Minimum Reflux Ratio for Ideal Solution

Note in this instance when R is originally unknown (it may simply be specified as multiples of the minimum reflux ratio, Rmin). We must first find out the value of Rmin.

Since R is unknown, the ROL cannot be plotted first. Therefore the first operating line to be drawn is the q-line, using known values of xF and q. Refer to the flowchart FChart1 for more information.

We then look at the methodology of finding Rmin. This requires the analysis of ROL when R decreases. Refer to the ROL equation.

With xD constant, as R decreases, the slope of ROL becomes less steep, i.e. (R/R+1) decreases, while its intercept (xD/R+1) increases. As R decreases, the ROL therefore rotates upwards around (xD, xD). The ROL moves closer to the equilibrium curve. Separation thus becomes more difficult as the driving force for mass transfer decreases. To achieve any separation, more theoretical stages are required.

R can be decreased until point N is reached. Point N is the point of intersection between the q-line and the equilibrium curve. See the Figure below.

At point N, the ROL crosses the equilibrium for the first time. This is the point where the driving force for mass transfer is zero (operation at equilibrium condition). Point N is also known as the Pinch Point. Separation is not possible at this point.

We cannot reduce R beyond this point. The value of R at this point is known as the minimum reflux ratio and is designated Rmin. Thus, the condition for Rmin occurs when the ROL (from xD) joins a point on the equilibrium curve (such as point N).

With minimum reflux ratio, we are returning the minimum amount of liquid to the column. Thus, this point also corresponds to the minimum reboiler heat duty and condenser cooling capacity required for the separation.

In the above analysis, the pinch point occurred at the intersection of the ROL and q-line and the equilibrium curve. This type of pinch is also known as the feed pinch, and it corresponds to infinite number of stages in the column on each side of the pinch point (i.e. in both rectifying and stripping sections of the column).

Minimum relfux is determined by the feed pinch in the case of equilibrium curves with no inflections ("distortions"), such as that in the Figure above, which is typical for ideal solutions or solutions with approximately constant relative volatilities.