Reflux Ratio, R

We have seen that, for a given reflux ratio, and using the McCabe-Thiele method, one can determine the number of theoretical trays required for a given separation. We now turn our analysis to the importance of reflux ratio. As we recall, the importance of the reflux ratio is that it can affects the separation efficiency, i.e. xD (mole fraction of MVC in distillate).

For a given separation (i.e. constant xD and xB) from a given feed condition (xF and q), using a higher reflux ratio (R) will results in lesser number of theoretical trays (N) required, and vice versa. In other words, there are many possible combination of reflux ratio R and number of theoretical trays, N. We therefore have a trade-off between R and N, as shown in left Figure (higher R, lower N), middle Figure (high R, low N) and right Figure (low R, high N) below:

Analysis of Reflux Ratio Changes

There is an inverse relationship between the reflux ratio and the number of theoretical stages. For a new design, of course the reflux ratio and number of theoretical stages can both be varied to achieve an optimum balance.

For an existing column, the number of trays used is fixed, hence higher distillate concentration (mole fraction xD) can only be obtained by increasing the reflux ratio. See the following animation:

Recall the operating line equation
for the rectifying section:

At a specified distillate concentration (i.e. constant xD), when R changes, the slope and intercept of the ROL changes. The ROL therefore rotates around the point (xD, xD).

When the required separation is clearly defined - with a given feed condition (i.e. xF and q fixed), and a specified product compositions (i.e. xD and xB fixed) - increasing R will results in lesser number of theoretical stages required.

From the ROL equation, we can see that when R increases (with xD constant), the slope of ROL becomes steeper, i.e. (R/R+1) and the intercept (xD/R+1) decreases. This is shown in the Figure below.

Thus, as R increases, the ROL rotates downwards around (xD, xD). The SOL also moved down accordingly. The area between the equilibrium curve and ROL is now larger, and we can draw larger triangles between the operating lines. This means that there are now greater driving force for separation, which in turns mean that lesser number of theoretical stages are required. The reverse is true when R decreases.

The reflux ratio can assume any number between a minimum value and an infinite value, and the number of theoretical stages required for separation changes accordingly. In the next sections, we will first look at two extremes of the reflux ratios, and then an analysis of how the most suitable reflux ratio is determined. At one end of the limit is the minimum reflux ratio (that results in infinite stages) and at the other end is the total reflux or infinite reflux ratio (which results in minimum stages).

The minimum reflux ratio and the infinite reflux ratio place a constraint on the range of separation operation. Any reflux ratio between Rmin and Total R will produce the desired separation, with the corresponding number of theoretical stages varying from infinity at Rmin to the minimum number (Nmin at Total R). The relationship between R and N is shown in the Figure below. The choice of reflux ratio to use is governed by cost considerations.