Escoamento bifásico em meio poroso: análise dos regimes do estado estacionário

Abstract

Immiscible displacement in disordered porous media exhibits a wide range of steady-state interfacial morphologies whose collective organization cannot be inferred from transport laws alone. These patterns arise from the competition between viscous, capillary, and inertial forces; however, descriptions that span different regimes and simultaneously connect dimensionless control parameters, morphology, and collective structure remain limited. In this work, we simulate the Navier-Stokes equations with periodic boundary conditions to resolve statistically steady two-phase flow in a disordered porous matrix consisting of a random array of non-overlapping disks, over wide ranges of pressure gradient and interfacial tension, covering multiple orders of magnitude in the Capillary and Forchheimer numbers. Using unsupervised machine learning, we identify three robust steady-state morphologies — bubbles, stripes, and mixtures — organized in a regime diagram (Fo, Ca) with sharp and consistent transitions governed by the balance between capillary, viscous, and inertial effects. Despite these pronounced morphological reorganizations, macroscopic transport varies smoothly: stripe and mixture states follow a Forchheimer-type V versus |∇p| relation, while bubble states deviate systematically due to the additional energy barrier arising from interface deformations. To characterize the collective organization underlying these morphologies, and following the precedent of pseudo-thermodynamic analogies for two-phase flows, we coarse-grain steady-state configurations into binary fields and infer pairwise maximum-entropy models. The inferred Hamiltonians reproduce the fitted first- and second-order statistics and, near some morphological transitions, accurately predict out-of-sample higher-order correlations. Thermodynamic analysis of the inferred models—in which temperature is a parameter of the statistical model, unrelated to the physical temperature of the fluid—reveals regime-dependent specific heat signatures: a considerable fraction of stripe morphologies operate near an order-disorder transition point, while bubble and mixture states correspond to supercritical organization. Taken together, the hydrodynamic regime map and the maximum-entropy representation establish a unified, dimensionless framework connecting interfacial morphology, macroscopic transport, and collective statistics in two-phase porous flows.