1. Introduction

During the operation and decommissioning of nuclear power plants, liquid and gaseous radioactive effluents are released into the atmosphere or water [1-3]. It is essential to evaluate the radiation dose to the general public from these released radionuclides, and various assessment tools are employed across different countries, such as INDAC, KDOSE-60, NRCDose3, PC-CREAM 08, and so on. Among these, NRCDose3 is an open-source and validated tool widely used to calculate offsite doses to nearby residents from radioactive materials released into the environment by nuclear facilities. Notably, NRCDose3 is based on the same assessment model, Regulatory Guide 1.109, which has also been adopted in Korea for radiation dose assessments.

However, NRCDose3 was primarily developed to meet the regulatory requirements and environmental conditions specific to the United States. Therefore, adaptations and adjustments may be necessary to address the specific environmental and regulatory conditions in Korea. To meet these needs, this study developed an in-house beta version code (hereinafter “KHU Code”) that allows for more flexible preliminary radiation dose calculations tailored to the local context. The KHU Code, developed on the Microsoft^® Excel platform, is also based on the Regulatory Guide 1.109 model.

To validate the KHU Code, a comparative analysis of calculation results was conducted using several test cases, applying identical input parameters and dose coefficients from the International Commission on Radiological Protection (ICRP) Publication 72 in both the KHU Code and NRCDose3 Code Version 1.1.4. Throughout this process, while the two codes produced nearly identical calculation results in most cases, several significant discrepancies were identified between their results in certain cases. First, significant relative errors were observed in the calculation results for the effective dose from ³H inhalation and ingestion between the KHU Code and the GASPAR module. Second, significant relative errors were found in the inhalation and ingestion dose calculations for ¹⁴C between the KHU Code and the GASPAR module. Third, the GASPAR module produced no dose output for newborns from the effective dose of ¹⁴C. Fourth, significant relative errors were identified in the inhalation dose calculations for ¹³¹I (in absorption type M and S) between the KHU Code and the GASPAR module. Fifth, significant relative errors were noted in the equivalent dose calculations for ⁶⁰Co and ¹³¹I to specific organs or tissues between the KHU Code and the GASPAR module. Finally, selecting the “Salt water” site type with ICRP-72 resulted in dose outputs for only three age groups (Adult, 15 YR, and 10 YR), instead of the expected six, in the LADTAP module.

This study aims to analyze the root causes of the five significant discrepancies identified as above between the calculation results of the KHU Code and NRCDose3 Code Version 1.1.4, and to propose improvement measures to address these potential errors and ultimately achieve accurate calculation results.

2. Materials and Methods

2.1 Identification and Analysis of Root Causes of Potential Errors in GASPAR Module

2.1.1 Test cases and input data for KHU code validation

To compare the calculation results of the KHU Code with the GASPAR module in NRCDose3 Code Version 1.1.4, the same scenarios and input data were used. Most parameters, such as chemical forms and absorption types, were applied identically in both codes using the default values provided by GASPAR. Additionally, parameters that either do not have specified defaults values (e.g., quantity and atmospheric dispersion factor) in GASPAR or were applied with values different from the defaults (e.g., dose coefficients) for this comparative evaluation are presented in Table 1. Here, it was assumed that individual radionuclides are released into the atmosphere at a rate of 1 Ci per year from a hypothetical nuclear power plant. The representative atmospheric dispersion factors widely used in Korea were applied. The remaining input data used were the default values of the GASPAR module. Table 1 shows the input values used in this comparative evaluation, apart from the default values of the GASPAR module. Most parameters, including chemical forms and absorption types, were set to the default values in NRCDose3.

For each of the major representative radionuclides (e.g., ³H, ¹⁴C, ⁶⁰Co, ¹³¹I, etc.), the same input data were entered into both the KHU Code and the GASPAR module for the aforementioned test cases. The relative error between the two code calculation results (i.e., effective dose for each pathway) was then calculated using the formula below.

where X_GASPAR is the value of radiation dose calculated by GASPAR (mSv∙y^⁻1), X_{KHU Code} is the value of radiation dose calculated by KHU Code (mSv∙y^⁻1).

