Experimental and theoretical study of gas/oil relative permeability

  • Zohreh Farmani
  • Reza AzinEmail author
  • Mohamad Mohamadi-Baghmolaei
  • Rouhollah Fatehi
  • Mehdi Escrochi
Original Paper


Gas injection is a proven economical process that significantly increases oil and condensate recovery from hydrocarbon reservoirs. Relative permeability is an important parameter in modeling, simulation, and evaluation of gas injection. In this study, new empirical-mathematical models are developed to predict the relative permeability of gas-oil systems in different rock and fluid systems. The Multi-Gene Genetic Programming (MGGP) technique is employed to develop relative permeability equations. The smart correlations presented in this work require capillary number, interfacial tension, API, gas molecular weight, and viscosity ratio as extra input variables to improve its precision and accuracy. The significance of each parameter is evaluated by statistical approach and Taguchi experimental design. The new models are evaluated by experimental data extracted from literature and validated by extensive error analysis. Additionally, laboratory tests were performed for determining gas-oil relative permeability which were used to check the accuracy of new developed correlations. In relative permeability curves for different gas flow rates, the coupling effect becomes strong and, in competition with the inertia effect, causes changes in the relative permeability with flow rate. The comparison of the experimental results of this study with the new proposed correlation resulted in a root-mean-square error (RMSE) of 0.0796 for gas relative permeability and 0.0564 for oil relative permeability. The results strongly admit the MGGP approach and high accuracy of developed mathematical correlations.


Relative permeability Gas injection Smart correlation MGGP Taguchi experimental design 



absolute permeability

\(S_{\mathrm {g},\max }\)

maximum gas saturation


American Petroleum Institute gravity


gas molecular weight


interfacial tension


ratio of gas viscosity to oil viscosity


capillary number


oil relative permeability


oil saturation


gas saturation

\(S_{\mathrm {o},\max }\)

maximum oil saturation


connate water saturation


residual oil saturation


critical gas saturation

\(K_{\text {ro},\max }\)

critical gas saturation

\(K_{\text {ro},\max }\)

maximum oil relative permeability

\(K_{\text {rg},\max }\)

