Extraction operating line

Figure 4.10, where any slight fall in the equilibrium Iine,i e.g. as a result of a change of acidity, causes the extraction operating line to move to the right and release additional solute into the rafiSnate. 

In extraction (qv), the distribution coefficient value is the slope of the equiUbrium line. In practice, the slope of the operating line is set at a value somewhat less than the distribution coefficient to provide driving force and fix the required theoretical extraction stages at some reasonable number. 

In case A the solvents are immiscible, so the rate of feed solvent alone in the feed stream F is the same as the rate of feed solvent alone in the raffinate stream R. In like manner, the rate of extraction solvent alone is the same in the stream entering S as in the extract stream leaving E (Fig. 15-12). The ratio of extraction-solvent to feed-solvent flow rates is therefore S /F = E /R. A material balance can be written around the feed end of the extrac tor down to any stage n (see Fig. 15-12) and then rearranged to a McCabe-Thiele type of operating line with a slope of F /S [Eq. (15-11)]. 

Likewise, one knows that Y will be on the equilibrium line with X (see Fig. 15-12). One can therefore calculate a pseudo concentration of solute in the inlet extraction solvent Yf that 011 fall on the operating line [Eq. (15-12)] where=Xr [Eq. (15-20)]. 

The concept of a mass-transfer unit was developed many years ago to represent more rigorously what happens in a differential contactor rather than a stagewise contactor. For a straight operating line and a straight equilibrium line with an intercept of zero, the equation for calculating the number of mass-transfer units based on the overall raffinate phase N r is identical to the Kremser equation except for the denominator when the extraction factor is not equal to 1.0 [Eq. (15-23)]. 

The equilibrium data from Table 10.2 are plotted in Figure 10.6a. It can be seen that this does not form a straight-line relationship overall. Figure 10.6a shows the operating line of maximum slope that touches the equilibrium line at xR = 0.1576 kg AA/kg Water. The slope of this line is the ratio of feed to extraction flowrates. If the liquids are immiscible, then the flowrate of solute-free feed (F) is equal to the flowrate of the... 

The graphical construction of an extraction isotherm, an operating line, and the stepwise evaluation of the number of stages in this manner is known as a McCabe-Thiele diagram. Flistorically, it found great application in a variety of mass transfer operations, from gas adsorption through distillation to solvent extraction. Flowever, the advent of modern computational techniques has made it largely redundant, as it is often easier and certainly more accurate to calculate the cascade directly. 

Equation 8.15 refers to a single phase, and [A]e is related to [A] at each point via the phase ratio (or operating line, which is the same thing). The NTU could be calculated for the extract phase instead of the aqueous phase, that is, either from the difference between [Aj and [Aj e or from that between [AE[e and [Ae]. 

The number of ideal stages and intermediate concentrations of the extract and the raffmate phases can be estimated graphically as shown in Figure 10. 6. The equilibrium line (y =Kx) and the operating line, Eq. (10.19), are plotted. The operating line passes a point (xF, yf) and has the slope of R/E. Then, steps are drawn as shown in Figure 10.6 until the final step passes a point (xNp ys). 

With this system, two extract delivery lines are required, one for each of the vessels as well as two delivery nozzles. The advantages of this mechanism are its simplicity, ease of operation, and its capacity. The mechanism is also compatible with the method-chaining program in the SUPREX. Since the extraction vessels are treated as pairs,when the program asks for a count number on the columns, an entry of six, which is the maximum allowable, will result in twelve extractions, i.e. 2N. An entry of four will result in eight extractions, etc. However, because at each actuation of the solenoids, a pair of columns is selected, this mechanism does not allow room for independent method use between the extraction vessel pairs. 

And the value of Ys will fall on the operating line for case C. The extraction factor for case C is calculated from Eq. (15-22). 

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