Operation Infinite Reach

As the reflux ratio is decreased from infinity for the total reflux condition, more theoretical steps or trays are required to complete a given separation, until the limiting condition of Figure 8-23 is reached where the operating line touches the equilibrium line and the number of steps to go from the rectifying to stripping sections becomes infinite. 

It is important to note that, if L m/mG m is less than 1, then a very large number of plates are required to achieve a high recovery, and even an infinite number will not give complete recovery. L m/mG m is the ratio of the slope of the operating line Lm/Gm to the slope of the equilibrium curve m, so that if L m/G m < m, or L m/mG m < 1, then the operating line will never cut the equilibrium curve and the gas leaving the top of the column will not therefore reach equilibrium with the entering liquid. 

If the number of determinants considered in (14) is increased, the lowest eigenvalue of (18) will be lowered more and more, and in the limit of an infinite complete set of determinants the true eigenvalue TFo of the Hamilton operator will be reached assymptotically, the convergence being rather slow... 

LIMITING REFLUX RATIOS. Just as in distillation, two limiting cases exist in operating a countercurrent extractor with reflux. As the reflux ratio Rj becomes very great, the number of stages approaches a minimum, and as is reduced, a minimum value of the reflux ratio is reached where the number of stages becomes infinite. The minimum number of stages and the minimum reflux ratio are found by exactly the same methods used to determine the same quantities in distillation. 

Since Equation 12 assumes no heat loss, the comparable performance ratio for a 20-effect boiling evaporator would be 20. If At — 0, Equation 12 reduces to R — n, the same as for the boiling evaporator, but this would require an infinite heat-transfer surface. (Experimental flash evaporators have been successfully operated with a At as low as 1° F.) One can conclude that a boiling evaporator requires less steam than a flash evaporator if the comparison is made under reasonably comparable conditions, a conclusion already reached from general thermodynamic considerations. 

Consider the case of minimum reflux ratio (infinite stages). As the amount of solvent is reduced, point M (equal to S + F) in Fig. 11.9 moves towards F, and P (equal to D + So) moves towards D. Point P" (equal to B - S) moves away from the equilibrium curve. The maximum distance that points M, P, and P" can be moved is determined by the slope of the tie lines. The minimum solvent ratio, which corresponds to the minimum reflux ratio, is reached when a tie line and an operating line coincide. A pinch point can occur either in the enriching or in the stripping section of the column, so it is necessary to seek the highest value of the minimum reflux ratio by trial and error. In this example, it occurs at the feed stage. The minimum reflux ratio is 0.58 and the corresponding minimum solvent ratio is 0.74. 

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