CAL-UDC-MD-000001, Rev 00, 'Updated Calculation of ... · Document Identifier: CAL-UDC-MD-000001 REV 00 Page 5 of 23 1. PURPOSE The purpose of this calculation is to update the estimate

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Waste Package Operations CalculationTitle: Updated Calculation of Probability of Criticality for the EDA 11 Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 Page 2 of 23

CONTENTS

Page

FIGURES.......................................................................................................................................3

1. PURPOSE...............................................................................................................................5

2. METHOD ................ 5

3. ASSUMPTIONS.....................................................................................................................7

4. USE OF COMPUTER SOFTWARE AND MODELS , ... 1.................................. 114.1 SOFTWARE APPROVED FOR QA WORK .................................................. 114.2 SOFTWARE ROUTINES ................................................. 114.3 MODELS ................................................. 11

5. CALCULATION ................................................... 125.1 CALCULATION INPUT ................................................... 12

5.1.1 Probability that a WP Is Located Under a Dripping Fracture ................................... 125.1.2 Time of Waste Package Breach ................................................. 125.1.3 Probability And Duration Of Waste Package Flooding ............................................ 135.1.4 Borated Stainless Steel Corrosion Rate.................................................................... 145.1.5 Waste Stream Data ................................................. 15

5.2 PROCEDURE ................................................................................................................... 15

6. RESULTS ................................................... 19

7. ATTACHMENTS................................................................................................................. 21

8. REFERENCES .. 22

- �l


FIGURES

Page

Figure 2-1. Degradation Sequence for the 21 PWR Absorber Plate Waste Package ........... ......... 7Figure 5-1. Cumulative Distribution for EDA II WP Breach Time ............................................ 13Figure 5-2. Cumulative Distribution for EDA II WP Bathtub Duration .................... ................. 14Figure 5-3. 304/316 Stainless Steel Corrosion Rate Weibull CDF ............................................. 15Figure 6-1. Conservative Estimate of the Expected Number of Criticalities for the Nominal and

Alternative Scenarios ..................................................... 20

Wjaste Packnot- Onprit-inne lrnlt"nCo" 1niwtn"A"Title: Updated Calculation of Probability of Criticality for the EDA i; Waste Package DesignDocument Identifier: CAL-UDC-MD-OOOOO1 REV 00 Page 4 of 23

TABLES

Page

Table 5-1. Weibull Parameters for WP Breach Time and Flood Duration .................................. 13Table 6-1. Comparison of Representative Cases .................................................. 19Table 7-1. List of Attachments .................................................. 21

Waste Pachaze Operations CalculationTitle: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 Page 5 of 23

1. PURPOSE

The purpose of this calculation is to update the estimate of the probability of criticality for wastepackages (WP) containing commercial pressurized water reactor (PWR) spent nuclear fuel(SNF). This update will reflect the degradation characteristics of the recently developedEnhanced Design Alternative II (EDA II) WP design (Ref 1, pp. 5-37 through 5-40, 5-44, and 5-45). These characteristics include the distribution of time of first waste package breach and theprobability of breach on the upper side before breach on the lower side (so that there can bestanding water in the waste package). The calculation simulates the degradation of the entireprojected inventory of PWR SNF up to 250,000 years after emplacement in the repository.

This calculation improves upon the most recent update of commercial PWR criticalityprobability (Ref. 2) by using a full Monte Carlo simulation of the waste package degradationprocesses. It updates the first Monte Carlo simulation (Ref. 3) by assuming the EDA II design.It improves upon both previous calculations by incorporating the incremental effect on criticalityof assembly collapse and fission product loss. Significant loss of iron oxide is considered to testthe sensitivity of the results to iron oxide loss because the possibility of iron oxide loss has beenmentioned in response to presentations of the standard degradation scenarios. Consideration ofiron oxide loss provides an extra measure of conservatism; there is no natural mechanism toproduce such a loss.

This calculation is associated with disposal criticality analysis and has been prepared inaccordance with procedure AP-3.12Q (Rev. 0, ICN 0, effective 06/30/1999).

2. METHOD

The likely internal degradation scenario for the commercial PWR SNF waste package is shownin six stages in Figure 2-1. The first stage (Figure 2-1A) is the intact configuration, which isassumed to exist just prior to breach of the waste package irrespective of the time to breach(Assumption 3.1). The water breaching the waste package will fill the waste package to the levelof the breach. For several hundred years following the filling of the waste package, the dominantdegradation process will be the corrosion of the carbon steel and aluminum components. Thefirst structural components to fail will be the carbon steel side guides and corner guides (Figure2-1 B). Following those failures, the rest of the structural material and thermal shunts will fail,leading to the fully collapsed basket configuration (Figure 2-1C).

The Monte Carlo simulation process tracks the loss of borated stainless steel following theattainment of the fully collapsed basket configuration of Figure 2-1C. Of course, there will besome degradation of borated stainless steel before the basket fully collapses, so it is conservativeto assume that the progression from the initial configuration to the fully collapsed basket (Figure2-1A through Figure 2-1C) is instantaneous (Assumption 3.2). The remaining configurations(Figure 2-lD through Figure 2-IF) show the results of the degradation of the borated stainlesssteel, the Zircaloy assembly spacer grids, and the Zircaloy cladding, respectively. In actuality,these components will degrade simultaneously, but the borated stainless steel will degrade at amuch faster rate than the Zircaloy, so the scenario is very likely to pass through a configurationresembling Figure 2-1D. Since the Zircaloy spacer grids (Ref. 4, Table 4.2-1) are thinner than

Waste Packagee Operations , ~~~~~~~~CalculationTitle: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier. CAL-UDC-MD-O00000 REV 00 Page 6 of 23

the Zircaloy fuel pin cladding (Ref. 5, p. 26), and since the spacer grids are exposed to corrosionfrom both sides while the cladding is only exposed to corrosion from one side, the assemblies aremore likely to collapse (Figure 2-1E) before significant degradation of the fuel matrix itself(Figure 2-IF). However, the Monte Carlo simulation does consider the possibility of theseprocesses occurring simultaneously, with appropriate probability weighting, to ensure that thefinal result represents a conservative estimate.

The degradation scenario illustrated in Figure 2-1 has been used as the basis for earlier estimatesof criticality probability for the commercial SNF waste package (Ref. 2, Section 2 and Ref. 3,Section 2), and it is consistent with the degradation analysis methodology established in Ref. 6(pp. 3-11 through 3-13).

The Monte Carlo technique is implemented by a software routine, "montecarlo.c" that builds theexpected criticality statistics from a file of expected assembly receipts at the repository. In thisfile, the assemblies are grouped in batches of from I to 50 assemblies representing commonreactor histories. Each batch is characterized by a set of parameters; the ones most important forcriticality are burnup and initial enrichment. The first step in the processing of each batch is toscreen for criticality potential; only those batches with criticality potential above a specifiedthreshold are then subject to the large number of Monte Carlo realizations. The number ofrealizations used for this calculation is 500. Each Monte Carlo realization begins with a randomselection of whether the package is dripped on and whether the package is breached on the topbefore it is breached on the bottom. For realizations that satisfy both conditions, the time beforebreach and the time between first top breach and first bottom breach (duration of waste package"bathtub" configuration) are randomly generated. Also generated at this time are the parametersfor the distribution of rates of assembly collapse and fission product loss (which results from thedegradation of the fuel matrix).

For each time step of the numerical integration of a Monte Carlo realization, the followingparameters are also calculated or generated randomly from a specified distribution: decrement inthickness of borated stainless steel, quantity of boron lost from the waste package, degree ofassembly collapse, and quantity of fission products lost from the fuel matrix. The kff of theremaining configuration is then calculated, using a regression as a function of: time sinceirradiation, burnup, initial enrichment, and parameters describing the degree of degradation ofthe borated stainless steel and the boron loss from the waste package. This regression is basedon over 1000 criticality calculations using MCNP4A, as described in Ref. 7 (pp. 4, 5, and 24).The regression is extended to include a parameter characterizing the degree of assembly collapseand a parameter characterizing the loss of neutron absorbing fission products from the fuelmatrix. This extension is based on an additional 400 criticality calculations, as described in Ref.8 (Section 6).

If the calculated klff is less than the criticality limit (CL), which is set at 0.98 for this calculation,then the calculation moves to the next time step and the process is repeated. If the calculated lffexceeds the CL the realization is ended and the time of criticality is sorted into discreteincrements or bins 1000 years wide for later processing. The simulation then moves to the nextrealization, and the process is repeated until the specified number of realizations has been

Wastep PatcIkave Clnprnfionn ralculaitionnWn�te Pswkn�e Ona�rntinn�t CnlrnlatiiinTitle: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 Page 7 of 23

generated for this batch of assemblies, after which the process begins again with the next batchof assemblies. After all the batches have been processed, the sununary statistics of the resultingprobability distribution are generated: the frequency of criticality, the cumulative probability ofcriticality, and the expected number of criticalities, all as a function of time up to 250,000 yearsin discrete time steps of 1000 years.

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D) Fully Degraded Basket E) Fully Degraded Basketwith Intact Assemblies and Assembly Structure

Intact Fuel RodsF) Fully Degraded Basket

and Fuel

Figure 2-1. Degradation Sequence for the 21 PWR Absorber Plate Waste Package

3. ASSUMPTIONS

3.1 It is assumed that the spent fuel and other internal components of the waste package donot degrade before the breach of the waste package. The basis for this assumption is thatthe dry interior of the package is to be rendered inert with helium before sealing (Ref. 9,p. 4-23), so there are no agents for chemical reaction. This assumption is used throughoutthe calculation.

3.2 It is assumed that after the waste package is breached, water fills the package andcorrodes the carbon steel and aluminum components instantaneously. The bases of this

Wose* PopkQOA (nnerofinne ^lenltinnTitle: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 Page 8 of 23

assumption are that (a) it is conservative to assume that the WP fills instantaneously and(b) Ref 6 (pp. C-17 through C-19) indicates that these components will degrade quicklyin comparison to the borated stainless steel components. This assumption is usedthroughout the calculation.

3.3 It is assumed that Babcock & Wilcox (B&W) Mark B 15 x 15 fuel type, which wasassumed in the criticality calculations (Ref 7, p. 6) that were used to estimate the fractionof fuel exceeding the critical limit, is bounding for all PWR fuel types. The bases for thisassumption are that (a) a previous evaluation performed for the BR-100 transportationcask established the B&W Mark B assembly as one of the most reactive PWR fueldesigns in the 30 GWd/MTU burnup range under intact fuel assembly and fixed basketgeometry conditions (Ref. 10, p. 11.6-6) and (b) the most important parameters predictingwhether a waste package will exceed the criticality limit are: time since irradiation,burnup, and enrichment of the fuel, rather than the specific fuel type. This assumption isused throughout the calculation.

3.4 It is assumed that only the 21 PWR WP design with 7-mm thick borated stainless steelabsorber plates (Ref. 11, pp. 21, 29, and 30) is used for the entire PWR waste stream.The basis for this assumption is that it is conservative because a more robust (lesssoluble) absorber may ultimately be used. This assumption is used throughout thecalculation.

3.5 Principal Isotope (PI) burnup credit is assumed to be an acceptable method to account forreduced reactivity of SNF in criticality evaluations. The basis for this assumption isControlled Design Assumption Key 009 (Ref. 12, p. 3-22). In addition, this assumptionwas used in the criticality calculations (Ref. 7, p. 15, Assumption 4.3.1) used to developthe keff regressions discussed in Section 5.2. This assumption is used throughout thecalculation.

3.6 It is assumed that a general corrosion rate for 304/316 stainless steel, when increased by a"boron factor" of 2.5 can be used to represent the bulk corrosion rate of Neutronit A978borated stainless steel in the repository environment. The basis for this assumption is thatNeutronit A978 is similar in composition to 316 stainless steel (Ref. 13, p. 96), andcorrosion data-in repository relevant environments is only available for 304/316 stainlesssteels. The boron factor of 2.5 is the mean of a uniform distribution ranging from 1 to 4.The basis for the upper bound of the boron factor distribution is that borated 304 stainlesssteel was found to have a corrosion rate up to 4 times that of unborated 304 stainless steelin a short-term corrosion test in a harsh environment (Ref. 7, pp. 11-13). The basis forthe lower bound is the expectation that the presence of boron will not decrease thecorrosion rate. The basis for-assuming a uniform distribution of uncertainty between thelower and upper bounds is a lack of more specific information about the effect of boronin the less harsh repository environment. The basis for choosing the mean value and,therefore, not propagating the uncertainty of the boron factor, is that whether or notcriticality is attained is expected to be more sensitive to other parameters, which aretreated stochastically. This assumption is used throughout the calculation.

Waste- PacL-kate (-nprationin rialelxatianTitle: Updated Calculation of Probability of Criticality for the EDA 11 Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 Page 9 of 23

3.7 It is assumed that the boron will immediately enter solution and be available for removalfrom the waste package (the effect of potential adsorption on iron oxide is ignored) onceit has been released from the borated stainless steel matrix. The basis of this assumptionis that it is conservative in light of (a) the discussion in (Ref. 7, pp. 11-13) of thecorrosion of borated stainless steel, which indicates that the boride particles wouldcorrode relatively quickly because they have a large surface-to-volume ratio. A furtherbasis is that neglecting the effects of boron adsorption on iron oxides is also conservativein light, of indications in (Ref. 7, p. 48) that adsorption on Fe2O3 may provide up to a1.4% reduction in ksff (greater reductions may occur if adsorption on Al oxides or othertypes of iron oxides is considered). This assumption is used throughout the calculation.

