Incorporation of Strain-Induced Permeability Model in a Deformation-Flow-Heat Transfer Simulator
Authors: Du J. , Wong R.C. 
Published: March 2010

Abstract
This paper extends the fully coupled geomechanics and reservoir simulator previously developed by the authors to include temperature effects using finite element methods (FEM). The strain-induced permeability model and the full permeability tensor are incorporated into the developed deformation-flow-heat transfer simulator. Numerical examples are given to evaluate the validity of the FEM model. The simulation results demonstrate that the strain-induced permeability model has significant effects on wellbore pressure response and geomechanical behaviour of the reservoir.

Introduction
The simulation of fluid flow and heat transfer through porous media has been a branch of research undergoing rapid growth in the chemical and petroleum field. Conventional reservoir simulators usually calculate the effects of deformation on pore volume change through the concept of reservoir compressibility and mainly focus on homogeneously or transversely isotropic porous structures, although in most practical problems the porous medium is anisotropic either due to geological processes or due to human beings' industrial activities.
Recently, much attention has been paid to the importance of geomechanics in reservoir simulation, particularly in the thermal recovery of oil from oil sands reservoirs. Deformations in an oil sands reservoir are induced by the changes of pore pressure and temperature due to fluid injection and production in thermal recovery processes. In turn, the changes in deformation affect permeability.
The permeability change of a reservoir formation subjected to deformation changes is usually assumed as a function of porosity or volumetric strain, which is a scalar variable. Thus, the changes in permeability are equal in all directions even though the changes in strains are different in each direction. Wong(1) analyzed the grain fabric of intact and sheared oil sand specimens using the thin section imaging method. He observed that even in intact natural oil sands specimens, the hydraulic radius and tortuosity factors vary in vertical and horizontal directions resulting in an intrinsic anisotropy in permeability. Based on theoretical and laboratory works, he developed a new permeability model for deformable porous media(2). This model assumes the permeability tensor is governed by induced principal strains. It can quantify the changes in permeability when the material experiences shear deformation and the changes in permeability can be anisotropic.
In order to account for reservoir deformations due to pore pressure and temperature changes resulting from production and fluid injection, coupled geomechanics reservoir heat transfer simulation is necessary(3). Conventional reservoir simulators usually use the finite difference method (FDM) and assume permeability is either an isotropic or diagonal tensor. It is impractical to develop coupled geomechanics reservoir simulators based on FDM numerical schemes due to the complexity. A coupled deformation-flow-heat transfer simulator using finite element methods (FEM) was developed by implementing temperature in an earlier developed geomechanics reservoir simulator(4). The full permeability tensor and the strain-induced permeability model were incorporated into the simulator. It was then used to conduct a coupling analysis of two-dimensional non-isothermal single-phase fluid flow in elastic porous media.

Coupled FEM Model Formulation
Prior to the formulation of the governing equations, we need to make a few assumptions with respect to the FEM model(5, 6):