Lattice Boltzmann Model for bubble flow simulation in thin rock fractures
Résumé
In the context of radioactive waste disposal in deep geological formations, the anaerobic corrosion of steel canisters is expected to produce hydrogen. The produced hydrogen behavior is then of interest because of its potential impacts on the radionuclides migration in the geological media. Thus, the major concern is the pressure build-up of trapped hydrogen inside disposal vault and consequently the potential fracking of the geological host-rock with an increase of the excavated damaged zone extension and of the rock permeability. A possible pathway for hydrogen to escape the repository vault is to flow through thin water saturated fractures of tens of micros in thickness. Assuming that hydrogen bubble flow can occur in those fractures, our objective is to study the behavior of the hydrogen bubbles by mean of numerical modeling.
On one hand, X-ray micro tomography allows today to precisely picture the rock fractures of interest and one the other hand, a large set of numerical tools can allow to model two-phase flow with interface description. We choose to use a Lattice Boltzmann approach for two main reasons: the first one lies in the simplicity of program writing with a sequential node description that allows full parallelism approach and the second one in the direct use of tomographic images without any meshing work to perform.
Among the large Lattice Boltzmann Methods zoology, we selected the color gradient model and mixed it with a Two Relaxation Time collision operator. The model was implemented using CUDA in order to run on different GPU units from laptop GPU to GPU clusters. Basic validation tests such as verification of Laplace law for a bubble in water or multiphase layered Poiseuille flow velocity profiles were successfully conducted.
Numerical simulation of bubble flow in real fracture geometries presenting a variable aperture exhibits a bubble trapping process which was not initially expected. In order to focus on this process some simulations were conducted on simplest academic geometries similar to the ones used in micro-fluidic problems where bubbles face smallest apertures during their displacement . The results obtained are presented and discussed.