3.8 It is assumed that the waste package is horizontally emplaced and floods instantaneouslyupon breach on the upper side, and drains instantaneously upon breach on the bottom.The basis for this assumption is the evaluation of waste package filling and drainingtimes performed in Ref. 14 (pp. 38-41) which indicated that the filling and draining timesare relatively short (a few tens to hundreds of years) in comparison to the potentialduration of flooding discussed in Section 5.1.3 of this calculation and the 1000 year timestep typically used in the mass-balance calculations. This assumption is used throughoutthe calculation.

3.9 It is assumed that the duration of waste package flooding is independent of waste packagebreach time. The TSPA results discussed in Ref. 3 (pp. 16-17) show that there is apositive correlation of flood duration and waste package breach time. This assumption isconservative in the early years because assuming independence implies longer floodduration at early breach times than would occur if flood duration and breach time werepositively correlated. On the other hand, assuming independence implies shorter floodduration in later years, which is not conservative in the later years. Flooding during theearlier years is of greater concern due to the expectation that the peak post-closure kefr(Ref. 7, p. 48) will occur in the early years between 10,000 and 35,000 years afterclosure. Therefore, the basis of this assumption is that it is conservative because it allowsfor longer flood duration during the more important early years. This assumption is usedthroughout the calculation.

3.10 It is assumed that the subcritical limit for all configurations evaluated in this calculationis 0.98. The basis for this 'assumption is a statistical estimate of bias for benchmarkcalculations that was developed using the same software systems (MCNP and SAS2H) asthose used to estimate the fraction of fuel that could exceed a given kiff value (Ref. 15,pp. 22 and 23). The cited calculation yielded a subcritical limit of 0.98 if no trendingparameters are used, and no administrative bias is applied. This assumption is usedthroughout the calculation.

3.11 It is assumed that water entering the WP after dripping onto the WP replaces boron-saturated water inside the WP with a transfer efficiency drawn from a uniform probabilitydistribution between 5 and 15 percent. The transfer efficiency is, in effect, the ratio of

Wsacte Pug-baco (Inoralinne Nstlanlœtinn

Title: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-00000l REV 00 Page 10 of 23

the volume of boron-saturated water leaving the WP to the volume of water entering theWP, with the rest of the water that enters the WP leaving unchanged in boronconcentration. The basis for this assumption is that it is approximately consistent with,and slightly more conservative than, the range of transfer efficiency used in Assumption4.3.4 of Ref. 14 (0.1 to 10 percent). Greater transfer efficiency implies greaterconservatism due to more rapid removal of boron from the WP. This assumption is usedthroughout the calculation.

3.12 It is assumed that estimated numbers of SNF assemblies by burnup and initial enrichmentfrom Reference 16 are appropriate for this calculation. Although a revised set of wastestream data has recently become available (Ref. 17), the earlier set is used. The data usedmay predict fewer low-burnup assemblies than will actually be present in the future wastestream. However, any concern about the criticality of WPs with low-burnup assemblieswill likely be handled by "derating" that is, disposing of the low-burnup assemblies inWPs with fewer assemblies. Because this calculation assumes that all assemblies,including low-burnup ones, are disposed of at a rate of 21 assemblies per WP, thiscalculation exaggerates the probability of criticality and is therefore conservative. Thebasis of this assumption is that it is conservative and maintains consistency with previouswork (Ref. 3). This assumption is used throughout the calculation.

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Title: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-O0000I REV 00 Page 11 of 23

4. USE OF COMPUTER SOFTWARE AND MODELS

4.1 SOFTWARE APPROVED FOR QA WORK

None used.

4.2 SOFTWARE ROUTINES

The Monte Carlo mass balance calculation was performed using a C software routine named"montecarlo.c", Version 1. The function of "montecarlo.c" is to (a) select a set of inputs byrandomly sampling the probability distributions that describe the repository environment andwaste package degradation (Section 5.1) and (b) using the selected inputs, perform adeterministic mass balance to determine whether a waste package exceeds the subcritical limitfor the selected inputs. This sampling and calculating process is repeated a specified number oftimes, resulting in a number of possible outcomes or realizations. Further discussion on theoperation of "montecarlo.c" is provided in Section 5.2.

The implementation of the Monte Carlo process is independently verified as part of the technicalcheck of this calculation. The source code for "montecarlo.c" is provided in Attachment II. Theinput and output files for the "montecarlo.c" scenarios that were run for this calculation areincluded as Attachments III and IV.

4.3 MODELS

None used.

Waste Parkave Onpratinnr. CalculationTitle: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 Page 12 of 23

5. CALCULATION

5.1 CALCULATION INPUT

5.1.1 Probability that a WP Is Located Under a Dripping Fracture

The probability that a waste package was located under a dripping fracture is taken to be 0.26 forall cases. This is consistent with the mean seepage fraction used for Total System PerformanceAssessment-Viability Assessment for the long-term average climate.

5.1.2 Time of Waste Package Breach

The parameters of two estimated Weibull cumulative distribution functions (CDFs) of wastepackage breach times for EDA II and VA waste packages under dripping fractures were obtainedfrom Ref. 2 (Section 5.1). The data used to estimate the CDF was developed using theWAPDEG software (Ref. 18, pp. 5 through 9, 24). The WAPDEG output for each caseestimates the times that first penetrations will occur on the top and bottom of the package (aboveand below the centerline) both for parts of the package under the drip and parts not under thedrip. The WAPDEG output contains this information for a sample of 400 waste packages.Under the convention adopted here, breaches on the top of the package are required to allowdripping water to enter. Therefore, the earliest time of any top penetration was used as the wastepackage breach time. This is conservative because only top breaches directly under a drip wouldbe expected to allow significant amounts of water to enter the waste package.

The Weibull distribution was chosen because of its ability to fit a wide variety of distributionshapes. The probability density function (pdf) of the Weibull distribution is given by:

fA) = (P-t(L ) exp[-(L2.) ] for t >0 Eq. 5-1

where a, JB, and 0 represent the scale, shape, and location parameters (Ref. 19, p. 77). Thelocation parameter gives the lower end of the range over which the equation defines thedistribution. For t < 0, the probability density is defined to be zero. Thus, the location parametershifts the time of earliest possible failure. All of the Weibull parameters are defined to be non-negative. The associated Weibull CDF is given by:

F(t) =1- ee for t ] 0. Eq. 5-2

For t < 0, the cumulative failure probability is defined to be zero.


The estimated Weibull parameters for EDA II waste package breach time are given in Table 5-1.Figure 5-1 (Ref 2, Figure 5.1.2-2) shows the fitted Weibull CDF for the waste package breachtime for the EDA II WP design along with the WAPDEG data that was used to estimate theWeibull parameters.

Table 5-1. Weibull Parameters for WP Breach Time and Flood Duration

Characteristic a 0.[ Flood ProbabilityBreach Time, VA 12.099 16.425 0.000 Not applicableFlood Duration, VA 10.849 8.228 0.000 0.4775Breach Time, EDA II 2.347 4.810 10.820 Not applicableFlood Duration, EDA II 11.881 10.218 0.000 0.4125

Source: SecUon 5.1 of Ret. 2.

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0A-

.0.5 - -- _

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0.2-

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010000 100000 1000000

Time (years since emplacement)

WAPDEG Data Point -Weibul CDF

Figure 5-1. Cumulative Distribution for EDA II WP Breach Time

5.13 Probability And Duration Of Waste Package Flooding

The parameters of two estimated Weibull CDFs of the duration of waste package flooding forEDA II and VA waste packages under dripping fractures (Table 5-1) were obtained from Ref. 2(Section 5.1). As indicated in Section 5.1.2, the WAPDEG output on which the CDFs are basedestimates the time of penetration of both the top and bottom surfaces of the waste package. If thewaste package is to accumulate water, it must be penetrated on the top surface, and not on thebottom surface. To obtain a distribution for the possible duration of this condition, the time

Waste Parknae lneratinn-v CalcuvlastionTitle: Updated Calculation of Probability of Criticality for the EDA 11 Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 Page 14 of 23

difference, At, between the earliest top penetration, and the earliest bottom penetration, wascalculated (Ref. 2, Section 5.1) for each of the 400 waste packages modeled in the WAPDEGoutput files. A little over half the EDA II waste packages had a negative t, indicating that theywere penetrated on the bottom first. Thus, at the time of top breach, the waste packages that hadbeen penetrated at the bottom first would be unable to accumulate water. The fraction of wastepackages with positive At is indicated as "flood probability" in Table 5-1.Figure 5-2 shows the data used in the fit along with the fitted Weibull CDF for the duration offlooding for waste packages that are capable of accumulating water according to the assumptionsstated (Ref. 2, Section 5.1).

MR

I I

Figure 5-2. Cumulative Distribution for EDA 11 WP Bathtub Duration

5.1.4 Borated Stainless Steel Corrosion Rate

Ref. 3 (pp. 18 and 19) provides a fit of the negative natural logarithm of 304/316 stainless steelcorrosion rates to a Weibull distribution. The estimated Weibull parameters are: ac = 4.852, P =4.041, and 0 = 4.605. Figure 5-4 shows the resulting Weibull CDF for the stainless steelcorrosion rate. In addition, Ref. 3 (pp. 19 and 20) assumed an increased corrosion rate forborated stainless to account for the presence of boron in the alloy. The author of Ref. 3implemented the assumption by multiplying the corrosion rate by a "boron factor" between 1 and4. For this calculation, the midpoint of the range from I to 4, that is, 2.5, was used as the boronfactor (Assumption 3.6).

Waste Package OiDemflons CalculationTitle: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-OOOOOl REV 00 Page 15 of 23

'1

1.0

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a 0.4 -

E 0.3 -

d 0.2 -

0.1 _

0.0 -

1.13+00 I.E+00 1.1E01 1.E-02 1.1E.03 1.1E.04 1.E-05 * 1.1E-06 i.LE-07

3041316 Stainless SteelGenemlCorrslonlRate (mm/yr)

Figure 5-3. 304/316 Stainless Steel Corrosion Rate Weibull CDF

5.1.5 Waste Stream Data

Estimated numbers of SNF assemblies by burnup and initial enrichment were taken fromReference 16. The specific electronic data file used is the uncompressed C IWSM.ZIP, withonly the information on the historic and projected PWR population used for this analysis.Although a revised set of waste stream data has recently become available (Ref. 17), the earlierset is used to maintain consistency with previous work (Ref. 3).

5.2 PROCEDURE

As mentioned in Section 2, the procedure for estimating the probability of criticality for thecommercial SNF waste stream is to use the software routine "montecarlo.c", which is listed inAttachment II. This software routine implements a Monte Carlo technique for generatingparameter values to use for inputs to a simple numerical integration of a set of mass balanceequations over a discrete set of time steps up to 250,000 years.

The input data used by the software routine are of two types: specific waste package designparameter values (e.g., dimensions, volumes, and masses) and parameters specifyingdistributions from which random values are sampled for the Monte Carlo realizations. Nominalvalues of these parameter values are hard coded into the software routine, but they can beoverridden by values entered in the input file "parameters.in" which thereby serves as a record ofvalues used for sensitivity exercises. Examples of this file are given in Attachment III. In thisfile there is one line for each override. The override line begins with the name of the parameterto be overridden preceded by the '$' character and followed by an equal sign which is thenfollowed by the numerical value to be assigned as override. The value may be followed by one,

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Title: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-Mb-000001 REV 00 Page 16 of 23

or more, blank spaces, which can then be followed by a comment indicating the purpose of theoverride. This override technique is similar to the namelist input of FORTRAN. This input filecan also contain comment lines, which are indicated by an '*' in the first column.

The characteristics of the commercial PWR SNF waste stream arriving at the repository areprovided by the file "data.in" (Assumption 3-12). This file contains approximately 20,000records, one for each batch of assemblies in the order in which they have been, or are expected tobe, discharged from a commercial reactor. The batch records are processed one at a time. Theburnup and enrichment values from "data.in" are used to compute a klff for a basket degradationcondition which is, or is close to, the worst case with respect to criticality; that is, stainless steelfully degraded so that all the boron is lost from the waste package. This value of kff is thencompared with a specified threshold, set well below (typically 5%) the criticality limit (0.98). Ifthe kcff is found to be below this value, the batch is assumed incapable of criticality; the numberof assemblies is incremented according to the number in the batch, and the program moves to thenext batch record.

For each batch that passes the screening criterion, there are a specified number of Monte Carlorealizations (500 for this calculation). Each realization begins with two random selections,which are based on the probabilities of their respective events. The first selection is for whetherthe waste package is dripped on. If the waste package is not dripped on another realization istried. If the waste package is dripped on, the next selection is for whether the waste packagebreaches first from the top (which means it can form a bathtub). If not, the next realization istried.

For those realizations that pass this further screening, the degradation scenario parameters aregenerated according to their respective probability distribution. The principal parametersgenerated in this manner are breach time, bathtub duration, and start and finish times for bothassembly collapse and fission product loss. Then the parameters for each successive time stepare generated. These include the transfer efficiency of the water entering the waste packagebathtub (Assumption 11) and the corrosion rate of borated stainless steel, which are drawn fromprobability distributions. The uncertainty implied by these two distributions could be appliedonce for each realization or once for each time step of each realization. The uncertainty isapplied each time step because there could be significant changes in the transfer efficiency andthe nature of the passivation layer that limits corrosion of the borated stainless steel in a 1000-year time step. After these parameters are generated, the remaining boron and iron oxide arecalculated (by the numerical integration of the mass balance equations), and a new value of k.if iscalculated from a regression dependent on burnup, initial enrichment, amount of oxide, andthickness of remaining borated stainless steel. The first two of these are characteristic of theassembly batch; the other two are calculated from the mass balance equations, as indicated in theprevious sentences.

