ML17089A231

30441R00022, Revision B, Source Term Analysis Design Calculation Report.

ML17089A231
Person / Time
Site:	University of Missouri-Columbia
Issue date:	01/27/2017
From:	Cluggish B, Ellis C General Atomics
To:	Office of Nuclear Reactor Regulation, Nordion (Canada), US Dept of Energy, National Nuclear Security Admin, Univ of Missouri - Columbia
References
DE-NA0002773 30441R00022, Rev B
Download: ML17089A231 (45)

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ATTACHMENT 5 30441R00022 Revision 8 REACTOR-BASED MOLYBDENUM-99 SUPPLY SYSTEM PROJECT SOURCE TERM ANALYSIS DESIGN CALCULATION REPORT Prepared by General Atomics for the U.S. Department of Energy/National Nuclear Security Administration and Nordion Canada Inc.

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ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B REVISION HISTORY Revision Date Description of Changes A 240CT16 Information Release Revised to include only in-pool source terms, incorporate MURR B 27JAN17 comments, and reflect changes to temperature and gap gas POINT OF CONTACT INFORMATION PREPARED BY:

Name Position Email Phone Brian Cluggish Scientist brian.cluggish@ga.com 858-676-7162 Chris Ellis Engineer chris.ellis@ga.com 858-455-3141 APPROVED BY:

Name Position Email Phone B. Schleicher Chief Engineer Bob.Schleicher@ga.com 858-455-4733 K. Murray Project Manager Katherine.Murray@ga.com 858-455-3272 K. Partain Quality Engineer Katherine.Partain@ga.com 858-455-3225 DESIGN CONTROL SYSTEM DESCRIPTION R&D DISC

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QA LEVEL SYS DV&S D DESIGN D T&E N I N/A D NA ii

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B TABLE OF CONTENTS REVISION HISTORY .................................................................................................................... ii

• POINT OF CONTACT INFORMATION ........................................................................................ ii DESIGN CONTROL SYSTEM DESCRIPTION .........................*....*.............*.*....*..*.*.....*.......*..... ii ACRONYMS ............**.............................*...............*...........................*....*.*.........*.........*.............. v 1 INTRODUCTION ...............................................*..............*.*....**..*..*........**.......*................ 1 2 APPLICABLE DOCUMENTS .**...*.................................................................................... 2 3 SCOPE AND OBJECTIVES ...*......................................................................................... 3 4 SOURCE TERMS ...........*...........*...............................*.......*............................................* 4 4.1 Methods ..................................................................................................................... 4 4.1.1 Total Nuclide Inventory at the End of Irradiation ............................................... 4 4.1.2 Nuclide Inventory in the Hottest Rod at the End of Irradiation ........................... 6 4.1.3 Post-Irradiation Evolution of the Nuclide Inventory ............................................ 6 4.1.4 Nuclide Inventory in the Gap Gas of the Hottest Rod ........................................ 7 4.1.5 Decay Heat for the Hottest Rod ....................................................................... 11 4.1.6 Post-Irradiation Total Nuclide Inventory and Decay Heat ................................ 17 4.2 Inputs ....................................................................................................................... 18 4.2.1 Operating Conditions ....................................................................................... 18 4.2.2 Geometry ......................................................................................................... 19 4.2.3 Power Density and Temperature Profiles ........................................................ 19 4.3 Results ....................................................................................................................21 5 MARGINS AND UNCERTAINTIES ................................................................................ 24 6

SUMMARY

...*...*......*....................*......*.....*.*............*..*.........*........................................*25 7 REFERENCES .................................................................................................................26 APPENDIX A - CALCULATION FILES FOR MCNP6/0RIGEN2/MCODE .**...*.........*............. A-1 APPENDIX B -CALCULATION FILES FOR OTSTM ....*.......*.*..**.......*****....*..*.....*.*.*...*.....*... B-1 APPENDIX C- EXAMPLE RELEASE-TO-BIRTH RATIO CALCULATION ........................... C-1 LIST OF FIGURES Figure 1. Simplified diagram of nuclide transport in the SGE facility ........................................... 2 Figure 2. Power density profile in the hottest rod ....................................................................... 20 Figure 3. Temperature profile in the hottest rod ............................................... ,......................... 21 Figure 4. Relative uncertainty in the decay heat versus cooling time for a - irradiation ... 25 iii

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B LIST OF TABLES Table 1: MCODE input parameters ............................................................................................... 5 Table 2: Gamma source spectra (per rod) vs. time since end of irradiation ............................... 17 Table 3: Input parameters for calculating source terms .............................................................. 18 Table 4: Summary of activity summed over nuclides .................................................................. 22 Table 5: Activity of selected fission gases in the gap gas of the hottest rod ............................... 22 Table 6: Summary of decay heat results .................................................................................... 23 Table 7: Percent gamma energy deposition versus time after irradiation ................................... 23 Table 8: Decay heat absorption versus time after irradiation ...................................................... 23 iv

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B ACRONYMS Acronym Description ANS American Nuclear Society ANSI American National Standards Institute GA General Atomics LEU Low Enriched Uranium MATLAB MATrix LABoratory (software by Mathworks,lnc.)

MCNP6 Monte .Qarlo N-E.article code version §.

MCODE MCNP-ORIGEN QSpletion Program MURR University of Missouri Research Reactor NIST National Institute of Standards and Technology Isotope Generation and Depletion Code Matrix Exponential ORIGEN2 Method, version 2 OTSTM Once Through Source Term Model RB-MSS Reactor-Based Molybdenum-99 Supply System SGE Selective Gas Extraction SI Systeme International {international system of units) v

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B 1 INTRODUCTION Predicting the generation, decay, and transport of radionuclides in the Reactor-Based Molybdenum-99 Supply System (RB-MSS) is important for defining shielding, cooling, and ventilation requirements. In addition, radiation source terms are needed for analyzing the effects of potential accidents. The purpose of this document is to report the source terms (and the procedures used to calculate them) used in the design and accident analysis of the in-pool portion of the RB-MSS. It is written in accordance with the Quality Assurance Program Document for the RB-MSS project [QAPD-30441-11]. Although the RB-MSS is not a power reactor, the decay heat from the radiation sources is calculated according to ANSl/ANS-5.1-2014 [ANS 2014], and the release fractions for volatile fission products are calculated according to ANSl/ANS-5.4-2011 [ANS 2011], since these methods provide conservative estimates of the decay heat and the fission gas release, respectively. NUREG-1537 [NRC 1996] was used as a guide in presenting the source term information.

The RB-MSS generates molybdenum-99 (Mo-99) by irradiating

• target assemblies in the MURR reactor pool. Each assembly holds up to

• rods so that up to

• rods are irradiated at one time. Each rod consists of a stack of uranium oxide (U02 ) pellets enclosed in Zircaloy cladding. The initial uranium content of the rods is uranium-238 (U-238) enriched with uranium-235 (U-235).

A simplified diagram of the RB-MSS is shown in Figure 1. The blue arrows show the path of the "uranium stream," that is the uranium plus any other actinides and fission products that go with it. The uranium stream moves through the system and changes physical and chemical form but all the actinides stay with the uranium stream. The uranium stream starts off in the target rods in the reactor pool where they undergo a number of irradiation periods. The rods are then I

allowed to cool for at least hours before being removed and sent to the hot cells, labeled C1-A, C1-B, and C1-C in Figure 1. The processing of the irradiated rods after removal from the pool will be discussed in an update to this report.

