Drained Solution for Elastoplastic Stress of Compressible Matrix around a Growing Poroelastic Inhomogeneity Inclusion

An analytical solution is presented for spherically symmetric growth of a fluid-saturated, poroelastic inhomogeneity inclusion embedded within a compressible elastoplastic matrix. A fluid source at the center causes the inclusion growth. The solution considers full poroelastic coupling of the inclusion pore fluid flow and solid phase deformation while solving for large deformation of the matrix via incremental elastoplasticity with associated flow rule and modified Mohr-Coulomb or Drucker-Prager yield models. Results obtained from the compressible (drained) solution are compared against the previously published solution pertaining to incompressible (undrained) matrix. Drained deformation is found to generally cause larger deviatoric stress, less compressive radial and hoop stresses, as well as faster growth of the plastic region, in the matrix. An example case study shows that compared with the undrained case, the drained matrix reaches the same elastoplastic strain with substantially smaller volume of injected fluid inside the embedded inclusion. The solution may be used as a proxy model of caprock integrity problem in CO2 geo-sequestration applications and further as a rigorous benchmark to verify the related numerical solvers.