PengRobinsonin

PengRobinsonin is a term sometimes used to refer to the Peng–Robinson equation of state (PR EoS), a widely used cubic equation of state in chemical and petroleum engineering. It was developed in 1976 by Ding-Yu Peng and Donald B. Robinson to model the PVT behavior and phase equilibria of real fluids, especially hydrocarbon systems.

The Peng–Robinson equation of state expresses pressure as a function of temperature, molar volume, and two fluid-specific parameters a and b that account for attractive and repulsive molecular interactions. For a pure component, b is given by 0.08664 RTc/Pc and a by 0.45724 R^2 Tc^2 / Pc. The temperature dependence of a is introduced through alpha(T) = [1 + kappa (1 - sqrt(T/Tc))]^2, where kappa = 0.37464 + 1.54226 omega − 0.26992 omega^2 and omega is the acentric factor. Then a(T) = a * alpha(T).

For mixtures, the parameters follow mixing rules: a_m = sum_i sum_j x_i x_j sqrt(a_i a_j) (1 − kij) and b_m = sum_i x_i b_i, where x_i are mole fractions and kij are binary interaction parameters. The compressibility factor Z is obtained by solving the cubic equation derived from combining the EOS with P, T, and V.

Applications of the PR EoS include predicting vapor–liquid equilibrium (VLE), PVT properties, and process design for natural gas and crude oil systems. It is valued for its simplicity and robustness but can be less accurate for highly polar or hydrogen-bonding fluids and for mixtures requiring precise interaction parameters.