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SPE 30752 Coupled Fluid Flow and Geomechanics in Reservoir Study I. Theory and Governing Equations

Society of Petroleum Engineers

H.-Y. Chen, SPE, L.W. Teufel, SPE, and R.L. Lee, SPE, New Mexico Institute of Mining and Technology

Copyright 1995, Society of Petroleum Engineers, Inc. This paper was prepared for presentation at the SPE Annual Technical Conference & Exhibition held inDallas, U.S.A., 22-25 October, 1995. This paper was selected for presentation by an SPE Program Committee folloWing review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are sUbject to correction by the author(s). The material, as presented, does not necessarily reflect anyposition of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are sUbject to pUblication review by Editorial Committees of the Society of Petroleum Engineers. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper ispresented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-214-952-9435.

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. Ourgoal 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 acoupled fluid-flow-geomechanics model. Consistent interpretation of various rock compressibilities and the effective stress law are shown to be criti'cal 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 pressuresatisfies 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. Weare 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,I-7 Biot's theory and the published applications are oriented more toward rock mechanics than fluid flow. Extension ofBiot'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. Severalexcellent 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 IO and Bear IS 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....