A Burnup Credit Methodology for PWR Spent Fuel Pool

A Burnup Credit Methodology for PWR Spent Fuel Storage Pool Thesis submitted to the Universitat Politècnica de València in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE In Nuclear and Chemical Engineering Author: Victor Faria de Castro Advisors: Rafael Miró Herrero Gumersindo Verdú Martín Departamento de Ingeniería Química y Nuclear May 2012 i A Burnup Credit Methodology for PWR Spent Fuel Storage Pool VICTOR FARIA DE CASTRO (ABSTRACT) In the past, criticality safety analyses for spent fuel storage and transport canisters assumed the spent fuel to be fresh (unburned) fuel with uniform isotopics corresponding to the maximum allowable enrichment. However, because this assumption ignores the decrease in reactivity as a result of irradiation, it is very conservative for fuel with significant burnup. The concept of taking credit for the reduction in reactivity due to fuel burnup is commonly referred to as Burnup Credit. In this work a methodology for giving Burnup Credit in development is presented. The final goal is to obtain the loading curve that determines the region on a spent fuel storage pool in which a fuel element must be stored. Several analyses on the code were carried out with the SCALE6.1 code package, more specifically, the TRITON depletion sequence, with KENO-VI and NEWT transport codes, and CSAS6 criticality sequence, which uses KENO-VI transport code. The methodology consists in determine the upper subcritical limit (USL) which is the limit for the keff at safety conditions. The USL was determined with a set of benchmark critical experiments available for SCALE. Once the bias and its uncertainty are determined the USL can be established and, with a conservative axial burnup profile, the loading curve can be obtained. ii INDEX ABSTRACT ...................................................................................................................................................... i I. INTRODUCTION .............................................................................................................................. 1 I.1 CRITICALITY ACCIDENT REQUIREMENTS ................................................................................................... 1 I.2 CRITICALITY SAFETY ANALYSIS METHOD AND COMPUTATIONAL CODE ............................................................ 2 II. THE SCALE CODE SYSTEM ............................................................................................................... 3 II.1 TRITON: TRANSPORT RIGOR IMPLEMENTED WITH TIME-DEPENDENT OPERATION FOR NEUTRONIC DEPLETION ... 3 II.2 CROSS-SECTION PROCESSING ............................................................................................................... 5 II.3 CSAS6/KENO-VI: ............................................................................................................................ 7 II.4 NEWT ............................................................................................................................................ 8 II.5 ORIGEN-S ...................................................................................................................................... 8 III. CRITICALITY ANALYSIS VALIDATION ......................................................................................... 10 III.1 INTRODUCTION ............................................................................................................................... 10 III.2 THE UPPER SUBCRITICAL SUPERIOR LIMIT (USL) ..................................................................................... 10 IV. BURNUP CREDIT METHODOLOGY IN A PWR POWER PLANT ..................................................... 13 IV.1 INTRODUCTION ............................................................................................................................... 13 IV.2 CHARACTERISTICS OF REGION II FOR FUEL STORAGE ................................................................................ 13 IV.3 CHARACTERISTICS OF THE FUEL ELEMENT .............................................................................................. 15 IV.4 GEOMETRIC MODEL OF REGION II OF THE FUEL ELEMENT POOL ................................................................. 15 V. BURNUP ISOTOPES ....................................................................................................................... 19 V.1 DETERMINATION OF ACTINIDES AND FISSION PRODUCTS .......................................................................... 19 VI. INFLUENCE OF THE OPERATION PARAMETERS ON ISOTOPE CALCULATIONS ............................ 20 VI.1 INTRODUCTION ............................................................................................................................... 20 VI.2 EFFECT OF THE AVERAGE BURNUP IN THE BURNUP CALCULATIONS.............................................................. 