Skip to main content Accessibility help
×
Home

Foam front advance during improved oil recovery: similarity solutions at early times near the top of the front

  • P. Grassia (a1) (a2), L. Lue (a1), C. Torres-Ulloa (a3) and S. Berres (a2)

Abstract

The pressure-driven growth model is used to determine the shape of a foam front propagating into an oil reservoir. It is shown that the front, idealised as a curve separating surfactant solution downstream from gas upstream, can be subdivided into two regions: a lower region (approximately parabolic in shape and consisting primarily of material points which have been on the foam front continuously since time zero) and an upper region (consisting of material points which have been newly injected onto the foam front from the top boundary). Various conjectures are presented for the shape of the upper region. A formulation which assumes that the bottom of the upper region is oriented in the same direction as the top of the lower region is shown to fail, as (despite the orientations being aligned) there is a mismatch in location: the upper and lower regions fail to intersect. Alternative formulations are developed which allow the upper region to curve sufficiently so as to intersect the lower region. These formulations imply that the lower and upper regions (whilst individually being of a convex shape as seen from downstream) actually meet in a concave corner, contradicting the conventional hypothesis in the literature that the front is wholly convex. The shape of the upper region as predicted here and the presence of the concave corner are independently verified via numerical simulation data.

Copyright

Corresponding author

Email address for correspondence: paul.grassia@strath.ac.uk

References

Hide All
Arnold, V. I. 2004 Lectures on Partial Differential Equations, 2nd edn. Springer.
Boeije, C. S. & Rossen, W. R. 2014 Gas-injection rate needed for SAG foam processes to overcome gravity override (Paper SPE-166244). SPE J. 20, 4959.
Farajzadeh, R., Andrianov, A., Krastev, R., Hirasaki, G. J. & Rossen, W. R. 2012 Foam-oil interaction in porous media: implications for foam assisted enhanced oil recovery. Adv. Colloid Interface Sci. 183–184, 113.
Grassia, P.2017 Foam front displacement in improved oil recovery in systems with anisotropic permeability. Colloids Surf. A, doi:10.1016/j.colsurfa.2017.03.059 (accepted for publication).
Grassia, P., Mas-Hernández, E., Shokri, N., Cox, S. J., Mishuris, G. & Rossen, W. R. 2014 Analysis of a model for foam improved oil recovery. J. Fluid Mech. 751, 346405.
Grassia, P., Torres-Ulloa, C., Berres, S., Mas-Hernández, E. & Shokri, N. 2016 Foam front propagation in anisotropic oil reservoirs. Eur. Phys. J. E 39, 42.
Kovscek, A. R., Patzek, T. W. & Radke, C. J. 1997 Mechanistic foam flow simulation in heterogeneous and multidimensional porous media. SPE J. 2, 511526.
Kurganov, A., Noelle, S. & Petrova, G. 2001 Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton–Jacobi equations. SIAM J. Sci. Comput. 23, 707740.
Lake, L. W. 2010 Enhanced Oil Recovery. Prentice Hall.
Ma, K., Ren, G., Mateen, K., Morel, D. & Cordelier, P. 2015 Modeling techniques for foam flow in porous media. SPE J. 20, 453470.
Mas-Hernández, E., Grassia, P. & Shokri, N. 2015a Foam improved oil recovery: foam front displacement in the presence of slumping. Colloids Surf. A 473, 123132; a collection of papers presented at the 10th EUFOAM conference, Thessaloniki, Greece, 7–10 July, 2014, edited by T. Karapantsios and M. Adler.
Mas-Hernández, E., Grassia, P. & Shokri, N. 2015b Foam improved oil recovery: modelling the effect of an increase in injection pressure. Eur. Phys. J. E 38, 67.
Mas-Hernández, E., Grassia, P. & Shokri, N. 2016 Modelling foam improved oil recovery within a heterogeneous reservoir. Colloids Surf. A 510, 4352; special issue: 29th Conference of the European Colloid and Interface Society, Bordeaux, France, 6th–11th September, 2015.
Osei-Bonsu, K., Shokri, N. & Grassia, P. 2015 Surfactant dependent foam stability in the presence and absence of hydrocarbons: from bubble- to bulk-scale. Colloids Surf. A 481, 514526.
Osei-Bonsu, K., Shokri, N. & Grassia, P. 2016 Fundamental investigation of foam flow in a liquid-filled Hele–Shaw cell. J. Colloid Interface Sci. 462, 288296.
Osher, S. & Fedkiw, R. 2003 Level Set Methods and Dynamic Implicit Surfaces, Applied Mathematical Sciences, vol. 153. Springer.
Peng, D., Merriman, B., Osher, S., Zhao, H.-K. & Kang, M. 1999 A PDE-based fast local level set method. J. Comput. Phys. 155, 410438.
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 1992 Numerical Recipes in C: The Art of Scientific Computing, 2nd edn. Cambridge University Press; see chap. 19. Partial Differential Equations.
Rossen, W. R. 1996 Foams in enhanced oil recovery. In Foams: Theory, Measurements and Applications (ed. Prud’homme, R. K. & Khan, S. A.), Surfactant Science Series, chap. 2, pp. 99187. Marcel Dekker.
Rossen, W. R. & Boeije, C. S. 2015 Fitting foam-simulation-model parameters to data: II. Surfactant-alternating-gas foam applications (Paper SPE-165282). SPE Res. Evaluation Engng 18, 273283.
Schramm, L. L. & Wassmuth, F. 1994 Foams: basic principles. In Foams: Fundamentals and Applications in the Petroleum Industry (ed. Schramm, L. L.), Advances in Chemistry, vol. 242, chap. 1, pp. 345. American Chemical Society.
Sethian, J. A. 1999 Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision and Materials Science. Cambridge University Press.
Shan, D. & Rossen, W. R. 2004 Optimal injection strategies for foam IOR. SPE J. 9, 132150.
Shi, J.-X.1996 Simulation and experimental studies of foam for enhanced oil recovery. PhD thesis, University of Texas at Austin.
Shi, J.-X. & Rossen, W. R. 1989 Improved surfactant-alternating-gas foam process to control gravity override (Paper SPE 39653). In Improved Oil Recovery Symposium, Tulsa, OK, 19th–22nd April. Society of Petroleum Engineers.
Torres-Ulloa, C.2015 Predicción del frente espuma-petróleo en coordenadas Eulerianas. Masters thesis, Universidad Católica de Temuco, in Spanish.
de Velde Harsenhorst, R. M., Dharma, A. S., Andrianov, A. & Rossen, W. R. 2014 Extension and verification of a simple model for vertical sweep in foam SAG displacements. SPE Res. Evaluation Engng 17, 373383; article number SPE-164891-PA.
Xu, Q. & Rossen, W. R. 2003 Experimental study of gas injection in surfactant-alternating-gas foam process (Paper SPE 84183). In SPE Annual Technical Conference and Exhibition, Denver, 5th–8th, October. Society of Petroleum Engineers.
Zeng, Y., Muthuswamy, A., Ma, K., Wang, L., Farajzadeh, R., Puerto, M., Vincent-Bonnieu, S., Eftekhari, A. A., Wang, Y., Da, C. et al. 2016 Insights on foam transport from a texture-implicit local-equilibrium model with an improved parameter estimation algorithm. Ind. Engng Chem. Res. 55, 78197829.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed