Page 281 - Separation process engineering

Equation (7-25) can be summed over all components to give the total vapor flow rate in the enriching
section at minimum reflux.

(7-26)

In the stripping section a similar analysis can be used to derive,

(7-27)

Since the conditions in the stripping section are different than in the rectifying section, in general

and .
Underwood (1948) described generalized forms of Eqs. (7-26) and (7-27) which are equivalent to
defining

(7-28)

Equations (7-26) and (7-27) then become polynomials in φ and and have C roots. The equations are

now

(7-29)

and

(7-30)

If we assume CMO and constant relative volatilities , Underwood showed there are common

values of φ and which satisfy both equations. Equations (7-29) and (7-30) can now be added. Thus, at
minimum reflux

(7-31)

where α is now an average volatility.