Computational Geosciences

, Volume 22, Issue 4, pp 975–991 | Cite as

An improved methodology for estimation of two-phase relative permeability functions for heavy oil displacement involving compositional effects and instability

  • Pedram MahzariEmail author
  • Usman Taura
  • Mehran Sohrabi
Original Paper


In heavy oil recovery by immiscible gas injection, adverse mobility ratio and gravity segregation along with influential mass transfer are the most crucial factors controlling displacement efficiencies. Obtaining relative permeability functions using conventional techniques that are based on a stable displacement front could be highly misleading. In this work, an improved methodology was proposed for estimating relative permeability curves under simultaneous effects of frontal instability and mass transfer using history-matching techniques. The compositional analysis of produced oil from a coreflood experiment was employed, which represents dynamic interactions more realistically. For the history matching, an optimum, high-resolution, two-dimensional core model was used, as opposed to the industry standard use of a one-dimensional model. The results of the simulation were then verified by a semi-empirical approach using the Koval model, which was then used to predict a similar experiment but in a vertical orientation. A good match was obtained between the forward simulation and the experiment. To highlight the effect of mass transfer on the shape of relative permeabilities, the simulation results from two immiscible gas injection corefloods were compared: CO2 injection with mass transfer and N2 injection without mass transfer. The results showed that the two estimated functions were quite similar, indicating that instability levels would determine the displacement pattern rather than local mass transfer. This integrated approach, therefore, highlights the importance of employing the right fluid model and an appropriate 2D-grid model in estimating relative permeabilities in displacement with instability and mass transfer against the current industry practice.


History matching Relative permeability Heavy oil CO2 injection Unstable displacement Compositional simulation 


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This work was carried out as a part of the Non-thermal Enhanced Heavy Oil Recovery joint industry project (JIP) in the Centre for Enhanced Oil Recovery and CO2 Solutions of the Institute of Petroleum Engineering at Heriot-Watt University.

Funding Information

The project was equally funded by Total E&P, ConocoPhillips, CONACyT-SENERHidrocarburos - Mexico, Pemex, Wintershall, and Eni, which is gratefully acknowledged. Usman Taura thanks the Petroleum Technology Development fund, Nigeria, for the financial assistance for this work.


