Infiltrative instability near topography with implication for the drainage of soluble rocks

Abstract

We present here numerical modeling of infiltration instability near a topographic edge of a water-saturated porous slice by analogy with a limestone formation devoid of initial heterogeneities such as fractures faults or joints and limited by a vertical cliff. In our runs a first dissolution finger develops near the cliff edge, and ends to intersect it above its mid height. Additional fingers develop upstream with a decreasing growth rate and an increasing width. This results from the decrease of the infiltration velocity with distance to the cliff in our models. A sensitivity study shows that a larger permeability contrast between the fingers and the initial undissolved porous medium produces a larger number of fingers, while increasing the dispersivity (lower Peclet number) produces wider fingers. A slower reaction rate (lower Damkháler number) produces fingers that follow the initial flow lines, since dissolution occurs simultaneously along the entire finger. These results suggest that alteration by dissolution of limestones or other soluble formations may produce different underground channel structures in the same drainage basin due to local changes of the non-dimensional P and Da numbers.