ML20045G886
| ML20045G886 | |
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| Site: | Crane  |
| Issue date: | 07/06/1993 |
| From: | Office of Nuclear Reactor Regulation |
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| NUDOCS 9307160104 | |
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Text
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UNITED STATES 17r NUCLEAR REGULATORY COMMISSION
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WASHINGTON, D.C. 20555-0001
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SAFETY EVALUATION BY THE OFFICE OF NUCLEAR REACTOR REGULATION RELATED TO CRITICALITY SAFETY ANALYSIS OF REACTOR VESSEL GPU NUCLEAR CORPORATION THREE MILE ISLAND NUCLEAR STATION. UNIT 2 FACILITY OPERATING LICENSE NO. DPR-73 DOCKET NO. 50-320 1.0 INTRODUCTIOS GPU Nuclear Corporation (GPUN, the licensee) submitted a revised criticality analysis for the Three Mile Island Unit-2 (THI-2) reactor vessel for NRC review in a letter dated December 18, 1992 (Reference a).
GPUN also submitted additional clarifying information in a letter dated April 8,1993 (Reference b) in response to NRC staff questions (Reference c). The revised criticality analysis, performed by Oak Ridge National Laboratory (ORNL),
demonstrated that the fuel remaining in the THI-2 reactor vessel would remain subcritical during long term storage. The analysis evaluated both a static and a worst case credible accident scenario.
2.0 BACKGROUND
During the March 28, 1979 accident at TMI-2, the core was severely disrupted and some melting of fuel and cladding occurred. Approximately 99 percent of the core was removed during the defueling process which took place from October of 1985 through April of 1990.
The initial core loading consisted of 3 batches of fuel with the most enriched batch having an initial enrichment of 2.96 wt percent of U-235.
The burnup during reactor operations of 2535 mwd /MTV reduced this value to 2.67 wt percent. The batch 3 fuel was located at the core periphery and sustained less damage than the batch 1 and 2 fuel located at the core center.
A wide variety of techniques were used during defueling, including scooping, drilling, grinding, plasma cutting, grappling, and vacuuming. The sum of the accident results and the removal techniques resulted in an unquantifiable bias toward preferential removal of the batch 3 fuel. The fuel which remains is largely in the form of either once molten, resolidified masses located in the Lower Core Support Assembly (LCSA) or widely dispersed fines. Although the remaining fuel is biased to enrichment below the core average " burned" enrichment of 2.24 wt percent, localized areas of the resolidified masses may exceed this value.
In an inspection report dated June 14, 1990 (reference d),
the NRC staff directed GPUN to use a Safe Fuel Mass Limit (SFML) of 9307160104 930706 PDR ADOCK 05000320 PDR
c c
4 l,
93 kilograms (205 pounds) (based on an enrichment of 2.67 wt percent)' for fuel in the reactor vessel until an additional safety analysis was approved by the NRC staff. The SFML is the amount of fuel which can be rearranged in any geometry with any reflector and/or moderator and still remain subcritical.
The NRC staff contracted with the Battelle Memorial Institute Pacific Northwest Laboratory (PNL) to provide assistance in the review of GPUN criticality analyses for the THI-2 reactor vessel.
3.0 EVALUATION The GPUN/ORNL and the NRC/PNL criticality analyses of the reactor vessel were based on a maximum remaining fuel estimate of 1322 kilograms (2915 pounds).
The licensee submittal of February 1,1993, revised the estimate of fuel remaining in the THI-2 reactor vessel to 925 kilograms (2040 pounds) with an uncertainty of f 40 percent. This would result in an estimate of fuel remaining in the reactor vessel with a range of 555 to 1295 kilograms (1224 to 2855 pounds). This revised estimate was based on the review and conclusions of a panel of experts headed by Dr. N. Rasmussen, of the Massachusetts Institute of Technology. The revised estimate does not invalidate the GPUN/0RNL or the NRC/PNL earlier criticality analysis since the upper limit of-the February 1,1993 revised estimate is less than the value t
used in both the GPUN/0RNL and the NRC/PNL analyses.
Two prin'.ipal cases were evaluated by GPUN/0RNL and NRC/PNL; the first was a steaoy, tate condition involving the residual fuel in its current location.
The second involved an accident or earthquake scenario. The calculational models were highly conservative.. In both cases, demineralized water was assumed to be present as a moderator even though the reactor vessel is dry and steps have been taken to prevent water intrusion.
In both cases a fuel enrichment of 2.67 wt percent was assumed, although an enrichment of
'~.
2.24 percent could have been justified for all fuel located outside the core barrel. No credit was taken for diluents in either case and only minimal credit taken for poisons in the accident scenario.
Both cases' assumed optimal credible geometry, reflection, pellet size and fuel to moderator ratio.
The steady state case was modelled as a series of annular rings, which included several times more fuel than is actually present in the reactor vessel. This added an additional degree of conservatism. Both the GPUN/0RNL analysis and the independent NRC/PNL review concluded that K,,, was <0.95, indicating a substantial margin of safety to criticality.
The accident criticality analysis assumes that an earthquake, load drop from a crane or some non-mechanistic event relocates the fuel fines to the lower head of the reactor vessel. GPUN/0RNL calculated a maximum K of 0.981 using the conservative models described above.
NRC/PNL independenlTy evaluated the methodology of the licensee and found it acceptable. The PNL review (Reference e) concluded that "there is no likelihood of an unintentional criticality occurring in the THI-2 RV."
PNL independently verified these conclusions in several parametric studies of minimum slab thicknesses, minimum annular ring thicknesses, and minimum masses in the accident scenario.
/
4.0 CONCLUSION
S The GPUN/0RNL analyses indicated that the residual fuel in the TMI-2 reactor vessel would remain subcritical with an adequate margin of safety during steady state and accident conditions. The independent review and analysis performed by the NRC and PNL confirmed the conclusions of the licensee. The assumptions in the analyses were very conservative, indicating that the margin of safety is considerably largar than the calculational results indicate. The NRC staff therefore finds the GPUN criticality analysis to be acceptable.
5.0 REFERENCES
a.
GPUN letter, C312-92-2080, R. L. Long to NRC, TMI-2 Reactor Vessel Criticality Safety Analysis, dated December 18, 1992.
b.
GPUN letter, C312-93-2021, R. L. Long to NRC, Response to NRC Questions on THI-2 RV Criticality Analyses and Post-Defueling Survey Report, dated April 8, 1993.
c.
NRC letter, M. T. Masnik to R. L. Long, request for additional information re: reactor vessel fuel survey and criticality report, dated March 22, 1993.
d.
NRC Inspection Report 50-320/90-03, E. C. Wenzinger to R. L. Long, dated June 14, 1990.
e.
PNL letter w/ attached analyses, R. I. Scherpelz to M. T. Masnik, re:
THI-2 Criticality Safety Analyses, dated April 30, 1993.
