Chapter 16
Capacity and economy of
multiple-effect evaporators
The increase in economy through the use of
multiple-effect evaporation is obtained at the
cost of reduced capacity.
It may be thought that by providing several
times as much heating surface the evaporating
would be increased, but it is not the case.
The total capacity of a multiple-effect
evaporator is usually not greater than that of
a single-effect evaporator having a heating
surface equal to one of the effects and
operating under the same terminal condition.
If the heating load and the heat of dilution are
neglected, the capacity of an evaporator is directly
proportional to the rate of heat transfer.
A1t1
q2  U 2 A2 t2
q3  U3 A3t3 (16-13)
The total capacity is proportional to the total
rate of heart transfer qT
qT  U1 A1t1  U 2 A2 t2  U 3 A3t3
(16-14)
Assume that the surface area is A in each e
ffect and that the overall coefficient U is a
lso the same in each effect.
Then
qT  UA(t1  t2  t3 )  UAt
(16-15)
Δt is the total temperature drop between the
steam in the first effect and the vapor in the
last effect.
Suppose now that a single-effect evaporator
with a surface area A is operating with the s
ame total temperature drop.
If the overall coefficient is the same as in each
effect of the triple-effect evaporator.
For the single effect
qT  UAt
This is exactly the same equation as that for t
he multiple-effect evaporator
The boiling-point elevation tends to make the
capacity of the multiple-effect evaporator
less than that of the corresponding single
effect.
Offsetting this are the changes in overall
coefficients in a multiple-effect evaporator.
The average coefficient for the multiple-effect
evaporator would be greater than that for the
single-effect.
Effect of liquid head and
boiling-point elevation
The liquid head and the boiling-point elevation
influence the capacity of a multiple-effect
evaporator even more than they do that of a
single effect
The reduction in capacity caused by the liquid
head, as before, cannot be estimated
quantitatively.
The liquid head reduces the temperature drop
available in each effect of a multiple-effect of
a multiple-effect evaporator.
The temperature drop in any effect is calculated
from the temperature of saturated steam at
the pressure of the steam chest, and not from
the temperature of the boiling liquid in the
previous effect.
This means that the boiling-point elevation in
any effect is lost from the total available
temperature drop.
This loss occurs in every effect of a
multiple-effect evaporator, and the
resulting loss of capacity.
• Consider the single-effect evaporator.
Of the total temperature drop of 181℃,
the shaded part represents the loss in
temperature drop 105℃
The actual driving force for heat transfer
is represented by the unshaded part.
176º
100º
temperature
105º
281º
The diagram for the double-effect evaporator
shows two shaded portions because there is a
boiling-point elevation in the two effect.
The residual unshaded part, 85º, is smaller
than in the diagram for the single effect.
281º
105º
246º
176º
100º
50º
226º
176º
100º
temperature
35º
281º
In the triple-effect evaporator there are
s
haded portions since there is a loss
t
emperature drop in each of three effects, a
nd the total net available temperature
dr
op ,79℃
281º
105º
246º
176º
100º
50º
226º
176º
100º
temperature
35º
281º
Substitution from Eq. (16-2)into Eq. (16-8)gives
m f c pf (t  t f ) W 
D

v
v
(16-16)
The economy of a multiple-effect evaporator is
not influenced by boiling-point elevations if
minor factors, such as the temperature of the
feed and changes in heats of evaporization,
are neglected. Then by Eqs. (16-16)
A kilogram of steam condensing in the first
effect generates about a kilogram of vapor,
which condenses in the second effect,
generating another kilogram there, and so
on.

The economy of a multiple-effect, evaporator
depending on heat-balance considerations
and not on the rate heat transfer.

The capacity, is reduced by the boiling- point
elevation
Optimum number of effects
The cost of each effect of an evaporator per
square meter of surface is a function of its
total area.
The investment required for an N-effect
evaporator is about N times that for a
single-effect evaporator of the same capacity.
The optimum number of effects must be found
from an economic balance between the
s
avings in steam obtained by multiple-effect o
peration and the added investment required.