Minimum Reflux Ratio and Number of Plates

Recall that in the discussion of the countercurrent gas scrubber, Section 7.2.2, we mention the limiting case that arises when the slope of the operating line and the associated solvent flow is progressively reduced until it intersects the equilibrium curve. This results in a condition termed a pinch and corresponds to a cascade with an infinite number of stages and a minimum solvent requirement. Any solvent flow rate below this value causes a rise in the effluent concentration and can therefore no longer meet the specified solute recovery. 

In distillation, the liquid reflux returned to the top of the column plays, in a sense, the role of a solvent. In the course of its downward flow, it dissolves residues of the heavy component contained in the vapor phase 

Two limiting conditions (a) minimum reflux and (b) minimum number of trays (total reflux). 

Mass Transfer and Separation Processes Principles and Applications 

These two asymptotic cases are immensely useful in conveying to the analyst the lower limits of R and N, below which the desired separation will no longer proceed. In an actual operation, these values evidently must be exceeded and both R and N will assume finite values. The best or optimum value of R and N to be used will be determined by economic considerations (i.e., when the total cost consisting of fixed and operating costs is at a minimum). Let us see how this minimum comes about. 

The feed plate (a) flow diagram (b) feed quality and the j-line. 

when the total cost consisting of fixed and operating costs is at a minimum. Let us see how this minimum comes about. 

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