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Chapter 16

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Capacity and economy of

multiple-effect evaporators

The increase in economy through the use of

multiple-effect evaporation is obtained at thecost of reduced capacity.

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The total capacity of a multiple-effectevaporator is usually not greater than that

of a single-effect evaporator having a

heating surface equal to one of the effectsand operating under the same terminal

condition.

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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.

(16-13)1 1 2 2 2 2 3 3 3 3A t q U A t q U A t

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The total capacity is proportional to the total

rate of heart transfer qT

(16-14)1 1 1 2 2 2 3 3 3Tq U A t U A t U A t

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Assume that the surface area is A in eacheffect and that the overall coefficient Uis

also the same in each effect.

Then

(16-15)1 2 3( )Tq UA t t t UA t

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tis the total temperature drop between the

steam in the first effect and the vapor in thelast effect.

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Suppose now that a single-effect evaporatorwith a surface area A is operating with thesame total temperature drop.

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If the overall coefficient is the same as in each

effect of the triple-effect evaporator.

For the single effect

Tq UA t

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This is exactly the same equation as that for

the multiple-effect evaporator

The boiling-point elevation tends to make the

capacity of the multiple-effect evaporator

less than that of the corresponding singleeffect.

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The average coefficient for the multiple-effectevaporator would be greater than that for thesingle-effect.

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Effect of l iquid head and

boil ing-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 asingle effect

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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.

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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 theprevious effect.

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This means that the boiling-point elevation in

any effect is lost from the total available

temperature drop.

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This loss occurs in every effect of a

multiple-effect evaporator, and the

resulting loss of capacity.

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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.

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105

temperature

100

176

281

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The diagram for the double-effect evaporatorshows two shaded portions because there is

a boiling-point elevation in the two effect.

The residual unshaded part, 85, is smaller

than in the diagram for the single effect.

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50

100

281

176

35

226

246

105

temperature

100

176

281

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In the triple-effect evaporator there areshaded portions since there is a loss

temperature drop in each of three effects,

and the total net available temperaturedrop ,79

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105

temperature

100

176

281

50

100

281

176

35

226

246

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Substitution from Eq. (16-2)into Eq. (16-8)gives

(16-16)( )f pf f

v v

m c t t WD

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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)

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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.

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Optimum number of effects

The cost of each effect of an evaporator per

square meter of surface is a function of its

total area.

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The investment required for an N-effect

evaporator is about Ntimes that for a

single-effect evaporator of the same capacity.

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