There are four forms of the regression equation, for the four combinations of the two booleanparameters: whether or not there remains any borated stainless steel and whether or not the oxideis uniformly distributed or settled to the bottom of the waste package (in which case it is lesseffective in controlling criticality by moderator displacement). These forms of the regression

Watep Parlkzag Anpriginnc CalculaionfnTitle: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 Page 17 of 23

equation were developed in Ref 3 (pp. 19-23) using over 1000 MCNP cases. Subsequent wastepackage design changes incorporated aluminum thermal shunts to minimize the peak fueltemperature. Since the aluminum is expected to corrode before the stainless steel, and occupythe lower portion of the waste package, it is also expected to limit the amount of iron oxide thatcould settle to the bottom of the waste package. It was therefore decided that the most likelydistribution would be the uniform oxide. The uniform oxide distribution is the one used in thiscalculation.

After the nominal k4ff calculation, the keff is adjusted for (1) boron remaining in solution, (2)collapse of the assembly, and (3) the loss of fission product neutron absorbers from degradationof the fuel matrix. These supplementary regressions are given in Ref. 8 (Section 6). Asmentioned above, the start and finish times of these two processes are generated randomlyaccording to specified uniform distributions, and measured from the time of breach of the wastepackage. For each time step between these start and finish times, the value of the two parameters(measuring degree of collapse and fission product loss) are determined by linear interpolation, asa function of the time between the respective start and stop times.

If the adjusted keff equals or exceeds the CL, then a criticality will be recorded. For this purpose,the total number of criticalities is incremented by the number of assemblies in the batch. Thetotal number of criticalities is also apportioned according to the time of occurrence of thecriticality using an array of bins, with one bin for each time step. For this purpose, the bincorresponding to this time step is also incremented by the number of assemblies in the batch.The simulation then moves to the next realization. If, on the other hand, the kftr < CL, then thesimulation moves to the next time step. If the time steps reach to the duration of the bathtub, therealization is considered to have had no criticality, and the next realization will begin all over.

After all the realizations have been processed for each batch that passes the screening threshold,the summary statistics can be generated over the time period covered, 250,000 years. Thefraction of assemblies participating in a criticality is determined by dividing the total number ofcriticalities by the number of chances for criticality. This number of chances is the product oftwo factors: the total number of assemblies, and the number of Monte Carlo realizations. Thisconsiders the assemblies that did not pass the keff screening threshold on the same basis as thosethat did. The probability density function (pdf, more properly called a frequency function, ff,since the distribution is characterized by discrete time steps) is similarly computed by dividingthe number of criticalities in each bin by the same number of chances for criticality. The CDF asa function of time is then calculated by summing the pdf's (or ff s) to that point in time.Although this fraction has been calculated as a fraction of assemblies that could be critical, it isequally valid as a fiaction of waste packages since x% of assemblies would also be x% of wastepackages. The expected number of waste packages that will experience criticality is then thefraction of waste packages that become critical (which is the probability of criticality) multipliedby the total number of waste packages (which is the total number of assemblies divided by thenumber of assemblies per waste package, 21).

The summary output file, "montecarlo.out" contains the date of the run, a descriptive title, andthe expected number of criticalities for each 1000-year time step. The output summary also

N

Waetp ParkVau (Onpratnna 1sruldl111tinnTitkle Updated Calculation of Probability of Criticality for the EDA 11 Waste Package DesignDocument Identifier: CAL-UDC-MD -000001 REV 00 Page 18 of 23

reports the number of batches screened into Monte Carlo processing and the number of wastepackages calculated for the observed number of assemblies. The number of waste packages isthe same for all cases, so it is used as a check on each run. The detailed time-step data is onlyused for the four cases in Figure 6-1. For the other cases, this calculation only reports the datafor the time steps at 10,000 years, 100,000 years, and 249,000 years, so only the summary partsof "montecarlo.out" (which give this information) are given in Attachment IV.

As with all Monte Carlo programs, the random numbers are generated by a pseudo-randomsequence generated by an algorithm in the code. By default, this algorithm will generate thesame sequence each time it is run; furthermore, since the sequence is only pseudo-random, it willrepeat after some large number of steps. With this default, the program will produce the samestatistics every time it is run with a specific set of input parameters in "params.in". The Ccompiler has capability to start this sequence at an arbitrary point, which is called seeding. Theprogram "montecarlo.c" can select the seed randomly by using the computer's internal clocktime as the argument of the seeding function (srand). In order to ensure reproducibility, thenominal cases do not use random seeding. However, to demonstrate the accuracy of the MonteCarlo simulation process, four randomly seeded repetitions of the nominal VA waste packagedesign run were executed; the standard deviations of the expected numbers of crificalities at100,000 and 250,000 years were computed for the five runs.

Waste Package Operations CalculationTitle: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 Page 19 of 23

6. RESULTS

With a screening CL=0.93, there were typically between 1000 and 2000 potentially criticalbatches (out of somewhat more than 18,000 PWR batches in the receipt scenario of the fileDATA.IN) for the cases considered in this calculation. With each of the potentially criticalbatches given 500 Monte Carlo realizations of waste package degradation, six representativecases are summarized in Table 6-1. Half of these cases are for the VA waste package design,which is expected to have a minimum time to breach somewhat less than 10,000 years. Theother half are for the EDA II waste package design which is expected to have a breach time ofmore than 100,000 years.

Table 6-1. Comparson of Representative Cases

Expected Number of CriticalitlesCase At 100,000 years At 249,000 years

1. VA Design, nominal 2.39 (0.055)* 6.51 (0.15)-2. VA Design, delayed collapse of assembly 2.83 7.593. VA Design, drastic loss of iron oxide 28.7 78.84. EDA It Design, nominal 0.00276 1.325. EDA II Design, delayed collapse of assembF 0.00924 1.626. EDA II Design, drastic loss of iron oxide 0.0384 15.6

*Standard deviations (in parentheses) are calculated for the nominal VA design (Case 1) from a sample consisting of thenominal unrandomized nan of 'montecarlo.e. and of four randomized additional runs with the same Input conditions(specified in PARAMS.IN).

There are two conservative variations on each of the nominal cases (Cases I and 4). Thedelayed-collapse variations (Cases 2 and 5) have the assembly collapse delayed until most of thefission products have been dissolved and removed from the waste package. In this way much ofthe neutron absorber material is removed from the waste package, while the assemblies are stillin their nearly optimum spacing; therefore, the kff for these variations would be expected to belarger than for the nominal case, as is observed in Table 6-1.

The other comparison cases consider the loss of 50% of the iron oxide that had originallyresulted from the steel corrosion. These cases are, which are presented here for comparison only,are unrealistically conservative because there is no physical mechanism for such a drastic lossand because the loss happens as the basket is degrading. A more realistic model would have thedistribution of the iron oxide loss stretched out in time so that the loss is not as likely to happenduring the bathtub period. By comparison, fission product loss is stretched out in time, so that ithas a much weaker effect.

It should be noted that the EDA II cases show no expectation of criticality at 10,000 years andmuch less than one expected criticality even at 100,000 years. The ratio between expectednumber of criticalities for 249,000 and 100,000 years is much larger for EDA II than for VAbecause 100,000 years is just below the threshold of waste package breach time for the EDA 11alternative. Therefore, the expected number of criticalities at 100,000 years is exceptionally low.By contrast, for the VA design, both the 100,000-year and the 249,000-year time steps are well

Wwste Pnekavre Onprutinnq CalculatfionWn�te Package Onerntinn� CalcnlntianTitle: Updated Calculation of Probability of Criticality for the EDA 11 Waste Package DesignDocument Identifier: CAL-UDC-M 00000 REV 00 Page 20 of 23

within the time range of criticality. A more detailed comparison of the expected numbers ofcriticalities as a function of time is given in Figure 6-1.

E

8

7

65

4

3

2

1

0- 0'- (0 (0 _ (- 0' - 0

_C IC W E) ON eM '0(0To v- v- v- ar

Thousands of years

Figure 6-1. Conservative Estimate of the Expected Number of Critcalities for the Nominal and AlternativeScenarios

The comparison of the VA and EDA II cases in Figure 6-1 shows not only that the onset of thepossibility of criticality for the EDA II case is delayed 100,000 years (because there is only avery small probability of waste package breach before 100,000 years) but also that the EDA IIcurves have a much smaller slope (as a function of time, and by comparison with the VA curves)once they do begin to climb. This is because the CDF for EDA II breach time shown in Figure5-1 shows a much slower rise with time, once it does begin to rise beyond 100,000 years, thandoes the corresponding curve for the VA design (Ref. 6, Appendix C, Figure C-3 1).

This calculation also tested the sensitivity to drip rate. For this purpose the best estimate of thecurrent drip rate, 0.05 m3/yr is used. All the other cases used a uniform distribution of drip ratesranging from 0.05 m3/yr to 0.5 m3/yr, which is the conservative assumption of the ControlledDesign Assumptions document (Ref. 12, TDSS 026, p. 10-19). The VA design was used for thiscomparison because it has more expected criticalities. The lower drip rate would be expected togive a lower number of criticalities because it would have a longer retention of boron in solution.The results for the lower drip rate are 2.33 and 6.16 for the 100,000-year and 249,000-yearexpectations, respectively. Comparison with the first line of Table 6-1 show that the 100,000-year expectation is only 0.06 lower than the nominal; this is only slightly larger than the standarddeviation (0.055), so the difference cannot be considered to be statistically significant. Thedifference between the nominal and the 249,000-year expectation is 0.35, which is somewhatmore than twice the standard deviation (0.15), so the difference can be considered to bemarginally significant.

Ws-te Pntrknote Onepratinne CanluaIntinnTitle: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 Page 21 of 23

7. ATTACHMENTS

Table 7-1 provides a list of attachments.

Table 7-1. List of Attachments

AttachmentNumber Description of Contents Extent of Attachment

I Document Input Reference Sheets (DIRS) 5 pagesSource code listing for montecarlo.c 7 pagesInputfties 'params.in used for all the cases in this calculation 2 pagesOutput files 'montecarlo.out' summarizing expected criticalities

IV at the representative time steps 10,000 yr. 100,000 yr, and 19 pages249,000 yr

Wwc&~ Pskeltnadg lnprat-inne Nsllrlllatirhn

Title: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 Page 22 of 23

S. REFERENCES

1. CRWMS M&O (Civilian Radioactive Waste Management System Management andOperating Contractor) 1999. License Application Design Selection Report. B00000000-017 17-4600-00123 REV 01. Las Vegas, Nevada: CRWMS M&O. ACC: MOL.19990528.0303.

2. CRWMS M&O 1999. Probability of PWR UCF WP Postclosure Criticalityfor EnhancedDesign Alternatives. BBAOOOOOO-01717-0210-00072 REV 00. Las Vegas, Nevada: CRWMSM&O. ACC: MOL.19990927.0365.

3. CRWMS M&O 1998. Probability of a PWR Uncanistered Fuel Waste Package PostclosureCriticality. BBAOOOOOO-01717-0210-00010 REV 00. Las Vegas, Nevada: CRWMS M&O.ACC: MOL.19980806.0607.

4. Toledo Edison 1998. Table 4.2-1 Fuel Assembly Dimensions and Materials and Table 4-1Fuel Design Parameters and Addendum 1, Unit 1, Cycle 12-Reload report from Davis-BesseNuclear Power Station No. 1: Updated Safety Analysis Report. Vol. 6. Rev. 21. Toledo, Ohio:Toledo Edison. TIC: 245410.

5. CRMWS M&O 1998. Summary Report of Commercial Reactor Criticality Datafor CrystalRiver Unit 3. BOOOOOOOO-01717-5705-00060 REV 01. Las Vegas, Nevada: CRWMS M&O.ACC: MOL.19980728.0189.

6. DOE (Department of Energy) 1998. Disposal Criticality Analysis Methodology TopicalReport. YMP/TR-004Q. Las Vegas, Nevada: DOE. ACC: MOL.19990210.0236.

7. CRWMS M&O 1997. Criticality Evaluation of Degraded Internal Configurations for thePWRAUCF Waste Package Designs. BBAOOOOOO-01717-0200-00056 REV 00. Las Vegas,Nevada:CRWMSM&O. ACC: MOL.19971231.0251.

8. CRWMS M&O 1999. Simulating the Effect on Criticality of Simultaneous MatrixDegradation and Assembly Collapse for 21 PWR Waste Package. CAL-EBS-NU-000002 REV00. Las Vegas, Nevada: CRWMS M&O. ACC: MOL.19990928.0234.

9. DOE 1998. Viability Assessment of a Repository at Yucca Mountain: Preliminary DesignConcepts for the Repository and Waste Package. Vol. 2. DOE/RW-0508. Las Vegas, Nevada:DOE. ACC: MOL.19981007.0029.

10. B&W Fuel Company 1991. Final Design Package - Babcock & Wilcox BR-100 - 100 TonRail/Barge Spent Fuel Shipping Cask 51-1203400-01. Lynchburg, Virginia: B&W FuelCompany. ACC: MOV.19960802.0083.