20 VI.3 EFFECT OF BURNUP TIME-DEPENDENT VARIATIONS ................................................................................. 21 VI.4 SENSITIVITY ANALYSIS WITH RESPECT TO OPERATIONAL PARAMETERS ......................................................... 24 VII. SCALE BURNUP PARAMETERS .................................................................................................. 28 VII.1 ADDNUX PARAMETER: .................................................................................................................... 31 VII.2 TIMETABLE BLOCK ........................................................................................................................ 34 VII.3 TIMETABLE AND ADDNUX ANALYSIS............................................................................................... 35 VII.4 CENTRM DATA ............................................................................................................................. 38 VIII. AXIAL BURNUP CREDIT METHODOLOGY ................................................................................... 40 VIII.1 INTRODUCTION ........................................................................................................................... 40 VIII.2 OBJECTIVE OF THE METHODOLOGY .................................................................................................. 42 VIII.3 AXIAL PROFILE CORRECTION ........................................................................................................... 42 VIII.4 CRITICALITY ANALYSIS OF REAL PROFILES ........................................................................................... 44 IX. CONCLUSIONS AND FUTURE WORKS ........................................................................................ 47 X. REFERENCES ................................................................................................................................. 48 iii FIGURES Figure 1: TRITON depletion sequence using NEWT as transport code ....................................................... 4 Figure 2: TRITON depletion sequence using KENO as transport code ....................................................... 5 Figure 3: Unit cell used for cross-section processing ................................................................................... 7 Figure 4: Region I and II of the spent fuel storage pool ............................................................................. 14 Figure 5: Guide tubes distribution on a fuel element.................................................................................. 15 Figure 6: Outline of the reference cell model ............................................................................................. 16 Figure 7: Full PWR fuel element on KENO3D .......................................................................................... 28 Figure 8: Top view of the PWR fuel element on KENO3D ....................................................................... 29 Figure 9: NEWT 2D plot of the PWR fuel element ................................................................................... 29 Figure 10: Reference cell of the spent fuel storage pool ............................................................................ 30 Figure 11: Axial view of the reference cell of the spent fuel storage pool ................................................. 30 Figure 12: kef variation with ADDNUX parameters ................................................................................... 33 Figure 13: Boron letdown curve applied to the calculations ...................................................................... 34 Figure 14: kef variation for ADDNUX cases with boron letdown using KENO-VI ................................... 36 Figure 15: kef variation for ADDNUX cases with boron letdown using NEWT ........................................ 36 Figure 16: Criticality analysis for the region II of the spent fuel storage pool (TRITON/KENO-VI depletion sequence) .................................................................................................................................... 37 Figure 17: Criticality analysis for the region II of the spent fuel storage pool (TRITON/NEWT depletion sequence) .................................................................................................................................................... 38 Figure 18: kef variation with CENTRM parameters .................................................................................... 39 Figure 19: Axial burnup distribution for a fuel element in a PWR reactor ................................................. 41 Figure 20: Outline representing the most important points developed in the methodology. ...................... 42 Figure 21: Description of Wilks methodology in order to obtain the most critical burnup profile ............ 