Simulating diffusion processes in discontinuous media: Benchmark tests

International audienceWe present several benchmark tests for Monte Carlo methods simulating diffusion in one-dimensional discontinuous media. These benchmark tests aim at studying the potential bias of the schemes and their impact on the estimation of micro-or macroscopic quantities (repartition of masses, fluxes, mean residence time,. . .). These benchmark tests are backed by a statistical analysis to filter out the bias from the unavoidable Monte Carlo error. We apply them on four different algorithms. The results of the numerical tests give a valuable insight of the fine behavior of these schemes, as well as rules to choose between them

Mesh Generation and Flow Simulation in Large Tridimensional Fracture Networks

International audienceFractures in the Earth's subsurface have a strong impact in many physical and chemical phenomena, as their properties are very different from those of the surrounding rocks. They are generally organized as multi-scale structures, which can be modeled by Discrete Fracture Networks (DFNs) that may contain hundreds of thousands of ellipses in the tridi-mensional space. This paper presents our approach to generate meshes of such large DFNs and to simulate single-phase flow problems using these meshes

Influence of fracture scale heterogeneity on the flow properties of three-dimensional discrete fracture networks (DFN)

International audienceWhile permeability scaling of fractured media has been so far studied independently at the fracture- and network- scales, we propose a numerical analysis of the combined effect of fracture-scale heterogeneities and the network-scale topology. The analysis is based on 2 106 discrete fracture network (DFNs) simulations performed with highly robust numerical methods. Fracture local apertures are distributed according to a truncated Gaussian law, and exhibit self-affine spatial correlations up to a cutoff scale Lc. Network structures range widely over sparse and dense systems of short, long or widely distributed fracture sizes and display a large variety of fracture interconnections, flow bottlenecks and dead-ends. At the fracture scale, accounting for aperture heterogeneities leads to a reduction of the equivalent fracture transmissivity of up to a factor of 6 as compared to the parallel plate of identical mean aperture. At the network scale, a significant coupling is observed in most cases between flow heterogeneities at the fracture and at the network scale. The upscaling from the fracture to the network scale modifies the impact of fracture roughness on the measured permeability. This change can be quantified by the measure a2, which is analogous to the more classical power-averaging exponent used with heterogeneous porous media, and whose magnitude results from the competition of two effects: (i) the permeability is enhanced by the highly transmissive zones within the fractures that can bridge fracture intersections within a fracture plane; (ii) it is reduced by the closed and low transmissive areas that break up connectivity and flow paths. Citation: de Dreuzy, J.-R., Y. Méheust, and G. Pichot (2012), Influence of fracture scale heterogeneit

ParaCircE, a parallel Gaussian Random Field (GRF) generator

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Simulations in large tridimensional Discrete Fracture Networks (DFN): I. Geometric modeling and mesh generation

International audienceFractures in the Earth's subsurface have a strong impact in many physical and chemical phenomena, as their properties (in particular their permeabil-ities) are very different from those of the surrounding rocks. They play a major role in diverse fields of applications such as groundwater extraction, oil and gas exploitation, geothermal energy production, CO2 sequestration, etc. In this presentation, we focus on the well-known Discrete Fracture Network (DFN) models and on efficient techniques to mesh them. The generated meshes are subsequently used to carry out numerical simulations *. In the DFN models, fractures are represented by ellipses that are randomly generated in the tridimensional space, following experimental statistics. To make this model suitable for classical surface and volume meshers, it is necessary to add some information, which is accomplished in several steps: computation of the intersections between fractures, selection of fractures using a graph structure, and construction of a conforming set of edges that can be used as input for a mesh generator. All these steps present special difficulties if there are large numbers of fractures with distances, lengths and angles spanning over several orders of magnitude. Computational times are also critical, and only linear time algorithms can be accepted. In this talk, a methodology for modeling and meshing DFNs will be presented, and recent meshes up to hundreds of thousands of fractures will be shown. * See Pichot et al. MASCOT 2018 abstract, Simulations in large tridimensional Discrete Fracture Networks (DFN): II. Flow simulations

Use of power-averaging for quantifying the influence of structure organization on permeability upscaling in on-lattice networks under mean parallel flow

International audienceWe numerically assess the relevance of power-averaging as a means for permeability upscaling on a variety of 2D and 3D, dense and sparse on-lattice networks. The power-average exponent \omega determined on a realization basis converges with the system size within the range of scales explored for all cases. Power-averaging is strictly valid only for the 2D dense square case for which \omega is equal to 0 with a numerical precision of 0.01 both for the lognormal and log-uniform permeability distributions consistently with the theoretical proof of Matheron [1967]. For all other cases, the variability of \omega with the local permeability distribution variance \sigma^2 is non negligible but remains small. It is equal to 0.09 for sparse networks and 0.14 for dense networks representing respectively 4.5% and 7% of the full possible range of \omega values. Power-averaging is not strictly valid but gives an estimate of upscaling at a few percents. \omega depends slightly on the local permeability distribution shape beyond its variance but mostly on the morphological network structures. Most of the morphological control on upscaling for on-lattice structures is local and topological and can be explained by the dependence on the average number of neighbour by points (effective coordination number) within the following structure (backbone)

Combination of HHO and Mesh refining/Coarsening Strategies for Efficient Flow Solvers in Fractured Rocks

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