2.1.2 Potential errors regarding dose coefficients for intake of ³H in GASPAR

2.1.2.1 Identification of potential errors in effective dose calculation from intake of ³H in GASPAR module

When comparing the relative errors between the calculation results of the two codes for the major representative radionuclides, the relative errors were found to be minimal in most cases, likely due to truncation errors in the calculation process. Tables 2 and 3 illustrate the relative errors for ⁶⁰Co and ¹³¹I, not exceeding 0.31%, which are examples of radionuclides where the two codes produced virtually identical calculation results. Therefore, under the given test cases and input data, the KHU Code can be considered validated against the GASPAR module for the majority of radionuclides.

However, the relative errors in the inhalation dose for ³H ranged from 41.38 to 58.18%, indicating a significant discrepancy between the two codes (see Table 4). This significant relative error in the inhalation dose suggests that one of the two codes may not be adequately reflecting the input data, such as the dose coefficients used in the inhalation dose calculation.

The calculation results in Table 4 pertain only to the default chemical form or absorption type V (HTO) of ³H. Therefore, potential errors in the application of dose coefficients for ³H intake, which vary based on chemical form, absorption type, and age group, were investigated. To confirm whether the dose coefficients for ingestion and inhalation of ³H were correctly applied in the calculations, the inhalation and ingestion doses for each chemical form or absorption type of ³H were calculated in the GASPAR module (see Table 5).

The dose coefficient values for the inhalation of ³H differ depending on V (OBT), V (HTO), V (HT), V (CH₃T), and absorption types F, M, and S. However, the dose calculation results from GASPAR are the same for all four chemical forms and the same for all three absorption types as shown in Table 5. Additionally, the dose coefficient values for the ingestion of ³H differ between OBT and the other chemical form. However, the results from GASPAR are the same for OBT and the other chemical form. It indicates that GASPAR may not have correctly applied the appropriate dose coefficients based on chemical form and absorption type. Consequently, this was identified as a potential error of GASPAR.

2.1.2.2 Root cause analysis of potential errors in application of dose coefficients for intake of ³H in GASPAR

An additional analysis was conducted to determine which of the codes, KHU Code or GASPAR, caused the calculation errors given in Table 4. The basic equation used for radiation dose assessment both in NRCDose3 and Regulatory Guide 1.109 is shown in Equation (2).

where R_aipj is the radiation dose to organ or tissue j, of an individual of age group a, from radionuclide i, via pathway p (Sv∙y^⁻1), C_ip is the concentration of radionuclide i in media of pathway p (Bq∙L^⁻1 or Bq∙kg^⁻1), U_ap is the pathway usage parameter representing intake associated with ingestion pathway p for age group a (L∙y^⁻1 or kg∙y^⁻1), D_aipj is the dose coefficient specific to age group a, radionuclide i, pathway p, and organ or tissue j (Sv∙Bq⁻1).

If the concentration (C_ip) was miscalculated in either of the two codes, the relative error would be almost the same across all age groups in Table 4. Since this is not observed, however, the error likely comes from the consumption rates (U_ap) or dose coefficients (D_aipj). Regarding the consumption rates (U_ap), the input data values used in the two codes were confirmed to be the same as those by rechecking the input file and supplemental report file from GASPAR, as well as the input and output data for the KHU Code. Therefore, it was concluded that no discrepancies exist in the consumption values between the two codes.

As shown in Table 4, when the chemical form is HTO and the absorption type is V, the relative error in the ingestion radiation dose for ³H between the two codes is approximately 1%. This indicates that the ingestion dose coefficients were accurately applied in the calculation. However, as shown in Table 5, the ingestion dose seems to be calculated as a single value, regardless of its chemical form (i.e., OBT or not).

On the other hand, the inhalation dose for ³H exhibits a much larger relative error as shown in Table 4. To investigate this, the dose coefficients for each chemical form and absorption type were applied in the KHU Code, and the relative errors in the inhalation dose of ³H were compared, as presented in Table 6.

