Analysis of a model for foam improved oil recovery

P. Grassia, E. Mas-Hernández, N. Shokri, S. J. Cox, G. Mishuris, W. R. Rossen

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

During improved oil recovery (IOR), gas may be introduced into a porous reservoir filled with surfactant solution in order to form foam. A model for the evolution of the resulting foam front known as ‘pressure-driven growth’ is analysed. An asymptotic solution of this model for long times is derived that shows that foam can propagate indefinitely into the reservoir without gravity override. Moreover, ‘pressure-driven growth’ is shown to correspond to a special case of the more general ‘viscous froth’ model. In particular, it is a singular limit of the viscous froth, corresponding to the elimination of a surface tension term, permitting sharp corners and kinks in the predicted shape of the front. Sharp corners tend to develop from concave regions of the front. The principal solution of interest has a convex front, however, so that although this solution itself has no sharp corners (except for some kinks that develop spuriously owing to errors in a numerical scheme), it is found nevertheless to exhibit milder singularities in front curvature, as the long-time asymptotic analytical solution makes clear. Numerical schemes for the evolving front shape which perform robustly (avoiding the development of spurious kinks) are also developed. Generalisations of this solution to geologically heterogeneous reservoirs should exhibit concavities and/or sharp corner singularities as an inherent part of their evolution: propagation of fronts containing such ‘inherent’ singularities can be readily incorporated into these numerical schemes.
LanguageEnglish
Pages346-405
Number of pages60
JournalJournal of Fluid Mechanics
Volume751
Early online date20 Jun 2014
DOIs
Publication statusPublished - Jul 2014

Fingerprint

oil recovery
foams
Foams
Oils
Recovery
Surface-Active Agents
Surface tension
Gravitation
Surface active agents
concavity
Gases
elimination
interfacial tension
surfactants
curvature
gravitation
propagation
gases

Keywords

  • computational methods
  • foams
  • porus material

Cite this

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. Journal of Fluid Mechanics, 751, 346-405. https://doi.org/10.1017/jfm.2014.287
Grassia, P. ; Mas-Hernández, E. ; Shokri, N. ; Cox, S. J. ; Mishuris, G. ; Rossen, W. R. / Analysis of a model for foam improved oil recovery. In: Journal of Fluid Mechanics. 2014 ; Vol. 751. pp. 346-405.
@article{500d09e725694404bbc2fbacb554123b,
title = "Analysis of a model for foam improved oil recovery",
abstract = "During improved oil recovery (IOR), gas may be introduced into a porous reservoir filled with surfactant solution in order to form foam. A model for the evolution of the resulting foam front known as ‘pressure-driven growth’ is analysed. An asymptotic solution of this model for long times is derived that shows that foam can propagate indefinitely into the reservoir without gravity override. Moreover, ‘pressure-driven growth’ is shown to correspond to a special case of the more general ‘viscous froth’ model. In particular, it is a singular limit of the viscous froth, corresponding to the elimination of a surface tension term, permitting sharp corners and kinks in the predicted shape of the front. Sharp corners tend to develop from concave regions of the front. The principal solution of interest has a convex front, however, so that although this solution itself has no sharp corners (except for some kinks that develop spuriously owing to errors in a numerical scheme), it is found nevertheless to exhibit milder singularities in front curvature, as the long-time asymptotic analytical solution makes clear. Numerical schemes for the evolving front shape which perform robustly (avoiding the development of spurious kinks) are also developed. Generalisations of this solution to geologically heterogeneous reservoirs should exhibit concavities and/or sharp corner singularities as an inherent part of their evolution: propagation of fronts containing such ‘inherent’ singularities can be readily incorporated into these numerical schemes.",
keywords = "computational methods, foams, porus material",
author = "P. Grassia and E. Mas-Hern{\'a}ndez and N. Shokri and Cox, {S. J.} and G. Mishuris and Rossen, {W. R.}",
year = "2014",
month = "7",
doi = "10.1017/jfm.2014.287",
language = "English",
volume = "751",
pages = "346--405",
journal = "Journal of Fluid Mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",

}

Grassia, P, Mas-Hernández, E, Shokri, N, Cox, SJ, Mishuris, G & Rossen, WR 2014, 'Analysis of a model for foam improved oil recovery' Journal of Fluid Mechanics, vol. 751, pp. 346-405. https://doi.org/10.1017/jfm.2014.287

Analysis of a model for foam improved oil recovery. / Grassia, P.; Mas-Hernández, E.; Shokri, N.; Cox, S. J.; Mishuris, G.; Rossen, W. R.

