Connectivity-consistent mapping method for 2-D discrete fracture networks

International audienceWe present a new flow computation method in 2-D discrete fracture networks (DFN) intermediary between the classical DFN flow simulation method and the projection onto continuous grids. The method divides the simulation complexity by solving for flows successively at a local mesh scale and at the global domain scale. At the local mesh scale, flows are determined by classical DFN flow simulations and approximated by an equivalent hydraulic matrix (EHM) relating heads and flow rates discretized on the mesh borders. Assembling the equivalent hydraulic matrices provides for a domain-scale discretization of the flow equation. The equivalent hydraulic matrices transfer the connectivity and flow structure complexities from the local mesh scale to the domain scale. Compared to existing geometrical mapping or equivalent tensor methods, the EHM method broadens the simulation range of flow to all types of 2-D fracture networks both below and above the representative elementary volume (REV). Additional computation linked to the derivation of the local mesh-scale equivalent hydraulic matrices increases the accuracy and reliability of the method. Compared to DFN methods, the EHM method first provides a simpler domain-scale alternative permeability model. Second, it enhances the simulation capacities to larger fracture networks where flow discretization on the DFN structure yields system sizes too large to be solved using the most advanced multigrid and multifrontal methods. We show that the EHM method continuously moves from the DFN method to the tensor representation as a function of the local mesh-scale discretization. The balance between accuracy and model simplification can be optimally controlled by adjusting the domain-scale and local mesh-scale discretizations

Semi-analytical solutions for solute transport and exchange in fractured porous media

International audienceFracture-matrix interactions can significantly affect solute transport in fractured porous media and rocks, even when fractures are major (or sole) conduits of flow. We develop a semi-analytical solution for transport of conservative solutes in a single fracture. Our solution accounts for two-dimensional dispersion in the fracture, two-dimensional diffusion in the ambient matrix, and fully coupled fracture-matrix exchange, without resorting to simplifying assumptions regarding any of these transport mechanisms. It also enables one to deal with arbitrary initial and boundary conditions, as well as with distributed and point sources. We investigate the impact of transverse dispersion in a fracture and longitudinal diffusion in the ambient matrix on the fracture-matrix exchange, both of which are neglected in standard models of transport in fractured media

Stochastic inversion for soil hydraulic parameters in the presence of model error: An example involving ground-penetrating radar monitoring of infiltration

International audienceProxy forward solvers are commonly used in Bayesian solutions to inverse problems in hydrology and geophysics in order to make sampling of the posterior distribution, for example using Markov-chain-Monte-Carlo (MCMC) methods, computationally tractable. However, use of these solvers introduces model error into the problem, which can lead to strongly biased and overconfident parameter estimates if left uncorrected. Focusing on the specific example of estimating unsaturated hydraulic parameters in a layered soil from time-lapse ground-penetrating radar data acquired during a synthetic infiltration experiment, we show how principal component analysis, conducted on a suite of stochastic model-error realizations, can for some problems be used to build a sparse orthogonal basis for the model error arising from known forward solver approximations and/or simplifications. Projection of the residual onto this basis during MCMC permits identification and removal of the model error before calculation of the likelihood. Our results indicate that, when combined with an informal likelihood metric based on the expected behaviour of the -norm of the residual, this methodology can yield posterior parameter estimates exhibiting a marked reduction in bias and overconfidence when compared to those obtained with no model-error correction, at reasonable computational cost

Comparison of REV size and tensor characteristics for the electrical and hydraulic conductivities in fractured rock

International audienceThe representative elementary volume (REV) is a critically important concept in fractured rock investigations as it tells us at what scale the fractured domain can be represented by an anisotropic tensor as opposed to requiring the details of each individual fracture for modelling purposes. Whereas the REV size and corresponding tensor characteristics for the hydraulic conductivity (K) in fractured rock have been the subject of numerous previous investigations, no studies to date have focused on the electrical conductivity (σ). This is despite the fact that geoelectrical measurements are arguably the most popular means of geophysically investigating fractured rock, typically via azimuthal resistivity surveying where the observed electrical anisotropy is commonly used to infer hydraulic characteristics. In this paper, we attempt to fill this void and present a systematic numerical study of the impacts of changes in fracture-network properties on the REV size and equivalent tensor characteristics for both the electrical and hydraulic conductivities. We employ a combined statistical and numerical approach where the size of the REV is estimated from the conductivity variability observed across multiple stochastic fracture-network realizations for various domain sizes. Two important differences between fluid and electric current flow in fractured media are found to lead to significant differences in the REV size and tensor characteristics for σ and K; these are the greater importance of the matrix in the electrical case and the single power instead of cubic dependence of electric current flow upon aperture. Specifically, the REV for the electrical conductivity will always be smaller than that for the hydraulic conductivity, and the corresponding equivalent tensor will exhibit less anisotropy, often with notably different principal orientations. These findings are of key importance for the eventual interpretation of geoelectrical measurements in fractured rock, where we conclude that extreme caution must be taken when attempting to make the link to hydraulic properties