  1. 1.
    Welge, H.J.: Displacement of oil from porous media by water or gas. Trans. AIME 179(01), 133–145 (1949)CrossRefGoogle Scholar
  2. 2.
    Johnson, E.F., Bossler, D.P., Naumann, V.O.: Calculation of relative permeability from displacement experiments. Pet. Trans. AIME 216(1), 370–372 (1959)Google Scholar
  3. 3.
    Jones, S.C., Roszelle, W.O.: Graphical techniques for determining relative permeability from displacement experiments. J. Pet. Technol. 30(05), 807–817 (1978)CrossRefGoogle Scholar
  4. 4.
    Benham, A.L., Olson, R.W.: A model study of viscous fingering. Soc. Pet. Eng. J. 3(2), 138–144 (1963)CrossRefGoogle Scholar
  5. 5.
    Pavone, D.: Observations and correlations for immiscible viscous-fingering experiments. SPE Reserv. Eng. 7(2), 187–194 (1992)CrossRefGoogle Scholar
  6. 6.
    Araktingi, U.G., Orr, F.M. Jr.: Viscous fingering in heterogeneous porous media. SPE Adv. Technol. Ser. 1(01), 71–80 (1993)CrossRefGoogle Scholar
  7. 7.
    Christie, M.A., Muggeridge, A.H., Barley, J.J.: 3D Simulation of viscous fingering and WAG schemes. SPE Reserv. Eng. 1, 19–26 (1993)CrossRefGoogle Scholar
  8. 8.
    Cuthiel, D., Kissel, G., Jackson, C., et al.: Viscous fingering effects in solvent displacement of heavy oil. J. Can. Pet. Technol. 45(7), 29–39 (2006)Google Scholar
  9. 9.
    Koval, E.J.: A method for predicting the performance of unstable miscible displacement in heterogeneous media. Soc. Pet. Eng. J. 3(2), 145–154 (1963)CrossRefGoogle Scholar
  10. 10.
    Todd, M.R., Longstaff, W.J.: The development, testing, and application of a numerical simulator for predicting miscible flood performance. J. Pet. Technol. 253(1), 874–882 (1972)CrossRefGoogle Scholar
  11. 11.
    Fayers, F.J., Newley, T.M.J.: Detailed validation of an empirical model for viscous fingering with gravity effects. SPE Reserv. Eng. 3(2), 542–550 (1988)CrossRefGoogle Scholar
  12. 12.
    Emadi, A.: Enhanced heavy oil recovery by water and carbon dioxide flood. PhD, Heriot-Watt University, Edinburgh (2012)Google Scholar
  13. 13.
    Desch, J.B., Larsen, W.K., Lindsay, R.F., et al.: Enhanced oil recovery by CO2 miscible displacement in the Little Knife Field, Billings County, North Dakota. J. Pet. Technol. 36(09), 1592–16-2 (1984)CrossRefGoogle Scholar
  14. 14.
    Kantar, K., Karaoguz, D., Issever, K., et al.: Design concepts of a heavy-oil recovery process by an immiscible CO2 application. J. Pet. Technol. 37(02), 275–283 (1985)CrossRefGoogle Scholar
  15. 15.
    Saner, W.B., Patton, J.T.: CO2 Recovery of heavy oil: Wilmington field test. J. Pet. Technol. 38(7), 769–776 (1986)CrossRefGoogle Scholar
  16. 16.
    Mohanty, K.K., Masino, W.H. Jr., Ma, T.D., et al.: The role of three-hydrocarbon-phase flow in a gas displacement process. SPE Reserv. Eng. 10(3), 214–221 (1995)CrossRefGoogle Scholar
  17. 17.
    Simon, R., Rosman, A., Zana, E.: Phase-behavior properties of CO2—reservoir oil systems. Soc. Pet. Eng. J. 18(01), 20–26 (1978)CrossRefGoogle Scholar
  18. 18.
    Nasrabadi, H., Firoozabadi, A., Ahmed, T.K.: Complex flow and composition path in CO2 injection schemes from density effects in 2 and 3D. In: Proceedingss, 2009 SPE Annual Technical Conference and Exhibition, New Orleans (2009)Google Scholar
  19. 19.
    Tan, C.T., Homsy, G.M.: Simulation of nonlinear viscous fingering in miscible displacment. Phys. Fluids 31(6), 1330–1338 (1998)CrossRefGoogle Scholar
  20. 20.
    Yortsos, Y.C.: Instabilities in displacement processes in porous media. J. Phys. Condens. Matter 2, SA443–SA448 (1990)CrossRefGoogle Scholar
  21. 21.
    Riaz, A., Meiburg, E.: Vorticity interaction mechanisms in variable-viscosity heterogeneous miscible displacments with and without density contrast. J. Fluid Mech. 517, 1–25 (2004)CrossRefGoogle Scholar
  22. 22.
    Moortgat, J., Firoozabadi, A., Li, Z., Esposito, R.: CO2 injection in vertical and horizontal cores: measurements and numerical simulation. SPE J. 18, 331–334 (2013)CrossRefGoogle Scholar