43 Figure 22: Model with KENO3D of a burnup node ni of the fuel pellet. The number of burnup nodes (n) is 32. ........................................................................................................................................................... 45 Figure 23: Model with KENO3D of a fuel pellet of n nodes of 341.5 cm. of maximum active length. The number of burnup nodes is 32. ................................................................................................................... 46 iv TABLES Table 1: Benchmark calculations for VALSCALE and BORON sets ........................................................ 11 Table 2: Characteristics of a fuel element in region II ............................................................................... 15 Table 3: Data of cell and fuel pins .............................................................................................................. 16 Table 4: Composition (% in volume) of Zircaloy-4 ................................................................................... 18 Table 5: Geometric data of the guide tube .................................................................................................. 18 Table 6: Data of the reference cell .............................................................................................................. 18 Table 7: Selected nuclides in the burnup calculations ................................................................................ 19 Table 8: Basis Case .................................................................................................................................... 20 Table 9: Results for burnup time-dependent variations at 3.0% ................................................................. 22 Table 10: Results for burnup time-dependent variations at 3.6% ............................................................... 22 Table 11: Results for burnup time-dependent variations at 4.5% ............................................................... 23 Table 12: Results for operational parameters variations at 3.0% ............................................................... 24 Table 13: Results for operational parameters variations at 3.6% ............................................................... 25 Table 14: Results for operational parameters variations at 4.5% ............................................................... 25 Table 15: Results for boron variations ....................................................................................................... 26 Table 16: Burnup conditions for the isotopic calculation ........................................................................... 27 Table 17: ADDNUX=1 (15 additional nuclides are added) ....................................................................... 31 Table 18: ADDNUX=-2 (49 additional nuclides for a total of 64) ............................................................. 31 Table 19: ADDNUX=2 (30 additional nuclides for a total of 94) .............................................................. 31 Table 20: ADDNUX=3 (136 additional nuclides for a total of 230) .......................................................... 32 Table 21: ADDNUX=4 (158 additional nuclides for a total of 388) .......................................................... 32 Table 22: kef variation with ADDNUX parameters .................................................................................... 33 Table 23: Boron letdown timetable applied to the calculations .................................................................. 34 Table 24: List of fuel nuclides automatically included by SAS2H in neutron transport calculation .......... 35 Table 25: kef variation for ADDNUX cases with boron letdown with KENO-VI ...................................... 35 Table 26: kef variation for ADDNUX cases with boron letdown with NEWT ........................................... 35 Table 27: Criticality analysis for the region II of the spent fuel storage pool ............................................ 36 Table 28: kef variation with CENTRM parameters ..................................................................................... 39 1 I. INTRODUCTION Unirradiated reactor fuel has a well-specified nuclide composition that provides a straightforward and bounding approach to the criticality safety analysis of transport and storage casks [1]. In the past, criticality safety analyses for spent fuel storage and transport canisters assumed the spent fuel to be fresh (unburned) fuel with uniform isotopics corresponding to the maximum allowable enrichment. This freshfuel assumption provides a well-defined, bounding approach to the criticality safety analysis that eliminates all concerns related to the fuel operating history, thus, considerably simplifying the analysis. However, because this assumption ignores the decrease in reactivity as a result of irradiation, it is very conservative for fuel with significant burnup [2] The concept