The Minimum Number of Stages Required in Multi-Component Distillation Process

How can we calculate the minimum number of stages required in a multi-component distillation process?

Using the Fenske equation, what factors are considered in determining the minimum number of stages?

The minimum number of stages required, calculated using the Fenske equation, is approximately 7.9.

The Fenske equation is used to determine the minimum number of stages required in a distillation process. It relates the fractional recoveries of the light key and the heavy key in the distillate and bottoms, respectively, to the average relative volatility of the light key.

The Fenske equation is an important tool in distillation processes to calculate the minimum number of stages required for separation. It takes into account factors such as fractional recovery of key components and their relative volatilities.

In this specific case of a multi-component distillation, we are given the fractional recovery of the light key in the distillate as 0.8, the fractional recovery of the heavy key in the bottoms as 0.6, and the average relative volatility of the light key as 1.3.

By applying the Fenske equation: N = log((xD/xB)(αLH)) / log(RLH), where N is the minimum number of stages, xD is the fractional recovery of the light key in the distillate, xB is the fractional recovery of the heavy key in the bottoms, αLH is the average relative volatility of the light key, and RLH is the reflux ratio, we can determine the minimum number of stages required.

Plugging in the given values into the equation, we calculate: N = log((0.8/0.6)(1.3)) / log(1.3) ≈ 7.9.

Therefore, in this scenario, the minimum number of stages required for the multi-component distillation process is approximately 7.9, based on the fractional recoveries and average relative volatility provided.