1

ATTACHMENT 5 Source Term Analysis Design Calculation' Report 30441 R00022/B Figure 1. Simplified diagram of nuclide transport in the SGE facility Radioactive material is generated in the in-pool portion of the RB-MSS when the target rods are irradiated. Most of the radionuclides remain in the U02 pellets, but during irradiation a small fraction diffuse out of the pellets and into the gap between the pellet and the cladding. This report presents calculations of the radioactive source terms used in the design and accident analysis of the in-pool portion of the RB-MSS.

This report is organized as follows. The scope and objectives of this report are given in Section 3. The assumptions and methods for calculating the source terms, followed by their results, are presented in Section 4. The uncertainty in the source terms is discussed in Section 5. A summary is presented in Section 6. References are provided in Section 7.

Description of the input and output files used in the source term calculations are presented in Appendices A and B. A detailed example of the release of iodine-131 (1-131) and krypton-88 (Kr-88) from the U0 2 pellets is provided in Appendix C.

2 APPLICABLE DOCUMENTS A list of applicable documents is provided below.

2

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B 30441R00031 Quality Assurance Program Document- Phase II, Reactor-QAPD-30441-11 Based Molybdenum 99 Supply System (RB-MSS) 3 SCOPE AND OBJECTIVES The objective of this report is to present source terms for use in designing the RB-MSS. Source terms are needed for determining the radiation dose received by personnel working near the pool and shielding requirements for the transfer casks used to remove the rods from the pool.

In addition, the heat load from radioactive decay after the end of irradiation is needed for designing cooling systems for the rods in the pool.

Source terms are also needed for performing accident analysis of the RB-MSS, such as the amount of radionuclides that would be released if a rod were to break open.

To meet the needs for design and accident analysis, the calculation of the following source terms are presented in this report:

• The total radionuclide inventory and decay heat load in a full "set" of

• target rods

• The nuclide inventory and decay heat load in the hottest of the

• rods

• The nuclide inventory in the "gap gas" of the hottest rod, volatile fission products released by the U02 pellets into the pellet-cladding gap during irradiation These source terms are calculated from 0 hours0 days <br />0 hours <br />0 weeks <br />0 months <br /> after the end of irradiation, when the activity and decay heat is highest, to I hours after the end of irradiation, just before the rods are removed from the pool.

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ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B 4 SOURCE TERMS This section presents calculation methods of the RB-MSS source terms followed by their results. Section 4.1 discusses the methods used, Section 4.2 discusses the inputs to the calculation, and Section 4.3 discusses the results.

For all source terms the activity in Curies of nuclide i, Acti, is defined by the following equation:

Here Ni and .A.i are the number of atoms and the decay constant of nuclide i, and 3. 7 x 1010 is the number of decays per second per Curie.

4.1 Methods Calculation of the total nuclide inventory for

• rods at the end of irradiation was performed with the assistance of MCODE [Xu 2006, , an open source linkage-program for combining MCNP6 [LANL 2013, and ORIGEN2 [Ludwig 2002, The MCODE results were then used as the input for the Once Through Source Term Model (OTSTM) , which was used to calculate post-irradiation decay of the nuclide inventory in the

• rod set, the hottest rod, and the gap gas, as well as the decay heats.

All equations in .this section are written assuming Systeme International (SI} units, unless otherwise noted.

4.1.1 Total Nuclide Inventory at the End of Irradiation Calculation of the nuclide inventory in a set of target rods at discharge (the end of the final irradiation period) was performed using MCODE to coordinate MCNP6 and ORIGEN2. A list of the libraries used is provided in Table 1. Tables of the calculation files used are presented in Appendix A.

At the start of this coupled simulation, the thermal power in the target during irradiation, Pset*

was held constant and the neutron flux was assumed to be uniform over the entire volume of U02 target material. The following steps were alternated by MCODE to simulate a sequence of depletion (irradiation) and decay (shut down} periods:

• Depletion step: MCODE, after a series of calls to MCNP6 and ORIGEN2, updates the ORIGEN2 cross section library using the MCNP6 calculated one-group cross sections.

The MCNP6 cross section library closest to the average temperature in the target rods was used. The updated cross sections apply to nuclides contributing to at least 99.9%

4

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B of all neutron absorptions as calculated by ORIGEN2. In this method the transmutation of isotopes are consistent between MCNP6 and ORIGEN2. Additionally, MCODE iterates on the ORIGEN2 input flux in multiple calls to achieve the desired power. After the cross section library is updated and input flux is converged, MCODE calls ORIGEN2 again to perform a depletion over the time step using its full burnup chain. The depletion was for a single MCNP6 material representing the entire U02 volume within

• target assemblies* target rods).

• Decay step: Using the target material composition at the end of the previous depletion time step, MCODE calls ORIGEN2 to perform the decay calculation using its decay library. MCODE then updates the target material composition in a new MCNP6 input for the subsequent time step.

Neutron irradiation of the target rods results in the production of additional nuclides due to fission and neutron absorption. The nuclide inventory further evolves with time due to nuclear decay, as well as additional fission and neutron absorption during the depletion steps.

See Table 1 for a list of the time steps modeled and more details on the MCODE input parameters. Note that this method resets the total target power to its fresh value at the beginning of each new depletion step, when in reality the power would slowly decrease with burnup. From a source term perspective, this method will yield conservative results. The MCNP6 geometry modeled the MURR with maximum burnup driver fuel which yielded the maximum target assembly power.

Table 1: MCODE input parameters Parameter Value ORIGEN2 decay library decay.lib ORIGEN2 gamma library gxuo2brm.lib ORIGEN2 cross section library pwru.lib MCNP6 cross section library ENDF/B-Vll.1 neutron absorption fraction threshold 0.999 5

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B 4.1.2 Nuclide Inventory in the Hottest Rod at the End of Irradiation The target rods are all initially identical and the number of fission events in a set of target rods is proportional to the fission power in the set. Therefore, the nuclide inventory in the hottest target rod at the end of irradiation is obtained from the nuclide inventory of the set by using the following equation:

Here t 0 and tEoi are the time at the start of the first irradiation and at the end of the last, respectively; Nt(rod, t) and Nt(set, t) are the number of atoms of nuclide i in the hottest rod and in the full set, respectively, at a time t; and Nrod is the number of rods in the set. Note that Nt(set, t 0 ) is equal to zero except for U-238, U-235, and 0-16. In this way, the nuclide inventory in the hottest rod is calculated from O to I hours after the end of irradiation.

4.1.3 Post-Irradiation Evolution of the Nuclide Inventory The decay of the nuclides into daughter nuclides is calculated by OTSTM. This MATLAB-based program solves a generalized Bateman equation [Bateman 191 O] successively for each nuclide in each decay chain, starting with the top level nuclide and working down through the generations of daughter nuclides. The general equation is:

dN*

_i dt = -A.1Nt + I ')} ]--+!*N*J A_.F.

j Here Nt is the number of atoms of nuclide i at time t, A.t is the decay rate of nuclide i, !J--+t is the fraction of nuclides j that decay into nuclide i, and the last term is the source of nuclide i due to the radioactive decay of parent nuclides.

