g ¼ 2a þ b=2 — v=2 þ 2d þ e=2 — /=2 i ¼ a þ b=2 — v=2 þ d þ e=2 — /=2

Substituting

(37)

 am

qa     lb Þðvv Þðqd Þðle Þðv/Þðr—a—b—d—e Þ

ad  / ð  VÞð V V

L L L

×ðd2aþb=2—v=2þ2dþe=2—/=2

aþb=2—v=2þdþe=2—/=2

Þ  ð38Þ

and then collecting terms with the same power-law exponents gives us the  following

 am

。q  d2g。a l

d1=2g

1=2!b !v

V

。q  d2g。d

e V L  e

ad  / r r d  g1=2 r

e

Figure 3。 Vapor-side  and  liquid-side  composition cor-

rection factors appearing in Eq。 25 for hHETPi。

l d1=2g

× r

1=2!e      v !/

de   g1=2

ð39Þ

 kxde b c or

ShL  ¼ c D

¼ ALReLScL (32)

1=    1   !b

These are the expressions for the mass-transfer coefficients that we will  use。

 a

/ ðBoV

d

  2    =2

a V   e

Þ r

。pffiFffiffirffiffiffiffiffi。v

ðBoLÞ

Next, consider the fractional mass-transfer area, am/ad。    Let

1=2

1=2!e

us assume that the fractional mass-transfer area in a packed tower is a function of the following physical   quantities

lLde   g

× r

。pffiFffiffirffiffiffiffiffi。/      ð40Þ

 am

Fðq ; l

; v  ; q ; l ; v ; r; d ; gÞ

These  dimensionless  groupings  are  less  well  known than

ad  ¼

V      V      V     L

m m

L     L e

m l

the Reynolds number, Weber number, and Froude   number

l

q ! l3 l ! l — t r ! t2 v ! t de  ! l    g ! t2

(33)

ReV ¼

devVqV lV

deqLv2

ReL ¼

devLqL lL

v2

Because there are nine quantities with physical   dimensions

and  three  units  of  dimension  (mass,  length,  and  time), the