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by difference.

x by difference.

Thus: rm = (0.424/0.272) = 1.558 arm/r„ = (1.558/1.393) = 1.12

and:

f = 1/(1 - 0.119) = 1.13 Thus: Rm = 1.08 is near enough.

Since there are no components lighter than the light key, the lower pinch is expected to be near the feed plate as it is, although the general method of taking the pinch temperature as one-third and two-thirds up the column was used above.

The small change in R from 1.12 to 1.08 gives a change in rn though very little change in rm. It is seen that the first estimation for Rm of 1.12 based on equation 11.108 for locating the upper pinch composition is nearly correct but that it gives the wrong pinch composition.

Minimum reflux ratio, using Underwood's method

For conditions where the relative volatilities remain constant, Underwood(40) developed the following two equations from which Rm may be calculated:

and:

where: x/B, x/C, xdB, xdC, etc., are the mole fractions of components A, B, C, etc., in the feed and distillate, A being the light and B the heavy key, q is the ratio of the heat required to vaporise 1 mole of the feed to the molar latent heat of the feed, as in equation 11.44, aB, aC, etc., are the volatilities with respect to the least volatile component, and

0 is the root of equation 11.114, which lies between the values of and «b .

If one component in the system has a relative volatility falling between those of the light and heavy keys, it is necessary to solve for two values of 0.

Example 11.16

A mixture of hexane, heptane, and octane is to be separated to give the following products. What will be the value of the minimum reflux ratio, if the feed is liquid at its boiling point?

Component

Feed