maximum gas relative permeability


gas relative permeability


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



  1. 1.
    Shaidi, S.MA.: Modelling of gas-condensate flow in reservoir at near wellbore conditions Heriot-Watt University (1997)Google Scholar
  2. 2.
    Kundu, P., Kumar, V., Mishra, I.M.: Experimental and numerical investigation of fluid flow hydrodynamics in porous media: characterization of pre-Darcy, Darcy and non-Darcy flow regimes. Powder Technol. 303, 278–291 (2016)CrossRefGoogle Scholar
  3. 3.
    Ostos, A., Maini, B.: Capillary number in heavy oil solution gas drive and its relationship with gas-oil relative permeability curves. In: SPE/DOE Symposium on Improved Oil Recovery (2004)Google Scholar
  4. 4.
    Honarpour, M., Mahmood, S.: Relative-permeability measurements: an overview. J. Pet. Technol. 40, 963–966 (1988)CrossRefGoogle Scholar
  5. 5.
    Blom, S., Hagoort, J.: How to include the capillary number in gas condensate relative permeability functions?. In: SPE Annual Technical Conference and Exhibition (1998)Google Scholar
  6. 6.
    Ali, J., Butler, S., Allen, L., Wardle, P.: The influence of interfacial tension on liquid mobility in gas condensate systems. In: Offshore Europe (1993)Google Scholar
  7. 7.
    Asar, H., Handy, L.L.: Influence of interfacial tension on gas/oil relative permeability in a gas-condensate system. SPE Reserv. Eng. 3, 257–264 (1988)CrossRefGoogle Scholar
  8. 8.
    Haniff, M., Ali, J.: Relative permeability and low tension fluid flow in gas condensate systems. In: European Petroleum Conference (1990)Google Scholar
  9. 9.
    Longeron, D.: Influence of very low interfacial tensions on relative permeability. Soc. Pet. Eng. J. 20, 391–401 (1980)CrossRefGoogle Scholar
  10. 10.
    Corey, A.T.: The interrelation between gas and oil relative permeabilities. Producers Monthly 19, 38–41 (1954)Google Scholar
  11. 11.
    Honarpour, M., Koederitz, L., Harvey, A.H.: Empirical equations for estimating two-phase relative permeability in consolidated rock. J. Pet. Technol. 34, 2,905–2,908 (1982)CrossRefGoogle Scholar
  12. 12.
    Lomeland, F., Ebeltoft, E., Thomas, W.H.: A new versatile relative permeability correlation. In: International Symposium of the Society of Core Analysts. Toronto, Canada (2005)Google Scholar
  13. 13.
    Chierici, G.L.: Novel relations for drainage and imbibition relative permeabilities. Soc. Pet. Eng. J. 24, 275–276 (1984)CrossRefGoogle Scholar
  14. 14.
    Ibrahim, M., Koederitz, L.: Two-phase relative permeability prediction using a linear regression model. In: SPE Eastern Regional Meeting (2000)Google Scholar
  15. 15.
    Kam, S., Rossen, W.: A model for foam generation in homogeneous media. SPE J. 8, 417–425 (2003)CrossRefGoogle Scholar
  16. 16.
    Coats, K.H.: An equation of state compositional model. Soc. Pet. Eng. J. 20, 363–376 (1980)CrossRefGoogle Scholar
  17. 17.
    Amaefule, J.O., Handy, L.L.: The effect of interfacial tensions on relative oil/water permeabilities of consolidated porous media. Soc. Pet. Eng. J. 22, 371–381 (1982)CrossRefGoogle Scholar
  18. 18.
    Fulcher, R.A. Jr, Ertekin, T., Stahl, C.: Effect of capillary number and its constituents on two-phase relative permeability curves. J. Pet. Technol. 37, 249–260 (1985)CrossRefGoogle Scholar
  19. 19.
    Betté, S., Hartman, K., Heinemann, R.: Compositional modeling of interfacial tension effects in miscible displacement processes. J. Pet. Sci. Eng. 6, 1–14 (1991)CrossRefGoogle Scholar
  20. 20.
    Whitson, C.H, Fevang, Ø: Generalized pseudopressure well treatment in reservoir simulation. In: Proc. IBC Conference on Optimisation of Gas Condensate Fields (1997)Google Scholar
  21. 21.
    Nghiem, L.X., Fong, D., Aziz, K.: Compositional modeling with an equation of state (includes associated papers 10894 and 10903). Soc. Pet. Eng. J. 21, 687–698 (1981)CrossRefGoogle Scholar
  22. 22.
    Wang, P., Stenby, E.H., Pope, G.A., Sepehrnoori, K.: Simulation of flow behavior of gas condensate at low interfacial tension. In Situ 20, 199–219 (1996)Google Scholar
  23. 23.
    Coats, K.H.: An equation of state compositional model. Soc. Pet. Eng. J. 20, 363–376 (1980)CrossRefGoogle Scholar
  24. 24.
    Mohamadi-Baghmolaei, M., Azin, R., Sakhaei, Z., Mohamadi-Baghmolaei, R., Osfouri, S.: Novel method for estimation of gas/oil relative permeabilities. J. Mol. Liq. 223, 1185–1191 (2016)CrossRefGoogle Scholar
  25. 25.
    Mohamadi-Baghmolaei, M., Azin, R., Zarei, Z., Osfouri, S.: Presenting decision tree for best mixing rules and Z-factor correlations and introducing novel correlation for binary mixtures. Petroleum 2, 289–295 (2016)CrossRefGoogle Scholar
