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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]
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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
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Copyright
© 2017 Cambridge University Press 

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