Peng-Robinson Equation of State

Written by Jerry Ratzlaff on . Posted in Thermodynamics

Article Links

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

\(\large{ p =  \frac{R \; T}{ V_m \;-\; b } - \frac{ a \; \alpha }{  V_m^2 \;+\; 2\;b \; V_m \;-\; b^2 }   }\)   

Where:

 Units 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 \(\large{R}\) \(\large{K}\)
\(\large{ T_r }\) = \(\frac{T}{T_c}\)  \(\large{R}\) \(\large{K}\)

 

P D Logo 1 

Tags: Gas Equations Ideal Gas Equations