of taking credit for the reduction in reactivity due to fuel burnup is commonly referred to as Burnup Credit. This reduction in reactivity that arises with fuel burnup is due to change in concentration of fissile nuclides and the production of parasitic neutron-absorbing nuclides. Actinide-only burnup credit refers to a methodology that considers only the two major actinides present in spent fuel: uranium and plutonium. Fission product burnup credit considers a number of fission products and minor actinides. Full burnup credit refers to a combination of actinide-only and fission product burnup credits. For over two decades, burnup credit has been sought for the transportation, storage, and disposal of spent commercial nuclear fuel. Progress has included the issuance of the first version of U.S. Nuclear Regulatory Commission (NRC) Interim Staff Guidance 8 (ISG8) in 1999. The latest version, Revision 2, has endorsed actinide-only burnup credit and was issued in 2002. Experimental data necessary for validation of the isotopic compositions and the nuclear cross sections of fission products have not been deemed to be adequate thus far, and approval of full burnup credit, including both actinides and fission products, has been subsequently delayed [3]. Since 2004, Oak Ridge National Laboratory (ORNL) has been working on a project whose goal is to develop scientific and technical information necessary to support preparation and review of a safety evaluation for cask designs that use full burnup credit to transport PWR spent fuel. Cooperative work between ORNL, NRC, the Electric Power Research Institute (EPRI), and the U.S. Department of Energy (DOE) was established in order to execute this full burnup credit project [4]. The issuance of the ISG8 – Revision 3 was predicted to 2011 and presumably will provide recommendations for full burnup credit. I.1 Criticality accident requirements Criteria in matters of criticality analysis were based on the NRC regulation 10 CFR 50.68 [5] along with the guidance document [6]. When giving credit for soluble boron it is assumed the hypothesis that there is no loss in boron inside the spent fuel storage pool. 2 1. For PWR fuel storage pools where no soluble boron credit is taken, the criticality safety analysis will follow the condition: a) If no credit for soluble boron is taken, the k-effective of the spent fuel storage racks loaded with fuel of the maximum fuel assembly reactivity must not exceed 0.95, at a 95 percent probability, 95 percent confidence level, if flooded with unborated water. 2. If soluble boron credit is taken, two conditions are to be analyzed: a) If credit is taken for soluble boron, the k-effective of the spent fuel storage racks loaded with fuel of the maximum fuel assembly reactivity must not exceed 0.95, at a 95 percent probability, 95 percent confidence level, if flooded with borated water, and; b) The k-effective must remain below 1.0 (subcritical), at a 95 percent probability, 95 percent confidence level, if flooded with unborated water. I.2 Criticality safety analysis method and computational code Following the recommendations of the [ISG8R2], the criticality safety analysis methods must adequately consider all the neutronic and geometric features of the storage pool. In particular, the storage racks that contain layers of neutron absorbing materials, or structural poisoned material (e.g. borated water), need detailed modeling. ISG8R2 recommendation calls for validation of the analysis tools using measured data to determine appropriate bias and uncertainties [7]. In this work the code system SCALE6.1 was used in order to obtain fresh fuel burnup details (isotopic concentrations) using TRITON, for later use in the criticality analysis in the spent fuel storage pool, using CSAS6. 3 II. THE SCALE CODE SYSTEM The SCALE code system, developed at Oak Ridge National Laboratory (ORNL) in the United States, provides a comprehensive, verified and validated, user-friendly tool set for criticality safety, reactor physics, spent fuel characterization, radiation shielding, and sensitivity and uncertainty analysis. SCALE6.1 is built on a modular design and provides a framework with 89 computational modules, including three deterministic and three Monte Carlo radiation transport solvers that are selected based on the desired solution. As mentioned before, two main control modules of SCALE6.1 were used for the calculations: TRITON, a code for transport, depletion and sensitivity and uncertainty analysis, and CSAS6, a criticality code for calculation of the neutron multiplication factor for the system. Both of these codes prepare a resonancecorrected cross-section library for subsequent use in the KENO-VI 3-D transport code. Unless specified, all cases were run with the 44-groups ENDF/B-V master library available on SCALE package. Also, NEWT deterministic transport code was used on TRITON depletion sequence as a means to compare the TRITON