Asymptotic derivation and simulation of a reduced-order two-phase thermo-poroelastic model in the framework of the theory of porous media
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2026
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Heat transfer in saturated porous media requires models that remain thermodynamically consistent while being efficient for repeated simulations, parameter studies, and multiphysics coupling. In this work, a coupled two-phase thermo-poroelastic model is formulated within the Theory of Porous Media by combining balance laws for mass, momentum, and energy with Darcy flow, linear elasticity, and conductive heat transfer. The governing equations are non-dimensionalized for thin domains and reduced asymptotically with respect to the slenderness parameter γ, yielding a leading-order limit model and a higher-order corrector. The formulation is assessed in two thermal consolidation benchmarks with non-uniform loading. For slender geometries, especially γ=1/10and 1/50, the limit model is nearly indistinguishable from the full-order solution for the dominant pore-pressure evolution, vertical settlement, and through-thickness temperature response. In the flux-driven benchmark, the corrected thermal field reproduces the full-order mid-height temperature range closely, 3.99-4.75 versus 3.95-4.69, with a top-right temperature difference below 0.1. The corrector also reconstructs transverse variations, but it may overestimate pressure and displacement effects and, under non-uniform Dirichlet heating, can underpredict the interior temperature level, 0.52-0.75 versus 0.99-1.22 at mid-height. Overall, the results demonstrate that asymptotic TPM reduction preserves the dominant coupled physics of thin saturated porous systems while explicitly identifying where higher-order corrections are beneficial or limited, making the approach attractive for geothermy and thermal-management applications.
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Except where otherwised noted, this item's license is described as CC BY