Imbibition Capillary Pressure and Relative Permeability of Mixed-Wet Microporous Rock: New Insights from History Matching

  • Yukie TaninoEmail author
  • Magali Christensen


We use a Darcy-scale simulator to extract residual oil saturation, forced imbibition capillary pressure, and relative permeability by history matching to measured pressure drop and cumulative oil production during multi-speed centrifuge experiments and constant-rate waterfloods in Indiana limestone cores under four different wettability states established by adding different naphthenic acids to the oil phase. Residual oil saturation decreases monotonically as advancing bulk contact angle increases from \(\theta _\text {a} = 110^\circ \) to \(150^\circ \), in sharp contrast to the non-monotonic dependence displayed by the core-averaged oil saturation which are often mis-interpreted to be representative of true residual saturation. The magnitude of the capillary pressure required to establish a particular water saturation increases with \(\theta _\text {a}\). Saturation-normalized water relative permeability exceeds one at \(\theta _\text {a}\ge 125^\circ \), with equivalent slip lengths of up to O(200) nm. The simulations indicate that capillary end effects may be significant during displacement experiments under typical laboratory conditions, even in mixed-wet media of relatively low permeability, and highlight the importance of using numerical simulation to interpret displacement experiments under capillary-dominated conditions.


Capillary trapping Multiphase flow Slippage Residual saturation History matching 



MC was supported by the University of Aberdeen College of Physical Sciences studentship. The authors gratefully acknowledge CYDAREX for providing an evaluation license for their software \(\hbox {CYDAR}^\text {TM}\), Koon-Yang Lee for the n-decane/brine static contact angle measurements on calcite (Supplementary Material S3), and Steffen Berg for his insightful comments and suggestions as a reviewer for conference paper Christensen and Tanino 2018 on which this paper builds. Finally, the authors thank the three anonymous reviewers for their detailed comments. All data used in this study are available from the corresponding author on reasonable request. In addition, the centrifuge data generated during this study are included as a Excel spreadsheet in the supplementary materials for this published article. One set of mercury injection capillary pressure measurements by Tanino and Blunt (2012) analysed in Text S2 are available in the Mendeley data repository,

Supplementary material

11242_2019_1280_MOESM1_ESM.docx (344 kb)
Supplementary material 1 (docx 343 KB)
11242_2019_1280_MOESM2_ESM.xlsx (86 kb)
Supplementary material 2 (xlsx 85 KB)