transport codes in a burnup calculation. II.1 TRITON: Transport Rigor Implemented with Time-dependent Operation for Neutronic depletion TRITON is a multipurpose SCALE control module for transport, depletion, and sensitivity and uncertainty analysis for reactor physics applications. TRITON can be used to provide automated, problem-dependent cross-section processing followed by multigroup neutron transport calculations for one-, two-, and threedimensional (1D, 2D, and 3D) configurations. Additionally, this functionality can be used in tandem with the ORIGEN depletion module to predict isotopic concentrations, source terms, and decay heat, as well as generate few-group homogenized cross sections for nodal core calculations. [15] TRITON provides the capability to perform deterministic transport analysis for 1D geometry using XSDRNPM and for a wide variety of 2D arbitrary geometry configurations using NEWT. TRITON also includes Monte Carlo depletion capabilities using KENO V.a and KENO-VI. Both KENO codes offer powerful 3D geometric representations for depletion calculations. With the rigorous treatment of neutron transport available within XSDRNPM, NEWT and KENO, coupled with the accuracy of ORIGEN depletion capabilities and SCALE multigroup cross-section processing calculations, TRITON provides a rigorous first-principles approach for calculation of cross sections and isotopic depletion source terms for fuel designs. 4 Five cross-section processing options are supported in TRITON: (1) the CENTRM-based discrete ordinates option, (2) the CENTRM-based two-region option, (3) the CENTRM-based doubly heterogeneous option, (4) the NITAWL-based option, and (5) the BONAMI-based option. Because the first option, CENTRM-based discrete ordinates, is the most rigorous and accurate [14] it was the chosen crosssection processing tool for all the calculations in the study presented. For this work, TRITON was used with the depletion sequences t-depl and t6-depl, which invokes NEWT and KENO-VI, respectively as transport model. Figure 1 shows the scheme used for the depletion calculation using NEWT, while Figure 2 shows a depletion scheme using KENO transport code. Figure 1: TRITON depletion sequence using NEWT as transport code 11 To obtain the USL, the bias  = (1 – kc) must be determined. The benchmark sets BORON and VALSCALE were used in order to calculate this bias. These sets of critical experiments used as benchmarks are considered representative for the composition, configuration and nuclear features of the system. The results for these benchmarks calculations are represented in the Table 1, where N is the number of experiments and kc, is the uncertainty in the bias  = (1 – kc). Table 1: Benchmark calculations for VALSCALE and BORON sets Experiment N kc kc VALSCALE 79 1.00035 0.0172691 BORON 8 0.99426 0.0059682 For the standard experiments set for validation of the SCALE code, VALSCALE, the values for βVS y ΔβVS are obtained: (2) for βVS < 0 Although the reference [8] implies the values of the USL take into account the values of the bias, negative or positive, in this study, in order to be conservative, the negative bias is discarded. For the experiments set that contain boron, BORON, the values for βVS y ΔβVS are obtained: (3) for βB > 0 12 The VALSCALE set provide the most conservative bias and uncertainty, so it will be the choice set for establishing the USL, which is the safety limit to determine when a storage pool is safe in terms of criticality. Further analysis of the results should give more statistical data so as to obtain the USL based not only on the uncertainties provided by the SCALE6.1 code, but the statistical confidence interval accordingly to the Spanish norm UNE [9] and [5]. 13 IV. BURNUP CREDIT METHODOLOGY IN A PWR POWER PLANT IV.1 Introduction In the storage pool of the studied PWR, two regions are differentiated: region I, which is the oldest, with a greater separation between element racks; and region II, with elements with a burnup degree and greater enrichment. The application of this methodology will focus on the acquisition of a criterion, which will decide the most suitable region for the safe storage of combustible material. Initially, the spent fuel storage pool was formed by the racks in region I. Due to the lack of storage space for combustible materials, the pool was later equipped with new steel racks with a greater content of boron and of a different design, to allow the storage of a greater number of materials. Region I can store both new and used combustible materials. Each storage position is equipped with a neutron-absorbing canal, made of bored steel with content in minimum weight of natural boron 1.6 wt%. Region II only permits the storage of used combustible materials, with a maximum initial enrichment of 4.5 wt% in 235U. These racks are made of bored steel with content in minimum weight of natural boron at 1.7 wt%. Region II only permits the storage of combustible materials that have reached a certain level of average burnup, depending on the initial enrichment. IV.2 Characteristics of Region II for fuel storage The distribution of the fuel racks of region II, as well as that of region I, is shown in Figure 4.. Region II racks can hold spent combustible materials. The pool is equipped with neutron-absorbing vessels, made of stainless steel poisoned by at least 1.7 wt% of natural boron, in a chessboard-like configuration. 