An analytical solution to this equation is found as follows starting with the top-level nuclide in the decay chain, which has no parent species. For that nuclide, the solution is:

N0 (t) = N0 (0) exp(-A.0 t)

Here the subscript "O" refers to the top-level parent nuclide, and N0 (0) is its number of atoms at time 0. For each succeeding generation the solution for the parent species is inserted in the equation for the daughter species, which is then solved analytically. Writing the general solution for a parent nuclide as a sum of exponential decays of nuclides k:

Ni =I k aik exp(-A.kt) 6

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B where the aik are constants, then the general solution for the daughter species is:

Ni = Ni(O)T/i + ['\'

L Jidr-*i '\' T/k - T/i]

L aik il* -il j k l k

T/i exp(-ilit), T/1r. exp(-ilkt)

Here j denotes the parents of nuclide i. Thus, the solution for the top-level nuclides can be used to find the solutions for their daughter nuclides, which can then in tum be used to find the solutions for their daughters, and so on for all succeeding generations.

Note that the solution does not diverge if il.i = ilk because:

This is accounted for numerically when calculating the number densities of the daughter species.

The decay rates and branching fraction data for each nuclide were obtained from the ORIGEN2 decay library. All 1307 nuclides in the ORIGEN2 decay library are tracked. The input and output files used by OTSTM for these calculations are discussed in Appendix B. OTSTM has been verified to have excellent agreement with ORIGEN2 in modeling radioactive decay

[Cluggishb].

4.1.4 Nuclide Inventory in the Gap Gas of the Hottest Rod At the high temperatures experienced by the rod during irradiation, almost all of the fission products are volatile and can diffuse out of the U02 pellets. The nuclide inventory in the gap gas of the hottest rod at the end of irradiation (t = 0) is calculated as:

Here Ni(gap, t) is the number of atoms of nuclide i in the gap gas at a time t after the end of the final irradiation, and (i) t is the "release to birth ratio" for nuclide i, (i.e. the fraction of atoms of nuclide i that are released from the pellets). The release-to-birth ratios are calculated according to ANSI standard ANSl/ANS-5.4-2011 as described in Section 4.1.4.1.

The nuclide inventories in the gap gas at times after the end of irradiation (t > 0) are calculated by solving the nuclide decay equations as described in Section 4.1.3. It is assumed that no further nuclides are released after the end of irradiation since the rod is much cooler and fission is no longer occurring.

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ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B Since the rods are only irradiated in the pool, the gap gas can only be released into the pool or I

after at least hours of cooling. Therefore, it is assumed that only the volatile halogen and noble gas fission products are released when the cladding is breached. Although the non-volatile nuclides in the gap are not released, they do contribute to the inventory of volatile nuclides through decay.

4.1.4.1 Release to Birth Ratios ANSl/ANS-5.4-2011 provides a method for calculating the release to birth ratio, R/B, for each nuclide. The release-to-birth ratio for a nuclide is the fraction of atoms of that nuclide that escape from the U02 matrix during irradiation. For fission products with half-lives less than 6 hours6.944444e-5 days <br />0.00167 hours <br />9.920635e-6 weeks <br />2.283e-6 months <br /> the release-to-birth ratio for the ith nuclide is calculated using equation 1 of Reference [ANS 2011], reproduced here:

Here~ is the surface area-to-volume ratio of the U02 matrix, and ai, Dt, and A.i are the precursor coefficient, diffusion coefficient, and decay rate, respectively, for nuclide i. The precursor coefficients are given in Table 1 of Reference [ANS 2011]. The diffusion coefficient in units of m2/s depends on the temperature and fission rate density in the U02 as follows [ANS 2011]:

Di= 7.6 x 10 - 11 exp ( - 35000)

T + 1.41x10- 2\1Fexp {"'i:. (

- 13800)

T + 2x10 - 4 °F.

Here T and ft are the highest temperature (in Kelvin) and fission rate density (in fissions/m 3/s) reached in the U02 during irradiation. The fission rate density is related to the power density, h, by:

. h F=-

Er Here Er is the recoverable energy per fission event. Reference [ANS 2011] specifies that l

Er = l.Ox10107l J =200 MeV.

The surface to volume ratio depends on the temperature as follows [ANS 2011]:

~ _ {120 cm- 1 T :::;; Tlink

- l V 650 cm- T > Tunk 8

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B Here Tunk is temperature at which the fission gas bubbles are assumed to become interlinked on the U02 grain boundaries allowing the gas to be released. It depends on the burnup as follows [ANS 2011]:

9800 Tlink = ln(l 76Bu) + 273 Bu~ 18.2 MWd/kgU

{

1434-12.85Bu + 273 Bu> 18.2 MWd/kgU Here Bu is the burnup in megawatt days per kg of initial uranium. It is calculated as follows:

Bu (MWd) = h (~) trun(days) kgU Mu/nR~L Here the power density is specified in MW/m3 , trun(days) is the total irradiation time in days, Mu is the initial mass of uranium in a rod in kg, Rp is the radius of the pellets, and L is the total height of the stack of pellets in the rod.

For nuclides with half-lives between 6 hours6.944444e-5 days <br />0.00167 hours <br />9.920635e-6 weeks <br />2.283e-6 months <br /> and 60 days the release-to-birth ratio is calculated using equation 3 of [ANS 2011 ], reproduced here:

Here <<asm.Kr and ilasmKr are the precursor coefficient and decay rate, respectively for metastable Kr-85.

Longer lived nuclides are not covered by ANSl/ANS-5.4-2011. Their release-to-birth ratios are estimated using the following formula:

Here coth is the hyperbolic cotangent function and µ is a dimensionless constant This is the solution to the Booth equation given in equation 3 in the Foreword of [ANS 2011), except that for long lived nuclides ili has been replaced by 1/4-un. since the escape of the nuclides from the pellet is limited by the total run time rather than radioactive decay.

Since the diffusion coefficient and surface-to-volume ratio at a given point in a target rod depends on the temperature, T, and the fission rate density, F, at that point, the average 9

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B release-to-birth ratio for a rod must be calculated by integrating the local, power density weighted, release-to..birth ratio over the rod and then dividing by the total power in the rod:

R

(-)i =

2rr f0Rv rdr R

I: dz h(r,z)

L

(~). (r,z) 1 B 2rr f0 P rdr f0 dz h(r, z)

Here rand z are the radial and axial coordinates in the rod, respectively, and Rp and Lare the radius of the pellets and the length of the rod, respectively. The power density, h(r,z), is included in the integral because the local rate of production of fission products is proportional to the local power density.

The temperature profile in a target rod is calculated as described in 30441R00021. The heat equation is solved in steady state using the power density calculated by ORIGEN2, the temperature dependent thermal conductivity of U02 , and the temperature dependent heat flux in the pellet-cladding gap.

The procedure used to calculate the release-to-birth ratios in the hottest rod at the end of irradiation is as follows:

1. A cylindrical grid is overlaid on the rod, with Nr equally spaced nodes in the radial direction and Nz equally spaced nodes in the axial direction.

2. The temperature at each grid node, T(r, z) is calculated as described in 30441 R00021.

3. The fission rate density, F(r, z) and burnup, Bu(r, z) are calculated at each point on the grid.

4. The release-to-birth ratio for fission product i at each grid node, (i). (r, z) is calculated l

for each fission product using the procedure set out in ANSl/ANS-5.4-2011. The local burnup and temperature are used to obtain the interlinkage temperature and then the surface-to-volume ratio of the U02 . The local temperature and fission rate density are used to calculate the diffusion coefficient.

