A priori risk-informed approach to ensure the compliance with discharge limits for liquid radioactive effluent to be discharged from APR 1400

ABSTRACT

In order to develop a methodology to guarantee the conformance to operational discharge limits for liquid effluent from a NPP at an early stage of design, a risk-informed approach was proposed and its applicability was verified for APR 1400. Existing methodology to calculate risk-based detection limit for a single radionuclide was improved by incorporating a new model to derive more realistic pathway dose factors. A new simple expression was also proposed to adjust risk-based detection limits for multiple radionuclides mixture if necessary. In addition, a new procedure to warrant the compliance with discharge limits by controlling detection limits of only a few principal radionuclides was established in accordance with risk-informed concept. Through case studies for APR 1400 to be commissioned at a hypothetical site, it was shown that calculated pathway dose factors are more realistic for majority of radionuclides. It also turns out that neither present detection limits nor unadjusted risk-based detection limits can be justified when the radionuclide composition is unknown, however further adjustment of detection limits or increasing additional dilution factor resolves the problem. Finally, ten principal radionuclides were identified and shown to be enough for liquid effluent control at APR 1400 from a risk-informed point of view.

KEYWORDS:

• Radioactive waste
• dispersion
• radionuclide
• risk-based
• risk-informed
• discharge limit
• detection limit
• liquid radioactive discharge
• effluent
• APR 1400

1. Introduction

The radioactivity in gaseous and liquid effluents released from nuclear power plants (NPPs) should be controlled under the so-called ‘discharge limits’ usually expressed in terms of discharge rate (in Bq/y), radioactivity concentration (in Bq/m³), and/or radiation dose to the critical group (in mSv/y) [1]. In order to assure that the discharge limits are satisfied with high confidence, the operator of NPPs should apply the radioactivity measurement method of sufficiently high sensitivity (i.e. low-enough detection limit) in quantifying the radioactivity released to the environment. Conventionally, the detection limits have been prescriptively specified in regulatory documents or standards in many countries as shown in Table 1 [2–5].

Table 1. Detection limits of selected radionuclides for liquid effluent from nuclear power plants in Germany, Japan, Korea, and the United State

	Required detection limits (Bq/m^3)
Radionuclides	Germany [2]	Japan [3]	Korea [4]	United States [5]
^3H	4 × 10^4	2 × 10^5	3.70 × 10^5	3.70 × 10^5 (1 × 10^−5 μCi/ml)
^55Fe	2 × 10^3	*	*	3.70 × 10^4 (1 × 10^−6 μCi/ml)
^63Ni	2 × 10^3	*	*	*
^60Co	1 × 10^3	2 × 10^4	1.85 × 10^4	1.85 × 10^4 (5 × 10^−7 μCi/ml)
^90Sr	5 × 10^2	7 × 10^2	1.85 × 10^3	1.85 × 10^3 (5 × 10^−8 μCi/ml)
^131I	1 × 10^3	2 × 10^4	3.70 × 10^4	3.70 × 10^4 (1 × 10^−6 μCi/ml)
^137Cs	1 × 10^3	2 × 10^4	1.85 × 10^4	1.85 × 10^4 (5 × 10^−7 μCi/ml)
Gross alpha	5 × 10^1 (as ^241Am)	4 × 10^3	3.70 × 10^3	3.70 × 10^3 (1 × 10^−7 μCi/ml)
Gross beta	*	4 × 10^4	*	*

*: Not specified

More flexible approaches to derive case-specific detection limits based upon potential risk have been reported since the late 2000s. In 2007, Sejkora pointed out the loose basis of the requirements for detection limits in the Offsite Dose Calculation Manual (ODCM), and proposed a general concept to derive dose-based detection limits (in pCi/L) for liquid effluent to yield annual total body dose and maximum organ dose of 1 mrem/y through drinking water and combined multiple exposure pathways, respectively [6]. However, the study was not extended to derivation of the ‘risk-based’ detection limits for a specific NPP or as per the requirements of effluent concentration limits. Traditionally, the United States Nuclear Regulatory Commission (USNRC) had requested NPP operators to apply detection limits prescribed in NUREG-1301, but changed its regulatory position in 2009 by allowing the operators to derive and adopt ‘risk-informed’ detection limits by considering site conditions as an alternative option [5,7]. However, the USNRC did not specify any practical methodology to derive the site-specific detection limits in Regulatory Guide 1.21, Revision 2. Lately, Cheong developed a methodology to derive the risk-based detection limits for liquid effluent appropriate to show the compliance with a set of discharge limits (i.e. activity concentration, effective dose, and maximum organ dose) by use of site-specific information such as dilution conditions and radioactivity actually released from three different Korean NPPs in operation [8].

Calculation of the risk-based detection limits may be useful not only for an operating NPP but for a NPP in design phase. In the design control document (DCD) for a NPP subject to the USNRC’s design certification, it is usually addressed that a series of site-specific information such as dilution or discharge flow rate is provided and the radiation dose to members of the public will be calculated later by the combined license (COL) applicant [9,10]. If the risk-based detection limits for a NPP design is estimated in advance, however, the information can be used to determine the sufficiency of dilution conditions of the proposed candidate site at which the NPP will be constructed and operated, and to optimize the design of radioactive effluent discharge system in order to conform to the requirements of detection limits. Nevertheless, no specific studies on the risk-based or risk-informed approach to establish detection limits for a NPP in design phase and its implications have been reported so far.

Thus, this study aims at establishing a practical approach to guarantee, a priori, the compliance with applicable discharge limits for a NPP to be commissioned at a proposed construction site with enough confidence. In order to attain the goal, a new methodology to derive risk-based detection limits for liquid radioactive effluent to be released from a reference NPP design in advance will be developed. In addition, a set of risk-informed approach to ensure the compliance with discharge limits for liquid radioactive discharges from a reference NPP design will be proposed as well.

2. Methodology

In this study, the Korean next-generation Advanced Power Reactor 1400 (APR 1400) designed by Korea Electric Power Corporation (KEPCO) and Korea Hydro & Nuclear Power Co., Ltd. (KHNP) was selected as a reference NPP design to be investigated [10]. Design certification of APR 1400 standard design was applied to the USNRC in December 2014 and it is now under licensing review process as per the USNRC’s regulations 10 CFR Part 52 as of May 2018 [11,12]. Therefore, it was assumed that a unit of APR 1400 will be constructed and operated after design certification at a hypothetical site in the United States. In this regard, the USNRC’s regulations for liquid radioactive effluent control was assumed to be fully applied to APR 1400. The basic methodology used in this study to derive the risk-based detection limits is adopted from the previous study unless otherwise specified [8].

2.1. Calculation of radioactivity concentration at unrestricted area boundary

The design basis concentration of radionuclide i ($C_{D,i}$ in Bq/m³) in the liquid effluent from APR 1400 at the unrestricted area boundary (UAB or discharge point) can be calculated by the following equation [10(10) $PD{F}_{TB,i}\cdot Q_{E,i}>(0.01)\cdot (0.03mSv/y)$(10) ]:

(1) $C_{D,i}=\frac{Q_{D,i}}{f_W+f_D}=\frac{C_{D0,i}\cdot f_W}{F}$(1)

where $Q_{D,i}$ is the design basis annual release of nuclide i (Bq/y), $C_{D0,i}$ is the design basis radioactivity concentration of nuclide i in the liquid discharge tank (Bq/m³), $f_W$ is average discharge rate of liquid waste from discharge tank (m³/y), $f_D$ is the average flow rate of dilution water provided by cooling tower blowdown, dilution pump, or other plant discharges at the discharge point (m³/y), and F is the liquid effluent flow rate at the UAB prior to additional dilution with receiving water body (m³/y).

