Time-Dependent Elastoplastic Stress of an Infinite Matrix around a Growing Poroelastic Inhomogeneity Inclusion

Abstract

This paper presents a time-dependent analytical solution for undrained elastoplastic response of a porous, fluid-saturated medium to fluid source at the center of an embedded spherical, porous, fluid-saturated inhomogeneity inclusion. The solution considers poroelastic coupling in the inclusion while solving for the surrounding matrix stress using a Lagrangian formulation of the incurring elastoplastic deformations. The solution for plastic deformation of the matrix is obtained using the large deformation theory of plasticity with associated flow rule of either the strain-hardening Drucker-Prager model or smoothed strain-hardening Mohr-Coulomb model. The obtained solution is used as a proxy model to study caprock stress evolution upon fluid injection in subsurface rocks to mimic applications such as CO2 geo-sequestration. Findings indicate that the (poro)elastic models that are predominantly utilized in the existing studies of the subject could substantially underestimate the caprock shear failure threshold. Results obtained from a presented case study show that 0.8% allowance for elastoplastic strain in the caprock could yield up to 100% increase in fluid injectivity of the embedded reservoir. The presented solution may further serve as a rigorous benchmarking tool for verification of related numerical solution schemes. Caprock integrity concerns arise when injecting fluid into an embedded rock formation, e.g., during CO2 geo-sequestration or when withdrawing fluid from a reservoir, e.g., during oil and gas production. This work assesses possible enhancement in the estimated caprock integrity threshold because of plastic deformation beyond elastic limit, yet prior to rock failure. A time-dependent analytical solution for a geometrically idealized model of porous and fluid-saturated reservoir and surrounding caprock is developed for this purpose. Findings indicate that 0.8% allowance in the caprock total elastoplastic strain beyond elastic limit of the rock results in more than a twofold increase in the injectivity of the embedded reservoir. Higher values of plastic strain-hardening parameter or total strain allowance would allow for higher injectivity thresholds. These results underline the necessity for consideration of plastic deformation and stress analysis in studies on caprock integrity analysis.