Encyclopedia of Environmental Science and Engineering, Volume I and II

PCBs AND ASSOCIATED AROMATICS 891

Residence time calculations can be made from consider-

ation of an ideal plug-flow reactor in which the temperature,

composition and velocity of the gases are considered to be

uniform within any cross-section of the furnace.

The mean residence time,

t

V

Q

 ⋅ 60

(5)

where

t  mean residence time in seconds

V  furnace volume, cu. Ft

Q  volumetric flow rate, scfm.

The actual flow rate is proportional to temperature,

Q
  Q · T (6)

where,

Q ′  actual flow rate

T  temperature

from equations (5) and (6),

t

V

QT



⋅

.

(7)

The flow through the incinerator is not isothermal and so is not

well approximated by the plug flow reactor unless the time-

temperature distribution is taken into account as follows.

The differential form of the residence time equation is:

d

d

ddf

t

V

Q

VAx





′

⋅

where

A f  the arc of the furnace

d x  an element of the axial length of the furnace.

Then, from equation (7),

dt

A

QT

 f dx

⋅

⋅.

(8)

If a linear temperature gradient is assumed along the incin-

erator axis, and the temperature at a point x m is T m and the

exit temperature T e is at a distance x e then,

()

()

()

()

.

TT

xx

TT

xx









m

m

em

em

=

Rearranging,

T

xx

 xT T T x T x



 

1

()

[( ) ].

me

⋅⋅me meem⋅ ⋅

Substituting into equation (8),

dd

d

f me

me meem

f me

t

A

Q

xx

xT T T x Tx

x

t

A

Q

xx

x





⋅

−

⋅⋅⋅

⋅

⋅

∫ ⋅

()

[( ) ]

()

[

 



(()TT TxTx]

x

me meem

d

⋅⋅

∫ ⋅

∴⋅

⎛

⎝⎜

⎞

⎠⎟

() ln⋅

()

()

tt

A

Q

T

T

xx

TT





m 

f

m

me

me

(9)

If T m is close to the furnace entrance, then

x m x e.

If t m  0, by definition, then

t

A

Q

T

T

x

TT







f

m

e

()me

⋅

⎛

⎝⎜

⎞

⎠⎟

ln ⋅

()

TABLE 22

Destruction Kinetics During the Incineration of Askarel

Compound Factor(1/sec)Frequency

Activation

Energy

(cal/g-mole)

Destruction Temperature(°K)/Residence Time (sec)

0.5 1 2 7

Monochlorobenzene 8.0 · 10^4 23,000 1,056 993 937 851

Dichlorobenzene 3.00 · 10^8 39,000 1,023 987 954 899

Trichlorobenzene 2.20 · 10^8 38,000 1,013 977 944 889

Tetrachlorobenzene 1.90 · 10^6 30,000 1,068 1,019 973 900

Hexachlorobenzene 1.90 · 10^6 72,600 983 965 948 918

Pentachlorobenzene 1.10 · 10^6 70,000 962 944 927 898

C016_003_r03.indd 891C016_003_r03.indd 891 11/18/2005 1:12:36 PM11/18/2005 1:12:36 PM