Admissible Parameters for Two-Phase Coreflood and Welge–JBN Method

  • A. Al-Sarihi
  • Z. You
  • A. Behr
  • L. Genolet
  • P. Kowollik
  • A. Zeinijahromi
  • P. BedrikovetskyEmail author


The Welge–JBN method for determining relative permeability from unsteady-state waterflood test is commonly used for two-phase flows in porous media. We discuss the theoretical criteria that limits application of the basic Buckley–Leverett model and Welge–JBN method and the operational criteria of the accuracy of measurements during core waterflood tests. The objective is determination of the waterflood test parameters (core length, flow velocity and effluent sampling frequency) that fulfil the theoretical and operational criteria. The overall set of criteria results in five inequalities in three-dimensional Euclidian space of these parameters. For known rock and fluid properties, a formula for minimum core length to fulfil Welge–JBN criteria is derived. For cases where the core length is given, formulae for test’s flow velocity and sampling period are provided to satisfy the test admissibility conditions. The application of the proposed methodology is illustrated by two coreflood tests.


Relative permeability Two-phase flow Welge–JBN method Coreflood parameters Mathematical model Laboratory waterflooding test 

List of Symbols


Fractional flow during steady-state


Minimum measured value of fractional flow


Capillary J-function


Permeability (m2)


Relative permeability


Relative permeability of oil at initial water saturation


Relative permeability of water at residual oil saturation


Core length (m)


Oil ganglion length (m)


Capillary number


Minimum number of samples


Corey’s oil exponent


Corey’s water exponent


Capillary pressure (Pa)


Pressure (Pa)


Minimum measured pressure (Pa)


Dimensionless pressure


Water mass rate per unit area for linear flow (kg/m2 s)


Radius (m)


Pore throat radius


Water saturation




Frontal saturation during waterflooding


Residual oil saturation


Connate water saturation




Minimum distinguishable volume


Distance (m)


Dimensionless distance

Greek Letters


Capillary–viscous ratio


Water-cut measurement accuracy


Pressure drop accuracy


Sampling period accuracy


Sampling period


Interfacial tension (N/m)




Viscosity (Pa s)


Density (kg/m3)


Interfacial tension (N/m)


Macroscopic contact angle


Total mobility


Self-similar coordinate





Maximum for velocity and for core length at maximum velocity















Breakthrough curve


Pressure drop curve









The paper is dedicated to the memory of Eng. C. Holleben (Petrobras) who initiated the work by Dos Santos et al. (1997). The authors are grateful to Dr. A. Badalyan (The University of Adelaide) for fruitful discussions. Deep gratitude is due to Profs. M. Lurie and A. Kurbanov (Moscow Oil–Gas Gubkin University), who introduced PB to waterflood mathematics.


