D.W. James
D.W. James & Associates

Scaling factors have always been used in some form for estimating the quantities of difficult to measure radionuclides in radioactive materials. The use of scaling factors became more formalized in 1983 with the introduction of the Low Level Waste Policy Act and its interpretation by the NRC in its Branch Technical Position on Radioactive Waste Classification introduced shortly following the Act. Utilities in the United States are nearing 15 years of experience in collecting sample data for long lived radionuclides and are beginning to look for ways to take advantage of this experience to reduce future sampling expenses. Experience can be used to advantage by trending data collected over a period of many years to develop statistically valid estimates that cover a range of operating conditions. Data collected at most plants demonstrate a pattern or signature distribution of radionuclides. By a rigorous examination the data, waste streams demonstrating similar ratios can be combined to reduce sample frequencies, ratios shown to be constant between wastes streams may be excluded from general analysis or examined in one or two samples per cycle. Sample cycles can be extended by showing that the range of operating conditions encountered have had little effect on the scaling factors determined from the samples collected.

In addition, the paper looks beyond the use of scaling factors by examining alternative analytical methods to take better advantage of the experience collected to date. The primary objective in deriving scaling factors is to obtain reasonable estimates of the amounts of long lived radionuclides in the waste. Scaling factors are not an end in themselves, rather, they represent a relatively simple means to achieve the stated objective.

If the beginning of scaling factors is defined as the introduction of the Low Level Waste Policy Act, then prior practices are more or less prehistoric and have to divined from corroborating evidence. From the evidence that we do have from mostly defunct disposal sites, it seems that there wasn’t too much effort put into the entire characterization process and much less put into determining concentrations of difficult to measure radionuclides. With the evolution of disposal site performance assessment methodologies in the late 70s it became evident that certain long-lived, difficult to measure radionuclides were going to dominate long term exposure risks for disposal sites. The requirement to monitor and report the concentrations of these radionuclides was codified with the introduction of 10CFR61 in 1982.

Prior to the introduction of 10CFR61, generators were already obligated to report concentrations of plutoniums and other TRU. Commercial laboratories were used routinely for these determinations. Scaling factors were derived from the sample for Pu-239 to Ce-144. Results of many of these analyses were compiled together for the data base presented and analyzed in NUREG CR-4101. Much of the data available for analysis at the time of publication were samples collected for TRU analysis. "Routine" sampling was conducted prior to 1982 as evidenced by the data compiled by SAI in 1985.

Shortly, following issuance of 10CFR61 much effort was exerted by the nuclear power industry to establish correlations to support 10CFR61 reporting requirements. As conceived by the NRC an initial effort would be made to develop a statistical basis for the ratios which could then be updated with confirmatory analysis collected on an annual basis. Updating could be performed by direct substitution of the old value with the new or no change to the old value if the new value was less than a factor of ten different from the old. This method survived as the leading method for maintaining scaling factors for many years – and is probably still in use at some sites. The primary problem with this method is the inherent variability of the sampling and measurement effort which may not be indicative of any real changes in the system and dispersal of long-lived contaminants. It isn’t unusual following this practice to have variations in concentrations of individual radionuclides ranging from 20 –100 from one year to the next. These kinds of variations are not consistent with experience and ultimately can lead to unacceptable results.

Linear regression of the sample data provides an improved prediction method over substitution. The regressions are performed on the logarithmic values on the basis that the measurements will be log-normally distributed. Linear regression has its adherents. One of the beauties of linear regression is the rich selection of statistical treatments available. Calculation packages are available that can perform every conceivable statistical test ranging from F-tests, chi-squared tests, t-tests, confidence intervals, etc. If you don’t trust the commercial programs, it can be interesting and educational, if not outright fun, to write a little program or a spread sheet macro to do the job. The problem with regression (imho) may be that it provides too much information. You now have two numbers to deal with , a y-intercept which represents, more or less, the actual scaling factor, and a slope which represents some variance in the scaling factor with key radionuclide concentration. Assuming that the regression is performed on logarithms, the resulting equation is y= bx^m, where y is the scaled radionuclide and x is the key radionuclide.

