PengRobinson

The Peng–Robinson equation of state is a cubic equation of state developed by Ding-Yu Peng and Donald Robinson in 1976 for predicting the thermodynamic properties of fluids and their phase equilibria. It is widely used in chemical engineering to model vapour–liquid equilibria, PVT behaviour, and mixtures of hydrocarbons and natural gas components. The formulation improves on earlier cubic EOS by providing better liquid densities and vapour pressures for many nonpolar and moderately polar substances.

For a pure component, the Peng–Robinson equation relates pressure P, temperature T, and molar volume V through P = RT/(V − b) − aα(T) / (V^2 + 2bV − b^2). The parameters a and b are functions of the critical properties and the acentric factor: a = 0.45724 R^2 Tc^2 / Pc, b = 0.07780 RTc / Pc. The temperature-dependent function α(T) = [1 + κ(1 − √Tr)]^2, with Tr = T/Tc and κ = 0.37464 + 1.54226ω − 0.26992ω^2, where ω is the acentric factor. For mixtures, a and b are obtained by mixing rules, typically a_mix = ∑i∑j x_i x_j a_ij with a_ij = √(a_i a_j)(1 − k_ij) and b_mix = ∑i x_i b_i; k_ij are binary interaction parameters calibrated to data.

Applications include modelling VLE, liquid densities, and P–T–x data for hydrocarbon systems and natural gases. Limitations include reduced accuracy for highly polar or associating compounds and near the critical region without appropriate interaction parameters. The PR EOS remains a standard tool in process simulation and design.