Peng-Robinson equation of state

The equation of state of Peng-Robinson is an equation of state for real gases . It is:

${\displaystyle p={\frac {RT}{V_{\mathrm {m} }-b}}-{\frac {a\alpha }{V_{\mathrm {m} }^{2}+2bV_{\mathrm {m} }-b^{2}}}}$

${\displaystyle a={\frac {0{,}457235\cdot R^{2}T_{\mathrm {c} }^{2}}{p_{\mathrm {c} }}}}$

${\displaystyle b={\frac {0{,}077796\cdot RT_{\mathrm {c} }}{p_{\mathrm {c} }}}}$

The individual symbols stand for the following quantities :

• ${\displaystyle V_{\mathrm {m} }}$- molar volume
• ${\displaystyle T}$- temperature
• ${\displaystyle T_{\mathrm {c} }}$- critical temperature
• ${\displaystyle p}$- pressure
• ${\displaystyle p_{\mathrm {c} }}$- critical pressure
• ${\displaystyle R}$- universal gas constant
• ${\displaystyle a}$- cohesive pressure
• ${\displaystyle b}$- covolume

This 1976 equation, like that of Redlich-Kwong-Soave, contains an additional correspondence factor and represents a considerable improvement over the Van-der-Waals equation . Like this, it describes both the gas phase and the liquid phase with the same set of parameters. The two-phase region and the vapor pressure curve can also be calculated using the Maxwell criterion .

${\displaystyle \alpha =\left(1+\left(0{,}37464+1{,}54226\,\omega -0{,}26992\,\omega ^{2}\right)\left(1-{\sqrt {T_{\mathrm {r} }}}\right)\right)^{2}}$

• ${\displaystyle T_{\mathrm {r} }}$- reduced temperature
• ${\displaystyle \omega }$- acentric factor

For an acentric factor : ${\displaystyle \omega >0{,}49}$

${\displaystyle \alpha =\left(1+\left(0{,}379642+\left(1{,}48503-\left(1{,}164423-1{,}016666\,\omega \right)\,\omega \right)\,\omega \right)\left(1-{\sqrt {T_{\mathrm {r} }}}\right)\right)^{2}}$

literature

1. ↑ D.-Y. Peng and DP Robinson: A New Two-Constant Equation of State. In: Ind. Eng. Chem. Fundam. 15 (1), pp. 59-64, 1976