Limiting Conditions

There are two possible limiting conditions which simplify the graphing process. These conditions are a result of maximizing or minimizing a parameter which has so far been ignored--the reflux ratio. The McCabe-Thiele method allows full control over reboiler duty, and it is not uncommon to first solve a problem assuming minimum reflux ratio. Results can be scaled to actual reflux ratio, typically R = 1.4*Rmin.	Example The following applet shows how a binary system would look at the two limiting conditions. While viewing the graphs, notice the differences: Minimum Reflux Infinite stages would be necessary to reach this condition Notice how the stages get infinitely smaller as they approach the intersection of the upper operating line, q-line, and equilibrium curve Total Reflux Minimum stages would be necessary to reach this condition Notice how both operating lines lie on the x=y diagonal
Maximum Reflux The condition of total reflux implies that both the upper and lower operating lines are situated on the diagonal. This is as far as the operating lines can be removed from the equilibrium curve, and therefore, the maximum separation possible is occurring at each stage. Further, this correlates to the minimum number of equilibrium stages necessary to reach the desired purity. The column is at maximum diameter, but there is no product because all of the overhead product is being returned to the column as reflux.
Minimum Reflux At minimum reflux, the intersection of the upper operating line and the q-line occurs on the equilibrium curve. This is a conceptual limit, as it implies that the entering and exiting streams of the stage are in equilibrium, and in reality it would take an infinite number of stages to accomplish this. When a McCabe-Thiele diagram is graphed using the condition of minimum reflux, the slope of the upper operating line is no longer necessary. Instead, the upper operating is drawn as the line between the point (xD,y1) and where the q-line meets the equilibrium curve. At this condition, infinite stages are necessary, and the column is at maximum height. Since this condition can never physically be obtained, actual columns are designed proportional to results.