The relevance of the linear stability theory to the simulation of unstable immiscible viscous-dominated displacements in porous media

Abstract The 2D governing equations for the immiscible two-phase flow admissible to linear stability analysis are inspected. The identification of the term v w s D δ s i D in the generalized Saffman–Taylor criterion is key to the analysis. It can be regarded as a predictor that correlates with observed immiscible instability in terms of the rate of advancement of the viscous pattern, the number of small protrusions, and their roughness in a given heterogeneous domain described by a correlated random field. The predictor is extended, heuristically, for polymer flooding shock-wise and used to characterize the instability of the two shocks. The extension is validated by simulation. The instability of the primary shock is essential when considering the breakthrough recovery. In light of the instability predictor, the geometric interpretations of the fractional flow are essential to understand the stability enhancement of the primary shock over the Buckley–Leverett shock in water flooding. It is also concluded that the end-point mobility ratio does not directly control the immiscible instability. This conclusion was arrived at by fixing the end-point mobility ratios for three sets of relative permeability curves, and yet noticeably different instabilities occur, both in transverse and correlated random fields. The criterion can predict the viscous instability in the laboratory experiments under certain flooding conditions and sample configurations. Concerning the instability in a field scale, the predictor is applicable if the field is regarded as a prototype of a given model experiment.