Buildup Factors Calculation for a 1-MeV Point Isotropic Source in Iron, Concrete, and. Water. Skyler Butler, Maria Pinilla

Transcription

1 Buildup Fators Calulation for a 1-MeV Point Isotropi Soure in Iron, Conrete, and Water Skyler Butler, Maria Pinilla Abstrat This experiment alulates the buildup fators for 1-MeV point isotropi soure of photons in three different media - iron, onrete, and water - and for three different geometries - infinite spherial, finite spherial, and inident on the surfae of a slab. Calulations are buildup fator per mean free path or optial thikness of 1-MeV photons in the test material. Results obtained orrelated well with existing data when available, and new data showed onsisteny and low unertainty. Introdution As nulear engineers, we are extremely onerned with the safe handling of radioative materials. To protet soiety, we must know the dose rate a person would reeive at any distane away from a radioative soure. We an easily alulate the unollided dose rate from a point soure at a distane using Equation 1. Unfortunately, unollided dose rate alulations grossly underestimate the dose reeived at distanes larger than a few mean free paths. Human protetion is always our most ritial onern, and therefore, underestimates are not aeptable. Sine alulating the unollided dose is easier, the total dose an be more aurately approximated by a oeffiient known as a buildup fator. Equation 1: Unollided Dose Eq. (6.13) from Textbook 1

2 A buildup fator is by definition the ratio of the ollided dose to the unollided dose. However, sine the buildup fator is dependent on the material, thikness, and geometry of the problem, many buildup fators must be alulated and tabulated for eah speifi senario. This ould be a lengthy and diffiult proess to do experimentally. Fortunately, this proess an also be done through omputer simulation using the Monte Carlo method, whih takes into aount the random nature of radiation interations and energy deposition through a medium. Buildup fators are very useful for produing quik and relatively aurate dose rate alulations for human health and safety, but an also play a role eonomially. Instead of rules of thumb that may be too onservative, whih may ause the use of more shielding material than neessary, buildup fators allow us to be muh more aurate in our estimates and make better use of resoures. MCNP Model Three different MCNP models were used to alulate the buildup fators for eah material in an infinite medium, a finite medium, and a slab shielding onfiguration. All three models share the basi MCNP ode struture of ell ards, surfae ards, and data ards with few alterations to eah model to fit its intended geometry. Eah input file began with a brief desription of the problem followed by a rough sketh of the shielding onfiguration. Next in the ode were the ell ards, whih ontain the boundary onditions and importane of eah ell as well as the density of the material within. Following ell ards are surfae ards, whih ontain planes or three dimensional geometrial boundaries used to onstrut ells. Finally, data ards ontain tally ards (or detetors), material speifiations as well as other speial MCNP features. 2

3 Figure 1: Infinite Medium Sample Geometry As seen in Figure 1, the infinite medium model onsisted of onentri spherial surfaes at eah optial thikness and one extra-large material filled shell used to approximate the results obtained in an infinite medium. Keep in mind that the optial thikness refers to the number of mean free paths from the soure to the detetor loation. Average surfae flux tallies were set to the surfae of eah shell to alulate the ollided and unollided exposure rates with the use of a dose energy ard. Figure 2: Finite Medium Sample Geometry 3

4 The finite medium ode was reated based on the previous model with a few minor hanges. Although the geometry remained the same, the large outer shell that was used for the infinite medium approximation was removed from the ode and replaed with the graveyard as seen in Figure 2. This hange allowed the tally at the outmost surfae to reord only outward flow, thus simulating finite media. A different input file was reated for eah optial thikness. To improve the statistial error assoiated with eah measurement, the onentri shell (or onion layered) struture as well as the importanes from the first model were used. Figure 3: Sample Slab Geometry The third and final MCNP model was used to alulate the buildup fators for a slab shielding onfiguration. This model had a ompletely different geometry than the previous two; planes were used to define eah ell instead of onentri spherial shells as seen in Figure 3. In this model, the importane of eah ell was alulated speifi to the geometry. Several speial features of MCNP were utilized in the ode. The Dose Energy ard was plaed under Data Cards in eah input file to perform a fluene to dose onversion. Also, sine the tallies in MCNP were modified, a Tally Comment Card was added to speify the units. A Speial 4