  1. Abbas, M.: An extension of Johnson, Bossler and Neumann JBN method for calculating relative permeabilities. In: SPE Annual Technical Conference and Exhibition 2016. Society of Petroleum Engineers (2016)Google Scholar
  2. Adler, P.M.: Multiphase Flow in Porous Media. Springer, Amsterdam (1995)CrossRefGoogle Scholar
  3. Adler, P.: Porous Media: Geometry and Transports. Elsevier, Amsterdam (2013)Google Scholar
  4. Adler, P.M., Thovert, J.-F.: Fractures and Fracture Networks, pp. 103–162. Springer, Berlin (1999)Google Scholar
  5. Akin, S.: Estimation of fracture relative permeabilities from unsteady state corefloods. J. Pet. Sci. Eng. 30(1), 1–14 (2001)CrossRefGoogle Scholar
  6. Al Shalabi, E.W., Sepehrnoori, K., Delshad, M.: Mechanisms behind low salinity water flooding in carbonate reservoirs. In: SPE Western Regional & AAPG Pacific Section Meeting 2013 Joint Technical Conference 2013. Society of Petroleum Engineers (2013)Google Scholar
  7. Arns, C., Adler, P.: Fast Laplace solver approach to pore-scale permeability. Phys. Rev. E 97(2), 023303 (2018)CrossRefGoogle Scholar
  8. Arns, J.-Y., Arns, C.H., Sheppard, A.P., Sok, R.M., Knackstedt, M.A., Pinczewski, W.V.: Relative permeability from tomographic images; effect of correlated heterogeneity. J. Pet. Sci. Eng. 39(3–4), 247–259 (2003)CrossRefGoogle Scholar
  9. Arns, C., Knackstedt, M., Mecke, K.: Boolean reconstructions of complex materials: integral geometric approach. Phys. Rev. E 80(5), 051303 (2009)CrossRefGoogle Scholar
  10. Aziz, K., Settari, A.: Petroleum Reservoir Simulation. Applied Science Publ. Ltd., London (1979)Google Scholar
  11. Badalyan, A., Carageorgos, T., Bedrikovetsky, P., You, Z., Zeinijahromi, A., Aji, K.: Critical analysis of uncertainties during particle filtration. Rev. Sci. Instrum. 83(9), 095106 (2012)CrossRefGoogle Scholar
  12. Banchoff, T.F., Lovett, S.T.: Differential Geometry of Curves and Surfaces. Chapman and Hall/CRC, London (2016)Google Scholar
  13. Barenblatt, G., Entov, V., Ryzhik, V.: Theory of Fluid Flows Through Natural Rocks. Kluwer, Dordrecht (1991)Google Scholar
  14. Barenblatt, G., Patzek, T.W., Silin, D.: The mathematical model of nonequilibrium effects in water–oil displacement. SPE J. 8(04), 409–416 (2003)CrossRefGoogle Scholar
  15. Bartels, W.-B., Mahani, H., Berg, S., Hassanizadeh, S.: Literature review of low salinity waterflooding from a length and time scale perspective. Fuel 236, 338–353 (2019)CrossRefGoogle Scholar
  16. Bedrikovetsky, P.: Mathematical Theory of Oil and Gas Recovery: With Applications to Ex-USSR Oil and Gas Fields, vol. 4. Springer, Berlin (2013)Google Scholar
  17. Borazjani, S., Behr, A., Genolet, L., Van Der Net, A., Bedrikovetsky, P.: Effects of fines migration on low-salinity waterflooding: analytical modelling. Trans. Porous Media 116(1), 213–249 (2017)CrossRefGoogle Scholar
  18. Borazjani, S., Behr, A., Genolet, L., Kowollik, P., Bedrikovetsky, P.: Ion-exchange inverse problem for low-salinity coreflooding. Trans. Porous Media 128(2), 571–611 (2019)CrossRefGoogle Scholar
  19. Buckley, S.E., Leverett, M.: Mechanism of fluid displacement in sands. Trans. AIME 146(01), 107–116 (1942)CrossRefGoogle Scholar
  20. Cao, J., James, L.A., Johansen, T.E.: Determination of two phase relative permeability from core floods with constant pressure boundaries. In: Society of Core Analysis Symposium, Avignon, France (2014)Google Scholar
