At any reflux less than total, the number of plates needed for given separation is larger than total reflux. The number of plate increases continuously as reflux ratio is decreased. As the ratio becomes smaller, no. of plates required becomes very large and at definite minimum reflux ratio, number of plate become infinite.
This minimum reflux ratio can be defined as the reflux ratio (Rm) that will require infinite no. of trays for given desired separation of XD and XB. This corresponds to minimum vapor flow in tower and hence minimum reboiler and condenser sizes. Read more