5 Treatment for Tallies Card was also added, whih allowed for identifying the number of ollisions. Finally, a TALLYX Input Card was inluded as required by the Speial Treatment for Tallies Card, whih was set to tally unollided and total dose rates. Problems enountered with MCNP Using MCNP for the first time was hallenging. Many of the problems enountered were easily solved, by either further reading or onsulting with veteran users of the program. One of the main problems enountered was unaeptable errors when tabulating dose rates at more than a few mean free paths. Near the outer most layers, the relative errors were well over 10%. The inside layers were quite aeptable, usually with errors of less than 1% on the losest layer to the soure. This was retified by inreasing the importane of the outer layers. This multiplied the number of partiles in eah subsequent ell to maintain a relatively stable photon population and derease the unertainty in the farther layers. Another problem enountered was not related diretly to MCNP. Sine eah tally ame with an error, and we divided the total dose by the unollided dose, the error propagation needed to be alulated. This was not initially onsidered and after it was mentioned, the topi of error propagation needed to be researhed. Of ourse, there are many resoures with this information, so this hallenge did not take long to overome. While it was an easy fix, it is worth mentioning. Also, with oding, there were oasional geometry errors and other typographial errors. Mainly, with geometry errors, elements were plaed a ertain distane away using values that referened a previous element and not the origin. This aused improperly defined ells and lost partiles. One again, this was an easy fix. Careful rereading of the ode quikly pointed out the problem. As quikly as the problem was disovered, the problem was also remedied. 5

6 Perhaps the biggest problem enountered was using the orret optial thikness. At first, book values were used. However, this was not the orret approah beause MCNP has its own ross setional data whih is used when performing alulations. To make our data ohesive, we had to get the ross setions for eah medium diretly from the MCNP program. Then we gathered the atom densities of eah material from output files and multiplied them by their respetive 1 MeV ross setion to get eah mass interation oeffiient. Then, the average mean free path for eah material was alulated by taking the inverse of eah mass interation oeffiient. All tabulated mean free paths and for eah medium are shown in table Table 1: Optial Thikness Mean Free Path Distane Equivalent Optial Thikness Iron MFP (m) Conrete MFP (m) Water MFP (m) Verifiation To verify the auray of our results we utilized Table 7.1 in the Radiation Shielding textbook by Shultis and Faw to ompare the buildup fators for an iron medium in an infinite, a finite, and a slab shielding onfiguration. A lot of the data obtained from MCNP is new data, however many buildup fators for infinite media have been tabulated previously and plaed in Appendix E of the book. Results from our MCNP runs orrelated well to urrent data with relative errors well below 10% in all ases. Tables 2-4 show the buildup fators alulated using MCNP with their 6

7 orresponding relative errors as well as the expeted book value. One important thing to note is that sine the MCNP odes were set to inlude oherent sattering, the experimental values are slightly higher than the book values. Table 2: Buildup Fators for Iron in an Infinite Medium Shielding Configuration Optial Thikness Unollided Dose Total Dose Buildup Fator Error Book Value E E % E E % E E % E E % E E % E E % E E % E E % E E % E E % E E % Table 3: Buildup Fators for Conrete in an Infinite Medium Shielding Configuration Optial Thikness Unollided Dose Total Dose Buildup Fator Error Book Value E E % E E % E E % E E % E E % E E % E E % E E % E E % E E % E E %