  1. Al-Gharbi, M.S., Jing, X., Kraaijveld, M., Hognestad, J.B., Udeh, P.O.: SCAL relative permeability measurements and analyses for a cluster of fields in South Oman. In: Proc., International Petroleum Technology Conference, 4-6 Dec., International Petroleum Technology Conference, Dubai, UAE (2007)
  2. Alhammadi, A.M., AlRatrout, A., Singh, K., Bijeljic, B., Blunt, M.J.: In situ characterization of mixed-wettability in a reservoir rock at subsurface conditions. Sci. Rep. 7, 1–9 (2017). CrossRefGoogle Scholar
  3. AlRatrout, A., Raeini, A.Q., Bijeljic, B., Blunt, M.J.: Automatic measurement of contact angle in pore-space images. Adv. Water Resour. 109, 158–169 (2017). CrossRefGoogle Scholar
  4. AlRatrout, A., Blunt, M.J., Bijeljic, B.: Wettability in complex porous materials, the mixed-wet state, and its relationship to surface roughness. Proc. Nat. Acad. Sci. 115(36), 8901–8906 (2018). CrossRefGoogle Scholar
  5. Amott, E.: Observations relating to the wettability of porous rock. Trans. AIME 216, 156162 (1959)Google Scholar
  6. Anderson, W.G.: Wettability literature survey part 4: effects of wettability on capillary pressure. J. Petrol Technol. 39(10), 1283–1300 (1987). CrossRefGoogle Scholar
  7. Anggraini, L.: Buckley-Leverett analysis of waterflood oil recovery from mixed-wet rock. Master’s thesis, University of Aberdeen, Scotland, UK (2013)Google Scholar
  8. Ayappa, K.G., Davis, H.T., Davis, E.A., Gordon, J.: Capillary pressure: centrifuge method revisited. AIChE J. 35(3), 365–372 (1989). CrossRefGoogle Scholar
  9. Bear, J.: Dynamics of Fluids in Porous Media. Dover Publications Inc, New York (1988)Google Scholar
  10. Berg, S., Cense, A.W., Hofman, J.P., Smits, R.M.M.: Two-phase flow in porous media with slip boundary condition. Transp. Porous Med. 74(3), 275–292 (2008)CrossRefGoogle Scholar
  11. Bowden, S.A., Tanino, Y., Akamairo, B., Christensen, M.: Recreating mineralogical petrographic heterogeneity within microfluidic chips: assembly, examples, and applications. Lab Chip 16, 4677–4681 (2016). CrossRefGoogle Scholar
  12. Brooks, R.H., Corey, A.T.: Hydraulic properties of porous media. Hydrology Papers 3, Colorado State University, Fort Collins, Colorado (1964)Google Scholar
  13. Brooks, R.H., Corey, A.T.: Properties of porous media affecting fluid flow. J. Irrig. Drain. Div. 92(2), 61–90 (1966)Google Scholar
  14. Burdine, N.T.: Relative permeability calculations from pore size distribution data. J. Petrol Technol. 5(3), 71–78 (1953). CrossRefGoogle Scholar
  15. Chen, J., Hopmans, J., Grismer, M.: Parameter estimation of two-fluid capillary pressure–saturation and permeability functions. Adv. Water Resour. 22(5), 479–493 (1999). CrossRefGoogle Scholar
  16. Chen, J., Hirasaki, G., Flaum, M.: NMR wettability indices: effect of OBM on wettability and NMR responses. J. Petrol Sci. Eng. 52(1), 161–171 (2006). CrossRefGoogle Scholar
  17. Christensen, M.: Impact of wettability on two-phase flow in oil/water/carbonate rock systems. PhD thesis, University of Aberdeen, Aberdeen, UK (2018)Google Scholar
  18. Christensen, M., Tanino, Y.: Enhanced permeability due to apparent oil/brine slippage in limestone and its dependence on wettability. Geophys. Res. Lett. 44(12), 6116–6123 (2017a). CrossRefGoogle Scholar
  19. Christensen, M., Tanino, Y.: Waterflood oil recovery from mixed-wet limestone: dependence on contact angle. Energy Fuel 31(2), 1529–1535 (2017b). CrossRefGoogle Scholar
  20. Christensen, M., Tanino, Y.: Residual oil saturation under mixed-wet conditions: optimal wettability revisited. In: Proc. International Symposium of the Society of Core Analysts, 27–30 Aug., Society of Core Analysts, Trondheim, Norway, SCA2018-011 (2018)Google Scholar
  21. Corey, A.T.: The interrelation between gas and oil relative permeabilities. Prod. Mon. 19, 3841 (1954)Google Scholar
  22. CYDAREX (2017) CYDAR-SCAL User-manual. CYDAREXGoogle Scholar
  23. Duchenne, S., de Loubens, R., Petitfrere, M., Joubert, T.: Modeling and simultaneous history-matching of multiple WAG coreflood experiments at reservoir conditions. In: Proc., Abu Dhabi International Petroleum Exhibition and Conference, 9–12 Nov., Society of Petroleum Engineers, Abu Dhabi, UAE, SPE-177531-MS. (2015)
  24. Dullien, F.A.L.: Porous media. Fluid Transport and Pore Structure, 2nd edn. Academic Press Inc, San Diego (1991)Google Scholar
  25. Dwarakanath, V., Jackson, R.E., Pope, G.A.: Influence of wettability on the recovery of NAPLs from alluvium. Environ. Sci. Technol. 36(2), 227–231 (2002). CrossRefGoogle Scholar
