Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-16T15:15:53.894Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  05 September 2017

P. Grassia Open the ORCID record for P. Grassia [Opens in a new window] ,
L. Lue ,
C. Torres-Ulloa  and
S. Berres
P. Grassia*
Affiliation:
Department of Chemical and Process Engineering, University of Strathclyde, James Weir Building, 75 Montrose St, Glasgow G1 1XJ, UK Departamento de Ciencias Matemáticas y Físicas, Universidad Católica de Temuco, Rudecindo Ortega 02950, Temuco, Chile
L. Lue
Affiliation:
Department of Chemical and Process Engineering, University of Strathclyde, James Weir Building, 75 Montrose St, Glasgow G1 1XJ, UK
C. Torres-Ulloa
Affiliation:
Escuela de Ingenería de Procesos Industriales, Universidad Católica de Temuco, Rudecindo Ortega 02950, Temuco, Chile
S. Berres
Affiliation:
Departamento de Ciencias Matemáticas y Físicas, Universidad Católica de Temuco, Rudecindo Ortega 02950, Temuco, Chile
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

JFM classification

Mathematical Foundations: Computational methods Complex Fluids: Foams Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 828 , 10 October 2017 , pp. 527 - 572
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arnold, V. I. 2004 Lectures on Partial Differential Equations, 2nd edn. Springer.CrossRefGoogle Scholar
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, 49–59.Google Scholar
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, 1–13.CrossRefGoogle ScholarPubMed
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).Google Scholar
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, 346–405.Google Scholar
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.Google Scholar
Kovscek, A. R., Patzek, T. W. & Radke, C. J. 1997 Mechanistic foam flow simulation in heterogeneous and multidimensional porous media. SPE J. 2, 511–526.Google Scholar
Kurganov, A., Noelle, S. & Petrova, G. 2001 Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton–Jacobi equations. SIAM J. Sci. Comput. 23, 707–740.Google Scholar
Lake, L. W. 2010 Enhanced Oil Recovery. Prentice Hall.Google Scholar
Ma, K., Ren, G., Mateen, K., Morel, D. & Cordelier, P. 2015 Modeling techniques for foam flow in porous media. SPE J. 20, 453–470.Google Scholar
Mas-Hernández, E., Grassia, P. & Shokri, N. 2015a Foam improved oil recovery: foam front displacement in the presence of slumping. Colloids Surf. A 473, 123–132; a collection of papers presented at the 10th EUFOAM conference, Thessaloniki, Greece, 7–10 July, 2014, edited by T. Karapantsios and M. Adler.Google Scholar
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.Google Scholar
Mas-Hernández, E., Grassia, P. & Shokri, N. 2016 Modelling foam improved oil recovery within a heterogeneous reservoir. Colloids Surf. A 510, 43–52; special issue: 29th Conference of the European Colloid and Interface Society, Bordeaux, France, 6th–11th September, 2015.CrossRefGoogle Scholar
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, 514–526.Google Scholar
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, 288–296.Google Scholar
Osher, S. & Fedkiw, R. 2003 Level Set Methods and Dynamic Implicit Surfaces, Applied Mathematical Sciences, vol. 153. Springer.Google Scholar
Peng, D., Merriman, B., Osher, S., Zhao, H.-K. & Kang, M. 1999 A PDE-based fast local level set method. J. Comput. Phys. 155, 410–438.Google Scholar
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.Google Scholar
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. 99–187. Marcel Dekker.Google Scholar
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, 273–283.Google Scholar
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. 3–45. American Chemical Society.Google Scholar
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.Google Scholar
Shan, D. & Rossen, W. R. 2004 Optimal injection strategies for foam IOR. SPE J. 9, 132–150.Google Scholar
Shi, J.-X.1996 Simulation and experimental studies of foam for enhanced oil recovery. PhD thesis, University of Texas at Austin.Google Scholar
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.Google Scholar
Torres-Ulloa, C.2015 Predicción del frente espuma-petróleo en coordenadas Eulerianas. Masters thesis, Universidad Católica de Temuco, in Spanish.Google Scholar
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, 373–383; article number SPE-164891-PA.Google Scholar
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.Google Scholar
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, 7819–7829.CrossRefGoogle Scholar