mass transfer in multiphase systems - Greenleaf University
mass transfer in multiphase systems - Greenleaf University
mass transfer in multiphase systems - Greenleaf University
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MASS TRANSFER IN MULTIPHASE SYSTEMS: VOLATILE ORGANIC COMPOUND<br />
REMOVAL IN THREE-PHASE SYSTEMS<br />
Multiply<strong>in</strong>g through by k D provides the differential (see Appendix C for relationships of<br />
different forms of the transport PDEs) based on the solid concentration:<br />
dX<br />
dt<br />
K<br />
<br />
a X<br />
<br />
k p<br />
<br />
A oa<br />
D A<br />
s A<br />
H<br />
A<br />
<br />
<br />
<br />
(19)<br />
To make Eq. 7 useable, need to solve for the molar rate, hence:<br />
<br />
oa D A<br />
t Ks aMsXA<br />
<br />
H<br />
A<br />
k p <br />
<br />
(20)<br />
Solv<strong>in</strong>g us<strong>in</strong>g the follow<strong>in</strong>g two, Eq. 21 and Eq. 23:<br />
<br />
<br />
pA<br />
t A<br />
t<br />
<br />
P () t <br />
A<br />
s<br />
(21)<br />
Assum<strong>in</strong>g:<br />
<br />
A<br />
<br />
s<br />
(22)<br />
p<br />
X<br />
(23)<br />
A A A<br />
Where:<br />
Λ<br />
A<br />
K<br />
<br />
<br />
<br />
P<br />
aM k<br />
oa<br />
s s D<br />
oa<br />
s<br />
Ks aMskD<br />
H<br />
A<br />
<br />
1<br />
s<br />
1<br />
<br />
oa<br />
PK aM k H<br />
s s D A<br />
(24)<br />
The above values are all known. Therefore, the f<strong>in</strong>al result is based on known quantities:<br />
dX<br />
dt<br />
A<br />
K<br />
oa<br />
s<br />
aX<br />
A<br />
Λ<br />
1<br />
H<br />
A<br />
A<br />
<br />
<br />
<br />
(25)<br />
Note that a similar result can be found <strong>in</strong> a liquid-vapor system conta<strong>in</strong><strong>in</strong>g no solids (high airstripp<strong>in</strong>g<br />
compared to <strong>mass</strong> <strong>transfer</strong> rate). This is shown <strong>in</strong> Eq. 27:<br />
25