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1 Applications
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case y is fixed, considerably simplifying matters. The content of crystals in the slurry is (Z - y)/(l - y), whereas total solute content is x. The most significant outcome of the above derivation is that motherliquor flow should be set in ratio to feed rate. Feedback from crystal density is not mandatory, because the process is self-regulating and extreme accuracy is not usually warranted. Evaporative crystallizers may be treated just like evaporat ors, since pure solvent is driven off by a proportional flow of heat. The only difference is t hat the part of the product which remains in solution is a function of solution temperature. The latter is not an independent variable, however, because the solut ion is boiling.
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EXTRACTION AND EXTRACTIVE DISTILLATION
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Ext,raction is defined as the transfer of a dissolved material between two immiscible solvents. The material being t ransferred may be solid, liquid, or gas in its ordinary state. The purpose of the extraction is to permit its separation from the first solvent or some contaminant in it. Many liquids whose boiling points are nearly identical, preventing their distillation, can be separated by extraction, often in conjunction with distillation. A serious problem area in distillation technology involves substances which form constant-boiling mixtures, called azeotropes. Azeotropes are encountered so often in chemical systems that their separation deserves special mention apart from the conventional distillation practices discussed in the previous chapter. Because the principles of extrac- , tion play a major role in azeotropic distillation, the subject will be discussed in detail.
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Extraction and Decantation
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In a single extraction stage, an equilibrium will be approached between the concentration of product in the two exit streams. Consider a product dissolved in solvent A being extracted into solvent B. If 21 is used to represent the concentration of product remaining unextracted, and y1 that of the product leaving in B, then
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21 =
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(12.26)
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where K is the equilibrium constant. Similarly, a material balance may be drawn across the stage: A(xo - XI> = B(y, - yo) (12.27)
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Recognize that A and B are mass flow rates of the two solvents, and that x0 and yo are the concentrations of product in each influent stream.
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Other Mass Transfer Operations
It is usually convenient to manipulate the flow of ext ractant B in response to changes in feed rate A and composition 20, in order to control the concentrat,ion of cxtract,cd product. If this is indeed the case, Eqs. (12.2G) and (12.27) may be solved for R in terms of yl:
B = A t ;$)
(12.28)
Sate once more the familiarity of the material-balance equation, particularly the rat,io existing between A, the feed rate, and B, the manipulated variable Whet,her single or multistage, control of extraction always involves manipulation of this ratio. l\lultist,age extra&ion may be carried out in a series of mixers, each followed by a set,tling chamber, where the solvents are separated and allowed to flow countercurrently. However, extraction is more commonly conduct#ed in packed towers, with extract ant flowing countercurrently to the feed. The less dense solvent must enter at the bottom, flowing upward at, a rate determined by its difference in density from the heavier solvent. Not only must liquid level be controlled, but interface as well, in order to maintain inventory of both solvents. Figure 12.8 shows how the control loops would be arranged for a typical extract ion column. The location of the interface between two solvents is easily measured as differential pressure between two taps or buoyant force on a displacer. In either case, the measurement reflects the average density across the vertical span of the instrument. Decanters arc used to separate two immiscible solvents following extraction, mixing, or condensation from the vapor phase. Like extracOvertlow light solvent Heavy solvent Underflow heovy solvent
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