Wact*p Pupg-Laa' (Inswatinne Irall-11fnsTtiTitle: Updated Calculation of Probability of Criticality for the EDA It Waste Package DesignDocument Idendtfier: CAL-UDC-MD-O00001 REV 00 Page 23 of 23

11. CRWMS M&O 1997. Determination of Waste Package Design Configurations.BBAAOOOOO-01717-0200-00017 REV 00. Las Vegas, Nevada: CRWMS M&O. ACC:MOL.19970805.0310.

12. CRWMS M&O 1998. ControlledDesign Assumptions Document. B00000000-01717-4600-00032 REV 05. Las Vegas, Nevada: CRWMS M&O. ACC: MOL.19980804.0481.

13. CRWMS M&O 1997. Waste Package Materials Selection Analysis. BBAOOOOOO-1717-0200-00020 REV 01. Las Vegas, Nevada: CRWMS M&O. ACC: MOL.19980324.0242.

14. CRWMS M&O 1996. Second Waste Package Probabilistic Criticality Analysis: Generationand Evaluation of Internal Criticality Configurations. BBAOOO000-01717-2200-00005 REV 00.Las Vegas, Nevada: CRWMS M&O. ACC: MOL.19960924.0193.

15. CRWMS M&O 1998. Calculation of Upper Subcritical Limits for Nuclear Criticality in aRepository. BOOOOOOO-01717-0210-00027 REV 00. Las Vegas, Nevada: CRWMS M&O.ACC: MOL.19980729.0420.

16. CRWMS M&O 1997. Input Files and Models Used in the Waste Quantity, Mix andThroughtputStudy. VA.SAI.MF.03/97.007. LasVegas,Nevada:CRWMSM&O. ACC:MOL.19970811.1264.

17. CRWMS M&O 1999. Transmittal of Site Recommendation Waste Streams. WP-SEV-9923.Ta. LasVegas,Nevada:CRWMSM&O. ACC: MOL.19990824.0138.

18. CRWMS M&O 1998. Software Routine Reportfor WAPDEG (Version 3.09). 30048-2999REV02. LasVegas,Nevada:CRWMSM&O. ACC: MOL.19981012.0224.

19. Modarres, M. 1993. What Every Engineer Should Know About Reliability and RiskAnalysis. New York, New York: Marcel Dekker, Inc. TIC: 238168.

Waaehp Paekiacr flni-rafnns Calcula2tinn

ATTACHMENT I, Page I-l of 1-5

OFFICE OF CMUAN RADIOACTIVE WASTE MANAGESENT

DOCUMENT INPUT REFERENCE SHEET1. Document Identitier NotRev Change: Tll

CALOC40113-000001 REV 009 WA Updated Calculation of Probability of Criticalty tor the EDA 11 Waste Package DesignInput Document +. T8V Due To

2. Technicl Product Input Source Title and 3f e. ctioll S. Input Description i SrMr Unql From Uncontrolled Un-Identifler(s) with Version Statue Used In Priority Source contirmed

2a CRWMS M&O (Civilian Radioactive Waste pP. 5-37 T8V- I EDA 11 WP design 3 X N/A WAManagement System Management end Operating thru 540, 3202

1 Contraco)1999 Lbense pplliceVon Desi 5-44,545Selection Report B00000WO017174600.00123REV 01. Las Vegas. Nevada: CRWlrS L&O.ACC: MOL19990528.0303.

2 CRWMS MO 199. Proebfto df tPA tUCF t/P Enthr WA I Passing reference to a previous WA WA WA WAPostclosure Crticalhlytor Enhan Deslnr calculation of probabilty criticalityAlterties. BaA000000417174217040072 REE00. Lea Vegas, Nevada: CRWS Mi&O. ACC: Section2 WfA 2 E Wdegr on enrio Nm A WA WA WAMOt.119990927.0355. Setin .W ..2 dgaainseai

5.1, Table 3203 Table 51 Estimated Webuil distributions for5.1.2.2 brach times of EDA 11 nd VA WP 3 x WA NIA

sci TBV- 5.1.3S.I.Table Tb Estimated WefiulI distributions for 3 X WA WA5.1.2-2 flood duration In EDA 11 end VAWiM

3 CRWMS M&O 19S8. babiltyofPV Entire WA I Passing refernce to a prevous N/A WA NIA WAUncarlsted &e Waste Package Pottobsure calculation of probability of iticattyC nftaAty. 8DDA00000041717.021040010 REV00. Las Vegas. Nevada: CRWMS M&O. ACC: Section 2 WA 2 degncratin cenario /WA WA WA WAMOL1199608606.0507. Scin2 W erdto cnd

pp. 16.17 TiV- 3 Evidence tha flooding duration and3206 waste package breach time are 3 X WA /A

positively correlated

pp. 18 19 TBiV- 6 Atofih negativenaturalogarlih 3 X mA WArates to e Waibul distrIbution

TBv- a Magnitude ofboron fc for 3 X WA WAcorroslon rate of borated stainlesspp. 19, 20 3208 teonl

Linear regressions giving Ik. es app. 19-23 TSV 52 functonofvarious vagiables 3 X ifA NIA

_ _ _ _ _ _ _ ___ _ 3205

Wootot Paekstaer nto"+;stnno Cstlelat12ionWaIet.- Pa4an lnrti- (apnf

ATTACHMENT 1, Page 1-2 of I-S

OFFICE OF CIVILIAN RADIOACTIVE WASTE MANAGEMENTDOCUMENT INPUT REFERENCE SHEET

1 Docunent Identifier NoJRev.: Change: TM:CALJUDC-MD-000001 REV OOB WIA Updated Calculation of Probability of Criticality brthEDA E II Weate Package Design

Input Document B. TBsV Due To

2. Technical Product Input Source Tide end 3. Su dion 46t S on t U1h. Input tOscripton 7.PvrABo Unquel. From Uncontrolled Un-_ tIdentilier(s) with Version Statu Used In priority Source confirmed4 Toledo Edison 1998. Table 4.2-1 Fuel Asernbly Table 4.2- TBV- 2 Thicneu of the Zrcloy epacer 3 X MA MA

Oimensions end Materials and Table 4-1 Fuel 1 3209 gridsDesign Parameters and Addendum 1, Unit 1. Cycle12-Reload report from Duos-Sesa. N earPowerStation ft. 1: Qodatr ed Safety Anaysi Report. VoLS. Rev. 21. Toledo. Ohio: Toledo Edison. TIC:245410.

5 CRWMSM101998. Sunmary Report of p. 25 TBV- 2 Thickness of the Zioeloy fuel pin 3 X WA WACommoodefReactor ftaly Data lbr Crytal 3210 claddingMwIr(nNI BD00OOO01717-8750-0006REV01. Las Vegas, Nevade: CRWMS U&O. ACC:MOL-1998072S.0189.

e DOE (Department ofEnergy) 1998. Disposa pp. 3.11 NrA 2 Evidence o consistencywfth WA WA WA WAC tsV Ana"Is Akhdvdwf Topical Report thru 3.13 establshed degradation analysisYMPTR-0040 REV 00. Los Vegas, Nevada: DOE. Appendix mehodsACC: M0L199902110.23. C.pp.eC- 3272 SupportforausumiptionVWt carbon 3 X WA

17 thru C- steel nd aluminun components Wll19 degrade quickly In comperison to the

borated stainless steel components

Ap41. C. wA Passing reference to the CDF fr VAFig. C.12 a broochtrne Om WA tVAA WA

Waste Package Operations Calculation

ATTACHMENT 1, Page 1-3 of 1-5

OFFICE OF CMUAN RADIOACTIVE WASTE MANAGEMENTDOCUMENT INPUT REFERENCE SHEET

1. Document Identiller NoJRev.: Change: Tte:

CAL-UDC-MD-0001 REV W1B |WA |Updated Calculation of Probabily of Cdticality for the EDA H Waste Packae Design

nput Document 8. TBV Due To

2. TechnIcal Produd Input Source Tle and 3. Sebnion 4. input 5. Becton . Input DescrIption 7 TBVIISD Unqwl From Uncontroled Un-_ Identifier(s) with Vesion St" Lled h Pdorty Source conf lrned

7 CRWMSM&01997. COftcllfyEvwllonof pp. 4 .24 TBV- 2 Resulofcrtcaliiycaicultions 3 X NIA NUADegred InemalClaiorthePWR 3212 using MCNP4AAUCFWP Desgna _B0A17OO 017174200I00056REV00. LsVegas Nevad: CRWMS P 23TBV- 3 o lon ofdBabcockAWilcox 3 X WeA NAM&O. ACC: MOL1fl971231.0251. 213 (B&1 Mar B 15 x 15 h typa

p. 15 NWA 3 Evidence thast Controlled DesignAsmption (CDA) Key 009 was 8UA NWA A WAused in critalcty calculations

Results of shor-term corrolson est NApW.1113 TBV- 3 harshanvronmentthatshowed 3 X NA

3214 that boasted 304 stainless steel has acorrosion ret. up to 4 tenes that ofunboratad 304 stainless steel andIndications that borxd partices would

p 4 TBV 3 corrode quicly3215 Evidence that adsorption on Feog%

may provlde upto al1.4% reduction 3 X WA NUAIn kw

Expectation that peak post-closureTBV- kw will occur between 10,00 and

p. 48 3211 3 30.000 yr ftr closure 3 X WA WA

8 CRWMS M& 1999. Smrdung te Effoct an SectIon . TBV- 2,5,6 Clticality caulations and 3 X WA bUAOcaDy oVfhnttanaoua AIatt 0egrdatron and 3216 supplemental regressions that

Assembly Collapse forts 21 PUR Wsb4t Introduce more varIablesPackage. CAL-EBS-NJ-L00002 REV O0k LasVegas, Nevada: CRWMS M&O. AOC:_ ,oL1n99905.0234.

9 DOE 1998. VlabiyAssesam of a4pos/ t p 4-23 TBV- 3 Support br the assumption that the 3 X NA N/AYucca Aunt/n: A e/nkabrayD*gn Conoa r 3217 waste package Is rendered Inert with&ee Ropoiaryand&ito, Package. Vol. heafum before salingDOEIRW-05. Las Vegas, Nevada: DOE ACC:MOL.19981007.0029.

Waste Package Operations Calculation

ATTACHMENT I, Page 1-4 of 1-5

OFFICE OF CMUAN RADIOACTIVE WASTE MANAGEMENTDOCUMENT INPUT REFERENCE SHEET

1. Document identifier NoJRe.: Change: Ttle:CAL4JOXID-000001 REV 00B WA Upated Calculation of Probabiliy of Criticalty for the EDA i Waste Package Design

Input Document 6_ TBV Due To

2. Technical Produt inrip Soure Tle and 3 Section 4. Input 5. Section S. Input Der~lrton 7. TBVrfBD Unou From Uncontroled Un-_tdentilbra) wfth Vesion 8tr_ _rIn Priority Source confirmed

10 B&W Fuel Company 1991. FhrelDeslgn Package pp. N." TBV- S Ev idense upporting the dairn that 3 X WA N/ABabcock & Wlcorr BR-1OO -100 Ton RA46rge end 114.7 3218 the BbW Mark B asembly Is one ofSpent Ful Sh4WpkV CaSk 51-1203400.01 Me mot reactive PNR Wel designsLynrhburg, Virginia: B&W Fuel Coompany. ACC: In the 30 GWdUMTU burnup rengeMOV199W608020083. under Intact fuel assembly end fixed

_______ basket geometry conditbonsIt CRWMS M&O 1997. Oenmnwto f VWatste pp. 21, 29, TBV- 3 Destlptlon of the 21 PWR WP 3 X WA WA

Package Design Conlgrualion. BB OOM- 30 3219 design with 7mn thick borated01717.0200-00017 REV 00. Las Vegas, Nevada: sthinless steel absorber platCRWMS M&O. ACCh M0L19970t05.0310.

12 CRWMS M&O 1998. Conblad Design p. 3.22 TBV- S Controled Design Asumption (CDA) 3 X N/A WAAssumptions Docuent. BOOOOOOO.01717400. 220 Key 009 (bumup credit).00032 REV 0f. Las Vegas. Nevada: CRWMS . CDA TOS 028 (uniform dtX WAM&O. ACC: MOt.19980804.0481. p. 10-19 TBV 6 n r X ____N/

13 CRWMSU&01997. Wsse PackageMateralt P. p 9 TBV 3 NeutronitA978x simluarin X WA WASelectionAnass BBA00OO-001717-00- 3221 compositlon to316 stainless steel00020 REV 01. Las Vegas, Nevada: CRMSM&O. ACC: MOL19980324.0242.

14 CRWMS M&O 1996. Second WestePackage pp. 341 TBV- 3 Estirles of WPtilling and draining 3 X NIA IVAProtabilst C catily Anatss Gentratio end 3222 timesEvaluation of ktdernal Co tay Conwf atnsBiA00tO00-01717-2200400005 REV 00. Las Asump Evidence of consistency withVegas. tevada: CRWMS M&O. ACC: 4.S.4 WA previous assumptions about transferMOL.19960924.0193. 3 etri ency NA WA WA WA

15 CRWMSM&O1998. Celcrdatincf(A06r pp. 22.23 TBV- S Estimates of basInMCNP 3 X NWA WASuhc4tlcaILhnb for Nuledar CrAtialfiy In a 3223 calculbtinna of kw for benchwarkRepository. B00000W0-001717.0210 027 REV cases00. Las Vegas, Nevada: CRMS M&O. ACCMO.19900729.0420.

