Why waterflood works: a linearized stability analysis
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abstract
The stability of the transient waterflood problem has been examined. The treatment includes both the effects of relative permeability and of capillary pressure. The analysis is formulated for a Buckley-Leverett type base state, although with capillary corrections. This base state is obtained for arbitrary water/oil relative permeabilities and capillary pressure functions, using the method of matched asymptotic expansions. The stability analysis is performed in a coordinate system co-moving with the base state; the transformation is a combined stretching and uniform translation in position. The growth rate of a perturbation is found to depend upon both the spatial position and the time of initiation of the instability.
