Analysis of physical mechanisms underlying density-dependent transport in porous media

Abstract

In this thesis, the interaction between (large) density gradients and flow and transport in porous media is studied. Large gradients in the density of groundwater exist for example near deep salt rock formations, which are considered as possible long-term storage sites for radioactive waste. Furthermore, density effects play a role in many other groundwater applications, such as salt water intrusion. Density gradients mainly affect the flow field and mass transport in two ways: by fluid volume changes (the compressibility effect) and by inducing gravity forces. The first part of the thesis deals with the compressibility effect, which is often disregarded. Contrary to the general belief, the (Oberbeck-)Boussinesq approximation is not consistent with the limit of infinitely small density variations, in which the gravity term disappears as well. In this thesis, limits are derived for which the compressibility effect can be neglected in comparison with the gravity effect. In addition, similarity solutions are presented for simultaneous heat and brine transport. For one-dimensional brine transport, approximate analytical solutions are derived that account for the density coupling between the fluid and salt mass balance. In the second part of the thesis, the effect of stabilizing gravity forces on hydrodynamic dispersion in a heterogeneous porous medium is investigated. High-accuracy numerical simulations are performed for multiple realizations of permeability fields with small-scale heterogeneities. Fresh water is displaced upward by denser brine. The reduction of the longitudinal dispersivity under the influence of density gradients is governed by the dimensionless gravity number. The numerical simulations show a large similarity to laboratory experiments in almost homogeneous porous media. Moreover, the ensemble-averaged simulation results are compared to predictions obtained with three different nonlinear dispersion models. One of these models is obtained by homogenization (a mathematical up-scaling technique) of the local scale brine transport equations. The main objective of the numerical experiments is to test and compare the different macroscopic dispersive transport models. Parameter dependencies are studied, and the applicability and limitations of the three different models are discussed.