Poroelastic Model for Production- and Injection-Induced Stresses in Reservoirs with Elastic Properties Different from the Surrounding Rock

Abstract

Closed-form and semianalytical solutions for induced poroelastic stresses and strains are extremely useful for the design of subsurface fluid storage in caverns because of their relative ease of implementation and their suitability for parameter sensitivity analyses. This paper describes the use of Eshelby’s inhomogeneity theory to derive equations that can be used to predict the induced stresses and strains for reservoirs that are elliptical in cross section, under plane strain conditions. Sensitivity analyses demonstrate that the induced stresses are relatively insensitive to the Poisson’s ratio of the surrounding rock, but they are strongly affected by the Poisson’s ratio of the reservoir, and the ratio of shear modulus of the reservoir to that of the surrounding rock. Results are presented in terms of dimensionless parameters, which facilitate their application to a broad range of reservoir dimensions and pressure-change magnitudes. These equations can also be used to predict the induced stresses around a cavity, which represents the special case of an inhomogeneity with a shear modulus of zero.