#### 3.1.1. General Pathway Dose Factors for Processing of Dismantled Steam Generators

The potential radiation dose to each receptor involved in the processing of an SG does not depend on the specific site or scenario but instead relies on the activity concentrations of existing radionuclides and weight of the SG, as implied in Equations (1) to (4). In order to derive general PDFs for the processing of an SG, anticipated doses to all potential receptors (i.e., S

_{1} to S

_{4}, and M

_{1} to M

_{7}, as shown in

Table 1) were calculated using RESRAD-RECYCLE code by assuming the unit activity concentration of each radionuclide.

The general PDF for each radionuclide and each receptor can be expressed in terms of

$\left(mSv/y\text{}\right)\text{}per\text{}\left(Bq/g\right)\xb7ton$, as below, from Equations (1) to (4):

where the value of

$TP$ is the reciprocal of time for processing 1 ton of steel scrap which can be derived from the default exposure time for processing 100 ton of steel scrap as proposed in the RESRAD-RECYCLE model [

19]. In addition, the values of

${f}_{M,P}$ for SG as steel scrap in Equation (5) are assumed to be 90% for ingot, 10% for slag, and 1% for dust using the default values in RESRAD-RECYCLE [

19]. The elements with low boiling points, such as cesium, typically concentrate in the dust, and the elements that easily oxidize tend to concentrate in the slag [

19]. It is noted that default dose coefficients for inhalation and ingestion (see Equations (3) and (4)) in RESRAD-RECYCLE, which are based upon Federal Guidance Report No. 11, have been replaced with those recently introduced in the International Commission on Radiological Protection (ICRP) Publication 119, in order to calculate the effective dose in accordance with the radiation protection recommendations of ICRP Publication 60 [

28,

29,

30]. The geometry and dimensions of objects handled by receptors participating in SG processing and the distance from the receptors are assumed to be the same as the reference values as proposed in the RESRAD-RECYCLE manual [

19]. Thus, the assumed

$DC{F}_{ext,i}$ is using a default value in the RESRAD-RECYCLE [

19]. Other parameters (

${C}_{D},\text{}\epsilon ,\text{}BR,\text{}{f}_{R},\text{}IR$) are also assumed to be the default value in the RESRAD-RECYCLE [

19].

^{3}H,

^{14}C, and

^{129}I are not taken into account in RESRAD-RECYCLE, which may be due to the fact that

^{3}H,

^{14}C, and

^{129}I emit very weak photons, and direct exposure from them is negligible [

31]. However, internal exposure from the inhalation and ingestion of these radionuclides may be of concern; radiological impacts from

^{3}H,

^{14}C, and

^{129}I have been frequently considered in the assessment of radioactive waste management [

20,

32]. In this study, internal exposure from the inhalation and ingestion of these radionuclides has therefore been separately calculated, whereas direct radiation has not been assessed for these three radionuclides.

Values of other parameters used in this study with regard to the processing of a SG are assumed to be the same as the default values in RESRAD-RECYCLE, as mentioned above.

Figure 2 shows the general PDF for each actinide and for each receptor involved in the processing of the SG, which is calculated using Equation (8).

It is worth noting that the general PDFs for receptors handling metal ingot (i.e., M

_{5} to M

_{7}) are calculated to be zero due to there being no elemental partitioning of actinides into ingot through the smelting process (see

Table 2 and Equation (5)) [

19].

Significant differences are not found in the general PDFs for receptors S_{1}, S_{2}, S_{4}, M_{1}, M_{2}, and M_{3}, while the PDFs for M_{4} show much higher values than for other receptors. Furthermore, the variability in PDF values among the eight actinides for a receptor is generally small (e.g., the highest ratio of the maximum to minimum PDF is 2.27), except for receptor S_{3}, for which the significant differences in the PDFs of actinides are observed (e.g., the ratio of the maximum to minimum PDF is about 50,000).

The small differences in the general PDFs for radionuclides (except receptor S

_{3}) can be ascribed to the comparable dose coefficients for intake among actinides (i.e., 1.1

$\times $ 10

^{−7} to 2.5

$\times $ 10

^{−7} Sv/Bq for ingestion and 2.1

$\times $ 10

^{−5} to 4.7

$\times $ 10

^{−5} Sv/Bq for inhalation) and the dominance of internal exposure for the respective receptors. In addition, irregularities of the general PDFs among the actinides observed for receptor S

_{3} (i.e., scrap transfer worker) result from the fact that direct radiation becomes the only applicable exposure pathway due to the general assumption of negligible portions of releasable radionuclides under normal transfer conditions [

33]. On the other hand, the higher values of general PDFs for receptor M

_{4} (i.e., slag worker) than other receptors, can be attributed to the longer exposure time, higher external dose conversion factor due to larger dimensions of objects, shorter distance from the receptor, and the higher slag-partitioning factor of actinides, as shown in

Table 2 [

19].

