Ghislain de Marsily

Pilot Point Methodology for Automated Calibration of an Ensemble of conditionally Simulated Transmissivity Fields: 1. Theory and Computational Experiments

A new methodology for solution of the inverse problem in groundwater hydrology is proposed and applied to a site in southeastern New Mexico with extensive hydrogeologic data. The methodology addresses the issue of nonuniqueness of the inverse solutions by generating an ensemble of transmissivity fields considered to be equally likely, each of which is in agreement with the measured transmissivity and pressure data. It consists of generating a selected number of conditionally simulated transmissivity fields and then calibrating each of the fields to match the measured steady state or transient pressures, in a least squares sense. The calibration phase involves an iterative implementation of an automated pilot point approach coupled with conditional simulations. Pilot points are the parameters of calibration. They are synthetic transmissivity data which are added to the transmissivity database to produce a revised conditional simulation during calibration. Coupled kriging and adjoint sensitivity analysis is employed for the optimal location of pilot points, and gradient search methods are used to derive their optimal transmissivities. The pilot point methodology is well suited for characterizing the spatial variability of the transmissivity field in contrast to methods using zonation. Pilot points are located where their potential for minimizing the objective function is the highest. This minimizes the perturbations in the transmissivities which are optimally assigned to the pilot point and results in minimal changes to the covariance structure of the transmissivity field. The calibrated fields honor the transmissivity measurements at their locations, preserve the variogram, and match the measured pressures in a least squares sense. Since there are numerous options in the execution of this methodology, computational experiments have been conducted to identify the most efficient among them. The method has been applied to the Waste Isolation Pilot Plant (WIPP) site, in southeastern New Mexico, where the U.S. Department of Energy is conducting probabilistic system assessment for the permanent disposal of transuranic nuclear waste. The resulting calibrated transmissivity fields are input to a Monte Carlo analysis of the total system performance. The present paper, paper 1 of a two-paper presentation, describes the methodology. Paper 2, a companion paper, presents the methodologys application to the WIPP site.

Application of the pilot point method to the identification of aquifer transmissivities

Abstract A method is presented to estimate smoothly varying (as opposed to zoned) hydraulic parameters, transmissivity in particular, appearing in a time-dependent flow equation. A finite difference model based on a nested grid discretization reduces the computational effort while allowing local refinement. Structuring of the unknown parameter field, use of a priori information, and parameterization of the inverse problem are geostatistically based. Calibration is carried out by minimizing a quadratic objective function depending on head data. A primal-adjoint discrete-gradient method is used, where the unknowns are parameter values at a number of user-defined points, the “pilot points”. The key feature of this method consists of kriging together the pilot point values and the measured values, if any, in order to generate the parameter field needed at each iteration to solve the primal and adjoint systems. Minimization is performed by a BFGS algorithm. Two numerical examples are considered, where transmissivity is the unknown. The first one is adapted from Carrera and Neumans [1] synthetic problem. The purpose is to compare kriged and zoned results obtained from different types of observation data sets e.g., stationary vs. transient head or drawdown. The second example is a case study of the Dijon (France) aquifer. Pilot point-based identification is applied to the same model (domain, equations, grid), which was manually calibrated in 1985. Only the measured data were made available. The results from manual calibration were kept unknown until the end of the inversion trials. Sensible use of pilot points and of a priori information appears to play a key role in yielding plausible results.

Models of the water retention curve for soils with a fractal pore size distribution

The relationship between water content and water potential for a soil is termed its water retention curve. This basic hydraulic property is closely related to the soil pore size distribution, for which it serves as a conventional method of measurement. In this paper a general model of the water retention curve is derived for soils whose pore size distribution is fractal in the sense of the Mandelbrot number-size distribution. This model, which contains two adjustable parameters (the fractal dimension and the upper limiting value of the fractal porosity) is shown to include other fractal approaches to the water retention curve as special cases. Application of the general model to a number of published data sets covering a broad range of soil texture indicated that unique, independent values of the two adjustable parameters may be difficult to obtain by statistical analysis of water retention data for a given soil. Discrimination among different fractal approaches thus will require water retention data of high density and precision.

Regards sur 40 ans de problèmes inverses en hydrogéologie

Abstract We review the main stages of the evolution of ideas and methods for solving the ‘inverse problem’ in hydrogeology, i.e. the identification of the permeability field in single phase flow on the basis of piezometric data, in mainly steady-slate conditions.

Palaeohydrogeology of the Senegal sedimentary basin: A tentative explanation of the piezometric depressions

Abstract The superficial aquifers of the Senegal sedimentary basin, like many other coastal and internal basins in Africa, have piezometric anomalies characterized by a large cone of depression, the bottom of which can even be below sea level, but without any significant artificial withdrawal in the area. Such depressions are often referred to as ‘hollow aquifers’. Several possible explanations for the cause of these anomalies have been given, such as excess loss by evapotranspiration in areas of negligible recharge or climatic and sea level variations on the Atlantic coast of Africa, following the last glaciation. The main objective of this work was to investigate the possibility that the Ferlo piezometric depression of the Senegal sedimentary basin might have been caused by the latter phenomenon. The instrument used for this investigation is a multilayered digital model of the entire hydrogeological system, integrating the superficial phreatic aquifer and the underlying Oligo-Miocene and Maestrichtian aquifers. Our simulations start from 18 000 BP, thus they cover the period from the maximum aridity and lowest sea level of the Ogolian to the present. We were able to reconstruct the hydrodynamic behaviour of the aquifers, in particular the present piezometry of the entire three-layer system, which is compatible with that observed today, including the depressed shape of the central zone of Ferlo. The simulations also enabled us to (a) evaluate the present evapotranspiration flux in the depressed zone of Ferlo, and compare it with other estimates of evaporation from deep phreatic aquifers; and (b) estimate the exploitable resources in the entire Maestrichtian aquifer, which is the most important aquifer of the area. As a result of this explanation of the piezometric depression of Ferlo, we have briefly reviewed the various cases of depressed aquifers of the internal basins of the sub-Saharan Africa. It may be concluded that not all the piezometric anomalies observed in Africa can be explained by the same factors.

