Semianalytical solutions for release of fluids from rock matrix blocks with different shapes, sizes, and depletion regimes

Abstract

[1] Dual-porosity (DP) models have been extensively used to simulate the flow of fluids (water or gas) in aggregate soils and fractured porous media. The fluid exchange between the rock matrix blocks and the fracture network is very important in DP models. In this study, we present semianalytical solutions for release of a single-phase liquid or gas from cylindrical and spherical matrix blocks with various block size distributions and different pressure depletion regimes in the fracture. The nonlinear pressure diffusivity equations for flow of gas and air are solved analytically using an approximate integral method. It is shown that this solution can be simplified to model flow of slightly compressible fluids like water in DP media. The effect of variable block size distribution on the release rate for different block geometries is studied. Practically it is not feasible to model a large-scale fractured reservoir based on a fine grid approach due to the requirement of large computational time. The presented semianalytical model can be incorporated into numerical models for accurate modeling of the amount of transferred fluid between matrix and fractures using a DP approach. It is shown that the results calculated by the developed model match well with those from fine grid numerical simulations. Furthermore, the developed model can recover the available solutions in the literature for slightly compressible fluids such as water or oil. It can be used to calculate two-or threedimensional flows in matrix blocks bounded by two or three sets of fractures, respectively.Citation: Ranjbar, E., H. Hassanzadeh, and Z. Chen (2013), Semianalytical solutions for release of fluids from rock matrix blocks with different shapes, sizes, and depletion regimes, Water Resour.

A Review of Flow Mechanism and Inversion Methods of Fracture Network in Shale Gas Reservoirs

“…Considering the multicontinuous media distributions in shale reservoirs, including organic matter, inorganic matter, and fracture network, scholars proposed the multicontinuous model to describe gas migration in shale gas reservoirs [35,36]. Since fracture network morphology and flow capacity have a greater impact on flow behavior, based on the conventional diffusion equation (uniform induced fracture spacing and uniform fracture network porosity/permeability, CDE), Cinco-Ley et al [37], Reis [38], Ranjbar et al [39], and other scholars proposed the modified conventional diffusion equations (MCDE) to simulate fluid flow between fractures and matrix. This equation takes into account the heteroge-neously distribution of induced fracture spacing and the uniformly distribution of fracture network porosity/permeability.…”

A Mixed Element Method for the Desorption‐Diffusion‐Seepage Model of Gas Flow in Deformable Coalbed Methane Reservoirs

“…In addition, there are some other studies [26,27] considering the influence of quadratic term u 2 . For example, Ranjbar et al [26] have considered the gas density variation in space and solved the nonlinear equations using semianalytical methods. However, they did not consider the effect of gas desorption and deformable media.…”

An Analytical Model With a Generalized Nonlinear Water Transfer Term for the Flow in Dual‐Porosity Media Induced by Constant‐Rate Pumping in a Leaky Fractured Aquifer

“…The neglect of spatial variation may be valid because the fracture has a much higher permeability than the matrix block, often by several orders of magnitude (Sen, 1995; Warren & Root, 1963). The LPA‐based model was commonly employed for the problems of gas flow (e.g., Dejam et al., 2018; Jerbi et al., 2017; Ranjbar et al., 2013; Ranjbar & Hassanzadeh, 2011), solute transport (Bibby, 1981; Brusseau et al., 1994; Samardzioska & Popov, 2005), and heat transfer (Heinze & Hamidi, 2017). Besides, the LPA‐based model was also applied to investigate the infiltration in variably saturated soils (Gerke & van Genuchten, 1993a, 1993b) and pump‐induced flow in fractured aquifers (De Smedt, 2011; Dougherty & Babu, 1984; Greene et al., 1999; Tamayo‐Mas et al., 2018; Wang & Xue, 2018) in the literature of subsurface flow.…”