14 Figure 4: Region I and II of the spent fuel storage pool 15 Figure 5: Guide tubes distribution on a fuel element IV.3 Characteristics of the fuel element The configuration of the fuel elements in the present paper is shown in Figure 5, whereas the characteristics and dimensions are given in Table 2. Table 2: Characteristics of a fuel element in region II Reticule 16 x 16 Number of fuel pins 236 Number of guide tubes 20 Pin pitch 14.3 mm Diameter of the fuel pellets 9.11 mm External diameter of the pin 10.75 mm Cladding thickness 0.725 mm Cladding material Zircaloy External diameter of the guide tube 13.8  0.03 mm Internal diameter of the guide tube 12.4 mm Material of the guide tube Zircaloy Mass of uranium by fuel element 473.2 kg  2% Active length 3400  15 mm IV.4 Geometric model of Region II of the fuel element pool 16 The fuel element pool can be modelled from a basic, or reference, cell, with boundary conditions of specular reflection on the XYZ axes, except for the case of axial burnup credit, where the reflection will exclusively be on axes X and Y (Figure 6). In Table 3 the most important data for the modelling of the reference cell and that of the uranium oxide pin is shown. Table 3: Data of cell and fuel pins Data Description Value Reference 1 Number of pins by element 236 KWU BT33-94-E065b 2 Number of guide tubes by element 20 KWU BT33-94-E065b 3 Diameter of the pellet (cm) 0.911 BT51-33-71331 BT41-33-72309 4 Radius of the pellet (cm) (3)/2 0.4555 Calculation 5 External diameter of the clad (cm) 1.075 BT51-33-71331 6 External radius of the clad (cm) (5)/2 0.5375 Calculation 7 Internal radius of the clad 0.93 BT51-33-71331 8 Internal radius of the clad (7)/2 0.465 Calculation 9 Width of the clad (cm) (6)-(8) 0.0725 Calculation 10 Thickness of the gap (cm) (8)-(4) 0.0095 Calculation 11 Active length of the element (cm) 340 BT41-33-72309 BT-51-33-71331 12 Maximum active length of the element (cm) 341.5 Calculation 13 Maximum active length of the element (cm) 384.5 BT-51-33-71331 14 Material of the clad Zircaloy-4 Department of Mechanical and Materials Engineering 15 Maximum effective density of the pellets (g/cc) 10.5156 Calculation 16 Pin pitch (cm) 1.43 BT51-33-71331 17 Width of the fuel element (16 x pin pitch) (cm) 16*1.43 = 28.8 Calculation 120 250 Cuarta parte de elemento combustible Acero borado Agua 2 6114.4 6 114.4 2 120 1 2 34 120 250 Cuarta parte de elemento combustible Acero borado Agua 2 6114.4 6 114.4 2 120 1 2 34 Figure 1: Outline of the reference cell model Figure 6: Outline of the reference cell model 17 The effective fuel pellet density is the density of the pellets averaged on:  The pellet cells  The active length of the fuel pins  The number of fuel pins by fuel element The contribution of the fuel cells can be obtained from the mass of uranium per fuel element, as specified in table 2, since this mass depends on the density of the pellet, the pellet cell, and the active length. Therefore, when considering the core fabrication tolerances specified in the previous table, the maximum possible effective density of the pellets is obtained:         3 2/5156.10 2 2cmgr LMín d N MMáx Máx U UO AFR U ef             Max(MU) = maximum mass of uranium per fuel element (473.2 kg + 2%) NFR = number of fuel rods per fuel element (NFR = 236) (1) d = Diameter of the pellet (9.11 mm) (2) Min(LA) = minimum active length of the fuel pins (3385 mm) (10)-15 mm  UO2 = molecular mass of UO2 (270)  U = atomic mass of uranium (238) The composition in volume of the Zircaloy-4 can be seen in Table 4. To obtain this, the values of the weight fractions of the constitutive elements were used: Zr (0.983), Sn (0.013), Fe (0.002), Cr (0.001) and O (0.0012), of the mixture density (~6.56 g/cc) and the densities of each compound Zr = 6.4 g/cc; Sn = 7.31 g/cc; Fe = 7.86 g/cc; Cr = 7.20 g/cc; O = 1.0 g/cc; according to the expression: 18 compound ofDensity density) Mixture ·fraction (Weight fraction Volume  . Table 4: Composition (% in volume) of Zircaloy-4 Element % in volume Zr 97.785 Sn 1.170 Fe 0.167 Cr 0.091 O 0.787 The guide tube is used to control the power and the neutron flux during the burnup of the element inside the reactor. In Table 5 can be seen the most significant data for the modelling of the guide tube. Table 5: Geometric data of the guide tube Data Description Value Reference 1 Number of guide tubes by fuel element 20 KWU BT33-94-E065b 2 Internal diameter of the guide tube (cm) 1.24 BT51-33-71331 