Transport in Porous Media

, Volume 89, Issue 3, pp 357–382 | Cite as

Network Modeling of EOR Processes: A Combined Invasion Percolation and Dynamic Model for Mobilization of Trapped Oil

  • S. F. BolandtabaEmail author
  • A. Skauge
Open Access


A novel concept for modeling pore-scale phenomena included in several enhanced oil recovery (EOR) methods is presented. The approach combines a quasi-static invasion percolation model with a single-phase dynamic transport model in order to integrate mechanistic chemical oil mobilization methods. A framework is proposed that incorporates mobilization of capillary trapped oil. We show how double displacement of reservoir fluids can contribute to mobilize oil that are capillary trapped after waterflooding. In particular, we elaborate how the physics of colloidal dispersion gels (CDG) or linked polymer solutions (LPS) is implemented. The linked polymer solutions consist of low concentration partially hydrolyzed polyacrylamide polymer crosslinked with aluminum citrate. Laboratory core floods have shown demonstrated increased oil recovery by injection of linked polymer solution systems. LPS consist of roughly spherical particles with sizes in the nanometer range (50–150 nm). The LPS process involve mechanisms such as change in rheological properties effect, adsorption and entrapment processes that can lead to a microscopic diversion and mobilization of waterflood trapped oil. The purpose is to model the physical processes occurring on pore scale during injection of linked polymer solutions. A sensitivity study has also been performed on trapped oil saturation with respect to wettability status to analyze the efficiency of LPS on different wettability conditions. The network modeling results suggest that weakly wet reservoirs are more suitable candidates for performing linked polymer solution injection.


Network model Trapped oil mobilization EOR processes Linked polymer solution Colloidal dispersion gel 

List of Symbols


Langmuir adsorption coefficient (cm3/g)


Constant coefficients (cm3/g)


Langmuir adsorption coefficient (cm3/g)


Critical concentration for log jamming mechanism (g/cm3)


Polymer concentration (g/cm3)


Critical concentration for straining mechanism (g/cm3)


Fractional flow rate (–)


Absolute pore element conductance


Water corner layer conductance


Bonds conductance


Water bulk conductance

i, j, k

Bonds index (–)


Capillary number (–)


Pressure (Pa)


Bonds flow rate (m3/s)


Flow rate (m3/s)


Bond radius (μm)


Polymer effective hydrodynamic radius (μm)


Log-jamming curve increase (–)


Oil-filled fractional in partially filled bond


Viscosity (Pa.s)


Water viscosity (Pa.s)


Interfacial tension (N/m)



The authors would like to acknowledge the PETROMAKS program at the Norwegian Research Council and Statoil for financial support to our EOR research.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