16 CRMWS M&O 1997. hkAFlAs &d dMdels tied FMi: T8V- 3 ,6 Enrichment and bumup for P9tWR 3 X WA NWAh the &sie Qhnlily, Mbi an 1broughiput Sludy. CitWS. 3431 SNF.V&SAI-MF.03197.007. Las Vegas. Nevada: ZIPCRWMS M&O. ACC. M6 19970811. 1264.

W00t0 prlat@ fnorafln.- Cab.,lotft n

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OFFICE OF CIVIUAN RADIOACTIVE WASTE MANAGEMENTDOCUMENT INPUT REFERENCE SHEET

1. Docurnent ldentfer NoJRev. Change; Tm.sCAL-UDC-MD4-001 REV008 N/A Upated Calcuktsion ot Probabilty oCriticality for the EDl H Waste Package Design

Input Docurnent 8. TBV Due To

2. Technical Product Input 3oreTtl n .Section 4. Input Sectiont6 Input Dscription 7. 1UVflBD Unqual. From Uncontrolled Un-IdenUts) with Ver mn T a sta Used In PrIoroty Source confinrmed

17 CRWMSM60199. T'ranamlaotStt Entinre NA 3 Not en hpuL Identifitlion tofdata WA WA WA NtARecominendation Waste Streamas WPSEV- that was not used.9923.Ta. La Vegas, Neveda: CRWMS M&O.ACC: MOL19O824.013.

1S CRWMS M&O 1998. Sohwwe Rouanse Repod for pp. 5 tOnu WA 5 Decriton of WAPOEG cornputer NtA NWA WA NtAWAPOEG (Version 109). 300t -2999 REV 02. 9,24 programLas Vegas. Nevada: CRWMS M&O. ACC:MOL19981012.0224.

19 Modarres, M. 1993. Mtt Evvey EngineerShould p. 77 NA 6 Definton of ie Welbul ditributlion WA WA WA WAKnow About RaelabriU and RiskAna New (CDF end pdf)York, New Yorku Marcel Dekker, Inc TIC: 238168.

Waste Package Operations CalculationTitle: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-O00000 REV 00 ATTACHMENT 11, Page 11-1 of 11-7

Attachment II. Source code for "montecarlo.c"

/* montecarlo.c Program to Monte Carlo simulate the degradation of the wastepackage contents, particularly the oxidation of steel and removal of boron.There is also an adjustment for the collapse of the assemblies and thesimultaneous removal of fission products. The program operates on therange of criticality characteristics for commercial SNF. The result isexpressed in terms of the fraction of packages that would go criticalbefore a certain time, and the results are expressed as a function oftime. Although the program is written to process the input stream ofcommercial SNF, which has a range of criticality affecting characteristics,it can also be used for fuels that have only one set of suchcharacteristics.

The program is based on a BASIC program written by John Massari but theapplication of the Monte Carlo technique is somewhat different. Bothprograms assume that the characteristics of any given assembly areavailable for filling the waste package. In actual practice each packagewill most likely contain a range of burnup and initial enrichment, andthe actual criticality would be less than what would be predicted fora homogeneously loaded package having the same average burnup and enrichment.Therefore the assumption of homogeneous loading is conservative.

The program has two input files. "data.in" contains the characteristics ofthe commercial SNF waste stream expected to be received at the repository.Iparams.in' contains any overrides on parameters that are nominallyhard coded. These overrides are accomplished in a manner similar to theFORTRAN namelist. In the file 'params.in" the variable name is precededby a '$' character and then a code line for reading that variable isinserted at an appropriate place in the program. The file sparams.in"is read in to the array lineitlOOl (which could be allocated dynamically,but will never contain more than 100 lines so why bother). The lines(larray is searched for a match starting in the position 1 of each element(line). At position 0 of each line(] is the 'S' character. Thiscapability is extended to arrays of float, with the differences: (1) Thearray name is followed by I]; (2) The values on the right side of the 'S'

are in a comma separated list; (3) The last element of the list must befollowed by a comma, after which there can be comments.

There are two different forms for comments in the file wparams.in":(1) Anything after the obligatory fields in a keyword statement;(2) Any line that begins with an '**. Comments of type 1 are copied intothe input array of lines, but not included in the read of the line oflinesO since each keyword keys a read of only a limited number of fieldsin the array lines(]. Comments of type 2 are simply diverted into thedebugging file, junk.out", so there is a record that they have been readbut not used.

The program presently reads all PWR assembly batches and calculates apreliminary keff, with the condition of basket degraded and allthe boron removed from the waste package. This preliminary keff is testedagainst a threshold criticality limit, testcl, so that only those batcheswith a reasonable chance of criticality will be subjected to thenumber of Monte Carlo realizations (rlztns). The number of assembliesbeing subject to the Monte Carlo realizations is counted by the parameternassyin. The actual criticalities are counted when keff exceeds cl.These criticalities are binned according to the time at which theyoccurred (numcritstl) and tallied in the parameter ntotalcrit. Sincethese counts are expanded by the number of Monte Carlo realizations (rlztns)they are converted to probabilities by dividing by the total number ofassemblies read (ntotassy) and dividing by the number of realizations(rlztns), so that the sample space is expanded to that which it would

Waste Package Operations CalculationTitle: Updated Calculation of Probability of Criticality for the EDA 11 Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 ATTACHMENT 11, Page 11-2 of 11-7

have been if all the assemblies had been subjected to the number ofrealizations. The pdf and CDF calculated in this manner are thus on aper assembly basis. To convert to a per package basis, we divide by thenumber of assembilies in a waste package, 21. The expected number ofcriticalities for all the commercial PWR packages is found by multiplyingthe CDF by ntotassy (which has been expanded by multiplication byrlztns) and dividing by the number of assembilies in a waste package andby the number of realizations.

At the present time the drip rate is only used to calculate the rate ofboron removal, which determines the boron in solution. This is of littleimportance because all the boron is removed from solution by the nextincrement following complete corrosion of borated stainless steel. Theprogram has the capability to use regressions that come from either theuniform or the settled distribution of the iron oxide. However, therecent addition of aluminum thermal shunts to the PWR waste packagelimits the space available for oxide settling, so the nominal modelof waste package degradation assumes a uniform distribution of the ironoxide.

*/

#include cstring.h>#include cstdlib.h>#include <stdio.h>#include <math.h>#include cmalloc.h#include <string.h>#include <ctype.h>#include ctime.h> -#define NUMBINS 250

float getfloatC),InvNorm(float.float),InvUni(float,float),InvLWeib(float,float,float),kcalc(int,float,float,float,float,float),findfloat(char*,int,int); f/used to find and read float override

int findint(char*,int,int); //used to find and read int overridelong int ntotassy-0; //counter for total assemblies readint getinto),inc-l000; //integration timestepint rlztns-100, //number of Monte Carlo realizations

dripflag-0; //O if one rate (or no drip) for each rlztn,/Il if new rate each timestep

char lineslOO][C100J;//for storage of override input file as an arrayFILE *ferr,*fout,*fin,*fparams;float prbt=O.4775, //probability of bathtub

prdripoO.26, //probability of drip on any given bathtubex-.l; //exchange flushing efficiencyvoidspO-3.733, //initial voidspace in CSNF pkg, m^3.mbwp-30110*.199, I/initial boron in BSS in gmbssthickO-7; //BSS initial thickness

int get2(char*,char*,char);void etrim(char*),ftrim(char*);void getfarray(char*,float*,int,int);

void main()mint i,it,k-O,numrisk-o,na,ndyr,nocrit,bssgone,nmlnsrandflag=O,npyr,

numpkgs-O, //number of waste packages usedusflagul, //nominal oxide distribution is uniformfueldegflagul; //nominal fuel degradation and FP loss

float x,b,akeff,pkeff,t,stime,etime,ptime,kav.o,ox,flowmav,cl-(float)O.98,testcl.(float)0.93,mbsol,clpsts,clpstf,voidsp,bsscr,bssthick,bssdelta,mclpsmfpl,ufox-33, //fully degraded uniform oxide vol %sfox.3.5, f/fully degraded settled oxide assy layers coveredupoxcs.30, //uniform oxide, part deg, from carbon steel percent

Waste Package Operations CalculationTitle: Updated Calculation of Probability of Criticality for the EDA 11 Waste Package DesignDocument Identifier: CAL-UDC-MD-00000l REV 00 ATTACHMENT H, Page 11-3 of I1-7

upoxss-10, //unifrm ox, part deg, from stainless steel percentspoxcs-8, //settled oxide, carbon steel (rows of rods/cell)spoxas-2, //settled oxide from stainless steel (rows of rods/cell)btimedisttl.{l2.099,16.425,O}, //VA breach time alph, beta, thetabdurdistt]{l10.849,8.228,O), //VA duration of bathtub alph, beta thetafpltsdist[1-{10000,20000),//start of fission product lossfpltfdist[l(.{40000,50000),//all fission products lostclpstsdisttlu{10000,20000),//atart of collapse of assembliesclpstfdiut[]l{60000,90000),//all assemblies collapsedflowdist[J.{.05,.5), //Flow min max m^3/yr for uniform distributionexdistfl-{.05, .15), //Exchg effic min maxbsscrdiet[l(.o000l,.0004),//BSS cran rate (mm/yr) min max, avoids use of bfacfplcvm.3, //CV for fission product (neutron absorber) lossclpscv-.3, //coefficient of variation for assy collapsefpltsfpltf;//start and finish times of fission product loss process

long int numcrits[NUMBINS].{O},numccritsENUM4BINSI-(O), //to accumulate criticalities in 1000 yr binsntotalcrit-O,nrecsin-onassyin-O,reccount-0;

float pdfcrits NUMBINS] (O),cdfcrits(NUMBINS]=(O);char buffer(3001,type,title[1(01;time t ltime; //variable for date & timetime( &ltime ); //fill ltime structure with current timeif ((fin-fopen("data. in","r"))--NULL) //waste stream

(printf("Can't open data.in\n");exit(0);)if ((fparams-fopen("params.in","r"))-mNULL) //overrides for this case

(printf("Can't open params.iznn");exit(0);)fout-fopen("montecarlo.out , w"); //probability and expected criticalitiesfprintf(fout, "The time is ts", ctime( &ltime ) );ferr-fopen("junk.out',"w"); //characteristics of each criticalityfgets(title,90,fparams); //first line of parameter file must be titlei-0; //read parameter overrides for this case into input array linesOwhile((fgets(buffer,90,fparams)I-NULL)&&Ci<lO0)) //read overrides

{if(buffer[01..'*') fprintf(ferr,"%s",buffer);//divert comment to "junk.out'else strcpy(linesli++],buffer);)

nmlns-i; //number of override parameter linesprintf("%d parameters read\n',nmlns);if((x-findfloat("$ufox",0,nmlns) ) -I) ufox-x;//search for any overridesif((x.findfloat("$upoxcs",0,nmlns))>-l) upoxcs-x;if((x-findfloat(m$upoxss",0,nmlns))>-l) upoxss-x;if((x-findfloat("$sfox",0,nmlns) ) -l) sfox-x;if((x-findfloat("$spoxcs",o,nmlns)) >-) spoxcs-x;if((x-findfloat("$spoxss",o,nmlns))>-l) spoxss-x;if((x-findfloat(m$prbt",O,nmlns))>-l) prbt-x;if((x-findfloat("$ex",O,nmlns))>-l) ex-x;getfarray('$btimedist(]",btimedist,3,nmlns);getfarray("$bdurdist l(",bdurdist,3,nmlns);getfarray("$clpstadistln",clpstsdist,2,nmlns);getfarray("$clpstfdistl(",clpstfdist,2,nmlns);getfarray("$fpltsdist(1",fpltsdist,2,nmlns);getfarrayC"$fpltfdistt(",fpltfdist,2,nmlns);getfarray("$flowdistol",flowdist,2,nmlns);ifC(i-findint("$usflag",0,nmlns))>-l) usflag-i;if (i-findint("$rlztns",o,nmlns))>-I) rlztns-i;if((i-findint(n$randflagu,o,nmlns))>-l) randflag-i;if((i-findint("$fueldegflag",0,nmlns))>-l) fueldegflag-i;if(randflag..l)srand( (unsigned)time( NULL ) ); //random seed for random number generator

while(fgets(buffer,300,fin) I-NULL)(if((type-buffer(1231)I-'P')continue; //PwR batches onlystime-20000; //time value for batch threshold screening onlyt-stime;reccount++;npyr-getint(buffer,287,4);if(reccountl000--O)printf("recsread- %ld\n",reccount);//Count PWR batches

Woetp PaswL-aa nneaStinnc CaolcumiationTitle: Updated Calculation of Probability of Criticality for the EDA 11 Waste Package DesignDocument Identifier. CAL-UDC-MD-O00000 REV 00 ATFACHMENT II, Page 11-4 of 11-7

ndyr-getint(buffer,71,8)j //discharge year, not used in this calculationb-getfloat(buffer,51,10)/1000 //burnup converted to GWd/MTUa.getfloat(buffer,41,10); //initial enrichmentna-getint(buffer,31,10); //number of assembliesif(l((npyr>O)&&(na>O)))continue; //this batch not picked upkeff-kcalc(usflag,a,b,t,sfox*(i-usflag)+usflag*ufox,0);kav+.na*keff; //average keff for all assembliesntotassy+-na; //total assembliesif(keff testcl)continue;//Criticality possible for this batch?nassyin+.na; //number of assemblies passing preliminary screeningnrecsin++; //number of batch records passing prelim screeningmbsol=0;for(i-o;icrlztns;i++)//following lines do bathtub time range from WAPDEG

