Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Modeling and Experimental Validation of Rheological Transition During Foam Flow in Porous Media


Flow of nitrogen foam stabilized by alpha olefin sulfonate (C14-16 AOS) was studied in a natural sandstone porous media using X-ray Computed Tomography. Foam was generated by a simultaneous injection of gas and surfactant solution into a porous medium initially saturated with the surfactant solution. It was found that the foam undergoes a transition from a weak to a strong state at a characteristic gas saturation of Sgc = 0.75 ± 0.02. This transition coincided with a substantial reduction in foam mobility by a two-order of magnitude and also with a large reduction in overall water saturation to as low as 0.10 ± 0.02. Foam mobility transition was interpreted by the surge of yield stress as gas saturation exceeded the Sgc. We proposed a simple power-law functional relationship between yield stress and gas saturation. The proposed rheological model captured successfully the mobility transition of foams stabilized by different surfactant concentrations and for different core lengths.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11


  1. Apaydin, O.G., Kovscek, A.R.: Transient foam flow in homogeneous porous media: surfactant concentration and capillary end effects. Transp. Porous Media 43(3), 511–536 (2001)

  2. Ashoori, E., Marchesin D., Rossen, W.R.: Multiple foam states and long-distance foam propagation in EOR displacements. In: SPE 154024, SPE Improved Oil Recovery Symposium, Tulsa, Oklahoma, USA, 14–18 Apr 2012

  3. Balan, H.O., Balhoff, M.T., Nguyen, Q.P., Rossen, W.R.: Network modeling of gas trapping and mobility in foam enhanced oil recovery. Energy Fuels 25(9), 3974–3987 (2011)

  4. Behenna, F.R.: Acid diversion from an undamaged to a damaged core using multiple foam slugs. In: SPE 30121, SPE European Formation Damage Conference, The Hague, Netherlands, 15–16 May 1995

  5. Bertin, H.J., Quintard, M.Y., Castanier, L.M.: Development of a bubble-population correlation for foam-flow modeling in porous media. SPE J. 3(4), 356–362 (1998)

  6. Chen, M., Yortsos, Y.C., Rossen, W.R.: Insights on foam generation in porous media from pore-network studies. Colloids Surf. A: Physicochem. Eng. Asp. 256(2–3), 181–189 (2005)

  7. Chen, Q., Gerritsen, M.G., Kovscek, A.R.: Modeling foam displacement with the local-equilibrium approximation: theory and experimental verification. SPE J. 15(1), 171–183 (2010)

  8. Cohen, D.G., Patzek, T.W., Radke, C.J.: Onset of mobilization and the fraction of trapped foam in porous media. Transp. Porous Media 28(3), 253–284 (1997)

  9. Exerowa, E., Kruglyakov, P.M.: Foam and Foam Films. Elsevier Science, Amsterdam (1998)

  10. Falls, A.H., Hirasaki, G.J., Patzek, T.W., Gauglitz, D.A., Miller, D.D., Ratulowski, T.: Development of a mechanistic foam simulator: the population balance and generation by snap-off. SPE Reserv. Eng. 3(3), 884–892 (1988)

  11. Falls, A., Musters, J.J., Ratulowski, J.: The apparent viscosity of foams in homogeneous bead packs. SPE Reserv. Eng. 4(2), 155–164 (1989)

  12. Friedmann, F., Chen, W.H., Gauglitz, P.A.: Experimental and simulation study of high temperature foam displacement in porous media. SPE Reserv. Eng. 6(1), 37–45 (1991)

  13. Friedmann, F., Smith, M.E., Guice, W.R., Gump, J.M., Nelson, D.G.: Steam-foam mechanistic field trial in the midway-sunset field. SPE Reserv. Eng. 9(4), 297–304 (1994)

  14. Gardiner, B.S., Dlugogorski, B.Z., Jameson, G.J., Chhabra, R.P.: Yield stress measurements of aqueous foams in the dry limit. J. Rheol. 42(6), 1437–1450 (1998)

  15. Gauglitz, P.A., Friedmann, F., Kam, S.I., Rossen, W.R.: Foam generation in homogeneous porous media. Chem. Eng. Sci. 57, 4037–4052 (2002)

  16. Hanssen, J.E., Dalland, M.: Gas blocking foams. In: Schramm, L.L. (ed.) Foams: Fundamentals and Applications in the Petroleum Industry. American Chemical Society, Washington (1994)

  17. Kam, S.I.: Improved mechanistic foam simulation with foam catastrophe theory. Colloids and Surf. A: Physicochem. Eng. Asp. 318(1–3), 62–77 (2008)