The annual average concentrations of radionuclides in liquid effluent at the UAB should not exceed the effluent concentration limits (ECLs) specified in Table 2 of Appendix B to 10 CFR Part 20 [13]. Therefore, the following conditions should be met at the UAB both for each radionuclide and for multiple radionuclides present in the liquid effluent:

Table 2. Parameters used for offsite dose calculation in Equation (3)(3) $R_{a,p,j}=U_{a,p}\cdot \sum _{i=1}^N(C_{p,i}\cdot D_{a,p,i,j})$(3)

	Dimension of parameter for each pathway
Parameter	Food ingestion	Drinking water ingestion	Shoreline exposure	Remark
$U_{a,p}$	kg/y	L/y	h/y	Usage factor for age group a and pathway p
$C_{p,i}$	Bq/kg	Bq/L	Bq/m^2	Radioactivity concentration of nuclide i for pathway p
$D_{a,p,i,j}$	Sv/Bq	Sv/Bq	$\frac{Sv/h}{Bq/m^2}$	Dose factor for nuclide i for age group a, pathway p and organ j

(2) $C_{D,i}\le EC{L}_i\mathrm{a}\mathrm{n}\mathrm{d}\sum _{i=1}^N\frac{C_{D,i}}{EC{L}_i}\le 1$(2)

where $EC{L}_i$ is the effluent concentration limit of radionuclide i specified in Appendix B to 10 CFR Part 20 (Bq/m³).

2.2. Calculation of offsite dose at unrestricted area boundary

Offsite dose received by individuals as a result of radioactive liquid release from APR 1400 were calculated using LADTAP II code in the DCD of APR 1400 [10,14]. In this study, however, the offsite dose incurred by radionuclides in liquid effluent was calculated in accordance with the methodology and model given in the Regulatory Guide 1.109 in order to fully conform to the USNRC’s regulatory position [15]. Thus, the generalized form of equations to calculate the offsite dose can be written as following:

(3) $R_{a,p,j}=U_{a,p}\cdot \sum _{i=1}^N(C_{p,i}\cdot D_{a,p,i,j})$(3)

where $R_{a,p,j}$ is the radiation dose (i.e. total body dose or organ dose) for age group a, pathway p and organ j (mSv/y), and the other parameters in Equation (3)(3) $R_{a,p,j}=U_{a,p}\cdot \sum _{i=1}^N(C_{p,i}\cdot D_{a,p,i,j})$(3) are summarized in Table 2.

$C_{p,i}$ can be calculated from anticipated liquid effluent source-term (in Bq/y) and additional parameters representing dilution and transport of radionuclide in the environmental media. For instance, the concentration of radionuclide i in the drinking water is given as [15]:

$C_{p,i}=\frac{Q_{E,i}\cdot {\mathrm{e}}^{-{\lambda }_i\cdot t_p}}{F\cdot DF}$

where $Q_{E,i}$ is the anticipated annual discharge of nuclide i in liquid effluent (Bq/y), ${\lambda }_i$ is the decay constant of nuclide i (s⁻¹), $t_p$ is the average transit time required for nuclide to reach the point of exposure (s), and DF is the additional dilution factor that dilute the effluent flow rate by the flow rate of the receiving water body (no dimension).

In accordance with the USNRC’s Regulatory Guide 1.109, radiation exposure to the maximally exposed individual was calculated for four different age groups a (i.e. Adult, teen, child, and infant) and five exposure pathways p (i.e. aquatic food ingestion, irrigated vegetation ingestion, animal product ingestion, drinking water ingestion, and shoreline exposure). Organs such as bone, liver, thyroid, kidney, lung, and lower large intestine of gastrointestinal tract (GI-LLI) were considered in the dose calculation. The liquid effluent is assumed to be discharged to freshwater (i.e. river or lake) as per the DCD of ARP1400 [10].

2.3. Calculation of risk-based detection limits

2.3.1. Risk-based detection limit for a single radionuclide

In order to keep the radioactivity concentration at the UAB below the ECL, sensitive enough radioactivity measurement should be conducted for the sample taken from a liquid discharge tank. Therefore, a detection limit for radionuclide i in the discharge tank can be derived by combining Equations (1)(1) $C_{D,i}=\frac{Q_{D,i}}{f_W+f_D}=\frac{C_{D0,i}\cdot f_W}{F}$(1) and (2(2) $C_{D,i}\le EC{L}_i\mathrm{a}\mathrm{n}\mathrm{d}\sum _{i=1}^N\frac{C_{D,i}}{EC{L}_i}\le 1$(2) ) as:

(4) $D{L}_{ECL,i}\le s\cdot \left(\frac{F}{f_W}\right)EC{L}_i$(4)

where $D{L}_{ECL,i}$ is the ECL-based detection limit for radionuclide i based on radioactivity concentration at the UAB (Bq/m³), and s is the safety factor set to ensure the compliance with the requirement for detection limits [8].

In addition, radiation dose-based detection limits should be also considered so as to control the offsite dose from liquid effluent for any individual in an unrestricted area from all pathways below applicable dose constraints (i.e. 0.03 mSv/y to the total body and 0.10 mSv/y to any organ) as specified in Appendix I to 10 CFR Part 50 [16]. The dose-based detection limits for radionuclide i in the discharge tank derived in the previous study can be rewritten as [8]:

(5) $D{L}_{TB,i}\le \left(\frac{s}{f_W}\right)\cdot \left(\frac{D{C}_{TB}}{PD{F}_{TB,i}}\right)$(5)

(6) $D{L}_{OG,i}\le \left(\frac{s}{f_W}\right)\cdot \left(\frac{D{C}_{OG}}{PD{F}_{OG,i}}\right)$(6)

where $D{L}_{TB,i}$ and $D{L}_{OG,i}$ are the dose-based detection limits (Bq/m³) for radionuclide i based on constraints for total body dose and organ dose, respectively; $D{C}_{TB}$ and $D{C}_{OG}$ are the dose constraints to total body (0.03 mSv/y) and to any organ (0.10 mSv/y), respectively; $PD{F}_{TB,i}$ and $PD{F}_{OG,i}$ are the pathway dose factors (mSv/y per Bq/y) of radionuclide i for total body dose and maximum organ dose, respectively.

In this study, two expressions to calculate pathway dose factors (PDFs) for APR 1400 were newly proposed as shown in Column 3 of Table 3.