(if((dripflagm=O)&&(prdrip<(float)rand()/JRANDMAX))continue;//this realization of pkg is not dripped on at any time

stime-InvLWeib(btimedist(Ol,btimedist[l],btimedist[21);//breach timeif(prbtc(float)rand()/RAND MAX) continue;//breach but no bathtubelse etime-stime+InvLWeib(bdurdist(0l,bdurdist [],bdurdist(21);t-stime; //time to start degradation of package componentsnocrit-l; //no criticality yetclpsts-t+InvUni(clpstsdist O],clpstsdisttl]),//start of assy collapseclpstfmt+InvUni(clpstfdist O],clpstfdistll);//finish, from breach timefplts-t+InvUni(fpltsdist[O),fpltsdistl l);//start of fission product lossfpltf-t+InvUni(fpltfdistOl,fpltfdist[l]);//finish, from breach timevoidsp-voidspo; //set voidspace to initial valuebssthick-bssthickO; //set BSS thickness to initial valuebsegonewo; //start with BSS presentpkeff-a; //reset peak keffwhile({tcetime)&&(nocrit.ml)&&(t NUMBINS*inc))//loop until bathtub

I/duration is exceeded, or criticality occurs, or time limit exceeded(if((dripflag.-OI)(prdrip> (float)rand(o/RAND MAX))

flow-InvUni(flowdist[0lflowdistll]);//flow in m^3/yrelse flow-a,. //pkg not dripped on during this timestepex-Invuni(exdist(O,exdist(1) ;//exchg efficiency of circulatory flowbsscr-InvUni(bsscrdist[O],bsscrdistCli);//generate BSS corosion rateif(bssgone-a) //compute thickness of BSS remaining, if any

(bssdelta.2*bsscr*inc;//BSS thickness reduction this timestepif (bssthickabssdelta)bssthick--bssdelta; //decrement BSS thicknesselse

(bssdelta-bssthick;//all remaining BSS is lost in this timestepbssthick-O;bssgonel;) //the next statement updates the boron in solution

mbsol+-bosdelta*mbwp/bssthickO-ex*flow*inc*mbsol/voidsp;if (mbsolO)mbsol=O;) //truncate negative values to zero

if(usflag=ua) //for settled oxide(if(bssthick:.O) ox-spoxcs+spoxss*(bssthickO-bssthick)/bssthickO;else ox-sfox;)//constant oxide amount after BSS is gone

else //for uniform oxide(ifCbssthick>O) ox-upoxcs+upoxss*(bssthicko-bssthick)/bssthickO;else ox.ufox;)

keff.kcalc(usflag,a,b,t,ox,bssthick);//primary keff calculationx-mbsol;if(x>30) //adjust keff for boron in solution

keff+-keff*(.0232558.-0356383*log(x)+.0142821*pow(log(x),2)-1.916S5E-03*pow(log(x),3));

if((tC tclpsts)&&(tcclpstf)) //calculate percent collapsed{mclps . 100*(t - clpsts)/(clpstf - clpsts);//mean value

mclps-InvNorm(mclps,clpscv*mclps);}//generate actual from normal dist.else if (tcclpsts) mclps=O; //no collapse yetelse mclps=100; //completely collapsedif((t.fplts)&&(t fpltf))//calculate percent fission product loss

(mfpl . 100*(t - fplts)/(fpltf - fplts);//mean valuemfpl=InvNorm(mfpl,fplcv*mfpl);)//generate actual from normal dist.

else if (t fplts) mfpl-0, //no FPL yet

wact-gh Par-lizatia nnprafinnc r~altemlatonn,. ae.t .Pa--za An, afmvc C -g'avhtn

Title: Updated Calculation of Probability of Criticality for the EDA 11 Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 ATTACHMENT 11, Page Il-S of 11-7

else mfpl.100; //complete loss of fission productsif(fueldegflag--l) //adjust keff for collapse and FPL

keff+- 0 .001114*mfpl-0.00l333*mclps;if(keff2pkeff) //keep track of the peak keff for this realization

(pkeff-keff;ptime.t;)if(keffocl) //criticality reached for this realization

{numcritsl(t/inc;tNUMBINS-l)?NUMBINS-l (intlt/inc]+=na;//increment//appropriate timestep bin, or max timestep bin

ntotalcrit+=na;//increment total criticalitiesfprintf(ferr,"it.%d brnp %.Of enrch %.2f mbsol %.3f bsthck %f nassy td\n",i,ba,mbsol,bssthick,na);//log characteristics of this criticalitynocrit-O;} //criticality found, end this realization

t+.inc;) //end this timestep//end this potential criticality and MC realization

kav/.ntotassy;numpkgs-ntotassy/21;ntotassy*.rlztns; //escalate for number of realizationsfprintf(ferr,"\n\n\n'); //header for log filefprintf(ferr,sll2sl2sl2s%22s1l2s\nu, "Kyearm,"pdf',"CDF","Crit pkgs","numcr");for(it-l;itcNUMBINS;it++)

(pdfcrits(it)-(float)numcrits(itl/ntotassy;//convert bins to pdf (or ff)numccrits(it]-numccrits lit-l]+numcrits[it];//accumulate number of critscdfcrits[itl](float)numccritstit]/ntotassy; //calculate CDF for this binfprintf(fout,U1l2d12.7f\n',it,cdfcrits[itl*numpkgs);fprintf(ferr,"%12d%12.7f12 .7fl2.4fl2ld\n",//statistics for this timestep

itpdfcrits(itI,cdfcrits[itl,cdfcritslitl*numpkgsnumcrits(it]);}fprintf(ferr,w\n\n");fprintf(ferr,010 timestep moving average, to demonstrate smoothing\n");fprintf(ferr,'%12s%12s\n', Kyear," pdf");mavo; //reset moving average pdf to zerofor(it.l;itcllwit++)mav+.pdfcrits[it];//initial moving average pdfmav/-10;for(it-S;it<NUMBINS-6;it++)

{fprintf(ferr, %12d%12.7f\n',it,mav);//print moving average pdfmav+.(pdfcrits[it+6]-pdfcrits[it-4])/10;)//moving avg for next timestep

printf('assy read. %ld nrecsin- %ld critpkg. %f\nw,ntotassy,nrecsin,cdfcrits(NUMBINS-.1*numpkgs);

printf('%s",title);printf(lnumcritselokyrs-tld explOO.%f exp249.*f\n",numccritsl1o],

cdfcritsl1oo0*numpkgs,cdfcrits[249]*numpkgs);//statistics for this runfprintf(fout,wts",title); //output file summaryfprintf(fout,"Number of batch records screened in-%ld numberpkgs=%d\n'',

nrecsin,numpkgs);fprintf(fout, numcritselOkyr-tld explO-tf explOO-%f exp249-%f\n",numccrits10],cdfcrits[10*]numpkgs,cdfcrits(100]*numpkgs,cdfcrits[249)*numpkgs);}

I/function to get a float from a specified character substringfloat getfloat(char *string, lnt start, int length){char temp(30];strncpy(tempstring+start,length);temp[length]='\0';return((float)atof(temp));)

//function to get an int from a specified character substringint getint(char *string, int start, int length){char temp[30];strncpy(temp,stringestartlength);temp[length]-'\O;return(atoi(temp));)

float InvNorm (float mean, float stdev){float norm-O;int i; //construct normal distribution from the central limit theorem

Waste Package Operations CalculationTitle: Updated Calculation oT Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-00000 I REV 00 ATTACHMENT II, Page 11-6 of 11-7

for(i-O;i<12;i++) norm . norm + (float)randol/RANDMAX;norm = norm - 6;return stdev * norm + mean;)

float InvUni Cfloat min, float max)(return min + (max - min)*(float)rando)/RANDMAX;)//uniform distribution

float InvLWeib (float alpha, float beta, float theta)//Weib for log(t)(float x,y;x=(float)randO/(RANDMAX+l);ya-log(I-x);return exp(theta + alpha*pow(y,1/beta));)

float kcalc(int D, float a, float b, float t, float O,float th)(float keff;if(t>25000O)t=250000; //assume constant time dependence beyond range of data

if(th>o) //partial degradation(if (D=-1) // use regression for uniform oxide distribution

{keff-2.35498-.0066737*b-1.8096E-0S*bab+.1418*a-.0071354*ava-.S193*log,(t)+.O59471*pow(log(t),2)-.0022406*pow(log(t),3)-.0O50889*0-.074906*th+.0l0646*th*th-5.2334E-04*pow(th,3);

keff-InvNorm(keff,.00S31);) //account for regression uncertaintyelse //use regression for settled oxide distribution

(keff-1.72095-.0067237*b-l.6667E-05*b*b+.13348*a-.0060497*a*a-.31232*log(t)+.037442*pow(log(t),2)-.0014715*pow(log(t),3)-.016797*0-.066316*th+.0094036*th*th-4.6905E-04*pow(th,3);

keff-InvNorm(keff, .00846);)) //account for regression uncertaintyelse(if(D(-i) // use regression for uniform oxide distribution

(keff--5.12955+1.65615*log(t)-8.52852E-03*b+.29266*a-.153971*pow(loglt),2)+.0046707*powvlog t),3)+6.8964E-05*b*b-1.63227E-07*powlb,3)-.0671372*a*a+5.36083E-03*pow(a,3)-4.0Bl5lE-04*log(t)*b+7.23708E-03*logCt)*a-5.25978E-03*0;

keff . InvNorm(keff, .00463);) //account for regression uncertaintyelse // use regression for settled oxide distribution

(keff=-l.2Sl6l+.683lS4*log(t)-6.65l33E-03*b+.266l45*a-.0640282*pow(log(t),2)+1.92631E-03*pow(log(t),3)-2.67041E-05*b*b+6.12197E-07*pow(b,3)-.0618276*a*a+5.203S2E-03*pow(a,3)-i.36497E-04*log(t)*b+.0050849*log(t)*a-.140918*0;

keffn InvNorm(keff, .00906);)) //account for regression uncertaintyreturn keff;)

//Find the float numerical value in a statement that begins with the specified//keyword (keystr). Presently designed to read from the array linesfloat findfloat(char* keystr,int startrow,int numrows)(int i-0;char stagC20,tempstr[1001;while ((strncmp(keystr,lineststartrow+il,strlen(keystr))=O)&&(i<=numrows))

i++,if (i--numrows+l) return -1;strcpy(tempstr,lines[startrow+i]);get2(stag,tempstr, =1);return (float)atof(tempstr);)

//Find the int numerical value in a statement that begins with the specified//keyword (keystr).int findint(char* keystr,int startrow,int numrows)(int i=0;char stag[201,tempetr(100];while ((strncmp(keystrlineststartrow+i],strlen(keystr)) =O)&&(i -numrows))i++;if (i>nnumrows) return -1;strcpy~tempstr,lineststartrow+i]);get2(stag,tempstr, wS);

return atoi tempstr);)

Wnrztp Prknop flnprafinr~ic t'alel1l1at;nn

Title: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-00000l REV 00 ATTACHMENT 11, Page 11-7 of 11-7

//copies the strings occurring before and after the separator c (e.g '.3int get2(char *stag,char *sdummy,char c)(int i,index,len;char *p;len-strlen sdummy);p-strchr(adummyc);i-Cint)(p-adummy);indexmi;strncpy(stag,sdummy,i); //copy string before separatorstag(il&.\0;etrim(stag);strcpylsdummy,p+l); //copy string following separatori-O;while((sdummy (ii - ')&&(iclen))i++;//read through leading blanksif((i==len)||(sdummytilw..\ns)) return -l;//can't find a second word on rt sidestrcpy(sdummy,sdummy+i); //copy front trimmed stringreturn index;)

void etrim(char *dummy)//trims trailing blanks(int i;iustrlen(dummy)-1;while(dummylil]<32)i--;dummy(i+ll '\O';)

//trims leading blanks; used in get2 so that fdummy starts with a non-blankvoid ftrim(char *dummy)(int inO;while(dummylil] 32)i++;strcpy(dummy,dummy+i);)

//Searches the override array lines[) for a line beginning with the string//passed in keystr. If the searchatring Ckeystr) is not found, it simply//returns. Othewise it takes num values in the comma separated list on the//right side of the 'ad and enters them in the float array farray, overriding//the values that were hard coded.void getfarray(char *keystr,float *farray,int num,int numrows)(int i-0;char stag(20],tempstr[100];while ((strncmpekeystr,lines[iJ,strlen(keystr))l-O)&&(icnumrows))

i++;if (i--numrows) return;//searchstring not found, so returnstrcpy(tempstr,lines[il);get2(stag,tempstr,'.');for(i-o;icnum;i++) //get all the elements from the comma separated list

{farray(il-atof(tempstr);strcpy(tempstr,strchr(tempstr, ',)+.);))

Weeta 'Pa g L aca ,nirtatinn e CalrulpftinnT V a p s "a .fl fo _ -

Title: Updated Calculation of Probability of Criticalityr for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-00000 I REV 00 ATTACHMENT III, Page 111-1 of 111-2

Attachment III, Input Files

"params.in"

Nominal VA Case with randomization to generate standard deviation

*VA uniform with fuel degradation, with randomization$randflag1 //randomize using the clock$fueldegflagu1 //-1 for fuel degradation

$pnobt-0.5225 //probability of no bathtub$ex.l //exchange flushing efficiency$cl-0.98 //criticality threshold$testcl-0 .93$rlztns=500 //extra iterations

Comparison cases for Table 6-1.

