Modélisation directe et inverse de l'écoulement souterrain dans les milieux poreux

Abstract

Résumé Le présent article montre l'intérêt des simulations mathématiques dans la compréhension des aquifères complexes et hétérogènes. Le réservoir côtier du Maroc occidental est un exemple qui traduit une répartition spatiale des corps perméables et imperméables, d'où la nécessité d'approfondir la connaissance de son fonctionnement hydrogéologique en termes de modélisation numérique. Le modèle hydrodynamique proposé repose sur la résolution du problème direct et inverse. La simulation de l'écoulement (problème direct) en régime permanent a montré la persistance de grands écarts entre la piézométrie mesurée et calculée. Cette anomalie de calage est expliquée principalement par le caractère hétérogène et fissuré, incompatible avec la dérivation de l'équation de diffusivité qui présuppose un milieu continu et un régime laminaire plutôt que turbulent. Deux cartes principales ont été obtenues: (a) une carte des polygones de la conductivité hydraulique dont les valeurs varient entre 50 10 -4 et 80 10 -4 m/s; et (b) une carte des polygones de recharge avec des valeurs comprises entre 4.5 10 -9 et 5 10 -14 m/s. Le calage du modèle d'écoulement recherché dans la résolution du problème inverse consiste à identifier les paramètres de l'aquifère à partir de la piézométrie connue. Le code d'inversion PEST (Parameter ESTimation) a été utilisé pour créer des cartes montrant des polygones de la conductivité hydraulique et de la recharge avec des valeurs très similaires aux résultats du modèle conceptuel.Mots clefs eaux souterraines; modélisation numérique; méthode directe; méthode inverse; code Groundwater Modelling System; PEST; points pilotes; caractéristiques hydrauliques; Maroc Direct and inverse modelling of the groundwater flow in porous mediaAbstract This article shows the role of mathematical simulation in the understanding of complex and heterogeneous aquifers. The coastal aquifer of the western Morocco is an example that reflects the spatial distribution of permeable and impermeable bodies. Hence the need to know its hydrological functioning in terms of numerical modelling. The hydrodynamic model proposed is based on solving the direct and inverse problem. In the steady state, the groundwater flow simulation (direct problem) showed the persistence of major differences between the measured and calculated heads. This calibration anomaly is mainly explained by heterogeneity and fissures, that are incompatible with the derivation of the diffusivity equation, which assumes a continuous and a laminar rather than turbulent flow. Two key maps have been obtained: (a) a map of hydraulic conductivity polygons whose values vary between 50 10 -4 and 80 10 -4 m/s; and (b) a map of recharge polygons whose values vary between 4.5 10 -9 and 5 10 -14 m/s. Calibration of the flow model, that was investigated in the solution of the inverse problem, leads to identification of the parameters of the aquifer from the known piezometric data. The inversion code PEST (Parameter ESTimation) was used to create maps of hydraulic conductivity and ...

Remediation scenario of the abandoned Kettara mine site (Morocco): acid mine drainage (AMD) transport modeling

“…The main goal of calibration is to reproduce the field measured heads by an iterative process. Calibration results were assessed using the root mean square error (RMSE) of the hydraulic head, and a good fit indicates that the model is calibrated and therefore potentially representative of the aquifer flow [53]:…”

“…In heterogeneous aquifers, the groundwater flow model has been calibrated by the inverse approach. Inverse approach modeling is becoming a powerful method to approximate and attribute relevant values to unknown features in hydrological models [5,24,40,49,53,56]. Inverse approach combines two compounds: hydrodynamic model code and optimization algorithm.…”

Numerical Modeling of Saltwater Intrusion in the Rmel-Oulad Ogbane Coastal Aquifer (Larache, Morocco) in the Climate Change and Sea-Level Rise Context (2040)

“…Nowadays, numerical modeling technology is an important tool for GW analysis. CC impacts, computational GW flow, and transport modeling have been investigated in many regions around the world [20][21][22][23][24][25][26][27][28][29].…”

Combination of FEM and CMA‐ES algorithm for transmissivity identification in aquifer systems

“…Accordingly, there needs to be some other approach to deriving suitable values for unknown parameters in the governing equations, to determine the parameters indirectly. Inverse modelling constitutes efficient tools for hydrogeologists to compute and to assign the hydrodynamics parameters to uncertain properties in hydrogeological models (Bastani, Kholghi, & Rakhshandehroo, ; Carrera, Alcolea, Medina, Hidalgo, & Slooten, ; Samuel & Jha, ; Toto, Zouhri, & Jgounni, ; Yang, Cronin, Elliot, & Kalin, ; Yeh et al, , ). The inverse modelling approach is based on seeking the values of aquifer parameters that minimize an objective function that computes the differences between the observed and the simulated values of state variables.…”