Modélisation de l'écoulement d'eau et du transport de masse en milieux poreux fracturés : application à l'intrusion saline et aux milieux non saturés

Ce mémoire de thèse traite de la modélisation des écoulements et du transport dans les milieux poreux fracturés, avec deux applications : l'intrusion saline dans les aquifères côtiers et l'écoulement dans la zone non saturée fracturée. Les principaux objectifs sont d'améliorer l'efficacité et la précision des modèles numériques afin de renforcer leur capacité à traiter des situations réelles de terrain. Une partie importante est consacrée au développement de solutions semi-analytiques pour l'intrusion d'eau de mer avec le modèle d'écoulement densitaire. Ces solutions sont utiles à des fins d'analyse comparative et de compréhension des processus physiques. Une technique robuste d’analyse de sensibilité avec un modèle de substitution est également développée pour étudier les incertitudes liées aux fractures sur l'intrusion saline. Une autre partie du mémoire décrit un schéma numérique efficace élaboré pour la simulation des écoulements variablement saturés dans les domaines fracturés. Ce nouveau schéma est utilisé pour étudier l'effet du changement climatique sur les ressources en eau souterraine dans un système fracturé au Liban.This work addresses the numerical modeling of flow and mass transport in fractured porous media with a focus on two applications: seawater intrusion in coastal aquifers and flow in the fractured vadose zone. The main objectives of this work are to improve the efficiency and accuracy of numerical models to enhance their capacity in dealing with real-world studies. A significant part is dedicated to the development of semi-analytical solutions for seawater intrusion with the variable density flow model. These solutions are useful for benchmarking purposes and understanding the physical processes. An appropriate and robust technique based on surrogate modeling is also developed to investigate the uncertainties related to fractures on seawater intrusion. An efficient numerical scheme is developed for the simulation of variably saturated flow in fractured domains. The new developed scheme is used to investigate the effect of climate change on groundwater resources in a karst aquifer/spring system in Lebanon

An efficient Discontinuous Galerkin -Mixed finite element model for variable density flow in fractured porous media

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Effect of Flow‐Direction‐Dependent Dispersivity on Seawater Intrusion in Coastal Aquifers

International audienceAbstract Flow‐direction‐dependent (FDD) dispersivity in coastal aquifers (CAs) may strongly affect the inland extend of seawater intrusion (SWI) and the accompanying vertical salinity distribution. FDD dispersivity may predict greater inland intrusion of the saltwater wedge, but less vertical spreading of salinity than does the classical flow‐direction‐independent (FDI) dispersivity, the standard currently employed in most numerical CA models. Dispersion processes play a key role in the SWI process and directly affect CA pumped water quality. Constant FDI dispersivities may be inappropriate in representing mixing processes due to large differences between depth and horizontal salinity transport scales, and due to typical structured heterogeneities in aquifer fabrics. Comparison of FDI and FDD model forecasts for the classical Henry problem (HP) steady‐state SWI, based on a new HP semianalytical solution with FDD and on a numerical FDI model modified to additionally represent FDD, highlights the theoretical types of differences implied by these alternative dispersivity assumptions and exactly how each parameter affects the solution. Large differences between FDI and FDD dispersivity forecasts of time‐dependent SWI in large scale heterogeneous aquifers occur in a typical CA (Akkar CA, Lebanon). The FDD model forecasts that future salinities in pumping wells will exceed the potable water limit, whereas the FDI model greatly underestimates the historic inland intrusion of the saltwater wedge and forecasts no impact on future Akkar CA potable water supply. These results indicate the importance of employing the appropriate dispersion process representation when creating model‐based SWI forecasts, especially for developing effective CA management strategies

Modeling variable-density flow in saturated-unsaturated porous media: An advanced numerical model

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An advanced discrete fracture model for variably saturated flow in fractured porous media

International audienceAccurate modeling of variably saturated flow (VSF) in fractured porous media with the discrete fracture-matrix (DFM) model is a computationally challenging problem. The applicability of DFM model to VSF in real field studies at large space and time scales is often limited, not only because it requires detailed fracture characterization, but also as it involves excessive computational efforts. We develop an efficient numerical scheme to solve the Richards equation in discretely fractured porous media. This scheme combines the mixed hybrid finite element method for space discretization with the method of lines for time integration. The fractures are modeled as lower-dimensional interfaces (1D), within the 2D porous matrix. We develop a new mass-lumping (ML) technique for the fractures to eliminate unphysical oscillations and convergence issues in the solution, which significantly improves efficiency, enabling larger field applications. The proposed new scheme is validated against a commercial simulator for problems involving water table recharge at the laboratory scale. The computational efficiency of the developed scheme is examined on a challenging problem for water infiltration in fractured dry soil, and compared with standard numerical techniques. We show that the ML technique is crucial to improve robustness and efficiency, which outperforms the commonly used methods that we tested. The applicability of our method is then demonstrated in a study concerning the effect of climate change on groundwater resources in a karst aquifer/spring system in El Assal, Lebanon. Simulations, including recharge predictions under climate change scenarios, are carried out for about 80 years, up to 2099. This study demonstrates the applicability of our proposed scheme to deal with real field cases involving large time and space scales with high variable recharge. Our results indicate that the water-table level is sensitive to the presence of fractures, where neglecting fractures leads to an overestimation of the available groundwater amount. The proposed numerical approach is generic for DFM model and can be extended to different 2D and 3D finite-element frameworks

