Modeling two-phase flows in columns equipped with structured packings : a multiscale porous medium approach.

Distillation in columns equipped with structured packings is today the most used technology for separating air in its primary components. This process is characterized by a counter-current gasliquid flow in a structure made of parallel corrugated sheets arranged in packs. The description of such system is constrained by the large dimensions of the columns and by the complexity of the local-scale phenomena. This leads to consider a strategy of upscaling, based on the volume averaging method, to describe the system at a scale at which a resolution is possible. The work is organized in three steps. As a first step, considering moderate flow rates, a methodology ofupscaling is developed to predict the pressure drop in the flow of the gas phase taking into account small scale roughnesses due to the structure itself or perturbations of the liquid film. At this stage, the effect of this rough surface is characterized by an effective boundary condition. The boundary value problem for the flow of the gas phase is volume averaged in order to derive a system of equations at large scale. The resulting momentum balance is a generalized Darcy's law for inertial flows, involving effective parameters accounting for the roughness at the microscale. The second step of this work focuses on the interaction between the two phases at higher flow rates. It is shown that models involving non-standard macroscopic cross-terms are more prone to describe the flow in packings at high Reynolds numbers than the models usually used in porousmedia sciences. More generally, these models are shown to characterize accurately processes in highly permeable media, where drastic changes of pressure drop and retention are observed. We finally study the distribution of the liquid phase in the structured packing. It is shown that a specific approach involving a multiphase model with liquid decomposition is required to capture the anisotropy generated in the flow of the liquid phase. Two methods involving two pseudo-phases and four pseudo-phases for the liquid phase are compared. This last method captures a number of very different distribution regimes in the column and offers additional flexibility to describepreferential paths of the liquid.