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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

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