Abstract
The hydrodynamic dispersion tensor (HDT) of a porous medium is a key parameter in engineering and environmental sciences. Its knowledge allows for example, to accurately predict the propagation of a pollution front induced by a surface (or subsurface) flow. This paper proposes a new mathematical model based on inverse problem-solving techniques to identify the HDT (noted D=) of the studied porous medium. We then showed that in practice, this new model can be written in the form of an integrated optimization algorithm (IOA). The IOA is based on the numerical solution of the direct problem (which solves the convection–diffusion type transport equation) and the optimization of the error function between the simulated concentration field and that observed at the application site. The partial differential equations of the direct model were solved by high resolution of (Δx=Δy=1 m) Lattice Boltzmann Method (LBM) whose computational code is named HYDRODISP-LBM (HYDRO-DISpersion by LBM). As for the optimization step, we opted for the CMA-ES (Covariance Matrix Adaptation-Evolution Strategy) algorithm. Our choice for these two methods was motivated by their excellent performance proven in the abundant literature. The paper describes in detail the operation of the coupling of the two computer codes forming the IOA that we have named HYDRODISP-LBM/CMA-ES. Finally, the IOA was applied at the Beauvais experimental site to identify the HDT D=. The geological analyzes of this site showed that the tensor identified by the IOA is in perfect agreement with the characteristics of the geological formation of the site which are connected with the mixing processes of the latter.
Highlights
Publisher’s Note: MDPI stays neutralGroundwater that supplies phreatic aquifers is one of the most important freshwater resources
We showed that in practice, this new model can be written in the form of an integrated optimization algorithm (IOA)
In this paper,Inwe presented a new IOA called in order to perform the identification of the dispersion tensor problem
Summary
Groundwater that supplies phreatic aquifers is one of the most important freshwater resources. Given the importance and the interest of these developments, the development of these plans must be based on a quality scientific approach. The management of water resources must involve a good understanding of the complex physical phenomena involved in the transformation cycle of groundwater. Among these phenomena, we evoke the mass transport by advection–diffusion in porous media which is present in many sectors of socioeconomic activity in relation to flows. Examples include medicine (flow of fluid through organs), geology (thermal rock, thermal energy management), environment (contamination of the water table, radioactive waste), chemistry Examples include medicine (flow of fluid through organs), geology (thermal rock, thermal energy management), environment (contamination of the water table, radioactive waste), chemistry (catalytic reactors, filtration . . . ), petroleum (production of natural gas, flow of petroleum), mechanics
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