1. Babatunde A. Bamgbade a,b, Yue Wu a,b, Mark A. McHugh a,b, Hseen O. Baled a,c,
Robert M. Enick a,c, Ward Burgess a, Deepak Tapriyal a,d,, Bryan D. Morreale a
• a National Energy Technology Laboratory RUA, Pittsburgh PA
• b Virginia Commonwealth University, Richmond VA
• c University of Pittsburgh, Pittsburgh PA •
• d URS, Pittsburgh, PA 15236, USA
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Chemical and Life Science Engineering Department
Website: http://www.chemical.egr.vcu.edu/
The petrochemical industries need predictive
thermodynamic models that are accurate at high-
temperature, high-pressure (HTHP) conditions at
temperatures to 533 K and pressures to 276
MPa, particularly with respect to density
prediction. Traditional cubic equations fail to
provide reliable predictions at HTHP conditions.
Incorporation of a HTHP volume correction term
improves the performance of the cubic equations.
Also, the performance of PC-SAFT with
parameters obtained from fitting HTHP
experimental data are reported.
Introduction
Soave-Redlich-Kwong Volume translated (VT)
(SRK-EoS) SRK-EoS
Volume translation, c, is correlated to reduced
temperature
A and B are correlated to molecular weight and acentric
factor
 
caRT
P
v b v v b

 
    
caRT
P
v c b v c v c b

 
    
expEoS rc v v v A B T      
  0 1 3 5
2 4 6
1 1 1
, , exp exp expA B f M k k k k
k M k M k M

  
      
         
     
Volume Translated Cubic EoS
Experimental Technique
Experimental Pentane PVT
data
Experimental Pentane PVT
data
40 mol% n-C6H14 + 60 mol% n-C16H34
Volume Translated Cubic EoS
Pentane
Pentane
HTHP Volume translated parameters have been
obtained for aromatics, normal and cyclic
hydrocarbons, from 7- 276 MPa and up to 533 K
a
hc
= ma
hs
- (m -1)ln(ghs
)
a
hs
=
4h - 3h2
(1- h)2
ghs
=
2 -h
2(1-h)3
PC-SAFT
a
res
= a
hc
+ a
disp
2
2 3 3 3
1 22 ( , ) ( , )
disp
B B
a m I m Cm I m
k T k T
 
     
   
     
   
C = 1+ m
8h - 2h2
(1-h)4
+ (1- m)
20h - 27h2
+12h3
- 2h4
[(1-h)(2 -h)]2
æ
èç
ö
ø÷
-1
Adjust reduced density, η, until Pcalc =
Pexperimental
Pentane
Dotted lines: NIST smoothed data
Lines: HTHP PC-SAFT
Dashed lines: GS PC-SAFT
Decane
Dotted lines: NIST smoothed data
Lines: HTHP PC-SAFT
Dashed lines: GS PC-SAFT
HTHP PC-SAFT parameters give superior performance
at pressure from 7- 276 MPa but do not perform as well
as the GS PC-SAFT parameters at pressures below 7 MPa
Conclusions
The performance of the cubic and PC-SAFT EoS are
improved at HTHP conditions that are important in
ultra deep well production of oils, condensates, and
natural gas. Parameters for the newly improved
equations are obtained from HTHP experimental
density data, up to 533K and 276 MPa.
Further work is in progress to increase the HTHP
experimental database to obtain even more robust
parameters for these equations of state. A group
contribution approach is being investigated to predict
PC-SAFT parameters at these HTHP conditions.
Acknowledgment
This technical effort was performed in support of the
National Energy Technology Laboratory's Office of Research
and Development support of the Strategic Center for Natural
Gas and Oil under RES contract DE-FE0004000
Hydrocarbon Mixtures: Phase behavior, density, and modeling
with PC-SAFT and a volume-translated, cubic EoS
W. Burgess, D. Tapriyal, H. Baled, R.M. Enick, Y. Wu, M.A. McHugh, B.D. Morreale, Fluid Phase Equilibria, 319, 55 (2012).
J.H. Dymond, K.J. Young, J.D. Isdale, J. Chem. Thermodyn., 11, 887 (1979).
E.U. Franck, S. Kerschbaum, G. Wiegand, Ber. Gesellschaft Phys. Chem. 102, 1794 (1998).
K. Liu, Y. Wu, M.A. McHugh, H. Baled, R.M. Enick, B.D. Morreale, J. SCF, 55, 701 (2010).
40 mol% n-C6H14 + 60 mol% n-C16H34