3 Internal radius of the guide tube (cm) (2)/2 0.62 Calculation 4 External diameter of the guide tube (cm) 1.38 BT51-33-71331 5 External radius of the guide tube (cm) (4)/2 0.69 Calculation 6 Pin Pitch (cm) 1.43 BT51-33-71331 7 Material of the guide tube Zircaloy-4 Department of Mechanical and Materials Engineering The reference cell is the basic unit that defines the spent fuel pool of region II. The data and their origin reference for the modelling of the reference cell are given in Table 6. Table 6: Data of the reference cell Data Description Value Reference 1 Fuel Pitch (mm) 250  0.5 KWU BT33-94-E065b 2 Internal length of the neutron-absorbing canal (mm) 240  1 KWU BT33-94-E065b 3 Wall thickness of the absorbing canal (mm) 2 KWU BT33-94-E065b 4 Temperature (except when otherwise indicated) (ºC) 4 Hypothesis Design criterion 5 Material of the absorbing canal Borated steel KWU BT33-94-E065b 6 Density of the absorbing canal (g/cc) 7.647 KWU BT33-94-E065b 7 Number of neutron generations 805 Hypothesis Design criterion 8 Number of neutrons per generation 600 Hypothesis Design criterion 9 Number of rejected generations 3 Hypothesis Design criterion 19 V. BURNUP ISOTOPES V.1 Determination of actinides and fission products Although ORIGEN-S can track over 2000 nuclides, this much detail is not necessary, because a great number of those nuclides decay very rapidly, while others are not presented in sufficient amounts as to be considered important in the kef calculations. The following criteria are recommended by DeHart [10] and are considered adequate for the nuclides to be considered in the analysis. 1. Those nuclides that contribute significantly to the absorption of thermal neutrons in spent fuel are to be included; 2. All fissile nuclides are to be included; 3. Nuclides must be fixed in the fuel matrix (i.e., no credit taken for volatile elements); and 4. The predicted concentrations of selected nuclides in spent fuel must be verifiable by comparison with chemical assay measurements. Criterion 2 requires 235U, 239Pu y el 241Pu to be included in the actinide set. Moreover the guide [6] clearly express that 135Xe must not be included. Table 7 shows the selected nuclides for the analysis. These nuclides are part of a TRITON set that adds trace quantities of specific nuclides for the ORIGEN-S calculations. As previously stated, the parameter ADDNUX was fixed to the value ADDNUX=2 from which, apart from the 135Xe, all nuclides added were used for the criticality analysis of the storage pool. Table 7: Selected nuclides in the burnup calculations Actinides 234U, 235U, 236U, 238U, 237Np, 238Pu, 239Pu, 240Pu, 241Pu, 242Pu, 241Am, 243Am, 242Cm, 243Cm, 244Cm Fission Products 1H, 10B, 11B, 14N, 16O, 83Kr, 93Nb, 94Zr, 95Mo, 99Tc, 103Rh, 105Rh, 106Ru, 109Ag, 126Sn, 135I, 131Xe, 133Cs, 134Cs, 135Cs, 137Cs, 143Pr, 144Ce, 143Nd, 145Nd, 146Nd, 147Nd, 147Pm, 148Pm, 149Pm, 148Nd, 147Sm, 149Sm, 150Sm, 151Sm, 152Sm, 151Eu, 153Eu, 154Eu, 155Eu, 152Gd, 154Gd, 155Gd, 156Gd, 157Gd, 158Gd, 160Gd, 91Zr, 93Zr, 95Zr, 96Zr, 95Nb, 97Mo, 98Mo, 99Mo, 100Mo, 101Ru, 102Ru, 103Ru, 104Ru, 105Pd, 107Pd, 108Pd, 113Cd, 115In, 127I, 129I, 133Xe, 139La, 140Ba, 141Ce, 142Ce, 143Ce, 141Pr, 144Nd, 153Sm, 156Eu Although [6] points that all fission products, but 135Xe can be used, a total of 15 actinides and 77 fission products were selected. 20 VI. INFLUENCE OF THE OPERATION PARAMETERS ON ISOTOPE CALCULATIONS VI.1 Introduction The isotope inventory of a fuel element depends on its burnup history: that is, not only on the operational cycles of the reactor, but also on the specific power at which the fuel element has been operating on the nucleus, as well as the thermal-hydraulic parameters of the operation. This implies that each burnup element has its own unique history, which differs from the rest of the elements [11]. Thus, the follow-up of the history of the specific operation of each fuel element is unfeasible for the proposals of design and security analysis, and, therefore, it is necessary to identify a simpler operation history, which is conservative in terms of kef. For a better understanding of the effects of the operation history with regard to power, the effects of the mean specific power and the burnup time must be separated in the isotope inventory. In order to analyse this effect, several calculations have been carried out, using the code TRITON to obtain the isotopic distribution resulting from the element burnup, from the initial enrichment and CSAS6 for the criticality calculations performed so to obtain the kef. VI.2 Effect of the average burnup in the burnup calculations Three burnup groups had been evaluated: 10, 20 and 30 GWd/MTU along with three types of enrichment: 3.0, 3.6, 4.5 wt%. To be even more conservative, no cooling time was assumed. The results in terms of Kef are presented in Table 8 and will serve as the case basis for the following calculations of this section. Table 8: Basis Case