Table 3. Comparison of equations to calculate pathway dose factors in this study and in the previous study [8]

Pathway Dose Factor	Previous study [8]	This study
$PD{F}_{TB,i}$	$\mathrm{m}\mathrm{a}\mathrm{x}\left(\frac{D_{TB,i}}{Q_{E,i}}\right)$	$\mathrm{m}\mathrm{a}\mathrm{x}\left(\frac{D_{TB,i,a_{max}}}{Q_{E,i}}\right)$
$PD{F}_{OG,i}$	$\mathrm{m}\mathrm{a}\mathrm{x}\left(\frac{D_{OG,i}}{Q_{E,i}}\right)$	$\mathrm{m}\mathrm{a}\mathrm{x}\left(\frac{D_{OG,i,a_{max},j_{max}}}{Q_{E,i}}\right)$

* Subscript i is the identification number for radionuclide i, a is the number for age group (a = 1 for infant, 2 for child, 3 for teen, and 4 for adult), and j is the number for organ (j = 1 for bone, 2 for liver, 3 for thyroid, 4 for kidney, 5 for lung, and 6 for GI-LLI).

In Table 3, $D_{TB,i}$ and $D_{OG,i}$ are annual radiation doses to total body and any organ (mSv/y), respectively, calculated by the USNRC’s Regulatory Guide 1.109 methodology due to $Q_{E,i}$ (Bq/y) whose value is given in the DCD of APR 1400 [10,15]. In calculation of $PD{F}_{TB,i}$, $a_{max}$ is the identification (ID) number for the age group which receives the maximum total body dose. That is,$a_{max}$ is the value of a which maximizes the value of $\sum _{i=1}{D}_{TB,i,a}$. On the other hand, $a_{max}$ and $j_{max}$ are defined as ID number for the age group and ID number for the organ which show the maximum organ dose, respectively, in calculation of $PD{F}_{OG,i}$. In other words, $a_{max}$ and $j_{max}$ are the values of a and j which maximize the value of $\sum _{i=1}{D}_{OD,ia,j}$.

Table 3 also compares the methodologies to calculate $PD{F}_{TB,i}$ and $PD{F}_{OG,i}$ in this study and those proposed in the previous study [8]. The compliance with the design objectives (i.e dose constraints) specified in Appendix I to 10 CFR Part 50 is applied to the total body dose for a specific age group receiving the highest total body dose, and to the organ dose for a specific age group and a specific organ which represent the maximum organ dose. Accordingly, the expressions in Column 2 of Table 3 which do not consider any specific age group and organ tend to overestimate the PDFs. Compared with the previous study, more realistic PDF values can be derived due to the practically modified equations proposed in this study as shown in Column 3 of Table 3.

If only one radionuclide is present in the liquid effluent, the risk-based detection limit for nuclide i (Bq/m³) is determined to be the minimum of the detection limits in Equations (4)(4) $D{L}_{ECL,i}\le s\cdot \left(\frac{F}{f_W}\right)EC{L}_i$(4) to (6) as proposed in the previous study [8]:

(7) $D{L}_{Risk,i}=min\left(D{L}_{ECL,i},D{L}_{TB,i},D{L}_{OG,i}\right)$(7)

2.3.2. Risk-based detection limit for multiple radionuclides mixture

Feasibility of the risk-based detection limits derived by Equation (7)(7) $D{L}_{Risk,i}=min\left(D{L}_{ECL,i},D{L}_{TB,i},D{L}_{OG,i}\right)$(7) for a liquid effluent in which more than one radionuclides coexist can be verified by applying all three inequality equations proposed in the previous study are rewritten and shown in Table 4 [8]:

Table 4. Equations to determine the feasibility of risk-based detection limits for radionuclides mixture present in liquid effluent [8]

When nuclide composition is available		When nuclide composition is not available
$\left(\frac{f_w}{F}\right)\cdot \sum _i^N\left(\frac{D{L}_{Risk,k}\cdot \left({\alpha }_i/{\alpha }_k\right)}{EC{L}_i}\right)\le S$	(12)	$\left(\frac{f_w}{F}\right)\cdot \sum _i^N\left(\frac{D{L}_{Risk,i}}{EC{L}_i}\right)\le S$	(15)
$\left(\frac{f_w}{D{C}_{TB}}\right)\cdot \sum _i^N\left(PD{F}_{TB,i}\cdot D{L}_{Risk,k}\cdot \left({\alpha }_i/{\alpha }_k\right)\right)\le S$	(13)	$\left(\frac{f_w}{D{C}_{TB}}\right)\cdot \sum _i^N\left(PD{F}_{TB,i}\cdot D{L}_{Risk,i}\right)\le S$	(16)
$\left(\frac{f_w}{D{C}_{OG}}\right)\cdot \sum _i^N\left(PD{F}_{OG,i}\cdot D{L}_{Risk,k}\cdot \left({\alpha }_i/{\alpha }_k\right)\right)\le S$	(14)	$\left(\frac{f_w}{D{C}_{OG}}\right)\cdot \sum _i^N\left(PD{F}_{OG,i}\cdot D{L}_{Risk,i}\right)\le S$	(17)

* S is the safety factor given for ensuring the compliance with the requirement of detection limits for radionuclide mixture; N is the total number of radionuclides in the mixture; α_i is the activity fraction of radionuclide i in the mixture; k is the radionuclide showing the maximum ratio of ${\alpha }_i/D{L}_{Risk,i}$.

Though equations in Table 4 were originally derived to test whether $D{L}_{Risk,i}$ calculated from Equation (7)(7) $D{L}_{Risk,i}=min\left(D{L}_{ECL,i},D{L}_{TB,i},D{L}_{OG,i}\right)$(7) can be applied to the radionuclides mixture, they may be used to determine the compliance with discharge limits can be warranted with a specific detection limit which has been adopted at an operating NPP site as well. If all three inequality equations in Table 4 are satisfied at the same time, $D{L}_{Risk,i}$ from Equation (7)(7) $D{L}_{Risk,i}=min\left(D{L}_{ECL,i},D{L}_{TB,i},D{L}_{OG,i}\right)$(7) can be ultimately regarded as the risk-based detection limit for radionuclide i coexisting with other radionuclide(s) in a liquid effluent.

2.3.3. Methodology to adjust risk-based detection limit for multiple radionuclides mixture

When equations in Table 4 are not satisfied simultaneously, $D{L}_{Risk,i}$ calculated from Equation (7)(7) $D{L}_{Risk,i}=min\left(D{L}_{ECL,i},D{L}_{TB,i},D{L}_{OG,i}\right)$(7) should be adjusted. That is, the risk-based detection limit for radionuclide i present in a multiple radionuclides mixture should be obtained by multiplying an adjustment factor which is a single value commonly applicable for all radionuclides in the mixture to the $D{L}_{Risk,i}$.

Table 5 compares the complex form of adjustment factor proposed in the previous study and much simpler form of adjustment factor newly suggested in this study.

Table 5. Comparison of equations to calculate adjustment factors proposed in this study and in the previous study [8]

Previous study [8]	$\frac{S}{max\left[\left(\frac{f_w}{F}\right)\cdot \sum _i^N\left(\frac{D{L}_{Risk,i}}{EC{L}_i}\right),\left(\frac{f_w}{D{C}_{TB}}\right)\cdot \sum _i^N\left(D{L}_{Risk,i}\cdot PD{F}_{TB,i}\right),\left(\frac{f_w}{D{C}_{OG}}\right)\cdot \sum _i^N\left(D{L}_{Risk,i}\cdot PD{F}_{OG,i}\right)\right]}$
This study	$\left(\frac{S/s}{N}\right)$

The simple form of adjustment factor proposed in this study (i.e. $\left(S/s\right)/N$) has an advantage over the previously proposed adjustment factor in that it can be also used to increase the detection limit when $\mathrm{N}<\left(S/s\right)$ irrespective of whether equations in Table 4 are satisfied simultaneously or not. For instance, if the liquid effluent with s = 1%, S = 10%, and N = 50 does not satisfy equations in Table 4 at the same time, the adjusted detection limit is decreased to $D{L}_{Risk,i}$ multiplied by $\left(0.1/0.01\right)/50$ or 0.2. On the other hand, however, the adjusted detection limit for the liquid effluent with s = 1%, S = 10% but N = 5 can be further increased to $D{L}_{Risk,i}$ multiplied by $\left(0.1/0.01\right)/5$ or 2 even if equations in Table 4 are met simultaneously.

