# Peng-Robinson Equation of State

on . Posted in Thermodynamics

Peng-Robinson equation of state was developed in 1976 at the University of Alberta in order to satisfy the following goals:

• The parameters should be expressible in terms ot the critical properties and the acentric factor.
• The model should provide reasonable accuracy near the critical point, particularly for calculations of the compressibility factor and liquid density.
• The mixing rules should not employ more than a single binary interaction parameter, which should be independant of temperature, pressure, and composition.
• The equation should be applicable to all calculations of all fluid properties in natural gas processes.

## Peng-Robinson Equation of State Formula

$$\large{ p = \frac{R \; T}{ V_m \;-\; b } - \frac{ a \; \alpha }{ V_m^2 \;+\; 2\;b \; V_m \;-\; b^2 } }$$
Symbol English Metric
$$\large{ p }$$ = pressure of gas $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ a }$$ = correction for the intermolecular forces $$\large{dimensionless}$$
$$\large{ b }$$ = adjusts for the volume occupied by the gas particles $$\large{in^3}$$ $$\large{mm^3}$$
$$\large{ \alpha }$$  (Greek symbol alpha) = $$\left( 1 + k \; \left( 1 - T_r^{0.5} \right) \right)^2$$ $$\large{dimensionless}$$
$$\large{ k }$$ = $$0.37464 + 1.54226 \;\omega - 0.26922\; \omega^2$$ $$\large{dimensionless}$$
$$\large{ \omega }$$  (Greek symbol omega) = acentric factor $$\large{dimensionless}$$
$$\large{ V_m }$$ = molar volume of gas $$\left( \frac{V}{n} \right)$$ $$\large{in^3}$$ $$\large{mm^3}$$
$$\large{ n }$$ = number of moles of gas $$\large{dimensionless}$$
$$\large{ R }$$ = specific gas constant (gas constant)  $$\large{\frac{ft-lbf}{lbm-R}}$$  $$\large{\frac{J}{kg-K}}$$
$$\large{ T }$$ = temperature of gas $$\large{R}$$ $$\large{K}$$
$$\large{ T_c }$$ = critical temperature of gas $$\large{R}$$ $$\large{K}$$
$$\large{ T_r }$$ = $$\frac{T}{T_c}$$  $$\large{R}$$ $$\large{K}$$