Analysis of a Model for Foam Improved Oil Recovery
Seminar Room 1, Newton Institute
AbstractCo-authors: Elizabeth Mas Hernandez (University of Manchester), Nima Shokri (University of Manchester), Simon Cox (Aberystwyth University), Gennady Mishuris (Aberystwyth University), William Rossen (Delft University of Technology)
A model (originally developed by Shan and Rossen (2004) and de Velde Harsenhorst et al. (2013)) is considered that describes foam motion into a porous reservoir filled with surfactant solution. The model for evolution of the foam front that results is called `pressure-driven growth', and it describes processes that occur during improved oil recovery (IOR) using foam. The mathematical structure of the model is found to correspond to a special case of a more general situation called the `viscous froth model' (Glazier and Weaire 1992, Weaire and McMurry 1996). However `pressure-driven growth' turns out to be a singular limit of the viscous froth system, owing to the fact that a surface tension term has been discarded. This permits (in principle) sharp corners and kinks in the shape of the foam front. Sharp corners however tend to develop from concave regions of the front shape, whereas the main solution of interest here has a convex front. Whilst the solution of interest appears to have no sharp corners (except for some kinks that might develop spuriously owing e.g. to errors arising in a numerical scheme), it does nevertheless exhibit milder singularities in front curvature: a long-time asymptotic analytical solution for the shape of the front makes this point clear. Numerical schemes which perform robustly (avoiding the development of any spurious kinks in the above mentioned solution) are considered. Moreover some simple generalizations of this solution, all of engineering relevance, can exhibit concavities and/or sharp corner singularities as an inherent part of their evolution: propagation of such `inherent' singularities can be readily incorporated into numerical schemes.
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