5. A factor of 5 conservatism (recommended in Section 8 of ANSl/ANS-5.4-2011) is applied to (R/B) at each grid node.

6. The rod averaged release fraction is then obtained by integrating over the volume of the rod. The integral is performed using trapezoidal integration.

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ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B A detailed example calculation of the net release-to-birth ratios for 1-131 and Kr-88 is presented in APPENDIX C.

4.1.5 Decay Heat for the Hottest Rod The decay heat for the hottest rod is calculated by OTSTM as set out in standard ANSl/ANS-5.1-2014 [ANS 2014]. ANSl/ANS-5.1-2014 defines 4 contributions to the decay heat:

1. Pd., the base decay heat from fission products

2. Pde* the decay heat correction due to neutron capture by fission products during irradiation

3. PdHE* the decay heat due to the heavy element nuclides U-239 and Np-239

4. PdA, the decay heat due to other actinides Items 1 and 3 are proportional to the fission power, whereas items 2 and 4 increase slightly more rapidly with increasing fission power than items 1 and 3.

The MCODE/MCNP6/0RIGEN2 calculations discussed in Section 4.1.1 indicate that over 99%

of the fission events during a I week irradiation are due to U-235 fissions. Therefore, for purposes of calculating the decay heat, we assume that all the fission power comes from U-235 fission. As recommended in Section C of Reference [ANS 2014] the energy released per fission event is set at Er = 200 MeV.

The decay heat is calculated as described in the standard; no alternate models are used. Also, to be conservative, the expression for the neutron flux and neutron absorption cross sections recommended in the standard are used, rather than those calculated with MCNP6 for the calculations described in Section 4.1.1. Because the irradiation time for each batch of rods is fairly short and the removal of Mo-99 from the pellets proceeds quickly, the anticipated operating conditions for the RB-MSS are well within the limits given in Reference [ANS 2014].

These limits include: less than 3 fissions per initial fissile atom, less than 4 years of operation, and less than 1010 seconds of cooling time after irradiation.

Combining equations 2 and 3 of Reference [ANS 2014] gives the following formula for the base fission product decay heat:

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ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B Nil"r tci =t + I k=i+l (tirr,k + toff,k)

Here Prod is the fission power in the hottest rod, tci is the cooling time after the ith irradiation, Nirr is the number of irradiations, tirr,i is the length of the ith irradiation, t 011 ,i is the time the reactor is shut down before the ith irradiations, t is the cooling time after the final irradiation, and the a1 and A.1 are fitting coefficients to empirical decay heat data. The values of the a1 and il.1 are given in Table 5 of Reference [ANS 2014]. Note that there is no sum over fissionable nuclides because we assume that 100% of the fission power comes from U-235 fission. The uncertainty in Pd. is calculated using the same formula as for Pd. itself, except that the factors of a1 are replaced with factors of p1, which are fitting coefficients given in Table 5 of Reference

[ANS 2014]. The other terms in the decay heat calculation are defined such that they do not contribute additional uncertainty.

For cooling times less than 10,000 seconds after the final irradiation the fission product decay heat due to neutron capture by fission products during irradiation is given by equation 13 of Reference [ANS 2014], reproduced here:

Pdc(t) = P~(t)G(t)

The factor G(t), which accounts for neutron capture in fission products, is given by equation 14 of Reference [ANS 2014], reproduced here:

G(t) = (3.24 x 10-6 + 5.23 x 10-10 t)T 0*4 1J1

'l" =I i (tirr.i + toff,i)

Here T is the total time from the beginning of the first irradiation to the end of the last and 1J1 is the number of fissions per U-235 atom, which is calculated as:

Here ft' is the fission rate density defined in Section 4.1.4.1, trun is the total irradiation time, mu235 is the atomic mass of U-235, and e is the initial U-235 enrichment in percent. This equation gives a value of 1J1 about 1% higher than the formula provided in equation C.6 of Reference [ANS 2014].

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ATTACHMENTS Source Term Analysis Design Calculation Report 30441 R00022/B For cooling times greater than 10,000 seconds after the final irradiation the fission product decay heat due to neutron capture in fission products is given by equation 22 of Reference [ANS 2014), reproduced here:

Here Pdcs is the correction due to neutron capture by Cs-133, and PdE is the contribution to the decay heat from neutron capture for the remaining fission products. Combining equations 15-20 of Reference [ANS 2014) gives the following expression for Pdcs:

Pdcs(t)

Prod

= -E f Y3E4A.4 exp(-A.4t) h+

1 - a4 4 0"4 a3 - a4

+ A.

CT3 CT4

}

a3 = exp(-cr3<1>Trun) a4 =exp(-A.4Trun - CT4<l>Trun)

Here Y3 is the effective cumulative fission yield of Cs-133, E4 is the energy per decay for Cs-134, A.4 is the decay constant for Cs-134, cr3 and cr4 are the neutron absorption cross sections for Cs-133 and Cs-134, respectively. Values for these quantities are given in Section 4.4.2 of Reference [ANS 2014). Also, is the effective neutron flux during irradiation.

The effective neutron flux is calculated using equation 18 of Reference [ANS 2014), reproduced here:

<t> = 104 (z.ss x 1013 _!.___)

Eef f Here Eetf is the effective enrichment (as defined in Section 4.4.2 of ANSl/ANS-5.1-2014), S is the specific power density in units of megawatts per ton of initial uranium and h is the power 10 density. The factor of  : in the formula for S converts it from Watts per kilogram to megawatts 10 per ton, and the factor of 104 in the formula for <t> converts it from n/cm2/s to n/m2/s. Note that this approximation gives a value of the neutron flux

• times higher 'than the more detailed modeling of the RB-MSS by MCODE and MCNP6. Nonetheless, the ANSl/ANS-5.1-2014 method is used in calculating the decay heat because it is more conservative.

The contribution to the decay heat from neutron capture for the remaining fission products (other than neutron capture by Cs-133) is calculated using equation 21 of Reference

[ANS 2014), reproduced here:

13

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B PdE(t) = Pd_(t)H(t)

Here His a constant interpolated from the values given in Table 13 of Reference [ANS 2014].

The decay heat of U-239 and Np-239 for one irradiation period is calculated using equations 23 through 25 of Reference [ANS 2014]. Combining those equations and summing over irradiation periods gives the following expression for PdHE:

Here, Eu and ENp are the average energies from the decay of one atom of U-239 and Np-239, respectively; and .ilu and .ilNp are_ the decay constants for U-239 and Np-239, respectively.

Values for these quantities are given in Section 5.1 of Reference [ANS 2014]. The parameter R is the atoms of U-239 produced by U-238 capture per fission evaluated at the time of shutdown, and is calculated using the following equation:

0"230<1> Er 1 - e/100)

R = n 238 - - .- = 10 ( 2.58 x 1013 u 238 F mu Eerr n238 = 2 Mu nRpLmu236

(

1--

E )

100 Here n 238 is the number density of U-238 atoms, mu238 is the atomic mass of U-238, and u 238 is the U-238 atomic cross section for neutron capture. A value of u 238 = 2.7 barns is given in Table C.2 of Reference [ANS 2014]. This value is - the cross-section calculated by MCNP6 for the source term calculations discussed in Section 4.1.1; nevertheless, the larger value from ANSl/ANS-5.1-2014 was used in order to be conservative. Using these equations with the expected values of Er = 200 MeV and e = gives R = -

• Note that both

and ft are proportional to the power density, but R is independent of power density.