Principal Contributor:
L. Thonus Date: July 6, 1993
~-
ENCIDSURE OBallelle Pacific Northwest Laboratories
~,
j Batte!!e Boulevard P.O. Bon 999 i
Richland, Washington 99352 Telephone w) 375-2454 April 00, 1000 Dr. Michael T. Masnik U.S. Nuclear Regulatory Commission Nuclear Reactor Regulation Mail Stop 11, Building 20 Washington, D.C.
20555
Dear Dr. Masnik:
I am enclosing the PNL review of the THI-2 Licensee's Criticality Safety Study. Please feel free to contact me at the above number if you have any questions or comments on this report.
S
- rely,
}
G Robert Scherpelz Senior Research Scientist Dosimetry Research Section i
HEALTH PHYSICS DEPARTHENT RIS/ag Enclosure cc:
L Thonus, USNRC R Harty, PNL
i REVIEW OF THE CRITICAllTY SAFETY ANALYSIS REPORT FOR THE THI-2 REACTOR VESSEL INTRODUCTION Criticality safety is one of the major safety issues addressed by the THI-2 Licensee as it prepares the plant for Post Defueling Monitored Storage status.
Since measurable amounts of reactor fuel containing fissile isotopes will remain in various locations of the plant, it is important to ensure that an unintentional criticality could not occur.
The licensee's approach to determining the degree of criticality safety was to first establish a Safe Fuel Mass Limit (SFML), which is a conservatively-calculated upper boundary for a mass of fuel that could not experience criti-cality under any configuration.
This limit was documented in the Defueling Completion Report (GPU Nuclear, 1990) as 140 kg UO.
Masses of fuel in various locations of the plant were compared to th$ SFML, and in nearly all cases the fuel quantities (including upper error bounds) were substantially below the SFML (GPU Nuclear, 1993). A separate criticality safety study was not necessary for any location with a quantity of fuel below the SFML, since the SFML study itself demonstrated criticality safety for that location.
The Reactor Vessel (RV) is the only location in the THI-2 plant containing a fuel mass greater than the SFML.
(The Nuclear Regulatory Commission's (NRC)
Safety Evaluation Review, USNRC,1992) recommended that a value of 93 kg may be more appropriate than 140 kg for the RV; either value would lead to the same conclu-sion, however.) The entire quantity of fuel, as reported in the final submit-tal of the Post-Defueling Survey Report, in the RV was determined to be 925 kg 370 kg (GPU Nuclear,1993). Earlier, unofficial estimates of the RV inven-tory were 652 kg (based on a video estimate) and 1322 kg (based on passive neutron measurements, before various measurement biases were identified).
Since these estimates are all greater than the SFML, a criticality safety study was performed for the RV residual fuel inventory.
The GPU study (GPU Nuclear,1992) evaluated two fuel conditions:
- 1) the Steady-State criticality condition; and 2) the Accident condition.
In the Steady-State condition, the study looked at the fuel in the configuration that currently exists in the RV. The study concluded that the configuration was not critical, and it evaluated the margin of safety.
In the Accident condi-tion, the study determined the maximum quantity of fuel that could credibly relocate into a single location in the bottom RV head, and evaluated this configuration to determine whether it could be critical. The study concluded that the Accident condition could not produce a criticality. The criticality study was performed
- ' ore the 925 kg estimate-of-record had been established for the RV fuel
_.. t o ry. Thus the study used the 1322 kg estimate for all RV criticalit3 c4culations.
The Pacific Northwest Laboratory (PNL) acted on a request from the NRC to review the GPU criticality safety studies for the RV. This report presents the findings of the PNL review. As part of its review, PNL performed several sets of calculations.
These studies are documented in Attachments 1 and 2 to this report.
STEADY STATE CRITICALITY For the steady state situation, the XSDRN-PH computer code was used to estimate the thickness of an annular cylinder of fuel, with outer diameter matching the inner wa'il of the RV and infinite in height, that would result in ak of 0.945 if it were filled with pure water. The thickness of this eu amiu.us is approximately 3.88 inches.' The target k of 0.945 used for this studyisbelowtheNRC'sacceptancecriterionof0.8whichisbasedonthe limit in the Standard Technical Specifications for spent fuel storage (USNRC 1991).
In determining the limiting thickness of fuel, the study made certain assump-tions about the nat contained 2.67wt%gr,eofthefuel.
It assumed that the uranium in the fuel U, and it assumed that other nuclides, such as Pu, were present in the fuel as a result of the reactor operation before the THI-2 accident.
For developing the cross sections used by the criticality codes, the fuel was assumed to be in the form of pellets in a dodecahedron lattice structure with a fuel volume fraction of 0.28.
After determining the thickness of a hypothetical annular ring, the study then looked at the fuel quantities estimated to remain in each of the nine zones of the RV to see how close the fuel deposits came to the 3.88-inch thickness.
For the individual zones 1-6, the study found that the fuel deposit thicknesses were far less than 3.88-inches, so each individual zone was safely below a k,,f=0.945.
For zones 6-9, the geometry was more complicated than a simple annular ring, so the KENO-V.a computer code was used to model the fuel deposits in these regions, and it found that the fuel quantities were well i
below what was required to produce a k@ed that the configuration was well of 0.945.
Finally, an analysis considered the RV as a whole and concl below a model of a 3.88-inch thick annular ring. Thus the steady-state configuration had a large margin of safety with respect to a critical condition.
It appears that proper methodology was used to assess the steady state criticality situation. The calculations showed a large margin of safety between the actual fuel deposits and the quantity of deposits required for criticality.
It should be noted that " steady state" refers to the configura-tion of the fuel in the RV, but the actual analysis assumes a dramatically i
abnormal condition: the presence of water in the RV.
Criticality cannot occur with fuel at such low fissile-isotope enrichment without moderator. Thus the study assumes that the RV is filled with water, and the study assumes that the water is pure, containing no boron or other neutron absorbers.
Precautions have been taken by the licensee to ensure that no water would inadvertently enter the RV. The steady state calculation therefore assumes that the residual fuel in the RV would be well below critical, even in_the presence of unanticipated quantities of moderating water.
2
~
/
ACCIDENTCRITICALITYANALYSIS for the Accident situation, the study looked at each zone and determined the quantity of fuel (620 kg) which could possibly, although non-mechanistically, relocate to the RV lower head region. The model assumed full flooding of the bottom head by water, that the fuel contained 0.009% boron, and that the fuel was in the form of pellets rather than powder. A parametric study was performed to test the effectiveness of these two parameters, and they found that the pellet configuration was conservative. They also found that no boron would result in k 1.
However, by using the stated assumptions, the study calculated 5yk of 0.981 for the relocated fuel.
Since the calculated valueisbelowthecr[terionk of 0.99, the study concluded that an acci-g dental fuel relocation would nit cause a criticality.
7 One of the key features of this study is determining the quantity of fuel that could relocate to the lower head. The study looked at each of zones 1-9 to determine the fraction of fuel that could be loose enough to relocate.
In the PNL review, a concern was raised about the fraction of fuel in zone 9, the lower head region, that could relocate, since it seems possible that all fuel in the lower head could be available for a relocated configuration.
