This paper extends the fully coupled geomechanics and reservoir simulator previously developed by the authors to include temperature effects using finite element method (FEM). The strain-induced permeability model and the full permeability tensor are incorporated in the deformation-flow-heat transfer simulator. Numerical examples are given to evaluate the validity of the FEM model.
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 being's industrial activities.
Recently, much attention has been paid to the importance of geomechanics in reservoir simulation, particularly in thermal recovery of oil sand reservoir. Deformations in an oil sand 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 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 sand 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 tensor permeability is governed by inducedprincipal 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 finite difference method (FDM) and assume permeability either isotropic or diagonal tensor. It is impractical to develop coupled geomechanics-reservoir simulators based on FDM numerical schemes due to its complexity. A coupled deformation-flow-heat transfer simulator using finite element method (FEM) was developed by implementing temperature in early version of a geomechanics-reservoir simulator (4). The full tensor permeability and the strain-induced permeability model were incorporated in the simulator. It was then used to conduct a coupling analysis of two-dimensional non-isothermal singlephase fluid flow in elastic porous media.
Prior to the formulation of the governing equations, we need to make a few assumptions with respect to the FEM model (5, 6):
Infinitesimal deformation theory holds.
Domains of interest are fully saturated.