2.3.4. Risk-informed detection limits as per USNRC’s Regulatory Guide 1.21, Revision 2

The above risk-based approach to derive and adjust detection limit for each radionuclide may be impractical to apply when various radionuclides are detected in the liquid effluent. In the case of liquid effluent from APR 1400 in which forty-seven different radionuclides are to be present, demonstration of the compliance with the risk-based detection limit for each radionuclide would be costly and time consuming. Furthermore, separate control of detection sensitivities for various gamma emitters, which are to be simultaneously quantified by a gamma spectroscopy under the same measurement conditions, may not be practical.

Therefore, a systematic approach to derive site-specific risk-informed detection limits in accordance with USNRC’s regulatory position addressed in Regulatory Guide 1.21, Revision 2 was newly developed and proposed in this study. First, radionuclides satisfying any one of the following conditions are selected as ‘principal radionuclides’ in a risk-informed context:

(8) $({\alpha }_i{)}_G>0.01$(8)

(9) $({\alpha }_i{)}_{NG}>0.01$(9)

(10) $PD{F}_{TB,i}\cdot Q_{E,i}>(0.01)\cdot (0.03mSv/y)$(10)

(11) $PD{F}_{OG,i}\cdot Q_{E,i}>(0.01)\cdot (0.1mSv/y)$(11)

where $({\alpha }_i{)}_G$ is the ratio of gamma emitting radionuclide i to the total gamma activity concentration in the liquid effluent, $({\alpha }_i{)}_{NG}$ is the ratio of nongamma emitting radionuclide i to the total nongamma activity concentration in the liquid effluent, and 0.03 mSv/y and 0.1 mSv/y are dose constraints to total body and to any organ, respectively.

Since the regulatory position of the USNRC addressed in Regulatory Guide 1.21, Revision 2 implicitly assumes that the radionuclide composition in the effluent is known, the risk-informed detection limit for each ‘principal radionuclide’ can be also calculated by Equation (7)(7) $D{L}_{Risk,i}=min\left(D{L}_{ECL,i},D{L}_{TB,i},D{L}_{OG,i}\right)$(7) and its feasibility can be verified by the equations in Column 1 of Table 4. If all equations in Column 1 of Table 4 are met, the risk-informed detection limits for principal radionuclides can be practically applied to the NPP. Otherwise, the risk-based detection limits for all forty-seven radionuclides should be considered, since the risk-informed approach controlling only principal radionuclides may not be justified for the plant.

Overall procedure for risk-informed approach as per USNRC’s Regulatory Guide 1.21, Revision 2 to apply detection limits for the liquid effluent from APR 1400 were established in this study as depicted in Figure 1.

Figure 1. Procedure for risk-informed approach to establish detection limits for liquid effluent from APR 1400 in accordance with USNRC’s Regulatory Guide 1.21, Revision 2.

3. Results and discussion

3.1. Comparison of calculation results in this study with DCD of APR 1400

In order to confirm that a set of calculation methods adopted in this study can give reasonable results, some of the calculation results were compared to those addressed in the DCD of APR 1400. At first, the sum of fractions in Equation (2)(2) $C_{D,i}\le EC{L}_i\mathrm{a}\mathrm{n}\mathrm{d}\sum _{i=1}^N\frac{C_{D,i}}{EC{L}_i}\le 1$(2) was calculated by using Equation (1)(1) $C_{D,i}=\frac{Q_{D,i}}{f_W+f_D}=\frac{C_{D0,i}\cdot f_W}{F}$(1) and specific values of the parameters for APR 1400 such as $f_W$ (341 L/min or 1.79 × 10⁵ m³/y), $F$ (37,854 L/min or 1.99 × 10⁷ m³/y) to be supplied by cooling tower blowdown, dilution pump, or other plant discharges at the discharge point, and $Q_{D,i}$ given for each radionuclide, as shown in Section 11.2 of the DCD of APR 1400 [10].

The fraction of $C_{D,i}$ to $EC{L}_i$ shows the maximum of 0.0803 for ¹³⁷Cs, and the sum of all fractions is 0.1798. The results are the same with those given in Table 11.2–10 of the DCD of APR 1400 up to two decimal places in the significant figures. It is noted that totally fifty-one radionuclides are considered in the DCD of APR 1400. In this study, however, forty-seven radionuclides were counted in the following calculations by excluding very short-lived radionuclides such as ^103mRu, ¹⁰⁶Rh, ¹¹⁰Ag, and ^137mBa of which half-lives are 56.11 min, 29.8 sec, 24.6 sec, and 2.5 min, respectively.

In addition, the offsite public dose (i.e. total body dose and maximum organ dose) to be incurred by radionuclides in liquid effluent from APR 1400 were calculated by Equation (3)(3) $R_{a,p,j}=U_{a,p}\cdot \sum _{i=1}^N(C_{p,i}\cdot D_{a,p,i,j})$(3) and Table 2. The values of parameters such as radionuclide-specific anticipated source-terms, irrigation rate (41.68 L/(m²-month)), fraction of animal feed in contaminated ground (i.e. 1), and midpoint of plant life (i.e. 30 y) given in the DCD of ARP-1400 were directly used for the calculation [10]. The other parameters not specified in the DCD of ARP-1400 were assumed to be the same with the default values given in Regulatory Guide 1.109, Revision 1 [15].

The total body dose calculated for four age groups (i.e. adult, teenager, child, and infant) are 0.0275, 0.022, 0.0281, and 0.00859 mSv/y, respectively. Table 6 shows the total body dose to the child, which is to receive the maximum total body dose, for each exposure pathway and for each radionuclide. For simplification, only ten radionuclides showing the top ten highest total body dose are listed in order of magnitude.

