Identification of aquifer heterogeneity through inverse methods

The paper underlines the contributions of Ghislain de Marsily (GdM) to the identification of aquifers heterogeneity using inverse methods mainly for modeling subsurface flow. Inverse methods require an objective function to express the goodness of fit of the chosen model, a parameterization to describe the spatial distribution of model parameters, and a minimization algorithm. The resulting inverse problem, which consists in seeking model parameters’ values that render model outputs close to the observations, is usually unstable. GdM developed seminal ideas for the two key inversion issues that are: to stabilize the inverse problem through regularization, and to parameterize it to reproduce the natural heterogeneity of the subsurface with a limited number of parameters. GdM conducted pioneering works that are the basis of current parameterization methods relying upon adaptive zonation and/or interpolation based on pilot points. We take here the opportunity to highlight the GdM’s contributions inspiring currently used techniques

Identification of aquifer heterogeneity through inverse methods

The paper underlines the contributions of Ghislain de Marsily (GdM) to the identification of aquifers heterogeneity using inverse methods mainly for modeling subsurface flow. Inverse methods require an objective function to express the goodness of fit of the chosen model, a parameterization to describe the spatial distribution of model parameters, and a minimization algorithm. The resulting inverse problem, which consists in seeking model parameters’ values that render model outputs close to the observations, is usually unstable. GdM developed seminal ideas for the two key inversion issues that are: to stabilize the inverse problem through regularization, and to parameterize it to reproduce the natural heterogeneity of the subsurface with a limited number of parameters. GdM conducted pioneering works that are the basis of current parameterization methods relying upon adaptive zonation and/or interpolation based on pilot points. We take here the opportunity to highlight the GdM’s contributions inspiring currently used techniques

Time domain random walk method to simulate transport by advection-dispersion and matrix diffusion in fracture networks

International audienceA method is proposed to calculate in one step the residence time of a particle by advection-dispersion and matrix diffusion in a bond of a fracture network. The calculation is very rapid and avoids the discretization of Eulerian methods or the multiple leaps of classical Lagrangian approaches. The method is accurate in most flow conditions prevailing in fracture networks. Therefore, the method will be useful to evaluate the conditions in which the different transport mechanisms are of influence at the scale of the entire network

Numerical simulation of geological reservoirs: improving their conditioning through the use of entropy

International audienceThe aim of this study is to demonstrate by means of numerical experiments that the simulation of random fields may provide images that are too spatially disorganized to represent correctly some continuous properties of geological reservoirs. Increasing the number of conditioning data does not provide a satisfactory answer to the problem. The study shows that the bivariate entropy calculated on the simulated fields is a sensitive indicator of their spatial disorder. By using this measure in the objective function of a simulated annealing procedure, previously simulated random fields can be post-conditioned on their bivariate entropy in order to reduce their spatial disorder

On the stability of the 2D interpolation algorithms with uncertain data

International audienceIn Earth Sciences, the 2D interpolation methods are used to make maps and vertical sections from a set of point data. Since every measure has an uncertainty, the aim of this paper is to study the sensitivity of the three most often used methods (weighting method, kriging and cokriging). The results are as follows: the three methods are more sensitive to an error of localization in space than to an error of measure. The geostatistical methods prove their worth by showing a more robust behavior as regard to the errors than the analytical ones

Approches multi-continuum de la dualité homogénéisation-inversion des propriétés hydrodynamiques en milieu poreux fracturé