8 Buildup Fator Table 4: Buildup Fators for Water in an Infinite Medium Shielding Configuration Optial Thikness Unollided Dose Total Dose Buildup Fator Error Book Value E E % E E % E E % E E % E E % E E % E E % E E % E E % E E % E E % Figure 4 shows a graphial interpretation of all buildup fators alulated for eah medium. All the data points follow a smooth trend line. The graph also inludes relative error marks whih are only visible in the last measurement at a distane of fifteen mean free paths Buildup Fators for Infinite Media Iron Conrete Water Optial Thikness Figure 4: Buildup Fators for Infinite Media 8

9 Results Verifying the previously alulated buildup fators assured auray of new data. When the data is plotted as seen in Figure 5, data exhibited a smooth urve to indiate onsistent results. The error per optial thikness starts small and grows as it moves outward from the soure origin, whih is also to be expeted. Overall, there is nothing in the experimental results to indiate poor data or inorret geometry. Tables 5-7 show the alulated build up fators for iron, onrete, and water in a finite medium shielding onfiguration. Textbook data is given when available. Table 5: Buildup Fators for Iron in a Finite Medium Shielding Configuration Optial Thikness Unollided Dose Total Dose Buildup Fator Error Book Value E E % E E % E E % E E % E E % E E % E E % E E % E E % E E % E E % 26.1 Table 6: Buildup Fators for Conrete in a Finite Medium Shielding Configuration Optial Thikness Unollided Dose Total Dose Buildup Fator Error E E % E E % E E % E E % E E % E E % E E % E E % E E % E E % E E % 9

10 Buildup Fator Table 7: Buildup Fators for Water in a Finite Medium Shielding Configuration Optial Thikness Unollided Dose Total Dose Buildup Fator Error E E % E E % E E % E E % E E % E E % E E % E E % E E % E E % E E % 45.0 Buildup Fators for Finite Media Iron Conrete Water Optial Thikness Figure 5: Buildup Fators for Finite Media 10

11 At this point, the experiment deviates from spherial geometry. The point isotropi soure is inident on the surfae of a slab of varying thiknesses made of iron, onrete, or water. Tabulated results were one again onsistent with the book values provided for iron. All relative error remained under 10% and oherent sattering was one again responsible for higher buildup fator values than those available in the book. Tables 8-10 show the buildup fators alulated at eah optial thikness with their respetive relative errors. Figure 6 shows a graphial representation of the data found in Tables Table 8: Buildup Fators for Iron in a Slab Shielding Configuration Optial Thikness Unollided Dose Total Dose Buildup Fator Error Book Value E E % E E % E E % E E % E E % E E % E E % E E % E E % E E % E E % Table 9: Buildup Fators for Conrete in a Slab Shielding Configuration Optial Thikness Unollided Dose Total Dose Buildup Fator Error E E % E E % E E % E E % E E % E E % E E % E E % E E % E E % E E % 11

12 Buildup Fator Table 10: Buildup Fators for Water in a Slab Shielding Configuration Optial Thikness Unollided Dose Total Dose Buildup Fator Error E E % E E % E E % E E % E E % E E % E E % E E % E E % E E % E E % Buildup Fators for Media in Slab Configuration Iron Conrete Water Optial Thikness Figure 6: Buildup Fators for Media in Slab Configuration 12

13 Suggestions for further work Although this projet was a great introdution to a omplex and robust program suh as MCNP, there was not enough time to fully explore the many features it offers. There are an infinite number of situations one an explore with MCNP, but only ertain situations have a broad impat. One an model a speifi reator ore, and while that is very useful, it is very speifi to a single situation. Buildup fators an be applied in many instanes, and while a nulear engineer needs to perform a omplete shielding analysis to make sure radiation exposure limits are never exeeded, buildup fators are very useful in bak-of-the-envelope alulations or as validation for more omplex omputations. One partiular area we would like to explore further would be to alulate buildup fators for ylinders of varying thiknesses and materials, whih ould have appliations in the alulation of total dose rates at the surfae of asks and other storage ontainers. It would also be interesting to explore the effetiveness of stratified media as radiation shields. One ould vary layers of onrete, iron, and different omposites to obtain maximum absorption. One again, many geometries exist, so hoosing a geometry that is widely appliable is important. The same is true for materials; lead makes more sense as a shielding material than less ommon and more expensive substane suh as titanium. 13