As shown in Table 6, the relative error in the inhalation dose for ³H was very small (i.e., less than 0.41%) only when the chemical form is OBT and the absorption type is V. Additionally, it can be inferred that GASPAR applies the chemical form of OBT when calculating the inhalation dose for ³H with absorption type V, since the inhalation doses for different chemical forms of absorption type V (i.e., OBT, HTO, HT, and CH₃T) was calculated to be a single value in GASPAR as shown in Table 5.

For absorption types F, M, and S, the inhalation dose for ³H calculated by GASPAR is presented as a single value (see Table 5). Moreover, the relative errors between the inhalation dose of ³H for F, M, and S calculated by GASPAR and the KHU Code are significantly large (58.40% to 1,979.87%) (see Table 6). This suggests that GASPAR applied a different inhalation dose coefficient not specific to absorption types F, M, and S. During the cause analysis, it was incidentally discovered that the inhalation dose of ³H for V (HTO) calculated by the KHU Code closely aligns with the inhalation doses calculated by GASPAR for absorption types F, M, and S. These values have been extracted and summarized in Table 7.

As indicated in Table 7, when the absorption type is F, M, or S, the dose coefficients used in the inhalation dose calculation for ³H are those corresponding to V (HTO).

In contrast, for ingestion dose, Table 4 shows that the relative error between the ingestion doses of ³H calculated by the KHU Code and GASPAR was less than 1.19%. However, as shown in Table 5, the ingestion dose of ³H calculated by GASPAR is the same for both the OBT and other chemical form. Therefore, the relative errors of the ingestion doses for OBT and other form calculated by GASPAR and the KHU Code were compared and are presented in Table 8.

As shown in Table 5, a single value for the ingestion dose of ³H was observed regardless of the chemical form. Additionally, in Table 8, the relative error for the ingestion dose in the other chemical form (not OBT) was very small (i.e., less than 1.10%). This suggests that the dose coefficient for the other form was applied across all chemical forms when calculating the ingestion dose for ³H. As a result, in Table 4, since the relative error was calculated using V (HTO) as the default form, the ingestion dose coefficient was applied as other chemical form, leading to a small relative error in the ingestion dose of ³H.

In summary, the inhalation and ingestion dose coefficients applied in the assessment of radiation dose for ³H in GASPAR can be summarized as shown in Table 9.

2.1.3 Potential errors regarding the consumption values, absence of the results for newborn and dose coefficients for intake of ¹⁴C in GASPAR

2.1.3.1 Identification of potential errors in the calculation of dose from intake of ¹⁴C in GASPAR

The inhalation and ingestion doses of ¹⁴C calculated by GASPAR and the KHU Code also showed significant relative errors, with discrepancies reaching up to 214.87% (see Table 10).

The relative error of the dose in newborns is not presented in Table 10, as GASPAR did not calculate the dose for ¹⁴C in newborns. Additionally, the results presented in Table 10 pertain only to the default chemical form or absorption type V (CO₂) of ¹⁴C. In response, potential inaccuracies in the application of intake dose coefficients for ¹⁴C were investigated, as these coefficients vary by chemical form, absorption type, and age group. To ensure the correct application, doses for each chemical form and absorption type were recalculated using GASPAR (see Table 11).

The ingestion dose coefficient for ¹⁴C is a single value, regardless of chemical form or absorption type. In contrast, the inhalation dose coefficients of ¹⁴C vary depending on the chemical forms—V (CO₂), V (CO), V (CH₄), V—and the absorption types F, M, and S. However, as shown in Table 11, the inhalation dose calculated by GASPAR is identical across all chemical forms or absorption types. This suggests that GASPAR may not have correctly applied the specific dose coefficients according to chemical form and absorption type when calculating the inhalation dose, indicating a potential error in the GASPAR calculations.

Furthermore, it was observed that the calculation result for newborns was not generated for any chemical form or absorption type, as shown in Table 11.

2.1.3.2 Root cause analysis of potential errors for ¹⁴C in GASPAR

The root cause analysis was performed using the same methodology outlined in Section 2.1.2.2. The ingestion dose coefficient for ¹⁴C does not vary with the chemical form, and as shown in Table 11, the ingestion dose in GASPAR was calculated as a single value for each age group. To investigate this, potential errors in the usage parameters in Equation (2), corresponding to the consumption values in GASPAR, were analyzed, as these could affect dose calculations across age groups and exposure pathways. Additionally, the recalculated total doses (inhalation, ingestion, and external dose) values, after adjusting the consumption value for the specific age group, are summarized in Table 12.