  18. Kam, S.I., Rossen, W.R.: A model for foam generation in homogeneous porous media. SPE J. 8(4), 417–425 (2003)

  19. Khan, S.A., Schnepper, C.A., Armstrong, R.C.: Foam rheology: III. Measurement of shear flow properties. J. Rheol. 32(1), 69–92 (1988)

  20. Kibodeaux, K.R., Zeilinger, S.C., Rossen, W.R.: Sensitivity study of foam diversion processes for matrix acidization. In: SPE 28550, SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 25–28 Sept 1994

  21. Kovscek, A.R., Radke, C.J.: Fundamentals of foam transport in porous media. In: Schramm, L.L. (ed.) Foams: Fundamentals and Applications in the Petroleum Industry. American Chemical Society, Washington (1994)

  22. Kovscek, A.R., Patzek, T.W., Radke, C.J.: Mechanistic foam flow simulation in heterogeneous and multidimensional porous media. SPE J. 2(4), 511–526 (1997)

  23. Mason, T.G., Bibette, J., Weitz, D.A.: Yielding and flow of monodisperse emulsions. Colloid Interface Sci. 179(2), 439–448 (1996)

  24. Mees, F., Swennen, R., Van Geet, M., Jacobs, P.: Application of X-ray computed tomography in the geoscience. Geol. Soc. Spec. Publ. Lond. 215, 1–6 (2003)

  25. Myers, T.J., Radke, C.J.: Transient foam displacement in the presence of residual oil: experiment and simulation using a population-balance model. Ind. Eng. Chem. Res. 39(8), 2725–2741 (2000)

  26. Nguyen, Q.P., Currie, P.K., Zitha, P.L.J.: Determination of foam induced fluid partitioning in porous media using X-ray computed tomography. In: SPE 80245, SPE International Symposium on Oilfield Chemistry, Houston, Texas, USA, 5–8 Feb 2003

  27. Nguyen, Q.P., Currie, P.K., Zitha, P.L.J.: Motion of foam film in diverging-converging channel. J. Colloid Interface Sci. 271(2), 473–484 (2004)

  28. Pal, R.: Yield stress and viscoelastic properties of high internal phase ratio emulsions. Colloid Polym. Sci. 277(6), 583–588 (1999)

  29. Patzek, T.W.: Description of foam flow in porous media by the population balance method. In: Smith, D.H. (ed.) Surfactant-Based Mobility Control Progress in Miscible-Flood Enhanced Oil Recovery. American Chemical Society, Washington (1988)

  30. Princen, H.M., Kiss, A.D.: Rheology of foams and highly concentrated emulsions: IV. An experimental study of the shear viscosity and yield stress of concentrated emulsions. Colloid Interface Sci. 128(1), 176–187 (1989)

  31. Quintero, C.G., Noïk, C., Dalmazzone, C., Grossiord, J.-L.: Modelling and characterisation of diluted and concentrated water-in-crude oil emulsions: comparison with classical behaviour. Rheol. Acta 47(4), 417–424 (2008)

  32. Ranshoff, T.C., Radke, C.J.: Mechanisms of foam generation in glass-bead packs. SPE Reserv. Eng. 3(2), 573–585 (1988)

  33. Robert, J.A., Mack, M.G.: Foam diversion modeling and simulation. SPR Prod. Facil. 12(2), 123–127 (1997)

  34. Rossen, W.R.: Theories of foam mobilization pressure gradient. In: SPE 17358, SPE/DOE Enhanced Oil Recovery Symposium, Tulsa, OK, 17–20 Apr 1988

  35. Rossen, W.R.: Minimum pressure gradient for foam flow in porous media: effect of interactions with stationary lamellae. Colloid Interface Sci. 139(2), 457–468 (1990)

  36. Rossen, W.R.: Foams in enhanced oil recovery. In: Prud’homme, R.K., Khan, S. (eds.) Foams: Theory, Measurements and Applications. Marcel Dekker, New York (1996)

  37. Rossen, W.R.: Foam generation at layer boundaries in porous media. SPE J. 4(4), 409–412 (1999)

  38. Rossen, W.R., Gauglitz, P.A.: Percolation theory of creation and mobilization of foam in porous media. AIChE J. 36(8), 1176–1188 (1990)

