The significantly low primary recovery from unconventional oil and gas reservoirs has led to an increased interest in shale enhanced oil recovery (EOR). Although researchers have evaluated different EOR methods, only the cyclic gas enhanced oil recovery (CGEOR) has been successfully demonstrated in the field. Considering the expected diffusion particularly during the soaking period of CGEOR in these tight rocks, this work seeks to understand the role of diffusion at typical reservoir conditions. An understanding and accurate model of diffusion could lead to a more optimal design of CGEOR in shale oil reservoirs.

The objective of this work is to present a rigorous model of diffusion in fractured shale oil and gas reservoirs. To this end, we extended the embedded discrete fracture model (EDFM) and projection-based embedded discrete fracture model (pEDFM) to account for the diffusion of multicomponent hydrocarbons from the matrix into each natural fracture in the simulation domain. Considering the high pressures and sharp pressures in hydraulically fractured tight rocks, we used the generalized Maxwell-Stefan diffusion model and compute the matrix of diffusion coefficients as a function of pressure and composition. In the effort to use a thermodynamically consistent diffusion coefficient matrix that accounts for diffusive flux under chemical potential gradient, we derive an activity-corrected Maxwell-Stefan (MS) diffusion coefficient matrix. The result of this derivation indicates that the inverse drag matrix could be used as the activity-corrected MS diffusion matrix in the generalized MS diffusion model, which is driven by the gradient of the natural logarithm of component fugacity.

Our simulation results indicate that the relative contribution of diffusive transport to recovery is more significant at high natural fracture intensities and low matrix permeabilities. We show that a high-resolution mesh is important to obtain reliable diffusion results because numerical diffusion could mask the effect of physical diffusion in coarse simulation grids. The effects of the composition- and pressure-dependence of diffusion are considerable because of the sharp pressure drops and attending compositional changes in tight rocks. So, it is important to use a robust diffusion model that accounts for these changes. The study of the contribution of the matrix-fracture diffusive transfer introduced into EDFM/pEDFM shows that this could be significant in reservoirs with natural fractures of considerable size.

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