PhD : Modeling of the behavior of a fractured porous medium submitted to gas pressurization
In the context of the Cigéo project, the excavation of underground galleries in the Callovo-Oxfordian claystone induces a network of fractures around the excavated zone. This fracturing exhibits a typical profile of propagation in mixed I/II mode, which originates from the instantaneous discharge of the claystone after excavation. The topology and spatial extent of the induced network of fractures has been widely studied by ANDRA around the excavations of the Laboratoire Souterrain de Meuse/Haute-Marne (LSMHM). Over long time, this network of fractures is expected to experience additional loadings by gas (mostly H2) originating from the corrosion of metals used in the envelop of nuclear waste packages and from water radiolysis. The accumulation of these gases induces a pressurization that can affect the fractured zone. ANDRA has been investigating the risks associated with gas pressurization since 2003. In particular, gas-fracturing tests have been performed in a vertical well drilled from the surface and in wells drilled from the LSMHM. These test have revealed a fracturing induced by the injection of gas. The interpretation of these tests is non trivial, for instance with a high sensibility to the injection kinetics or a crack propagation at gas pressures below the average in-situ stress. The process of gas injection involves many phenomena in the porous medium coupling transport (diffusion/convection), poro-mechanics and cracking/damage. Moreover, this process occurs in the complex geometry of the pre-existing fracture network due to the initial excavation. Accordingly, an approach by numerical simulation taking into account these different couplings appears necessary to evaluate the risk of fracturing under gas pressurization.
The goal of this PhD project is to set up a theoretical and numerical model able to simulate and predict the mechanical response of a porous fractured medium submitted to gas pressurization, while taking into account the various couplings that take place in claystone. The project is organized in three parts: 1- formulation of the problem coupling gas transport and mechanics, 2- set up of the model in a numerical tool, 3- numerical study under THM loadings in presence of gas and confrontation experience-simulation.
We propose to set up the numerical simulation based on Disroc. Discroc is a finite element code dedicated in particular to the simulation of the fractured media. Cracking is accounted for by cohesive zone models, which are well adapted to the modeling of brittle and quasi-brittle media. Disroc has already been used for the study of fracturing in similar contexts. In particular, the propagation of fracture under hydromechanical couplings has been addressed in the PhD thesis of Z. Ouraga  (IFPEN) dedicated to the natural fracturing of sedimentary formations (oil and gas reservoirs), and of T. D. Vo  dedicated to the desiccation cracking of soils. A more recent research work  investigated the propagation of fractures under the effect of a fluid injection (cf. figure). The study of fracturing due to gas pressurization requires extending these works, dedicated to the case of a single incompressible fluid, to the case of a multi-phase fluid (liquid + compressible gas) in an unsaturated medium with possible effects of adsorption associated with bound water ,.
Figure: Explicit modeling of the fractures induced by the injection of a pressurized fluid in a porous medium
The numerical model developed in this work will aim at predicting the cracking induced by a gas pressurization in order to better understand the roles of the various couplings involved and help interpret the in-situ tests. This modeling will take into account the various gas transport mechanisms in the porous medium, the presence of a damaged zone around the excavation and the influence of the different geological layers. The parameters of the numerical tool will be calibrated so as to reproduce the behavior of the Callovo-Oxfordian claystone. In this respect, various experimental results available in the literature or obtained in other ANDRA projects will be considered. The behaviors of the non-adsorbed fluids (gas, free water) will be accounted for with usual models (ideal gas, incompressible, or empirical equation of states if these two limit cases prove inappropriate in the range of temperatures-pressures of interest). The behavior of the bound water will be obtained by crossing experimental data of the THM couplings and molecular simulation data available in the literature.
The numerical tool will be applied on simple cases to evaluate the main factor influencing the gas fracturing. Special attention will be paid to the role of the peculiar couplings in claystone. Then, in order to help interpreting the in-situ tests, the numerical tool will be used to explore some phenomena of interest identified experimentally (e.g., effect of the injection kinetics). In agreement with ANDRA, the numerical model will be used to simulate the gas-fracturing tests performed at LSMHM or other lab tests performed for ANDRA during this PhD. The 3D aspects will be accounted for with the future version of Disroc that shall be released during this PhD.
Practical details and applications
The applicants must hold a Master of Science or equivalent in the field of mechanics and physics of (geo)-materials, with a strong taste for numerical approaches. Interested applicants are invited to send a CV, a motivation letter and their transcripts to L. Brochard (firstname.lastname@example.org) or A. Pouya (email@example.com).
Localization: Navier lab (https://www.navier-lab.fr), 6-8 avenue Blaise Pascal, 77455 Champs-sur-Marne, France
Duration: 3 years, starting in Fall 2021
Funding: Agence nationale pour gestion des déchets radioactifs (ANDRA)
 Armand et al. (2014) Rock Mech. Rock Eng., 47, 21-41. doi:10.1007/s00603-012-0339-6.
 De La Vaissière et al. (2014). Gas injection test in the Callovo-Oxfordian claystone: data analysis and numerical modelling. Geological Society, London, Special Publications, 400(1), 427-441. https://doi.org/10.1144/SP400.10
 De La Vaissière et al. (2019, August). From Two-Phase Flow to Gas Fracturing into Callovo-Oxfordian Claystone. In 53rd US Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association.
 Ouraga (2017) Modélisation de la fracturation naturelle des sédiments: impacts sur la modélisation de bassin. PhD thesis ENPC.
 Ouraga (2017) Modélisation de la fracturation naturelle des sédiments : impacts sur la modélisation de bassin. PhD thesis ENPC.
 Vo (2017) Modélisation Numérique et Analytique de la Fissuration de séchage des Sols Argileux. PhD thesis ENPC.
 Jung et al. (2020) Fracture Closure Mechanisms during Flowback from Hydraulic Fracture Networks, in preparation.
 Brochard et al. (2012) Journal of the Mechanics and Physics of Solids, 60(4), 606–622. http://doi.org/10.1016/j.jmps.2012.01.001
 Brochard et Honório (2020). Revisiting thermo-poro-mechanics under adsorption: Formulation without assuming Gibbs-Duhem equation. International Journal of Engineering Science, 152, 103296. https://doi.org/10.1016/j.ijengsci.2020.103296
 Honorio et al. (2017) Langmuir, 33(44), 12766–12776. http://doi.org/10.1021/acs.langmuir.7b03198