Optimum Reflux Ratio

As we had seen in the previous section, we will use neither the minimum nor the infinite reflux ratio for actual design. Nonetheless, these 2 numbers are useful in helping us to identify the lower and upper limits of "useable" reflux ratio. Intuitively, the reflux ratio to be used should fall in-between the minimum and infinite reflux ratios. See the Figure below.

Optimum Reflux Ratio

 

We must therefore evaluate the trade-off between reflux ratio R, and number of theoretical trays N.

For new design, the reflux ratio to be used should be the optimum, or the most economical, for which the total cost will be the least. This is shown in the Figure below.

Note that there are 2 components of total cost: fixed costs (such as those for purchase of the distillation column and internals, reboiler, condenser, and other equipment) and operating costs (costs associated with operation of the plant, e.g. utilities like condenser cooling water, reboiler steam, pump horsepower, etc).

Minimum Total Cost for Optimum R

At minimum reflux ratio, the fixed cost is infinite (due to infinite number of stages required), but the operating cost is at a minimum, because minimum amount of liquid is to be handled (e.g. consuming lesser pump horsepower, lesser cooling capacity, etc).

As reflux ratio increases, less stages are required but larger equipment are now needed to handle the increased reflux liquid and reboiled vapour load. Thus the fixed cost initially decreased but eventually increase again when the reflux ratio approaches total reflux. The fixed cost this falls through a minimum and then rise again to infinity. As for the operating cost, it will continue to increase with increasing reflux ratio.

The total cost, which is the sum of fixed cost and operating cost, must therefore passes through a minimum. The reflux ratio at this minimum total cost is the optimum (or economical) reflux ratio. Typically the optimum reflux ratio is approximately 1.2 to 1.5 times Rmin.

[ Treybal, R.E., "Mass Transfer Operations", 3rd. Ed., McGraw-Hill, pp.387-389 & 410-412 ]

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