M.Sc Thesis
M.Sc Student Tobias Yael A Coupled Flow and Dissolution Model for a Soil and Salt-Rock Environment Department of Civil and Environmental Engineering Professor Uri Shavit

Abstract

The formation of the Dead Sea sinkholes is a major hazard to infrastructure and human live. It is believed that reduced ground water levels caused the entrance of fresh water into previously salt saturated salt rock layers, causing those layers to dissolve and create cavities and sinkholes.

The process of dissolution affects the pore-scale geometrical properties and as a result porosity is changing in time and space. In order to correctly model the dissolution, we have to consider the role of the porosity change and its influence on solute transport including advection and dispersion. While the impact on advection is commonly represented by permeability functions such as the Kozney-Carmen formula, the impact on dispersion was not included in previous studies. The goal of this research is to analyze the role of porosity-dependent-dispersion on the propagation of the dissolution front. In order to achieve this goal I have developed a 1D macroscale dissolution model that is based on three coupled differential equations, describing the solute transport, porosity change and solution flux.

Existing models link the dispersion coefficient to Péclet number but do not provide a separation between the effect of velocity and the effect of porosity. To solve this I used a 2D pore scale model that was solved for a range of porosities and velocities. The obtained data set of porosity dependent dispersion was used to solve the dissolution 1D macroscale model.

Numerical solutions of the 1D macroscale model show that a sharp dissolution front is formed and propagates through the salt layer in an accelerated rate. The results show that the accelerated behavior is not affected by the dispersive flux and that for the investigated case there is no need to account for the effect of porosity dependent dispersion.

On the basis of the sharp front of the dissolution phenomenon I developed an approximated model. This model divides the domain into two areas, dissolved and un-dissolved. Assuming a linear relationship between the front propagation rate and the water flux I derived an equation that predicts the location of the dissolution front. A comparison of these results to the macroscopic 1D model shows that under the tested conditions this model is exact.