A potential-game formulation for thermodynamic equilibrium of two-phase systems in pore networks

Thermodynamic equilibrium configurations in heterogeneous porous media remain poorly characterized due to the dominance of flow-driven experimental and numerical approaches. We introduce an equilibrium modeling framework that formulates pore-scale phase distribution as an exact potential game, where each pore minimizes total interfacial free energy without external forcing. This approach directly targets equilibrium states—bypassing displacement dynamics—and converges within seconds for networks of thousands of pores. Simulations on mixed-wet networks reveal a fundamental finding: multiple morphologically distinct equilibrium states coexist under identical energetic parameters, exhibiting water saturations ranging from 0.48 to 0.77 and varying interfacial area distributions. Crucially, all configurations yield a narrowly confined thermodynamic contact angle (θₜ ≈ 94.5°), demonstrating that θₜ is an intrinsic property of the solid–fluid–fluid system rather than a morphology-dependent observable. The predicted θₜ shows close agreement (within 6°) with values inferred from steady-state experiments under intermediate fractional flow, despite the absence of imposed flow or pressure gradients. These results establish that equilibrium wettability cannot be inferred from a single saturation state; instead, it emerges from thermodynamic relationships between multiple equilibrium configurations sharing identical pore geometry and wettability distributions. The framework provides a computationally efficient equilibrium reference (runtime \(\:<10\) s) for interpreting pore-scale wettability, benchmarking dynamic simulations, and isolating intrinsic thermodynamic behavior from flow-history effects. By decoupling equilibrium physics from displacement pathways, this work offers a rigorous baseline for distinguishing true wettability signatures from non-equilibrium artifacts in porous media characterization.