  1. Aarra, M.G., Bjørsvik, M., Høiland, H., Skodvin, T., Skauge, A.: Linked polymer solutions for improved oil recovery by waterflooding. In: 13th European Symposium in Improved Oil Recovery. 25–27 April. SPE. Budapest, Hungary (2005)Google Scholar
  2. Al-Gharbi, M.S., Blunt, M.J.: Dynamic network modelling of two-phase drainage in porous media. Phys. Rev. E 71, 016308 (2005)Google Scholar
  3. Avraam D.G., Payatakes A.C.: Flow mechanisms, relative permeabilities and coupling effects in steady-state two-phase flow in porous media. The case of strong wettability. Ind. Eng. Chem. Res. 38, 778–786 (1999)CrossRefGoogle Scholar
  4. Berkowits B., Balberg I.: Percolation theory and its application to groundwater hydrology. Water Res. 29, 775–794 (1993)CrossRefGoogle Scholar
  5. Bjørsvik, M.: Physico-chemistry characterization of colloidal dispersion gels. PhD thesis, University of Bergen, Norway (2008)Google Scholar
  6. Bjørsvik, M., Høiland, H., Skauge, A.: Formation of colloidal dispersion gels from aqueous polyacrylamide solutions. Colloids Surfaces A (2007). doi: 10.1016/j.colsurfa.2007.11.025
  7. Blunt M., King M.J., Scher H.: Simulation and theory of two-phase flow in porous media. Phys. Rev. A 46(12), 7680–7699 (1992)CrossRefGoogle Scholar
  8. 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, 1069–1089 (2002)CrossRefGoogle Scholar
  9. Bolandtaba, S.F., Skauge, A., Mackay, E.: Pore-scale modeling of linked polymer solution (LPS)—a new EOR process. In: EAGE IOR Conference, Paris, 27–29 April (2009)Google Scholar
  10. Broadbent S.R., Hammersley J.M.: Percolation processes, I and II. Proc. Camb. Philos. Soc. 53, 629–645 (1957)CrossRefGoogle Scholar
  11. Chang H.L., Sui X., Xiao L., Guo Z., Yao Y., Xiao Y., Chen G., Song K., Mack J.C.: Successful field pilot of in-depth colloidal dispersion gel (CDG) technology in daqing oil field. SPE Res. Eval. Eng. 9(5), 664–673 (2006)Google Scholar
  12. Chatzis I., Dullien F.A.L.: Modelling pore structures by 2-D and 3-D networks with application to sandstones. J. Can. Petrol. Technol. 16, 97–108 (1977)Google Scholar
  13. Constantinides G.N., Payatakes A.C.: Network simulation of steady-state two-phase flow in consolidated porous media. AIChE J. 42, 369–382 (1996)CrossRefGoogle Scholar
  14. 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 (1986a)CrossRefGoogle Scholar
  15. Dias M.M., Payatakes A.C.: Network models for two-phase flow in porous media. Part 2. Motion of oil ganglia. J. Fluid Mech. 164, 337–358 (1986b)CrossRefGoogle Scholar
  16. Dias, D., Somaruga, C., Norman, C., Romero, J.: Colloidal dispersion gels improve oil recovery in a heterogeneous Argentina waterflood. SPE 113320-MS-P. In: SPE/DOE Improved Oil Recovery Symposium, Tulsa, Oklahoma, USA, 19–23 April (2008)Google Scholar
  17. Dixit A.B., Mc Dougall S.R., Sorbie K.S., Buckley J.S.: Pore-scale modeling of wettability effects and their influence on oil recovery. SPE Reserv. Eval. Eng. 2, 25–36 (1999)Google Scholar
  18. Dominguez, J.G., Willhite, G.P.: Retention and flow characteristics of polymer solutions in porous media. Soc. Pet. Eng. J. April, 111–121 (1977)Google Scholar
  19. Dong, H., Puhua, Y., Weili, L.Y., Qingxia, L., Shaozi, C., Zhengyu, S., Jinxing, T., Xiaolei.: Flow mechanism investigation and field practice for low concentration flowing gel. In: SPE 50929 SPE International Conference and Exhibition. Beijing, China 2–6 November (1998)Google Scholar
  20. Fatt I.: The network model of porous media. I. Capillary pressure characteristics. Trans. AIME 207, 144–159 (1956a)Google Scholar
  21. Fatt I.: The network model of porous media. II. Dynamic properties of a single size tube network. Trans. AIME 207, 160–163 (1956b)Google Scholar
  22. Fatt I.: The network model of porous media. III. Dynamic properties of networks with tube radius distribution. Trans. AIME 207, 164–181 (1956c)Google Scholar
