(9)

Then, the average slope of the equilibrium curve for each

stage must be calculated  from

where k (¼ m at total reflux) is some type of average value

mn ¼

n — n—1

ym¼ Fðx; PÞ (17)

whose value or method of calculation is rarely reported。6,16,17 Clearly

xn — xn—1

ln k¯

1 X lnðknÞ

(10)

Finally, the overall mass-transfer coefficient must be cal- culated at each stage  from

。KOyam。ðk¯ — 1Þ 6¼ N

n¼1

ðKOyamÞjmn ðkn

— 1Þ

1 1 m

  n

(18)

It is also generally true  that

KOyamjn ¼ kyamjn þ kxamjn

ln k¯

N lnðknÞ

(11)

With this, all of the information necessary to compute the necessary summation is available。  Obviously, this    procedure

ðk¯ — 1Þ 6¼ N

n¼1

ðkn — 1Þ

involves a great deal of  calculation。

If the number of stages is large enough and the variation in the local binary relative volatility is not too severe, then a good approximation can be made to the summation in Eq。 8 by replacing it with an integral。*18,19 If we consider a small composition change over a small increment in stage number where  the  relative  volatility  is  approximately  constant, then

Let us now assume that the terms kya and kxa vary only slightly over the length of bed in question and that they can be withdrawn from their respective integrals and replaced by an average value for the length of bed in question。 Then

  !

it is easy to show from the Fenske equation    that†

Z

hHETPi ¼ N ¼ G

Cy Cx

k  a   þ k a

(25)

dn 1

(19)

y  m x  m

dx ¼ xð1 — xÞ ln½aðxÞ]

Equation 19 was derived assuming that the relative volatil- ity can be considered  constant  during the differentiation    but

where

R xt 。

xb

1

xð1—xÞ ln½aðxÞ]

。  ln½mðxÞ]

mðxÞ—1

。 ln½mðxÞ] 。

(26)

then replaced with the compositionally dependent a after the differentiation。 Thus

Cy ¼

R xt dx

xb   xð1—xÞ ln½aðxÞ]

¼ mðxÞ— 1

R xt  。 mðxÞ 。  ln½mðxÞ] 。 。

xb        xð1—xÞ ln½aðxÞ]

mðxÞ—1 dx

 mðxÞ ln½mðxÞ]