In: Journal of Fluid Mechanics, Vol. 751, 07.2014, p. 346-405.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Analysis of a model for foam improved oil recovery

AU - Grassia, P.

AU - Mas-Hernández, E.

AU - Shokri, N.

AU - Cox, S. J.

AU - Mishuris, G.

AU - Rossen, W. R.

PY - 2014/7

Y1 - 2014/7

N2 - During improved oil recovery (IOR), gas may be introduced into a porous reservoir filled with surfactant solution in order to form foam. A model for the evolution of the resulting foam front known as ‘pressure-driven growth’ is analysed. An asymptotic solution of this model for long times is derived that shows that foam can propagate indefinitely into the reservoir without gravity override. Moreover, ‘pressure-driven growth’ is shown to correspond to a special case of the more general ‘viscous froth’ model. In particular, it is a singular limit of the viscous froth, corresponding to the elimination of a surface tension term, permitting sharp corners and kinks in the predicted shape of the front. Sharp corners tend to develop from concave regions of the front. The principal solution of interest has a convex front, however, so that although this solution itself has no sharp corners (except for some kinks that develop spuriously owing to errors in a numerical scheme), it is found nevertheless to exhibit milder singularities in front curvature, as the long-time asymptotic analytical solution makes clear. Numerical schemes for the evolving front shape which perform robustly (avoiding the development of spurious kinks) are also developed. Generalisations of this solution to geologically heterogeneous reservoirs should exhibit concavities and/or sharp corner singularities as an inherent part of their evolution: propagation of fronts containing such ‘inherent’ singularities can be readily incorporated into these numerical schemes.

AB - During improved oil recovery (IOR), gas may be introduced into a porous reservoir filled with surfactant solution in order to form foam. A model for the evolution of the resulting foam front known as ‘pressure-driven growth’ is analysed. An asymptotic solution of this model for long times is derived that shows that foam can propagate indefinitely into the reservoir without gravity override. Moreover, ‘pressure-driven growth’ is shown to correspond to a special case of the more general ‘viscous froth’ model. In particular, it is a singular limit of the viscous froth, corresponding to the elimination of a surface tension term, permitting sharp corners and kinks in the predicted shape of the front. Sharp corners tend to develop from concave regions of the front. The principal solution of interest has a convex front, however, so that although this solution itself has no sharp corners (except for some kinks that develop spuriously owing to errors in a numerical scheme), it is found nevertheless to exhibit milder singularities in front curvature, as the long-time asymptotic analytical solution makes clear. Numerical schemes for the evolving front shape which perform robustly (avoiding the development of spurious kinks) are also developed. Generalisations of this solution to geologically heterogeneous reservoirs should exhibit concavities and/or sharp corner singularities as an inherent part of their evolution: propagation of fronts containing such ‘inherent’ singularities can be readily incorporated into these numerical schemes.

KW - computational methods

KW - foams

KW - porus material

U2 - 10.1017/jfm.2014.287

DO - 10.1017/jfm.2014.287

M3 - Article

VL - 751

SP - 346

EP - 405

JO - Journal of Fluid Mechanics

T2 - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -

Grassia P, Mas-Hernández E, Shokri N, Cox SJ, Mishuris G, Rossen WR. Analysis of a model for foam improved oil recovery. Journal of Fluid Mechanics. 2014 Jul;751:346-405. https://doi.org/10.1017/jfm.2014.287