  23. Fenwick D.H., Blunt M.J.: Network modeling of three-phase flow in porous media. SPE J. 3, 86–97 (1998)Google Scholar
  24. Flory P.J.: Principles of Polymer Chemistry. Cornel University Press, Ithaca (1953)Google Scholar
  25. Gunstensen A.K., Rothman D.H.: Lattice Boltzmann studies of immiscible two-phase flow through porous media. J. Geophys. Res. 98(B4), 6431–6441 (1993)CrossRefGoogle Scholar
  26. Heiba A.A., Sahimi M., Scriven L.E., Davis H.T.: Percolation theory of two-phase relative permeability. SPE Reserv. Eng. 7, 123–132 (1992)Google Scholar
  27. Hou J.: Network modeling of residual oil displacement after polymer flooding. J. Pet. Sci. Eng. 59(2007), 321–332 (2007)CrossRefGoogle Scholar
  28. Hughes R.G., Blunt M.J.: Pore-scale modeling of multiphase flow in fractures and matrix/fracture transfer. SPE J. 6(21), 26–36 (2001)Google Scholar
  29. Huh, C., Lange, E.A., Cannella, W.J.: Polymer retention in porous media. SPE 20235. In: SPE/DOE Enhanced Oil Recovery Symposium. Tulsa, Oklahoma, USA, 22–25 (1990)Google Scholar
  30. Jerauld G.R., Salter S.J.: Effect of pore-structure on hysteresis in relative permeability and capillary pressure: pore-level modeling. Transp. Porous Media 5, 103–151 (1990)CrossRefGoogle Scholar
  31. Joekar-niasar, S.M., Hassanizadeh, H.K., Dahle, H.K.: Non-equilibrium effects in capillarity and interfacial area in two-phase flow: dynamic pore-network modelling. J. Fluid Mech. (2010). doi: 10.1017/S0022112010000704
  32. Koplik J., Lasseter T.J.: Two-phase flow in random network models of porous media. Soc. Petrol. Engng. J. 25, 89–100 (1985)Google Scholar
  33. Kovscek A.R., Wong H., Radke C.J.: Scenario for the development of mixed wettability in oil reservoirs. AIChE J. 39(6), 1072–1085 (1993)CrossRefGoogle Scholar
  34. Lenormand, R., Zarcone, C.: Role of roughness and edges during imbibition in square capillaries. In: 59th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers of AIME, SPE 13264. Houston, Texas (1984)Google Scholar
  35. Mack, J.C., Smith, J.E.: In-depth colloidal dispersion gels improve oil recovery efficiency. SPE/DOE 27780. In: SPE/DOE 9th Symposium on Improved Recovery. Tulsa, Oklahoma, 17–20 April (1994)Google Scholar
  36. Mogensen K., Stenby E.H.: A dynamic two-phase pore-scale model for imbibition. Transp. Porous Media 32, 299–327 (1998)CrossRefGoogle Scholar
  37. Mohanty, K.K., Salter, S.J.: Multiphase flow in porous media pore level modeling. Paper SPE 11018. In: SPE Annual Technical Conference And Exhibition. New Orleans, Louisiana, 26–29 September (1982)Google Scholar
  38. Morrow N.R.: Effects of surface roughness on contact angle with special reference to petroleum recovery. J. Can. Pet. Technol. 14, 42–53 (1975)Google Scholar
  39. Nguyen, V., Sheppard, A, Pinczewski, W, Knackstedt, M.: A dynamic network model for imbibition, Society of Petroleum Engineers International Petroleum Conference, Puebla, Mexico, November 9, SPE Paper Number 90365 (2004)Google Scholar
  40. Øren P.E., Bakke S., Arntzen O.J.: Extending predictive capabilities to network models. SPE J. 3, 324–336 (1998)Google Scholar
  41. Osterloh, W.T., Law, E.J.: Polymer transport and rheological properties for polymer flooding in the North Sea Captain Field. SPE 39694. In: SPE/DOE Enhanced Oil Recovery Symposium, Tulsa, Oklahoma, USA, 19–22 April (1998)Google Scholar
  42. Patzek T.W.: Fundamentals of Multiphase Flow in Porous Media, 1st edn. Berkeley, U.C. Berkeley (1998)Google Scholar
  43. Payatakes A.C.: Dynamics of oil ganglia during immiscible displacement in water-wet porous media. Ann. Rev. Fluid Mech. 14, 365–393 (1982)CrossRefGoogle Scholar
  44. Ranganathan, R., Lewis, R., McCool, C.S., Green, D.W., Willhite, G.P.: Experimental study of the gelation behavior of a polyacrylamide/aluminum citrate colloidal-dispersion gel system. SPE J. December, 337–342 (1998)Google Scholar
