Detailed Hydrodynamics in Membrane Reactor

The permeate is continuously withdrawn through the membrane from the feed sueam. The fluid velocity, pressure and species concentrations on both sides of the membrane and permeate flux are made complex by the reaction and the suction of the permeate stream and all of them depend on the position, design configurations and operating conditions in the membrane reactor. In other words, the Navier-Stokes equations, the convective diffusion equations of species and the reaction kinetics equations are coupled. The transport equations are usually coupled through the concentration-dependent membrane flux and species concentration gradients at the membrane wall. As shown in Chapter 10, for all the available membrane reactor models, the hydrodynamics is assumed to follow prescribed velocity and sometimes pressure drop equations. This makes the species transport and kinetics equations decoupled and renders the solution of 

expectedly no rigorous mathematical models are available that can accurately describe the detailed flow behavior of the fluid streams in a membrane separation process or membrane reactor process. Recent advances in computational fluid dynamics (CFD), however, have made this type of problem amenable to detailed simulation studies which will assist in efficient design of optimal membrane filtration equipment and membrane reactors. 

Only a limited number of studies has begun to emerge in this area. The available studies encompass various levels of details. Some use CFD to focus the simulation on the How of liquid and particles through membrane pores while others model fluid flow through a single membrane tube. CFD simulation of fluid flow through a multi-channel monolithic membrane element has also been done. 

Ilias and Govind [1993] also used the CFD approach to solve coupled transport equations of momentum and species describing the dynamics of a tubular ultraflltration or reverse osmosis unit. An implicit finite-difference method was used as the solution scheme. Local variations of solute concentration, u ansmembranc flux and axial pressure drop can be obtained from the simulation which, when compared to published experimental data, shows that the common practice of using a constant membrane permeability (usually obtained from the data of pure water flux) can grossly overestimate 

Wai and Fumeaux [1990] applied CFD to crossflow membrane filtration to provide an array of data such as local pressures and fluid velocities on both sides of a membrane, shear stresses on the membrane surface and local concentrations of retentate species. This type of information is useful for designing the membrane unit as a separator or a reactor. With a commercial CFD code, the authors simulated the fluid flow, on both the feed and permeate sides, along the membrane channel and through the membrane. Frictional effects between the fluid and membrane surfaces depend on the nature of the fluid flow. For flow parallel to the essentially flat membrane surface, standard wall friction expressions based on logarithmic velocity profiles adjacent to the wall arc used. 

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