Le sous-échantillonnage est une plaie quasi systématique dans l étude des milieux souterrains. En l occurrence, la question reste posée d interpréter des données recueillies in situ pour déterminer les paramètres macroscopiques régissant l écoulement et le transport de soluté dans ces milieux. L objet de ce travail est de proposer des outils d inversion de données hydrodynamiques en gardant une approche physique (par opposition à systémique) du fonctionnement du réservoir. Des mesures de rabattements hydrauliques ont été acquises en deux campagnes de tests d interférence sur l aquifère carbonaté fracturé du Site Expérimental Hydrogéologique (SEH) de l Université de Poitiers. Elles sont interprétées selon des modèles continus double milieu, et intègrent en particulier les effets de drainance karstique observés sur la seconde campagne de mesures. Un outil d inversion du transfert de masse est également proposé sur la base d un calcul Lagrangien dans le domaine des temps pour des réseaux de liens. Entre autres sophistications, l inversion est assortie d une dérivation analytique des sensibilités aux paramètres. Enfin, la trace du réseau de liens est éliminée en substituant les équations classiques du transport par les équations de Langevin. Elles intègrent un champ de forces à l origine d un terme hyperbolique qui pourrait représenter les éventuels effets de chenalisation d un réseau. Plusieurs développements analytiques en régime transitoire et asymptotique du déplacement moyen et de la dispersion attestent de la faisabilité d une telle substitution. Le travail doit cependant être poursuivi, notamment la comparaison avec des données de traçage acquises sur le terrain.The quite-systematic scarcity of sampled data hampers the study of underground media. This is why the question remains of getting suited interpretations based on in situ data to evaluate macroscopic parameters ruling flow and mass transport in underground reservoirs. The aim of this work is to invert dynamic data by means of tools with a physical view on the reservoir functioning (opposed here to a systemic approach). Hydraulic interference testing has been held in two campaigns over the fractured limestone aquifer of the Hydrogeological Experimental Site (HES) in Poitiers (France). Drawdown data are interpreted by enhanced dual-medium approaches, with special care given to karstic draining observed on data of the second campaign. A tool for mass transport inversion is also developed with calculations handled by a Lagrangian approach in time over bond networks. Among various refinements, inversion is coupled with an analytical derivation of the model sensitivity to parameters. Finally, the trace of the network is eliminated by substituting the classical transport equations by the Langevin equations. The latter include a force field yielding a hyperbolic term that would mimic the eventual channelling effects of a network. Several analytical developments of the mean displacement and dispersion of particles, both in transient and asymptotic context, testify that the substitution is feasible. This work should be pursued however, for instance by addressing with the tools mentioned above field tracer test experiments carried out in various contextsPOITIERS-BU Sciences (861942102) / SudocSudocFranceF

Study of the permeability upscaling by direct filtering of geostatistical model

PARIS-BIUSJ-Thèses (751052125) / SudocPARIS-BIUSJ-Sci.Terre recherche (751052114) / SudocSudocFranceF

Simulating Solute Transport in Porous or Fractured Formations Using Random Walk Particle Tracking: A Review

International audienceSince the first attempts some 20 yr ago in the field of hydrology, random walk (RW) particle tracking as applied to solute transport has experienced profound changes. Concepts and mathematical techniques have improved to the point that numerically difficult problems (e.g., advection-dominated transport in highly heterogeneous media, or reactive transport) are now much easier to address. Random walk has never been widely used for multiphase flow, probably because numerical dispersion is not a major problem for modeling exercises at large scales. However, vadose zone hydrologic studies often point out very strong variations in fluid velocity over relatively short distances. Random walk methods may be well suited for such studies, a possibility which motivated us to write this review. We first give a comprehensive discussion of the theoretical context of the method. The Fokker-Planck-Kolmogorov equation (FPKE) is established for solute transport, as well as the ordinary Langevin equation and its simplifications for transport of small particles (e.g., colloids). Next, numerical methods are developed for the motion of particles in space. An important section is subsequently dedicated to recent RW concepts in the time domain, and to their application to anomalous (non-Fickian) transport and inverse problems. Adaptations of RW to transport with solute-solid reactions are also provided, as well as several numerical recipes for resolving a few computational difficulties with the RW method. We purposely did not include any comparisons with Eulerian and Lagrangian approaches. These approaches are discussed at length in several references cited in this review. We note, however, that today's computing capabilities provide new incentives to using RW methods for problems where Eulerian methods are potentially unstable or hampered by numerical diffusion