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Emerging challenges in phase behavior modeling of reservoir fluids at high-pressure high-temperature (HPHT) conditions

  • Faith Uchenna BabalolaEmail author
  • Oluwadare Abiodun Badejo
  • Bosun Abbas Roy-Layinde
Original Article
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Abstract

Global energy demand is driving the oil and gas industry to explore uncharted areas leading to unconventional reservoirs at extreme temperature (T > 420 K) and pressure (P > 68 MPa) conditions where widely used equations of state (EOS) models fail to accurately predict properties of reservoir fluids and model their phase behavior. This work compares promising and adaptable EOS models for HPHT systems, highlighting their concomitant shortfalls in specified scenarios which need to be addressed by researchers in the quest for accurate predictive tools at extreme T and P reservoir conditions. Five EOS models were used for density prediction for n-heptane at 323 K and 423 K over a pressure range of 28–270 MPa where PC SAFT emerged the overall best. At 520 K however, VT PR-EOS and VT SRK-EOS performed better. For a binary system of C3/nC10, PC SAFT, which was highly promising, began to drop in accuracy with increase in temperature from 277 to 510 K. Furthermore, four EOS were tested for volume and z-factor prediction of pure systems (C1–C6) and their binaries. While PC SAFT is most promising, significant drawbacks are evident when applied to binary systems and are expected to worsen with increase in number of constituents. It was made clear that a pressure-dependent correction factor will significantly improve the accuracy of the PC-SAFT model. Suggestions on novel alternative routes for EOS model development and improvement are also given.

Keywords

Equation of state Reservoir Modeling HPHT 

List of symbols

\( A \)

Constant for fitted HPHT volume-translation term, \( {\text{L}}^{3} \), \( {\text{m}}^{3} \)

\( a \)

Attractive force term, \( \frac{{{\text{m}}\; {\text{L}}^{5} }}{\text{mol}} \), \( \frac{{ {\text{m}}^{6} \; {\text{Pa}}}}{\text{mol}} \)

\( B \)

Constant for for fitted HPHT volume-translation term, \( {\text{L}}^{3} \), \( {\text{m}}^{3} \)

b

Effective molecular volume repulsion term, \( {\text{L}}^{3} \), \( {\text{m}}^{3} \)

\( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{B} \)

Correlation for BWRS equation of state \( \frac{{{\text{L}}^{3} }}{\text{mol}} \), \( \frac{{ {\text{m}}^{3} }}{\text{mol}} \)

\( c \)

Systematic volume deviation, \( {\text{L}}^{3} \), \( {\text{m}}^{3} \)

\( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{D} \)

Correlation for BWRS equation of state, \( \left( {\frac{{{\text{L}}^{3} }}{\text{mol}}} \right)^{4} \), \( \left( {\frac{{ {\text{m}}^{3} }}{\text{mol}}} \right)^{4} \)

\( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{E} \)

Correlation for BWRS equation of state, \( \left( {\frac{{{\text{L}}^{3} }}{\text{mol}}} \right)^{2} \), \( \left( {\frac{{ {\text{m}}^{3} }}{\text{mol}}} \right)^{2} \)

\( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{F} \)

Correlation for BWRS equation of state, \( \left( {\frac{{{\text{L}}^{3} }}{\text{mol}}} \right)^{2} \), \( \left( {\frac{{ {\text{m}}^{3} }}{\text{mol}}} \right)^{2} \)

\( M \)

Molecular weight, \( \frac{\text{mol}}{{{\text{L}}^{3} }} \), \( \frac{\text{mol}}{{{\text{M}}^{3} }} \)

\( P \)

Gas pressure, liquid pressure, \( \frac{\text{M}}{{{\text{L}}\; {\text{t}}^{2} }} \), \( {\text{MPa}} \)

\( P_{c} \)

Critical pressure, \( \frac{\text{M}}{{{\text{L}}\; {\text{t}}^{2} }} \), \( {\text{MPa}} \)

R

Universal gas constant, \( \frac{{{\text{ML}}^{2} {\text{T}}^{2}\uptheta}}{\text{mol}} \), \( \frac{{{\text{m}}^{3} \;{\text{Pa}}}}{{{\text{K}}\; {\text{mol}}}} \)

