Poroelastic model for induced stresses and deformations in hydrocarbon and geothermal reservoirs

Fluid migration and heat transport result in changes in pore pressure and temperature within a reservoir, which can induce stresses and deformations in the reservoir and the bounding rock system through poroelastic and thermoelastic couplings. Analytical and semi-analytical solutions for investigating the induced stresses and deformations are therefore extremely useful when applied to both predicting and monitoring the reservoir volume changes and associated subsurface and surface deformation. The poroelastic and thermoelastic eigenstrains are used here to characterize the pore pressure change and temperature variation, respectively, in the reservoir. The induced stresses and deformations are then obtained by using the single- and double-inclusion models, and are expressed in terms of the Galerkin vector stress function, which is related to the corresponding eigenstrains in a straightforward way. The difference in mechanical properties between the reservoir and the bounding rocks is accounted for using the theory of inhomogeneous inclusions. The effect of the reservoir shape, elastic properties, and the distribution of pore pressure change within the reservoir on the surface deformation has been investigated. The magnitude and pattern of the induced surface tilt have been compared with those produced by a hydraulic fracture. The analytical expressions obtained here for the displacement and tilt fields can serve as a useful forward model for monitoring and mapping hydraulic fractures, subsurface fluid migration and heat transport associated with injection or production of fluid into or from a reservoir by surface deformation-based monitoring techniques, such as tiltmeter monitoring.