*VA uniform with fuel degradation, no randomization$randflag=l //randomize using the clock$fueldegflag-1 //-1 for fuel degradation$pnobtm0.5225 //probability of no bathtub$ex-.1 //exchange flushing efficiency$cl-0.98 //criticality threshold$testcl-0.93$rlztns=500 //extra iterations

*VA uniform with fuel degradation, delayed assy collapse no randomization$fueldegflag1 //-, for fuel degradation$pnobt=0.5225 //probability of no bathtub$ex-.l //exchange flushing efficiency$cl-0.98 //criticality threshold$testcl-0. 93$rlztns-500 //extra iterations$clpstsdist(1=60000,70000, //delayed collapse start$clpstfdist (390000,90000, //delayed collapse finish

*VA uniform with fuel degradation, drastic iron loss no randomization$fueldegflag-l //-. for fuel degradation$ufox=13 //drastic loss of iron oxide, uniform ox$upoxcsu13 //drastic loss of iron oxide, uniform ox$upoxss=s //drastic loss of iron oxide, uniform ox$pnobtaO.5225 //probability of no bathtub$ex..l //exchange flushing efficiency$cl-0.98 //criticality threshold$testcl-0.93$rlztns=500 //extra iterations*$flowdist(]m.05,.05, //current drip rate

*EDA2 uniform with fuel degradation, no randomization*$randflag1 //randomize using the clock$fueldegflag=1 //-I for fuel degradation$pnobt-0.5225 //probability of no bathtub.$exm.l //exchange flushing efficiency$cl-0.98 //criticality threshold$testclo .93

Wacta lPaAA-amm nmairef;nine ral.Wlllo+;^nTV c*n&u A %.ro F v A "q'%.a SAO T AS a PJ ILA U A"u 316&

Title: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 ATTACHMENT III, Page 111-2 of ill-2

$rlztns-500 //extra iterations

*EDA2 uniform with fuel degradation, delayed assy collapse no randomization*$randflagl1 //randomize using the clock$fueldegflag-1 //1. for fuel degradation$pnobt=0.5225 //probability of no bathtub$ex=.1 //exchange flushing efficiency$c1=0.98 //criticality threshold$testclu0.93$rlztns500 //extra iterations$btimedist(]-2.347,4.810,10.820, //EDA breach time alph, beta, theta$bdurdist1l11.881,10.218,0, //EDA duration of bathtub alph, beta theta$clpstsdist[1-60000,70000, //delayed collapse start$clpstfdistl[180000,90000, //delayed collapse finish

*EDA2 uniform with fuel degradation, drastic iron loss no randomization$fueldegflag-I //-1 for fuel degradation$ufoxm13 //drastic loss of iron oxide, uniform ox$Upoxcs=13 //drastic loss of iron oxide, uniform ox$upoxss-S I/drastic loss of iron oxide, uniform ox$pnobt-O.5225 //probability of no bathtub$ex.l //exchange flushing efficiency$c1-0.98 //criticality threshold$testcl-0.93$rlztns=500 //extra iterations$btimedist[]-2.347,4.8l0,10.820, //EDA breach time alph, beta, theta$bdurdist(J-11.881,10.218,0, //EDA duration of bathtub alph, beta theta

Comparison case: drip rate at current best estimate

*VA uniform with fuel degradation, drip rate reduced$fueldegflag.1 //-I for fuel degradation$pnobt=O.5225 //probability of no bathtub$ex-.1 //exchange flushing efficiency$cl=O.98 //criticality threshold$testcl-0 .93$rlztns=500 //extra iterations$flowdistfl-.05,.05, //current drip rate

to current value

Wnate PVskpau Qneratinne Le1^..1s

Tile pdt--t, : _ _-xav - a %- uMaLunTitle: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 ATTACHMENT IV, Page IV-1 of IV-19

Attachment IV, Output Files

Nominal VA Case, without randomization, for Table 6-1 basic comparison

The time is Mon Aug 16 23:36:55 19991 0.00000002 0.00000003 0.00000004 0.00000005 0.00000006 0.00000007 0.00000008 0.00000009 0.0000000

10 0.000000011 0.000000012 0.000285713 0.002666414 0.003618615 0.009427516 0.010379717 0.017997918 0.028282419 0.034948320 0.049613321 0.064659222 0.074658023 0.089894324 0.102750025 0.113605926 0.125890227 0.139793328 0.153125129 0.175979630 0.191215931 0.205785732 0.227021333 0.244352634 0.266826235 0.285300236 0.312916137 0.340055838 0.362815139 0.384526840 0.411857041 0.441948742 0.467755343 0.485277044 0.520415845 0.546698546 0.567172347 0.601263648 0.627070149 0.655352650 0.691824551 0.7287726

-

Waste Package Operations CalculationTitle: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-00000I REV 00 ATTACHMENT IV, Page IV-2 of IV-19

52 0.757436053 0.787051554 0.818857455 0.851806056 0.886849557 0.912179958 0.944271459 0.987504560 1.022452961 1.059210562 1.085778863 1.115965964 1.151199965 1.186814866 1.213954567 1.241475168 1.269186169 1.308229270 1.345272571 1.388219972 1.421168673 1.454688474 1.483827975 1.512491376 1.553534177 1.589720378 1.618955179 1.649713480 1.681614581 1.719991082 1.746464183 1.778460384 1.822931585 1.854737386 1.904064887 1.941298688 1.974628189 2.009481390 2.045477191 2.086615292 2.129372193 2.156226194 2.186984495 2.227931996 2.257166897 2.295543498 2.321349799 2.3577267

100 2.3941033101 2.4282898102 2.4628572103 2.5038049104 2.5421814105 2.5732254106 2.6047456107 2.6427410108 2.6790225

Waste Package Anpratinne ^X1^..|+:

Title: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-00000 I REV 00 ATTACHMENT IV, Page IV-3 of IV-l 9

109 2.7244460110 2.760727511. 2.7933902112 2.8260531113 2.8647154114 2.8914741115 2.9163283116 2.9655607117 3.0041278118 3.0427899119 3.0679298120 3.0957361121 3.1315415122 3.1604907123 3.2065805124 3.2403861125 3.2820955126 3.3187580127 3.3535157128 3.3860834129 3.4034147130 3.4277929131 3.4573132132 3.4902619133 3.5387325134 3.5742522135 3.6088196136 3.6501481137 3.6828108138 3.7168070139 3.7471845140 3.7748956141 3.8036541142 3.8305080143 3.8650756144 3.8871682145 3.9272586146 3.9556363147 3.9941080148 4.0192480149 4.0645761150 4.0902875151 4.1104756152 4.1398056153 4.1627554154 4.1897998155 4.2217961156 .4.2443650

157 4.2670290158 4.2981681159 4.3244507160 4.3436867161 4.3769208162 4.4052985163 4.4337716164 4.4769094165 4.5106199

Waste Packave Onprationri 1"ln I l ";^"Waste ax_,age Oners,--n--…%."A16, % nh.li

Title: Updated Calculation of Probability of Criticality for the EDA 1I Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 ATTACHMENT IV, Page IV-4 of IV-19

166 4.5431874167 4.5768978168 4.6108937169 4.6366051170 4.6649826171 4.6935508172 4.7190719173 4.7439259174 4.7675423175 4.8000146176 4.8252497177 4.8578178178 4.8821002179 4.9091449180 4.9316184181 4.9673287182 4.9980871183 5.0217987184 5.0575085185 5.0804582186 5.1065503187 5.1337653188 5.1582586189 5.1792090190 5.2042533191 5.2312028192 5.2589136193 5.2860535194 5.3050035195 5.3319530196 5.3553791197 5.3803282198 5.3955644199 5.4278464200 5.4533676201 5.4895537202 5.5062183203 5.5353580204 5.5536414205 5.5742106206 5.6058260207 5.6319181208 5.6502020209 5.6638195210 5.6926732211 5.7099093212 5.7310495213 5.7437149214 5.7609510215 5.7861861216 5.8124685217 5.8319900218 5.8571299219 5.8788421220 5.8956019221 5.9229321222 5.9456915

Waste Package Operations CalculationTitle: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-00000 I REV 00 ATTACHMENT IV, Page IV-5 of IV-19

223 5.9657845224 5.9917814225 6.0087315226 6.0258724227 6.0500603228 6.0708199229 6.0915789230 6.1151953231 6.1312890232 6.1536673233 6.1718555234 6.1945198235 6.2098512236 6.2307059237 6.2501322238 6.2642260239 6.2934604240 6.3219335241 6.3547869242 6.3753557243 6.3974485244 6.4214455245 6.4374440246 6.4577273247 6.4782960248 6.4885809249 6.5061976

*RDA2 uniform with fuel degradation, no randomizationNumber of batch records screened in-599 numberpkgs=4516numcritselOkyr=O explOmO.000000 explOO-2.394103 exp249-6.506198

Nominal VA Case with randomization to generate standard deviation

The time is Mon Aug 09 22:51:38 1999*VA uniform with fuel degradation, with randomizationNumber of batch records screened in=597 numberpkgs=4516numcrits@lOkyr=34 explOoO.003238 explOO=2.455525 exp249=6.548669

The time is Mon Aug 09 22:52:32 1999*VA uniform with fuel degradation, with randomizationNumber of batch records screened in=602 numberpkgs=4516numcritsOlOkyr=6 explO.0.000571 explOO-2.383628 exp249=6.222231

The time is Mon Aug 09 23:03:35 1999*VA uniform with fuel degradation, with randomizationNumber of batch records screened in=591 numberpkgs=4516numcrits~lOkyr-d8 explo-0.001714 explOO=2.424766 exp249-6.370975

The time is Mon Aug 09 23:05:40 1999*VA uniform with fuel degradation, with randomizationNumber of batch records screened in-586 numberpkgs=4516numcrits~lOkyr-16 explO0w.001524 explOO=2.319540 exp249-6.262226

Comparison cases for Table 6-1.

Waste Package Operations CalculationTitle: Updated Calculation of Probability of Criticality forthe EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 ATFACHMENT IV, Page IV-6 of IV-19

The time is Mon Aug 16 23:52:01 19991 0.00000002 0.00000003 0.00000004 o.00000005 0.00000006 0.00000007 0.00076188 0.00152369 0.0015236

10 0.002285411 0.002380712 0.003713913 0.003809114 0.007046815 0.014760216 0.017807517 0.024092418 0.031805819 0.042947420 0.047232621 0.060088322 0.076467323 0.088085024 0.095131825 0.107606626 0.118557727 0.135412928 0.152458529 0.168361430 0.186740231 0.223117032 0.249399633 0.279396234 0.295108635 0.319486836 0.351578337 0.374242338 0.397382539 0.429188340 0.463946241 0.501560942 0.530509943 0.555173744 0.589265045 0.621737446 0.670303247 0.703727948 0.731153349 0.760768950 0.789813151 0.819809752 0.859900353 0.888563654 0.923892855 0.9603648

Waste Package Operations CalculationTitle: Updated Calculation of Probability of Criticality for the EDA 11 Waste Package DesignDocument Identifier: CAL-UDC-MD-O00000 REV 00 ATTACHMENT IV, Page IV-7 of IV-19

56 0.991408857 1.032737458 1.068733259 1.103776860 1.137677561 1.184338862 1.227381463 1.272233464 1.29975406S 1.338130666 1.386886867 1.423739668 1.462592369 1.504777970 1.549439371 1.603623672 1.649142173 1.692279974 1.729513775 1.766747476 1.805980977 1.862641178 1.906826479 1.948536080 2.001767981 2.038239882 2.079187483 2.114611884 2.156416585 2.198316486 2.246025387 2.286115788 2.327920689 2.363344990 2.406768591 2.437812492 2.491520693 2.534753694 2.567416595 2.613506496 2.649311997 2.692449798 2.738063299 2.7804393

100 2.8312907101 2.8645248102 2.9060439103 2.9572760104 2.9908912105 3.0228875106 3.0705961107 3.1025926108 3.1499203109 3.1812500110 3.2181981111 3.2658118112 3.2973318

Waste Package OnkInratinne t'N 1 I .. I-A. :

Title: Updated Calculation of Probability of Criticality for the EDA [I Waste Package DesignDocument Identifier: CAL-UDC-MD-oooool REV 00 ATTACHMENT IV, Page IV-S of IV-19

113 3.3354226114 3.3812270115 3.4136993116 3.4561705117 3.4901667118 3.5424462119 3.5779660120 3.6132000121 3.6491958122 3.6873818123 3.7334716124 3.7677535125 3.8150812126 3.8553622127 3.9915486128 3.9385908129 3.9624926130 4.0096303131 4.0404836132 4.0752416133 4.1145705134 4.1611364135 4.1996081136 4.2420793137 4.2798844138 4.3094048139 4.3573993140 4.3866340141 4.4297718142 4.4660536143 4.5010968144 4.5410923145 4.5807067146 4.6129888147 4.6570787148 4.6968840149 4.7384026150 4.7706846151 4.8071567152 4.8474377153 4.8835287154 4.9204771155 4.9489496156 4.9855169157 5.0236077158 5.0736022159 5.1072169160 5.15S4975161 5.1908267162 5.2181568163 5.2563428164 5.2969093165 5.3267157166 5.3598546167 5.3939457168 5.4230854169 5.4587952