In my own experience, I found that the regressions weren’t very trust worthy. A bad value would impact the slope more aggressively than the intercept. If the bad value was removed, the slope invariably approached 1 in which case the intercept was equivalent to the geometric mean. To reduce the importance of outliers, a robust regression was defined which regressed about median values rather than the average values. With more experience, it became apparent that the regression result was only meaningful if the slope was at or near to a value of one. If the slope was not close to one, the data would most likely pass a statistical test for the slope equals to zero (i.e. H:m = 0 at the 95% confidence level) which is equivalent to regression failure or no meaningful correlation. This happened when the data was comprised of primarily less than values (or specious real values), and for cases involving C-14 and H-3 when regressed with any key radionuclide. The conclusion of this exercise, which was spread out over the better part of a year, was to abandon regression. If the slope is near a value of 1, it would pass a slope = 1 (H:m = 1) statistical test, if the slope was not close to one it would likely pass a slope = 0 test. Realistically, if there isn’t a direct correlation, all we really know about the relationship is that one doesn’t exist, we do not know that it is log linear, we do not know that it is exponential, we do not know that it is quadratic, or any other relation.

Most scaling factor analysis today relies heavily on the use of the geometric mean. Consider it to be equivalent to a linear regression of the logs where the slope always comes out equal to one. As an approximation of the median, the geometric mean has the quality of reducing the effect of the inherent variability of the data. A justification for the use of the geometric mean was presented in EPRI-4073. It is easy to calculate and relatively easy to understand. Use of the geometric mean with reasonable dispersion values produces consistent scaling factor results and minimizes year to year variations caused by sampling variability.

The radionuclides controlled by 10CFR61 (and regulations promulgated in most generator countries outside of the US) can be broken down into three scaling factor groups: Activation products scaled to Co-60, fission products scaled to Cs-137, and transuranic radionuclides scaled to Ce-144

Ce-144 has traditionally been used as the key radionuclide for determining transuranic radionuclide concentrations. Since it is a fission product with transport properties similar to plutonium, it provided very consistent correlations. The correlations were not particularly sensitive to wastes streams or age of the material. Once established the relations could be regarded as constant. As fuel performance improved through the 1980s, detection of Ce-144 in normal gamma spectroscopy became increasingly rare. Furthermore, TRU concentrations as well were becoming disappearingly small. If you don’t find the Ce-144 in the gamma spectrum but know that there is reportable concentrations of TRUs, there are two options 1) assume that by the obvious lack of Ce-144 that there is no TRU or 2) look for another scaling factor. Choosing the first option will likely merit an inspection citation by the NRC and a rather urgent exercise to implement the second option.

One solution was offered by the laboratory results for the DTM radionuclides. The lab report nearly always included a Ce-144 measurement as well as one for Cs-137. You could still scale TRU to Ce-144 but you use another scaling factor, Ce-144/Cs-137, to determine the Ce-144. Ce-144 scales about as well to Cs-137 as Pu-239 (or any of the other TRU). If there is no Cs-137 in the gamma spec conceivably you could go one step further and define a ratio for the cesium, Cs-137/Co-60. Since Cs-137 is also a fission product, its concentration is also rarely observed in normal gamma specs. (Both Cs-137 and Ce-144 are still detectable by radiochemical methods.) Notwithstanding "NRC approval" of this approach and its providing a cornerstone for characterization calculations in some popular computer programs, it is observed that the process offers a pretty obscure view of how the TRU concentrations relate to what you are seeing in the gamma spec. Many plants in the United States, blessed by good fuel performance year after year, have moved away from the multi-layered scaling and are defining TRU concentrations directly from Co-60. Similarly, if Cs-137 consistently isn’t showing up in the gamma spec, other fission product concentrations will have to defined from Co-60 as well.

Given a good measurement history ratios between TRU radionuclides are very stable from one year to the next and usually do not vary between waste streams. For the most part it should be sufficient having established these ratios, to measure only one of the TRU radionuclides (e.g. Pu-239 or Pu-241) for relating to a key radionuclide. The remaining TRU can be determined from the constant ratios. This will offer significant savings from year to year on costs for radiochemical analysis.

Scaling factors for Sr-90/Cs-137 and for TRU/Ce144 should still be evaluated if the laboratory data supports it, however, alternative scaling factors for Sr-90/Co-60 and TRU/Co60 must also be defined.

