat ratio and length ratio are explicitly modeled in three dimensional (3D) structured regular lattices. The results indicate that, up to pore-throat ratios of 5, restricted diffusion is considerable in lattices with zero length throats. Furthermore, restricted diffusion decreases with the increase in length ratio. To reduce computational cost, a statistical method was developed to render simulating the effects of connectivity and pore size distribution on 3D unstructured multiscale networks feasible.

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