  26. Forbes, P.: Simple and accurate methods for converting centrifuge data into drainage and imbibition capillary pressure curves. Log Anal. 35(4), 31–53 (1994)Google Scholar
  27. Gharbi, O., Blunt, M.J.: The impact of wettability and connectivity on relative permeability in carbonates: a pore network modeling analysis. Water Resour. Res. 48(12) (2012).
  28. Hassenkam, T., Skovbjerg, L.L., Stipp, S.L.S.: Probing the intrinsically oil-wet surfaces of pores in north sea chalk at subpore resolution. PNAS 106(15), 6071–6076 (2009). CrossRefGoogle Scholar
  29. Honarpour, M., Koederitz, L.F., Harvey, A.H.: Empirical equations for estimating two-phase relative permeability in consolidated rock. J. Pet. Technol. 34(12), 2905–2908 (1982). CrossRefGoogle Scholar
  30. Huang, D.D., Honarpour, M.M.: Capillary end effects in coreflood calculations. J. Petrol. Sci. Eng. 19(1), 103–117 (1998). CrossRefGoogle Scholar
  31. Huang, D.M., Sendner, C., Horinek, D., Netz, R.R., Bocquet, L.: Water slippage versus contact angle: a quasiuniversal relationship. Phys. Rev. Lett. 101(22), 226,101 (2008). CrossRefGoogle Scholar
  32. Humphry, K.J., Suijkerbuijk, B.M.J.M., van der Linde, H.A., Pieterse, S.G.J., Masalmeh, S.K.: Impact of wettability on residual oil saturation and capillary desaturation curves. In: Proc., International Symposium of the Society of Core Analysts, 16–19 Sept., Society of Core Analysts, Napa Valley, CA, SCA2013-025 (2013)Google Scholar
  33. Iglauer, S., Ferno, M.A., Shearing, P., Blunt, M.J.: Comparison of residual oil cluster size distribution, morphology and saturation in oil-wet and water-wet sandstone. J. Colloid Interf. Sci. 375(1), 187–192 (2012). CrossRefGoogle Scholar
  34. Jadhunandan, P.P., Morrow, N.R.: Effect of wettability on waterflood recovery for crude-oil/brine/rock systems. SPE Reserv. Eng. 10(1), 40–46 (1995). CrossRefGoogle Scholar
  35. Jerauld, G.: Prudhoe bay gas/oil relative permeability. SPE Res. Eng. 12(1), 66–73 (1997). CrossRefGoogle Scholar
  36. Jerauld, G.R., Rathmell, J.J.: Wettability and relative permeability of Prudhoe Bay: a case study in mixed-wet reservoirs. SPE Reserv. Eng. 12(1), 58–65 (1997). CrossRefGoogle Scholar
  37. Joekar-Niasar, V., Hassanizadeh, S.M., Leijnse, A.: Insights into the relationships among capillary pressure, saturation, interfacial area and relative permeability using pore-network modeling. Transp. Porous Med. 74(2), 201–219 (2008). CrossRefGoogle Scholar
  38. Kennedy, H.T., Burja, E.O., Boykin, R.S.: An investigation of the effects of wettability on oil recovery by water flooding. J. Phys. Chem. 59(9), 867–869 (1955). CrossRefGoogle Scholar
  39. Kovscek, A.R., Wong, H., Radke, C.J.: A pore-level scenario for the development of mixed wettability in oil reservoirs. AIChE J. 39(6), 1072–1085 (1993). CrossRefGoogle Scholar
  40. Li, X., Fan, X., Askounis, A., Wu, K., Sefiane, K., Koutsos, V.: An experimental study on dynamic pore wettability. Chem. Eng. Sci. 104, 988–997 (2013). CrossRefGoogle Scholar
  41. Li, X., Fan, X., Brandani, S.: Difference in pore contact angle and the contact angle measured on a flat surface and in an open space. Chem. Eng. Sci. 117, 137–145 (2014). CrossRefGoogle Scholar
  42. Liu, Y., Buckley, J.S.: Evolution of wetting alteration by adsorption from crude oil. SPE Format. Eval. 12, 5–11 (1997). CrossRefGoogle Scholar
  43. Lomeland, F., Ebeltoft, E., Thomas, W.H.: A new versatile relative permeability correlation. In: Proc. International Symposium of the Society of Core Analysts, 21–25 Aug., Toronto, Canada, SCA2005-32 (2005)Google Scholar
  44. Lorentz, P.B., Donaldson, E.C., Thomas, R.D.: Use of centrifugal measurements of wettability to predict oil recovery. In: Technical Report, 7873, USBM, Bartlesville Energy Technology Center (1974)Google Scholar
  45. Manthey, S., Hassanizadeh, S.M., Helmig, R., Hilfer, R.: Dimensional analysis of two-phase flow including a rate-dependent capillary pressuresaturation relationship. Adv. Water Resour. 31(9), 1137–1150 (2008). CrossRefGoogle Scholar
  46. Masalmeh, S.K.: Impact of capillary forces on residual oil saturation and flooding experiments for mixed to oil-wet carbonate reservoirs. In: Proc. International Symposium of the Society of Core Analysts, 27–30 Aug., Aberdeen, UK, SCA2012-11 (2012)Google Scholar
  47. Min, Q., Duan, Y.Y., Wang, X.D., Liang, Z.P., Si, C.: Does macroscopic flow geometry influence wetting dynamic? J. Colloid Interf. Sci. 362(1), 221–227 (2011). CrossRefGoogle Scholar
  48. Morrow, N.R.: The effects of surface roughness on contact angle with special reference to petroleum recovery. J. Can. Petrol. Technol. 14(4), 42–53 (1975). CrossRefGoogle Scholar
