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Application of Coarse Grained Drag Law In Computational Fluid Dynamics Simulations of Fluidized Beds

Alvin U. Chen and E. Nicholas Jones. ExxonMobil Research and Engineering Company, Fairfax, VA 22037

Scale-up of fluidized beds for industrial applications has typically been carried out using dimensional analysis similar to single-phase fluid flow. However, it is impossible to keep all dimensionless groups constant, and therefore impossible to accurately scale up industrial fluidized solids processes using traditional scaling arguments. Because of this inability to fully understand factors affecting scale-up, designs based on small cold-flow experiments or even larger pilot units may overlook critical factors influencing operability of commercial units.

Computational fluid dynamics (CFD) has the potential to directly simulate behavior of reactive commercial scale units, thus overcoming gaps in scale-up methodology. However, CFD technology itself is not without limitations. The popular Eulerian-Eulerian approach (which treats gas and solids phases as interpenetrating continua) suffers from the dependence of predicted dynamics on the computational mesh resolution. Because of this grid dependence, scale-up of the CFD simulations themselves can be difficult or impractical since the grid resolution must be held constant between a typically small validation experiment and a large commercial scale simulation.

The dependence of predicted dynamics on grid resolution arises from ignoring small-scale flow structures which are not adequately resolved with coarse grids. The use of highly resolved computational grids which fully resolve small-scale flow structures can overcome this hurdle (analogous to DNS for single-phase flows), but such fine grid resolutions are impractical for commercial scale systems. Another more computationally efficient method uses so-called coarse grained models which adjust parameters such as interphase drag with changing grid size to capture effects of the small-scale flow structures on overall bed dynamics. Thus, a commercial gas fluidized solids unit can be simulated at relatively low mesh resolution while capturing most features of the overall dynamics.

In this paper, we use such a coarse grained Eulerian-Eulerian model to simulate dynamics of a small-scale cold-flow model of a fluid coker. By comparing our CFD results with experimental measurements, we demonstrate the utility of coarse grain models for fluid-solids flow and also the accuracy of our simulations. We are able to accurately predict gross flow structures in the fluidized bed as well as local voidage and velocity profiles, thus building confidence in the simulation of commercial scale cokers.