Coupled Fluid Flow and Geomechanics in Reservoir Study - I. Theory and Governing Equations

Abstract

Abstract The purpose of this study is to examine Biot's two-phase (fluid and rock), isothermal, linear poroelastic theory from the conventional porous fluid-flow modeling point of view. Biot's theory and the published applications are oriented more toward rock mechanics than fluid flow. Our goal is to preserve the commonly used systematic porous fluid-flow modeling and include geomechanics as an additional module. By developing such an approach, complex reservoir situations involving geomechanical issues (e.g., naturally fractured reservoirs, stress-sensitive reservoirs) can be pursued more systematically and easily. We show how the conventional fluid-flow formulations is extended to a coupled fluid-flow-geomechanics model. Consistent interpretation of various rock compressibilities and the effective stress law are shown to be critical in achieving the coupling. The "total (or system) compressibility" commonly used in reservoir engineering is shown to be a function of boundary conditions. Under the simplest case (isotropic homogeneous material properties), the fluid pressure satisfies a fourth-order equation instead of the conventional second-order diffusion equation. Limiting cases include nondeformable, incompressible fluid and solid, and constant mean normal stress are analyzed. Introduction All petroleum reservoir problems involve two basic elements: fluid and rock. We are interested in two particular processes associated with them: fluid flow and geomechanics. Fluid flow is essential in a petroleum reservoir study. Geomechanics is believed to be important in the study of naturally fractured reservoirs and in reservoirs exhibiting stress-sensitivity. The theory describing fluid-solid coupling was first presented in a series papers by Biot. Biot's theory and the published applications are oriented more toward rock mechanics than fluid flow. Extension of Biot's theory to reservoir studies is not straightforward, especially to nongeomechanical or fluid-flow oriented engineers. The purpose of this paper is to describe how the conventional fluid-flow modeling can be extended to a coupled fluid-flow and geomechanical modeling. Identification of the linkages and consistent interpretations between the flow and deformation fields are emphasized. Several excellent reviews or re-interpretations of Biot's poroelasticity have been presented in, e.g., Refs. 8 through 15. Among these references, the works by Verruijt and Bear are the two most pertinent to this study. They also considered porous fluid-flow modeling approach coupled with Biot's theory. Both works, however, assumed incompressible solid phase in both flow and deformation fields. The solid phase compressibility, although not the primal mechanism in rock deformations, is a necessity for a complete interpretation of Biot's theory. Specifically, the solid compressibility is implicit in the so-called effective stress coefficient which, as will be shown, is the most important and critical concept in the theory of poroelasticity. The assumption of incompressible solid phase effectively eliminates the consideration of effective stress coefficient and greatly simplifies the problem. P. 507