Stephen A. McGuire
Office of Nuclear Regulatory Research
U. S. Nuclear Regulatory Commission
Washington, DC 20555

On July 21, 1997, the U. S. Nuclear Regulatory Commission published a final regulation on radiological criteria for license termination (62 Federal Register 39058). That regulation permits the release of sites for unrestricted use if the annual dose to the average member of the critical group would not exceed 0.25 mSv (25 mrem) and the residual radioactivity has been reduced to a level that is as low as is reasonably achievable (ALARA). The regulation also permits the release of sites under restricted conditions if the annual dose would not exceed 0.25 mSv (25 mrem) with the restrictions in place and 1 mSv (100 mrem) (or 5 mSv (500 mrem) under certain conditions) if the restrictions were not in place. The levels or residual radioactivity would also have to be as low as is reasonably achievable. The NRC is developing a Regulatory Guide on how to comply with the new regulation. The subjects in the guide are: (1) methods to calculate the dose from a concentration of residual radioactivity, (2) survey methods, (3) release of a site under restricted conditions, and (4) methods to perform an ALARA analysis. This paper will discuss a methodology to meet the requirements to demonstrate that residual radioactivity levels are ALARA for relatively simple situations.

The NRC's new decommissioning regulations published in July 1997 (Reference 1) require that residual radioactivity has been reduced to a levels that is as low as is reasonably achievable (ALARA) as a condition for terminating the license for a site. This ALARA requirement is in addition to and independent from the requirement to demonstrate compliance with a dose limit.

This paper describes a simple quantitative method to demonstrate compliance with the ALARA requirement. The method described in this paper is applicable to relatively simple situations such as release for unrestricted use. The method can be built upon for restricted release, but that is not done in this paper.

Several characteristics are desirable in a method to determine if levels of residual radioactivity are ALARA:

1. The method should be simple.
2. The method should not be biased.
3. The method should use the same dose modeling that is used to relate concentrations to dose.
4. The method should be usable as a remediation planning tool.
5. The demonstration that the ALARA criterion has been met should use the results from the final site survey.

The method should be simple because the effort needed for very sophisticated models cannot be justified. The primary benefit of a remediation action, radiation doses averted in the future, is not really knowable. It is not possible to know the future land uses or number of people that will actually occupy a site. For example, the residential scenario assumes people will build a house on the site, use a well for their drinking water, and eat crops grown on the site. But will a house really be built there or will the area be an unoccupied field? If there is a house, how many occupants will it have? Will a well be drilled at a location that has residual radioactivity? Will the site residents really grow their own food on the site? The answers to these questions are not knowable. Thus, future collective dose cannot be known with precision regardless of how much effort is made. Because of this inherent limitation on our ability to precisely determine the future collective dose at a particular site, it is not appropriate to perform a complicated and expensive analysis when a simple analysis will suffice.

The method should not be biased. Dose limits typically define an adequate level of protection. When determining compliance with a dose limit that provides adequate protection, a measurement with a conservative bias is often sought. This assures that compliance with the limit established to provide adequate protection has been met. An ALARA analysis is an optimization technique that seeks the proper balance between costs and benefits below the dose limit. A balance requires that each factor be determined with as little bias as possible. If the analysis were intentionally biased in either direction, it would cause a misallocation of resources. A misallocation of resources would deprive society of the benefits from other uses of the resources.

There are different ways that a remediation action can affect the future well being of society. A remediation action can avert future dose, which is a benefit. The remediation action can also cost money, which can be a detriment. According to modern research in economic theory, loss of the effective use of this capital will deprive future generations of the return on the investment of this money, which is a detriment to society. Thus, if a great deal of money is spent for a cleanup that would have a very small future benefit, it would be detrimental to future generations. The OMB guidance to Federal agencies that implements President Clinton's Executive Order 12866 (Reference 2) incorporates this approach in analyzing the potential benefits of federal regulations (Reference 3).

The choice of the dose model used involves a trade-off between the objectives of simplicity and achieving a lack of bias. The objective to reduce bias is not met when we use the same dose models to demonstrate compliance with the dose limit and the ALARA criterion. The critical group used in the dose models was intentionally selected to be a group with characteristics defined to maximize dose, not to give a best estimate of the most likely value of dose to typical site occupants. Thus, the calculated benefits (averted doses) due to reducing levels of residual radioactivity would not be likely to be fully realized. On the other hand, dose models are difficult to develop and to use. Therefore it may be appropriate to compromise on the objective of lack of bias in order to avoid unnecessary complexity.