Most US power plants define on the order of five to seven individual waste streams. This is consistent with the NRC’s original perception of what would constitute major waste streams. Some more analytically thinking individuals would argue that there is no good reason why fuel pool filter media will be the same as filter media collected from the radwaste systems or that DAW from the unit 1 reactor building will not be the same as DAW from the Unit 2 reactor building. For PWR cartridge filters, one could readily identify seven or eight individual streams in each plant. These wastes streams can be combined for the purpose of sampling and furthermore a justification can be developed if necessary. Even for major dissimilar waste streams such as primary resins and primary, it some individual scaling factors are the same and are not effected by media.

It can be demonstrated that certain wastes streams can be treated as equivalent as they relate to sampling and scaling factor determination.(19)

To perform the comparison a pooled variance was calculated using logarithmic from:

(1)

The pooled variance is then used to define a test statistic, t, that can be compared with table values such that:

(2)

key:

This formulation could also be used to demonstrate conformance with a larger data base.

The calculated t was compared with ta /2 where a = .025 (95% Confidence Level). The value R represents a ratio or a difference factor between the two mean values. If R=1, there is no difference - that is, at the 95% level we cannot say that the ratio of the two means is different than 1. There is a 95% confidence that there is no difference between the geometric means given the number of samples compared and the observed variance. If R = 2, there is a significant difference of a factor of 2. On comparisons conducted with two filter waste streams from the same plant, no significant differences in the data were observed, on the basis that given the number of samples, the variance in the data, even though the means were different by as much as a factor of 10 the data tested the same with a factor 2 which is well within the general objective for prediction within a factor of 10.

Care should be exercised when applying this method when making comparisons with a larger data set that already contains the data being tested. For example, if you are comparing your data with an industry wide database that includes your data. The variance of the industry wide database will already include the variance of your data and the overall variance will be very high. In effect, everything will look like that data since it is a compilation of everything.

If the data shows little or no change over several sample cycles, it may be appropriate to extend the sample frequency. Most US plants now have experience collection data over a period of more than 15 years. Many of the scaling factor ratios show little change from year to year.

Fig. 1 demonstrates the general stability of a particular scaling factor as measured in a single plant. This data shows a slight downward trend over a period of many years, however changes from one year to the next are very slight. This ratio is shown because the dispersion of the data is low and its easy to see that it really isn’t changing. Other ratios often are characterized by higher dispersion which tends to obscure the general trend of the measurements, that is, its difficult to determine if the ratio is changing or not.

Tc-99 and I-129 have always presented a special problem in low-level waste characterization. Generally, the activities of these very long-lived radionuclides are so low that they are rarely reported. Problems with the determination of these radionuclides was noted in NUREG CR-4101. It was noted in that report that it was not always possible to meet the NRC criteria for LLD (1% of the lowest 10CFR61 limit). It was also noted that the limits were most compromised in the higher activity material in which case a higher limit would apply anyway and that, therefore, the NRC should consider relaxing the LLD criteria in these cases.

In fact, the laboratories routinely don’t meet the LLD objective for higher activity radwaste. This presents a problem for the generators since scaling factors must be defined from the data. All that the data really shows is that the LLDs drift upward slightly as the activity of the waste increases. If a scaling factor is defined from the data it will be roughly equivalent to the LLD. For higher activity wastes (>10 µCi/cc Cs-137), these radionuclides (particularly I-129) will become classification controlling and possibly bump the Class C limit. Fig. 2, below, shows a typical plot derived from ;laboratory data. The scaling factor associated with this data would be about 6.7x10-3. Basically any waste with a Cs-137 concentration approaching 0.12 µCi/cc would be Class C.

Based on what is known about radionuclide production in fuel, the production ratio of I-129/Cs-137 is basically constant at 2E-7. Given comparable release and transport properties, this would imply by comparison with the achievable sensitivities (refer to Table II) that it will never be detected by radiochemical methods. Some efforts have been made to peg the I-129 concentrations by mass spectrometry. All of these results confirm the general observation that the actual scaling factor is at or near the production ratio. Even at the Class C limit for Cs-137 (4600 µCi/cc), the I-129 concentration would still be almost a factor of 10 below its Class A limit. All of the data represented in Fig. 2 is derived from reported LLD values. If we look at I-129 independently of scaling factors, as shown in Fig. 3, we find that the median concentration of I-129 reported in this data is ~3x10-5 µCi/cc and the preponderance of data is within a factor 10 or this value. It was already shown in Fig. 2 that the reported concentrations of I-129 is independent of the Cs-137 concentration. Therefore, the concentration could be treated as an upper bound concentration for all of the wastes enveloped by the analysis. Even if the concentration was assumed to be a factor of 10 higher, it would still only be a fraction of the NRC Class A limit and insignificant relative to disposal site performance assessment.