Figure 3 shows the calculated general PDF for each non-actinide and for each receptor involved in the processing of the SG, in accordance with Equation (8).

For receptors S_{1} to S_{4}, which are involved prior to the smelting process, where the mass of metal scrap and the constituent elements are redistributed into resulting matrices, the external exposure pathway is dominant, and thus the radiological impacts from gamma-emitting radionuclides ^{60}Co, ^{94}Nb, ^{154}Eu, ^{137}Cs, ^{129}I, and ^{54}Mn are higher than for other radionuclides.

In the beginning of the smelting process, in which the receptors M

_{1} and M

_{2} are involved, both direct radiation from scrap metal and internal exposure from the intake of radioactive dust at the smelter or furnace are in effect. Therefore, the general PDF values of radionuclides emitting high-energy gamma rays (e.g.,

^{60}Co,

^{94}Nb, and

^{154}Eu) and partitioned into dust (e.g.,

^{137}Cs,

^{129}I and

^{65}Zn) are remarkably high (see

Table 2). For receptor M

_{3}, which handles the baghouse filter, the general PDF values of radionuclides that preferably partition into the dust phase (e.g.,

^{137}Cs and

^{65}Zn) are higher compared to the others. Likewise, the general PDFs of

^{94}Nb,

^{154}Eu,

^{129}I,

^{54}Mn, and

^{125}Sb, which tend to be redistributed into slag, turn out to be dominant for slag workers (receptor M

_{4}). It is also noted that the general PDFs for receptor M

_{4} are much higher than other receptors, as shown in

Figure 3, which can be ascribed to the same arguments already addressed to interpret the similar trend observed in

Figure 2. In addition, gamma-emitting radionuclides preferably partitioned into ingot (i.e.,

^{60}Co,

^{54}Mn,

^{125}Sb,

^{106}Ru,

^{65}Zn, etc.) induce higher PDF values for receptors handling ingot (i.e., M

_{5} to M

_{7}).

Due to the volatile characteristics of

^{3}H,

^{14}C and

^{129}I, however, the radionuclides may not be trapped by the baghouse filter and may ultimately be dispersed into the atmosphere [

20]. As implied in the footnote of

Table 2, significant portions of volatile elements are released into the atmosphere from the processing facility and the radiological impacts from them may require additional care regarding public exposure, due to the release of airborne radionuclides. In this regard, the activity concentration of radionuclide i at the boundary of the processing facility,

${C}_{B,i}$ (Bq/m

^{3}), can be calculated as [

34]

where

${f}_{D,i}$ is the dischargeable fraction of the volatile element i, 1000 is the factor used to convert tons into grams, 31,536,000 is the factor used to convert seconds to years, and

$X/Q$ is the atmospheric dispersion factor (

$\mathrm{s}/{\mathrm{m}}^{3}$). By applying

${C}_{S,i}$ of 1 Bq/g,

$W$ of 1 ton/year and

${f}_{D,i}$ of 90%, 36.5%, and 50% for

^{3}H,

^{14}C and

^{129}I, respectively, as well as

$X/Q$ of 4.605

$\times $ 10

^{−6} $\mathrm{s}/{\mathrm{m}}^{3}$ (at 1000 m downwind distance) as suggested in comparable studies,

${C}_{B,i}$ for

^{3}H,

^{14}C, and

^{129}I were calculated and compared to the effluent concentration limit for airborne radionuclide (

$EC{L}_{A,i}$) set forth in 10 CFR Part 20 Appendix B, based upon the annual radiation dose limit (i.e., 1 mSv/year) for the members of the public, as shown in

Table 3 [

20,

35].

As shown in

Table 3, the ratio of

${C}_{B,i\text{}}$ to

$EC{L}_{A,i}$ lies within a range from an order of approximately 10

^{−14} to 10

^{−9}, and the activity concentrations equivalent to the ratio of

${C}_{B,i\text{}}$ to

$EC{L}_{A,i\text{}}$ to unity are calculated to be 2.03

$\times $ 10

^{8} to 2.81

$\times $ 10

^{13} Bq/g, which conforms to a total activity of each radionuclide of 1.09

$\times $ 10

^{11} to 1.52

$\times $ 10

^{16} MBq in the SG (i.e., 540 tons). It is noted that the above estimated total activity for each volatile radionuclide equivalent to the public dose limit is much lower than the actual radioactive source terms of SGs in

Section 3.2.1. Thus, the potential exposure due to volatile radionuclides released into the atmosphere from a processing plant are not further taken into account in this study, since their contributions to radiological impacts turn out to be negligible.