In a more detailed explanation from GPU, we found that 0.6 kg of fuel would be lodged in incore instrument nozzles that are far enough from the location of the relo-cated mass of fuel to be neutronically decoupled from the mass. The fuel that is assumed to reside in the incore instrument guide tubes left suspended from the flow distributor, is also assumed to be neutronically decoupled from the relocated mass because of the vertical distance from the bottom of the RV.
Thus only 58.7 kg of fuel from zone 9 is assumed to be available for the relocated mass.
MODEllNG ASSUMPTIONS AND CONSERVATISM The criticality safety study depends on modeling the RV and internal debris, and the modeling necessarily includes some approximation.
In good engineering practice, any approximation is made with some degree of conservatism built in.
In the various safety studies that have been performed for THI-2, a number of assumptions must be made in any modeling, since there have been uncertainties associated with measured quantities, and because some aspects of the study are hypothetical. Much of the PNL review of the criticality studies has been concerned with evaluating the assumptions that must be made and the effect of -
the conservatisms that are built into the modeling.
Some of the assumptions and conservatisms that are part of the study include:
1) mass of fuel available for criticality; 2) fuel configuration enrichment in fissile material, inclusion of neutron-absorbing material (" neutron poisons"),
3 l
4 fuel density, lattice or pellet configuration; 3) neutron moderation and reflection; 4) additional neutron poisons; 5) shape and dimensions of fuel configuration; and 6) analytical bias in k,,f.
Mass of Fuel Available for Criticality The mass of fuel available for criticality is bounded by the amount of fuel that could be present in the RV. The GPU criticality study (GPU Nuclear,1992) assumed that the amount of fuel in the RV is 1322 kg, whereas their estimate of record is 925 kg, with a one-sigma error bound of 370 kg. Thus the plus-one-sigma bound of the estimate of record is 1295 kg. The criticality safety study is using a mass higher than this, which is an appropriate conservatism.
Fuel Confiouration Enrichment of Fuel in Fissile Material The criticality study needed to make an assumption about the composition of the fuel.
Fuel from different reggns of the original core contained different enrichments in U, so it was important that the study choose an enrichment that is the highest value likely to be encountered in the fuel debris. The enrichment of 2.67 wt% ggU was chosen as the highest enrichment that could be encountered. The inclusion of Pu isotopes in the fuel mixture also ensured that the quantity of fissile material would not be underestimated.
Inclusion of Neutron Poisons in the Fuel The December 1992 report included the results of a parametric study modeling the effect of boron in the fuel.
For the configuration used to model the Accident case, this study found that totally omitting boron from the fuel region would result in a k
-1.023, including 0.009% boron would give k
=0.981, and 0,.d72% boron (representative of the residual fu'e'l in the RV) would give k,, ion for a degree of conservatism.The steady state study omitted boro 0.735.
cal cu1*at The Accident study included 0.009% boron in the fuel region, which is about 10% lower than the minimum quantity of boron found in the debris samples that have been analyzed.
t 4
/
Fuel Density The bulk density of the fuel is a major concern in calculating reactivity. The model assumes that the fuel region is a mixture of fuel and water, but the assumed ratio of fuel to water is a crucial factor in determining the k of a specific configura-tion.
In a set of calculations perYormed by PNL, critical f
configurations were calculated for fuel having a bulk density of 3
3.78 g UO,/cm (the density that gave the minimum slab thickness),
and these were compared to identical configurations with fuel having a density of 2.06 g U0,/cm (the density giving the 3
smallest mass).
In every case, the lower density produced a critical configuration with a smaller mass than the similar case l
with the higher density fuel. The higher density case required about 67% more mass to produce a critical configuration than did the lower density.
The PNL comparison only used two densities, and it would be incorrect to conclude that decreasing the density always increases the reactivity. The valid conclusion is that the bulk density of the fuel is an important determinant of the reactivity of a configuration, and the study should carefully choose a reasonable value. The GPU Accident study used a fuel volume fraction of 3
0.26, which is the same as a bulk fuel density of 2'85 g U0,/cm 3
(assuming that pure UD has a density of 10.97 g/cm ).
The report states that this value,is optimized for the assumed lattice structure. This assumption is therefore conservative, because if fuel were to relocate to the bottom of the RV, it is unlikely that it would necessarily fall into a configuration with the optimum bulk density.
Lattice or Pellet Confiouration Criticality calculations must make an assumption about the configuration of the material in the fuel. The December 1992 report included the results of a study that compared a pellet-type configuration to an infinitely dilute solution of UO in water.
The dilute solution of U0, in water gave lower k,,, va, lues than the pellet configuration, so a pellet configuration was used to assure conservatism in the calculation.
PNL performed a series of criticality calculations to understand i
the effects of various assumptions in the criticality study.
In one set of calculations, the fuel was assumed to be in a rod configuration (neutronicallysimiQrtoapelletconfiguration).
In one case, the rods were assumed to have a diameter of 0.6 cm, and in another case they had a diameter of 0.254 cm. The results of these calculations are summarized in Figures I and 2 and they are explained in Attachment 2.
The.254-cm rods always required a larger mass to attain the same vnue of k,,, compared to a similar 5
Full Water Reflection,0.6-cm Rods, k-eff =0.95 U(2.67)O2 - Water, Annular Geometry, with outside diameter = 202 cm i
1000 3
l 900 l
800 700 "N
m,,,,,,,e 600
_a e
5 500
-=
y I
Min. Mass = 674 kg w
2 400
^
(Min. Mass, Bottom of Vessel, = 416 kg) 300 l
200 100 -
0
^
0 10 20 30 40 50 60 70 80 90 100 Annulus Inner Radius (cm)
Full Water Reflection,0.254-cm Rods, k-eff = 0.95 U12.67)O2 - Water, Annular Geometry, with outside diameter =202 cm 1000 900 800 700 N amanan=""
600 u
- 5
!i 500
~
=
Min. Mass = 694 kg m
E 2 400 (Min. Mass, Bottom of Vessel, = 432 kg) 300 200 100 0
O 10 20 30 40 50 60 70 80 90 100 Annulus inner Radius (cm)
O O
.~
configuration based on 0.6-cm rods. The required masses were larger by 2 to 4% for the.254-cm rods. Thus it is clear that the lattice configuration is an important consideration, and the GPU study chose a conservative configuration.
Neutron Moderation and Reflection it is certainly possible to have a critical configuration without any neutron moderation, but such a " fast" system requires a high enrichment of fissile isotopes.
For the enrichments encountered in the THI-2 fuel, neutron moderation is required to produce a critical configuration, and the amount of neutron moderation determines the reactivity of the system. The criticality studies are conservative in this respect, because both the Steady State and the Accident case assume that there is sufficient water to provide the necessary moderation to achieve maximum k
In reality, the RV does not contain water.and efforts have been t$e.n to ensure that water does not accidentally enter the RV.
The study also assumes a degree of neutron reflection, with either water or steel present to reflect neutrons escaping from the fuel region back into the fuel.
