Skip to main content
SpringerLink
Log in

Modeling wetting-phase relative permeability hysteresis based on subphase evolution

  • Original Paper
  • Published:
Computational Geosciences Aims and scope Submit manuscript

Abstract

A recently introduced subphase framework for modeling the nonwetting phase relative permeability is extended to the wetting phase. Within this framework, the wetting phase is divided into four subphases, which are distinguished by their connectivity; backbone, dendritic, isolated and corner-film subphases. The subphase saturations evolve according to inter-subphase volume transfer terms, which require modeling. An advantage of distinguishing the subphases is that wetting phase relative permeability relations as functions of these constituent subphases can be developed. In order to develop models for the inter-subphase volume transfer and the wetting phase relative permeability in a strongly wetted system, quasi-static flow simulations in pore networks were conducted to analyze the evolution of the wetting subphases during drainage and imbibition. The simulation results suggest that hysteresis trends apparent in experimentally obtained wetting phase relative permeability curves for Berea sandstone may be explained by accounting for corner-film flow.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Akbarabadi, M., Piri, M.: Relative permeability hysteresis and capillary trapping characteristics of supercritical co 2/brine systems: an experimental study at reservoir conditions. Adv. Water Resour. 52, 190–206 (2013)

    Article  Google Scholar 

  2. 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), 247–259 (2003)

    Article  Google Scholar 

  3. Arns, J.Y., Robins, V., Sheppard, A.P., Sok, R.M., Pinczewski, W., Knackstedt, M.A.: Effect of network topology on relative permeability. Transp. Porous Media 55(1), 21–46 (2004)

    Article  Google Scholar 

  4. Bakke, S., ØRen, P.: 3-d pore-scale modelling of sandstones and flow simulations in the pore networks. SPE J. 2(2), 136–149 (1997)

    Article  Google Scholar 

  5. Bear, J.: Dynamics of fluids in porous media. In: Dynamics of Fluids in Porous Media. American Elsevier (1967)

  6. Bennion, B., Bachu, S., et al.: Relative permeability characteristics for supercritical Co2 displacing water in a variety of potential sequestration zones. In: SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers (2005)

  7. Benson, S., Pini, R., Reynolds, C., Krevor, S.: Relative permeability analysis to describe multi-phase flow in co2 storage reservoirs Global CCS Institute (2013)

  8. Berg, S., Armstrong, R., Georgiadis, A., Ott, H., Schwing, A., Neiteler, R., Brussee, N., Makurat, A., Rucker, M., Leu, L.: Onset of oil mobilization and nonwetting-phase cluster-size distribution. Petrophysics 56(01), 15–22 (2015)

    Google Scholar 

  9. Blunt, M.J.: Effects of heterogeneity and wetting on relative permeability using pore level modeling. SPE J. 2(01), 70–87 (1997)

    Article  Google Scholar 

  10. Blunt, M.J.: Flow in porous media - pore-network models and multiphase flow. Current opinion in colloid & interface science 6(3), 197–207 (2001)

    Article  Google Scholar 

  11. Blunt, M.J., Jackson, M.D., Piri, M., Valvatne, P.H.: Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow. Adv. Water Resour. 25(8), 1069–1089 (2002)

    Article  Google Scholar 

  12. Blunt, M.J., Jackson, M.D., Piri, M., Valvatne, P.H.: Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow. Adv. Water Resour. 25(8), 1069–1089 (2002)

    Article  Google Scholar 

  13. Carlson, F.: Simulation of relative permeability hysteresis to the nonwetting phase. In: SPE Annual Technical Conference and Exhibition (1981)

  14. Constantinides, G.N., Payatakes, A.C.: Network simulation of steady-state two-phase flow in consoliyeard porous media. AIChE J 42(2), 369–382 (1996)

    Article  Google Scholar 

  15. Dias, M.M., Payatakes, A.C.: Network models for two-phase flow in porous media part 1. Immiscible microdisplacement of non-wetting fluids. J. Fluid Mech. 164, 305–336 (1986)

    Article  Google Scholar 

  16. Fatt, I.: The network model of porous media (1956)

  17. Gunstensen, A.K., Rothman, D.H.: Lattice-boltzmann studies of immiscible two-phase flow through porous media. Journal of Geophysical Research: Solid Earth 98(B4), 6431–6441 (1993)

    Article  Google Scholar 

  18. Herring, A.L., Harper, E.J., Andersson, L., Sheppard, A., Bay, B.K., Wildenschild, D.: Effect of fluid topology on residual nonwetting phase trapping: implications for geologic co 2 sequestration. Adv. Water Resour. 62, 47–58 (2013)

    Article  Google Scholar 

  19. Hilfer, R.: Macroscopic capillarity without a constitutive capillary pressure function. Physica A: Statistical Mechanics and its Applications 371(2), 209–225 (2006)

    Article  Google Scholar 

  20. Hilfer, R., ØRen, P.: Dimensional analysis of pore scale and field scale immiscible displacement. Transp. Porous Media 22(1), 53–72 (1996)

    Article  Google Scholar 

  21. Huang, H., Meakin, P., Liu, M.: Computer simulation of two-phase immiscible fluid motion in unsaturated complex fractures using a volume of fluid method. Water Resour. Res. 41(12) (2005)

  22. Idowu, N.A., Blunt, M.J.: Pore-scale modelling of rate effects in waterflooding. Transp. Porous Media 83(1), 151–169 (2010)

