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                  3.8 T Fluid–Solid Fluidized Bed Reactors w o-Phase,  225


                    If a fluidized and a fed bed are operated at the same  ix  Re  p  , the mass transfer coef icient f
                    ix
                   we
                   ,
                   er
                  is higher in the latter. Ho the fed bed can be operated only in dow mode, wnflo
                   v
                  because the solids would be entrained in upflow, at high Re ynolds numbers.   Re  p  should be
                  lower than the value of 1.8 times the minimum   Re  p  for fluidization to avoid excessive attri-
                  tion of the particles in the fluidized bed. For the system shown in Figure 3.65, the minimum
                  Re  p  for fluidization is about 8, and thus, the upper limit for the fixed-bed operation in down-
                  flow mode is lower than 13. Furthermore, high residence times and thus low superf icial
                  velocities and low   Re  p  are met in fixed beds. For example,  Re  p  values lower than 8 are typ-
                  ical in ion exchange and adsorption from liquid phase in fixed beds. For the system shown
                  in Figure 3.65, if the   Re  p  in the fixed bed is lower than 8 but is higher than this value in the
                  fluidized bed, the fluidized-bed mass transfer coefficient is higher than that in the fixed bed.
                    For 5     Re  p    100, the follo obtained by Rahman and Streat for mass wing correlation,
                     v
                  transfer, is valid for conentional liquid fluidized beds (Rahman and Streat, 1981;
                  Hausmann   et al  ., 2000):
                                                  0.86  0.5  1 3
                                              Sh     Re Sc                          (3.542)
                                                        p
                                                    f
                  For lower Reynolds numbers (0.22     Re  p    1), the Koloini–Sospic–Zumer correlation is
                  oloini  more accurate (K  et al  ., 1977; Hausmann   et al  ., 2000).

                                                   0.7        13
                                               Sh     Re Sc                         (3.543)
                                                        p
                                                     f
                  Here, the   Re  p  is based on superficial v. elocity


                        0.018
                        0.016              Smith, Fixed Bed
                                           Smith, Fluidized Bed
                        0.014
                                           Wilson-Geankoplis
                        0.012
                         0.01

                       f  (cm/s)
                        0.008 k
                        0.006
                        0.004

                        0.002

                           0
                             1                          10                        100
                                                        Re  p

                  Figure 3.65  Comparison of mass transfer coefficients for fixed and fluidized beds (system: w ater at
                  20 °C,      1,      2.08 g/cm  3  ,     0.4,  D    10    5  cm  2  /s, and   d    1 mm).
                        S     h                   f               p
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