Semianalytical solutions for contaminant transport under variable velocity field in a coastal aquifer

International audienceExisting closed-form solutions of contaminant transport problems are limited by the mathematically convenient assumption of uniform flow. These solutions cannot be used to investigate contaminant transport in coastal aquifers where seawater intrusion induces a variable velocity field. An adaptation of the Fourier-Galerkin method is introduced to obtain semi-analytical solutions for contaminant transport in a confined coastal aquifer in which the saltwater wedge is in equilibrium with a freshwater discharge flow. Two scenarios dealing with contaminant leakage from the aquifer top surface and contaminant migration from a source at the landward boundary are considered. Robust implementation of the Fourier-Galerkin method is developed to efficiently solve the coupled flow, salt and contaminant transport equations. Various illustrative examples are generated and the semi-analytical solutions are compared against an in-house numerical code. The Fourier series are used to evaluate relevant metrics characterizing contaminant transport such as the discharge flux to the sea, amount of contaminant persisting in the groundwater and solute flux from the source. These metrics represent quantitative data for numerical code validation and are relevant to understand the effect of seawater intrusion on contaminant transport. It is observed that, for the surface contamination scenario, seawater intrusion limits the spread of the contaminant but intensifies the contaminant discharge to the sea. For the landward contamination scenario, moderate seawater intrusion affects only the spatial distribution of the contaminant plume while extreme seawater intrusion can increase the contaminant discharge to the sea. The developed semi-analytical solution presents an efficient tool for the verification of numerical models. It provides a clear interpretation of the contaminant transport processes in coastal aquifers subject to seawater intrusion. For practical usage in further studies, the full open source semi-analytical codes are made available at the website https://lhyges.unistra.fr/FAHS-Marwan

Uncertainty analysis for seawater intrusion in fractured coastal aquifers: Effects of fracture location, aperture, density and hydrodynamic parameters

International audienceIn this study we use polynomial chaos expansion (PCE) to perform uncertainty analysis for seawater intrusion (SWI) in fractured coastal aquifers (FCAs) which is simulated using the coupled discrete fracture network (DFN) and variable-density flow (VDF) models. The DFN-VDF model requires detailed discontinuous analysis of the fractures. In real field applications, these characteristics are usually uncertain which may have a major effect on the predictive capability of the model. Thus, we perform global sensitivity analysis (GSA) to provide a preliminary assessment on how these uncertainties can affect the model outputs. As our conceptual model, we consider fractured configurations of the Henry Problem which is widely used to understand SWI processes. A finite element DFN-VDF model is developed in the framework of COMSOL Multiphysics (R). We examine the uncertainty of several SWI metrics and salinity distribution due to the incomplete knowledge of fracture characteristics. PCE is used as a surrogate model to reduce the computational burden. A new sparse PCE technique is used to allow for high polynomial orders at low computational cost. The Sobol' indices (SIs) are used as sensitivity measures to identify the key variables driving the model outputs uncertainties. The proposed GSA methodology based on PCE and SIs is useful for identifying the source of uncertainties on the model outputs with an affordable computational cost and an acceptable accuracy. It shows that fracture hydraulic conductivity is the first source of uncertainty on the salinity distribution. The imperfect knowledge of fracture location and density affects mainly the toe position and the total flux of saltwater entering the aquifer. Marginal effects based on the PCE are used to understand the effects of fracture characteristics on SWI. The findings provide a technical support for monitoring, controlling and preventing SWI in FCAs

Coupling mixed hybrid and extended finite element methods for the simulation of hydro-mechanical processes in fractured porous media

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A Generalized Semi-Analytical Solution for the Dispersive Henry Problem: Effect of Stratification and Anisotropy on Seawater Intrusion

The Henry problem (HP) continues to play a useful role in theoretical and practical studies related to seawater intrusion (SWI) into coastal aquifers. The popularity of this problem is attributed to its simplicity and precision to the existence of semi-analytical (SA) solutions. The first SA solution has been developed for a high uniform diffusion coefficient. Several further studies have contributed more realistic solutions with lower diffusion coefficients or velocity-dependent dispersion. All the existing SA solutions are limited to homogenous and isotropic domains. This work attempts to improve the realism of the SA solution of the dispersive HP by extending it to heterogeneous and anisotropic coastal aquifers. The solution is obtained using the Fourier series method. A special hydraulic conductivity–depth model describing stratified heterogeneity is used for mathematical convenience. An efficient technique is developed to solve the flow and transport equations in the spectral space. With this technique, we show that the HP can be solved in the spectral space with the salt concentration as primary unknown. Several examples are generated, and the SA solutions are compared against an in-house finite element code. The results provide high-quality data assessed by quantitative indicators that can be effectively used for code verification in realistic configurations of heterogeneity and anisotropy. The SA solution is used to explain contradictory results stated in the previous works about the effect of anisotropy on the saltwater wedge. It is also used to investigate the combined influence of stratification and anisotropy on relevant metrics characterizing SWI. At a constant gravity number, anisotropy leads to landward migration of the saltwater wedge, more intense saltwater flux, a wider mixing zone and shallower groundwater discharge zone to the sea. The influence of stratified heterogeneity is more pronounced in highly anisotropic aquifers. The stratification rate and anisotropy have complementary effects on all SWI metrics, except for the depth of the discharge zone