## Peng-Robinson Equation of State

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 of 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 independent of temperature, pressure, and composition.
- The equarion should be applicable to all calculations of all fluid properties in natural gas processes.

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## Peng-Robinson Equation of State Formula

\(\large{ p = \frac{R \; T}{ V_m \;-\; b } - \frac{ a \; \alpha }{ \sqrt{T} \; V_m^2 \;+\; \left(2\;b\right) \;V_m \;-\; b_2 } }\) |

### Where:

\(\large{ p }\) = pressure of gas

\(\large{ a }\) = correction for the intermolecular forces

\(\large{ b }\) = adjusts for the volume occupied by the gas particles

\(\large{ \alpha }\) (Greek symbol alpha) = \(\large{ \left( 1 + k \; \left( 1 - T_r^{0.5} \right) \right)^2 }\)

\(\large{ V_m }\) = molar volume of gas \(\left( \frac{V}{n} \right) \)

\(\large{ n }\) = number of moles of gas

\(\large{ R }\) = specific gas constant (gas constant)

\(\large{ T }\) = temperature of gas

\(\large{ T_c }\) = absolute temperature at the critical point

\(\large{ T_r }\) = \(\frac{T}{T_c} \)