Table 6. Calculated total body dose to child per each exposure pathway for liquid effluent from APR 1400

		Pathway-specific dose to the age group ‘child’ (mSv/y)
Nuclide		Potable water	Aquatic food	Irrigated vegetation	Animal product	Shoreline exposure	Total body
^3H		8.67 × 10^−3	1.06 × 10^−4	9.28 × 10^−3	6.31 × 10^−3	0.00	2.44 × 10^−2
^134Cs		4.56 × 10^−5	1.23 × 10^−3	1.54 × 10^−4	1.53 × 10^−4	2.79 × 10^−6	1.59 × 10^−3
^137Cs		3.78 × 10^−5	1.02 × 10^−3	1.48 × 10^−4	1.02 × 10^−5	1.03 × 10^−5	1.23 × 10^−3
^32P		2.86 × 10^−7	3.78 × 10^−4	5.60 × 10^−8	8.19 × 10^−8	0.00	3.78 × 10^−4
^136Cs		8.11 × 10^−6	2.14 × 10^−4	1.25 × 10^−6	4.04 × 10^−6	2.15 × 10^−8	2.27 × 10^−4
^106Ru		5.31 × 10^−6	7.18 × 10^−7	1.71 × 10^−5	7.76 × 10^−5	1.10 × 10^−6	1.02 × 10^−4
^60Co		1.12 × 10^−5	7.56 × 10^−6	4.01 × 10^−5	2.64 × 10^−5	1.26 × 10^−5	9.79 × 10^−5
^63Ni		1.59 × 10^−6	2.16 × 10^−6	7.09 × 10^−6	2.35 × 10^−5	0.00	3.43 × 10^−5
^90Sr		4.86 × 10^−6	1.97 × 10^−6	2.03 × 10^−5	1.33 × 10^−6	0.00	2.84 × 10^−5
^65Zn		4.08 × 10^−7	1.10 × 10^−5	1.41 × 10^−6	4.47 × 10^−7	9.63 × 10^−9	1.33 × 10^−5
Sum of other nuclides		7.43 × 10^−6	8.83 × 10^−6	1.05 × 10^−5	2.89 × 10^−6	7.14 × 10^−7	3.04 × 10^−5
SUM	This study	8.79 × 10^−3	2.99 × 10^−3	9.67 × 10^−3	6.60 × 10^−3	2.76 × 10^−5	2.81 × 10^−2
	LADTAP II	8.78 × 10^−3	2.99 × 10^−3	9.68 × 10^−3	6.72 × 10^−3	2.76 × 10^−5	2.82 × 10^−2
	APR 1400 DCD	8.80 × 10^−3	2.99 × 10^−3	9.44 × 10^−3	6.39 × 10^−3	2.12 × 10^−5	2.76 × 10^−2
Relative error (%)		0.126	0.103	2.45	3.31	30.8	1.73

In addition, the results calculated by Equation (3)(3) $R_{a,p,j}=U_{a,p}\cdot \sum _{i=1}^N(C_{p,i}\cdot D_{a,p,i,j})$(3) in this study are compared with the total body dose to child addressed in the DCD of APR 1400 which were calculated by using LADTAP II computer code [14]. The pathway doses calculated in this study are comparable to the values given in the DCD of APR 1400 with a maximum relative error of 30.8%. In order to verify the results further, the pathway doses were independently calculated by LADTAP II computer code in this study using the same input parameters. It turns out that LADTAP II computer code gives rise to pathway doses closer to the results of this study rather than the values in the DCD of APR 1400. The small differences in pathway doses from three different approaches can be ascribed to the fact that not all of input parameter values are listed in the DCD of APR 1400, and some values assumed in this study might be different from those actually used for calculation in the DCD of APR 1400. Furthermore, the discrepancy of ingestion dose coefficient for ⁹⁰Sr in Regulatory Guide 1.109 (0.00431 mrem/pCi or 0.00116 mSv/Bq) and LADTAP II (0.000515 mrem/pCi or 0.000139 mSv/Bq) is to contribute to the differences in calculated total body doses [14,15].

However, more detailed direct comparison of nuclide-specific pathway doses is not possible, since the DCD of APR 1400 shows only the total value (i.e. sum of pathway doses for all radionuclides) rather than listing nuclide-specific pathway doses. In addition, the calculated total body dose (i.e. 0.0222–0.0281 mSv/y) for APR 1400 meets the design objective of total body dose at the UAB (i.e. 0.03 mSv/y) as per Appendix I to 10 CFR Part 50.

As shown in Table 7, organ dose to GI-LLI of adult was calculated to be 0.0455 mSv/y, which shows the maximum among organ doses to the other age groups; that is, 0.0369, 0.0412, and 0.0099 mSv/y for teenager, child, and infant, respectively.

Table 7. Organ-specific radiation dose to adult for each radionuclide for liquid effluent from APR 1400

		Organ-specific dose to the age group ‘adult’ (mSv/y)
Nuclide		Bone	Liver	Thyroid	Kidney	Lung	GI-LLI	Maximum
^106Ru		3.90 × 10^−4	0.00	0.00	7.53 × 10^−4	0.00	2.52 × 10^−2	2.52 × 10^−2
^3H		0.00	1.54 × 10^−2	1.54 × 10^−2	1.54 × 10^−2	1.54 × 10^−2	1.54 × 10^−2	1.54 × 10^−2
^95Nb		8.15 × 10^−7	4.53 × 10^−7	0.00	4.48 × 10^−7	0.00	2.75 × 10^−3	2.75 × 10^−3
^32P		6.98 × 10^−3	4.34 × 10^−4	0.00	0.00	0.00	7.85 × 10^−4	7.85 × 10^−4
^60Co		0.00	1.59 × 10^−5	0.00	0.00	0.00	2.99 × 10^−4	2.99 × 10^−4
^144Ce		7.87 × 10^−7	3.29 × 10^−7	0.00	1.95 × 10^−7	0.00	2.66 × 10^−4	2.66 × 10^−4
^137Cs		5.79 × 10^−3	7.91 × 10^−3	0.00	2.69 × 10^−3	8.93 × 10^−4	1.53 × 10^−4	1.53 × 10^−4
^134Cs		3.18 × 10^−3	7.56 × 10^−3	0.00	2.45 × 10^−3	8.12 × 10^−4	1.32 × 10^−4	1.32 × 10^−4
^110mAg		2.94 × 10^−7	2.72 × 10^−7	0.00	5.36 × 10^−7	0.00	1.11 × 10^−4	1.11 × 10^−4
^54Mn		0.00	2.44 × 10^−5	0.00	7.25 × 10^−6	0.00	7.47 × 10^−5	7.47 × 10^−5
Sum of other nuclides		5.47 × 10^−4	4.84 × 10^−4	8.19 × 10^−4	2.60 × 10^−4	4.00 × 10^−5	3.11 × 10^−4	3.11 × 10^−4
SUM	This study	1.69 × 10^−2	3.18 × 10^−2	1.62 × 10^−2	2.15 × 10^−2	1.71 × 10^−2	4.55 × 10^−2	4.55 × 10^−2
	LADTAP II	1.70 × 10^−2	3.22 × 10^−2	1.64 × 10^−2	2.17 × 10^−2	1.72 × 10^−2	4.76 × 10^−2	4.76 × 10^−2
	APR 1400 DCD	1.64 × 10^−2	3.15 × 10^−2	1.61 × 10^−2	2.10 × 10^−2	1.70 × 10^−2	3.32 × 10^−2	3.32 × 10^−2
Relative error (%)		2.95	1.01	0.640	2.57	0.762	37.1	37.1

The organ doses calculated by Regulatory Guide 1.109 model in this study turn out to be comparable with the values given in the DCD of APR 1400 within a maximum relative error of 37.1% in organ dose to GI-LLI. However, the organ dose to GI-LLI separately calculated by LADTAP II computer code show 0.0476 mSv/y, which is closer to the result of this study (0.0455 mSv/y) rather than the value in the DCD of APR 1400 (0.0332 mSv/y), which implies that non-negligible difference of the GI-LLI dose in this study from the DCD of APR 1400 can be attributed to the fact that some input parameters used in this study would be not the same with the values actually used for calculation in the DCD of APR 1400 but not listed therein. In addition, the calculated maximum organ dose (i.e. 0.0369–0.0455 mSv/y) for APR 1400 meets the design objective of maximum organ dose at the UAB (i.e. 0.1 mSv/y) set forth in Appendix I to 10 CFR Part 50.

