Soave-Redlich-Kwong equation of state

The Soave-Redlich-Kwong equation of state is an equation of state for real gases and a further development of the Redlich-Kwong equation of state .

Equation of state

Soave-Redlich-Kwong's equation of state is

${\displaystyle p={\frac {RT}{V_{\mathrm {m} }-b}}-{\frac {a\alpha }{V_{\mathrm {m} }\left(V_{\mathrm {m} }+b\right)}}}$

${\displaystyle a={\frac {0{,}42747\cdot R^{2}T_{\mathrm {c} }^{2}}{p_{\mathrm {c} }}}}$

${\displaystyle b={\frac {0{,}08664\cdot RT_{\mathrm {c} }}{p_{\mathrm {c} }}}}$

The individual symbols stand for the following quantities :

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

With this equation, a significant improvement was achieved in 1972 compared to the Van der Waals equation by introducing an additional correspondence parameter and thus taking into account subtleties in the molecular structure, such as a deviation from the spherical shape. To do this, Giorgio Soave replaced the term in the Redlich-Kwong equation with the function : ${\displaystyle {\frac {a}{\sqrt {T}}}}$ ${\displaystyle \alpha (T_{r},\omega )}$

${\displaystyle \alpha =\left(1+\left(0{,}48+1{,}574\,\omega -0{,}176\,\omega ^{2}\right)\left(1-{\sqrt {T_{\mathrm {r} }}}\right)\right)^{2}}$

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

A specification of the function reads ${\displaystyle \alpha }$

${\displaystyle \alpha =\left(1+\left(0{,}48508+1{,}55171\,\omega -0{,}15613\,\omega ^{2}\right)\left(1-{\sqrt {T_{\mathrm {r} }}}\right)\right)^{2}}$

For hydrogen also applies

${\displaystyle \alpha =1{,}202\exp \left(-0{,}30288\,T_{\mathrm {r} }\right)}$

Dimensionless form

With the compressibility factor and the dimensionless parameters and follows the formulation of the Soave-Redlich-Kwong equation of state as a cubic polynomial ${\displaystyle Z={\frac {pV_{\mathrm {m} }}{RT}}}$ ${\displaystyle A={\frac {ap}{(RT)^{2}}}}$ ${\displaystyle B={\frac {bp}{RT}}}$

${\displaystyle 0=Z^{3}-Z^{2}+\left(A-B-B^{2}\right)Z-AB}$

the Z. B. can be solved analytically with the Cardan formulas .

parameter

From the conditions at the critical point

${\displaystyle {\frac {\mathrm {d} p}{\mathrm {d} V_{\mathrm {m} }}}={\frac {\mathrm {d} ^{2}p}{\mathrm {d} V_{\mathrm {m} }^{2}}}=0}$

the two parameters follow the equation of state

${\displaystyle a=\Omega _{a}\,{\frac {R^{2}T_{\mathrm {c} }^{2}}{p_{\mathrm {c} }}}\,,\qquad b=\Omega _{b}\,{\frac {RT_{\mathrm {c} }}{p_{\mathrm {c} }}}}$

with the two constants

${\displaystyle \Omega _{a}={\frac {1}{9(2^{1/3}-1)}}\approx 0{,}42748}$

${\displaystyle \Omega _{b}={\frac {2^{1/3}-1}{3}}\approx 0{,}08664}$

See also

• PSRK equation of state ( predictive Soave-Redlich-Kwong equation of state ): A method for estimating mixture properties

Individual evidence

1. ^ Giorgio Soave: Equilibrium constants from a modified Redlich-Kwong equation of state . In: Chemical Engineering Science . tape 27 , no. 6 , June 1972, p. 1197-1203 , doi : 10.1016 / 0009-2509 (72) 80096-4 .
2. ↑ MS Graboski, TE Daubert: A Modified Soave Equation of State for Phase Equilibrium Calculations. 1. Hydrocarbon Systems . In: Ind. Eng. Chem. Process Des. Dev. Band 17 , no. 4 , March 1978, p. 443-448 , doi : 10.1021 / i260068a009 .
3. ↑ MS Graboski, TE Daubert: A Modified Soave Equation of State for Phase Equilibrium Calculations. 3. Systems Containing Hydrogen . In: Ind. Eng. Chem. Process Des. Dev. Band 18 , no. 2 , October 1978, p. 300-306 , doi : 10.1021 / i260070a022 .
4. ↑ Jean-Noël Jaubert, Romain Privat: Relationship between the binary interaction parameters (kij) of the Peng – Robinson and those of the Soave – Redlich – Kwong equations of state: Application to the definition of the PR2SRK model . In: Fluid Phase Equilibria. 295, 2010, pp. 26-37. doi : 10.1016 / j.fluid.2010.03.037 .