Page 190 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

188 Chapter 6 Evaporators

Removal of noncondensable gases in vertical tube evaporator is not very efficient. Noncondensable
gases are transferred to the condensate steam chest in horizontal tube, long tube vertical and forced
circulation evaporators.

6.6.2 Multiple effect evaporation

The equations for a single effect are valid for the individual effects of the multiple-effect evaporator.
The rate of heat transfer for any effect ‘i’ is thus, given by

q i ¼ U i A i DT eff;i (6.8)
Assuming that the feed enters the first effect at its boiling point and the condensate leaving effect
2 is at the temperature of vapor obtained from the boiling liquid in the first effect (T 1 ), the entire heat
used in generating vapors in the first effect must be given out when the same vapor condenses in the
second effect and so on.
Mathematically,

(6.9)
q i ¼ q i 1 ¼ q iþ1
or

U i A i DT eff ;i ¼ U i 1 A i 1 DT eff ;i 1 ¼ U iþ1 A iþ1 DT eff ;iþ1 (6.10)
Where DT eff,i for each effect is given by Eq. 6.2.
In ordinary practice, to obtain economy of construction, all A i s are preferred to be equal, which
gives e

(6.11)
U i DT eff ;i ¼ U i 1 DT eff ;i 1 ¼ U iþ1 DT eff ;iþ1
Therefore, the temperature difference across the heating surface in each effect (DT eff,i )ofa
multiple-effect evaporator is inversely proportional to the heat transfer coefficient.

Optimum number of effects in a multiple-effect system
Assuming that the latent heat is not significantly influenced by pressure, it can safely be considered
that the latent heat required to evaporate 1 kg steam is same in each effect and for every 1 kg steam
supplied to the first effect, N kg water will be evaporated in an N-effect evaporator while the evaporator
capacity remains substantially constant.
Total amount of heat required to achieve the evaporator capacity (total evaporation per hour) for N
effects is
N N
X X
q total ¼ q i ¼ U i A i DT eff ;i (6.12)
i¼1 i¼1
For all effects having equal area (A i ¼ A i 1 ¼ A iþ1 ) and an average coefficient U av

q total ¼ U av ADT ov (6.13)
Where DT ov , the overall temperature difference in the evaporator system is given by

(6.14)
DT ov ¼ T steam T V