Beyond Biot – Nonlinear stiffening of the bulk modulus in fluid-saturated porous media

This paper comprehensively investigates the elastic behavior of fluid-saturated porous media, considering a far-field stress, a range of pore pressures, and varying pore sizes. A Linear Superposition Method (LSM) was used to quantify the stress distribution and effective bulk moduli within a synthetic micropore model under both drained and undrained conditions. Our a posteriori upscaling approach reveals a significant nonlinear stiffening of the bulk modulus with increasing pore pressure—up to 25 % in high-pressure regimes—driven by pore size, porosity, and localized stress concentrations, a behavior unpredicted by conventional poroelasticity theories reliant on a priori upscaling. Unlike Biot's framework, which assumes uniform stress and linear softening with porosity, we demonstrate distinct stiffening regimes where elevated pressures enhance stiffness at higher porosity levels, challenging traditional assumptions. This elastic stiffening, quantified through closed-form solutions, emphasizes poroelasticity as a nonlinear, pore-scale process rather than a macroscopic property. A practical method is proposed for a posteriori upscaling of micropore model results into an analytical expression, for direct use in reservoir engineering operations, where huge variations in pore pressure may occur over the project-life of the reservoir, such as geological carbon sequestration. These findings provide a robust, predictive framework for understanding and managing porous media in dynamic subsurface environments.