Calibrating and Scaling Semi-empirical Foam Flow Models for the Assessment of Foam-Based EOR Processes (in Heterogeneous Reservoirs)

  • O. Gassara
  • F. DouarcheEmail author
  • B. Braconnier
  • B. Bourbiaux


Models for simulating foam-based displacements fall into two categories: population-balance (PB) models that derive explicitly foam texture or bubble size from pore-level mechanisms related to lamellas generation and coalescence, and steady-state semi-empirical (SE) models that account implicitly for foam texture effects through a gas mobility reduction factor. This mobility reduction factor has to be calibrated from a large number of experiments on a case-by-case basis in order to match the physical effect of parameters impacting foam flow behaviour such as fluids saturation and velocity. This paper proposes a methodology to set up steady-state SE models of foam flow on the basis of an equivalence between SE model and PB model under steady-state flow conditions. The underlying approach consists in linking foam mobility and foam lamellas density (or texture) data inferred from foam corefloods performed with different foam qualities and velocities on a series of sandstones of different permeabilities. Its advantages lie in a deterministic non-iterative transcription of flow measurements into texture data and in a separation of texture effects and shear-thinning (velocity) effects. Then, scaling of foam flow parameters with porous medium permeability is established from the analysis of calibrated foam model parameters on cores of different permeability, with the help of theoretical representations of foam flow in a confined medium. Although they remain to be further confirmed from other well-documented experimental data sets, the significance of those scaling laws is great for the assessment of foam-based enhanced oil recovery (EOR) processes because foam EOR addresses heterogeneous reservoirs. Simulations of foam displacement in a reservoir cross section demonstrate the necessity to scale foam SE models with respect to facies heterogeneity for reliable evaluation.


Multi-phase flow Porous media Foam Scaling laws Heterogeneity Models Reservoir simulation Reservoir engineering Enhanced oil recovery 



The authors thank L. Nabzar and L. G. Pedroni for useful discussions and IFPEN for permission to publish this work.