  49. Morrow, N.R., Mason, G.: Recovery of oil by spontaneous imbibition. Curr. Opin. Colloid Inter. Sci. 6(4), 321–337 (2001). CrossRefGoogle Scholar
  50. Morrow, N.R., Cram, P.J., McCaffery, F.G.: Displacement studies in dolomite with wettability control by octanoic acid. Soc. Petrol. Eng. J. 13(4), 221–232 (1973). CrossRefGoogle Scholar
  51. Øren, P.E., Bakke, S., Arntzen, O.J.: Extending predictive capabilities to network models. Soc. Petrol. Eng. J. 3(4), 324–336 (1998). Google Scholar
  52. Owens, W.W., Archer, D.L.: The effect of rock wettability on oil-water relative permeability relationships. J. Petrol. Technol. 23(7), 873–878 (1971). CrossRefGoogle Scholar
  53. Powers, S.E., Tamblin, M.E.: Wettability of porous media after exposure to synthetic gasolines. J. Contam. Hydrol. 19(2), 105–125 (1995). CrossRefGoogle Scholar
  54. Powers, S.E., Anckner, W.H., Seacord, T.F.: Wettability of NAPL-contaminated sands. J. Environ. Eng. 122(10), 889–896 (1996). CrossRefGoogle Scholar
  55. Pugh, V.J., Thomas, D.C., Gupta, S.P.: Correlations of liquid and air permeabilities for use in reservoir engineering studies. Log Anal. 32, 493–497 (1991)Google Scholar
  56. Romanello, L.: Impact of wettability on relative permeability. Master’s thesis, University of Aberdeen, Aberdeen, UK (2015)Google Scholar
  57. Ryazanov, A.V., van Dijke, M.I.J., Sorbie, K.S.: Two-phase pore-network modelling: existence of oil layers during water invasion. Transp. Porous Med. 80, 79–99 (2009). CrossRefGoogle Scholar
  58. Ryazanov, A.V., van Dijke, M.I.J., Sorbie, K.S.: Pore-network prediction of residual oil saturation based on oil layer drainage in mixed-wet systems. In: Proc. SPE Improved Oil Recovery Symposium, 24–28 April, Society of Petroleum Engineers, Oklahoma, USA, (2010)
  59. Salathiel, R.A.: Oil recovery by surface film drainage in mixed-wettability rocks. Soc. Petrol. Eng. J. 25(10), 1216–1224 (1973). Google Scholar
  60. Scanziani, A., Singh, K., Blunt, M.J., Guadagnini, A.: Automatic method for estimation of in situ effective contact angle from X-ray micro tomography images of two-phase flow in porous media. J. Colloid Interf. Sci. 496, 51–59 (2017). CrossRefGoogle Scholar
  61. Singh, K., Bijeljic, B., Blunt, M.J.: Imaging of oil layers, curvature, and contact angle in a mixed-wet and a water-wet carbonate rock. Water Resour. Res. 52(3), 1716–1728 (2016). CrossRefGoogle Scholar
  62. Skjaeveland, S.M., Siqveland, L.M., Kjosavik, A., Thomas, W.L.H., Virnovsky, G.A.: Capillary pressure correlation for mixed-wet reservoirs. SPE Reserv. Eval. Eng. 3(1), 60–67 (2000). CrossRefGoogle Scholar
  63. Subbey, S., Monfared, H., Christie, M., Sambridge, M.: Quantifying uncertainty in flow functions derived from SCAL data. Transp. Porous Med. 65(2), 265–286 (2006). CrossRefGoogle Scholar
  64. Tanino, Y., Blunt, M.J.: Capillary trapping in sandstones and carbonates: dependence on pore structure. Water Resour. Res. 48(8), W08525 (2012). CrossRefGoogle Scholar
  65. Tanino, Y., Blunt, M.J.: Laboratory investigation of capillary trapping under mixed-wet conditions. Water Resour. Res. 49(7), 4311–4319 (2013). CrossRefGoogle Scholar
  66. Tanino, Y., Akamairo, B., Christensen, M., Bowden, S.A.: Impact of displacement rate on waterflood oil recovery under mixed-wet conditions. In: Proc. International Symposium of the Society of Core Analysts, Society of Core Analysts, St. John’s Newfoundland and Labrador, Canada, SCA-A031 (2015)Google Scholar
  67. Valvatne, P.H., Blunt, M.J.: Predictive pore-scale modeling of two-phase flow in mixed wet media. Water Resour. Res. 40(7), W07,406 (2004). CrossRefGoogle Scholar
  68. Wood, A.R., Wilcox, T.C., MacDonald, D.G., Flynn, J.J., Angert, P.F.: Determining effective residual oil saturation for mixed wettability reservoirs: Endicott Field, Alaska. In: Proc. SPE Annual Technical Conference and Exhibition, 6–9 Oct., Society of Petroleum Engineers, Dallas, Texas, SPE 22903 (1991)
  69. Wu, Y., Shuler, P.J., Blanco, M., Tang, Y., Goddard III, W.A.: An experimental study of wetting behavior and surfactant EOR in carbonates with model compounds. Soc. Petrol. Eng. J. 13(1), 26–34 (2008). Google Scholar
  70. Yaralidarani, M., Shahverdi, H.: Co-estimation of saturation functions (kr and Pc) from unsteady-state core-flood experiment in tight carbonate rocks. J. Petrol. Explor. Prod. Technol. 8(4), 1559–1572 (2018). CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.School of EngineeringUniversity of AberdeenAberdeenUK

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