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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 the cost of reduced capacity.

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It may be thought that by providing several times as much heating surface the evaporating would be increased, but it is not the case.

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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.

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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)

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**The total capacity is proportional to the total rate of heart transfer qT**

(16-14)

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Assume that the surface area is A in each effect and that the overall coefficient U is also the same in each effect. Then (16-15)

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Δt is the total temperature drop between the steam in the first effect and the vapor in the last effect.

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Suppose now that a single-effect evaporator with a surface area A is operating with the same 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

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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 single effect.

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**Offsetting this are the changes in overall coefficients in a multiple-effect evaporator.**

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The average coefficient for the multiple-effect evaporator would be greater than that for the single-effect.

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**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

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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 the previous 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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281º 105º temperature 176º 100º

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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.

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281º 281º 35º 246º 105º 226º temperature 50º 176º 176º 100º 100º

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In the triple-effect evaporator there are shaded portions since there is a loss temperature drop in each of three effects, and the total net available temperature drop ,79℃

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281º 281º 35º 246º 105º 226º temperature 50º 176º 176º 100º 100º

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

(16-16)

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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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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

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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 N times that for a single-effect evaporator of the same capacity.

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The optimum number of effects must be found from an economic balance between the savings in steam obtained by multiple-effect operation and the added investment required.

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