Page 143 - Separation process principles 2

108 Chapter 3 Mass Transfer and Diffusion

At the phase interface, CA, and p~~ are assumed to be in ~lternatively, (3-207) to (3-209) can be combined to
phase equilibrium. Applying a version of Henry's law differ- define an overall mass-transfer coefficient, KG, based on the
ent from that in Table 2.3,' gas phase. The result is

Equations (3-207) to (3-209) are a commonly used combina-
tion for vapor-liquid mass transfer. Computations of mass- In this case, it is customary to define: (1) a fictitious gas-
transfer rates are generally made from a knowledge of bulk phase partial pressure p: = cAb/HA, which is the partial
concentrations, which in this case are p~~ and CA~. TO obtain pressure that would be in equilibrium with the bulk liquid;
an expression for NA in terms of an overall driving force for and (2) an overall mass-transfer coefficient for the gas phase,
KG, based on a partial-pressure driving force. Thus, (3-216)
mass transfer, (3-207) to (3-209) are combined in the fol-
lowing manner to eliminate the interfacial concentrations, can be rewritten as
CA, and PA,. Solve (3-207) for p~~ :

where
:
Solve (3-208) for CA~

In this, the resistances are l/kp and l/(HAkc). When
Ilkp >> l/HAkc,
Combine (3-21 1) with (3-209) to eliminate CA~ and combine
the result with (3-210) to eliminate p~~ to give NA = kp(~~b - P:) (3-219)

Since the resistance in the liquid phase is then negligible, the
liquid-phase driving force is CA, - CA, % 0 and CA, % CA,.
The choice between using (3-213) or (3-217) is arbitrary,
It is customary to define: (1) a fictitious liquid-phase
but is usually made on the basis of which phase has the
concentration cz = HA, which is the concentration that
largest mass-transfer resistance; if the liquid, use (3-213); if
would be in equilibrium with the partial pressure in the bulk the gas, use (3-217). Another common combination for
gas; and (2) an overall mass-transfer coefficient, KL. Thus,
vapor-liquid mass transfer uses mole fraction-driving forces,
(3-212) is rewritten as
which define another set of mass-transfer coefficients:

In this case, phase equilibrium at the interface can be
where
expressed in terms of the K-value for vapor-liquid equilib-
rium. Thus,
KA = YA~ /xAi (3-221)

in which KL is the overall mass-transfer coefficient based on Combining (3-220) and (3-221) to eliminate y~~ and xA, ,
the liquid phase. The quantities HA/kp and l/kc are measures
of the mass-transfer resistances of the gas phase and the
liquid phase, respectively. When l/kc > > HA/kp, (3-2 14)
This time we define fictitious concentration quantities and
becomes
overall mass-transfer coefficients for mole-fraction driving
forces. Thus, xi = yAb/ KA and y; = KAxAb. If the two
Since resistance in the gas phase is then negligible, the gas- values of KA are equal, we obtain
phase driving force is p~~ - p~~ % 0 and p~~ % p ~ ~ .

'Many different forms of Henry's law are found in the literature. They and
include
PA = HAXA. PA = -. and y~ = HAxA
c A
HA
When a Henry's-law constant, HA, is given without citing the equation that
where Kx and Ky are overall mass-transfer coefficients based
defines it, the defining equation can be determined from the units of the
constant. For example, if the constant has the units of atm or atmtmole on mole-fraction driving forces with
fraction, Henry's law is given by p~ = HAXA. the units are mol/L-rnrnHg,
If
c A
.
Henry's law is p~ = -
HA