Modified Peng-Robinson equation of state for confined fluids: Critical pore size and phase behavior in shale nanopores

Shale reservoirs are dominated by nanopores, where wall-fluid adsorption and anomalous fluid intermolecular interactions lead to substantial deviations from conventional equation of state (EOS) predictions. This study proposes a modified Peng-Robinson equation of state (m-PR EOS) that incorporates two innovative key corrections: (1) a refined molar volume term accounting for wall-fluid adsorption effects; and (2) introduction of the contact angle in the attractive term to rectify anomalous fluid intermolecular interactions. The m-PR EOS quantitatively captures the shifts in critical properties of confined hydrocarbons and pioneeringly integrates critical pore size determination, identifying confinement thresholds for pure hydrocarbons. The critical pore radii of methane were determined as 18.62 nm (based on temperature shift) and 51.33 nm (based on pressure shift). The analysis reveals that hydrocarbons with larger Lennard-Jones molecular sizes exhibit larger critical pore sizes and greater deviations in critical properties at the same confinement scale. The model validated with binary hydrocarbons was applied to simulate pore-size-dependent phase behavior in shale condensate systems and Constant Composition Expansion experiments. Results demonstrate that reducing pore size causes phase envelope to contract towards the lower-left quadrant in the P-T phase diagram, with accelerated contraction rates. Constant Composition Expansion simulations show that the retrograde condensation volume curve exhibits a similar contraction trend as the phase envelope. By incorporating wettability effects, the m-PR EOS model extends its applicability to a wide range of reservoirs. The m-PR EOS provides a thermodynamic foundation for accurately predicting nanoscale phase behavior and optimizing condensate recovery in unconventional reservoirs.