Page 13 - Academic Press Encyclopedia of Physical Science and Technology 3rd Chemical Engineering

P1: LDK Revised Pages
Encyclopedia of Physical Science and Technology EN001H-01 May 7, 2001 16:18

10 Absorption (Chemical Engineering)

Combining these to eliminate dG M and integrating gives It is therefore a measure of the efficiency of contacting
provided by the particular device used in the tower.

G M dy
y 1
h T = , (15c) Mass transfer data are often expressed in terms of H G
N A a(1 − y)
y 2 and H L , and these are used to obtain the value of H OG .
Substituting Eq. (6a) for N A gives The relationship between H OG , H G , and H L is obtained
by substituting the expressions for H G , H L , and H OG in

y 1
G M y BM dy
h T = (15d) Eqs. (16a)–(16c), together with Eqs. (7a)–(7c), in Eq. (5)

k a(1 − y)(y − y i )
y 2 G to give

The group G M /k a is independent of concentration and
G y BM mG M x BM
can be taken out of the integral, giving H OG = H G + H L (17)
y ∗ L M y ∗
BM BM

y 1
G M y BM dy
h T = = H G N G (16a)
k a (1 − y)(y − y i )

G y 2
2. Dilute Systems
Here N G is dimensionless and is referred to as the number
of gas-phase transfer units; H G has the dimension of length For dilute systems, the x BM , y BM , and 1 − y terms ap-
or height and is referred to as the height of a gas-phase proach unity, and Eqs. (16e) and (17) can be rewritten
transfer unit. y 1 dy
Here N G is dimensionless and is called the number of N OG = (18a)
y − y ∗
gas-phase transfer units;H G has the dimension of length y 2
or height and is referred to as the height of a gas-phase G M
H OG = H G + m H L (18b)
transfer unit. As shown in Eq. (16a), the required height L M
of the packed bed h T is the product of H G and N G .
When Henry’s law is valid [Eq. (1c)], Eq. (18a) can be
A similar derivation can be carried out in terms of liquid
analytically integrated; alternatively, the graphical form
concentrations and flows, giving shown in Fig. 8 can be used for evaluating N OG . Expres-

x 1 sions for cases in which the equilibrium curve cannot be
L M x BM dx
h T = H L N L = (16b) linearly approximated are available in several texts, such

k a (1 − x)(x i − x)
L x 2
as Hines and Maddox (1985). Figure 8 shows that the num-
A derivation similar to the preceding one but in terms of
ber of transfer units increases with the ratio mG M /L M .
the overall mass transfer coefficient K [Eq. (6)] gives
OG When this ratio increases above unity, the number of trans-

y 1 ∗ fer units, and therefore column height, rapidly increase;
G M y BM dy
h T = = H OG N OG (16c)
K a (1 − y)(y − y )
∗
OG y 2
where
H OG = G M /K OG a (16d)

and
y BM dy

y 1 ∗
N OG = (16e)
(1 − y)(y − y )
∗
y 2
Equation (16c) is of great practical interest. It is the basis
for computing the required packed height for a given sepa-
ration, and takes into account mass transfer resistances on
bothsidesoftheinterface.Also,itavoidstheneedtocalcu-
late the interfacial concentrations required for Eqs. (16a)
and (16b).
The N OG in Eq. (16e) is termed the overall number of
transfer units. It is dimensionless and is the ratio of the
change of bulk-phase concentration to the average concen-
tration driving force. It is essentially a measure of the ease
of separation. The H OG in Eq. (16d) is termed the overall
height of a transfer unit. It has the dimension of length and
defines the vertical height of contactor required to provide FIGURE 8 Number of overall gas-phase transfer units at constant
a change of concentration equivalent to one transfer unit. mG M /L M .