ML20030A463
| ML20030A463 | |
| Person / Time | |
|---|---|
| Site: | Big Rock Point File:Consumers Energy icon.png |
| Issue date: | 12/22/1959 |
| From: | Ayers J CONSUMERS ENERGY CO. (FORMERLY CONSUMERS POWER CO.), MICHIGAN, UNIV. OF, ANN ARBOR, MI |
| To: | |
| References | |
| NUDOCS 8101090570 | |
| Download: ML20030A463 (5) | |
Text
i A Preliminary " Worst Condition" Estimate of Dilutions To Be Expected in Little Traverse Bay Submitted by:
John C. Ayers Great Lakes Research Institute The University of Michigan Ann Arbor, Michigan l
22 December 1959
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At the request of Mr. R. D. Allen of Consumers Power Company, I have made a preliminary estimate of the " worst-condition" dilution of radioactive material in Little Traverse Bay. This esti-mate is only approximate, but it does represent the probable order of magnitude of dilution of waste materials in the Bay under the
" worst" conditions assumed.
It has been assumed that an accident occurred in the plant condenser system in such a way that the entire mass of radio-active water from the reactor vessel was discharged into the effluent condenser-cooling water instantaneously.
It has been further as-sumed that the entire body of radioactive water was discharged into the Bay in one minute by the 100,000 gpm flow of cooling vater. A further assumption is that this accident occurred at the peak of summer thermal conditions in which the entire Bay contained a very strong density stratification that limited all mixing processes to the upper 50 feet of the Bay water.
It is still further assumed that the vinds for the previous several days had been from the pre-valling westerly quarters and of only " normal" velocities. A fur-ther assumption is that some very unusual current condition was in effect whereby the currents of Little Traverse Bay were completely cut off from all intermixing with the adjacent currents of Lake Michigan. Each of the above assumptions is quite unrealistically "wors t. " These assumptions are followed by a sotill further assumption
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- w that mixing processes in the Bay operated to spread the contaminant uniformly throughout the upper 50 feet of Bay water. The latter assumption is unrealistic in the opposite direction, i.e.,
it as-sumes a favorable diffusion which is not apt to occur completely.
The group of assumptions are all but one unrealis-tically conservative in the direction of poor dilution. The ex-ception is the last assumption, which is inclined toward unreal-istically good dilution, of the total, then, there are five which are unrealistic toward poor dilution and one which is unrealistic toward good dilution. To the best of my, judgment the resultant complexion of the group of assumptions is very heavily toward un-realistically worst conditions.
In the present state of our knowledge, estimates of more realistic nature cannot be made be-cause of lack of specific fundamental data.
Little Traverse Bay, east of a line from the tip of Mt. McSauba Point northeast to the intersection of latitude 45 30" with the north shore of the Bay, has a surface area of 289,539,000,000 square inches. In midsummer the primani density stratification lies at 50 feet, or 600 inches, below the surface of the water. The volume of the water above the density discontinuity is then 289,536 x lo square inches x 600 inches or 173,721,600,000,000 cubic inches.
one gallon of water contains 231 cubic inches, and the number of gai-lons in the upper layer of the Bay is then 173,721,600,000,000
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9 cubic inches divided by 231 cubic inches or 752 x 10 ganons.
In the minute after the minute in which the water from the reactor accident is assumed to have been discharged into the Bay, the Bay's upper layer would contain the 1 x 10' gallons,just 5
discharged and 7,519,999 x 10 gallons derived from Lake Michigan and previous uncontaminated condenser discharge.
Since it is assumed that the load of contaminant be-comes uniformly distributed in the upper layer of the Bay, the pro-portion of contaminated to uncontaminated water would be 1 :
7,519,999 or an approximate dilution of 8 x 106 (8 million times).
It has been our custom and that of others to consider that a dilution sufficient to equal the sensitivity of good stan-dard chemical analyses is, in its effect, an infinite dilution. The 8 million times dilution to be expected under the above unrealis-tically " worst" conditions is equivalent to one part in eight million, while a good standard analysis is sensitive to one part in ten mil-lion. Since the atsumptions have been on the whole unrealistically severe and the estimated dilution approaches the limit of analysis sensitivity, even slightly more realisti estimates would indicate a
that a one-shot introduction of contaminant would be, in effect, in-finitely diluted.
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1 In the event that a " worst" time-rate of dilution should be a more useable figure, the following can be given.
Discharge through a shore channel into the littoral current has similarities to discharge from a barde moving at slow speed through essentially still water. We have had occasion to measure to spread and dilution from such a barge operating outside New York harbor. With slight modification the be-havior of the plume behind the barge can be made applicable to "vorst" conditions in the Little Traverse Bay region. Under essentially vind-less conditions (no wave action, no surf along shore) in midsummer (mixing limited to only the upper layers of water) and ignoring the turbulent mixing immediately behind the barge, the barge's plume may be taken as representative of the plume from the discharge channel of the plant. Assuming, as before, instantaneous " spill" and instantaneous discharge to the Bay the single slug of contaminant might be expected to spread (be diluted) at the same rate as the plume.
The barge's plume spread from a cross-sectional area of 400 ft to one of 22,500 ft in 25 minutes.
If this increment repre-sents the admixing of uncontaminated water, as it must, the increment represents a dilution of 56X in 25 minutes or about 120X per hour.
As a check on this, we may consider the following. The band of alongshore current at the plant site appears to be about 8000 ft wide and moves at an average velocity about 0.1 mph.
In the upper 3
50 feet this current vould carry a flow of 2 x 10 ft/hr. The channel 3
discharge of 100,000 gpm would be equivalent to 8 x 10 ft/hr.
If the channel effluent completely mixes with the current it vill be diluted
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250X in the first hour. The agreement is satisfactory.
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