The decay heat of the other actinides is calculated using equation 26 of Reference [ANS 2014],

reproduced here:

10-4 A(t)Bua(t)]

PdA(t) = Pd(t) [- - - - -

Eeff a(t) =1.5 exp (- 1: 9 8) 14

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B B _ s )'""Tun U .= ( 1000 tda;y Here Bu is the uranium burnup in units of gigawatt days per ton of initial uranium (with S in units of megawatts per ton), tda;y is the number of seconds in a day, and A is obtained by interpolating from the values given in Table 14 of Reference [ANS 2014].

The procedure used to calculate the decay heat in one rod irradiated Nirr times at a time t after the final irradiation is as follows:

1. The uncorrected fission product decay heat is calculated for the each irradiation.

2. The decay heats for the individual irradiations are added up to get Pd., the uncorrected, fission product, decay heat for the Nirr irradiations.

3. A cylindrical grid is overlaid on the rod, with Nr equally spaced nodes in the radial direction and Nz equally spaced nodes in the axial direction.

4. The specific power density, S, neutron flux, , number of neutron captures per fission, R, number of fissions per U-235 atom, t/J, and burnup, Bu, are calculated at each grid node as shown above.

5. The neutron absorption correction to the decay heat density, hde* and the decay heat densities from U-239 and Np.,-239, hdHE* and other actinides, hdA, are calculated at each node on the grid.

6. The total decay heat in the rod, Pdt* at time t is obtained by integrating the eorrected decay heat densities over the volume of the rod:

Pde= 2n LRP rdr LLdzhde(r,z)

PdHE = 2n LRp rdr LL dzhdHE(r, z)

Rp LLdzhd.A(r,z)

Pd.A= 2n L rdr 0 0 Pd 1 (t) = Pd.(t) + Pde(t) + PdHE(t) + Pd.A(t)

Here Pde* PdHE* and Pd.A are the corrections to the decay heat due to neutron capture by fission products, Np-239 and U-239, and the other actinides, as defined in Reference [ANS 2014]. The integrals are performed numerically using trapezoidal integration.

15

ATTACHMENTS Source Term Analysis Design Calculation Report 30441 R00022/B 4.1 ..5.1 Correction due to gamma ray escape During in-pool cooling, not all of the decay heat in the target rods is absorbed in the U02 . Some of the gamma rays escape from the rods and are absorbed in the surrounding water.

The decay heat absorbed in a target rod, Pabs* is given by the following equation.

Pabs = [1- fy + frfabs]Pd1 Here fy is the fraction of the decay heat due to gamma emission, labs is the fraction of decay heat due to gamma emission that is absorbed in the rod, and Pdi is the decay heat in one rod.

The fy parameter was obtained from the ORIGEN2 output files produced from the calculations described in Section 4.1.1. Obtaining labs also requires data from the ORIGEN2 output files, in addition to a separate MCNP6 model. In this model, calculations were performed using the F6 (energy deposition) tally. The geometry modeled was a single target rod centered within a 1 meter radius sphere of water. Only photons (gammas) were tracked in the model. The nuclide inventory in the rod was obtained at multiple time steps by taking the ORIGEN2 output concentrations and dividing by

• to get the value for a single rod. The gamma ray source definition (the SDEF card) was also obtained from the ORIGEN2 output files. The spectra of the gamma ray source at 5 different times after the end of irradiation are provided in Table 2. The gamma ray source includes the contribution of fission products plus actinides and .daughters.

The MCNP6 cross section library used the 2012 continuous-energy photoatomic data from ENDF/B-Vl.8 (library name mcplib84). It was assumed that 100% of the gammas originate in the U02 - target clad activation was neglected and assumed to be small.

16

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B Table 2: Gamma source spectra (per rod) vs. time since end of irradiation Mean Energy (MeV) 1.000E-02 2.500E-02 3.750E-02 5.750E-02 8.500E-02 1.250E-01 2.250E-01 3.750E-01 5.750E-01 8.500E-01 1.250E+OO 1.750E+OO 2.250E+OO 2.750E+OO 3.500E+OO 5.000E+OO 7.000E+OO 9.500E+OO 4.1.6 Post-Irradiation Total Nuclide Inventory and Decay Heat The post-irradiation nuclide inventory of the

• rod set is cb1culated by scaling from that of the hottest rod by inverting the equation in Section 4.1.2, which bives:

Here t ~ tEoI is the post-irradiation time at which the nuclide inventory of the set is to be calculated.

The decay heat is proportional to the fission power. Since the pre-irradiation decay heat is negligible, the total decay heat for the. rod target, Pdset* is obtained by multiplying the decay heat generated in the hottest rod by the ratio of the total fission power to the power in the hottest rod:

17

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B 4.2 Inputs This section describes the numeric inputs used in calculating the source terms. The input

• parameters are summarized in Table 3 and further described in the subsequent sub-sections.

Table 3: Input parameters for calculating source terms Parameter Down time between irradiations, t 0 Number of weeks of irradiation, N,.

Initial mass of uranium in 1 rod U-235 enrichment, e Number of radial nodes in rod rid, N, Number of axial nodes in rod rid, N, 4.2.1 Operating Conditions To be conservative, the operating conditions that would produce the highest radioactivity and decay heat terms were used in calculating the source terms. The linear fission power density, Pi. profiles in each of the* rods in the two target assemblies, as well as the total fission power in each rod, Prod* and in the two target assemblies, Pset* has been calculated over the complete range of expected operating conditions for the RB-MSS [30441R00031]. This data was used in choosing the following conservative operating conditions:

1. The source term activity of the target rods at the end of irradiation is approximately proportional to the bumup, so the maximum value of the fission power was conservatively used. For two target assemblies containing* target rods, the maximum expected fission power is calculated to be._ kW, with the power dropping slowly with time [30441R00031]. To be conservative and account for uncertainty, two standard deviations ~ kW) were added to this maximum power and the drop in power with time was neglected. Therefore, the source term was calculated assuming a constant fission power of Pset =- kW during each irradiation.

2. To maximize the gap gas activity, the linear power density profile from the operating conditions that give the highest expected linear power density was used as the linear power density profile for the hottest rod. This produces the highest temperatures and therefore the highest release-to-birth ratios. Including two standard deviations of uncertainty, the expected peak linear power is PL = - kW/m and the power in the 18

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B hottest rod is Prod= - kW [30441R00031]. Note that these values of PL and Prod are higher than the values in the hottest rod at the highest maximum total power and so are doubly conservative. Furthermore, the temperature profile was calculated under the assumption that the cooling water flow was at 85% of the nominal rate for the entire I week irradiation, which gives higher temperatures in the rod.

3. Under normal operation, up to* target rods are expected to be irradiated for I weeks at up to

• hours per week. However, occasionally a batch of rods may be irradiated for I weeks Therefore, to be conservative, the source terms were calculated for a

• rod set that undergoes Nirr = I irradiations, each tirr =- hours in length and separated by shut down periods of duration toff =I hours. The total irradiation time is trun = ltirr =-hours. days).