#### 3.1.2. General Pathway Dose Factors for Transportation and Handling of Dismantled Steam Generators

Using Equation (6), the general PDF for each radionuclide and each receptor (i.e., T1 to T3) involved in the transport operations can be defined in terms of

$\left(mSv/y\text{}\right)\text{}per\text{}\left(Bq/g\right)\xb7km$, as below:

and receptor H, involved in the handling operations, can be defined in terms of

$\left(mSv/y\text{}\right)\text{}per\text{}\left(Bq/g\right)\xb7ton$ as follows:

where

${D}_{handle,i}$ (in mSv/year) can be calculated by replacing

$DC{F}_{ext,i}$ with

$D{R}_{i}$ in Equation (2).

In order to calculate the radiation dose from transportation using RADTRAN 6, the dose rate 1 m from the package should be provided as an input [

32]. Thus, the dose rate 1 m from a package containing 1 Bq/g of each radionuclide listed in

Table 4 has been derived using the MicroShield

^{®} computer code with regard to the SG in one piece, and a container containing processed (i.e., segmented or smelted) objects [

36]. For simplification, each radionuclide is assumed to be homogeneously distributed in the total volume of the SG weighing 540 tons in one piece, defined in

Section 3.1, and in the International Organization for Standardization (ISO) 1496/1 container (length 12 m, width 2.4 m, and height 2.5 m), which is widely used in the transportation of low and intermediate level radioactive waste (LILW), containing 20 tons of processed objects [

23]. As such, the dose rate 1 m from each package containing each of the 11 key radionuclides for SG transportation at unit activity concentration was derived as shown in

Table 4, ranging in the order of 10

^{−7}–10

^{−4} $\left(mSv/h\text{}\right)\text{}per\text{}\left(Bq/g\right)$. It should be noted that other radionuclides showing negligibly low dose rates ranging in the order of 10

^{−25}–10

^{−15} $\left(mSv/y\text{}\right)\text{}per\text{}\left(Bq/g\right)$ are not given in

Table 4.

In

Table 4, the ratio of the dose rate 1 m from the SG to that from the ISO 1496/1 container that emplaced segmented objects is about 1.6, on average, except for

^{57}Co and

^{237}Np. The higher dose rate 1 m from the SG than from the container can be attributed to the difference in total radioactivity present in the whole SG and in one container; that is, there is 27 times higher radioactivity in the SG than in the single container for segmented SG. Due to the redistribution of radionuclides after smelting, for some radionuclides that are concentrated to ingot after smelting as the concentration of these radionuclides can be calculated by Equation (5) (i.e., Co

^{57}, Co

^{60}, Nb

^{94} and Ru

^{106}) using the values in

Table 2, the dose rate at 1 m from the container containing smelted SG (i.e., ingot) is higher than that for segmented SG. However, for other nuclides that are not redistributed to ingot after smelting (i.e., Cs

^{137}, Ce

^{144}, Eu

^{154} and Np

^{237}), no radiological impacts of these nuclides for smelted SG transportation were observed. The much lower ratios for two low-energy photon emitters

^{57}Co and

^{237}Np (a few keV of average photon energy) can be ascribed to the fact that the low-energy photon is very susceptible to self-absorption [

37].

As shown in

Figure 4, the general PDFs for T1–T3 and H have been derived using the RADTRAN 6 code in accordance with Equations (10) and (11), using the assumed values of parameters referenced from the open literature, as given in

Table 5.

As shown in

Figure 4, the general PDF values for receptors T1 and T2 which use road transportation are 766 to 1952 times higher than those for the waterway transport workers, T3, and the general PDFs for the receptor involved in the transportation/handling of the processed SG are about two to six times higher than those for SG in one piece. The higher PDF values for the road transportation than for the waterway transportation result from an inspector checking the packaging for only two minutes per day being considered a crew member for waterway transport in the RADTRAN 6 model, while a driver for road transportation, exposed during the whole transport operation, is assumed to be a crew member [

32].

On the other hand, the higher general PDF values for the processed SG transportation/handling for receptors T1, T2 and H than those for SG in one piece can be attributed to

${N}_{trans}$ which have values of 27

${y}^{-1}$ for the segmented SG transportation and 24.3

${y}^{-1}$ for smelted SG because the loading limit of the container is 20 ton so that 540 ton of segmented objects are transported in 27 times, and 486 ton that are partitioned to the ingot mass (90%) of smelted objects are transported in 24.3 times. Furthermore, although the dose rate at 1 m from the container containing smelted SG is higher than that containing segmented SG for Co

^{57}, Co

^{60}, Nb

^{94} and Ru

^{106} given in

Table 4, the general PDF values for segmented SG are higher than those for smelted SG due to the

${N}_{trans}$ mentioned in the previous paragraph. Thus, the effect of

${N}_{trans}$ is greater than that of the concentrated radioactivity concentration of the ingot.

However, for waterway receptor, T3,

${N}_{trans}$ is the same whether the transportation of SG in one piece or in the container including processed objects. Therefore, the general PDFs for SG in one piece is higher than that for the containers with processed objects, which conforms to the relative magnitudes of the dose rate at 1 m from package calculated in this study (see

Table 4).