3-D modelling of salt and heat transport during the 248 m.y. evolution of the Paris basin : diagenetic implications

A 3-D model of the Paris basin was constructed to reconstitute its 248 m.y. geologic history from the Trias to the present. The model is based on detailed stratigraphic and lithographic data from about 1,100 petroleum drillings. Its scale is regional and it covers a surface area of 700,000 km(2), which exceeds the present extent of the basin in order to allow the paleogeographic evolution of the European plate to be taken into account. The geological history is simulated with the numerical model NEWBAS from the Ecole des Mines de Paris. The model simulates sedimentation, erosion, compaction, fluid flow and processes of solute and heat transport. The objective of this article is to demonstrate the value of this type of modelling for estimating and quantifying the role of fluid circulation in geological processes. Studies of diagenetic cements in the Dogger and Keuper aquifers in the Paris basin have often led their authors to consider the involvement of regional fluid circulation. These studies provide estimates of paleotemperature and paleosalinity which impose constraints on the modelling but the latter may, in turn, contribute to date the events and estimate the relevant processes. By reconstructing heat and salt transport, as proposed in this article, it is therefore possible to define the influence of hydrodynamics on these processes. The history of heat and salt in the basin is shown at various stages on a representative NW-SE cross-section of a present-day flow line which is also valid for Tertiary times. We demonstrate that the role of hydrodynamics may be predominant for salt transport by gravity-driven flow, which explains the salinity increase in the Keuper aquifer and the role of the Bray fault in the salinisation of the Dogger. Although the heat transport is dominated by the conductive component, it is also influenced by the hydrodynamics with a possible convective cooling effect when the head in the aquifers increased at the end of the Tertiary erosion period. This may partly explain the higher temperatures, deduced from fluid inclusions in the Keuper, at the end of the chalk deposition as compared to present ones. According to our simulations, the early Tertiary is the period most compatible with the diagenetic observations for thermal (maximum burial and convective cooling effect) and chemical reasons (topography allowing migration of brines in the Keuper and the Dogger).

Transport in a 2-D saturated porous medium : a new method for particle tracking

A new method for solving the transport equation based on the management of a large numbe of particles in a discretized 2-D domain is presented. The method uses numerical variables to represent the number of particles in a given mesh and is more complex than the 1-D problem. The first part of the paper focuses on the specific management of particles in a 2-D problem. The method also would be valid for three dimensions as long as the medium can be modeled similar to a layered system. As the particles are no longer tracked individually, the algorithm is fast and does not depend on the number of particles present. The numerical tests show that the method is nearly numerical dispersion free and permits accurate calculations even for simulations of low-concentration transport. Because each mesh is considered as a closed system between two successive time steps, it is easy to add adsorption phenomenon without any problem of numerical stability. The model is tested under conditions that are extremely demanding for its operating mode and gives a good fit to analytical solutions. The conditions in which it can be used to best advantage are discussed.

Sur une nouvelle approche de modélisation de la mise en place des sédiments dans une plaine alluviale pour en représenter l'hétérogénéité

This article proposes a multi-agent approach to modelling the genesis of alluvial sediments. The aim is to generate a set of sedimentary structures such as channels, point-bars and oxbow lakes by means of sedimentary process simulations. These structures will later be used to study groundwater flow. The major deposition-erosion processes are represented in an approximate and stochastic manner. The behaviour of sedimentary entities is defined by empirical rules derived from the local geometry of the flume. The emphasis of this paper is on the capacity of the model to reproduce stream evolution. The model was tested on the West Fork White River (Indiana), and shows the main trend in the evolution of a meandering system despite the simplicity of imposed rules. Expected future developments of this approach are outlined.

Solute transport in heterogeneous media: A discussion of technical issues coupling site characterization and predictive assessment

Abstract Long-term predictive evaluation of solute transport and transformation in geologic media is a critical element in the performance assessment of nuclear waste geologic repositories and in the environmental restoration or control of contaminated sites that is facing many countries today. Since the geologic media are heterogeneous and their details can never be known deterministically, long-term prediction of flow and transport in such systems requires new thinking. Thus, it is no longer possible to consider site characterization and predictive modeling calculations to be separate activities; rather they are highly coupled. This paper presents a discussion of the coupling and proposes a framework of technical issues that need to be studied.

Caractérisation des matières colloidales évacuées au cours du drainage agricole : incidence sur l'évolution pédogénétique des sols

Abstract During the drainage season, significant quantities of suspended matter can be exported from a drain collector. Their nature has been determined with a methodology linking chemical analysis, X-ray diffraction, and electronic microscopy associated with image analysis. The majority of these particles are smaller than 200 nm. They are composed of 2:1 phyllosilicates and iron particles usually in amorphous form. 137 Cs, phosphorus and organic matter clearly demonstrate the superficial origin of these particles. Drainage modifies natural leaching of soil by exporting definitively particles from the soil profile.