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 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.

A New Multicontinuum Model for Advection-Diffusion Process of Single-Phase Nonlinear Flow in a Multiscale Fractured Porous Media

“…For each point in the domain, we define a microscale averaging volume having internal heterogeneities with permeable interfaces. The governing equations for fluid transport were developed from the mass conservation and momentum equations defined in equations ( 1) and (2) [7]. Thus, an initial-boundary value problem for fluid flow in α-phase in an averaging volume, V , is obtained as follows:…”

“…Considering the closure problem, the source terms and the boundary terms are represented in terms of the averaged variables identified as ∇hP α i α , ∇hP η i η , and hP β i − hP α i: It is therefore obvious for the solution of the twoequation model to be dependent on the source terms. Hence, following the concept in the works of [7,17,20,21], the spatial deviations are represented as functions of the averaged variables of the macroscopic source terms written as follows:…”

“…To successfully model these flow processes, a more tactful approach is required. Various attempts have been made via the multicontinuum approach, resulting in triple-porosity and triple-porosity/permeability models ( [1,[3][4][5][6][7]) that are superior to dual porosity and permeability models ( [3,8]). However, because they are based on much simplified assumptions, these models are less reliable to study advection/diffusion in fractured porous medium with nonlinear flow behaviors.…”