  45. Rocha, C.A., Green, D.W., Willhite, G.P., Michnick, M.J.: An experimental study of the interactions of aluminum citrate solutions and silica sand. SPE 18503. In: SPE International Symposium on Oilfield Chemistry. Houston, TX, February 8–10 (1989)Google Scholar
  46. Ryazanov A.V., van Dijke M.I.J., Sorbie K.S.: Two-phase pore-network modeling: existence of oil layers during water invasion. Transp. Porous Media 80, 79–99 (2009)CrossRefGoogle Scholar
  47. Porter M.L., Schaap M.G., Wildenschild D.: Simulations of the capillary pressure–saturation–interfacial area relationship for porous media. Adv. Water Resour. 32(11), 1632–1640 (2009)CrossRefGoogle Scholar
  48. Sahimi M.: And Transport in Porous Media and Fractured Rock—From Classical Methods to Modern Approaches. Weinheim, VCH (1995)Google Scholar
  49. Salter, S.J., Mohanty, K.K.: Multiphase flow in porous media: 1. Macroscopic observations and modeling. SPE 11017, Society of Petroleum Engineers. The paper was presented at the 57th Annual Fall Technical Conference and Exhibition of the Society of Petroleum Engineers, New Orleans, LA, Sept. 26–29.(1982)Google Scholar
  50. Savins J.: Non-Newtonian flow through porous media. Ind. Eng. Chem. 61(10), 18–47 (1969)CrossRefGoogle Scholar
  51. Shah, C.: Flow and immiscible displacement of power-law fluids and bingham plastics in porous media. PhD Thesis, University of Southern California, USA (1994)Google Scholar
  52. Shiyi, Y., Dong, H., Qiang, W., Hua, Y.: Numerical simulator for the combination process of profile control and polymer flooding. SPE 64792. In: SPE International Oil and Gas Conference and Exhibition in China. Beijing, China, 7–10 November (2000)Google Scholar
  53. Singh M., Mohanty K.K: Review: dynamic modeling of drainage through three-dimensional porous materials. Chem. Eng. Sci. 8, 1–18 (2003)Google Scholar
  54. Skauge, A., Ottesen, B.: A summary of experimentally derived relative permeability and residual saturation on north sea reservoir cores. In: International Symposium of the SCA. Monterey, CA, September (2002)Google Scholar
  55. Sorbie K.S.: Polymer-Improved Oil Recovery. Blackie and Son, Bishopbriggs, Glasgow (1991)Google Scholar
  56. Spildo, K., Skauge, A., Aarra, M.G., Tweheyo, M.T.: A new polymer application for north sea reservoirs. SPE 113460. In: SPE/DOE Improved Oil Recovery Symposium. Tulsa, Oklahoma, USA, 20–23 April 2008 (2008)Google Scholar
  57. Szabo M.T.: An evaluation of water-soluble polymers for secondary oil recovery—part 1 and 2. J. Pet. Technol. 31(5), 553–570 (1979)Google Scholar
  58. Van der Marck S.C., Matsuura T., Glas J.: Viscous and capillary pressures during drainage: network simulations and experiments. Phys. Rev. E 56, 5675–5687 (1997)CrossRefGoogle Scholar
  59. Valvatne, P.H., Blunt, M.J.: Predictive pore-scale modelling of two-phase flow in mixed wet media. Water Resour. Res. 40, W07406 (2004)Google Scholar
  60. Valvatne P., Piri M., Lopez X., Blunt M.J.: Predictive pore-scale modeling of single and multiphase flow. Transp. Porous Media 55, 71–89 (2004)CrossRefGoogle Scholar
  61. Van Brakel J.: Pore space models for transport phenomena in porous media: review and evaluation with special emphasis on capillary liquid transport. Powder Technol. 11, 205–236 (1975)CrossRefGoogle Scholar
  62. Van Kats F.M., Egberts P.J.P.: Simulation of three-phase displacement mechanisms using a 2D Lattice–Boltzmann model. Transp. Porous Media 37(1), 55–68 (1999)CrossRefGoogle Scholar
  63. Wilkinson D., Willemsen J.F.: Invasion percolation: a new form of percolation theory. J. Phys. A 16, 3365–3376 (1983)CrossRefGoogle Scholar

Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Center for Integrated Petroleum Research (CIPR)BergenNorway

Personalised recommendations