A new macro-scale volume averaged transport model for diffusive dominated non-Darcian flow problem in multi-scaled naturally fractured reservoirs

Abstract Diffusive transport in porous media is a complex process multi-scaled fractured modeling. This paper presents diffusive model for non-Dacian flow naturally reservoir with triple porosity and permeability. To address the non-Darcian behavior associated fluid media, Darcy/Forcheimer equation was used. A point-diffusive obtained from mass conservation Darcy–Forcheimer momentum equation; this used together interface conditions to incorporate microscopic properties of domain. Subsequently, resulting spatially smoothed obtain an effective macroscopic average model. The obtained, unlike existing models, has cross-diffusive term by induced fluxes transfer accounting between matrix surrounding fractures via interface. numerical simulation displayed horizontal-linear network instead radial matrix. results further suggest that despite aiding transport, they enhance production compared