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                    162                             3. Heterogeneous Processes and Reactor  Analysis


                    For   N openings, the diameter of each one is
                                                         A 4   o  0.5
                                                  D                                 (3.343)
                                                   o     N    
                      Considering that the distance between the openings   L  o  should be the same, and keeping the
                    same distance between the wall of the bed and the ends of the distributor, the distance   L  o  is
                                                       L   ND
                                                  L          o                        (3.344)
                                                   o
                                                        N   1
                    The total number of openings   N af v and  w rate, fects the flo , elocity  Re  D  in the region of the
                    last opening, which is determined to (1/  N ) of the opening at the entrance of the distrib . utor
                    So,  Re  D  at the first and the last opening of the distributor can be calculated, and in turn, the
                    corresponding values of the fanning friction factors can be estimated. The mean value of
                    these two factors should be used in the calculations in this procedure.
                      Finally, gien the length of the distributor—which is approximately equal to the bed
                       v
                    diameter, the feed rate and the distributor material, the diameter of the distrib utor’ s open-
                    ings can be calculated on the grounds that the diameter and the number of openings has
                    been chosen. In practice, the diameter of the distrib which is a small percentage of the utor ,
                    bed (    and the number of openings define the   Re  D  number at the ends of the dis-
                          20%),
                    tributor, which should be high (typically    2100). From this point of vie the design pro- , w
                    cedure is a trial-and-error process, based largely on e xperience.
                      During calculations, it has to be taken into account that the pressure drop     across the dis- p
                    tributor should be always negative. Moreover, for   M  do    5%, this pressure drop should be
                    approximately equal to one-tenth the mean pressure drop at the openings. Finally, the number
                    of openings should be chosen appropriately to lead to easy construction of the distributor.

                    Example 6
                    Suppose that a perforated-pipe distributor made from iron will be used for a feed rate of 428
                    L/h. The distributor has a length of 1.8 cm (8.5% of the diameter of the bed,  D   21 cm),
                    and length shortly less than the diameter of the bed (20.9 cm). According to the calculations,
                    for the specific feed rate, the distributor will hae four round openings with a diameter of v
                    6.6 mm each. The distance between the openings as well as the distance between the ter-
                    minal openings and the ends of the distributor is 36 mm. Ho these calculations can er v , we
                    be repeated for various feed rates to choose the optimum distributor design.
                    Gas-phase distribution in fixed beds
                    The problem of gas distribution is similar and typical gas distributors are given in Figure 3.43.


                    3.6.4 External heat and mass transfer

                    Liquid–solid systems

                    The liquid mass transfer coefficient (or convection coefficient) is a flow-dependent param-
                      v
                    eter, which can be ealuated from seeral correlations found in the related literature.
                       v
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