14 Conlusion A omplete analysis of a shielding problem should be done with the best tools available. This generally means using software to run simulations like the ones performed in this experiment using MCNP. Buildup fators are straightforward and easy to alulate and an provide verifiation for more omplex alulations; aiding in the disovery of ritial errors in analysis and providing a simple way of approximating total dose from an unollided flux. In this experiment, buildup fators for iron, water, and onrete were alulated for three different shielding onfigurations: finite, infinite, and slab medium. Experimental results show good orrelation to the data present in the Radiation Shielding textbook by Shultis and Faw. All data aquired had a low relative error well below 10%. Although the buildup fators alulated were slightly larger than the values present in the book, this disrepany an be aounted for by inluding oherent sattering in all MCNP alulations. 14

15 Bibliography Works Cited Shultis, J. Kenneth., and Rihard E. Faw. An MCNP Primer. Manhattan: Kansas State University, Print. Shultis, J. Kenneth., and Rihard E. Faw. Radiation Shielding. La Grange Park, IL: Amerian Nulear Soiety, Print. 15

16 Appendix I Sample Infinite Medium MCNP Code Point 1-MeV gamma soure in infinite iron medium: Buildup-fator alulation GEOMETRY C z-axis ^ graveyard C \ \ \ \ \ \ C \ \ \ \ \ \ C Fe Fe Fe Fe Fe Fe C x > x-axis C soure C / / / / / / C / / / / / / mfp(s) large outer shell C for inf. med approx CELL CARDS imp:p=1 $ 0.5 mfp shell imp:p=1 $ 1 mfp shell imp:p=1.2 $ 2 mfp shell imp:p=2.0 $ 3 mfp shell imp:p=3.7 $ 4 mfp shell imp:p=7.4 $ 5 mfp shell imp:p=15.5 $ 6 mfp shell imp:p=34.0 $ 7 mfp shell imp:p=76.0 $ 8 mfp shell imp:p=179.0 $ 10 mfp shell imp:p=993.3 $ 15 mfp shell imp:p=70500 $ large Fe shell for inf med approx imp:p=0 $ graveyard SURFACE CARDS so $ sphere r 0.5 mfp 51 so $ sphere r 1 mfp 52 so $ sphere r 2 mfp 53 so $ sphere r 3 mfp 54 so $ sphere r 4 mfp 55 so $ sphere r 5 mfp 56 so $ sphere r 6 mfp 57 so $ sphere r 7 mfp 58 so $ sphere r 8 mfp 59 so $ sphere r 10 mfp 60 so $ sphere r 15 mfp 61 so 1000 $ large Fe sph for inf med approx DATA CARDS C SOURCES SDEF POS ERG=1.000 PAR=2 $ point isotropi 1-MeV photon soure mode p $ photon mode only nps $ number of histories to be run 16

17 ambient photon dose equiv. H*(10mm) Sv (ICRP Report 51, 1987) de E E E E E E E E E E E E E E E E E E E E E E E E E+01 df E E E E E E E E E E E E E E E E E E E E E E E E E DETECTORS F2:p $ average surfae flux tallies FT2 INC FU T $ tally: unollided & total dose MATERIALS m $ natural iron (density 7.86 g/m^3) 17

