Composition-corrected mechanical criticality for estimating mixture critical points with the Peng–Robinson equation of state

Mixture critical-point calculations with cubic equations of state usually require thermodynamic stability analysis, including the singularity of a stability matrix and a higher-order criticality condition. This work develops a composition-corrected mechanical criticality method for estimating regular vapor–liquid critical points of mixtures described by the Peng–Robinson equation of state. The method starts from the fixed-composition mechanical degeneracy of the cubic equation of state, which provides universal Peng–Robinson constants for the reduced critical volume and attraction ratio. Direct application of these constants to mixtures gives a computationally short estimate, but it systematically underpredicts critical temperature and pressure and overpredicts critical molar volume relative to Heidemann–Khalil/Peng–Robinson reference points. To reduce this bias, the universal mechanical constants are replaced by composition-dependent corrected constants expressed through physically interpretable mixture descriptors. The resulting calculation preserves the mechanical structure of the cubic equation of state: the critical volume is obtained explicitly, the critical temperature is obtained from one scalar equation, and the critical pressure is obtained by direct substitution. The method was evaluated using the thirty-two multicomponent benchmark mixtures originally reported by Peng and Robinson, for which a consistent Heidemann–Khalil/Peng–Robinson baseline is available. Leave-one-out validation gave mean absolute percentage errors of 1.240% for critical temperature, 4.979% for critical pressure, and 6.015% for critical molar volume. For the same benchmark, the uncorrected mechanical formulation gave errors of 6.517%, 32.920%, and 19.845%, respectively. Comparisons with Kay’s rule, Li-type extension, and Chueh–Prausnitz-type estimates show that the proposed correction provides a more balanced simultaneous estimate of critical temperature, pressure, and molar volume. The method is therefore positioned as a low-cost benchmark estimator for regular Peng–Robinson mixture critical points, not as a replacement for rigorous thermodynamic criticality calculations when branch multiplicity or strong extrapolation is involved.