Piston flow model with mass transfer

LS.4.2.1. Piston flow model with mass transfer coeflUcient... 

It has been shown by Chavarie and Grace (15) that the decomposition of ozone in a fluidized-bed is best described by Kunii and Levenspiel s model (16) but that the Orcutt and Davidson models (17) gave the next best approximation for the overall behaviour and are easier to use and were chosen for the simulation. They suppose a uniform bubble size distribution with mass transfer accomplished by percolation and diffusion. The difference between the two models is the presumption of the type of gas flow in the emulsion phase piston flow, PF, for one model and a perfectly mixed, PM, emulsion phase for the other model. The two models give the following expressions at the surface of the fluidized bed for first-order reaction mechanism ... 

In fact the piston flow model, as well as the diffusion model, gives too ideal picture of the structure of the flows. They take into account neither the diffusion boundary layer nor the real movement of the phases. These models are especially far from the real situation in flie apparatus in respect to the liquid phase which moves not like a piston flow but in the form of film, drops and jets which are not only separate in space but have also different and continuously changing velocities. Nevertheless, not only the diffusion model but in some cases also its simpler variant, the piston flow model, gives oflxm very good description of the mass transfer processes in industrial apparatuses. This can be explained with the comparatively weak influence of the real structure of the flows on the mass transfer. On the other side using in the model such experimentally obtained values as mass transfer coefficient, effective surface, and Peclet number, it is possible to take into account the important for the mass transfer rate characteristics of the flows structures. In Chaptra 8 the cases when it is possible to use the simpler piston flow model, and when it is necessary to use the diffusion model are considered and specified. 

As already mentioned foe mass transfer coefficients used for calculations in chemical engineeting are rather parameters in foe calculation model than physical values. That is diy speaking of methods for determination of these coefficients we should distinguish methods for determination of foe mass transfer coefficients for foe piston flow model and for foe diffusion model. Since for foe latter model foese coefficients are connected with foe axial mixing coefficients in gas and liquid phase, foe methods for their determination are discussed after foe mefoods for determination of foe axial mixing coefficients. 

The meliiod gives also the possibility to calculate the mass transfer coefficient for the diflhision model with the corresponding data from the piston flow model. 

The tube is packed with catalyst pellets. Flow may be either laminar or turbulent. The velocity profile is assumed to be flat. Transfer of heat and mass in the radial direction is modeled using empirical diffusion coefficients that combine the effects of convection and true diffusion in the radial direction. There is no axial diffusion. Details are given in Chapter 9. This model is important only for nonisothermai reactors. It reduces to piston flow if the reaction is isothermal. 

The reactor is turbulent, the velocity profile is flat, radial mixing is complete, and there is some transfer of heat and mass in the axial direction. The tube can be either packed (e.g., with a catalyst) or open. This model provides an estimate of reaction yields in highly turbulent reactors that is more conservative than assuming piston flow. 

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