## 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.

## 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

$$\large{ T_r }$$ = $$\frac{T}{T_c}$$