2.5-D discrete-dual-porosity model for simulating geoelectrical experiments in fractured rock

International audiencePrevious work has demonstrated that geoelectrical measurements, acquired either along the Earth’s surface or in boreholes, can be sensitive to the presence of fractures. However, a lack of numerical approaches that are well suited to modelling electric current flow in fractured media prevents us from systematically exploring the links between geoelectrical measurements and fractured rock properties. To address this issue, we present a highly computationally efficient methodology for the numerical simulation of geoelectrical data in 2.5-D in complex fractured domains. Our approach is based upon a discrete-dual-porosity formulation, whereby the fractures and rock matrix are treated separately and coupled through the exchange of electric current between them. We first validate our methodology against standard analytical and finite-element solutions. Subsequent use of the approach to simulate geoelectrical data for a variety of different fracture configurations demonstrates the sensitivity of these data to important parameters such as the fracture density, depth, and orientation

A new particle-tracking approach to simulating transport in heterogeneous fractured porous media

International audienceParticle-tracking methods are often used to model contaminant transport in fractured porous media because they are straightforward to implement for fracture networks and are able to take into account the matrix effect without mesh generation. While classical methods assume infinite matrix or regularly spaced fractures, we have developed a stochastic method adapted to solute transport in complex fracture networks associated with irregular matrix blocks. Diffusion times in the matrix blocks are truncated by the finite size of the blocks. High ratios of matrix diffusion to fracture advection, small fracture apertures, and small blocks favor the transfer of particles to nearby fractures through matrix diffusion. Because diffusion occurs on both sides of the originating fracture before particles reach one of the neighboring fractures, transfer times to both neighboring fractures are strongly affected by the network configurations on both sides of the fracture. This new particleƒ]tracking method is able to deal with complex fracture networks by considering heterogeneous configurations on both sides of the fracture. We finally show on simple Sierpinski lattice structures that neglecting the finite size of the matrix blocks may lead to orders of magnitude overestimations of the transfer times

Impact des structures géologiques sur les échanges entre fractures et matrice dans les milieux poreux fracturés.

Fractured porous media are characterized by the presence of fractures at several scales with heterogeneous properties implying areas highly permeable by comparison with the rock. Hydraulically, these media are characterized by short reaction times, due to the fractures, and long reaction times, due to the rock. These media are important for several topics as contaminated sites, element storage and resources exploitation. The main challenge of fracture porous media modeling is the representation of the geometrical and physical heterogeneities. As an exact representation of the medium is not possible, it is necessary to determine the key properties of the medium. This study aims at determining the impact of the geometrical and physical properties of the fractures and the matrix from the local to the global scales. A first part consists in creating methods to evaluate structure effects on the exchange between the fractures and the matrix and a second part consists in using these methods on several media. Finally, we describe a new discrete dual-porosity model taking into account the properties of the media characterizing its behavior.Les milieux poreux fracturés sont des milieux composés d'une roche présentant des zones de fracturation. Géologiquement, ces milieux sont caractérisés par la présence de fractures sur plusieurs échelles avec des propriétés hétérogènes créant des zones fortement perméables à comparer de la roche environnante. Hydrauliquement, ces milieux sont caractérisés par des temps de réponses courts correspondant aux sollicitations des structures fortement perméables et des temps de réponses longs correspondant aux sollicitations des structures faiblement perméables. Ce type de milieux est impliqué dans de nombreux enjeux sociétaux tels que l'étude de sites contaminés, le stockage d'éléments et l'exploitation de ressources. Le principal défi de la modélisation des milieux poreux fracturés réside en la représentation des hétérogénéités géométriques et physiques caractérisant ces milieux. Une représentation exacte du milieu naturel étant impossible, il s'agit de déterminer quelles sont les propriétés caractéristiques de ces milieux, c'est-à-dire les propriétés principales "responsables" de leur comportement. Mes travaux de thèse ont consisté à étudier l'impact des propriétés géométriques et physiques des fractures et de la matrice de l'échelle locale de la fracture et du bloc matriciel à l'échelle globale du réseau de fractures. Une première partie du travail correspond à la mise au point de méthodes d'évaluation des effets des structures et de leurs propriétés sur les échanges et une seconde partie en l'exploitation de ces méthodes. Au final, je propose un modèle double-porosité discret prenant en compte les propriétés du milieu identifiées comme caractéristiques de son comportement