As shown in Table 12, it was confirmed that the consumption values for different age groups had been incorrectly applied in the calculation of radiation doses for ¹⁴C (V (CO₂)) in GASPAR. To resolve this issue, the consumption values were corrected to reflect the appropriate values for each age group in GASPAR (e.g., applying adult values to the 15 YR, 15 YR values to the 10 YR, and so on), and the relative errors between the two codes were recalculated and presented in Table 13.

As shown in Table 13, after adjusting the consumption values for each age group in GASPAR, the relative errors between the two codes substantially decreased to approximately 1%.

Furthermore, according to Table 11, GASPAR calculates both the inhalation and ingestion doses of ¹⁴C as single values for each age group, regardless of the chemical form or absorption type. To resolve this issue, the dose coefficients for each chemical form and absorption type were applied in the KHU Code, and the relative errors in the inhalation dose of ¹⁴C were compared, as shown in Table 14. The results from GASPAR, reflecting the corrected consumption values previously discussed, corroborate this assessment.

Notably, the relative error for ¹⁴C is about 0.4% for V (CO₂), but at least 54.01% for other forms. Therefore, it can be inferred that GASPAR uniformly applies the V (CO₂) value when calculating the inhalation dose for ¹⁴C.

2.1.4 Potential errors regarding dose coefficients for intake of ¹³¹I in GASPAR

2.1.4.1 Identification of potential errors in the calculation of dose from intake of ¹³¹I in GASPAR

Based on the evaluation of ³H and ¹⁴C, similar errors in the application of dose coefficients were identified for ¹³¹I, as shown in Table 15.

The dose coefficient values for the inhalation of ¹³¹I vary depending on the chemical forms V (CH₃I) and V (I2), as well as the absorption types F, M, and S. However, as shown in Table 15, the dose calculation results from GASPAR are identical for both chemical forms and all three absorption types. Therefore, it can be concluded that this represents a potential error in GASPAR.

2.1.4.2 Root cause analysis of potential errors in application of dose coefficients for intake of ¹³¹I in GASPAR

The inhalation dose coefficients for each chemical form and absorption type were applied using the KHU Code, and the relative error compared to GASPAR was calculated, as shown in Table 16.

As shown in Table 16, the relative error in the inhalation dose for ¹³¹I with absorption type V was minimal with CH₃I, and among absorption types F, M, and S, it was smallest with type F. Therefore, it can be inferred that GASPAR calculates using the value for CH₃I regardless of chemical form when the absorption type is V, and applies the value for absorption type F when the absorption types are F, M, or S.

2.1.5 Potential errors regarding equivalent dose of ⁶⁰Co and ¹³¹I in GASPAR

2.1.5.1 Identification of potential errors in the calculation of equivalent dose from ⁶⁰Co and ¹³¹I in GASPAR

Sections 2.1.2 to 2.1.4 focused on comparing the effective doses, while Section 2.1.5 extended the analysis to include a comparison of organ or tissue equivalent doses. After correcting potential errors related to dose coefficients and consumption values (as described in Sections 2.1.2 to 2.1.4), most relative errors in equivalent doses were around 1%. However, significant discrepancies were found for certain radionuclides (e.g., ⁶⁰Co, ¹³¹I) and specific organs or tissues (e.g., kidneys, liver, muscle, ovaries, pancreas, red marrow, and extrathoracic airways). Examples of these errors for ⁶⁰Co and ¹³¹I are shown in Tables 17 and 18.

2.1.5.2 Root cause analysis of potential errors in the calculation of equivalent dose from ⁶⁰Co and ¹³¹I in GASPAR

The equivalent doses calculated by the two codes were compared for the seven organs or tissues that exhibited large relative errors as shown in Tables 17 and 18. No such phenomena were observed for ³H and ¹⁴C, likely because the intake dose coefficients for these seven organs or tissues were applied with the same values for the default chemical form or absorption type. Therefore, the committed equivalent doses by inhalation of ⁶⁰Co and ¹³¹I for the seven organs were first directly compared between the two codes, with the results presented in Tables 19 and 20.