In the Accident calculation, it was assumed that 500 gallons of unborated water were present above the fuel region to provide neutron reflection. This assumption is a conservatism, since it assumes that water introduced into the RV must be sufficient to not only saturate the fuel region, but also to provide the reflecting layer.
Additional Neutron Poisons The Accident case assumed that the fuel contained 0.009% boron, but the study assumed no additional poisoning from items such as material from the control rods or internal structural material mixed in with the fuel.
It is likely that any fuel debris could contain such neutron poisoning material, which would decrease its reactivity, but no credit was taken for the presence.
As a mitigating measure for criticality safety, the licensee dumped three drums of borated glass shards into the bottom of the RV.
For the steady state study, this glass would have almost no effect, but for the Accident case, it could have a small effect that was not considered in the study.
Fuel that would relocate into the bottom of the RV would consist, to some degree, of fine particles that could drift down and settle into the spaces between the shards. These fuel particles would be neutronically separated from the larger mass of fuel that settled on the top surface of the layer of shards.
It is difficult to quantify, for the hypothetical case, what portion of the 620 kg of relocated fuel would fall into the glass shards, but any amount would have the effect of lowering k below the calculated value.
m 8
/
Lh pe and Dimensions of the Fuel Confiouration A
The Accident analysis assumes that fuel relocates from the upper regions of the RV into the lower head region, and the shape of this relocated configuration is an important determinant of the reactivity of the configuration. One important feature of the shape of the configuration is the surface-to-volume ratio, since a shape with large surface area would experience high neutron leakage and therefore lowered reactivity (this accounts for the spherical shape of the unmoderated, potentially super-critical assemblies deployed by the military).
The GPU study assumes that the relocated fuel falls into a configuration with a hemispherical bottom surface, matching the curvature of the inside of the RV, and a flat top (like the top of a slab). The hemispherical bottom ignores the presence of the glass shards in the bottom of the RV: the presence of these shards would provide a base to support the relocated fuel, giving more of a nearly flat surface for the bottom. The flat bottom would have a lower reactivity than the curved bottom.
PNL performed a number of criticality calculations for these, configura-tions. The PNL calculations investigated three basic shapes:
1) a slab (actually a short cylinder, with the outside radius matching the inner wall of the RV); 2) an annulus (similar to the slab, but with a large hole in the center); and 3) a flat top with a hemispherical bottom. The annular shape was chosen because of the greater possibility that debris falling from the inner walls of the RV would collect in a ring shape rather than a uniform slab.
In the first set of PNL calculations, the slab was compared to the annulus. This study found that the annulus could achieve a critical configuration with 40% less fuel than a similar slab, assuming that the inner gap dimension was chosen for optimal reactivity.
In the second set of PNL calculations, the annular geometry was further investigated, and it was compared to the slab with a hemispherical bottom.
Figure 3 illustrates this comparison. The shape with a hemispherical bottom could achieve a critical mass with 34% less fuel than the annular shape.
Of the three shapes investigated by PNL, the flat top with a l
hemispherical bottom required the smallest mass to achieve a critical configuration.
Thus the licensee's choice of this configuration for its-Accident analysis is conservative, since the bottom surface would be flattened by the presence of glass shards.
Analytical Bias in k;,,
All criticality studies all included an analytical bias in k,,,deling.
to account for uncertainties in the computer codes used in the mo They determined that a conservative margin of safety could be attained
)
i 9
t Full Water Reflection, O.G-cm Rods, k-eff = 0.99 U(2.67)O2 - Water, Annular Geometry, with outside diameter =202 cm 1200
=-
1000 goo N
s**
s-easse I'
n y
e 5
5 600 o
=
ca 2
Min. Mass = 807 kg
~
E E
"(Min. Mass, Bottom of Vessel, = S29 kg) 400 200 0
O 10 20 30 40 50 60 70 80 90 100 Annuius Inner fladius (cm) 9 9
by increasing every calculated value of k by 2.5%.
Thus the k,,,d in reporttdinthestudyresultsisgreaterby0.025thanthek,,,isno foun the conputer code's output. This practice ensures that there chance for the computer code's modeling methodology to introduce a non-conservative uncertainty into the study results.
CONCLUS10NS The criticality study performed for the THI-2 RV used appropriate methods for analysis. The computer codes and cross sections are all accepted by the industry as state-of-the-art, so the analysis conforms to industry conventions.
Since the steady state configuration resulted in a large margin of safety from a critical configuration, the analysis was simplified by omitting many criticality-inhibiting mechanisms.
In order to perform the study, an assump-tion was made that the RV was filled with pure, unborated water. This assumption is grossly conservative.
Thus the steady state analysis adequately demonstrates that there is no likelihood of criticality without fuel relocation.
~
The Accident analysis used a quantity of relocated fuel that could be critical under certain ideal conditions. Thus this part of the study needed to include more criticality-suppressing mechanisms, so the presence of boron was acknowledged in the fuel region.
Even so, the study still made a number of assumptions that were conservative, as described earlier in this review. With the proper use of analytical procedures and the incorporation of appropriate conservatism, this study demonstrated that there is no likelihood of an unin-tentional criticality occurring in the TMI-2 RV.
11
REFERENCES GPU Nuclear.
1990. THI-2 Defuelina Comoletion Reoort. Final Submittal. GPU Nuclear letter 4410-90-L-0012, dated February 22, 1990.
GPU Nuclear.
1992.
Criticality Safety Analysis Report for the Three Mile island Unit ? Reactor Vessel. GPU Nuclear letter from R. L. Long to U.S.
Nuclear Regulatory Commission, dated December 18, 1992.
GPU Nuclear.
1993.
Post-Defuelina Survey Report Executive Summary. of GPU Nuclear letter from R. L. Long to U.S. Nuclear Regulatory Commission, dated February 1, 1993.
U.S. Nuclear Regulatory Commission.
1991. Standard Technical Specifications for Babcock & Wilcox Plants. NUREG-26-1430.
U.S. Nuclear Regulatory Commission, Washington, DC.
U.S. Nuclear Regulatory Commission.
1992.
Safety Evaluation by the Office of Nuclear Reactor Reaulation Related to Post-Defuelina Monitored Storaae Facility Operatina License No. DPR-73. GPU Nuclear Corooration. Three Mile Tsland Nuclear Station Unit 2.
February, 1992.
12
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ATTACHMENT 1 1
i f
8
l CRITICALITY ASPECTS OF FUEL DEBRIS IN THE TMI-2 REACTOR VESSEL
.l INTRODUCTION The TMI-2 licensee has performed a detailed study of the quantity of fuel material that remains in the THI-2 facility. The results of this study
= e.nc,niled in the Defuelino Completion Report (DCR), submitted to the USNRC on February 22, 1990.
The DCR summarized fuel quantities in different locations of the TMI-2 facility, and compared these quantities to a " Safe Fuel Mass Limit" (SFML).