  21. Cao, J., Liu, X., James, L., Johansen, T.: Analytical interpretation methods for dynamic immiscible core flooding at constant differential pressure. In: Society of Core Analysis Symposium, St. John’s Newfoundland and Labrador, Canada, pp. 16–21 (2015)Google Scholar
  22. Chatzis, I., Morrow, N.R., Lim, H.T.: Magnitude and detailed structure of residual oil saturation. Soc. Pet. Eng. J. 23(02), 311–326 (1983)CrossRefGoogle Scholar
  23. Chen, Z.: Reservoir Simulation: Mathematical Techniques in Oil Recovery, vol. 77. SIAM, Philadelphia (2007)CrossRefGoogle Scholar
  24. Chen, X., Kianinejad, A., DiCarlo, D.A.: An extended JBN method of determining unsteady-state two-phase relative permeability. Water Resour. Res. 52(10), 8374–8383 (2016)CrossRefGoogle Scholar
  25. Civan, F., Donaldson, E.: Relative permeability from unsteady-state displacements with capillary pressure included. SPE Form. Eval. 4(02), 189–193 (1989)CrossRefGoogle Scholar
  26. Dake, L.P.: Fundamentals of Reservoir Engineering, vol. 8. Elsevier, Amsterdam (1983)Google Scholar
  27. Dos Santos, R.L., Bedrikovetsky, P., Holleben, C.R.: Optimal design and planning for laboratory corefloods. In: Latin American and Caribbean Petroleum Engineering Conference. Society of Petroleum Engineers (1997)Google Scholar
  28. Farajzadeh, R., Ameri, A., Faber, M.J., Van Batenburg, D.W., Boersma, D.M., Bruining, J.: Effect of continuous, trapped, and flowing gas on performance of Alkaline Surfactant Polymer (ASP) flooding. Ind. Eng. Chem. Res. 52(38), 13839–13848 (2013)CrossRefGoogle Scholar
  29. Farajzadeh, R., Lotfollahi, M., Eftekhari, A., Rossen, W., Hirasaki, G.: Effect of permeability on implicit-texture foam model parameters and the limiting capillary pressure. Energy Fuels 29(5), 3011–3018 (2015)CrossRefGoogle Scholar
  30. Farajzadeh, R., Guo, H., van Winden, J., Bruining, J.: Cation exchange in the presence of oil in porous media. ACS Earth Space Chem. 1(2), 101–112 (2017)CrossRefGoogle Scholar
  31. Honarpour, M., Koederitz, F., Herbert, A.: Relative permeability of petroleum reservoirs. CRC Press, United States (1986)CrossRefGoogle Scholar
  32. Hussain, F., Cinar, Y., Bedrikovetsky, P.G.: Comparison of methods for drainage relative permeability estimation from displacement tests. In: SPE Improved Oil Recovery Symposium. Society of Petroleum Engineers (2010)Google Scholar
  33. Hussain, F., Cinar, Y., Bedrikovetsky, P.: A semi-analytical model for two phase immiscible flow in porous media honouring capillary pressure. Trans. Porous Media 92(1), 187–212 (2012)CrossRefGoogle Scholar
  34. Hussain, F., Zeinijahromi, A., Bedrikovetsky, P., Badalyan, A., Carageorgos, T., Cinar, Y.: An experimental study of improved oil recovery through fines-assisted waterflooding. J. Pet. Sci. Eng. 109, 187–197 (2013)CrossRefGoogle Scholar
  35. Hussain, F., Pinczewski, W.V., Cinar, Y., Arns, J.-Y., Arns, C., Turner, M.: Computation of relative permeability from imaged fluid distributions at the pore scale. Trans. Porous Media 104(1), 91–107 (2014)CrossRefGoogle Scholar
  36. Islam, M.R., Bentsen, R.: A dynamic method for measuring relative permeability. J. Can. Pet. Technol. 25(01), 39–50 (1986)Google Scholar
  37. Johansen, T.E., James, L.A.: Solution of multi-component, two-phase Riemann problems with constant pressure boundaries. J. Eng. Math. 96(1), 23–35 (2016)CrossRefGoogle Scholar
  38. Johnson, E., Bossler, D., Bossler, V.: Calculation of relative permeability from displacement experiments (1959)Google Scholar
  39. Jones, S., Roszelle, W.: Graphical techniques for determining relative permeability from displacement experiments. J. Pet. Technol. 30(05), 807–817 (1978)CrossRefGoogle Scholar
