Page 144 - Separation process principles 2

3.7 Two-Film Theory and Overall Mass-Transfer Coefficients 109

and For the liquid phase, using kc or k,,

For the gas phase, using k,, ky, or kc,
When using correlations to estimate mass-transfer coeffi-
cients for use in the above equations, it is important to deter- k - k
kt = -- (3-230)
mine which coefficient (k,, kc, k,, or k,) is correlated. This
(1 - YA)LM (YB)LM
can usually be done by checking the units or the form of the
The expressions for kt are most readily used when the
Sherwood or Stanton numbers. Coefficients correlated by
the Chilton-Colburn analogy are kc for either the liquid or mass-transfer rate is controlled mainly by one of the two
resistances. Experimental mass-transfer coefficient data re-
gas phase. The different coefficients are related by the fol-
ported in the literature are generally correlated in terms of k
lowing expressions, which are summarized in Table 3.16.
rather than kt. Mass-transfer coefficients estimated from the
Liquid phase: Chilton-Colburn analogy [e.g . , equations (3- 166) to (3- 17 I)]
are kc, not k:.

Liquid-Liquid Case
ZdeaGgas phase:
For mass transfer across two liquid phases, equilibrium is
again assumed at the interface. Denoting the two phases by
L(') and L(~), (3-223) and (3-224) can be rewritten as

Typical units are

SI American Engineering
kc m/s ft/h and
k, kmo~s-m2-k~a lbmolih-ft2-atm (1) - (I)*
(1)
(1) - (I)*
k,, kx kmoUs-m2 lbmolih-ft2 N~ = Kx (xAb XA X~
) = (l/k$l') + (KD~/~;~))
When unimolecular diffusion (UMD) occurs under non-
(3-232)
dilute conditions, the effect of bulk flow must be included in /I
where I I
the above equations. For binary mixtures, one method for _(I) I
doing this is to define modified mass-transfer coefficients,
designated with a prime, as follows.

Case Of Large Driving Forces for Mass
Table 3.16 Relationships among Mass-Transfer Coefficients
- - -- -
When large driving forces exist for mass transfer, phase
Equimolar Counterdiffusion (EMD):
equilibria ratios such as HA, KA, and KDA may not be con-
Gases: NA = ky AyA = kc AcA = kp ApA stant across the two phases. This occurs particularly when
P
k, = kc - kp P if ideal gas one or both phases are not dilute with respect to the diffusing
=
R T solute, A. In that case, expressions for the mass-transfer flux
Liquids: NA = k, AxA = kc heA must be revised.
kx = kcc, where c = total molar For example, if mole-fraction driving forces are used, we
concentration (A + B)
write, from (3-220) and (3-224),
Unimolecular Diffusion (UMD):

Gases: Same equations as for EMD with k replaced Thus,
k
byk' = -
(YB)LM
Liquids: Same equations as for EMD with k replaced by
1
I
k =- k -- - (YA~ - YA,) + (YA, - Y;) - 1 1 YA, - YA
(XB)LM *)
ky
ky
K~ ky (YA~ - YA, - +-( YA~ - YA,
When using concentration units for both phases, it is convenient (3-236)
to use:
From (3-220),
kG(AcG) = kc(Ac) for the gas phase
kx (YA~ - YA,)
- -
kL(AcL) = kc(Ac) for the liquid phase - (3-237)
k, (XA, - XA,)