The equivalent inclusion method for poroelasticity problems

In this paper, we extend the poroelastic solution of a single poroelastic inclusion proposed by Rudnicki (2002) to two interacting poroelastic inclusions with arbitrary shape and orientations with respect to each other. The methodology used in this paper is a combination of Rudnicki works for a poroelastic inclusion and Moschovidis and Mura's approach to include interactions between inclusions with different poroelastic and fluid pore pressure properties. In the present work, the interacting poroelastic inhomogeneities are replaced with equivalent inclusions. This problem has a lot of application in geomechanics and biology. As an example, we used the derived solution to calculate fracture gradient changes in a formation with multiple compartments, where one of the compartments is already depleted (low pore pressure) due to fluid production. The results were tested with a numerical finite difference model to check the accuracy of the proposed solution.