  1. Alvarez, J.M., Rivas, H.J., Rossen, W.R.: Unified model for steady-state foam behavior at high and low foam qualities. SPE J. 6(3), 325–333 (2001)CrossRefGoogle Scholar
  2. Bergeron, V., Radke, C.J.: Equilibrium measurements of oscillatory disjoining pressures in aqueous foam films. Langmuir 8(12), 3020–3026 (1992)CrossRefGoogle Scholar
  3. Bernard, G., Jacobs, W.L.: Effect of foam on trapped gas saturation and on permeability of porous media to water. Soc. Pet. Eng. J. 5(04), 295–300 (1965)CrossRefGoogle Scholar
  4. Boeije, C.S., Rossen, W.R.: Fitting foam-simulation-model parameters to data: I. Coinjection of gas and liquid. SPE Reserv. Eval. Eng. 18(02), 264–272 (2015)CrossRefGoogle Scholar
  5. Bond, D.G., Holbrook, O.C.: Gas drive oil recovery. Patent no. US Pat 2866507 (1958)Google Scholar
  6. Bretherton, F.P.: The motion of long bubbles in tubes. J. Fluid Mech. 10(2), 166 (1961)CrossRefGoogle Scholar
  7. Brooks, R.H., Corey, T.: Properties of porous media affecting fluid flow. J. Irrig. Drain. Div. IR2 (Proceedings of the American Society of Civil Engineers) (1966)Google Scholar
  8. Chen, H.-L., Ke, M.-J., Chuang, T.-K., Flumerfelt, R.W.: Experimental studies of capillary pressure effects of foams in porous media. SPE paper 20069 (1990)Google Scholar
  9. Chen, Q., Kovscek, A.R., Gerritsen, M.: Modeling foam displacement with the local-equilibrium approximation: theory and experimental verification. SPE J. 15(01), 171–183 (2010)CrossRefGoogle Scholar
  10. Cheng, L., Reme, A.B., Shan, D., Coombe, D.A., Rossen, W.R.: Simulating foam processes at high and low foam qualities. In: SPE/DOE Improved Oil Recovery Symposium, Tulsa, Oklahoma (2000)Google Scholar
  11. Dholkawala, Z.F., Sarma, H.K., Kam, S.I.: Application of fractional flow theory to foams in porous media. J. Pet. Sci. Eng. 57(1–2), 152–165 (2007)CrossRefGoogle Scholar
  12. Dullien, F.A.L.: Porous Media: Fluid Transport and Pore Structure, 2nd edn. Academic Press, London (1992)Google Scholar
  13. Ettinger, R.A., Radke, C.J.: Influence of texture on steady foam flow in Berea sandstone. SPE Reserv. Eng. 7(1), 83–90 (1992)CrossRefGoogle Scholar
  14. 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(03), 884–892 (1988)CrossRefGoogle Scholar
  15. Farajzadeh, R., Lotfollahi, M., Eftekhari, A.A., Rossen, W.R., Hirasaki, G.J.H.: Effect of permeability on implicit-texture foam model parameters and the limiting capillary pressure. Energy Fuels 29(5), 3011–3018 (2015)CrossRefGoogle Scholar
  16. Friedmann, F., Chen, W.H., Gauglitz, P.A.: Experimental and simulation study of high-temperature foam displacement in porous media. SPE Reserv. Eng. 6(01), 37–45 (1991)CrossRefGoogle Scholar
  17. Gassara, O., Douarche, F., Braconnier, B., Bourbiaux, B.: Equivalence between semi-empirical and population-balance foam models. Transp. Porous Media 120(3), 473–493 (2017a)CrossRefGoogle Scholar
  18. Gassara, O., Douarche, F., Braconnier, B., Bourbiaux, B.: Calibrating and interpreting implicit-texture models of foam flow through porous media of different permeabilities. J. Petrol. Sci. Eng. 159, 588–602 (2017b)CrossRefGoogle Scholar
  19. Gauglitz, P.A., Friedmann, F., Kam, S.I., Rossen, W.R.: Foam generation in homogeneous porous media. Chem. Eng. Sci. 57(19), 4037–4052 (2002)CrossRefGoogle Scholar
  20. Green, D.W., Willhite, G.P.: Enhanced oil recovery, volume 6 of SPE Textbook Series. In: Henry L. Doherty Memorial Fund of AIME, Society of Petroleum Engineers (1998)Google Scholar
  21. Heller, J.P., Boone, D.A., Watts, R.J.: Field test of \(\text{CO}_2\) mobility control at Rock Creek. Soc. Pet. Eng. Paper SPE-14395-MS (1985)Google Scholar
  22. Hirasaki, G.J., Lawson, J.B.: Mechanisms of foam flow in porous media: apparent viscosity in smooth capillaries. Soc. Pet. Eng. J. 25(02), 176–190 (1985)CrossRefGoogle Scholar
  23. Holm, L.W.: Foam injection test in the Siggins field, Illinois. Soc. Petrol. Eng. 22, 1–499 (1970)Google Scholar
  24. Jonas, T.M., Chou, S.I., Vasicek, S.L.: Evaluation of a \(\text{ CO }_2\) foam field trial: Rangely Weber sand unit. Soc Pet Eng 74–92 (1990)Google Scholar
  25. Kam, S.I.: Improved mechanistic foam simulation with foam catastrophe theory. Colloids Surf A Physicochem. Eng. Asp. 318(1–3), 62–77 (2008)CrossRefGoogle Scholar
  26. Kam, S.I., Nguyen, Q.P., Li, Q., Rossen, W.R.: Dynamic simulations with an improved model for foam generation. SPE J. 12(01), 35–48 (2007)CrossRefGoogle Scholar
  27. Kapetas, L., Vincent-Bonnieu, S., Farajzadeh, R., Eftekhari, A.A., Mohd-Shafian, S.R., Kamarul Bahrim, R.Z., Rossen, W.R.: Effect of permeability on foam-model parameters—an integrated approach from coreflood experiments through to foam diversion calculations. In: 18th European Symposium on Improved Oil Recovery, Dresden, 14–16 April (2015)Google Scholar
