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                                                                    Heat Transfer                                          193

                              parameter for two-phase physical properties, for use  B. Heat Transfer: Simplified Method
                               with Figures 10-114, 10-115, 10-116, and 10-117.  Fair recommends this method rather than his stepwise
                               Although   is not constant, in general an average  method given in the article, because it avoids increments of
                               constant value may be assumed. 45           calculations but is sufficiently reliable for most design cases.
                      10. Calculate the circulation rate, W T , by (see Table 10-29):  This procedure is duplicated by permission. 45
                                                                             See Table 10-29.
                             2
                           g a 1   L 31  L    tp 2 Z    L  W s 4
                       W T
                        2
                                             2                               1. The previously established circulation rate is used, but
                                  L i      a i
                              2f Li    	 2f L t a b p                          the exchanger dimensions must be checked for heat
                                 D i       a t
                                                                               transfer. Obtain additional overall average values:
                                                                               a. Heat transfer coefficient for liquid, h L (equation fol-
                              L Bc  2     2   L cD
                         p c     	
 11   x2     d p                               lowing).
                             D t             D t
                                                                               b. Heat transfer coefficient for two-phase mixture,
                                                                                  _
                                                                                  h tp , at x   0.4x E (Figure 10-117).
                                                                (10-181)
                                            2   L DA     a i  2                c. Boiling coefficient correction factors:
                                          a i
                                              2
                                       2
                         p 	 2f LE 11   x E 2 a  b 
 E    	 a  b
                                         a E    D E      a E
                     where                                                   ' at x     0.4x E  and   E  at x     x E
                            tp   effective average two-phase density, lb/ft 3               _
                          _
                            tp   average density, lb/ft , two phase            Figure 10-118;   from Equation 10-184.
                                               3
                           2
                          
   effective average (two-phase)/liquid phase pressure  d. Nucleate boiling coefficient, h b , from Table 10-30 or
                               drop ratio corresponding to effective average      other source. (An estimate of the film temperature
                               vaporization x                                     drop is required.)
                         a i /a t   cross-sectional area ratio, inlet line/total tubes
                        a i /a E   cross-sectional areas ratio, inlet line/exit line  2. Calculate the process side heat transfer coefficient, h p ,
                           a i   cross-sectional area, inlet feed pipe, ft 2   from Equations 10-185 and 10-186).
                           Z   height of driving leg for thermal circulation, ft  3. Calculate the total heat transferred to the process fluid
                          W T   mass rate, lb m /sec, total flow, or W         check against the required value. The adjustments
                          W s   shaft work done by system, ft liquid
                              change from one condition to another             required may result in a new exchanger configuration
                          L i   change in equivalent length of pipe, ft, inlet piping  and a new calculation of circulation rate.
                               system
                          D i   inlet diameter, feed pipe ft
                           _ f   fanning friction factor dimensionless       Design Comments
                           
   average value of 
                            These comments are directed to the inexperienced
                           L   equivalent length of pipe, ft               designer, and in general, amplify material previously pre-
                              acceleration loss group, dimensionless       sented. The comments are somewhat random in nature but
                                                                           are nonetheless important considerations in optimum
                                11   x2  2    L  x 2                       design.
                               c       	    a  b   1d
                                  R L      g  R g
                                                                             • The thermosiphon reboiler has inherent instabilities. A
                     (Evaluate at outlet values of x, R L , and R g )          valve or other flow restriction in the inlet line helps
                           _
                           x   average value of weight fraction of vapor or gas,  overcome these instabilities. Adjustment possibilities of
                               dimensionless                                   a valve also compensate for variations in reboiler duty
                           E   subscript, exit reboiler vapor                  as imposed by changes in operation of the fractionator.
                         This equation can be used to shorten the design by  • For once-through natural circulation reboilers, the liq-
                         carefully selecting the overall average values. If specific  uid backup height is calculated from the pressure bal-
                         data is not available, Fair 45  recommends using the  ance equation. If this height, plus an allowance for
                         guidelines in Table 10-28.                            froth, reaches the bottom tray level, flooding of the
                      11. Calculate the boil-up and check against the required  tower will occur.
                         process balance value.                              • Economic optimum design usually implies high circu-
                      12. Calculate boil-up and check against the required bal-  lation rates, although not high enough to give “mist”
                         ance for process balance.                             flow.
                      13. Repeat calculations, adjusting flow as necessary, until  • The large fraction of tube length used for sensible heat-
                         the assumed X E (weight fraction of vapor in reboiler  ing in vacuum reboilers leaves little density difference
                         exit) produces the proper boil-up rate.               for thermal circulation. This fact, plus the frequent
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