In this paper we analyze a model for brine transport in porous media, which includes a mass balance for the fluid, a mass balance for salt, Darcy's law and an equation of state, which relates the fluid density to the salt mass fraction. This model incorporates the effect of local volume changes due to variations in the salt concentration. Density variations affect the compressibility of the fluid, which in turn cause additional movement of fluid. Two specific situations are investigated that lead to self similarity. We study the relative importance of the compressibility effect in terms of the relative density difference. Semi-analytical solutions are obtained as well as asymptotic expressions in terms of the relative density difference. It is found that the volume changes have a small but noticeable effect on the mass transport only when the salt concentration gradients are large. Some results on the simultaneous transport of brine and dissolved (radioactive) tracers are presented.

Nonlinear parabolic equations (msc 35K55), Flows in porous media; filtration; seepage (msc 76S05)
CWI
Department of Analysis, Algebra and Geometry [AM]

van Duijn, C.J, Peletier, L.A, & Schotting, R.J. (1996). Brine transport in porous media self-similar solutions. Department of Analysis, Algebra and Geometry [AM]. CWI.