As shown in Tables 19 and 20, it was observed that the equivalent dose calculated for the kidneys by the KHU Code is identical to the equivalent dose calculated for the liver by GASPAR. Similarly, the equivalent doses calculated by the KHU Code for the liver, muscle, ovaries, pancreas, red marrow, and extrathoracic airways were found to have similar values to those calculated by GASPAR for the muscle, ovaries, pancreas, red marrow, extrathoracic airways, and kidneys, respectively. This same phenomenon was also observed in the ingestion pathway, where the equivalent doses for these organs or tissues were incorrectly output.

To analyze the cause of this, the dose coefficients (D_aipj) related to the organs or tissues were examined. It was identified that there is a discrepancy between the order of organs or tissues listed in the “Dose Factors” tab in GASPAR (i.e., kidneys, liver, muscle, ovaries, pancreas, red marrow, extrathoracic airways) and the order of organs or tissues in the equivalent doses in the output file (i.e., liver, muscle, ovaries, pancreas, red marrow, extrathoracic airways, and kidneys).

Therefore, it appears that the equivalent dose was calculated according to the organs or tissues order in the “Dose Factors” tab. However, when the results were output by GASPAR, the order of the organs or tissues was altered, leading to incorrect equivalent dose values for certain organs and tissues. In summary, the discrepancy between the order of organs and tissues in the “Dose Factors” tab and the output file seems to have caused the incorrect output of equivalent dose values for seven organs or tissues.

2.2 Identification and Analysis of Root Causes of Potential Error in LADTAP Module

2.2.1 Test cases and input data for KHU Code validation

To compare the calculation results of the KHU Code with those from the LADTAP module in NRCDose3 Code Version 1.1.4, identical scenarios and input data were utilized. The analysis assumed that individual radionuclides were discharged into water at 1 Ci from a hypothetical nuclear power plant. Since nuclear power plants in Korea are typically located near the sea, the site type was set to “Salt water”. Due to the absence of default data, certain inputs in the “Selections” and “ALARA Locations” tabs of the LADTAP module were assumed. All other input parameters were set to the default values in the LADTAP module. Table 21 presents the values of the input parameters used in this comparative evaluation, excluding the default values of the LADTAP module. Most parameters, including chemical forms and absorption types, were kept at the default settings in NRCDose3.

2.2.2 Potential errors regarding the absence of dose calculation results for specific age groups in LADTAP

2.2.2.1 Identification of potential errors in the calculation of dose for specific age groups in LADTAP

When comparing the relative errors between the calculation results of the two codes for the major representative radionuclides, the relative errors were found to be minimal in most cases, likely due to truncation errors in the calculation process. Tables 22 to 25 illustrate the relative errors for ³H, ¹⁴C, ⁶⁰Co and ¹³¹I, not exceeding 0.49%, which are examples of radionuclides where the two codes produced virtually identical calculation results. Therefore, under the given test cases and input data, the KHU Code can be considered validated against the LADTAP module for the majority of radionuclides.

As shown in Tables 22 to 25, the radiation dose for the 5 YR, 1 YR, and Newborn was not assessed in LADTAP. According to the NRCDose3 Manual, when the dose coefficient is selected as ICRP-72, radiation dose should be calculated for six age groups [4]. However, the evaluation of major radionuclides revealed that only three of these six age groups were assessed. This suggests a potential error in LADTAP.

2.2.2.2 Root cause analysis of potential errors in the calculation result in LADTAP

Despite applying the ICRP-72 in LADTAP, results were printed for only 3 of the 6 age groups, rather than for all 6. This was not due to the results being displayed as zero; instead, the results for certain age groups were entirely absent, ruling out the possibility of incorrect input values. To investigate further, the Site Type was changed from “Salt water” to the default “Fresh water”. When set to “Fresh water”, results were generated for all 6 age groups. As the manual specifies that the difference between “Fresh water” and “Salt water” affects only the exposure pathways, not the age groups, it was concluded that this is a display error in LADTAP.

