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.