  39. Rossen, W.R., Wang, M.-W.: Modeling foams for acid diversion. SPE J. 4(2), 92–100 (1999)

  40. Rouyer, F., Cohen-Addad, S., Höhler, R.: Is the yield stress of aqueous foam a well-defined quantity? Colloids Surf. A: Physicochem. Eng. Asp. 263(1–3), 111–116 (2005)

  41. Saint-Jalmes, A., Durian, D.J.: Vanishing elasticity for wet foams: equivalence with emulsions and role of polydispersity. J. Rheol. 43(6), 1411–1422 (1999)

  42. Schramm, L.L., Wassmuth, F.: Foams: basic principles. In: Schramm, L.L. (ed.) Foams: Fundamentals and Applications in the Petroleum Industry. American Chemical Society, Washington (1994)

  43. Shah, S.Y., Wolf, K.H., Pilus, R.M., Rossen, W.R.: Foam generation by capillary snap-off in flow across a sharp permeability transition. In: SPE Improved Oil Recovery Conference, 14–18 Apr 2018. Society of Petroleum Engineers, Tulsa, Oklahoma, USA (2018)

  44. Simjoo, M., Dong, Y., Andrianov, A., Talanana, M., Zitha, P.L.J.: A CT scan study of immiscible foam flow in porous media for EOR. In: SPE 155633, SPE EOR Conference at Oil and Gas West Asia, Muscat, Oman, 16–18 Apr 2012a

  45. Simjoo, M., Dong, Y., Andrianov, A., Talanana., M., Zitha, P.L.J.: Novel insight into foam mobility control. In: SPE 15338, International Petroleum Technology Conference, Bangkok, Thailand, 7–9 Feb 2012b

  46. Simjoo, M., Nguyen, Q.P., Zitha, P.L.J.: Rheological transition during foam flow in porous media. Ind. Eng. Chem. Res. 51(30), 10225–10231 (2012c)

  47. Simjoo, M., Zitha, P.L.J.: Modeling of foam flow using stochastic bubble population model and experimental validation. Transp. Porous Media 107, 799–820 (2015)

  48. Simjoo, M., Zitha, P.L.J.: New insight into immiscible foam for enhancing oil recovery. In: Narayanan, N., Mohanadhas, B., Mangottiri, V. (eds.) Flow and Transport in Subsurface Environment. Springer, Berlin (2018)

  49. Tanzil, D., Hirasaki, G.J., Miller, C.A.: Mobility of foam in heterogeneous media: flow parallel and perpendicular to stratification. In: SPE 63228, SPE Annual Technical Conference and Exhibition, Dallas, Texas, 1–4 Oct 2000

  50. Tanzil, D., Hirasaki, G.J., Miller, C.A.: Conditions for foam generation in homogeneous porous media. In: SPE 75176, SPE/DOE Symposium on Improved Oil Recovery, Tulsa, OK, 13–17 Apr 2002

  51. Turta, A.T., Singhal, A.K.: Field foam applications in enhanced oil recovery projects: screening and design aspects. In: SPE 48895, International Oil and Gas Conference and Exhibition, Beijing, China, 2–6 Nov 1998

  52. van Lingen, P.P.: Quantification and reduction of capillary entrapment in cross-laminated oil reservoirs. Ph.D. dissertation, Delft University of Technology, the Netherlands (1998)

  53. Yang, S.H., Reed, R.L.: Mobility control using CO2 forms. In: SPE 19689, SPE Annual Technical Conference and Exhibition, San Antonio, TX, 8–11 Oct 1989

  54. Yortsos, Y.C., Chang, J.: Capillary effects in steady-state flow in heterogeneous cores. Transp. Porous Media 5, 399–420 (1990)

  55. Zhdanov, S.A., Amiyan, A.V., Surguchev, L.M., Castanier, L.M., Hanssen, J.E.: Application of foam for gas and water shut-off: review of field experience. In: SPE 36914, European Petroleum Conference, Milan, Italy, 22–24 Oct 1996

  56. Zitha, P.L.J., Du, D.X.: A new stochastic bubble population model for foam flow in porous media. Transp. Porous Media 83(3), 603–621 (2010)

Download references


We thank H. van Asten, J. Etienne, and M. Friebel of TU Delft for their technical support. M. Simjoo acknowledges the financial support of Iran Ministry of Science, Research, and Technology for this study.

Author information

Correspondence to M. Simjoo.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Simjoo, M., Zitha, P.L.J. Modeling and Experimental Validation of Rheological Transition During Foam Flow in Porous Media. Transp Porous Med 131, 315–332 (2020).

Download citation


  • Foam flow
  • Mobility transition
  • Yield stress
  • Porous media