  23. 23.
    Chuoke, R.L., van Meurs, P., van der Poel, C.: The Instability of Slow, Immiscible, Viscous Liquid-Liquid Displacements in Permeable Media.Society of Petroleum Engineers, General document, SPE-1141-G (1959)Google Scholar
  24. 24.
    Berg, S., Ott, H.: Stability of CO2-brine immiscible displacemnt. Int. J. Greenhouse Gas Control 11, 188–203 (2012)CrossRefGoogle Scholar
  25. 25.
    Christie, M.A.: High resolution simulation of unstable flows in porous media. SPE Reserv. Eng. 4(03), 297–203 (1989)CrossRefGoogle Scholar
  26. 26.
    Christie, M.A., Jones, A.D.W., Muggeridge, A.H.: Comparison between laboratory experiments and detailed simulations of unstable miscible displacement influenced by gravity. In: North Sea oil and gas reservoirs—II: Proceedings of the 2nd North Sea Oil and Gas Reservoirs Conference organised and hosted by the Norwegian Institute of Technology (NTH), Trondheim, Norway, May 8–11, 1989 (1990)Google Scholar
  27. 27.
    Blunt, M.J., Barker, W.J., Rubin, B., et al.: Predictive theory for viscous fingering in compositional displacement. SPE Reserv. Eng. 9(1), 73–80 (1994)CrossRefGoogle Scholar
  28. 28.
    Barker, J.W., Evans, S.C.: Predictive model for viscous fingering in compositional wag. SPE Reserv. Eng. 10(02), 116–121 (1995)CrossRefGoogle Scholar
  29. 29.
    Farzaneh, S.A., Seyyedsar, S.M., Sohrabi, M.: Enhanced heavy oil recovery by liquid CO2 injection under different injection strategies. In: Proceedings, SPE Annual Technical Conference and Exhibition, p. 21. Dubai (2016)Google Scholar
  30. 30.
    Peng, D.Y., Robinson, D.B.: A new two-constant equation of state. Ind. Eng. Chem. Fundam. 15, 59–64 (1976)CrossRefGoogle Scholar
  31. 31.
    Pedersen, K.S., Fredenslund, A.: An improved corresponding states model for the prediction of oil and gas viscosities and thermal conductivities. Chem. Eng. Sci. 42, 182 (1987)CrossRefGoogle Scholar
  32. 32.
    Christie, M.A., Bond, D.J.: Detailed simulation of unstable processes in miscible flooding. SPE Reserv. Eng. 2(04), 514–522 (1987)CrossRefGoogle Scholar
  33. 33.
    Lomeland, F., Ebeltoft, E, Thomas, W.K.: A new versatile relative permeability correlation. In: Proceedings of the International Symposium of the Society of Core Analysts, Toronto (2005)Google Scholar
  34. 34.
    Blunt, M.J., Christie, M.A.: Theory of viscous fingering in two phase, three component flow. SPE Adv. Technol. Ser. 2(2), 52–60 (1994)CrossRefGoogle Scholar
  35. 35.
    Fayers, F.J., Muggeridge, A.H.: Extensions to Dietz theory and behavior of gravity tongues in slightly tilted reservoirs. SPE Reserv. Eng. 5(04), 487–494 (1990)CrossRefGoogle Scholar
  36. 36.
    Dong, X. et al.: Non-Newtonian flow characterization of heavy crude oil in porous media. J. Pet. Explor. Prod. Technol. 3, 43–53 (2013)CrossRefGoogle Scholar
  37. 37.
    Bassane, J., Sad, C., Neto, D., Santos, F., Silva, M., Tozzi, F., Filgueiras, P., Castro, V., Romao, W., Santos, M., Silva, J., Lacerda, V.: Study of the effect of temperature and gas condensate addition on the viscosity of heavy oils. J. Pet. Sci. Eng. 142, 163–169 (2016)CrossRefGoogle Scholar
  38. 38.
    Maini, B.B., Okazawa, T.: Effects of temperature on heavy oil-water relative permeability of sand. Petroleum Society of Canada. J. Can. Pet. Technol. 26, 33–41 (1987)CrossRefGoogle Scholar
  39. 39.
    Alkindi, A., Muggeridge, A.H., Al-Wahaibi, Y.: The influence of dispersion and diffusion on heavy oil recovery by VAPEX. In: Proceedings, SPE International Thermal Operations and Heavy Oil Symposium, Calgary (2008)Google Scholar
  40. 40.
    James, L.A., Rezaei, N., Chatzis, I.: VAPEX, Warm VAPEX and Hybrid VAPEX—the state of enhanced oil recovery for in-situ heavy oils in Canada. J. Can. Pet. Technol. 47, 1–7 (2008)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Centre for EOR and CO2 SolutionsHeriot Watt UniversityEdinburghUK

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