Brine Transport in Porous Media: On the Use of Von Mises and Similarity211 Transformations. Modelling, Analysis and Simulation

摘要

In this paper, we use a Von Mises transformation to study brine transport in211u001eporous media. The model involves mass balance equations for fluid and salt, 211u001eDarcy's law and and equation of state, relating the salt mass fraction to the 211u001efluid density. Application of the Von Mises transformation recasts the model 211u001eequations into a single nonlinear diffusion equation. A further reduction is 211u001epossible if the problem admits similarity. This yields a formulation in terms of 211u001ea boundary value problem for an ordinary differential equation which can be 211u001etreated by semi-analytical means. Three specific similarity problems are 211u001econsidered in detail: (i) One-dimensional, stable displacement of fresh water and 211u001ebrine in a porous column, (ii) Flow of fresh water along the surface of a salt 211u001erock, and (iii) Mixing of parallel layers of brine and fresh water.