Cornaton, Fabien

2013-9-2, Benabderrahmane, Hakim, Kerrou, Jaouhar, Deman, Gregory, Tacher, Laurent, Cornaton, Fabien, Perrochet, Pierre

2007, Cornaton, Fabien, Perrochet, Pierre

2006, Milnes, Ellen, Perrochet, Pierre, Renard, Philippe, Cornaton, Fabien

2004, Cornaton, Fabien, Goldscheider, Nico, Jeannin, Pierre-Yves, Perrochet, Pierre, Pochon, Alain, Sinreich, Michael, Zwahlen, François, Zwahlen, François

2013-1-1, Kerrou, Jaouhar, Renard, Philippe, Cornaton, Fabien, Perrochet, Pierre

2007, Cornaton, Fabien, Perrochet, Pierre

We thank T.R. Ginn for his interest in our recently published article (1) on the subject of groundwater age modelling and reservoir theory. In his previous comment (2), T.R. Ginn expresses concern about some conceptual inconsistencies in the formulations presented in our work. We basically agree with the fundaments of his comments, and we wish to continue the discussion. (1) F. Cornaton and P. Perrochet, Groundwater age, life expectancy and transit time distributions in advective–dispersive systems: 1. Generalized reservoir theory, Adv Water Res 29 (2006), pp. 1267–1291, doi :10.1016/j.advwatres.2005.10.009 (2) Ginn TR. Comment on “Groundwater age, life expectancy and transit time distributions in advective–dispersive systems: 1. Generalized reservoir theory”, by F. Cornaton and P. Perrochet. Adv Water Res, in press, doi :10.1016/j.advwatres.2006.09.005.

2006, Cornaton, Fabien, Perrochet, Pierre

Groundwater age and life expectancy probability density functions (pdf) have been defined, and solved in a general three-dimensional context by means of forward and backward advection-dispersion equations [Cornaton F, Perrochet P. Groundwater age, life expectancy and transit time distributions in advective-dispersive systems; 1. Generalized reservoir theory. Adv Water Res (xxxx)]. The discharge and recharge zones transit time pdfs were then derived by applying the reservoir theory (RT) to the global system, thus considering as ensemble the union of all inlet boundaries on one hand, and the union of all outlet boundaries on the other hand. The main advantages in using the RT to calculate the transit time pdf is that the outlet boundary geometry does not represent a computational limiting factor (e.g. outlets of small sizes), since the methodology is based on the integration over the entire domain of each age, or life expectancy, occurrence. In the present paper, we extend the applicability of the RT to sub-drainage basins of groundwater reservoirs by treating the reservoir flow systems as compartments which transfer the water fluxes to a particular discharge zone, and inside which mixing and dispersion processes can take place. Drainage basins are defined by the field of probability of exit at outlet. In this way, we make the RT applicable to each sub-drainage system of an aquifer of arbitrary complexity and configuration. The case of the well-head protection problem is taken as illustrative example, and sensitivity analysis of the effect of pore velocity variations on the simulated ages is carried out. (c) 2005 Elsevier Ltd. All rights reserved.

2012-10-22, Kerrou, Jaouhar, Cornaton, Fabien, Tacher, Laurent, Benabderrahmane, Hakim, Perrochet, Pierre

2006, Cornaton, Fabien, Perrochet, Pierre

Groundwater age and life expectancy probability density functions (pdf) have been defined, and solved in a general three-dimensional context by means of forward and backward advection–dispersion equations [Cornaton F, Perrochet P. Groundwater age, life expectancy and transit time distributions in advective–dispersive systems; 1. Generalized reservoir theory. Adv Water Res (xxxx)]. The discharge and recharge zones transit time pdfs were then derived by applying the reservoir theory (RT) to the global system, thus considering as ensemble the union of all inlet boundaries on one hand, and the union of all outlet boundaries on the other hand. The main advantages in using the RT to calculate the transit time pdf is that the outlet boundary geometry does not represent a computational limiting factor (e.g. outlets of small sizes), since the methodology is based on the integration over the entire domain of each age, or life expectancy, occurrence. In the present paper, we extend the applicability of the RT to sub-drainage basins of groundwater reservoirs by treating the reservoir flow systems as compartments which transfer the water fluxes to a particular discharge zone, and inside which mixing and dispersion processes can take place. Drainage basins are defined by the field of probability of exit at outlet. In this way, we make the RT applicable to each sub-drainage system of an aquifer of arbitrary complexity and configuration. The case of the well-head protection problem is taken as illustrative example, and sensitivity analysis of the effect of pore velocity variations on the simulated ages is carried out.

2004-11-05, Cornaton, Fabien, Perrochet, Pierre, Diersch, Hans-Jörg

A simple finite element formulation of the outlet gradient boundary condition is presented in the general context of convective-diffusive transport processes. Basically, the method is based on an upstream evaluation of the dependent variable gradient along open boundaries. Boundary normal unit vectors and gradient operators are evaluated using covariant bases and metric tensors, which allow handling finite elements of mixed dimensions. Even though the presented method has implications for many fields where diffusion processes are involved, discussion and illustrative examples address more particularly the framework of contaminant transport in porous media, in which the outlet gradient concentration is classically, but wrongly assumed to be zero.