3. Results and Discussion

3.1 Summary of Identified Potential Errors in NRCDose3

In this study, four potential errors in GASPAR and one potential error in LADTAP were identified. A summary of these potential errors is provided in Table 26.

3.2 Correction Methods for Accurate Calculations in NRCDose3

3.2.1 Radiation dose calculation for ³H in GASPAR

In GASPAR, the inhalation and ingestion dose calculations for ³H do not appropriately account for the dose coefficients based on chemical forms or absorption types, as outlined in Table 9. To obtain accurate dose estimates, users of NRCDose3 Code Version 1.1.4 are advised to apply the correction factors provided in Table 27 to the pathwayspecific doses calculated by GASPAR.

3.2.2 Radiation dose calculation for ¹⁴C in GASPAR

As described in Section 2.1.3, the dose assessment for ¹⁴C in GASPAR incorrectly applies age-specific consumption and inhalation rates. To temporarily obtain accurate results, users should adjust the consumption and inhalation rates for the 15 YR to the values designated for adults, shift the values for 10 YR to those for 15 YR, and apply this adjustment across all age groups accordingly. Furthermore, as the dose coefficients for ¹⁴C based on chemical form and absorption type are not correctly considered in GASPAR, the calculated dose must be further corrected by applying the correction factors provided in Table 28. However, since GASPAR does not calculate doses for newborns, an independent calculation must be performed for this age group.

3.2.3 Radiation dose calculation for ¹³¹I in GASPAR

As described in Section 2.1.4, the inhalation dose calculation for ¹³¹I in GASPAR does not properly account for dose coefficients based on chemical form or absorption type. Therefore, accurate values can be temporarily obtained by multiplying the results calculated in GASPAR by the correction factors presented in Table 29.

3.2.4 Organs or tissue equivalent dose calculation for ⁶⁰Co and ¹³¹I in GASPAR

In the calculation of committed equivalent doses using GASPAR, discrepancies were identified in the equivalent doses for radionuclides such as ⁶⁰Co and ¹³¹I across seven organs. This discrepancy is attributed to the difference in the ordering of organs or tissues between the “Dose Factors” tab and the output window in GASPAR. To obtain accurate results, it is necessary to interpret the output values according to the organ or tissue order listed in the “Dose Factors” tab.

3.2.5 Radiation dose calculation in LADTAP

When the site type is set to “Salt water” and the dose coefficients are selected as ICRP-72, the radiation dose is calculated for only 3 out of 6 age groups. This issue is due to a limitation in the code that requires correction. Until the code is updated, the radiation doses for the missing age groups must be calculated through independent methods.

4. Conclusion

In this study, five potential errors were identified and analyzed in NRCDose3 Code Version 1.1.4, specifically within the GASPAR and LADTAP modules.

First, the GASPAR module did not appropriately apply dose coefficients that account for the chemical form or absorption type when calculating inhalation and ingestion doses for ³H, leading to discrepancies in the calculated doses. Second, for ¹⁴C, the GASPAR module incorrectly applied consumption values across different age groups and dose coefficients according to chemical form or absorption type, resulting in significant relative errors in both ingestion and inhalation doses. Additionally, the dose for newborns was not calculated, indicating an omission in the module. Third, for ¹³¹I, the GASPAR module failed to properly account for dose coefficients based on chemical form or absorption type, causing discrepancies in inhalation dose calculations. Fourth, significant errors were found in the calculation of equivalent doses for specific organs or tissues, particularly for radionuclides such as ⁶⁰Co and ¹³¹I. These potential errors were attributed to a misalignment in the ordering of organs or tissues between the input and output files, leading to incorrect dose outputs for certain organs or tissues. Lastly, in the LADTAP module, a display error was observed where doses for certain age groups— specifically the 5 YR, 1 YR, and Newborn groups—were not displayed when using ICRP-72 with the “Salt water” site type, resulting in incomplete dose assessments.

Users of NRCDose3 Code Version 1.1.4 should be aware of these identified potential errors when performing dose calculations. By considering these issues and applying the interim correction methods proposed in this study, it is possible to obtain accurate dose values.