Scaling Haline Flows in Saturated Heterogeneous Formations
Density-driven flows occur in deep aquifers due to temperature differences, in coastal aquifers due to salt mass differences but also in contaminant migration at refuse dumps. Its relevance therefore cuts across many applications like exploitation of geothermal energy resources, oil recoverly from aquifers and remediation of contaminated sites. A typical feature of density dependent flow problems is that they can become unstable (physically or numerically). A big challenge todate is to derive a general criterion that states the following two properties of the flow problem: 1.Is the flow physically stable or unstable? and 2. What is the computational grid resolution one needs to solve the problem without creating numerical (artificial) instabilities? Flow instabilities determine how much oil and contaminants can be recovered from aquifers. The ability to predict the onset and magnitude of instabilities therefore determines the viability of petroleum exploration and remediation (soil vapour extraction and air sparging) at a given site. Attempts have been made in the past to predict the onset of viscous fingers by for example . Their approach only used the perturbation theory, which on its own cannot suffice when big concentration gradients are present.  also transformed the physical properties into Fouries space which blurred their contributions in the final results. My work developed an explicit criterion based on techniques from homogenization and perturbation theories. It was a continuation of the ideas developed in . The criterion first included the effects of density and viscosity differences for homogeneous media. I then included dispersion for a homogeneous medium and then parameters of a heterogeneous medium. The criterion was presented in a simple mathematical formulation where the contributions from each physical variable were extensively tested through numerical simulations.