Encyclopedia of Environmental Science and Engineering, Volume I and II

890 PCBs AND ASSOCIATED AROMATICS

500 600 700 800 900 1000 1100 1200 1300

T(K)

Formation of PCDDs from PCPs During Incineration

PCDD (mol/L)

Case (iv)

2E-13

2E-13

2E-13

2E-13

2E-13

1E-13

1E-13

1E-13

8E-14

6E-14

4E-14

2E-14

0E0

FIGURE 38

8E-10

7E-10

6E-10

5E-10

4E-10

3E-10

2E-10

1E-10

0E0

500 600 700 800 900 1000 1100 1200 1300

Case (III)

PCDD (mol/L)

T(K)

Formation of PCDDs from PCPs During Incineration

Case (III)

FIGURE 37

Rate constants can be expressed in terms of an Arrhenius

expression:

kAe

ERT





⋅

()( ⋅

(3)

where

A  frequency factor

E  activation energy

R  Universal gas constant.

From statistical mechanics, the term exp[– E / RT ] can be taken

to mean the fraction of molecular collisions which have an

energy E or greater. The pre-exponential term was applied

to introduce into the theory a steric collision term intended

to describe the need for an orientation of the colliding mol-

ecules to produce reaction.

8E-6

7E-6

6E-6

5E-6

4E-6

3E-6

2E-6

1E-6

0E0

500 600 700 800 900 1000 1100 1200 1300

Case (I)

PCDD (mol/L)

T(K)

Formation of PCDDs from PCPs

FIGURE 39

Substituting for k in equation (2) yields:

t

AERT

C

C

C

C

At

E

RT







(^10)
0
⋅⋅
⋅
⎛
⎝⎜
⎞
⎠⎟
⎛
⎝⎜
⎞
⎠⎟
⋅⋅
⋅
⎛
⎝⎜
⎞
exp [ ( )]
ln
ln exp
/
⎠⎠⎟
∴
⎛
⎝⎜
⎞
⎠⎟
⋅⋅
⋅
⎛
⎝⎜
⎞
⎠⎟
C
C
At
E
RT
(^0) exp [ exp
∴
−
⋅⋅
⋅
⎛
⎝⎜
⎞
⎠⎟
CC
C
N
At
E
RT
(^0) 

Destruction Efficiency, ( )
exp exp 11
1
⎡
⎣
⎢
⎤
⎦
⎥
∴⋅⋅
⋅
⎛
⎝⎜
⎞
⎠⎟
⎡
⎣
⎢
⎤
⎦
(NAt) exp exp ⎥.
E
RT
 
Rearranging, T
E
RNAt

⋅[ln (ln( 1  )) ln ln ] (4)
where
N  destruction efficiency
A  frequency factor (second −1 )
E  activation energy (cal/g-mole)
R  universal gas constant
 1.987 (cal/g-mole-°K)
T  combustion temperature (°K).
Table 22 shows the destruction kinetics for several compo-
nents of transformer askarels and the calculated temperatures
necessary to achieve a destruction efficiency of 99.9999%
with a range of residence times.
C016_003_r03.indd 890C016_003_r03.indd 890 11/18/2005 1:12:36 PM11/18/2005 1:12:36 PM