What should always be avoided is determining a scaling factor from LLD values or multiplying an LLD based concentration by a dose to curie conversion factor. Outside of the fact that there is law requiring the reporting of I-129 for all radioactive wastes. The data collected in more than 3000 samples, industry wide, in the United States, shows effectively a null result, nuclear power plant wastes have not been and will not be a significant source of I-129 in the disposal site, Virtually all wastes disposed of to date have contained only a small fraction of the Class A limit and do not contribute significantly to disposal inventories. Reporting requirements for I-129 could be relaxed with no risk to public safety.

Tc-99 can be treated similarly to I-129. The preponderance of data shows that the concentrations measured in waste samples are well below the Class A limit for disposal. Getting a good fix on Tc-99 is complicated by the fact that it is both an activation product and a fission product. Exposed fuel can produce very low concentrations of Tc-99 in the reactor coolant. If the cesium concentrations are low, which is the case when there are no significant fuel failures, Tc-99 will follow Co-60. Table III shows scaling factors for activation products defined on the basis of reactor materials. Type 316 is the material most commonly used in BWRs in contact with reactor coolant. Inconel is the corresponding material in PWRs. Basically, these scaling factors are consistent with observed values for both plant types. Values for Tc-99/Co-60 are very consistent with actual scaling factor determinations in operating power plants. This ratio will be effected by fuel performance but is unlikely to go much below this value. Most plants can define this scaling factor with existing data. Arguments for using a constant concentration "less than" value can be also be made as in the case of I-129.

C-14 and H-3 are two more radionuclides that must be tracked and that defy conventional scaling factor methods. Both radionuclides are formed in the reactor coolant independently of fuel performance and crud behavior. There is no well understood reason for expecting that either radionuclide would follow Co-60 or Cs-137. In fact, the preponderance of data shows that they do not. (Although, C-14 can generally be safely correlated with Co-60 in filter waste streams.) Conventional practice is to scale C-14 to Co-60 and to estimate the tritium activity from the amount of moisture in the waste and an upper bound concentration found in reactor coolant. Some generators define a scaling factor between tritium and Co-60 as well.

Scaling factors can be safe to use if they are defined for each major waste stream, and the Co-60 concentration does not vary much between sampling. In this case the scaling factor will appear to be pretty constant, exhibit low dispersion, and have very little relevance much more than a factor of 10 above or below the reference Co-60 concentration. It is more likely in the case of C-14, excluding filters, that the concentration is constant in various waste streams assuming a constant production and release of gaseous C-14 and uniform handling of materials through the process cycle. When examined on a waste stream specific basis, laboratory data shows very consistent results for some waste streams through several cycles of operation. If a constant concentration is used as the characterization basis, then the value should not be scaled to dose to curie results. This is because the dose rate is driven by crud concentrations and fuel performance. Neither effects production and release of tritium and C-14.

If tritium is estimated by moisture content and coolant concentration, there must be cognizance of two points, 1) moisture content varies from batch to batch and can be difficult to determine, and 2)tritium will not necessarily be at equilibrium between the reactor coolant and the various process streams. Again, tritium activity should not be scaled to dose rate. In practice, it would seem that the reference moisture content of a waste stream could be estimated by the ratio of tritium in reactor coolant to the concentration of tritium in the laboratory sample. At least one plant, has been very successful in tracking this ratio. As an aside, if the reactor coolant tritium is relatively constant over time, using a ratio offers no advantage over directly using the concentration or the average concentration of the laboratory samples.

