Parameter Identification by High-Resolution Inverse Numerical Model Based on LBM/CMA-ES: Application to Chalk Aquifer (North of France)

Lahcen Zouhri,Hassan Smaoui,Sami Kaidi

doi:10.3390/w13111574

Abstract

The present paper proposes the numerical solution of an inverse problem in groundwater flow (Darcy’s equation). This solution was achieved by combining a high-resolution new code HYSFLO-LBM (Hydrodynamic of Subsurface Flow by Lattice Boltzmann Method), based on LBM, to solve the direct problem, and the metaheuristic optimization algorithm CMA-ES ES (Covariance Matrix Adaptation-Evolution Strategy) to solve the optimization step. The integrated optimization algorithm which resulted from this combination, HYSFLO-LBM/CMA-ES, was applied to the hydrogeological experimental site of Beauvais (Northern France), instrumented by a set of sensors distributed over 20 hydrogeological wells. Hydrogeological parameters measured by the sensors are necessary to understand the aquifer functioning and to serve as input data for the identification of the transmissivity field by the HYSFLO-LBM/CMA-ES code. Results demonstrated an excellent concordance between the integrated optimization algorithm and hydrogeological applied methods (pumping test and magnetic resonance sounding). The spatial distribution of the transmissivity and hydraulic conductivity are related to the heterogeneous distribution of aquifer formations. The LBM and CMA-ES were chosen for their proven excellent performance and lesser cost, in terms of both money and time, unlike the geophysical survey and pumping test. The model can be used and developed as a decision support tool for integrated water resources management in the region.

Highlights

Chalk formations form the most important and considerable aquifer in the northern part of France as groundwater represents 97% of the water supply in the “Hauts-de-France” region—especially for drinking water, public consumption, agricultural and industrial activities, and supporting river flows
The mapping of these parameters is very complex because: (i) the cost of experimental tests in hydrogeological wells is very high in terms of time and budget, especially in the hydrogeological context related to deeper wells; and (ii) the application of geophysical surveys, especially magnetic resonance soundings (MRS), is not obvious as the quality of results are influenced and perturbed by noise measurements in the field, which depend on urban areas and can makes measurements very difficult to acquire
The integrated optimization algorithm HYSFLO-Lattice Boltzmann method (LBM)/CMA-ES was applied to the instrumented zone described in the previous paragraph

Summary

Introduction

Chalk formations form the most important and considerable aquifer in the northern part of France as groundwater represents 97% of the water supply in the “Hauts-de-France” region—especially for drinking water, public consumption, agricultural and industrial activities, and supporting river flows. Groundwater flow is governed by the estimation of hydrodynamic properties, namely the transmissivity, hydraulic conductivity, and water content values. The mapping of these parameters is very complex because: (i) the cost of experimental tests in hydrogeological wells is very high in terms of time and budget, especially in the hydrogeological context related to deeper wells; and (ii) the application of geophysical surveys, especially magnetic resonance soundings (MRS), is not obvious as the quality of results are influenced and perturbed by noise measurements in the field, which depend on urban areas and can makes measurements very difficult to acquire. It is necessary to identify other approaches to deriving suitable values in order to understand and to define the principal parameters which govern the heterogeneity of the groundwater flow and, especially, to identify the transmissivity by adopting indirect processes

Objectives

Results

Conclusion