Lee-Kesler Generalized Correlations for Gases
Authors: Housam Binous and Ahmed Bellagi
Lee-Kesler Generalized Correlations for Gases
Authors: Housam Binous and Ahmed Bellagi
Authors: Housam Binous and Ahmed Bellagi
Using a modified version of the Benedict–Webb–Rubin equation of state, Lee and Kesler [1, 2] generated several tables to estimate the following properties at a reduced pressure and temperature .1. and or the compressibility factor ,2. and or the residual enthalpy =R+ω,3. and or the residual entropy =R+ω, and4. and or the fugacity coefficient .In the preceding expressions, and are the acentric factor and critical temperature of methane, respectively (i.e., and =190.6K). These two parameters must be modified in case you select another alkane. You can also choose any other value for and . Here, we set =0.40 and =0.65 for illustration purposes . Here, we display all of the cited thermodynamic properties in the form of a table.
0
Z
1
Z
Z=+ω
0
Z
1
Z
0
R
H
R
T
c
1
R
H
R
T
c
R
H
T
c
0
R
H
R
T
c
1
R
H
R
T
c
0
R
S
R
1
R
S
R
R
S
0
R
S
R
1
R
S
R
0
ϕ
1
ϕ
ϕ=
ω
0
ϕ
1
ϕ
ω
T
c
ω=0.012
T
c
T
r
P
r
P
r
T
r
References:
[1] J. M. Smith, H. C. Van Ness, M. M. Abbott and M. T. Swihart, Introduction to Chemical Engineering Thermodynamics, 9th ed., Boston: McGraw-Hill, 2022.
[2] B. I. Lee and M. G. Kesler, "A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States," AlChE Journal, 21(3), 1975 pp. 510–527. doi:10.1002/aic.690210313.
[1] J. M. Smith, H. C. Van Ness, M. M. Abbott and M. T. Swihart, Introduction to Chemical Engineering Thermodynamics, 9th ed., Boston: McGraw-Hill, 2022.
[2] B. I. Lee and M. G. Kesler, "A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States," AlChE Journal, 21(3), 1975 pp. 510–527. doi:10.1002/aic.690210313.
Reduced temperature and pressure (user can change these values if needed)
In[]:=
Tre=0.65;Pre=0.40;
Acentric factor and critical temperature of Methane (user can select a different alkane if needed)
In[]:=
w=0.012;Tc=190.6;
Universal gas constant
In[]:=
R=8.314;
Following Ref. 2, we compute:1. 2. 3. 4.
0
Z
0
R
H
R
T
c
0
R
S
R
0
ϕ
Ba0=b10-b20/Tre-b30/Tre^2-b40/Tre^3;Ca0=c10-c20/Tre+c30/Tre^3;Da0=d10+d20/Tre;Ea0=c40/2/Tre^3/gamma0(beta0+1-(beta0+1+gamma0/Vre^2)Exp[-gamma0/Vre^2]);Vre=ZTre/Pre;eq0=Z1+Ba0/Vre+Ca0/Vre^2+Da0/Vre^5+c40/Tre^3/Vre^2(beta0+gamma0/Vre^2)Exp[-gamma0/Vre^2];b10=0.1181193;b20=0.265728;b30=0.154790;b40=0.030323;c10=0.0236744;c20=0.0186984;c30=0.0;c40=0.042724;d10=0.15548810^-4;d20=0.62368910^-4;beta0=0.65392;gamma0=0.060167;Z0=Z/.FindRoot[eq0,{Z,0.01,0.95}];H0overRTc=Tre(Z0-1-(b20+2b30/Tre+3b40/Tre^2)/Tre/Vre-(c20-3c30/Tre^2)/2/Tre/Vre^2+d20/5/Tre/Vre^5+3Ea0)/.ZZ0;phi0=Exp[Z0-1-Log[Z0]+Ba0/Vre+Ca0/2/Vre^2+Da0/5/Vre^5+Ea0/.ZZ0];S0overR=Log[Z0]-(b10+b30/Tre^2+2b40/Tre^3)/Vre-(c10-2c30/Tre^3)/2/Vre^2-d10/5/Vre^5+2Ea0/.ZZ0;
Following Ref. 2, we compute:1. 2. 3. 4.
1
Z
1
R
H
R
T
c
1
R
S
R
1
ϕ
Ba=b1-b2/Tre-b3/Tre^2-b4/Tre^3;Ca=c1-c2/Tre+c3/Tre^3;Da=d1+d2/Tre;Ea=c4/2/Tre^3/gamma(beta+1-(beta+1+gamma/Vre^2)Exp[-gamma/Vre^2]);b1=0.2026579;b2=0.331511;b3=0.027655;b4=0.203488;c1=0.0313385;c2=0.0503618;c3=0.016901;c4=0.041577;d1=0.4873610^-4;d2=0.074033610^-4;beta=1.226;gamma=0.03754;wr=0.3978;eq1=Z1+Ba/Vre+Ca/Vre^2+Da/Vre^5+c4/Tre^3/Vre^2(beta+gamma/Vre^2)Exp[-gamma/Vre^2];Zc=Z/.FindRoot[eq1,{Z,0.01,0.95}];Z1=(Zc-Z0)/wr;H1overRTc=((Tre(Z-1-(b2+2b3/Tre+3b4/Tre^2)/Tre/Vre-(c2-3c3/Tre^2)/2/Tre/Vre^2+d2/5/Tre/Vre^5+3Ea)/.ZZc)-H0overRTc)/wr;phi1=Exp[((Z-1-Log[Z]+Ba/Vre+Ca/2/Vre^2+Da/5/Vre^5+Ea/.ZZc)-Log[phi0])/wr];S1overR=((Log[Z]-(b1+b3/Tre^2+2b4/Tre^3)/Vre-(c1-2c3/Tre^3)/2/Vre^2-d1/5/Vre^5+2Ea/.ZZc)-S0overR)/wr;
Generating a table with the thermodynamic properties of methane at the reduced pressure and temperature (=0.40 and =0.65):
1- compressibility factor
2- residual enthalpy
3- residual entropy
4- fugacity coefficient
One can easily check our results against the values reported in the corresponding Tables of Appendix D of Ref. 1.
P
r
T
r
1- compressibility factor
2- residual enthalpy
3- residual entropy
4- fugacity coefficient
One can easily check our results against the values reported in the corresponding Tables of Appendix D of Ref. 1.
In[]:=
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