As discussed above, it is concluded that the offsite dose calculation methods based upon Regulatory Guide 1.109 model and adopted in this study (see Equation (3)(3) $R_{a,p,j}=U_{a,p}\cdot \sum _{i=1}^N(C_{p,i}\cdot D_{a,p,i,j})$(3) and Table 2) can be used with enough credibility in the next step to derive risk-based detection limits.

3.2. Calculation of detection limits for APR 1400 using risk-based approach

3.2.1. Risk-based detection limit for a single radionuclide

As an initial step to derive the risk-based detection limits for liquid effluent from APR 1400, the values of $PD{F}_{TB,i}$ and $PD{F}_{OG,i}$ were calculated for forty-seven radionuclides using the new expressions in Column 3 of Table 3. In addition, the values of PDFs were calculated by use of the approach taken in the previous study as shown in Column 2 of Table 3. Figure 2 shows the PDFs for total body dose calculated by using the new expressions proposed in this study and the approach taken in the previous study.

Figure 2. Comparison of pathway dose factors to total body calculated using new expressions proposed in this study and in the previous study for liquid effluent from APR 1400.

It is noted that the PDF for ¹²⁴Sb is not plotted in Figure 2 because ¹²⁴Sb is not considered in Regulatory Guide 1.109 whose model was adopted to calculate the offsite dose in this study [15].

As already expected in Section 2.3.1, the new expressions for PDFs proposed in this study give rise to more realistic (lower) values than the PDFs derived by using the methods adopted in the previous study. Figure 2 shows that the calculated PDFs in this study to total body for forty-two out of totally forty-seven radionuclides (e.g. ¹⁴⁴Pr, ^91mY, ¹³¹Te, ⁹⁵Zr, ¹⁴⁰La, etc.) show lower than the values compared to the values from previous method. However, many of the points from the two methods may not be visually distinguished in the semi-log scale Figure 2 since the PDFs in this study lie between 95% and 100% of the PDFs calculated by the previous method for twenty-two radionuclides. The minimum ratio of the calculation results from the two methods is 0.209 for the radionuclide ¹⁴⁴Pr, which shows the most realistic result obtained in this study compared to the previous study.

Likewise, Figure 3 compares the PDFs for maximum organ dose calculated from the two different methods.

Figure 3. Comparison of pathway dose factors to maximum organ calculated using new expressions proposed in this study and in the previous study for liquid effluent from APR 1400.

As shown in Figure 3, the calculated PDFs in this study are equal to or lower than those derived by previous study’s method. In more specific, the calculated PDFs in this study to any organ for twenty-eight out of totally forty-seven radionuclides (e.g. ¹³¹I, ¹³²I, ¹³³I, ⁶³Ni, ¹²⁹Te, etc.) show lower than the values compared to previous method. The minimum ratio of the calculation results from the two methods is 0.000469 for the radionuclide ¹³¹I.

Detection limits for each radionuclide regarding radioactivity concentration, total body dose, and maximum organ dose were calculated from Equations (4)(4) $D{L}_{ECL,i}\le s\cdot \left(\frac{F}{f_W}\right)EC{L}_i$(4) to (6) by assuming the safety factor s is 1% (or 0.01) and the calculated PDFs shown in Figures 2 and 3. The calculation results are depicted in Figure 4.

Figure 4. Present detection limit and calculated risk-based detection limit for a single radionuclide with regard to radioactivity concentration, total body dose, and maximum organ dose for liquid effluent from APR 1400 (s = 1%). The smallest value for each radionuclide represents the risk-based detection limit ($D{L}_{Risk,i})$ calculated from Equation (7)(7) $D{L}_{Risk,i}=min\left(D{L}_{ECL,i},D{L}_{TB,i},D{L}_{OG,i}\right)$(7) .

In Equation (7)(7) $D{L}_{Risk,i}=min\left(D{L}_{ECL,i},D{L}_{TB,i},D{L}_{OG,i}\right)$(7) , $D{L}_{Risk,i}$ was determined by $D{L}_{ECL,i}$ for ten radionuclides (^91mY, ¹²⁴Sb, ¹²⁹Te, ¹³¹Te, ¹³¹I, ¹³²I, ¹³³I, ¹³⁴I,¹³⁵I, and ¹⁴⁴Pr), by $D{L}_{TB,i}$ for twelve radionuclides (³H, ²⁴Na, ³²P, ⁵⁵Fe, ⁶⁰Co, ⁶³Ni, ⁶⁵Zn, ⁸⁹Sr, ⁹⁰Sr, ¹³⁴Cs, ¹³⁶Cs, and ¹³⁷Cs), and by twenty-five radionuclides (⁵¹Cr, ⁵⁴Mn, ⁵⁹Fe, ⁵⁸Co, ⁹¹Sr, ⁹¹Y, ⁹³Y, ⁹⁵Zr, ⁹⁵Nb, ⁹⁹Mo, ^99mTc, ¹⁰³Ru, ¹⁰⁶Ru, ^110mAg, ^129mTe, ^131mTe, ¹³²Te, ¹⁴⁰Ba, ¹⁴⁰La, ¹⁴¹Ce, ¹⁴³Ce, ¹⁴⁴Ce, ¹⁴³Pr, ¹⁸⁷W, and ²³⁹Np) among totally forty-seven radionuclides considered in this study.

In addition, the present detection limit as per NUREG-1301 turns out to be sensitive enough for twenty-four out of forty-seven radionuclides. For the nongamma emitting radionuclides of which detection limits are not explicitly specified in NUREG-1301 (e.g. ³²P, ⁶³Ni, ¹⁰⁶Ru, and ²³⁹Np), the applicability of newly derived detection limits cannot be compared with current practice.

It may be of safety concern for nineteen radionuclides of which $D{L}_{Risk,i}$ is smaller than the present detection limit ($D{L}_{Present,i}$) like ⁹⁵Nb, ¹³⁴Cs, ¹³⁷Cs, and so forth. The ratio of $D{L}_{Risk,i}$ to $D{L}_{Present,i}$ lies between 0.00852 and 0.942 for those radionuclides, which implies that the present level of detection limit for the radionuclides may not be justified in the risk-based consideration.

Finally, Figure 4 implies the potential need for applying detection limits for ³²P and ¹⁰⁶Ru of which detection limits are not specified in the present USNRC’s regulatory report in spite of its significant contribution to the anticipated liquid effluent source term. As shown in Tables 6 and 7, it is also noted that the ranks of ³²P and ¹⁰⁶Ru are the fourth and the sixth, respectively, in contribution to the total body dose, and the first and the fourth, respectively, in contribution to the maximum organ dose for the liquid effluent from APR 1400. With regard to this issue, establishment of a detection limit requirement for gross beta activity as adopted in Japan may be considered instead of specifying detection limit for each non-gamma emitting radionuclide (see Table 1) [3].

Furthermore, the detection limit for each radionuclide using the PDFs in accordance with previous study were derived and then plotted in Figure 5 together with the PDF values calculated in this study.

Figure 5. Comparison of risk-based detection limits calculated using the new expressions proposed in this study and the previous study for the liquid effluent from APR 1400.

