Reconstruction of unknown storativity and transmissivity functions in 2D groundwater equations

Adel Hamdi (1) , Abderrahim Jardani (2)

1 LMI - Laboratoire de Mathématiques de l'INSA de Rouen Normandie
2 M2C - Morphodynamique Continentale et Côtière

The paper deals with the identification of unknown storativity and transmissiv-ity distributions within a 2D confined aquifer using pumping tests. We introduce a change of variables that transforms the groundwater equation into a diffusion-reaction one, where the diffusion term is the fraction transmissivity/storativity whereas the reaction term yields the right hand side of a second order nonlinear partial differential equation satisfied by the unknown storativity function. Using records of the drawdown at some measuring wells within the monitored aquifer, we establish identifiability results on the introduced diffusion and reaction terms as well as on the storativity values at the employed wells. We develop an identification approach that starts by determining the auxiliary diffusion and reaction variables. Afterwards, this approach uses an assumption related to the incompressibility of water to develop a local determination procedure of the unknown storativity function. Besides, based on the interpolation of its values at the employed wells, a global determination procedure of this function is also developed. The unknown transmis-sivity is then determined by the product of the identified storativity and fraction transmissivity/storativity functions. Some numerical experiments are presented.

Mots clés: Nonlinear inverse problem; partial differential equations: 2D Groundwater equations; identification of storativity and transmissivity; impulse response techniques and optimisation; 2D confined aquifer

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]; Optimisation et contrôle [math.OC]

Adel Hamdi, Abderrahim Jardani. Reconstruction of unknown storativity and transmissivity functions in 2D groundwater equations. Inverse Problems in Science and Engineering, 2020, ⟨10.1080/17415977.2020.1768250⟩. ⟨hal-02428213⟩