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                    122                             3. Heterogeneous Processes and Reactor  Analysis


                    Another parameter, similar to fractional holdup but different in v is the volume frac- alue,
                    tion of solid and liquid in the slurry (K 1996; Kantarci  oide,  et al  ., 2005).

                                                         V
                                                          S                           (3.172)
                                                    S
                                                       V
                                                          V
                                                        S  L
                                                         V
                                                          S                           (3.173)
                                                    L
                                                       V
                                                          V
                                                        S  L
                      In this def the term “slurry” is used to denote the phase consisting of the liquid
                      inition,
                    and the solid, and thus the term “b would be a more appropriate term to ubble-free slurry”
                    be used for this phase.
                      Smith (1981) uses the parameter   V  B  , referred to in his book as “gas holdup, which is ”
                    defined as “the volume of bubbles per unit volume of liquid, which is different from the ”
                    fractional holdup v alue:

                                              V  G  V  G  V  tot  V  G  V  tot  h  G
                                          V  B                                        (3.174)
                                              V    V  V    V   V    h
                                                L   L  tot  tot  L   L
                    Then, follo the “total gas holdup” is
                     wing Smith’
                    ,
                     s terminology
                                                    VV  V                             (3.175)
                                                     BL   G
                    which is simply the total volume of gas in the reactor .
                      The fractional gas holdup can be easily measured from the height of the expanded col-
                    umn height   Z  f  and the settled slurry height   Z , i.e. the height of the column before aeration
                                                        s
                    (liquid volume plus solids volume) (DOE, 1985; NTIS, 1983):
                                                       Z  Z
                                                   h     f  s                         (3.176)
                                                    G
                                                         Z
                                                           f
                    Define the mass concentration of solids in a slurry as

                                                         M
                                                    m      S                          (3.177)
                                                      s
                                                         V
                                                          L
                    where   V  L  is the volume of liquid then
                                                         M
                                                    V      S                          (3.178)
                                                     L
                                                         m
                                                           s
                    and f inally
                                                     V  S  m  s
                                                                                      (3.179)
                                                     V
                                                      L   p
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