For twenty-three out of totally forty-seven radionuclides, the ratio of $D{L}_{Risk,i}$ calculated in this study to the value derived in accordance with previous study’s approach is higher than one, which implies that the new method in this study bring up with more practical (or realistic) results than the previous study. The most benefitted radionuclides in this aspect are ¹³¹I (94 times higher $D{L}_{Risk,i}$ than previous method), ¹³³I (79 times higher $D{L}_{Risk,i}$), ¹³⁵I (26 times higher), and so on.

3.2.2. Risk-based detection limits for multiple radionuclides mixture

The risk-based detection limit for a single radionuclide was calculated using Equation (7)(7) $D{L}_{Risk,i}=min\left(D{L}_{ECL,i},D{L}_{TB,i},D{L}_{OG,i}\right)$(7) together with the results shown in Figure 4 and s = 1%. Since it is expected that there exist forty-seven radionuclides in the liquid effluent to be discharged from APR 1400, each value of the left hand side (LHS) of Equations (12)–(14) and (15)–(17) was calculated and listed in Table 8 by assuming the safety factor S = 10%.

Table 8. Calculated values of LHSs in Equations (12)–(17) for risk-based detection limits and for present detection limits

	Calculated value of the LHS in each equation of
	(12)	(13)	(14)	(15)	(16)	(17)
Types of detection limits	When nuclide composition is available			When nuclide composition is not available
Risk-based detection limits	4.32 × 10^−4	1.41 × 10^−2	1.67 × 10^−3	1.15 × 10^−1	1.70 × 10^−1	2.90 × 10^−1
Present detection limits	2.19 × 10^−4	7.11 × 10^−3	8.46 × 10^−4	2.74 × 10^−1	1.06 × 10^+0	1.63 × 10^+0

* LHS: Left-hand side

$D{L}_{Risk,i}$ derived from Equation (7)(7) $D{L}_{Risk,i}=min\left(D{L}_{ECL,i},D{L}_{TB,i},D{L}_{OG,i}\right)$(7) can be directly applied to the mixture of radionuclides without any adjustment if the nuclide composition is available, since all values of LHSs in Equations (12)–(14) are calculated to be less than S = 0.1 as shown in Table 8. When the nuclide composition is not available, however, all three values of LHSs in Equations (15)–(17) exceed S = 0.1 and $D{L}_{Risk,i}$ from Equation (7)(7) $D{L}_{Risk,i}=min\left(D{L}_{ECL,i},D{L}_{TB,i},D{L}_{OG,i}\right)$(7) should be adjusted. Regarding this, the adjustment factor of 0.213 was calculated by the new simplified expression proposed in this study (refer to Row 2 in Table 5), which is more conservative (i.e. lower) than the adjustment factor of 0.345 derived using the method proposed in the previous study (refer to Row 1 in Table 5).

In order to compare the equations to calculate adjustment factor, two equations in Table 5 were plotted under the discharge and dilution conditions of liquid effluent at APR 1400 by increasing the total number of radionuclides (N) from one to forty-seven in order of atomic mass number of radionuclides as shown in Figure 6.

Figure 6. Comparison of adjustment factors calculated using two equations in Table 5 (i.e. a simple equation proposed in this study and more complex equation in the previous study [8]) for the liquid effluent from APR 1400 by increasing total number of radionuclides (N) from five to forty-seven.

As shown in Figure 6, the previous method always gives more practical (i.e. higher value of) adjustment factor than the simple adjustment factor equation proposed in this study does. However, the maximum relative difference of the adjustment factors resulting from two equations is about 44.8%. Therefore, the simple form of equation (Row 2 in Table 5) instead of relatively complex expression (Row 1 in Table 5) may be used to calculate adjustment factor, for screening purpose or when quick and simple adjustment calculation is needed.

On the other hand, Table 8 also shows the calculation results of LHSs in Equations (12) to (14) when the present detection limits in NUREG-1301 rather than the calculated risk-based detection limits are used. Four non-gamma emitters such as ³²P, ⁶³Ni, ¹⁰⁶Ru, and ²³⁹Np of which present detection limits are not given in NUREG-1301 were excluded in this calculation. When the nuclide composition is known, the present detection limits in NUREG-1301 can be used since the LHSs of Equations (12)–(14) are less than S = 0.1. If the present detection limits in NUREG-1301 is to be used for the mixture when the nuclide composition is not available, however, the present detection limits should be adjusted because the LHSs of Equations (15)–(17) are higher than S = 0.1. The adjustment factor calculated by the method proposed in the previous study (see Row 1 in Table 5) is 0.061, which may not be practicable to apply in the filed since the present detection limit for each radionuclide should be reduced to below 6.1%. It is noted that the simple method to calculate adjustment factor proposed in this study cannot be applied to the above case, since the present detection limits are not risk based (i.e. not dependent upon s).

3.3. Consideration of site-specific detection limits for APR 1400

For APR 1400, both the risk-based detection limit $D{L}_{Risk,i}$ derived from Equation (7)(7) $D{L}_{Risk,i}=min\left(D{L}_{ECL,i},D{L}_{TB,i},D{L}_{OG,i}\right)$(7) and the present detection limits in NUREG-1301 should be adjusted if the information on nuclide composition is not available as shown in Table 8. The DCD of APR 1400 conservatively assumes the ‘additional dilution factor’ for aquatic food, boating, shoreline, swimming, and drinking water pathways to be five (5) for normal operating conditions. In order to find out the condition at which the risk-based detection limits or the present detection limits in NUREG-1301 can be applied to APR 1400 without adjustment, the values of LHSs of Equations (15)–(17) were calculated by varying the additional dilution factor.

The LHSs of Equations (15)–(17) decrease whiling increasing the additional dilution factor, and all values of the LHSs become equal to or below the safety factor S = 0.1 when the additional dilution factor increases up to 14.5 for the risk-based detection limits from this study, and 81.1 for the present detection limits in NUREG-1301 (see Figures 7 and 8).

Figure 7. Calculated values of LHSs of Equations (15)–(17) using risk-based detection limits while varying additional dilution factor.

Figure 8. Calculated values of LHSs of Equations (15)–(17) using present detection limits [5] while varying additional dilution factor.

It was also found that the fresh water sites for thirty-two units out of forty units of Pressurized Water Reactors (PWRs) in the United States have the additional dilution factors higher than 14.5 [17]. The risk-based detection limits can be adopted to the fresh water sites for thirty-two units of PWRs without guaranteeing on the nuclide composition in the liquid effluent of APR 1400 from a risk-based point of view. On the other hand, the fresh water sites for twenty-six units out of forty units of US PWRs showing additional dilution factors higher 81.1 may continue to use the present detection limits specified in NUREG-1301 to APR 1400 assumed to be commissioned at the site [17].

3.4. Risk-informed approach based on Regulatory Guide 1.21, Revision 2

From a risk-based point of view, $D{L}_{Risk,i}$ should be derived for all radionuclides existing in the liquid discharge using Equation (7)(7) $D{L}_{Risk,i}=min\left(D{L}_{ECL,i},D{L}_{TB,i},D{L}_{OG,i}\right)$(7) and Table 4 as proposed in this study. However, application of different detection limits for all forty-seven radionuclides present in the liquid effluent from APR 1400 may not be practicable. Hence, the more practical approach to apply the risk-based detection limits to a few dominant radionuclides contributing to the radioactivity discharged or radiological dose to the public are developed in this study, which reflects the regulatory position addressed in Regulatory Guide 1.21, Revision 2 (see Figure 1).

