mass transfer in multiphase systems - Greenleaf University

MASS TRANSFER IN MULTIPHASE SYSTEMS: VOLATILE ORGANIC COMPOUND
REMOVAL IN THREE-PHASE SYSTEMS
The molar rates of mass transfer are the same through each phase. There is significant adsorption
of various material including VOCs and water in and on solids of various particle sizes. This
analysis assumes the solid on the dry basis (units and analogies are presented in Appendix A).
Mass transfer e from the solid is:
i
s* i1
N k X X k k C C
(6)
A s A A s D A A
In the equation above, the mass transfer coefficient, k s , is related to Knudson diffusion:
k
s
D
R
K
L
(7)
It is assumed for this paper that this coefficient is very large compared to the solid-liquid and
liquid mass transfer coefficients and is therefore neglected.
The next mass transfer rate is sometimes referred to the solid-liquid mass transfer
coefficient (Oldshue 1983).
i1
B
A sL D A A
N k k C C
(8)
As shown in Figure 10, it is the transfer across the liquid film outside of the solid. It
cannot exceed the solubility in the liquid media. Most workers ignore the transfer relation in
Figure 10. This will be examined later. Like a liquid mass transfer coefficient, the so-called solidto-liquid
coefficient depends on the process. It is defined by the Sherwood number
(dimensionless groups are discussed in Appendix B) for solids treatment defined as:
2
ksLasdp
Sh (9)
D
iw
e Overall mass transfer coefficients can be based on any phase, liquid is used in this analysis
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