The United States has led the development of a scaling factor approach for difficult to measure radionuclides. This leadership was not derived so much from an altruistic desire to do the right thing but out of necessity to define a manageable methodology that could be implemented quickly in support of new disposal site regulations. At the time that the methodology came into play in the US most other countries hadn’t really addressed long term disposal issues. Outside of the US most of the waste is packaged in 220 liter drums and is nationally managed. This situation allows for stricter definition and control of waste types and the creation of detailed specification based on waste type that includes generalized scaling factors. The scaling factors are supplied to drum counter systems that provide a complete characterization report either at the shippers facility or at the disposal site. The US requirements to update the scaling factors on an annual basis and that they be defined on a plant and waste stream specific basis is very problematic in many other countries. Furthermore, only in the last few years has an intensive international effort been undertaken to develop laboratory capabilities to do the necessary radiochemical analyses. Many of these countries are stumbling over the same issues and examining some of the same quick fixes which were popular in the US 10 or 12 years ago.

While it is unlikely that scaling factors can be eliminated entirely, there may be enough experience and data available to reduce the effort and expense of this process. Nearly all plants in the United States have collected sufficient data to establish a clear characterization basis for their low level waste. There is neither need nor incentive for these plants to align with an industry wide data base. They can through judicious use of their own data reduce the number of waste streams sampled, the scope of laboratory analysis, and the frequency of sampling. Individual plants should do this, however, with cognizance of the national experience. It’s still easy to be misled by bad data.

1. Radioactive Waste Policy Act of 1982. Public Law
2. Radioactive Waste Policy Amendments Act of 1985. Public Law
3. Cline, J.E., "Possible Generic Scaling Factors for Low-Level Waste - Summary of Data Base", Characterization Guidelines Meeting (sponsored by EPRI), August 1995, Pittsburg Pennsylvania
4. Assessing the Impact of NRC Regulation 10CFR61 on the Nuclear Industry, Palo Alto, CA, Electric Power Research Institute, NP-5983, August 1988.
5. An Assessment of 10CFR61 Waste Classification Methods, Utility Nuclear Waste Management Group, Washington, DC, August 1986.
6. An Examination of Low_level Waste Scaling Factor Data Base, Project RP-2414-53, Palo Alto, CA, Electric Power Research Institute, Unpublished.
7. Code of Federal Regulations Title 10 Part 61, "Licensing Requirements for Land Disposal of Radioactive Waste", U.S. Nuclear Regulatory Commission, Washington DC.
8. Low-Level Waste Licensing, Branch Technical Position on Radioactive Waste Classification, US Nuclear Regulatory Commission, May 1983, Washington, DC.
9. Assay of Long Lived Radionuclides in Low Level Wastes From Power Reactors, Washington DC. US Nuclear Regulatory Commission, NUREG/CR-4101, April 1985
10. Technical Position of Concentration Averaging and Encapsulation, (Revision in Part to Waste Classification Technical Position) , US. Nuclear Regulatory Commission, January 1995, Washington DC.
11. Radionuclide Correlations in Low-Level Radwaste, Electric Power Research Institute, Palo Alto, CA, EPRI - 4037, June 1985
12. Updated Scaling Factors in Low Level Radwaste, Electric Power Researh Institute, EPRI-5077, March 1987.
13. Methodologies for Classification of Low Level Radioactive Wastes from Nuclear Power Plants, Atomic Industrial Forum, Bethesda, MD, AIF\NESP-027, December 1983
14. Allen, J.A., "Scaling Factor Determination at WNP-2 Using the Scan Computer Code", EPRI/ASME Radwaste Operators Workshop, Newport News, VA, 1994,
15. James. D.W., "Evaluating Long-Lived Nuclides in Low-Level Waste Streams" Proceedings of the 1993 International Conference on Nuclear Waste Management and Environmental Remediation, Volume 1. Low and Intermediate Level Waste Management", p.373
16. Johnson, T.C., Lohaus, P.H., Roles, G.W., "Implementation of 10CFR Part 61 Waste Classification and Waste Form Requirements:, Proceedings of International Symposium on Waste Management, Waste Management '83, Tucson, AZ , Vol. 1, p.401.
17. Bell, S.,. Commonwealth Edison's 10CFR61 Waste Classification and Compliance Program", International Low-Level Waste Conference and Exhibit Show, sponsored by EPRI, Monterey,California, November, 1993.
18. Miller, C. and Claytor, L., "Consolidation of Waste Correlation Factors", Radwaste Magazine, March 1996, pp.67-70.
19. Walpole,R.E., Meyers, R.H., Probability and Statistics For Engineers and Scientists, Fourth Edition, MacMillan Publishing Company, New York, 1989, pp 246-248.

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