Page 108 - Applied Process Design For Chemical And Petrochemical Plants Volume III

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76 Applied Process Design for Chemical and Petrochemical Plants

applies to counter-current and parallel flow only, it can be used Tube Wall Temperature
with reasonable accuracy for multipass flow. 107
70
The caloric value of hot fluid (from Kern, by permis- Refer to Figure 10-28. The temperature of the outside of
sion): the tube wall is based on hot fluid being on the outside of
the tubes:
t h t h2 F e 1t h1 t h2 2 (10-21)
h io
t w t h 1t h t c 2 (10-24)
h io h o
The caloric value of the cold fluid:
or
t c t c1 F c 1t c2 t c1 2 (10-22)
h o
t w t c 1t h t c 2 (10-25)
t c t 1 t h t h1
F c or (10-23) h io h o
t 2 t 1 t h2 t h1
where where
t h caloric value or hot fluid, °F h io inside film coefficient referred to outside of tube,
t h1 inlet hot fluid temperature, °F Btu/hr (ft ) (°F)
2
t h2 outlet hot fluid temperature, °F h o outside film coefficient referred to outside of tube,
t c caloric value of cold fluid, °F Btu/hr (ft ) (°F)
2
t c1 inlet cold fluid temperature, °F t w temperature of outside wall of tube, °F
t c2 outlet cold fluid temperature, °F
F c correction factor, F, (see Reference 70 for details),
The outside tube wall temperature for hot fluid on the
Figure 10-38. The insert allows for more rapid calcu-
inside of the tubes is
lation for petroleum fractions.
h io
t w t c 1t h t c 2 (10-26)
h io h o
For heat exchangers in true counter-current (fluids flow-
ing in opposite directions inside or outside a tube) or true or
co-current (fluids flowing inside and outside of a tube, par- t w t h h o 1t h t c 2 (10-27)
allel to each other in direction), with essentially constant h io h o
heat capacities of the respective fluids and constant heat An alternate and possibly less accurate calculation (but
transfer coefficients, the log mean temperature difference not requiring the calculation of caloric temperature) using
may be appropriately applied, see Figure 10-33. 107 reasonably assumed or calculated film coefficients and bulk
For a variation in heat transfer coefficient from one end rather than caloric temperature is
of the exchanger to the other where the average fluid tem- For hot fluid on shell side:
perature is considered approximately linear, the physical
h o
properties of the fluids can be approximated by evaluating t w t c c d1t h t c 2 (10-28)
them using Figure 10-38. To use this figure, the temperature h i h o
t w the outside surface temperature of wall
change of each fluid multiplied by the F factor from the
chart is added to its respective cold terminal temperature to
For hot fluid in tubes:
obtain the average temperature. The t c and t h from the
figure represent the cold and hot terminal temperature dif- h i
t w t c c d1t h t c 2 (10-29)
ferences, and C of the chart represents the fractional h i h o
change in heat transfer coefficient as a parameter of the
chart. For hydrocarbon fluids, the C may be simplified using where
the insert in Figure 10-38. 107 Other less frequently used t w tube wall temperature, neglecting fouling and metal
exchanger arrangements are discussed by Gulley. 129 Note wall drop, °F
t c cold fluid bulk temperature, °F
that the F factor for Figure 10-38 is not the same F factor as
t h hot fluid bulk temperature, °F
given in Figures 10-34A—J.
The C ratio (disregard sign if negative) is evaluated from
Often this may be assumed based upon the temperature
the estimated overall coefficients based on the temperatures
of the fluids flowing on each side of the tube wall. For a
at the cold and hot ends, respectively. For Figure 10-38, the
more accurate estimate, and one that requires a trial-and-
hot terminal difference is t h t h1 t c2 ; the cold terminal
error solution, neglecting the drop-through tube metal wall
temperature difference is t c t h2 t c1 .
(usually small):