A mathematical framework for multiphase poromechanics in multiple porosity media

Computers and Geotechnics, 146:104728, 2022.

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Summary

A mixture-theory framework is developed for deformable porous materials containing several pore scales and one or two fluid phases. The formulation identifies the governing field equations and the constitutive relationships needed to describe their interaction. An effective stress, $\sigma^{\prime}$, follows from the energy balance and can be used for elastic as well as elastoplastic deformation; its construction accounts for the fractions and fluid saturations of the different pore systems. The framework supports both flow-only calculations and simulations that couple flow with deformation. For the flow-only case, Laplace transformation and numerical inversion reveal successive stages of depletion in a naturally fractured reservoir. Coupled examples include strip loading and two-phase flow in a deformable three-dimensional reservoir. These applications demonstrate how plastic response, multiple pore scales, exchange between pore systems, and capillary pressure alter the predicted response.