Section: New Results

Models and simulations for flow and transport in porous fractured media

An adaptive sparse grid method for elliptic PDEs with stochastic coefficients

Participant : Jocelyne Erhel.

Grants and projects: HYDRINV 9.3.3 , H2MN04 9.1.1

Publications: [14] .

Abstract: The stochastic collocation method based on the anisotropic sparse grid has become a significant tool to solve partial differential equations with stochastic inputs. The aim is to seek a vector of weights and a convenient level of interpolation for the method. The classical approach uses an a posteriori approach on the solution, which causes an additional prohibitive cost.

In this work, we discuss an adaptive approach of this method to calculate the statistics of the solution. It is based on an adaptive approximation of the inverse diffusion parameter. We construct an efficient error indicator which is an upper bound of the error on the solution. In the case of unbounded variables, we use an appropriate error estimation to compute suitable weights for the method. Numerical examples are presented to confirm the efficiency of the approach, and to show that the cost is considerably reduced without loss of accuracy.

A global reactive transport model applied to the MoMaS benchmark

Participant : Jocelyne Erhel.

Grants and projects: H2MN04 9.1.1

Software: GRT3D 6.3

Publications: [19] .

Abstract: Reactive transport models are very useful for groundwater studies such as water quality, safety analysis of waste disposal, remediation, and so on. The MoMaS group defined a benchmark with several test cases. We present results obtained with a global method and show through these results the efficiency of our numerical model.

About some numerical models for geochemistry

Participant : Jocelyne Erhel.

Grants and projects: H2MN04 9.1.1

Publications: [16] , [17] .

Abstract: Reactive transport models are very useful to study the fate of contaminants in grounwater. These models couple transport equations with geochemistry equations. In this talk, we focus on precipitation and dissolution chemical reactions, because they induce numerical difficulties.

We consider a set of solute species and minerals, with precipitation occuring when a saturation threshold is reached. A challenge is to detect which minerals are dissolved and which minerals are precipitated. This depends on the total quantities of chemical species. We propose an analytical approach to build a phase diagram, which provides the interfaces between the different possible cases. We illustrate our method with three examples arising from brine media and acid mine drainage.

Power-averaging method to characterize and upscale permeability in DFNs

Participants : Jean-Raynald de Dreuzy, Géraldine Pichot.

Publications: [21] .

Abstract: In a lot of geological environments, permeability is dominated by the existence of fractures and by their degree of interconnections. Flow properties depend mainly on the statistical properties of the fracture population (length, apertures, orientation), on the network topology, as well as on some detailed properties within fracture planes. Based on an extensive analysis of 2D and 3D DFNs as well as on reference connectivity structures, we investigate the relation between the local fracture structures and the effective permeability. Defined as the relative weight between the two extreme harmonic and arithmetic means, the power-law averaging exponent gives a compact way to compare fracture network hydraulics. It may further lead to some comprehensive upscaling rules.