    Article  Google Scholar 

  23. Jerauld, G., Salter, S.: The effect of pore-structure on hysteresis in relative permeability and capillary pressure: pore-level modeling. Transp. Porous Media 5(2), 103–151 (1990)

    Article  Google Scholar 

  24. Joekar-Niasar, V., Hassanizadeh, S., Dahle, H.: Non-equilibrium effects in capillarity and interfacial area in two-phase flow: dynamic pore-network modelling. J. Fluid Mech. 655(1), 38–71 (2010)

    Article  Google Scholar 

  25. Joekar-Niasar, V., Hassanizadeh, S.M.: Uniqueness of specific interfacial area–capillary pressure–saturation relationship under non-equilibrium conditions in two-phase porous media flow. Transp. Porous Media 94(2), 465–486 (2012)

    Article  Google Scholar 

  26. Khayrat, K.: Modeling hysteresis for two-phase flow in porous media: from micro to macro scale. Ph.D. thesis, Dissertation, ETH-zürich, 2016, Nr.23273 (2016)

  27. Khayrat, K., Jenny, P.: Subphase approach to model hysteretic two-phase flow in porous media. Transp. Porous Media 111(1), 1–25 (2016)

    Article  Google Scholar 

  28. Killough, J.: Reservoir simulation with history-dependent saturation functions. Old SPE J 16(1), 37–48 (1976)

    Google Scholar 

  29. Land, C.S.: Calculation of imbibition relative permeability for two-and three-phase flow from rock properties. Soc. Pet. Eng. J 8(02), 149–156 (1968)

    Article  Google Scholar 

  30. Lenormand, R., Zarcone, C., Sarr, A.: Mechanisms of the displacement of one fluid by another in a network of capillary ducts. J. Fluid Mech. 135, 337–353 (1983)

    Article  Google Scholar 

  31. Li, X., Zhang, Y., Wang, X., Ge, W.: Gpu-based numerical simulation of multi-phase flow in porous media using multiple-relaxation-time lattice boltzmann method. Chem. Eng. Sci. 102, 209–219 (2013)

    Article  Google Scholar 

  32. Moebius, F., Or, D.: Inertial forces affect fluid front displacement dynamics in a pore-throat network model. Phys. Rev. E. 90(2), 023–019 (2014)

    Article  Google Scholar 

  33. Oak, M., Baker, L., Thomas, D.: Three-phase relative permeability of berea sandstone. J. Petrol. Tech. 42(08), 1–054 (1990)

    Article  Google Scholar 

  34. Øren, P., Bakke, S., Arntzen, O.: Extending predictive capabilities to network models. SPE J 3, 324–36 (1998)

    Article  Google Scholar 

  35. Raeini, A.Q., Blunt, M.J., Bijeljic, B.: Direct simulations of two-phase flow on micro-ct images of porous media and upscaling of pore-scale forces. Adv. Water Resour. 74, 116–126 (2014)

    Article  Google Scholar 

  36. Ransohoff, T., Radke, C.: Laminar flow of a wetting liquid along the corners of a predominantly gas-occupied noncircular pore. J. Colloid Interface Sci. 121(2), 392–401 (1988)

    Article  Google Scholar 

  37. Reeves, P.C., Celia, M.A.: A functional relationship between capillary pressure, saturation, and interfacial area as revealed by a pore-scale network model. Water Resour. Res. 32(8), 2345–2358 (1996)

    Article  Google Scholar 

  38. Sahimi, M., Imdakm, A.: The effect of morphological disorder on hydrodynamic dispersion in flow through porous media. J. Phys. A Math. Gen. 21(19), 3833 (1988)

    Article  Google Scholar 

  39. Schlüter, S., Berg, S., Rücker, M., Armstrong, R., Vogel, H.J., Hilfer, R., Wildenschild, D.: Pore-scale displacement mechanisms as a source of hysteresis for two-phase flow in porous media. Water Resources Research (2016)

  40. 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 Resources Research (2016)

  41. Tokunaga, T.K.: Physicochemical controls on adsorbed water film thickness in unsaturated geological media. Water Resour. Res. 47(8) (2011)

  42. Tomin, P., Lunati, I.: Hybrid multiscale finite volume method for two-phase flow in porous media. J. Comput. Phys. 250, 293–307 (2013)

    Article  Google Scholar 

  43. Tsakiroglou, C., Aggelopoulos, C., Terzi, K., Avraam, D., Valavanides, M.: Steady-state two-phase relative permeability functions of porous media: a revisit. Int. J. Multiphase Flow 73, 34–42 (2015)

    Article  Google Scholar 

  44. Wilkinson, D., Willemsen, J.F.: Invasion percolation: a new form of percolation theory. J. Phys. A Math. Gen. 16(14), 3365 (1983)

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to acknowledge Soheil Esmaeilzadeh for conducting preliminary pore-network simulations of the wetting subphase saturations during a semester project at ETH Zurich. The authors would also like to thank Total SA for financial support of this work.

Author information

Authors and Affiliations

  1. ETH Zurich, Zurich, Switzerland

    Karim Khayrat & Patrick Jenny

Authors
  1. Karim Khayrat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Patrick Jenny
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Karim Khayrat.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khayrat, K., Jenny, P. Modeling wetting-phase relative permeability hysteresis based on subphase evolution. Comput Geosci 21, 863–875 (2017). https://doi.org/10.1007/s10596-017-9655-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10596-017-9655-y

Keywords

Search

Navigation