Peng-Robinson Equation of State
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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 | \(\large{R}\) | \(\large{K}\) |
\(\large{ T_r }\) = \(\frac{T}{T_c}\) | \(\large{R}\) | \(\large{K}\) |