Waste Pai - lmnd r C-impi-…wn rl..|s

Title: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-O00000 REV 00 ATTACHMENT IV, Page IV-9 of IV-19

170 5.4991719171 5.5416431172 5.5705920173 5.6101113174 5.6462022175 5.6711519176 5.7016243177 5.7300974178 5.7646648179 5.7925664180 5.8297998181 5.8533210182 5.8786513183 5.9136950184 5.9355018185 5.9751167186 5.9932098187 6.0282529188 6.0616779189 6.0909128190 6.1179570191 6.1496675192 6.1748075193 6.2009952194 6.2263255195 6.2501322196 6.2787004197 6.3117442198 6.3400265199 6.3628811200 6.3960201201 6.4226836202 6.4556323203 6.4817243204 6.5054359205 6.5406699206 6.5736185207 6.6079956208 6.6297072209 6.6530376210 6.6824628211 6.7139831212 6.7452178213 6.7696912214 6.7911168215 6.8204469216 6.8522526217 6.8819638218 6.9033900219 6.9253871220 6.9626210221 6.9885227222 7.0183286223 7.0413740224 7.0644189225 7.0812739226 7.1018431

Waste Package Operations CalculationTitle: Updated Calculation of Probability of Criticality for the EDA 11 Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 ATTACHMENT IV, Page IV-1O of IV-19

227 7.1274589228 7.1481233229 7.1689780230 7.1937368231 7.2116395232 7.2319233233 7.2620146234 7.2866788235 7.3093426236 7.3333401237 7.3622890238 7.3837152239 7.4082837240 7.4221866241 7.4354235242 7.4515167243 7.4753234244 7.4928450245 7.5043674246 7.5202708247 7.5456011248 7.5612185249 7.5855961

*EDA2 uniform with fuel degradation, no randomizationNumber of batch records screened in=595 numberpkgs-4516numcritsrlOkyrw24 explO0.002285 explOO=2.831291 exp249=7.585596

The time is Tue Aug 10 00:05:21 1999*VA uniform with fuel degradation, drastic iron loss no randomizationNumber of batch records screened in=8589 numberpkgs-4516numcritsllOkyr-249 explO-0.023712 explO0=28.652296 exp249-78.759530


10 0.000000011 0.000000012 0.000000013 0.000000014 0.000000015 0.000000016 0.000000017. 0.000000018 0.000000019 0.000000020 0.000000021 0.000000022 0.000000023 0.0000000

Waste Package Onerntinnc Rstirwwlt;rxn--- -- r -^ -aiw.umv u iazu

Title: Updated Calculation of Probability of Criticality for the EDA 11 Waste Package DesignDocument Identifier: CAL-UDC.MD.000001 REV 00 ATTACHMENT IV, Page IV-1 I of IV-19

24 0.000000025 0.000000026 0.000000027 0.000000028 0.000000029 0.000000030 0.000000031 0.000000032 0.000000033 0.000000034 0.000000035 0.000000036 0.000000037 0.000000038 0.000000039 0.000000040 0.000000041 0.000000042 0.000000043 0.000000044 0.000000045 0.000000046 0.000000047 0.000000048 0.000000049 0.000000050 0.000000051 0.000000052 0.000000053 0.000000054 0.000000055 0.000000056 0.000000057 0.000000058 0.000000059 0.000000060 0.000000061 0.000000062 0.000000063 0.000000064 0.000000065 0.000000066 0.000000067 0.000000068 0.000000069 0.000000070 0.000000071 0.000000072 0.000000073 0.000000074 0.000000075 0.000000076 0.000000077 0.000000078 0.000000079 0.000000080 0.0000000

Waste Package Operations CalculationTitle: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier. CAL-UDC-MDOO00001 REV 00 ATTACHMENT IV, Page IV-12 of IV-19

81 0.000000082 0.000000083 0.000000084 0.000000085 0.000095286 0.000095287 0.000095288 0.000095289 0.000095290 0.000380991 0.000380992 0.001523693 0.001618994 0.001809395 0.001809396 0.001809397 0.001809398 0.002571199 0.0025711

100 0.0027616101 0.0028568102 0.0029520103 0.0029520104 0.0037139105 0.0054279106 0.0056184107 0.0057136108 0.0084752109 0.0087609110 0.0102845111 0.0114272112 0.0117129113 0.0119034114 0.0128557115 0.0128557116 0.0146650117 0.0147602118 0.0179027119 0.0255208120 0.0297108121 0.0334247122 0.0340913123 0.0362815124 0.0382813125 0.0415190126 0.0459947127 0.0470422128 0.0488515129 0.0529462130 0.0549460131 0.0563744132 0.0591360133 0.0626594134 0.0690396135 0.0703728136 0.0733248137 0.0738962

Waste Packageo Oneratirnn ^61^..|X+:

Title: Updated Calculation of Probability of Criticality for the EDA 11 Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 ATTACHMENT IV, Page IV-13 of IV-19

138 0.0778005139 0.0837046140 0.0884659141 0.0915132142 0.0950366143 0.0982743144 0.1676066145 0.1132250146 0.1174150147 0.1222715148 0.1283661149 0.1307467150 0.1361747151 0.1420788152 0.1445547153 0.1466497154 0.1560771155 0.1596005156 0.1686471157 0.1757891158 0.1827407159 0.1895970160 0.1952155161 0.2026432162 0.2101661163 0.2153084164 0.2259738165 0.2313065166 0.2419719167 0.2488283168 0.2569226169 0.2689212170 0.2779678171 0.2849193172 0.2918709173 0.2994891174 0.3132018175 0.3306283176 0.3387226177 0.3558635178 0.3671003179 0.3746232180 0.3830032181 0.3965254182 0.4058577183 0.4157613184 0.4221415185 0.4300454186 0.4455673187 0.4559471188 0.4684219189 0.4798491190 0.4854675191 0.4915620192 0.5040368193 0.5171781194 0.5278435

Waste Package Operations CalculationTitle: Updated Calculation of Probability of Criticality for the EDA 11 Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 ATTACHMENT IV, Page IV-14 of IV-19

195 0.5354617196 0.5409849197 0.5511742198 0.5637442199 0.5814564200 0.5908839201 0.6014540202 0.6085009203 0.6166904204 0.6330694205 0.6427826206 0.6509721207 0.6561143208 0.6820162209 0.6915389210 0.7050611211 0.7153456212 0.7286774213 0.7439137214 0.7578169215 0.7667682216 0.7750530217 0.7886704218 0.8006690219 0.8158101220 0.8287610221 0.8440926222 0.8622809223 0.8769459224 0.8930393225 0.9156081226 0.9317967227 -0.9529371228 0.9695066229 0.9817909230 1.0068356231 1.0197865232 1.0334992233 1.0544491234 1.0747325235 1.0902545236 1.1073954237 1.1252980238 1.1366301239 1.1556754240 1.1679598241 1.1852911242 1.2055744243 1.2200490244 1.2348092245 1.2453794246 1.2612823247 1.2780422248 1.2888982249 1.3195612

*RDA2 uniform with fuel degradation, no randomizationNumber of batch records screened in.600 numberpkgsu4516

Wanqte Pnekina'p AnprastinncTitle: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-000001 REV 00 ATTACHMENT IV, Page IV-15 of IV-19

numcritselOkyr=O explua .000000 explOO=0.002762 exp249*1.319561


10 0.000000011 0.000000012 0.000000013 0.000000014 0.000000015 0.000000016 0.000000017 0.000000018. 0.000000019 0.000000020 0.000000021 0.000000022 0.000000023 0.000000024 0.000000025 0.000000026 0.000000027 0.000000028 0.000000029 0.000000030 0.000000031 0.000000032 0.000000033 0.000000034 0.000000035 0.000000036 0.000000037 0.000000038 0.000000039 0.000000040 0.000000041 0.000000042 0.000000043 0.000000044 0.000000045 0.000000046 0.000000047 0.000000048 0.000000049 0.000000050 0.000000051 0.000000052 0.000000053 0.000000054 0.0000000

Waste Package Opprationn Pe1^..16+:

WatePck~ Oentn~ -a,_ lE-i-------- w4IIcusaluunTitde: Updated Ciculation of Probability of Criticality for the EDA 11 Waste Package DesignDocument Identifier: CAL-UDC-MD6-00000 REV 00 ATTACHMENT IV, Page IV-16 of IV-19

55 0.000000056 0.000000057 0.000000058 0.000000059 0.000000060 0.000000061 0.000000062 0.000000063 0.000095264 0.000095265 0.000095266 0.000095267 0.000095268 0.000095269 0.000095270 0.000095271 0.000095272 0.000095273 0.000095274 0.000095275 0.000095276 0.000095277 0.000095278 0.000095279 0.000095280 0.000857081 0.000857082 0.000857083 0.000952384 0.001428485 0.001428486 0.001999887 0.002656888 0.002952089 0.003047390 0.003047391 0.003809192 0.003809193 0.004094894 0.004761495 0.006094596 0.006189897 0.007999198 0.007999199 0.0085704

100 0.0092370101 0.0093323102 0.0098084103 0.0105702104 0.0105702105 0.0110463106 0.0126652107 0.0127604108 0.0141888109 0.0173313110 0.0188550111 0.0193311

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W At- as' Iraugii ow. ̂ zm _S Clcula-ionTitle: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-OOOOo1 REV 00 ATTACHMENT IV, Page IV-17 of IV-19

112 0.0215213113 0.0228545114 0.0261874115 0.0316154116 0.0352340117 0.0354245118 0.0368529119 0.0379004120 0.0399001121 0.0447567122 0.0463756123 0.0505656124 0.0565649125 0.0582790126 0.0628499127 0.0676112128 0.0737057129 0.0738962130 0.0779910131 0.0803716132 0.0836093133 0.0897991134 0.0958936135 0.1004645136 0.1106538137 0.1128441138 0.1187481139 0.1276042140 0.1332226141 0.1421740142 0.1504587143 0.1572199144 0.1646476145 0.1718848146 0.1775984147 0.1796934148 0.1810266

149 0.1848357150 0.1880734151 0.2026432152 0.2104518153 0.2166415154 0.2311160155 0.2365440156 0.2586367157 0.2664453158 0.2695878159 0.2764441160 0.2793962161 0.2898712162 0.2997748163 0.3136779164 0.3181536165 0.3284381166 0.3333899167 0.3428174168 0.3504355

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Title: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier: CAL-UDC-MD-00oooI REV 00 ATTACHMENT IV, Page IV-18 of IV-I9

169 0.3615771170 0.3666242171 0.3800512172 0.3871932173 0.3967159174 0.4070956175 0.4207131176 0.4310928177 0.4428058178 0.4516619179 0.4582326180 0.4700407181 0.4860389182 0.5013704183 0.5119406184 0.5246058185 0.5377472186 0.5489839187 0.5656487188 0.5866939189 0.5953595190 0.6184045191 0.6333551192 0.6431635193 0.6678273194 0.6782070195 0.6870632196 0.6968716197 0.7148694198 0.7304867199 0.7439137200 0.7550553201 0.7723866202 0.7953363203 0.8076206204 0.8200001205 0.8370458206 0.8479969207 0.8638045208 0.8777077209 0.9027524210 0.9178935211 0.9266544212 0.9406528213 0.9505564214 0.9665546215 0.9801720216 0.9973129217 1.0132158218 1.0269285219 1.0439741220 1.0579725221 1.0719709222 1.0867311223 1.1013961224 1.1272979225 1.1392012

Wn-.ttp- PnPL-airip Onp-ratinne ralerllstiatnnWs,�te Pnekgorp Anprs�tinnt Ca I�,,IatinnTitle: Updated Calculation of Probability of Criticality for the EDA II Waste Package DesignDocument Identifier. CAL-UDC-MD-000001 REV 00 ATTACHMENT IV, Page IV-19 of IV-19

226 1.1554850227 1.1747208228 1.1888145229 1.2024320230 1.2182397231 1.2321428232 1.2466173233 1.2672815234 1.3003253235 1.3179423236 1.3371782237 1.3603184238 1.3837442239 1.4097413240 1.4249776241 1.4516411242 1.4701152243 1.4995404244 1.5236329245 1.5390595246 1.5587716247 1.5771504248 1.5982908249 1.6164792

*EDA2 uniform with fuel degradation, delayed collapse no randomizationNumber of batch records screened in-591 numberpkgs-4516numcritselOkyr=O explO 0.000000 explOO-0.009237 exp249=1 .616479

The time is Mon Aug 09 23:50:12 1999*EDA2 uniform with fuel degradation, drastic iron loss no randomizationNumber of batch records screened in8583 numberpkgsw4516numcrits2lOkyru0 explO0.000000 explOO=0 .038377 exp249-15 .583335

Comparison case: drip rate at current best estimate

The time is Tue Aug 10 10:03:19 1999*VA uniform with fuel degradation, drip rate reduced to current valueNumber of batch records screened in=593 numberpkgs=4516numcritsel0kyr-O explo0. 000000 explOO-2 .330492 exp249=6. 161190

Documents

CAL-UDC-MD-000001, Rev 00, 'Updated Calculation of ... · Document Identifier: CAL-UDC-MD-000001 REV 00 Page 5 of 23 1. PURPOSE The purpose of this calculation is to update the estimate