  26. 26.
    MohamadiBaghmolaei, M., Mahmoudy, M., Jafari, D., MohamadiBaghmolaei, R., Tabkhi, F.: Assessing and optimization of pipeline system performance using intelligent systems. J. Nat. Gas Sci. Eng. 18, 64–76 (2014)CrossRefGoogle Scholar
  27. 27.
    Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans. Evol. Comput. 3, 257–271 (1999)CrossRefGoogle Scholar
  28. 28.
    Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computing, vol. 53. Springer, Berlin (2003)CrossRefGoogle Scholar
  29. 29.
    Darwin, C., Bynum, W.F.: The origin of species by means of natural selection: or the preservation of favored races in the struggle for life: AL Burt (2009)Google Scholar
  30. 30.
    Banzhaf, W., Nordin, P., Keller, R.E., Francone, F.D.: Genetic Programming: an Introduction vol 1: Morgan Kaufmann San Francisco (1998)Google Scholar
  31. 31.
    Koza, J., Bennett, F., Stiffelman, O.: Genetic programming as a Darwinian invention machine. Genet. Program. 651–651 (1999)Google Scholar
  32. 32.
    Garg, A., Garg, A., Tai, K.: A multi-gene genetic programming model for estimating stress-dependent soil water retention curves. Comput. Geosci. 18, 45 (2014)CrossRefGoogle Scholar
  33. 33.
    Vijayaraghavan, V., Garg, A., Wong, C., Tai, K.: Estimation of mechanical properties of nanomaterials using artificial intelligence methods. Appl. Phys. A 116, 1099–1107 (2014)CrossRefGoogle Scholar
  34. 34.
    Roy, R.K.: Design of Experiments Using the Taguchi Approach, vol. 16. Wiley, New York (2001)Google Scholar
  35. 35.
    Al-Abri, A., Sidiq, H., Amin, R.: Mobility ratio, relative permeability and sweep efficiency of supercritical CO 2 and methane injection to enhance natural gas and condensate recovery: coreflooding experimentation. J. Nat. Gas Sci. Eng. 9, 166–171 (2012)CrossRefGoogle Scholar
  36. 36.
    Badrul, M.J., Ucok, W.S., Robert, L.L.: Effect of permeability distribution and interfacial tension on gas condensate relative permeability: an experimental study. In: SPE Asia Pacific Oil and Gas Conference and Exhibition (2003)Google Scholar
  37. 37.
    Henderson, G., Danesh, A., Tehrani, D., Al-Kharusi, B.: The relative significance of positive coupling and inertial effects on gas condensate relative permeabilities at high velocity. In: SPE Annual Technical Conference and Exhibition (2000)Google Scholar
  38. 38.
    Henderson, G., Danesh, A., Tehrani, D., Peden, J.: The effect of velocity and interfacial tension on relative permeability of gas condensate fluids in the wellbore region. J. Petroleum Sci. Eng. 17, 265–273 (1997)CrossRefGoogle Scholar
  39. 39.
    Kalla, S., Leonardi, S.A., Berry, D.W., Poore, L.D., Sahoo, H., Kudva, R.A., et al.: Factors that affect gas-condensate relative permeability. In: IPTC 2014: International Petroleum Technology Conference (2014)Google Scholar
  40. 40.
    Munkerud, P., Torsaeter, O.: The effects of interfacial tension and spreading on relative permeabilityin gas condensate systems. In: IOR 1995-8th European Symposium on Improved Oil Recovery (1995)Google Scholar
  41. 41.
    Parvazdavani, M., Masihi, M., Ghazanfari, M.: Gas–oil relative permeability at near miscible conditions: an experimental and modeling approach. Sci. Iran. 20, 626–636 (2013)Google Scholar
  42. 42.
    Shahverdi, H., Sohrabi, M., Fatemi, M., Jamiolahmady, M.: Three-phase relative permeability and hysteresis effect during WAG process in mixed wet and low IFT systems. J. Pet. Sci. Eng. 78, 732–739 (2011)CrossRefGoogle Scholar
  43. 43.
    Fatemi, S.M., Sohrabi, M., Jamiolahmady, M., Ireland, S.: Experimental and theoretical investigation of gas/oil relative permeability hysteresis under low oil/gas interfacial tension and mixed-wet conditions. Energy Fuel 26, 4366–4382 (2012)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Zohreh Farmani
    • 1
  • Reza Azin
    • 1
    • 2
    Email author
  • Mohamad Mohamadi-Baghmolaei
    • 3
  • Rouhollah Fatehi
    • 4
  • Mehdi Escrochi
    • 5
    • 6
  1. 1.Department of Petroleum Engineering, Faculty of Petroleum, Gas and Petrochemical EngineeringPersian Gulf UniversityBushehrIran
  2. 2.Gas Condensate and Carbon Management (GCCM) Research GroupPersian Gulf UniversityBushehrIran
  3. 3.Department of Chemical Engineering, Faculty of Petroleum, Gas and Petrochemical EngineeringPersian Gulf UniversityBushehrIran
  4. 4.Department of Mechanical Engineering, Faculty of EngineeringPersian Gulf UniversityBushehrIran
  5. 5.Department of Petroleum Engineering, School of Chemical and Petroleum EngineeringShiraz UniversityShirazIran
  6. 6.IOR-EOR Research InstituteShiraz UniversityShirazIran

Personalised recommendations