Robust and Efficient Newton-Based Algorithm for Phase Equilibrium Calculation in Tight Porous Media at Given Temperature and Volume

Summary Nanopores in unconventional reservoirs significantly alter fluid phase behavior via capillary pressure (Pc), yet this effect is often neglected by commercial simulators. Traditional algorithms for phase equilibrium calculations (PECs) suffer from poor convergence under isothermal-isochoric (T-V) conditions, and reference-phase pressure selection in the isothermal-isobaric (T-P) framework lacks rigorous justification. With this study, we present two key contributions: First, we extend the trust-region (TR) Newton algorithm to Pc-integrated T-V phase stability analysis (PSA) and flash calculations (FCs), establishing a unified and efficient framework; second, we pioneer the verification of thermodynamic consistency between Pc-integrated T-V and T-P frameworks using T-V results as the benchmark. Numerical validation on three fluid systems demonstrates efficient convergence at small pore scales (5 nm), universal Pc effects on phase boundaries and component distributions, and critical findings on reference-pressure configurations: The “system pressure = vapor-phase pressure” configuration achieves full-range consistency with T-V results, while the “system pressure = liquid-phase pressure” configuration cannot cover the negative pressure region (NPR) due to physical constraints. This study provides critical technical tools and theoretical foundations for compositional simulation of unconventional reservoirs.