Poromechanics: from Linear to Nonlinear Poroelasticity and Poroviscoelasticity

Abstract

Due to the impact on productivity and oil in place estimates, reliable modeling of rock behavior is essential in reservoir engineering. This paper examines several aspects of rock poroelastic behavior within the framework of Biot's mechanics of fluid saturated porous solids. Constitutive laws of linear and nonlinear poroelasticity are first determined from a fundamental stress decomposition, which allows to clearly connect linear and nonlinear models. Concept of effective stress and rock compressibility are considered. Linear incremental stress-strain relations are derived from the proposed nonlinear constitutive law by defining tangent elastic properties. These characteristics are naturally functions of strains and pore pressure, but explicit expressions as functions of stresses and pore pressure are established herein. Experiments performed on a reservoir sandstone illustrate these points. A constitutive law of poroviscoelasticity is finally presented and applied to experimental data obtained on clay.