In most locations, the fuel quantities were substantially below the SFML levels, but in the reactor vessel, the estimated fuel quantity was above the SFML. The licensee therefore performed a criticality safety analysis for the fuel in the reactor vessel to ensure that there was no potential for a criti-cality. The licensee's study gave a k,,, of 0.945, which is below the NRC's acceptance criterion of 0.95 for fuel storage facilities.
At the request of the USNRC, PNL performed an independent study of the criticality potential in the reactor vessel.
BORATED GLASS IN THE REACTOR VESSEL Since the DCR was written, three 55 gallon drums of borated glass shards have been dumped into the reactor vessel. Although the borated shards would have little if any poisoning effect on debris accumulating on their top sur-face, they do serve to isolate residual material already in the bottom head from any fuel debris that may fall into the vessel in the future. The shards also create a larger surface area in the bottom head over which fallen debris can be distributed. Distributing a fixed amount of a given debris mixture over a larger area increases neutron leakage and thus decreases the reactivity-of' the system. However, distributing material over a larger area also pro-vides a mechanism whereby an undermoderated system can become optimally moderated and thus have a greater reactivity. Thus it is important to model the possible accumulation of fuel debris that could collect on the top surface of the debris as though it accumulated in optimum configuratio'ns.
CRITICALITY IN A SLAB CONFIGURATION The criticality calculations reported in the DCR (p 5 55, rev. 4/0496P) found that an accumulation in the bottom reactor vessel head of an optimal mixture of 500kg of core debris and water would have a k,,, of 0.921 (not including bias) when fully reflected on top by water.
Based on data in DP-1014 (Clark, 1966), the minimum critical thickness of a fully water reflected, optimally moderated slab of U(2.67)0, pellets in water is 15.2cm.. At optimum moderation the H/rasU atom ratio is 199 (for 2.67% enrichment) and the U0, bulk density is 3.78 g/cc (which closely ap-proximates the 3.38 g/cc reported in the DCR, p 5-23, for the reactor vessel debris).
The unobstructed region in the reactor vessel above the bottom head has a diameter of about 241 cm (DCR Figures 5-31, 35, 36, & 36). The glass shards, at 165 gallons, create a surface area about 208 cm in diameter across the bottom head as indicated in Figure 1.
An accumulation of optimally mod-erated mixture of U(2.67)0, and water at least 15.81cm deep on top of these shards is required before criticality would be possible.
In other words, criticality can not be achieved ur,less the thickness of a uniform slab of debris on top of the shards is at least 15.81cm. Under these conditions the critical mass is 2428 kg of U0,.
If only nominal neutron reflection is considered credible (which seems more reasonable than full reflection), the critical thickness will be slightly larger (19.83cm) and the critical mass will increase to 3163 kg of U0,.
Although the thickness of any such accumulation of debris on top of the shards must exceed either the 15.81cm (if full water reflection is credible) or the 19.83cm (if only nominal reflection is considered credible) for criti-cality to occur, criticality can occur at smaller masses than those given above - but at lower densities and larger volumes, The above masses of 2428 kg and 3163 kg correspond to the U(2.67)0, density (3.78 g UO,/cc) that results in the smallest critical slab thickness. The minimum critical mass, however, occurs at a lower density of about 2.06 g 00 /cc for 2.67% enriched 3
00. This results in a larger critical slab thickness but a smaller critical 2
mass. At a density of 2.06 g U(2.67)0 /cc, the minimum critical slab thick-2 2
4
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l 208cm 244 cm Figure 1 Reactor Vessel Diagram Showing Glass Shards and Accumulated Thickness of Optimum Moderated U (2.67) O. Water 2
39205127.1 FH 3
C ness of a fully water reflected slab of UO, in water is 15.95 cm. The minimum critical thickness of U(2.67)D,-water on top of the glass shards at this density of 2.05 g UO,/cc is about 16.74 cm and the critical mass is about 1413 kg U0,. If nominal neutron reflection is considered credible, the minimum critical thickness on top of the shards increases to 21.74 cm and the critical mass increases to about 1922 kg of UO,.
CRITICALITY IN AN ANNULAR CONFIGURATION The mass of material needed for criticality could be considerably less than that required for the slab geometry discussed above if the debris were to accumulate on top of the shards in the form of an irregular ring with water in the center region. The height of any such accumulation must, however, always exceed 15.81cm if criticality is to occur. This limit for a fully reflected, optimum moderated slab is valid irrespective of fuel density.
If the density is greater than 3.78 g U(2.67)0,/cc the critical slab thickness will be greater than 15.81cm. If the fuel density is less than 3.78 g U(2.67)0 /cc, 2
the critical slab thickness will also be greater than 15.81cm.
" Geometrical buckling" is a parameter used in neutronics calculations to describe the dimensions of a simple critical assembly. An empirical expres-sion for calculating the geometrical buckling of annular rings was developed to investigate the effects that ring geometry has on the critical size of such accumulations of fuel debris on top of the glass shards. The empirical buck-ling relationship is shown in Figure 2 along with a sketch of the annular ring model used in the calculations (note that the maximum diameter of the annular ring model used in studying these effects is 202 cm, which is slightly smaller than the diameter estimated for the top surface of the shards).
Calculated critical sizes, and corresponding masses, based on this empirical buckling expression are given in Table 1,as a function of the annulus width.
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B n Critical Buckling e
h Extrapolation Distance 39205127.4 FH Figure 2 Annular Ring Model 4
I I
I J
4.s 5
1 TABLE 1
Estimated Critical Sizes of Optimally Moderated U(2.67)0,-Water in Annular Geometry Having an Outside Diameter of 202 cm (Full Water Reflection and 3.78 g UO,/cc)
{
i Annulus Width Inner Radius Critical Height Critical Mass KENO-IV (cm)
(cm)
(cm)
(ka 00,)
k,,f 15.25*
0 INFINITE INFINITE 1.003(0.004) 25 76 28.67 1506 1.005(0.003) 1 30 71 23.12 1414 32 69 21.90 1415 35 66 20.57 1428 40 61 19.13 1472 l
45 56 18.22 1529 1.007(0.003) 80 21 16.05 1860 90 11 15.91 1904 101 0
15.84 1919 1.028(0.003)
- Critical radius of a cylinder of U(2.67)D,-water, infinite in length.
The calculated results shown in Table 1 indicate that the most favorable accumulation of fuel in an annular geometry on top of the glass shards in the reactor vessel botton head would have an annulus width of about 32 cm and contain 1414 kg of U0, at 3.78g U(2.67)0,/cc. The height of this fuel would be about 21.9 cm. These results are graphically presented in Figure 3.
Although the results presented in Table 1 yield the smallest critical size for an annual ring of fuel, a smaller mass could achieve criticality as discussed previously for a uniform slab accumulation of fuel. Calculated results are given in Table 2 for annular rings of fuel at the optimum density of 2,06 g UO,/cc corresponding to the minimum critical mass for a U(2.67)0,-water mixture.