18 Appendix II Sample Finite Medium MCNP Code Point 1-MeV gamma soure in finite onrete medium: Buildup-fator alulation GEOMETRY C z-axis ^ graveyard C \ \ \ \ \ \ C \ \ \ \ \ \ C C C C C C C x > x-axis C soure C / / / / / / C / / / / / / mfp(s) CELL CARD imp:p=1.1 $ 0.5 mfp shell imp:p=1 $ 1 mfp shell imp:p=1.1 $ 2 mfp shell imp:p=1.6 $ 3 mfp shell imp:p=2.8 $ 4 mfp shell imp:p=5.4 $ 5 mfp shell imp:p=11.1 $ 6 mfp shell imp:p=23.7 $ 7 mfp shell imp:p=52.3 $ 8 mfp shell imp:p=126 $ 10 mfp shell imp:p=718 $ 15 mfp shell imp:p=0 $ graveyard SURFACE CARD so $ sphere r 0.5 mfp 51 so $ sphere r 1 mfp 52 so $ sphere r 2 mfp 53 so $ sphere r 3 mfp 54 so $ sphere r 4 mfp 55 so $ sphere r 5 mfp 56 so $ sphere r 6 mfp 57 so $ sphere r 7 mfp 58 so $ sphere r 8 mfp 59 so $ sphere r 10 mfp 60 so $ sphere r 15 mfp SOURCES SDEF POS ERG=1.000 PAR=2 $ point isotropi 1-MeV photon soure mode p $ photon mode only nps $ number of histories to be run ambient photon dose equiv. H*(10mm) Sv (ICRP Report 51, 1987) de E E E E E E-02 18

19 6.000E E E E E E E E E E E E E E E E E E E+01 df E E E E E E E E E E E E E E E E E E E E E E E E E DETECTORS F2:p $ average surfae flux tallies FT2 INC FU T $ tally: unollided & total dose MATERIALS ************************************************************ CONCRETE: ANSI/ANS-6.4.3; density = 2.32 g/m^3 Composition by mass fration ************************************************************ m

20 Appendix III Sample Slab Shielding Configuration MCNP Code Point 1-MeV gamma soure normally inident on an iron slab Buildup fator alulation GEOMETRY ^ z-axis Problem boundary ell # surfae # X > x-axis soure normal inidene void void graveyard CELL CARDS imp:p=1 $ inner void with soure imp:p=1 $ shld ell 0.5 mfp imp:p=1 $ shld ell 1 mfp imp:p=1 $ shld ell 2 mfp imp:p=1.8 $ shld ell 3 mfp imp:p=3.3 $ shld ell 4 mfp imp:p=6.5 $ shld ell 5 mfp imp:p=13.3 $ shld ell 6 mfp imp:p=28.3 $ shld ell 7 mfp imp:p=63 $ shld ell 8 mfp imp:p=154 $ shld ell 10 mfp imp:p=851 $ shld ell 15 mfp imp:p=0 $ outer void region :-91:92:-93:94:-95 imp:p=0 $ graveyard SURFACE CARDS C slab planes 20 px $ hot surfae 21 px $ 0.5 mfp surfae 22 px $ 1 mfp right fae 23 px $ 2 mfp right fae 24 px $ 3 mfp right fae 25 px $ 4 mfp right fae 26 px $ 5 mfp right fae 20

21 27 px $ 6 mfp right fae 28 px $ 7 mfp right fae 29 px $ 8 mfp right fae 30 px $ 10 mfp right fae 31 px $ 15 mfp right fae Problem boundary planes 90 px 500 $ max x plane 91 px -100 $ min x plane 92 py 500 $ max y plane 93 py -500 $ min y plane 94 pz 500 $ max z plane 95 pz -500 $ min z plane DATA CARDS mode p $ photon mode only nps $ number of histories ambient photon dose equiv. H*(10mm) Sv (ICRP Report 51, 1987) de E E E E E E E E E E E E E E E E E E E E E E E E E+01 df E E E E E E E E E E E E E E E E E E E E E E E E E MeV monodiretional point neutron soure SDEF POS ERG=1.000 PAR=2 VEC DIR= DETECTORs F2:p $ average surfae flux FT2 INC FU T $ tally: unollided & ollided dose MATERIALS m $ elemental H and atomi abundane $ elemental O and atomi abundane 21