Risk of subsidence and aquifer contamination due to evaporite dissolution : modelization of flow and mass transport in porous and free flow domains

The thesis is divided into three sections: i) the numerical part, ii) the analytical part, iii) the dissolution problem.
In the first part I developed numerical schemes to solve the density driven flow problem in porous media and in free flow media.
In porous media the numerical model is based on Mixed Finite Element (MFE) to solve the flow equation and the Multipoint Flux
Approximation coupled with the Discontinuous Galerkin (DG) methods to solve the advection-dispersion transport equation. In free
flow media the numerical model is based on the Crouzeix-Raviart (CR) finite element to solve the Stokes equation and the MPFA-DG
to solve the transport equation. The numerical models were compared against a well developed semi-analytical solution. The classical
Henry problem was used to test the numerical model in porous media where a new approach is used to calculate the semi-analytical
solution. The new approach consists of solving the Fourier series by using the Levenberg-Marquardt algorithm. With the Levenberg-Marquadt
algorithm it was possible to solve the Henry problem with small diffusion coefficient. The semi-analytical solution of the Henry problem
was modified by using the Stokes equation instead of Darcy’s. The numerical model CR-MPFA-DG was tested against the modified semi-analytical
solution and the results prove the validity of the developed numerical scheme. The numerical schemes are used to simulate the salt dissolution
process on a 2D cross section based on field measurement in the region of Muttenz-Pratteln located in north-western Switzerland.
In this area, the dissolved salt which is related to salt solution mining lead to land subsidence and collapses. To study the dissolution
process and the fracture enlargement due to dissolution, I developed a numerical model that adapts the size of the finite elements with
respect to the amount of dissolution that occurs. With the Dynamic Mesh Method (DMM) the size of the elements increases to simulate the salt
dissolution at the boundaries. To be validated, the developed numerical scheme with dissolution was compared against a laboratory experiment
of dissolution on a vertical salt fracture. The dissolution profiles prove the validity of the numerical dissolution model when compared
against the experimental results. Finally, a large set of simulations were conducted over the 2D cross section. Simulation results show
that highest amount of subsidence is expected near the fault zones.