The method should be usable as a remediation planning tool. In other words, before starting a remediation action, the user should be able to determine what concentration of residual radioactivity would require a remediation action to meet the ALARA criteria. It is inefficient if the user can not tell whether the area would pass the ALARA test until after the remediation were done.

The method should allow use of the results from the final site survey to identify locations whose concentrations are high enough that a remediation actions should have been taken. It is inefficient to require an additional set of measurements to demonstrate remediation actions were taken wherever appropriate to meet the ALARA criteria if the set of measurements used to demonstrate compliance with the dose limit can be used for both.

The ALARA analysis compares the monetary value of the desirable effects (benefits) of a remediation action, for example, the monetary benefit of averted dose, with the monetary value of the undesirable effects, for example, the costs of waste disposal. If the benefits of a remediation action would exceed the costs, then the remediation action should be taken to meet the ALARA requirement:

(1)

The primary benefit from a remediation action is the collective dose averted in the future - the sum of the doses received by the entire exposed population. Assume:

1. You have a location with residual radioactivity at a concentration C.
2. The concentration equivalent to 0.25 mSv (25 mrem)/yr (DCGL_W) for the site has been determined (for soil or for building surfaces, as appropriate).
3. The residual radioactivity at a site has been adequately characterized so that the effectiveness of a remediation action can be estimated in terms of the fraction F of the residual radioactivity that the action will remove.
4. The peak dose rate occurs at time 0 and decreases thereafter by radiological decay.

The derived concentration guideline (DCGL_W) is the concentration of residual radioactivity that would result in a total effective dose equivalent to an average member of the critical group of 0.25 mSv (25 mrem)/yr. Acceptable methods to calculate the DCGL_W are discussed in Section C.1 of the NRC Regulatory Guide, "Demonstrating Compliance with the Radiological Criteria for License Termination" (Reference 4). Therefore, the annual dose D to the average member of the critical group from residual radioactivity at a concentration C is:

(2)

If a remediation action would remove a fraction F of the residual radioactivity present, then the annual averted dose AD_individual to an individual is:

(3)

The annual collective averted dose AD_collective can be calculated by multiplying the individual averted dose, AD_individual, by the number of people expected to occupy the area A containing the residual radioactivity. The number of people in the area containing the residual radioactivity is the area A times the expected future population density P_D for the site. Thus:

(4)

The annual monetary benefit rate at time 0, B₀, due to the averted collective dose in dollars/yr can be calculated by multiplying the annual collective averted dose AD_collective by $200,000/person-sievert ($2000/person-rem) (Reference 5):

(5)

The total monetary benefit of averted doses can be calculated by integrating the annual benefit over the exposure time in years considering both the present worth of future benefits and radiological decay. It is NRC policy to use the present worth of both benefits and costs that occur in the future (Reference 5).

The equation for the present worth PW of a series of constant future annual benefits B₀($/yr) for N years at a monetary discount rate of r (per year) using continuous compounding is:

(6)

The continuous compounding form of the present worth equation is used because it permits an easy formulation that includes radiological decay. If the annual benefit rate B is not constant but is decreasing from its original rate B₀ due to radiological decay, the radiological decay rate acts like an additional discount rate that can be added to the monetary discount rate of decline so that the present worth factor PW becomes:

(7)

As N ® ¥, Equation 7 has the limit:

(8)

When the radionuclide has a very long half-life (l ® 0), the present worth of future benefits PW will be inversely proportional to the monetary discount rate r. As (r + l)N ® 0, Equation 7 has the limit:

(9)

The total benefit B_total is the present worth of the annual benefits. B_total can be calculated by combining equations 5 and 7:

(10)

Now consider the costs of a remediation action, C_RA. As a rough approximation, when one can achieve reasonable economies of scale, the cost of a remediation action C_RA will be proportional to the area to be remediated. Defining the cost per unit area C_UA as the proportionality constant, the costs included in C_UA are: (1) the direct cost of the remediation action itself, (2) the cost of waste disposal including its shipping cost, (3), the monetary costs of workplace accidents during the remediation, (4) the monetary costs of transportation accidents during the shipping of waste, and (5) the monetary value of the dose that remediation workers receive. Thus,

(11)

where

(12)

Both the benefits (Equation 10) and the costs (Equation 11) include the area A. Therefore when we take a benefit/cost ratio by dividing Equation 10 by Equation 11, and the area A cancels out.

