Nþ1 xt

Cx ¼ ¼

(27)

Z Z dx

R xt dx

mðxÞ— 1

dn ¼ N þ 1 ffi

0 xb

xð1 —

xÞ ln½aðxÞ]

(20)

xb   xð1—xÞ ln½aðxÞ]

Z

G 。Cy

Cx。

or for any two stages in the   column

hHETPi ¼ N ¼ a

ky  þ kx

(28)

n1

Z

dn ¼ ni — nj ffi

nj

xi

Z dx

xð1 — xÞ ln½aðxÞ]

xj

(21)

Although the calculations look overwhelming, they are actually quite easy to perform numerically—in fact, these integrals are substantially easier to evaluate than the sums discussed  earlier。  Further,  there  is  no  restriction  on    these

Note that the restriction of the Fenske equation to constant relative volatility has been  removed。

Next, the packed-height calculation can be   approximated

equations to constant relative  volatility。

Even without evaluating these integrals some important conclusions can be drawn。 First, note that hHETPi now depends explicitly on the bottom and top compositions。 So,   it

0

Z

Z ¼ HETPðnÞdn ¼

xt

Z  HETP  x  dn dx

dx

is not enough to just report hHETPi, one must also report the top and bottom compositions as well。 Second, as the bottom and top compositions depend on the packed depth, we   should

Nþ1 xb

xt

expect to see that   HETP   is packed depth dependent。  Indeed,

20–22

Z 。 1

mðxÞ。。 1

。 ln½mðxÞ]

this  is  oftentimes observed,

and  the  effect  is sometimes

ffi kyam

þ kxam

xð1 — xÞ ln½aðxÞ]

dx

mðxÞ— 1

even    included    in    packed-column    mass-transfer correla-

4,23,24

xb tions。 Figure 3 shows how Cy  and Cx  vary with the  mole

fraction of the light component for a fictitious binary    mixture

with a ¼ 1。2 and the bottom composition fixed at xb  ¼ 0。05。

Dimensional  analysis

First, we consider expressions for the mass-transfer coefficients

hHETPi ¼ N ffi G

R xt dx

xb   xð1—xÞ ln½aðxÞ]

R xt 。

xb

1

kx am

。。 mðxÞ

xð1—xÞ ln½aðxÞ]

。  ln½mðxÞ]

mðxÞ—1

ky  ¼ KyðvV; qV; lV; cV; DV; deÞ