912 PCBs AND ASSOCIATED AROMATICS
12.3 10 2 0.58 g
7,100 g askarel 5,000 g PCB.If it is assumed that the pseudo-plateau shown in the figure
above does allow a reasonable approximation of the total
PCB leached into the bulk oil within the service lifetime of
the transformer then,X { X s − [785 (ppm PCB) 10 −6 (0.878 8.34)
(lb/gal) 270 (gal.) 454 (g/lb)]}.If the paper quantity is assumed, for the purpose of calcula-
tion, to be proportional to fluid volume from one design to
another then,Xs
12 3 10 0 58 270 8 4
22 931../^3
,gtherefore,X∞=−
=22 931 705
22 226,
,gthat is ,XX∞/..s0 969The calculation puts an upper bound on the extent of the leach-
ing problem since the model used in the calculation assumes
that sufficient time has been allowed to achieve equilibrium.
In the experimental arrangement used, the time to reach equi-
librium was not a limiting factor since this was long com-
pared with the time required for the diffusion of PCBs into
and out of single, as opposed to bundled, sheets of paper. A
transformer, however, presents a more complicated situation:
the time to achieve true equilibrium may be beyond the ser-
vice live-expectancy of the transformer since the migration of
PCBs through different thicknesses of layered paper is the rate
determining factor which governs the total fractional uptake.
The data shown in the above figure for a retrofilled askarel
transformer suggest that PCBs will leach at the rate of about
1.3 ppm PCB/day for a period of perhaps years. It is there-
fore not possible to determine with any accuracy what mass of
PCBs migrate into the oil when a final equilibrium is reached.
If one assumes that, in the best case, a saturation level has been
reached after 240 days, then an approximate ‘best case’ correla-
tion curve can be calculated between b 1/2 and X t / X as follows.
From above, X / X s 0.969ab=−=×=⋅∞∞−132 10^22X
X
X
XDt
dss
..Assume that D 7.6 10 −^10 (cm^2 /sec)
d 1 (cm)
then, β 7.6 10 −^10 ⋅ t (sec).If the transformer is to be reclassified as ‘PCB contaminated’
then it must not be greater than 500 ppm PCB after 90 days
of operation after the retrofill,that is,X
Xt
∞==500
7850 637..By interpolation,b 1/2 0.036 when X t / X 0.638
that is , 0.0362 7.6 10 −10 · t
hence, t 19.7 days.In other words, an initial clean layer of 1 cm of paper will
allow the bulk oil to reach 500 ppm PCB in about 20 days.
The correlation shown in Figure 42 has been calculated
between the depth of the cleaned layer and the time required
for the PCB concentration of the bulk oil to reach 500 ppm
PCB using different values for the diffusion coefficient.
The experimentally determined diffusion coefficient
for the migration of Inerteen 70/30 through kraft paper is
about 7.6 10 −10 cm^2 /sec. Under these conditions, if the
cleaned layer is about 4.3 cm deep, the transformer will
become a PCB transformer one year after the retrofill has
been completed.
If the transformer is to be reclassified as ‘non-PCB,’ then
it must not be greater than 50 ppm PCB 90 days after the
retrofill procedure has been completed,i.e.,X
Xt
∞==50
7850 064.hence, t 7 days.The correlation between the depth of the cleaned layer and
the time of reach 50 ppm PCB is shown in Figure 43 for dif-
ferent values of the diffusion coefficient. Clearly, the time
to reach a bulk oil concentration of 50 ppm PCB is much
shorter for a given depth of cleaned layer and is critically
dependent upon the diffusion coefficient.
Figure 44 shows how the depth of the cleaned layer
must vary for different values of the diffusion coefficient in
order to obtain a defined reclassification status. If the diffu-
sion coefficient becomes larger than about 10 −8 or 10 −9 cm^2 /
sec then the correlation shows that the depth of the cleaned
layer must become much greater than it is practicable to
achieve.
It is interesting to note that if the cleaned layer is 4.3 cm
and the diffusion coefficient is the experimentally measured
value of 7.6 10 −10 cm^2 /sec, then there is little doubt that the
transformer would be reclassified after 90 days. However, after
one year of operation it would become a PCB transformerC016_003_r03.indd 912C016_003_r03.indd 912 11/18/2005 1:12:40 PM11/18/2005 1:12:40 PM