Minimum solvent-to-feed ratio

If the feed, solvent, and extract compositions are specified, and the ratio of solvent to feed is gradually reduced, the number of ideal stages required increases. In economic terms, the effect of reducing the solvent-to-feed ratio is to reduce the operating cost, but the capital cost is increased because of the increased number of stages required. At the minimum solvent-to-feed ratio, the number of ideal stages approaches infinity and the specified separation is impossible at any lower solvent-to-feed ratio. In practice the economically optimum solvent-to-feed ratio is usually 1.5 to 2 times the minimum value. 

For dilute solutions and a high degree of solute removal, the minimum solvent to feed ratio (Smin/F) may be estimated from the inverse of the distribution coefficient. 

Minimum and Maximum Solvent-to-Feed Ratios Normally, it is possible to quickly estimate the physical constraints on solvent usage for a standard extraction application in terms of minimum and maximum solvent-to-feed ratios. As discussed above, the minimum theoretical amount of solvent needed to transfer a high fraction of solute i is the amount corresponding to % =. In practice, the minimum practical extraction factor is about 1.3, because at lower values the required number of theoretical stages increases dramatically. This gives a minimum solvent-to-feed ratio for a practical process equal to... 

The initial solvent and feed concentrahons, the desired hnal concentrations, and equilibrium behavior determine the direction of mass transfer, the minimum solvent-to-feed ratio, and the minimum theoretical tray requirements. These theoretical trays (or stages) are analogous in many respects to theoretical plates of a distillation colnmn, and absorption (or stripping) columns discussed by Fair in another chapter. For any particnlar solvent-to-feed ratio, equilibrium relationships and the operating line determine theoretical stage reqnirements. 

For the case of a constant distribution coefficient, Treybal (1968) shows that the theoretical minimum solvent-to-feed ratio necessary to extract all of a component from a feed stream is equal to the inverse of the distribution coefficient. Recall, however, that the theoretical minimum value of the solvent-to-feed ratio requires an infinitely tall column. In actual practice a greater solvent-to-feed ratio, typically 1.3 to 1.5 times minimum, is employed. We present some elementary but informative graphical design procedures to illustrate the relationship between the distribution coefficient and the operation of the supercritical fluid extraction process for separating ethanol-water. 

Tie lines, of course, cannot cross in the two-phase region within the binodal curve of Fig. 7.3-4. Furthermore, a line from A must not coincide with a tie line in the region between lines L,A and LiA, since this would cause contact (pinch) between the operating and equilibrium curves of Fig. 7.3-5, signifying zero driving force for the transfer of A. Such coincidence occurs in the use of a minimum solvent-to-feed ratio. The condition is avoided by using solvent in excess of the minimum solvent-to-feed ratio for the prescribed separation, which is established as follows with reference to Fig. 7.3-ti. 

All tie lines to the left of—and including—the one that extends through are extrapolated to intersect the extended line , G. The farthest intersection (if below the triangle) or the nearest (if above the triangle) gives cotrespondtog to the minimum solvent-to-feed ratio. The line AttOi ihm locates Ig. at its intersection with the binodal curve. Z is found at the intersection of lines Lfi2 and so that... 

FIGURE 7.3-6 Constiuction to determine the minimum solvent-to-feed ratio,... 

The minimum solvent-to-feed ratio is determined by the intercept of the operating line and equilibrium curve (dot-dashed line, Xextract.out = 0.53). Here we obtain a flow rate of 0.34 kmol solvent h and a minimum solvent-to-feed ratio of0.0034. 

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