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umidity easurement
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FIG 12.4. If the influent air is very dry, heat may not be required, and the louvres are manipulated.
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Dehumidification requires cooling of the humid air, with or without compression, depending on the dryness required. Manipulation of cooling under constant pressure is effective.
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EVAPORATION AND CRYSTALLIZATION
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These operat,ions may he conducted separately or in combination in an effort to separate a solid from its solvent. The product from an evaporat ion is a concentrated solution, whereas a crystallizer discharges a slurry of crystals in a saturated solution. These two operations may not be technically classified as mass transfer, in that no equilibrium exists bet,ween t)he composition of t he t#wo phases-the vapor leaving an evaporator and the crystals in the crystallizer are both essentially pure. Yet the control of both these operations is heavily dependent on the material balance.
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Multiple-effect Evaporation
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To conserve steam, evaporation is usually carried out in two or more stages, each stage being heated by the vapors driven from the previous stage. To maintain a temperature difference across each heat transfer surface, a pressure difference must be controlled between stages. The most economic operation is realized with low-pressure steam heating, requiring each stage to be maintained under a different vacuum. A double-effect evaporator is shown in Fig. 12.5; recognize that the arrangement could be extended indefinitely, but the practical limit seems to be six effects. The arrangement shown in Fig. 12.5 is forward feed, in that the feed stream enters the first effect only. Backward feed, i.e., entering the last
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Other Mass Transfer Operations
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Product w2 3x2
FIG 12.5.
A double-effect evaporator with forward feed.
effect first, is another possibility. In addition, each effect can receive fresh feed, which arrangement, is called parallel feeding. The first described is t hc most common. The controlled variable is product concentration. It can be determined by density measurement, electrolytic conductivity, refractive index, or by measuring the elevation in boiling point or the depression in freezing point of the solvent. In the past, control of product composition typically entailed manipulation of the discharge valve. The level controllers for each effect were left to manipulate each inflow, ultimately affecting feed rate. This arrangement results in a series of interactions between flows and compositions from the last effect to the first and back again. Furthermore, production rate can only be adjusted by altering the heat input, which constitutes a prime source of disturbance. These deficiencies prompted the investigation of material-balance control.
Material-balance Control
A certain amount of solvent is evaporated in each effect relative to its heat input; all the solids in the feed are discharged with the product. Let W1 represent the mass flow of feed whose solids content is ~1 (weight fraction) such that X is the mass flow of solids in the feed: x = WlXl (12.13) The total flow of solution leaving the effect, WE, contains x2 weight fraction of solids: x = wzxz (12.14) (12.15) The rate of evaporation is designated 1/s: vz = WI - wz
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By combining Eqs. (12.13) through (12.15), it is possible to calculate the rat e of evaporation required to convert a feed of known composition to a specified product composition:
vz = WI 1 - 2 ( >
(12.16)
The heat input to the effect, in t he form of vapor or st eam, will flow at a rate V1 with a latent heat H1 in order to cause the evaporation of 1 2, whose latent heat is Hz, if the feed is preheated to the boiling point: VIH, = VzHz (12.17) Combining the last two expressions gives the relationship between t he input variables necessary to maintain a desired output quality: V,H, = WI 1 - 2 Hz ( > To apply this to a double-effect evaporator, let Eq. (12.18) represent conditions existing in the second effect. The material balance for t he two effects can be derived in the same way as Eq. (12.16), relating total evaporation to inflow rate IV0 and weight fract ion solids ~0: VI + vz = w o 1 - 2 ( > Relating first-effect vapor inflow I IO, of ernhalpy Ho, to VI and Vz as was done in Eq. (12.17) permits elimination of the latter two variables: VoHo = wdl - dzd ~/HI + l/Hz Extension to an n-effect evaporator follows directly: VoHo = wdl - dzd i=n 2 l/Hi
(12.19)
Enthalpies through subsequent effects can be represented by an average value H which is slightly greater than Ho because of decreasing pressure in each effect. The denominator in Eq. (12.19) can therefore be approximated by n/H. Equation (12.19) may be implemented for control of product quality by manipulating either heat input or feed rate in relation to the other. The choice depends on t,he relative availability of each. If short-term reductions in steam availability are common, feed rate should be manipulated accordingly. But if feed is coming from another processing unit without intermediate surge capacity, the alternate arrangement is favored.
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