This paper evaluates the relevance of Hele-Shaw (HS) model based linear stability results to fully developed flows in enhanced oil recovery (EOR). In a recent exhaustive study [Transport in Porous Media, 93, 675–703 (2012)] of the linear stability characteristics of unstable immiscible three-layer “Hele-Shaw” flows involving regions of varying viscosity, an optimal injection policy corresponding to the smallest value of the highest rate of growth of instabilities was identified among several injection policies. Relevance of this HS model based result to EOR is established by performing direct numerical simulations of fully developed tertiary displacement in porous media. Results of direct numerical simulation are succinctly summarized including characterization of the optimal flooding scheme that leads to maximum oil recovery. These results have been compared with the HS model based linear stability results. The scope for potential application of the HS model based results to the development of fast methods for optimization of various chemical flooding schemes is discussed. Numerical experiments with more complex flooding schemes in both homogeneous and heterogeneous reservoir are also performed and results analyzed to test the universality of the generic optimal viscous families in a broader setting.

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