Hydro-mechanical modelling of multiphase flow in naturally fractured coalbeds applied to CBM recovery or CO2 storage

This thesis is dedicated to the modelling of multiphase flows in naturally fractured rocks and, in particular, to the recovery of methane, or reversely to the storage of carbon dioxide, in coalbeds. In this context, some hydro-mechanical couplings can likely affect the permeability of the reservoir. On the one hand, the increase in effective stress after the reservoir depletion tends to decrease the permeability. On the other hand, the matrix shrinkage following gas desorption tends to increase the permeability. These phenomena are highlighted with some experimental tests carried out in laboratory. Some numerical models are developed in this thesis to properly take into account the permeability evolution during the gas production/storage. As coal is rarely dry \textit{in situ}, constitutive models are developed for unsaturated conditions. These models are implemented in the finite element code Lagamine.

The first model is developed at the macroscale, as generally followed in the literature for reservoir modelling. Then, fractures and matrix blocks are directly modelled with a microscale model. Particular attention is paid to the applicability of unsaturated formalism to a single fracture (modelled with an interface finite element). The numerical permeability model at the fracture scale is also compared to the analytical solution of a simple geometry. Finally, in order to model a reservoir, the modelling of the representative elementary volume is integrated in a multiscale approach with the finite element square method.

The first part of the thesis presents the context of the research. After a literature review of some remarkable experimental results, an experimental study on a Australian coal is then presented in the second part. The macroscale (reservoir scale), the microscale (laboratory scale) and the multiscale (from the laboratory to the reservoir) models are then presented in distinct parts. Finally, the last part contains the general conclusions of the thesis.