4.2.2 Geometry All of the target rods are identical. The U02 pellets in the rods are and have a radius Rp = *

• lo of theoretical density mm. Each pellet is fabricated from uranium enriched to E = -

U-235 wt. %. The stack of pellets in each rod is of length L =

• m. The total initial mass of The effect of variations in the density and enrichment of the pellets is accounted for in the

- kW of uncertainty in the target power. Furthermore, since the target power is fixed at

. . kW, changes in the density and enrichment have a negligible effect on the calculated source terms.

For the gap gas and decay heat calculations a numerical grid is imposed on the stack of pellets.

The grid has Nr = 25 equally spaced radial grid points and Nz = 51 equally spaced axial grid points.

4.2.3 Power Density and Temperature Profiles The power density profile used for the hottest rod is shown in Figure 2 [30441 R00031, 30441R00021]. The power density is essentially proportional to the neutron flux.

19

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B Figure 2. Power density profile in the hottest rod The power density is slightly lower along the centerline of the rod due to the neutron self-shielding effect.

The temperature profile in the target rod is needed for calculating the fission gas release. The temperature profile for the hottest rod is shown in Figure 3 [30441R00021]. The temperature is highest where the linear power density is highest.

20

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B Figure 3. Temperature profile in the hottest rod The volumetric-average temperature in the hottest rod is . . K. For this reason, the MCNP6 1200 K cross section library was used in calculating the total nuclide inventory. Cross section temperature dependence becomes less significant at temperatures above 1200 K, therefore the cross sections are appropriate for source term calculations during irradiation.

4.3 Results The total activity and decay heat in a set of

• rods and the hottest rod are shown in Table 4 at 0 to I hours after the end of irradiation. The total activity of the set decreases by a factor of 5 with I hours of cooling, and the activity of the set is - times larger than the hottest rod.

21

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B Table 4: Summary of activity summed over nuclides Time (hours) t--~~~~~.~~~~~--t-~~~

• Rod Total (Ci)

'----~-+-~~~

Hottest Rod (Ci)

---

'-~~~

I I

I Tables of the activity per nuclide for the* rod set, the hottest rod, and the halogens and noble gases in the gap gas are provided in the spreadsheet that accompanies this document

[Cluggish 2016c].

The activity of the most important nuclides in the gap gas of the hottest rod is shown in Table 5, with the total activity of all halogen and noble gas isotopes shown in the last row. Note that the activities of 1-132, Kr-85, and Xe-135 are higher at I hours than at 0 hours0 days <br />0 hours <br />0 weeks <br />0 months <br /> due to the decay of Te-132, Kr-85m, and 1-135, respectively. Also, the sum of the individual activities in Table 5 is slightly lower than the total Br, I, Kr, and Xe activity shown in Table 5, because some minor, short lived nuclides are not included in Table 5. The activity of the gap gas is much smaller than the whole rod, but decreases relatively slowly due to the production of 1-132 by the decay of Te-132.

Table 5: Activity of selected fission gases in the gap gas of the hottest rod Fission Product Half-life RIB Activi hrs 1-131 8.041 d 1-132 2.3 h 1-133 20.8 h 1-134 52.6m 1-135 6.611 h Kr-85 10.72 Kr-85m Kr-87 Kr-88 Kr-89 3.17m Kr-90 32.32 s Xe-133 5.245 d Xe-133m 2.19 d Xe-135 9.089 h Xe-135m 15.29 m Xe-137 3.83m Xe-138 14.17 m Xe-139 39.5s Total Br, I, Kr, Xe 22

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B The total decay heat of the set of* rods and that of the hottest rod are shown in Table 6 at O to I hours after the end of irradiation. The decay heat decreases by a factor of 10 during I hours of cooling.

Table 6: Summary of decay heat results Time (hours)

I I

Rod Total (W)

Hottest Rod (W)

I I

The fractions of the gamma heat absorbed in the U02 , cladding, and cooling water are provided in Table 7. The table shows that of the total gamma energy generated in the U02 about

• is deposited in the target rod.

Table 7: Percent gamma energy deposition versus time after irradiation Material U02 Cladding Surrounding Water The fraction of the decay heat that comes from gammas, and the fraction of the total decay heat that is absorbed in the U02 are shown in Table 8. The symbols are defined in Section 4.1.5.1.

Table 8: Decay heat absorption versus time after irradiation Quantity - - -

Fraction gamma power absorbed by U02, !abs - - -

Fraction decay heat due to gammas, f..

1------------"-'---------f-

- -+--

- -+--

Fraction total decay heat absorbed by U02, 1 - f.. + f.. !abs Decay heat generated by the hottest rod (W), Pd 1 Decay heat absorbed by U02 in hottest rod (W), Pabs This table shows that about - of the decay heat in the rods is absorbed in the U02. The rest is absorbed in the cladding or the surrounding cooling water.

23

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B 5 MARGINS AND UNCERTAINTIES The uncertainty in the fission power has been implicitly included by calculating the source terms at the nominal maximum fission power plus two standard deviations so the uncertainty in the fission power is not added to the uncertainties in the source term and decay heat calculations.

The remaining uncertainty is the statistical uncertainty in the MCNP6 calculation and the uncertainty in the decay heat.

There is statistical uncertainty in the calculation of the nuclide inventory at discharge (the end of irradiation) as calculated using MCNP6. The average standard deviation in the neutron flux and one-group cross section tallies of the MCNP6 calculations is about 2%. This uncertainty carries through to the source terms for the fission gas release.

The uncertainty in the decay heat calculated using ANSl/ANS-5.1-2014 is given by equation 7 of Reference [ANS 2014]:

( Pd l1~d_) + (l1Prod) 2 2 Prod As described in Reference [ANS 2014] the uncertainty in the fission power is implicitly accounted for in the source terms so only l1Pd. is included in the uncertainty and is calculated as described in Reference [ANS 2014] using the following equation:

Nirr 23 l1Pd(t) = P~ad LL~ exp(-iljtci) [1- exp(-il;tirr,i)]

f i=l j=1 1 Nirr tci =t + L (tirr,k + taff,k) k=i+l The P; and il; coefficients are obtained from Table 5 of Reference [ANS 2014], _and other terms are defined in Section 4.1.5. Figure 4 shows l1Pd./Pd. as a function of time since the end of irradiation. The uncertainty is about 3% immediately after the end of irradiation, dropping to about 2% for cooling times over 1O seconds.

24

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B 0.023 0.022 a_"O 0.021

.... "O a..

<J 0.02 0.019 0.018 Cooling time [hours]

Figure 4. Relative uncertainty in the decay heat versus cooling time for a - irradiation The uncertainty in the fission gas release from the pellets during irradiation (the gap gas) is difficult to quantify. For this reason, the fission gas results presented in Table 5 include a factor of 5 conservatism, as recommended in Section 8 of ANSl/ANS-5.4-2011.

6

SUMMARY

I The radionuclide inventory in a set of* target rods from 0 to hours after irradiation has been calculated using MCODE to coordinate MCNP6 and ORIGEN2. The radionuclide inventory in the hottest rod was obtained from the inventory of the

• rod set by scaling with fission power and the number of rods as described in Section 4.1.2. The radionuclide inventory of the gap gas in the hottest rod was obtained using OTSTM to multiply the inventory of the rod by release-to-birth ratios calculated according to ANSl/ANS-5.4-2011. OTSTM was then used to calculate the decay of the gap gas.

