Reactor configurations, hydrodynamic operating conditions

The permeate is continuously withdrawn through the membrane from the feed sueam.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... 

The modelling of the bed scale hydrodynamic contributions to these processes always requires the introduction of the parameter Ljjj. This term characterizes the interactions between the liquid and the solid. As pointed out above, it represents the local liquid velocity in an isolated rivulet inder its more stable flow configuration. This configuration and consequently may be dependent on the actual operating conditions i.e. the ones prevailing under reactor operation (and not the ones prevailing for isolated rivulets). 

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