Advanced modelling of transport phenomena in granular poroux media
Etudiant :Aboubacar DJIBO SOUMANA
Directeur ou Directrice :I. Pitault
Financement :Bourse MRES
Co-direction : B. Maschke et M.L. Zanota (CP2M)
The models used to simulate transport phenomena in granular fixed beds are generally of two types. The first are process engineering-type models that consist in making balances of mass, energy and momentum on the solid-fluid system. These are either so-called pseudo-homogeneous models which represent the solid-fluid system as a continuum with parameters taking into account the two phases, or so-called heterogeneous models which separately describe the two phases with parameters for each phase. The second type of model are of the Computational Fluid Mechanics type which solve the Navier-Stokes equations (momentum balance), energy, continuity and specie balances on each cell of the granular porous medium mesh. The latter is either considered homogeneous and uniformly meshed with finer mesh at the reactor outer wall, or considered heterogeneous with two distinct phases, the solid and the fluid. In the latter case, the particle surfaces are also considered as walls during meshing.
Process engineering-type models give acceptable results if the reactor diameter (D) is about 15 times larger than the particle size (d) i.e. D / d> 15 and if the chosen models and correlations are suited to the studied problem. But when the D / d <15, like for instance fixed bed reactors used for methane steam reforming where very endothermic chemical reactions take place with high temperature conditions (approximately 800° C), these models cannot accurately simulate the transport phenomena. As for Computational Fluid Mechanics type models, they can be precise but require very significant computing resources and time.
My thesis proposes a new type of model which would be a compromise between the precision and the computational resources necessary for the simulation. This is a CPH-type model (Cell Port-Hamiltonian model), already used for metallic foams, which considers the structure of the particle stack and the pore network respectively as two graphs associated with solid and fluid phases, which are connected by a third solid-fluid coupling graph. These graphs can be obtained by processing tomographic images of the particle stack using dedicated software such as iMorph. The balance equations are written and solved using the formalism of Port-Hamiltonian systems.