Numerical assessment of effective bulk moduli of porous rocks using high-performance computing on GPUs

The coupled process models incorporate fluid flow, chemical transport, and mechanical deformation equations. These equations adhere to the thermodynamic principles ensuring the preservation of mass and energy within the system. However, for accurate predictions, it is crucial to establish closure equations that provide additional information and ensure the model's completeness. Closure equations are derived either from extrapolating experimental data or from micromechanical models that consider processes at the scale of individual grains or particles. Microscale models are often based on simplified analytical solutions obtained for idealized conditions, which may not fully capture the complexity of real-world situations. For instance, these models may assume a dilute concentration of voids or pores, neglecting interactions between the pores. While this assumption may be suitable for very small porosities below 1%, it may not accurately reflect interactions at porosities around 10%, influencing the compaction process. One approach to address this challenge is to derive more sophisticated analytical solutions, which may sometimes be impractical. Alternatively, a common strategy is to retain simplified solutions and validate them against numerical simulations that include multiple interacting voids. Effective bulk modulus, frequently employed to describe compaction-driven fluid flow in porous rocks, relies on effective media models. We propose a new effective media model based on a Representative Volume Element consisting of multiple interacting pores. To address stress and strain field interactions caused by multiple pores in an elastoplastic matrix, we utilize the numerical simulator CAE Fidesys, implementing classical associated plastic flow laws with von Mises and Tresca yield criteria. For viscoplastic rocks, the correspondence principle is applied. We derive 2D effective stress-strain relations for porous viscoelastoplastic rocks under a general non-hydrostatic stress field and compare the results with existing and novel analytical solutions.