T

Temperature, \( \uptheta \), \( {\text{K }} \)

\( T_{c} \)

Critical temperature, \( \uptheta \), \( {\text{K }} \)

\( T_{r} \)

Reduced temperature

\( V \)

Gas volume, liquid volume, \( {\text{L}}^{3} \), \( {\text{m}}^{3} \)

\( V_{EOS} \)

Volume predicted by equation of state, \( {\text{L}}^{3} \), \( {\text{m}}^{3} \)

\( V_{EXP} \)

Volume obtained from experiment, \( {\text{L}}^{3} \), \( {\text{m}}^{3} \)

\( u \)

Constant for generalized equation of state for PR and SRK

\( w \)

Constant for generalized equation of state for PR and SRK

\( Z \)

Compressibility factor

\( Z_{hc} \)

Hard-chain contribution for the repulsive molecular interactions

\( Z_{disp} \)

Attractive Term

\( \alpha \)

Correlation for \( T_{c} \;and\; \omega \)

\( \rho \)

Molar density, \( \frac{\text{mol}}{{{\text{L}}^{3} }} \), \( \frac{\text{mol}}{{{\text{M}}^{3} }} \)

\( \omega \)

Acentric factor

Notes

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

References

  1. Babalola FU, Susu AA (2018) Model development of a suitable equation of state for multicomponent multiphase systems: application to crude oil phase stability requirements. Int J Thermodyn 21(2):111–118.  https://doi.org/10.5541/ijot.419923 CrossRefGoogle Scholar
  2. Baker AC, Price M (1990) Modelling the performance of high-pressure high-temperature wells. Presented at the European petroleum conference, The Hague Netherlands, 21–24 October. SPE-20903-MS.  https://doi.org/10.2118/20903-MS
  3. Baled HO (2012) Density and viscosity of hydrocarbons at extreme conditions associated with ultra-deep reservoirs- measurement and modeling. Doctoral Dissertation, University of Pittsburgh, Pittsburgh (November 2012)Google Scholar
  4. Benedict M, Webb GB, Rubin LC (1940) An empirical equation for thermodynamic properties of light hydrocarbons and their mixtures I. Methane, ethane, propane and n-butane. J Chem Phys 8(4):334–345.  https://doi.org/10.1063/1.1750658 CrossRefGoogle Scholar
  5. Burgess W, Tapriyal D, Morreale B, Wu Y, McHugh M, Baled H, Enick R (2012) Prediction of fluid density at extreme conditions using the perturbed-chain SAFT equation correlated to high temperature, high pressure density data. Fluid Phase Equilib 319:55–66.  https://doi.org/10.1016/j.fluid.2012.01.032 CrossRefGoogle Scholar
  6. Chapman WG, Gubbins KE, Jackson G, Radosz M (1989) SAFT: equatio-of-state solution model for associating fluids. Fluid Phase Equilib 52:31–38CrossRefGoogle Scholar
  7. Chapman WG, Gubbins KE, Jackson G, Radosz M (1990) New reference equation of state for associating liquids. Ind Eng Chem Res 29(8):1709–1721CrossRefGoogle Scholar
  8. Danesh A (2007) PVT and phase behaviour of petroleum reservoir fluids, 1st edn. Elsevier, AmsterdamGoogle Scholar
  9. Fazelabdolabadi B, Bahramian A (2012) The acoustic determination of the thermophysical properties of a north sea gas condensate from 298.65 K to 373.45 K and up to 70 MPa. Pet Sci Technol 30(4):393–401.  https://doi.org/10.1080/10916461003735129 CrossRefGoogle Scholar
  10. Gozalpour F, Danesh A, Fonseca M, Todd A, Tohidi B, Al-Syabi Z (2005) Physical and rheological behaviour of high pressure-high temperature fluids in presence of water. Presented the SPE Europec/EAGE annual conference, 13–16 June, Madrid, Spain. SPE-94068-MS.  https://doi.org/10.2118/94068-MS