By applying the criteria in Equations (8)(8) $({\alpha }_i{)}_G>0.01$(8) to (11) along with the procedure in Figure 1, it turns out that six gamma-emitters (⁹⁹Mo, ¹³³I, ¹³⁵I, ¹³⁴Cs, ¹³⁶Cs, and ¹³⁷Cs), one non-gamma emitter (³H), four radionuclides (³H, ³²P, ¹³⁴Cs, and ¹³⁷Cs), and three radionuclides (³H, ⁹⁵Nb, and ¹⁰⁶Ru) meet Equations (8)(8) $({\alpha }_i{)}_G>0.01$(8) –(11(11) $PD{F}_{OG,i}\cdot Q_{E,i}>(0.01)\cdot (0.1mSv/y)$(11) ), respectively. Therefore, totally ten radionuclides, seven gamma emitters (i.e. ⁹⁵Nb, ⁹⁹Mo, ¹³³I, ¹³⁵I, ¹³⁴Cs, ¹³⁶Cs, and ¹³⁷Cs) and three nongamma emitters (i.e. ³H, ³²P, and ¹⁰⁶Ru) were ultimately selected as ‘principal radionuclides’ as shown in Table 9.

Table 9. Basis for selection of principle radionuclides and feasibility of the risk-informed approach to liquid effluent from APR 1400

Principal radionuclide		$({\alpha }_i{)}_G$or$({\alpha }_i{)}_{NG}$	$PD{F}_{TB,i}\cdot Q_{E,i}$(mSv/y)	$PD{F}_{OG,i}\cdot Q_{E,i}$(mSv/y)	$\frac{{\left({\alpha }_i\right)}_G}{D{L}_{Risk,i}}$or$\frac{{\left({\alpha }_i\right)}_{NG}}{D{L}_{Risk,i}}$	LHS of
						Equation (12)	Equation (13)	Equation (14)
Gamma emitter	^95Nb	1.43 × 10^−3	2.83 × 10^−7	2.75 × 10^−3	9.10 × 10^−6	2.20 × 10^−2	2.58 × 10^−2	9.97 × 10^−3
	^99Mo	1.25 × 10^−2	1.95 × 10^−7	8.23 × 10^−7	6.55 × 10^−8
	^133I	1.76 × 10^−1	3.89 × 10^−7	5.03 × 10^−7	6.08 × 10^−7
	^135I	3.18 × 10^−2	5.32 × 10^−8	7.09 × 10^−8	2.55 × 10^−8
	^134Cs	3.58 × 10^−2	1.59 × 10^−3	1.35 × 10^−4	8.35 × 10^−5
	^136Cs	7.32 × 10^−2	2.27 × 10^−4	4.67 × 10^−5	6.88 × 10^−5
	^137Cs	6.11 × 10^−1	1.24 × 10^−3	1.62 × 10^−4	7.62 × 10^−4
Nongamma emitter	^3H	9.99 × 10^−1	2.44 × 10^−2	1.54 × 10^−2	2.69 × 10^−7	1.08 × 10^−3	1.02 × 10^−2	5.10 × 10^−3
	^32P	1.23 × 10^−7	3.78 × 10^−4	7.85 × 10^−4	4.18 × 10^−9
	^106Ru	4.87 × 10^−5	9.96 × 10^−5	2.52 × 10^−2	8.37 × 10^−8
Sum						2.31 × 10^−2	3.60 × 10^−2	1.51 × 10^−2

* LHS: Left-hand side

Because ¹³⁷Cs and ³H show the maximum ratios of $({\alpha }_i{)}_G/D{L}_{Risk,i}$ and $({\alpha }_i{)}_{NG}/D{L}_{Risk,i}$ among gamma and nongamma emitters, respectively, they are designated with the identification number ‘k’ as addressed in Table 4. In addition, the values of LHSs in Equations (12) to (14) were also calculated for gamma and nongamma emitters and then summed. As shown in Table 9, all values of summed LHS in Equations (12)–(14) were calculated to be less than S = 0.1. This means that 10% (i.e. S = 0.1) of discharge limits would not be exceeded when ¹³⁷Cs and ³H are present at the level of risk-based detection limits and other radionuclides exist below the risk-based detection limits and proportional to the nuclide composition of liquid mixture. In other words, the risk-informed approach developed in this study can be applied to the liquid effluent from APR 1400 design with sufficient safety margin. It is further noted that all values of LHSs of Equations (12)–(14) in Table 9 (i.e. 2.31 × 10⁻², 3.60 × 10⁻², 1.51 × 10⁻²) are higher than the counterparts in Table 8 (i.e. 4.32 × 10⁻⁴, 1.41 × 10⁻², 1.67 × 10⁻³), which implies that the risk-informed approach for selected principal radionuclides gives rise to more practical results than the direct application of risk-based detection limits to all radionuclides.

4. Conclusion

A new methodology to ensure, in advance, the compliance with applicable liquid discharge limits for a reference design NPP was established. Using a practical model to calculate more realistic pathway dose factors than previous study, risk-based detection limits of radionuclides in liquid effluent to be discharged from a reference design NPP can be calculated. A risk-informed approach to warrant the conformance to the discharge limits by controlling only a few selected principal radionuclides was newly developed in order to improve the field applicability of the risk-based detection limits.

The methodology developed in this study has been applied to APR 1400 assumed to be commissioned at a freshwater site in the United State. For majority (i.e. 60–89%) of radionuclides, pathway dose factors calculated in this study are more realistic than those using the previous method. Present detection limits may not be sensitive enough for 40% of radionuclides, and the need of establishing a new detection limit for gross beta was proposed to control non-gamma emitters such as ³²P and ¹⁰⁶Ru whose contributions to the offsite dose are of relatively high ranks. When the information on nuclide composition is not available, neither risk-based detection limits derived in this study nor present detection limits cannot be justified, and adjustment of detection limit for each radionuclide is to be considered. Otherwise, the risk-based detection limits can be justified if APR 1400 is commissioned at a freshwater site with additional dilution factor higher than 14.5, and the present detection limits may be also justified for the site with additional dilution factor not less than 81.1 without adjustment.

It was shown that the risk-informed approach to guarantee the compliance with discharge limits can be more practically applied to APR 1400 compared to direct use of risk-based detection limits. Totally ten radionuclides, ³H, ³²P, ⁹⁵Nb, ⁹⁹Mo, ¹⁰⁶Ru, ¹³³I, ¹³⁵I, ¹³⁴Cs, ¹³⁶Cs, and ¹³⁷Cs. were selected as principal radionuclides for the liquid effluent. It was demonstrated that discharge limits would not be exceeded with the safety factor S = 10% by controlling only ten principal radionuclides rather than total forty-seven, which shows the acceptability of the approach to APR 1400 from a risk-informed point of view.

Acknowledgments

This work was supported by the Nuclear Safety Research Program through the Korea Foundation Of Nuclear Safety (KOFONS), granted financial resource from the Nuclear Safety and Security Commission (NSSC), Republic of Korea (No. 1605008).

Disclosure statement

No potential conflict of interest was reported by the authors.