Foam improved oil recovery: Foams on the verge of a nervous breakdown

Dr. Paul Grassia (University of Strathclyde)

Thursday 21st January, 2016 14:00-15:00 Maths 203


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

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