6 1
1
.i Annuius Height, cm 14 15 16 17 18 10 10 21 22 23 24 25 26 27 28 29 30.31 2000 g
4 g
g g
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1900 1800 o3 2 1700 ei E2
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-2 1 1600 2.405 K
u=
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1500 -0 B s 0 03911577 cm 2 c
h 7.0cm 1400 n
1300 k g-0.95 e
1200
-.e,
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1 I
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20 30 40 50 60 70 80 90 100 110 Annulus Width, cm 3e205127.3 FH Figure 3 Estimated Critical Size of Optima!y Moderated U(2.67)OyWater in Annular Geometry Having an Outside Diameter of 202 cm (full water reflection and 3.78g UO /CC) 2 o
7 l
TABLE 2 Estimated Critical Masses of Optimally Moderated U(2.67)0,-Water in Annular Geometry Having an Outside Diameter of 202 cm (Full Water Reflection ar,d 2.06 g UO,/cc)
Annulus Width Inner Radius Critical Height Critical Mass KENO-IV
_ (cm)
(cm)
(cm)
(ko U0 )
k,,,
2 INFINITE O
15.95*
INFINITE 1.005(0.007) 25 76 31.75 909 1.027(0.009) 30 71 25.61 855 32 69 24.14 850 33 68 23.54 849 1
35 66 22.54 852 40 61 20.80 872 45 56 19.70 900 0.989(009) 80 21 17.10 1080 90 11 16.06 1099 101 0
16.79 1108 0.991(0.011)
- Critical thickness of a slab of U(2.67)0,-water, infinite in two dimensions.
The calculated results presented in Table 2 indicate that the minimum critical mass of fuel in an annular geometry on top of the glass shards in the bottom of the reactor vessel would be about 849kg U(2.67)0,. The annulus width would be about 33 cm with an height of 23.54 cm. These calculated results are graphically presented in Figure 4.
Since the calculated values shown in Tables 1 and 2 are based on an unverified empirical expression for the geometrical buckling of an annular ring, k,,, values were calculated using the KENO-IV computer code for a few of
_the rings as a means of verifying the validity of the buckling expression.
These calculated k,,, values are shown in the right-hand columns of Tables I and 2.
As can be seen, the critical sizes calculated,using the buckling expression agree reasonably well with the calculated k,,7 Also shown in Tables 1 and 2 are calculated k,,, values for an infinite cylinder (top entry, Table 1) and an infinite slab (top entry, Table 2) of U(2.67)0,-water. These two entries were included because the expressions for geometrical buckling for these configurations had been used in criticality 8
Annulus Height, em 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 12008 i
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1100 O
A D 1000 2
er E2 900 E
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-2
-2 800 2.405 x
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Rod-1.11 Rl+1 He+2A kg= 0.95 U = 0.009666 cm4 700 c
{
A-8.0 cm 600 20 30 40 50 60 70 80 90 100 110 Annulus Width, em 39205127.2 FH j
Figure 4 Estimeted Critical Mass of Optimaly Moderated U(2.67)O Water j
2 in Annular Geometry Having an Outside Diameter of 202 cm.
(full water reflection and 2.06 UO /CC) 2 9
.i
/
i calculations long before the empirical expression was developed. Since these values are consistent with the other entries in the table, it increases our confidence in the empirical expression.
To estimate the effect that a 5% reduction of k.fr from critical would have on the size of the annular ring, buckling conversions were made to the i
ring having the smallest volume and to the ring having the smallest mass.
For the smallest volume case, the height at a k,,, of 0.95 is 18.6 cm (1200 kg U(2.67)0,) as compared to 21.9 cm (1415 kg U(2.67)0,) at the critical con-dition. For the smallest mass case, the height at a k,,, of 0.95 is 19.16 cm (691 kg U(2.67)0,) as compared to 23.54 cm (849 kg U(2.67)0 ) at the critical 2
condition.
CONCLUSIONS Minimum Thickness: The calculations performed in this study indicate that a slab thickness of at least 15.81 cm for a U0,-water mixtur'e on top of the glass shards in the reactor vessel bottom head is required before criti-cality is possible. This slab would contain 2428 kg of U(2.67)0,, at a density of 3.78 g U0,/cc.
Minimun Mass: At a bulk density (2.06 g UO,/cc) much lower than that postulated for the reactor vessel debris (3.38g UO,/cc) only about 1413 kg of U(2.67)0, is required before criticality would be possible.
In this config-uration, the depth of debris on top of the glass shards would be greater (16.74 cm vs 15.81 cm) than the thickness for a 3.78 g/cc slab. Should the debris accumulate in the form of a well-defined annular ring on top of the shards, the massofU(2.67)0 required for criticality to be possible is further reduced to 2
about 849 kg. These values are based on full water reflection and optimum neutron moderation with respect to either volume or mass.
Limiting the quan-tity of water in the reactor vessel significantly, increases the amount of material required before criticality would be possible in the above geometries.
Potential for Criticality in THI-2 Reactor vessel: The current best i
estimate for the quantity of fuel in the reactor vessel is 609 kg. Obviously this quantity is below the minimum mass required for a criticality in a geometry that is reasonably attainable, 849 kg. The 609-kg estimate is based 10
~
on viden imaging techniques, however, and a more recent estimate using active and passive neutron measurements indicates that the inventory may be higher, possibly as much as double the 609-kg estimate.
1200 kg of UO, is more than the minimum mass required for a criticality, but 849 kg of UO, could result in a criticality only if a number of ide,a1 conditions were satisfied.
These
]
conditions require that the fuel has a density of 2.06 g/cc and it must fall into the ideal annular configuration with an annulus width of 33 cm and height of 23.54 cm. These ideal conditions also require a fully-reflecting water supply.
The calculations show that any deviations from this density, these dimensions and the reflective condition would increase the mass of fuel re-quired for criticality. Most changes in the configuration would increase the minimum required mass by a substantial amount: for example, increasing the fuel j
density to 3.78 g/cc would increase the minimum required mass to 1414 kg, which is greater than even the upper estimate of U0, mass in the reactor vessel.
Under the conditions of this study, it is incredible that the fuel re-maining in the reactor vessel could fall into a critical configuration. This fuel exists in various locations, in differing forms (surface films, loose powders, re-solidified fuel) and densities. The mechanism for bringing more than 850 kg into one location is not realistic - some of the fuel is already covered by borated glass shards and are thus neutronically isolated from additional fuel that could collect on top of the shards, and other fuel is located behind baffle plates that would prevent it from falling into the bottom head. The fuel exists in densities different than the optimum 2.06 g/cc, which also argues against the possibility of criticality.
Finally, the ability of the fuel to collect in an annular configuration with the precisely correct dimensions is extremely unlikely. Thus the PNL study supports the conclusion that there is no danger from a criticality.
11
)
^
l
\\
i REFERENCES Clark, H. K.,
1966.
" Critical And Safe Masses And Dimensions of Lattices of U And UO, Rods in Water". DP-1014. Savannah River Laboratory, Aiken South Carolina.
l I
12
F 4
ATTACHMENT 2 I
R L4 n.,
,e=
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, -,.. ~, - -
w
-.~.
