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                  3.8 T Fluid–Solid Fluidized Bed Reactors w o-Phase,  223


                  For the cloud phase,
                                      K  C (  C    K )  C   C (  r )    (     )     (3.537)
                                       bc  b  c  ce  c  e  c  c,vs

                  For the gas in the emulsion phase (dense phase),


                                            K  C (  C    )   r (    )               (3.538)
                                             ce  c  e  e  s e,v
                  3.8.4 Liquid–solid particulate fluidization (liquid–solid catalysis,
                        adsorption, and ion exchange)


                  Three models of the fluidized-bed process can be considered (Menoud   et al  ., 1998):

                  •  complete backmixing of the liquid and the solid (CSTR model);
                  •  near plug flow of the liquid and a complete backmixing of the solid, which is the plug-
                     flow model with backmixing of the solid;
                  •  near plug-flow of the liquid with no backmixing of the solid, which is the plug-flo w
                     model.

                    Since the particulate flow regime is characterized by a relatiely uniform expansion of v
                  the bed without the formation of bubbles, it can be approximated as an expanded fixed bed
                   ,
                  (Wen, 1984; Hopper 2001). Thus, the fed bed models can be used for the particulate
                    ix
                  flow regime in fluidized beds for catalysis as well as for adsorption and ion e xchange.
                  Fluidized-bed operation in adsorption and ion exchange is rare and has been studied for
                  heavy metals removal from the liquid phase to a chelating resin, and for the determination
                  of mass transfer rates in a magnetically stabilized liquid fluidized bed of magnetic ion-
                  exchange particles (Menoud   et al  ., 1998; Hausmann   et al  ., 2000).
                    The main mass transport resistance in liquid fluidized beds of relatiely small particles v
                  Thus,
                  ilm.
                  lies in the liquid f for ion exchange and adsorption on small particles, the mass
                  transfer limitation provides a simple liquid-film diffusion-controlled mass transfer process
                  (Hausmann   et al  ., 2000; Menoud   et al  ., 1998). The same holds for catalysis.
                  It should be noted that in the material balances, the fluidized bed voidage should be used
                  instead of fixed-bed voidage, and that the appropriate mass transfer correlations should be
                  used for particulate fluidization.

                  3.8.5 External mass transfer

                  In fluidized beds, mass transfer ines two different mechanisms. The first one is the
                   v
                   olv
                  ordinary mass transport between the fluid and the solid. The treatment of this type of trans-
                  port is quite similar to fluid–solid mass transfer found in other types of operations such as
                  fixed beds and agitated tank reactors. This mechanism of mass transfer is not alays sig- w
                  nificant in fluidized beds and can be totally neglected in some cases.
                    In contrast, the second mechanism is quite dif ferent and it is found only in fluidized-bed
                  reactors. It concerns the mass transfer between the bubbles and the particulate phase
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