OTSTM was used to calculate the decay heat in the hottest rod according to ANSl/ANS-5.1-2014. The decay heat for the

• rod set was then calculated by multiplying the hottest rod 25

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B result by the ratio of the batch fission power to fission power in the hottest rod as discussed in Section 4.1.6. The reduction in the decay heat load in the hottest rod due to the escape of gamma rays was also obtained using MCNP6 to calculate the fraction of gamma ray power not absorbed by the rod.

All source terms and decay heat are calculated using the worst case scenarios for irradiation of the target rods I weeks of irradiation a t

• hours per week). The source term for the gap gas is calculated using the factor of 5X conservatism on the release to birth ratios, as recommended by ANSl/ANS-5.4-2011.

7 REFERENCES

[ANS 2011] "Method for Calculating the Fractional Release of Volatile Fission Products from Oxide Fuel," ANSl/ANS-5.4-2011, published by the American Nuclear Society.

[ANS 2014] "Decay Heat Power in Light Water Reactors," ANSl/ANS-5.1-2014, published by the American Nuclear Society.

[Bateman 1910] Bateman, H., "Solution of a System of Differential Equations Occurring in the Theory of Radio-active Transformations," Proc. Cambridge Phil. Soc. IS, 423 (1910).

[LANL 2013] "MCNP6 User's Manual," LA-CP-13-00634, Rev. 0, May 2013.

26

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B

[Ludwig 2002] Ludwig, S., "Revision to ORIGEN2 -* Version2.2," ORNL transmittal memo, May 2002.

[NIST 2016] "Boiling Point Data" by R.L. Brown and S.E. Stein in NIST Chemistry WebBook, NIST Standard Reference Database Number 69, Eds. P.J.

Linstrom and W.G. Mallard, National Institute of Standards and Technology, Gaithersburg MD, 20899, http://webbook.nist.gov, (retrieved August 4, 2016).

[NRC 1996] "Guidelines for Preparing and Reviewing Applications for the Licensing of Non-Power Reactors: Format and Content (NUREG 1537, Part 1)," Published in 1996 by Division of Reactor Program Management, Office of Nuclear Reactor Regulation, U.S. Nuclear Regulatory Commission, Washington, DC 20555-0001 i'

[NRC 2016] "Annual Limits on Intake (Alls) and Derived Air Concentrations (DACs) of Radionuclides for Occupational Exposure; Effluent Concentrations; Concentrations for Release to Sewerage", U.S. NRC Regulations, Title 10, Code of Federal Regulations, Part 20, Appendix B.

[Xu 2006] Xu, Z., Hejzlar, P., and Kazimi, M.S., "MCODE, Version 2.2 - An MCNP-ORIGEN DEpletion Program," Center for Advanced Nuclear Energy Systems (CANES), Nuclear Science & Engineering Department, Massachusetts Institute of Technology, Cambridge, MA, February 2006.

27

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B APPENDIX A - CALCULATION FILES FOR MCNP6/0RIGEN2/MCODE Calculation files are stored on the General Atomics (GA) Engineering ("O") Drive

(\\torna01.ga.com). Locations of files in Table 9 and Table 10 below all imply their storage in the base directory of:

The analysis was performed on the Northshore High Performance Computing (HPC) cluster (northshore.ga.com).

Table 9: Calculation files supporting source term calculation File Description File Type Location*

MCNP6 model, followed by MCNP6and source\max-44-burn-r1 MCODE inout MCODE inout Script to run MCODE modules Shell script source\run.sh Script for MCNP6 execution Shell script source\mce.sh Script to call 'run.sh' PBS script source\nshore.pbs cross sections for MURR driver MCNP6 input source\heu091 fuel cross section directory listing MCNP6 input source\xsdir decay library ORIGEN2 input source\decay.lib gamma library ORIGEN2 input source\gxuo2brm.lib cross section library ORIGEN2 input source\pwru.lib output after running mcodeout MCODE output source\INP.out module inputs for each depletion step MCNP6 inputs source\mcstepi ORIGEN2 outputs at the end of ORIGEN2 source\itx_TAPE6_Pm21101_step.OUT each depletion step outputs MCNP6 model, followed by MCODE input, for* hour MCNP6 and source-max-:44-burn-r2 gamma source spectra in MCODE input Table2 ORIGEN2 output for hour source-gamma source spectra in ORIGEN2 output itx_TAPE6_Pm21101_006.0UT Table2

• step = depletion steps from Table 1 A-1

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B Table 10: Calculation files supporting gamma absorption calculation File Description File Type Location MCNP6 model for step 6 MCNP6 input gamma\gamma-abs*

MCNP6 model for step 7 MCNP6 input gamma\gamma-abs.

MCNP6 model for step 8 MCNP6 input gamma\gamma-abs*

Script to run MCNP6 inputs PBS script gamma\run.pbs cross section directory listing MCNP6 input gamma\xsdir Step 6 output MCN P6 output gamma\gamma-abs* . o Step 7 output MCN P6 output gamma\gamma-abs* . o Step 8 output MCN P6 output gamma\gamma-abs* . o A-2

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B APPENDIX B - CALCULATION FILES FOR OTSTM OTSTM reads the input data from an Excel spreadsheet file. The input file is provided as a supplement to this report in Reference OTSTM uses the nuclear data in the ORIGEN2 "decay.lib" file listed in Table 9.

OTSTM output is in the form of an Excel file that includes the worksheets shown in Table 11.

Table 11: Description of each worksheet in the OTSTM output file Worksheet name Data contained in worksheet ReadMe Information about the OTSTM code and the output file format Parameters Input parameters, including the power density, temperature profiles, and burnup profiles Hottest Rod Activity of each nuclide and decay heat vs. time for the hottest rod Gap Gas Activity of each nuclide volatile nuclide and decay heat vs. time for the gap gas in the hottest rod. Also the release fraction for each nuclide Process step Activity of each nuclide in the batch of rods as well as the gap gas summed over all rods, at the end of the time step.

Summary Total activity and decay heat in the batch of rods as well as the gap gas summed over all rods, at the end of each process step.

Oflnterest Number of moles, activity, and decay heat vs time for some nuclides and elements of interest Gammas Shows the gamma ray power spectrum for the entire set of

• rods as a function of time The OTSTM output file is provided in Reference [Cluggish 2016e].

B-1

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B APPENDIX C - EXAMPLE RELEASE-TO-BIRTH RATIO CALCULATION This appendix presents an example the calculation of the release-to-birth ratio for two specific radionuclides, 1-131 and Kr-88, using ANSl/ANS-5.4-2011. The calculation gives the net release-to-birth ratio averaged for the hottest target rod.

The method starts with the fission power density profile in the hottest rod, h, shown in Figure 2.

The power density and the total irradiation time are used to calculate the burnup, Bu, in MWd/kgU using the following equation:

Bu (MWd) = h (~) 4-un(days) kgU Mu/rrR~L The burnup profile in the rod after a I week irradiation at

• hours per week and maximum power is shown in Figure 5.

