Coupling methods and numerical reductions to accelerate simulations of CO2 or H2 underground storages

Numerical simulation is essential to model flow in porous media and in particular to study underground storages of CO2 or H2. It indeed allows one to test different scenarii by simulating coupled physical mechanisms stemming from various domains (geology, geochemistry, flow and soil mechanics...)
The costs of the calculations can however be quite large. 
This cost is partly due to the dimensions of the space domain. Indeed, this area should often be extended beyond the zone of interest by lack of knowledge of the boundary conditions or to quantify the impact of the storage on the nearby environment.
Besides a simulator is often implemented so that it only uses one single model for the whole time-space domain. 
Yet, the same effort in the calculations is not necessarily required everywhere. A simplification of the initial physical model can be considered within the surrounding aquifers and in the over- and under-burdens, for instance. A single-phase flow coupled to a poro-elastic rock behaviour may then be sufficient. On the other hand, this last type of problem is a-priori well suited to reduction strategies like reduced bases.
This thus provides a strategy of fast simulations by means of coupling and reduction techniques of physical models.
A first step in this PhD work will then consist in testing different reduction solutions for a poro-mechanical model implemented at IFPEN and based on finite volumes and virtual elements. In the following this reduced model will be coupled to more complex porous-media flow and mechanical models. The aim of this PhD consists in defining efficient strategies through analysis and simulation.

Keywords: porous media flows, geomechanics, reduced basis, finite-volume methods, virtual-element methods

• Academic supervisors    BOYAVAL Sébastien, Laboratoire d’hydraulique Saint-Venant, Ecole des Ponts ParisTech, Inria Matherials TRAN Quang Huy, IFPEN, Département de Mathématiques Appliquées
• Doctoral School    Ecole Doctorale Sciences, Ingénierie et Environnement, www.paris-est-sup.fr/ecoles doctorales/ecole-doctorale-sciences-ingenierie-et-environnement-sie/
• IFPEN supervisor    ENCHERY Guillaume, IFPEN, Département de Mathématiques Appliquées, guillaume.enchery@ifpen.fr
• PhD location    IFPEn, Rueil-Malmaison, France  
• Duration and start date    3 years, starting in fourth quarter 2021
• Employer    IFPEn, Rueil-Malmaison, France  
• Academic requirements    Master degree in Numerical Analysis and Partial Differential Equations
• Language requirements    English
• Other requirements    Object-oriented programming skills (C++,...)