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Cornaton, Fabien
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Cornaton, Fabien
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- PublicationAccès libreReply to “Comment on groundwater age, life expectancy and transit time distributions in advective–dispersive systems : 1. Generalized reservoir theory” by Timothy R. Ginn(2007)
; 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. - PublicationAccès libreGroundwater age, life expectancy and transit time distributions in advective–dispersive systems ; 2. Reservoir theory for sub-drainage basins(2006)
; 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. - PublicationMétadonnées seulementGroundwater age, life expectancy and transit time distributions in advective-dispersive systems; 2. Reservoir theory for sub-drainage basins(2006)
; 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. - PublicationAccès libreA finite element formulation of the outlet gradient boundary condition for convective-diffusive transport problems(2004-11-05)
; ; Diersch, Hans-JörgA 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. - PublicationMétadonnées seulement
- PublicationAccès libreAnalytical 1D dual-porosity equivalent solutions to 3D discrete single-continuum models. Application to karstic spring hydrograph modellingOne-dimensional analytical porosity-weighted solutions of the dual-porosity model are derived, providing insights on how to relate exchange and storage coefficients to the volumetric density of the high-permeability medium. It is shown that porosity-weighted storage and exchange coefficients are needed when handling highly heterogeneous systems—such as karstic aquifers—using equivalent dual-porosity models. The sensitivity of these coefficients is illustrated by means of numerical experiments with theoretical karst systems. The presented 1D dual-porosity analytical model is used to reproduce the hydraulic responses of reference 3D karst aquifers, modelled by a discrete single-continuum approach. Under various stress conditions, simulation results show the relations between the dual-porosity model coefficients and the structural features of the discrete single-continuum model. The calibration of the equivalent 1D analytical dual-porosity model on reference hydraulic responses confirms the dependence of the exchange coefficient with the karstic network density. The use of the analytical model could also point out some fundamental structural properties of the karstic network that rule the shape of the hydraulic responses, such as density and connectivity.
- PublicationAccès libreGroundwater age, life expectancy and transit time distributions in advective–dispersive systems : 1. Generalized reservoir theory(2000-02-20)
; We present a methodology for determining reservoir groundwater age and transit time probability distributions in a deterministic manner, considering advective–dispersive transport in steady velocity fields. In a first step, we propose to model the statistical distribution of groundwater age at aquifer scale by means of the classical advection–dispersion equation for a conservative and non-reactive tracer, associated to proper boundary conditions. The evaluated function corresponds to the density of probability of the random variable age, age being defined as the time elapsed since the water particles entered the aquifer. An adjoint backward model is introduced to characterize the life expectancy distribution, life expectancy being the time remaining before leaving the aquifer. By convolution of these two distributions, groundwater transit time distributions, from inlet to outlet, are fully defined for the entire aquifer domain. In a second step, an accurate and efficient method is introduced to simulate the transit time distribution at discharge zones. By applying the reservoir theory to advective–dispersive aquifer systems, we demonstrate that the discharge zone transit time distribution can be evaluated if the internal age probability distribution is known. The reservoir theory also applies to internal life expectancy probabilities yielding the recharge zone life expectancy distribution. Internal groundwater volumes are finally identified with respect to age and transit time. One- and two-dimensional theoretical examples are presented to illustrate the proposed mathematical models, and make inferences on the effect of aquifer structure and macro-dispersion on the distributions of age, life expectancy and transit time.