  11. Gross J, Sadowski G (2001) Perturbed-chain SAFT: an equation of state based on a perturbation theory for chain molecules. Ind Eng Chem Res 40(4):1244–1260.  https://doi.org/10.1021/ie0003887 CrossRefGoogle Scholar
  12. Liu K, Wu Y, McHugh M, Baled H, Enick R, Morreale B (2010) Equation of state modeling of high-pressure, high-temperature hydrocarbon density data. J Supercrit Fluids 55(2):701–711.  https://doi.org/10.1016/j.supflu.2010.10.004 CrossRefGoogle Scholar
  13. Nichita D, Gomez S, Luna E (2002) Phase stability analysis with cubic equations of state by using a global optimization method. Fluid Phase Equilib 194:411–437.  https://doi.org/10.1016/s0378-3812(01)00779-8 CrossRefGoogle Scholar
  14. Peng DY, Robinson DB (1976) A new two-constant equation of state. Ind Eng Chem Fundam 15(1):59–64CrossRefGoogle Scholar
  15. Polishuk I (2010) About the numerical pitfalls characteristic for SAFT EOS models. Fluid Phase Equilib 298(1):67–74.  https://doi.org/10.1016/j.fluid.2010.07.003 CrossRefGoogle Scholar
  16. Rushing JA, Newsham KE, Van Fraassen KC, Metha SA, Moore GR (2008) Natural gas Z-factors at HP/HT reservoir conditions: comparing laboratory measurements with industry-standard correlations for a dry gas. Presented at the CIPC/SPE gas technology symposium 2008 joint conference, Calgary, Alberta, Canada, 16–18 June. SPE-114518-MS.  https://doi.org/10.2118/114518-MS
  17. Seddighin A, Krishngee R, Zeb L (2014) High-pressure high-temperature fluids modeling: one of the crucial keys to ultra-deep gas drilling. Presented at the offshore technology conference, Houston, Texas, 5–8 May. OTC-25343-MS.  https://doi.org/10.4043/25343-MS
  18. Smith JM, Van Ness HC, Abbott MM (2005) Introduction to chemical engineering thermodynamics, 6th edn. McGraw-Hill, New Delhi, pp 58–96Google Scholar
  19. Soave G (1972) Equilibrium constants from a modified Redlich–Kwong equation of state. Chem Eng Sci 27(6):1197–1203.  https://doi.org/10.1016/0009-2509(72)80096-4 CrossRefGoogle Scholar
  20. Starling K (1973) Fluid thermodynamic properties for light petroleum systems, 1st edn. Gulf Publishing Company, Houston, TXGoogle Scholar
  21. Wu Y, Bamgbade B, Liu K, McHugh M, Baled H, Enick R, Burgress W, Tapriyal D, Morreale B (2011) Experimental measurements and equation of state modeling of liquid densities for long-chain N-alkanes at pressures to 265 MPa and temperatures to 523 K. Fluid Phase Equilib 311:17–24.  https://doi.org/10.1016/j.fluid.2011.08.020 CrossRefGoogle Scholar
  22. Yan K, Liu H, Sun C, Ma Q, Chen G, Shen D, Xiao X, Wang H (2013) Measurement and calculation of gas compressibility factor for condensate gas and natural gas under pressure up to 116 MPa. J Chem Thermodyn 63:38–43.  https://doi.org/10.1016/j.jct.2013.03.025 CrossRefGoogle Scholar
  23. Yan W, Varzandeh F, Stenby EH (2015) PVT modeling of reservoir fluids using PC-SAFT EoS and Soave-BWR EoS. Fluid Phase Equilib 386:96–124.  https://doi.org/10.1016/j.fluid.2014.11.022 CrossRefGoogle Scholar
  24. Zdenka N (1996) Exploring the fascinating world of reservoir fluid phase behaviour. J Can Pet Technol.  https://doi.org/10.2118/96-01-0 Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Faith Uchenna Babalola
    • 1
    Email author
  • Oluwadare Abiodun Badejo
    • 1
  • Bosun Abbas Roy-Layinde
    • 1
  1. 1.Department of Chemical and Petroleum EngineeringUniversity of LagosLagosNigeria

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