}
OBalleIIe Pacific Northwest Laboratories intoma! Disttlbution SR Bierman ost.
14 October 1992 j
To R.I. Scherpelz From A.W. Prichard cut 4.et Additional Criticality Analysis for THI-2
References:
SR Bierman to R Harty; Residual Debris in THI-2 Reactor Vessel; 10 June 1992.
SR Bierman to RI Scherpelz; Additional Criticality Analysis - TMI-2; 23 July 1992.
Clark, H.K.; 1956; DP-1014;
" Critical and Safe Masses and Dimensions of Lattices of U and 00, Rods in Water"; Savannah River Laboratory, Aiken, South Carolina Reardon, W. A.; "An Approximate Buckling of Partially Filled Spheres and Application to Critical Experiments; " Physics Research Quarterly Report, October, November, December, 1963; HW-80020; 15 January 1964 In Dr. Bierman's memo to you, he indicated that your sponsor wanted several different conditions analyzed, I am responding to that request.
For the additional cases requested, I determined the minimum thickness and minimum annular mass of material to achieve the requested K-effective.
The minimum dimensions include a 2.5% bias in K-effective for consistency with previous analysis.
The Case 1 conditions are full water reflection, 2.06 g 00 /cc, 0.6 cm diameter pellets, and 2.67% U-235. The target k-effective is 0.95.
To 2
achieve the target K-effective in the bottom of the vessel, the height is 19.7 cm, the volume is 202 liters, and the mass is 416 Kg U0,.
For annulus of material the maximum diameter is 202 cm.
The minimum annulus height required for a K-effective of 0.95 is 14.5 cm, the minimum mass is 674 Kg UO.
The height, volume, and mass of several different annular regions is sh,own in Table 1.
The Case 2 conditions are identical to Case 1 except for the target K-effective.
The Case 2 conditions are full water reflection, 2.06 g UD /cc, 0.6 cm diameter pellets, and 2.67% U-235.
The target k-effective is 0.9h. To achieve the target K-effective in the bottom of the vessel, the height is 22.3 cm, the volume is 2571, and the mass is 529 Kg UD,,
For annulus of material the maximum diameter is 202 cm.
The minimum annulus height required for a K-effective of 0.99 is 16.6 cm, the minimum mass is 807 Kg 00 The height, volume, and mass of several different annular regions is sh,.own in Table 2.
M19004101(tut)
R.l. Scherpelz 14 M*cter !?02
- .;.g. 2 The Case 3 conditions are identical to Case 1 except for the pellet size.
The Case 3 conditions are full water reflection, 2.06 g U0,/ce, 0.254 cm diameter pellets, and 2.67% U-235.
The target k-effective is 0.95.
To achieve the target K-effective in the bottom of the vessel, the height is 20.1 cm, the volume is 2101, and the mass is 432 Kg U0,.
For annulus of material the maximum diameter is 202 cm.
The minimum annulus height required for a K-effective of 0.95 is 14.8 cm, the minimum mass is 694 Kg 00. The height, volume, and mass of several different annular regions is show,n in Table 3.
The Case 4 conditions are identical to Case 1 except for being reflected on the bottom by borated glass shards instead of water. The borated glass shards are treated as nominal reflector, which has a reflector saving 2 cm less than full water reflection. The Case 4 conditions are full water reflection on the tops and sides, nominal reflection on the bottom (simulation of the Boron glass shards), 2.06 g U0 /cc, 0.6 cm diameter pellets, and 2.67% U-235.
The targetk-effectiveis0.65. The maximum annulus is 202 cm in diameter. The minimum height required for a K-effective of 0.95 is 16.5 cm, the minimum mass is 739 Kg UO regions is sb. The height, volume, and mass of several different annular own in Table 4.
The Case 5 conditions are identical to Case 4 except for being unreflected.
The unreflected conditions are treated as a full reflection with 4 cm less reflector savings. The Case 5 conditions are unreflected, 2.06 g UO /cc, 0.6 cm diameter pellets, and 2.67% U-235.
The target k-effective is 0.9$. The maximum annulus is 202 cm in diameter.
The minimum height required for a K-effective of 0.95 is 20.5 cm, the minimum mass is 1044 Kg U0,.
The height, volume, and mass of several different annular regions is shown in Table 5.
The Case 6 conditions are identical to Case 4 except fo different pellet diameter.
The Case 6 conditions are full reflection on. ' tops and sides, nominal reflection on the bottom, 2.06 g UO,/cc. 0.254 cm diameter pellets, and 2.67% U-235. The target k-effective is 0.95.
The maximum annulus is 202 cm in diameter. The minimum height required for a K-effective of 0.95 is 17.1 cm, the minimum mass is 781 Kg U0. The height, volume, and mass of several 2
different annular regions is shown in Table 6.
i V
R.I. Scherpelz 14 October 1992 Page 3 Table 1.
Estimated Dimensions and Masses of U(2.67)0 - Water in an Annular Geometry having an Outside Diameter,of 202 cm. for a X-effective of 0.95 with Full Water Reflection, 2.06 grams UO,/cc, and 0.6 cm Rods Annulus Inner Width Radius Height Volume Mass (cm)
(cm)
(cm)
(liters)
(kg)
Bottom of Vessel 79.9 0
19.7 202 416 14.1 0
Infinite 25 76 24.4 339 699 26 75 23.2 334 688 27 74 22.3 330 681 1
28 73 21.4 328 676 29 72 20.8 327 674 -
30 71 20.2 327 674 31 70 19.7 328 675 32 69 19.2 329 677 33 68 18.8 330 680 35 66 18.2 334 688 40 61 17.1 347 715 45 56 16.3 363 747 80 21 14.7 450 927 90 11 14.5 460 947 101 0
14.5 463 955 Infinite 0
14.0*
Radius of an infinite cylinder of U(2.67)0 - Water at target X-effective Height of an infinite slab of U(2.67)0, - dater at target K-effective
R.I. Sclierpelz 14.0ctober 1992 D qe /
.)
?
Table 2.
Estimated Dimensions and Masses of U(2.67)0 - ifater in an
- i 4
Annular Geometry having an Outside Diameter,of i'02 cm. for
{
a K-effective of 0.99 with Full Water Reflection, 2.06 grams UO /ce, and 0.6 cm Rods j
g Annulus Inner Width Radius Height Volume
' Mass (cm)
(cm)
(cm)
(liters)
.(kg)
Bottom of Vessel 84.6 0
22.3 257 529 15.6 O
Infinite 25 76 30.6 46 877 26 75 28.8 414 852 27 74-27.3 405 835 28 73 26.1 400 823 l
29 72 25.1 396 815 30 71 24.3 393 810 31 70 23.6 392 808 32 69 22.9 392 807 33 68 22.4 392 808 i
35 66 21.5-395 813 40 61 20.0 407 838 45 56 19.0 423 871.
