Semicontinuum model of saturation overshoot and gravity-driven fingering in porous media

Gravity-driven multiphase flow in porous media is observed to be unstable under certain conditions. This Saffman-Taylor instability is driven by an inversion of the water saturation profile known as saturation overshoot that standard continuum models forbid. We hypothesize that the overshoot and the large-scale instability are created by different pore-filling mechanisms and patterns at the discrete pore scale. We present a new model that bridges continuum-scale and pore level physics which predicts the observed dependence of overshoot on grain size and fluid properties of the invading liquid.