In this paper we use a Von Mises transformation to study brine transport in porous media. The model involves mass balance equations for fluid and salt, Darcy's law and an equation of state, relating the salt mass fraction to the fluid density. Application of the Von Mises transformation recasts the model equations into a single nonlinear diffusion equation. A further reduction is possible if the problem admits similarity. This yields a formulation in terms of a boundary value problem for an ordinary differential equation which can be treated by semi-analytical means. Three specific similarity problems are considered in detail: (i) One-dimensional, stable displacement of fresh water and brine in a porous column, (ii) Flow of fresh water along the surface of a salt rock, (iii) Mixing of parallel layers of brine and fresh water.

Degenerate parabolic equations (msc 35K65), Heat and other parabolic equation methods (msc 58J35), Flows in porous media; filtration; seepage (msc 76S05)
CWI
Modelling, Analysis and Simulation [MAS]

van Duijn, C.J, & Schotting, R.J. (1997). Brine transport in porous media. Modelling, Analysis and Simulation [MAS]. CWI.