Gravity currents with residual trapping

By Marc A. Hesse, F. Orr, Hamdi A. Tchelepi. Journal of Fluid Mechanics, 2008

305 citations recorded by the source corpus.

Motivated by geological carbon dioxide (CO2) storage, we present a vertical-equilibrium sharp-interface model for the migration of immiscible gravity currents with constant residual trapping in a two-dimensional confined aquifer. The residual acts as a loss term that reduces the current volume continuously. In the limit of a horizontal aquifer, the interface shape is self-similar at early and at late times. The spreading of the current and the decay of its volume are governed by power-laws. At early times the exponent of the scaling law is independent of the residual, but at late times it decreases with increasing loss. Owing to the self-similar nature of the current the volume does not become zero, and the current continues to spread. In the hyperbolic limit, the leading edge of the current is given by a rarefaction and the trailing edge by a shock. In the presence of residual trapping, the current volume is reduced to zero in finite time. Expressions for the up-dip migration distance and the final migration time are obtained. Comparison with numerical results shows that the hyperbolic limit is a good approximation for currents with large mobility ratios even far from the hyperbolic limit. In gently sloping aquifers, the current evolution is divided into an initial near-parabolic stage, with power-law decrease of volume, and a later near-hyperbolic stage, characterized by a rapid decay of the plume volume. Our results suggest that the efficient residual trapping in dipping aquifers may allow CO2 storage in aquifers lacking structural closure, if CO2 is injected far enough from the outcrop of the aquifer.

Subfields: Environmental Chemistry, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/35c115be7807817b8a9b49aa333eb76ce1b75288

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Citations in the corpus

Capillary trapping for geologic carbon dioxide storage - From pore scale physics to field scale implications (2015, methodology): “The first set of such models developed were the sharp interface models, where CO2 saturation, Sg, was either at a maximum, Sg = 1 − Swc, where Swc is the connate water saturation, or at a single residual saturation, Sgr (Hesse et al., 2008; Farcas and Woods, 2009; Gasda et al., 2009; Juanes et al., ”
Measurements of the capillary trapping of super‐critical carbon dioxide in Berea sandstone (2011, background): “Simulation and analytical studies imply that this region covers the majority of the plume [Hesse et al., 2008; Qi et al., 2009].”
Vertically averaged approaches for CO2 migration with solubility trapping (2011, methodology): “Analytical and semianalytical methods [e.g., Huppert and Woods, 1995; Lyle et al., 2005; Nordbotten and Celia, 2006; Hesse et al., 2008; Juanes et al., 2010; Neufeld and Huppert, 2009] are limited in the complexity of processes and systems that can be modeled.”