Ali Zidane

Modelling variable density flow problems in heterogeneous porous media using the method of lines and advanced spatial discretization methods

Modelling variable density flow problems under heterogeneous porous media conditions requires very long computation time and high performance equipments. In this work, the DASPK solver for temporal resolution is combined with advanced spatial discretization schemes in order to improve the computational efficiency while maintaining accuracy. The spatial discretization is based on a combination of Mixed Finite Element (MFE), Discontinuous Galerkin (DG) and Multi-point Flux Approximation methods (MPFA). The obtained non-linear ODE/DAE system is solved with the Method of Lines (MOL) using the DASPK time solver. DASPK uses the preconditioned Krylov iterative method to solve linear systems arising at each time step. Precise laboratory-scale 2D experiments were conducted in a heterogeneously packed porous medium flow tank and the measured concentration contour lines are used to evaluate the numerical model. Simulations show the high efficiency and accuracy of the code and the sensitivity analysis confirms the density dependence of dispersion.

On the effects of subsurface parameters on evaporite dissolution (Switzerland)

Uncontrolled subsurface evaporite dissolution could lead to hazards such as land subsidence. Observed subsidences in a study area of Northwestern Switzerland were mainly due to subsurface dissolution (subrosion) of evaporites such as halite and gypsum. A set of 2D density driven flow simulations were evaluated along 1000 m long and 150 m deep 2D cross sections within the study area that is characterized by tectonic horst and graben structures. The simulations were conducted to study the effect of the different subsurface parameters that could affect the dissolution process. The heterogeneity of normal faults and its impact on the dissolution of evaporites is studied by considering several permeable faults that include non-permeable areas. The mixed finite element method (MFE) is used to solve the flow equation, coupled with the multipoint flux approximation (MPFA) and the discontinuous Galerkin method (DG) to solve the diffusion and the advection parts of the transport equation. Results show that the number of faults above the lower aquifer that contains the salt layer is considered as the most important factor that affects the dissolution compared to the other investigated parameters of thickness of the zone above the halite formation, a dynamic conductivity of the lower aquifer, and varying boundary conditions in the upper aquifer.

A combination of Crouzeix-Raviart, Discontinuous Galerkin and MPFA methods for buoyancy-driven flows

Purpose – The purpose of this paper is to develop an efficient non-iterative model combining advanced numerical methods for solving buoyancy-driven flow problems. Design/methodology/approach – The solution strategy is based on two independent numerical procedures. The Navier-Stokes equation is solved using the non-conforming Crouzeix-Raviart (CR) finite element method with an upstream approach for the non-linear convective term. The advection-diffusion heat equation is solved using a combination of Discontinuous Galerkin (DG) and Multi-Point Flux Approximation (MPFA) methods. To reduce the computational time due to the coupling, the authors use a non-iterative time stepping scheme where the time step length is controlled by the temporal truncation error. Findings – Advanced numerical methods have been successfully combined to solve buoyancy-driven flow problems on unstructured triangular meshes. The accuracy of the results has been verified using three test problems: first, a synthetic problem for which t...

The role of tectonic structures and density-driven groundwater flow for salt karst formation

Groundwater circulation in evaporite bearing horizons and the resulting evolution of karst frequently causes geotechnical problems such as land subsidence or collapses. Even comparably small subsidence rates can significantly affect sensitive urban infrastructure. Dissolution of deep-seated evaporites occurs when groundwater, undersaturated with respect to highly soluble minerals, enters into contact with an evaporite body. Groundwater can interact from all directions in space. Laboratory dissolution experiments were carried out to study the effect of freshwater in contact with rock salt, accounting for the effect of dipping interfaces as an abstraction of inclined geological formations. The dissolution experiments were carried out both in 2D and 3D. The approach allows studying dissolution in a normal fault juxtaposing a developing intrastratal salt karst against a salt layer or against a poorly soluble layer. Modeling experiments were conducted to study the effect of variable density flow in inclined aquifers bordering halite formations and the effect of different fault geometries. The numerical simulations of density driven flow were evaluated along 1,000 m long and 150 m deep 2D cross sections to study the effect of tectonic horst and graben structures. Results show that a large fault zone consisting of a set of smaller hydraulically higher conductive faults is a major factor for dissolution.

Examples and Case Studies

The presented examples and case studies illustrate specific applications of adaptive management of water resources in the region of Basel, Northwestern Switzerland. Such concepts together with the setup of tools and process-oriented experiments allow testing hypotheses. The applied methods facilitated us to fill several gaps of knowledge of subsurface processes. The examples focus on questions with practical as well as research. Most topics are relevant for urban areas and the sustainable use of subsurface resources in general.