A Coupled Double-Porosity Model for Water- Oil Flow in Deformable Fissured Sandstone Reservoirs

Abstract A coupled double-porosity model is presented to simulate oil-water flow in fissured sandstone reservoirs. The model is developed by fully coupling an extended geomechanics model with a double-porosity model for water-oil two-phase reservoir flow. Deformation of fissured reservoir bears important influence on the water-oil flow process. To evaluate fissure's role during the enhanced production, an integrated elastic module is introduced. The model also reveals some important aspects of coupling effects between stress/deformation and fluid flow. By introducing further assumptions to the governing equations, an uncoupled FEM numerical scheme is proposed, which describes the pressure, water phase saturation and solid deformation respectively. In order to derive an efficient numerical solution scheme, a FEM with a fully implicit and sequential iterative algorithm is used. The numerical results show that the efficiency of water displacement in fissured reservoir may be controlled by aperture's flow conductivity and oil/water PVT property. Introduction The "double-porosity" model for fractured porous rock domain was first introduced in the literature by Barenblatt in [1] and at present a large number of articles on the similar subjects exist spanning over several scientific and engineering disciplines, including geology, hydrology, petroleum reservoir engineering and environmental engineering; see, for instance, [2,3,4]. In these models the fractured systems were treated by a large number of matrix blocks containing most of the stored fluid together with a system of high-conductivity fissures. The aperture width is considerably greater than the characteristic dimension of the pores and the permeability k1 of the fissure system considerably exceeds the permeability k2 of the individual blocks of porous media. At the same time, the fissures occupy a smaller volume than the pores, so the ratio of porosity of any individual block of porous media. To obtain the double porosity model, the fissure system's local properties are averaged over a volume containing both the aperture and matrix. The so-called dual-porosity model for a porous medium consists of an equivalent coarse-grained porous medium in which the fissures play the role of "pores" and the blocks of porous media play the role of "grains". All previous models developed for fissure systems treated the system either as a rigid body or otherwise, deformation of the system was taken into account in an uncoupled manner. In the latter, the interactive effect of the deformation and fluid flow was usually ignored and thus, only the flow equations were required. Aifantis presented a model coupling the soil deformation and single-phase fluid flow through a fractured porous media [5, 6]. His study identified the strong coupling effects between fluid flow and solid deformation. The main goal of this paper is to provide a mathematical description of the dual-porosity model for water-oil flow through a deformable fractured system. Basic assumptions in our model are listed as follows:A continuum medium made of fissures, porous system, saturated water and oil phases. Concepts of overlapping continua and REV (representative element volume) are used to build each phase's mass conservation;Double porosities for fissure and porous blocks are defined as (equation) (Available in full paper)