Diffusive transport in porous media is a complex process in multi-scaled fractured media modeling. This paper presents a diffusive transport model for non-Dacian flow in a naturally fractured reservoir with triple porosity and permeability. To address the non-Darcian flow behavior associated with fluid transport in fractured porous media, the Darcy/Forcheimer equation was used. A point-diffusive equation was obtained from mass conservation and the Darcy–Forcheimer momentum equation; this is used together with interface conditions to incorporate the microscopic properties of the domain. Subsequently, the resulting equation was spatially smoothed to obtain an effective macroscopic average model. The macroscopic model obtained, unlike the existing models, has a cross-diffusive term for mass transport by induced fluxes and a mass transfer term accounting for mass transfer between the matrix and the surrounding fractures via the interface. The numerical simulation displayed a horizontal-linear flow behavior in the fractured network instead of a radial flow in the matrix. The results further suggest that despite the fractures aiding in fluid transport, they enhance fluid production in the reservoir compared to the matrix.
Fractured porous media modeling and simulation has seen significant development in the past decade but still pose a great challenge and difficulty due to the multiscale nature of fractures, domain heterogeneity, and the nonlinear flow fields due to the high flow velocity and permeability resulting from the presence of fractures. Therefore, modeling fluid transport that is influenced by both advection and diffusion in fractured porous media studies becomes a generic problem, which this study seeks to address. In this paper, we present a study on non-Darcian fluid transport in multiscale naturally fractured reservoirs via an upscaling technique. An averaged macroscopic equation representing pressure distribution in a three-phase multiscale fractured porous medium was developed, consisting of the matrix and a 2-scale fractured network of length-scales
ℓ
m
and
ℓ
M
. The resulting macroscopic model has cross-advective and diffusive terms that account for induced fluxes between the interacting domains, as well as a mass transfer function that is dependent on both physical and geometric properties of the domain, with both advective and diffusive properties. This model also has effective diffusive and advective coefficients that account for reservoir properties such as viscosity, fluid density, and flow velocity. From the numerical simulation, a radial, a horizontal-linear flow behavior, and a transient and quasi-steady-state flow regime that is typical of naturally fractured porous media was observed. The findings of this study will provide researchers a reliable tool to study fractured porous media and can also help for better understanding of the dynamics of flow in fractured reservoirs.
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