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Water Resources Research

Channelization of buoyant nonwetting fluids in saturated porous media

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Abstract

[1] We study the development of capillary instabilities during the invasion of a buoyant nonwetting phase in a saturated porous media. Capillary instabilities are generally attributed to heterogeneities in the porous medium resulting in the existence of fluid pathways opposing different resistance to the flow (“passive control”). We use a simple macroscale theoretical model based on the postulate that the nonwetting fluid will be distributed in the porous medium to minimize the resistance to transport. This theoretical argument is used to show that after their formation, some capillary instabilities can grow at the expense of others. The competitive growth between capillary channels arises because of pore-scale fluid interactions that occur even in a porous medium offering identical pathways at the pore scale. The evolution of the pore volume fraction of nonwetting fluid in capillary fingers is therefore dynamically controlled by fluctuations in the nonwetting phase saturation and its effect on the relative permeability (“active control”). The theoretical model predicts (1) the growth of heterogeneities in nonwetting fluid saturation among competing capillary channels if the second derivative of the invading phase relative permeability with respect to its saturation is positive, and (2) that the amplitude of the perturbation in nonwetting fluid content between competing fingers increases with the interfacial tension. We use a pore-scale multiphase flow numerical model to test the validity of the postulate for optimal transport of nonwetting fluids and the two ensuing predictions. We observe that the numerical calculations are in excellent agreement with the theoretical predictions.

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