80 21 16.9 518 1067 90 11 16.7 529 1090 i
101 0
16.6 533 1098 Infinite 0
16.0*
l Radius of an infinite cylinder of U(2.67)0 - Water at target K-effective Height of an infinite slab of U(2.67)0, - dater at target K-effective 9
a t
1
-~
R.I. Scherpelz 14 October 1992 Page 5 Table 3.
Estimated Dimensions and Masses of U(2.67)0 - Water in an Annular Geometry having an Outside Diameter,of 202 cm. for a K-effective of 0.95 with Full Water Reflection, 2.06 grams UD,/cc, and 0.254 cm Rods Annulus Inner Width Radius Height Volume Mass (cm)
(cm)
(cm)
(liters)
(kg)
Bottom of Vessel 80.6 0
20.1 210 432 14.3*
0 Infinite 25 76 25.3 351 724 26 75 24.0 345 711 27 74 23.0 341 703 28 73 22.1 339 698 29 72 21.4 337 695 1
30 71 20.8 337 694 31 70 20.2 337 695 32 69 19.8 338 696 33 68 19.4 339 699 35 66 18.7 343 707 40 61 17.5 356 733 i
45 56 16.7 371 765 80 21 15.0 459 946
)
90 11 14.8 469 967 j
101 0
14.8 473 974 j
Infinite 0
14.2*
Radius of an infinite cylinder of U(2.67)0 - Water at target K-effective Height of an infinite slab of U(2.67)0, - dater at target K-effective 9
i
~
R.I. Scherpelz 14.0ctober 1992 rage e Table 4.
Estimated Dimensions and Hasses of U(2.67)0 - Water in an Annular Geometry having an Outside Diameter,of 202 cm. for a K-effective of 0.95 with Full Water Reflection on Top of Glass Shards, 2.06 grams UO,/ce, and 0.6 cm Rods Annulus Inner Width Radius Height Volume Mass (cm)
(cm)
(cm)
(liters)
(kg) 14.1*
O Infinite 25 76 26.4 367 757 26 75 25.2 363 747 27 74 24.3 360 742 28 73 23.4 359 739 29 72 22.8 359 739 30 71 22.2 359 741 31 70 21.7 361 743 32 69 21.2 363 747 33 68 20.8 365 752 35 66 20.2 371 764 40 61 19.1 388 799 45 56 18.3 407 838 80 21 16.7 511 1053 90 11 16.5 523 1078 101 0
16.5 527 1087 Infinite 0
16.0*
Radius of an infinite cylinder of U(2.67)0 - Water at target K-effective Height of an infinite slab of U(2.67)0, - dater at target K-effective
4 R.I. Scherpelz i
14 October 1992 Page 7 i
Table 5.
Estimated Dimensions and Hasses of U(2.67)D - Water in an r
Annular Geometry having an Outside Diameter of 202 cm. for a K-effective of 0.95 with Unreflected on Top of Glass Shards, 2.06 grams U0,/cc, and 0.6 cm Rods Annulus Inner Width Radius Height Volume Mass (cm)
(cm)
(cm)
(liters)
(kg) 18.l*
0 Infinite 25 76 84.8 1179 2428 26 75 57.4 825 1699 27 74 46.7 693 1428 28 73 40.8 624 1286 29 72 37.0 582 1200 30 71 34.3 555 1144 31 70 32.3 537 1106 32 69 30.7 525 1081 33 68 29.5 516 1063 35 66 27.6 507 1044 40 61 24.9 507 1045 45 56 23.5 521 1074 80 21 20.8 638 1315 90 11 20.6 653 1345 101 0
20.5 657 1353 Infinite 0
20.0*
Radius of an infinite cylinder of U(2.67)0 - Water at target K-effective Height of an infinite slab of U(2.67)0, - dater at target K-effective e
-.n
l 1
R.I. Scherpelz 1'OyeLee 1552
.reye o Table 6.
Estimated Dimensions and Masses of U(2.67)0 - Water in an Annular Geometry having an Outside Diameter,of 202 cm. for a K-effective of 0.95 with full Water Reflection on Top of Glass Shards, 2.06 grams UO,/cc, and 0.254 cm Rods Annulus Inner Width Radius Height Volume Mass (cm)
(cm)
(cm)
(liters)
(k )
9 14.6*
O Infinite 25 76 28.2 392 808 26 75 26.8 386 795 27 74 25.7 382 787 28 73 24.8 380 783 29 72 24.1 379 781 30 71 23.4 379 781 31 70 22.8 380 783 32 69 22.3 382 787 33 68 21.9 384 791 35 66 21.2 389 802 40 61 20.0 406 837 45 56 19.2 425 876 80 21 17.4 532 1097 90 11 17.2 545 1122 101 0
17.1 549 1131 Infinite 0
16.6*
Radius of an infinite cylinder of U(2.67)0 - Water at target K-effective Height of an infinite slab of U(2.67)0, - dater at target X-effective s
9 4
,,-r
.{
s R.I. Scherpelz 14 October 1992 Page 9 The methods used for calculating annuluses are described by Dr. Bierman in his memo to R Harty.
X, K,u2=
(1) 1+M'eB,uy g
Equation I gives the goal K in terms of M, K-infinity, and the goal B'. M,
2 2
K-infinity, and reflector savings constants (used in equation 4) were interpolated from data given in DP-1014. The goal K is the target K-effective i
minus the 2.5% bias in K-effective, the only unknown is the goal B,.
1 Rearranging equation 1 gives equation 2.
2 B
2=M'*K (2) yu3 From Bierman (June, 92), BI for annular rings of fuel is given in equation 3.
This memo indicated that equation 3 had been tested and that the results were less than 2.5% different in estimating K-effective.
2 2.'405 n
B=
(3)
R,+ A,+1.11 *Rj + A,
H+A,+A,
j 3
R = outside radius of the annulus R = inside radius of the annulus H = height of the annulus 1, = reflector savings for the inside of the annulus 1, = reflector savings for the outside of the annulus 1, - reflector savings for the top of the annulus 1, - reflector savings for the bottom of. the annulus 4
H,u3=
-A,-A3 K.-K,u y 2.405 (4)
%,Na.gy,,
R,+ A.-l.11 *Rj + Aj,
d R.'I. Scherpelz I
J9.UCLoDer 1992 l' age 10 1
Equation 4 is a result of equating B2 solving for H, the height of the annfifus(. equation 2) with B' (equation 3) and 3
The annulus height is a function of i
the inner radius and the outer radius (set a 202 cm for this analysis).
The methods used for calculating the critical buckling for partially filled
!?heret i: fr=. W.A. Reardon, which is given in equation 5.
E'= 4 0. 0 8 8 4 *R*S/ V+9. 613 6 V
(5)
R - radius of the sphere S - surface area of the partially filled sphere V - volume of the partially filled sphere P
When the dimensions of the sphere and the partially filled sphere have been G
increased by the reflector savings.
The equation orginally developed by W.A.
Reardon was for spheres more than half filled.
However, the method of development implies that the equation should apply to spheres less than half filled.
4 4
b0
..