(13)

What we are most interested in is the concentration C at which the benefit B_total equals the cost C_RA. Thus, in Equation 13, we set the ratio B_total/C_RA equal to 1. When this is done we can solve Equation 13 for the concentration C relative to the DCGL_W or C/DCGL_W:

(14)

Equation 14 is our result. Equation 14 can be used to determine the concentration at any location for which a remediation action should be taken to meet the ALARA criterion. The equation appears complicated, but the calculation can be done in a few minutes with a hand-held calculator, and it only has to be done once for each type of remediation action at a site. P_D, N, and r are constants. Generic values for P_D and N are given in Reference 6 or may be determined on a site specific basis. Values for r are given in Reference 5. The only site specific information that the licensee needs is the cost per unit area, C_UA, and the effectiveness F for each remediation action being evaluated. Some examples of the use of Equation 14 are shown below.

Consider a building with cesium-137 residual radioactivity (l = 0.023/yr). The remediation action to be considered is washing of surfaces. The licensee estimates that this will cost $1/m² and will remove half (F = 0.5) of the residual radioactivity. For buildings, generic parameters are: P_D = 0.09 person/m², r = 0.07/yr, and N = 70 years. Using these values in Equation 14 gives:

	(15)
	(16)

This result means that to meet the ALARA requirement any spot with a concentration exceeding about 4% of the DCGL_W must be washed. Note that this is much more stringent than the dose limit. A licensee with measurable cesium-137 would probably decide to wash all the surfaces. The alternate is to show that all surfaces have a concentration below 4% of the DCGL_W. This would be a much more stringent survey than a survey designed to demonstrate compliance with the dose limit.

This is the same example as above except that scabbling to a depth of 1/8 inch. The licensee estimates the total cost of the scabbling will be $50/m² and estimates that it will remove all the residual radioactivity. Using these values in Equation 14 gives:

	(17)
	(18)

In this case, the ALARA requirement is more stringent than the dose limit requirement. Scabbling would be required at any location exceeding 0.97 DCGL_W to meet the ALARA requirement.

Soil is found to contain radium-226 (l = 0.000247/yr) residual radioactivity to a depth of 15 cm. The licensee estimates that the cost of removing the soil (F = 1) will be $100/m². For soil, the generic parameters are: P_D = 0.0004 person/m², r = 0.03/yr, and N = 1000 yr. Using these values in Equation 14 gives:

	(19)
	(20)

Thus, meeting the dose limit would be limiting by a considerable margin. It would rarely be necessary to ship soil to a waste disposal facility to meet the ALARA requirement.

The advantage of this approach, aside from its simplicity, is that it allows the user to know the ALARA target level prior to starting remediation and prior to planning the final status survey. Thus, it is a powerful planning tool letting the user know where he will need to go early in the planning process.

1. U. S. NUCLEAR REGULATORY COMMISSION, "Radiological Criteria for License Termination; Final Rule," 62 Federal Register 39058 (July 21, 1997).
2. W. J. CLINTON, President of the United States, Executive Order 12866, "Regulatory Planning and Review," (1993).
3. OFFICE OF MANAGEMENT AND BUDGET, "Economic Analysis of Federal Regulations under Executive Order 12866 (January 11, 1996). (Available on the web at http://www1.whitehouse.gov/WH/EOP/OMB/html/miscdoc/riaguide.html).
4. U. S. NUCLEAR REGULATORY COMMISSION, Regulatory Guide, "Demonstrating Compliance with the Radiological Criteria for License Termination," (to be published in 1998). (Working drafts of this document may be viewed on the web at http://techconf.llnl.gov/cgi-bin/topics).
5. U. S. NUCLEAR REGULATORY COMMISSION, "Regulatory Analysis Guidelines of the U. S. Nuclear Regulatory Commission," NUREG/BR-0058, Revision 2 (1995).
6. U. S. NUCLEAR REGULATORY COMMISSION,"Generic Environmental Impact Statement in Support of Rulemaking on Radiological Criteria for License Termination of NRC-Licensed Nuclear Facilities," NUREG-1496 (1997).

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