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Viscous fingering in CCS - A general criterion for viscous fingering in porous media

Maas, Jos G. / Springer, Niels / Hebing, Albert / Snippe, Jeroen / Berg, Steffen

Abstract For many practical applications such as the ${CO}_{2}$ injection for carbon capture and sequestration (CCS) or gas injection for underground energy storage it is important to understand whether this displacement is stable or unstable. Viscous instability may occur in a porous medium when a fluid with higher mobility displaces a fluid with lower mobility, and is therefore an obvious question for CCS since the viscosity of injected ${CO}_{2}$ is typically much less than the displaced brine. Historically, several different criteria have been developed to predict the onset of viscous fingering. That leaves significant uncertainty which criterion is now valid since for the criterion of shock front mobility ratio the ${CO}_{2}$ -brine displacement could be stable while the shock front total mobility ratio or the end point mobility ratio criterion suggests an unstable displacement. The root-cause of this level of ambiguity is that for multiphase displacement in porous media it is not sufficient to consider only fixed values for saturation upstream and downstream. Instead, the whole Buckley–Leverett saturation profile needs to be considered. In this work, we present a new approach to derive a general criterion for viscous fingering in porous media that removes the ambiguity around the question of displacement stability. This new criterion contains all earlier derived criteria as limiting cases, whether for porous media or for Hele-Shaw cells, with and without gravity, immiscible and miscible. It has been validated by Darcy scale numerical flow simulations in 2D. The new criterion is particularly useful for CCS and we discuss how, depending on exact pressure and temperature conditions, CCS can be viscous-unstable. Viscous-unstable displacement has implications for both laboratory-scale “core flooding” experiments where displacement stability influences the interpretation in terms of relative permeability, and also for the field scale for CCS where viscous-unstable displacement may lead to ${CO}_{2}$ plume migration beyond a spill point and in that way may reduce the storage capacity. We show that the Dietz criterion for stability of displacement on the scale of the field is a special case of our new criterion and how the Dietz formula needs to be corrected given the new insight we have developed. Finally, we discuss how the new criterion impacts the design of the laboratory experiments as well as how it can be used in the design of the gridding of field-scale simulations.

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Highlights • A general criterion for viscous fingering in porous media. • All traditional criteria are limiting cases. • No choice of shock front vs. endpoint (total) mobility ratio required. • The new criterion considers the whole saturation profile. • According to the new criterion, situations relevant for CCS can be viscous-unstable.