  40. Katika, K., Ahkami, M., Fosbøl, P.L., Halim, A.Y., Shapiro, A., Thomsen, K., Xiarchos, I., Fabricius, I.L.: Comparative analysis of experimental methods for quantification of small amounts of oil in water. J. Pet. Sci. Eng. 147, 459–467 (2016)CrossRefGoogle Scholar
  41. Kianinejad, A., Chen, X., DiCarlo, D.A.: Direct measurement of relative permeability in rocks from unsteady-state saturation profiles. Adv. Water Resour. 94, 1–10 (2016)CrossRefGoogle Scholar
  42. Kim, C., Lee, J.: Experimental study on the variation of relative permeability due to clay minerals in low salinity water-flooding. J. Pet. Sci. Eng. 151, 292–304 (2017)CrossRefGoogle Scholar
  43. Krause, M.: Modeling and investigation of the influence of capillary heterogeneity on relative permeability. In: SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers (2012)Google Scholar
  44. Krause, M.H., Benson, S.M.: Accurate determination of characteristic relative permeability curves. Adv. Water Resour. 83, 376–388 (2015)CrossRefGoogle Scholar
  45. Kuo, C.-W., Benson, S.M.: Numerical and analytical study of effects of small scale heterogeneity on CO2/brine multiphase flow system in horizontal corefloods. Adv. Water Resour. 79, 1–17 (2015)CrossRefGoogle Scholar
  46. Kuo C.-w., Perrin J.-C., Benson, S.M.: Effect of gravity, flow rate, and small scale heterogeneity on multiphase flow of CO2 and brine. In: SPE Western Regional Meeting. Society of Petroleum Engineers (2010)Google Scholar
  47. Lake, L.W., Johns, R., Rossen, W.R., Pope, G.A.: Fundamentals of enhanced oil recovery (2014)Google Scholar
  48. Maplesoft™: Solver for a system of inequalities. (2019). Accessed 10 March 2019
  49. MathWorks®: Meshgrid, Surf Commands (2019). Accessed 10 March 2019
  50. McPhee, C., Reed, J., Zubizarreta, I.: Core Analysis: A Best Practice Guide, vol. 64. Elsevier, Amsterdam (2015)Google Scholar
  51. Miller, M.A., Ramey Jr., H.: Effect of temperature on oil/water relative permeabilities of unconsolidated and consolidated sands. Soc. Pet. Eng. J. 25(06), 945–953 (1985)CrossRefGoogle Scholar
  52. Nasralla, R.A., Mahani, H., van der Linde, H.A., Marcelis, F.H., Masalmeh, S.K., Sergienko, E., Brussee, N.J., Pieterse, S.G., Basu, S.: Low salinity waterflooding for a carbonate reservoir: experimental evaluation and numerical interpretation. J. Pet. Sci. Eng. 164, 640–654 (2018)CrossRefGoogle Scholar
  53. Odeh, A., Dotson, B.: A method for reducing the rate effect on oil and water relative permeabilities calculated from dynamic displacement data. J. Pet. Technol. 37(11), 2051-052058 (1985)CrossRefGoogle Scholar
  54. Pereira, B.M.F., Shahverdi, H., Sohrabi, M.: Refinement of relative permeability measurements by accounting for viscous fingering in coreflood experiments. In: SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers (2014)Google Scholar
  55. Perrin, J.-C., Krause, M., Kuo, C.-W., Miljkovic, L., Charoba, E., Benson, S.M.: Core-scale experimental study of relative permeability properties of CO2 and brine in reservoir rocks. Energy Proc. 1(1), 3515–3522 (2009)CrossRefGoogle Scholar
  56. Rabinovich, A.: Estimation of sub-core permeability statistical properties from coreflooding data. Adv. Water Resour. 108, 113–124 (2017)CrossRefGoogle Scholar
  57. Rabinovich, A.: Analytical corrections to core relative permeability for low-flow-rate simulation. SPE J. (2018)Google Scholar
