910 PCBs AND ASSOCIATED AROMATICS
penetration takes place and the PCB in the outer layer of paper
is replaced with solvent. When the transformer is filled with
oil and put back into operation, the non-viscous solvent held
in the paper quickly diffuses into the much larger quantity of
more viscous dielectric fluid. During this time, the PCB con-
centration of the absorbed solvent is high because the con-
centration gradient which it sees is between an initial value of
zero and about 700,000 ppm PCB in the interior of the paper.
The initial leaching of absorbed solvent into the oil therefore
gives a rapid rise in bulk oil PCB concentration. When the
outer layer of trapped solvent has been replaced by slightly
contaminated bulk oil there is again an almost constant con-
centration gradient but now the PCBs must diffuse through
a medium which is about 450 times more viscous than the
originally trapped solvent. Diffusion rate is inversely propor-
tional to viscosity. Overall, the observed leaching rate of PCB
will depend upon the relative viscosities of the solvent and oil
(and hence temperature) and the depth of penetration of the
solvent i.e., the distance the PCB must diffuse.
The depth of penetration attainable by vapor degreasing
alone is unknown. The results which have so far been
obtained indicate that the leaching rate in the first 90 days
is sufficient to increase the PCB concentration to more than
the allowed 50 ppm PCB limit and, depending upon the effi-
ciency of the operation, can be greater than 500 ppm PCB
after 90 days. Thus the depth of penetration of the degreas-
ing solvent, using existing techniques, can only be very
small and the main action of the process is to remove bulk
PCB from tank walls and core/coil surfaces.
In the Webber process, which is unique, the leaching
effect of residual impregnated PCBs is mitigated by a physico-
chemical process. The method has been proven in a pilot plant
to allow the permanent reclassification of transformers in a
single operation. The recontamination of the replacement fluid
can be either totally eliminated or reduced to such an extent
that the transformer stays reclassified for the remainder of its
useful life. Further tests are planned to extend and further vali-
date the data so that warranties can be made concerning the
future reclassified usage of the retrofilled equipment.
Figure 41 shows a curve relating the increase in resid-
ual PCB concentration with time of transformer operation
after application of a vapor phase cleaning apparatus to a 750
kVA network transformer which originally contained about
270 gal. of askarel. The curve consists of two main regions,
an initially steep slope leading to a pseudo-plateau region
which extends for more than 250 days. The initial slope of
the curve is about 6 ppm PCB/day for the first 90 days after
the transformer was put back in operation and about 1.3 ppm
PCB/day thereafter.
In an isotropic medium, Fick’s first law of diffusion
states that the amount of a substance diffusing through a
medium is proportional to the concentration gradient acting
as the driving force and a constant for the medium which is
the diffusivity, that is,XDC
x(^)
(12)
where
X mass of diffusing substance,
D diffusivity,
C concentration of diffusing substance,
x distance.
Fick’s second law of diffusion describes the flux of dif-
fusing substance:
C
tx
D
C
x
⋅
⎡
⎣⎢
⎤
⎦⎥
where
C
x
⎤
⎦
concentration change measured in the x -direction
For the sake of approximation and mathematical simplicity,
assume that D, the diffusion coefficient, is constant.
Then,
C
t
D
C
x
⋅
2
2
(13)
The diffusion of PCBs through insulating paper into the bulk
oil of the transformer can be modeled as follows.
Assume that the x − y dimensions of an impregnated paper
are large compared with its thickness so that edge effects can be
ignored. Assume that the paper is homogeneous and of thick-
ness 2 d, and also that the bulk oil is maintained homogeneous.
The space occupied by the paper is d x d
The space occupied by the oil is d a x d
and, d x a
where ‘ a ’ is the depth of the bulk oil in the x -direction.
The boundary conditions are:
t 0, C 0 at d x d
and, C 0 otherwise.
At equilibrium, the rate at which PCBs leave the paper is
equal to the rate at which PCBs enter the paper, that is,
a
C
t
D
C
x
⋅⋅xd
∂
∂
2
2 ,t^0
(14)
The solution to a problem of this sort is given by J. Crank
(1956) in terms of an infinite series as follows:
X
X
t
∞
⋅
⋅
⎡
⎣
⎢
⋅⋅ ⋅⋅
()
()
()(
(^11) /
24
12 12
3
12 12
5
12 1
a
a
b
a
b
a
b
^22 )
...
⎤
⎦
⎥
(15)
C016_003_r03.indd 910C016_003_r03.indd 910 11/18/2005 1:12:39 PM11/18/2005 1:12:39 PM