C-1

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B Figure 5. Bumup profile at end of irradiation in hottest rod The burnup is highest in the center of the rod where the power density is highest. Next, the interlinkage temperature, Tunk* is calculated from the burnup. Since the burnup is everywhere less than 18.2 MWd/kgU, ANSl/ANS-5.4-2011 states that the following equation should be used to calculate Tunk:

9800 Tunk(K) = ln(176Bu) + 273 This is the temperature in K at which the fission gas bubbles in the U0 2 matrix are assumed to become interlinked on the grain boundaries allowing the fission gas to be released, thus increasing the theoretical surface-to-volume ratio, i.e., decreasing the diffusion distance for release. The profile of Tunk in the hottest rod (in degrees C) is shown in Figure 6.

C-2

ATTACHMENTS Source Term Analysis Design Calculation Report 30441 R00022/B Figure 6. lnterlinkage temperature profile in hottest rod at end of irradiation The interlinkage temperature is lowest in the middle of the rod where the burn up is highest.

The fission gas bubbles interlink where the local temperature, T, (shown in Figure 3) is larger than Tunk

• This is shown in Figure 7. The interlinkage temperature is exceeded in the region colored red.

C-3

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B r (cm)

Figure 7. Portion of the hottest rod where the interlinkage temperature is exceeded The surface area-to-volume ratio, SJV , of the U02 matrix is depends on whether the interlinkage rod temperature exceeds the interlinkage temperature. In accordance with ANSl/ANS-5.4-2011 ,

SJV is set to 650 cm*1 in the red region of Figure 7 and 120 cm* 1 in the blue region.

Next, the diffusivity of fission products, D, in the U0 2 matrix is determined using the following expression :

D = 7.6 x 10

-11 exp ( - 35000)

T + 1.41x10 -25 vIT.F exp -

( 13800)

T + 2 x 10 - 40.F Here we have taken the expression for D given in ANSl/ANS-5 .4-2011 and converted it to SI units so that D is given in m2/s. In addition , the radial variation in the fission power density, h, is taken into account in calculating the fission rate density, P. ANSl/ANS-5.4-201 1 assumes that h is independent of radius so that:

C-4

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B Here Pi is the fission power per unit length in the hottest rod and Rp is the radius of the U02 pellets. The same equation is used here, except that h, and therefore F, is a function of radial as well as axial position . Note that this equation can be written as:

. h F=-

Er 1

Here E1 = 1.o x 10 10 11:

J = 200 MeV is the recoverable energy per fission .

In the hottest parts of the target rods the diffusivity is dominated by the first (thermal) term . The diffusivity in the hottest rod is shown in Figure 8 as a function of position.

Figure 8. Diffusivity in the hottest rod C-5

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B The diffusivity is strongly peaked where the temperature is highest. The diffusivity profile is the same for all nuclides, but is multiplied by 2, 4, and 20 for isotopes of cesium , tellurium , and bromine, respectively.

Up until this point the calculation is the same for both 1-131 and Kr-88. However, the release-to-birth ratio, R/B , is calculated from S/V , D, and the decay constant, A., and the precursor coefficient a. The half-life of 1-131 is 8.041 days, so A.= 9.978 x 10- 7 s- 1 . Since the half-life of 1-131 is greater than 6 hours6.944444e-5 days <br />0.00167 hours <br />9.920635e-6 weeks <br />2.283e-6 months <br /> and less than 60 days, the release-to-birth ratio is calculated using Equation 3 of Reference [ANS 2011]:

_R = (a11.asmKr ) o.2s _S 1

aasmKr D

B A.aasmKr V AasmKr Here A.asmKr = 4.30 x 10- 5 s-1 and a 8 smxr = 1.31 are the decay constant and precursor coefficient for metastable Kr-85. The precursor coefficients, a, for select nuclides are given in Table 1 of Reference [ANS 2011]. 1-131 is not in this table, so its precursor coefficient is set to a =1 in accordance with Section 6 of ANSl/ANS-5.4-2011 . The half-life of Kr-88 is 2.839 hours0.00971 days <br />0.233 hours <br />0.00139 weeks <br />3.192395e-4 months <br />, so for it A. = 6. 782 x 10- 5 s* .

1 Since the half-life of Kr-88 is less than 6 hours6.944444e-5 days <br />0.00167 hours <br />9.920635e-6 weeks <br />2.283e-6 months <br /> the release to birth ratio is calculated using Equation 1 of Reference [ANS 2011]:

The precursor coefficient of Kr-88 is a = 1.03.

The values of R/B calculated with the above equations are multiplied by a factor of 5 in accordance with Section 8 of ANSl/ANS-5.4-2011, which states:

For licensing analyses within the United States, Eq. 1 for short-Jived nuc/ides and Eq. 3 for Jong-lived nuc/ides should be multiplied by 5 to obtain a bounding prediction at a 95195 tolerance level.

The release-to-birth ratio of 1-131, including the factor of 5, is shown in Figure 9 as a function of position.

C-6

ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B Nuclide =1311 z (cm)

Figure 9. Release-to-birth ratio profile for 1-131 in the hottest rod The release-to-birth ratio profile is highest where the diffusivity is highest. The steep "cliff' around the peak is due to the abrupt change in the surface area to volume ratio where the T > Tunk* shown in Figure 7. Since A. and a are independent of position , the release-to-birth ratio profile of Kr-88 has the same shape as that of 1-131 but is smaller by a factor of:

a1311AasmKr)o.zs aasmKrAaaKr = 3.39

(

A1311aasmKr aaaKrAasmKr The net release-to-birth ratio in the rod , (R/B) is calculated by performing a power density weighted integral of R/B over the volume of the U02 pellets in the rod and dividing by the total fission power in the rod as follows:

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ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B This is the equivalent of Equation 2 in Reference [ANS 2011 ]. Here Pro d = 2rr f 0 Rp rdr f: dz h.

The quantity in the square brackets is called the "weighted release-to-birth ratio." Its value for 1-1 3 1 is shown in Figure 10 as a function of position in the hottest rod .

Nuclide= 1311 Figure 10. Weighted release-to-birth ratio profile for 1-131 in the hottest rod The weighted Rf B is small on the axis of the target rod because r ~ 0 there . Therefore, most of the 1-131 that is released into the gap gas comes from locations where cm and

- cm. The weighted release-to-birth ratio profile for Kr-88 has the same shape but is a factor of 3.39 smaller.

Integrating the weighted R/B over the radius and length of the U0 2 pellets in the rod using trapezoidal integration gives a net release-to-birth ratio for 1-131 of (R/B} =-Vo. The net release-to-birth ratio for Kr-88 is (R/B} = m>!o , a factor of 3.39 smaller. The release-to-birth ratio of 1-131 is larger because its half-life is much larger.

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ATTACHMENT 5 Source Term Analysis Design Calculation Report 30441 R00022/B The numbers of atoms of 1-131 and Kr-88 in the gap gas at the end of irradiation are obtained by multiplying the numbers of atoms of 1-131 and Kr-88 in the rod by their respective (R/B).

The numbers of atoms of 1-131 and Kr-88 in the gap gas at later times are found by evolving the nuclide inventory in the gap as described in Section 4.1.3 of this report. For 1-131 , this includes the production of 1-131 by the decay of ground state and metastable Te-131 , even though tellurium is not volatile in the rod after the end of irradiation.

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ATTACHMENT 5