  58. Rabinovich, A., Li, B., Durlofsky, L.J.: Analytical approximations for effective relative permeability in the capillary limit. Water Resour. Res. 52(10), 7645–7667 (2016)CrossRefGoogle Scholar
  59. Rapoport, L., Leas, W.: Properties of linear waterfloods. J. Pet. Technol. 5(05), 139–148 (1953)CrossRefGoogle Scholar
  60. Richmond, P., Watsons, A.: Estimation of multiphase flow functions from displacement experiments. SPE Reserv. Eng. 5(01), 121–127 (1990)CrossRefGoogle Scholar
  61. Sigmund, P., McCaffery, F.: An improved unsteady-state procedure for determining the relative-permeability characteristics of heterogeneous porous media (includes associated papers 8028 and 8777). Soc. Pet. Eng. J. 19(01), 15–28 (1979)CrossRefGoogle Scholar
  62. Sorop, T.G., Masalmeh, S.K., Suijkerbuijk, B.M.J.M., van der Linde, H.A., Mahani, H., Brussee, N.J., Marcelis, F.A.H.M., Coorn, A. Relative Permeability Measurements to Quantify the Low Salinity Flooding Effect at Field Scale (2015)Google Scholar
  63. Tao, T., Watson, A.: Accuracy of JBN estimates of relative permeability: part 2-algorithms. Soc. Pet. Eng. J. 24(02), 215–223 (1984)CrossRefGoogle Scholar
  64. Torsæter, O., Abtahi, M.: Experimental Reservoir Engineering Laboratory Workbook. Department of Petroleum Engineering and Applied Geophysics, Norwegian University of Science and Technology (NTNU), Trondheim (2003)Google Scholar
  65. Toth, J., Bodi, T., Szucs, P., Civan, F.: Direct determination of relative permeability from nonsteady-state constant pressure and rate displacements. In: SPE Production and Operations Symposium. Society of Petroleum Engineers (2001)Google Scholar
  66. Toth, J., Bodi, T., Szucs, P., Civan, F.: Convenient formulae for determination of relative permeability from unsteady-state fluid displacements in core plugs. J. Pet. Sci. Eng. 36(1–2), 33–44 (2002)CrossRefGoogle Scholar
  67. Virnovsky, G., Guo, Y.: Relative permeability and capillary pressure concurrently determined from steady-state flow experiments. In: IOR 1995-8th European Symposium on Improved Oil Recovery (1995)Google Scholar
  68. Virnovsky, G., Vatne, K., Skjaeveland, S., Lohne, A.: Implementation of multirate technique to measure relative permeabilities accounting. In: SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers (1998)Google Scholar
  69. Welge, H.J.: A simplified method for computing oil recovery by gas or water drive. J. Pet. Technol. 4(04), 91–98 (1952)CrossRefGoogle Scholar
  70. Zeinijahromi, A., Farajzadeh, R., Bruining, J.H., Bedrikovetsky, P.: Effect of fines migration on oil–water relative permeability during two-phase flow in porous media. Fuel 176, 222–236 (2016)CrossRefGoogle Scholar
  71. Zhou, K., Hou, J., Fu, H., Wei, B., Liu, Y.: Estimation of relative permeability curves using an improved Levenberg–Marquardt method with simultaneous perturbation Jacobian approximation. J. Hydrol. 544, 604–612 (2017)CrossRefGoogle Scholar
  72. Zou, S., Hussain, F., Arns, J.-Y., Guo, Z., Arns, C.H.: Computation of relative permeability from in situ imaged fluid distributions at the pore scale. SPE J. 23(03), 737–749 (2018)CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • A. Al-Sarihi
    • 1
  • Z. You
    • 3
  • A. Behr
    • 2
  • L. Genolet
    • 2
  • P. Kowollik
    • 2
  • A. Zeinijahromi
    • 1
  • P. Bedrikovetsky
    • 1
    Email author
  1. 1.Australian School of PetroleumThe University of AdelaideAdelaideAustralia
  2. 2.Wintershall Holding GmbH, EOT/RKasselGermany
  3. 3.The University of QueenslandBrisbaneAustralia

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