  28. Khatib, Z.I., Hirasaki, G.J., Falls, A.H.: Effects of capillary pressure on coalescence and phase mobilities in foams flowing through porous media. SPE Reserv. Eng. 3(3), 919–926 (1988)CrossRefGoogle Scholar
  29. Kovscek, A.R., Bertin, H.J.: Foam mobility in heterogeneous porous media. Transp. Porous Media 52(1), 37–49 (2003)CrossRefGoogle Scholar
  30. Kovscek, A.R., Radke, C.J.: Fundamentals of foam transport in porous media. In: Comstock, M.J., Schramm, L.L. (eds.) Foams: Fundamentals and Applications in the Petroleum Industry, American Chemical Society Advances in Chemistry (1994)Google Scholar
  31. Kovscek, A.R., Patzek, T.W., Radke, C.J.: A mechanistic population balance model for transient and steady-state foam flow in Boise sandstone. Chem. Eng. Sci. 50(23), 3783–3799 (1995)CrossRefGoogle Scholar
  32. Lake, L.W.: Enhanced Oil Recovery. Prentice Hall, Englewood Cliffs (1989)Google Scholar
  33. Lawson, J.B., Reisberg, J.: Alternate slugs of gas and dilute surfactant for mobility control during chemical flooding. In: SPE/DOE Enhanced Oil Recovery Symposium (1980)Google Scholar
  34. Lotfollahi, M., Farajzadeh, R., Delshad, M., Varavei, A., Rossen, W.R.: Comparison of implicit-texture and population-balance foam models. J Nat. Gas Sci. Eng. 31, 184–197 (2016)CrossRefGoogle Scholar
  35. Lotfollahi, M., Kim, I., Beygi, M.R., Worthen, A.J., Huh, C., Johnston, K.P., Wheeler, M.F., DiCarlo, D.A.: Foam generation hysteresis in porous media: experiments and new insights. Transp. Porous Media 116(2), 687–703 (2017)CrossRefGoogle Scholar
  36. Ma, K., Lopez-Salinas, J.L., Puerto, M.C., Miller, C.A., Biswal, S.L., Hirasaki, G.J.: Estimation of parameters for the simulation of foam flow through porous media. Part 1: the dry-out effect. Energy Fuels 27(5), 2363–2375 (2013)CrossRefGoogle Scholar
  37. Ma, K., Farajzadeh, R., Lopez-Salinas, J.L., Miller, C.A., Biswal, S.L., Hirasaki, G.J.: Non-uniqueness, numerical artifacts, and parameter sensitivity in simulating steady-state and transient foam flow through porous media. Transp. Porous Media 102(3), 325–348 (2014)CrossRefGoogle Scholar
  38. Marle, C.M.: Multiphase Flow in Porous Media, 3rd edn. Gulf Publishing Company, Houston (1981)Google Scholar
  39. Martinsen, H., Vassenden, F.: Foam assisted water alternating gas (FAWAG) process on Snorre. In: 10th European Symposium on Improved Oil Recovery, Brighton, UK (1999)Google Scholar
  40. Moradi-Araghi, A., Johnston, E.L., Zornes, D.R., Harpole, K.J.: Laboratory Evaluation of Surfactants for \(\text{ CO }_2\)-foam Applications at the South Cowden Unit. International Symposium on Oilfield Chemistry, Houston (1997)Google Scholar
  41. Osterloh, W.T., Jante, M.J.: Effects of gas and liquid velocity on steady-state foam flow at high temperature. Soc. Pet. Eng. (SPE/DOE 24179) 237–248 (1992)Google Scholar
  42. Patzek, T.W.: Description of foam flow in porous media by the population balance method. In Duane, H.S. (ed.) Surfactant-Based Mobility Control, American Chemical Society Symposium Series (1988)Google Scholar
  43. Peaceman, D.W.: Fundamentals of Numerical Reservoir Simulation, Developments in Petroleum Science, vol. 6. Elsevier, Amsterdam (1977)Google Scholar
  44. Pedroni, L., Nabzar, L.: New insights on foam rheology in porous media. In: Rio Oil and Gas Expo and Conference 2016 Proceedings (IBP. ISSN 2525 7560) (2016)Google Scholar
  45. Rossen, W.R., Gauglitz, P.A.: Percolation theory of creation and mobilization of foams in porous media. AIChE J. 36(8), 1176–1188 (1990)CrossRefGoogle Scholar
  46. Rossen, W.R., Zhou, Z.H.: Modeling foam mobility at the limiting capillary pressure. SPE Adv. Technol. Ser. 3(01), 146–153 (1995)CrossRefGoogle Scholar
  47. Sheng, J.J. (ed.): Foams and their applications in enhancing oil recovery. In: Enhanced Oil Recovery Field Case Studies, pp. 251–280. Elsevier, Amsterdam (2013)Google Scholar
  48. Trangenstein, J.A., Bell, J.B.: Mathematical structure of the black-oil model for petroleum reservoir simulation. SIAM J. Appl. Math. 49(3), 749–783 (1989)CrossRefGoogle Scholar
  49. Zhou, Z., Rossen, W.R.: Applying fractional flow theory to foam processes at the limiting capillary pressure. SPE Adv. Technol. Ser. 3(01), 154–162 (1995)CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Geosciences DivisionIFP Energies nouvellesRueil-Malmaison CedexFrance
  2. 2.Mechatronics and Numerics DivisionIFP Energies nouvellesRueil-Malmaison CedexFrance

Personalised recommendations