Enrichment 10 GWd/MTU 20 GWd/MTU 30 GWd/MTU 3.0% 1.03302 ± 0.00085 0.93620 ± 0.00082 0.84582 ± 0.00081 3.6% 1.08608 ± 0.00095 0.99546 ± 0.00092 0.90840 ± 0.00089 4.5% 1.14761 ± 0.00094 1.06515 ± 0.00089 0.98748 ± 0.00086 In general, the results reveal that the value calculated for kef increases as the specific power is increased. This behaviour is because the creation of fission products depends on the specific power, but not on the decay rate. On the other hand, there are some contrasting effects. Thus, an increase in the concentration of 235U is quite probable as the specific power increases, since there is an increase in the concentration of plutonium isotopes, and therefore, the fissions of 239Pu and 241Pu cause a decrease in the fission rates of 27 presents little variation throughout the reactor operation, and therefore, a reasonable estimation of an upper limit can be obtained. With regard to the boron concentration, it is observed that the kef increases with the boron concentration during the burnup process, once again, due to the spectrum hardening, caused by the absorption of thermal neutrons in the boron. The burnup of the fuel element is smaller, causing a greater kef. However, with greater enrichments, the boron concentrations become increasingly larger at the beginning of the cycle, and as such, it will be necessary to carry out calculations with average boron concentrations, sufficient to restrict all sorts of burnup fuel elements. In the methodology developed, in the isotope analysis, the following parameters have been taken as base values: as average fuel temperature, 1040K, as average moderator temperature, 586K, corresponding to a specification of 313C, as boron concentration of 1000 ppm (assuming that an average concentration of 1000 ppm of boron throughout a cycle is considered conservative). The burnup conditions for the isotopic calculation can be seen in Table 16. Table 16: Burnup conditions for the isotopic calculation Parameter Average moderator temperature 586 K (313  C) Average fuel temperature 1040 K (767  C) Temperature of the sheath 618 K (345  C) Density of the moderator 0.7052 g/cc Boron concentration on the moderator 1000 ppm 28 VII. SCALE BURNUP PARAMETERS Following the methodology, SCALE parameters were analyzed in order to compare with previous works using SAS2H sequence on SCALE5.1. For these calculations a burnup of 39.95 GWd/TU was evaluated for a fresh fuel enrichment of 3.7 wt% on U-235. Figure 7 shows an isometric view of the PWR simulated in KENO-VI, while Figure 8 depicts an axial view of the reactor with its fuel pins and guide tubes configuration, both obtained with KENO3D visualization tool. Figure 9 shows a 2D plot obtained with NEWT, along with the computational mesh. Figure 7: Full PWR fuel element on KENO3D 29 Figure 8: Top view of the PWR fuel element on KENO3D Figure 9: NEWT 2D plot of the PWR fuel element Following the burnup calculations, the isotopic concentrations for the nuclides on Table 19 are collected and used for the criticality analysis on the spent fuel pool. Figure 9 and Figure 10 show the reference cell of the spent fuel storage pool 30 Figure 10: Reference cell of the spent fuel storage pool Figure 11: Axial view of the reference cell of the spent fuel storage pool 31 Some TRITON parameter blocks for burnup were modified so to evaluate their influence over the burnup calculations: VII.1 ADDNUX parameter: Adds to all fuel materials trace quantities (1.0E–20 atoms/b-cm) of a set of nuclides that have been determined to be important in the characterization of spent fuel. TRITON provides user control of the set of nuclides added to a fuel material through the parm=(addnux=N) control parameter, where N is an integer value. For N = 0, no nuclides are added, which is generally a very poor approximation and should only be used when the ramifications are fully understood. For N = 1, a bare minimum set of 15 nuclides (actinides) are added; this will generate improved number density estimates for actinides in low-burnup fuels but will not update cross sections for fission products of primary importance. Again, use of this option is discouraged unless it addresses special modeling needs. For N = 2, the default setting for the TRITON depletion sequences, 94 nuclides are added. N = 3 and N = 4 add 230 and 388 nuclides, respectively; this much detail is generally not needed for depletion calculations unless one wishes to closely estimate keff near the end of life. At such high burnups, these nuclides have little effect on the system spectrum, but taken as a whole, they do contribute to the total system reactivity. Table 17 through Table 21 list the set of nuclides added in trace quantities for each value of addnux. Table 17: ADDNUX=1 (15 additional nuclides are added) 234U 235U 236U 238U 237Np 238Pu 239Pu 240Pu 241Pu 242Pu 241Am 242Am 243Am 242Cm 243Cm Table 18: ADDNUX=-2 (49 additional nuclides for a total of 64) 1H 10B 11B 14N 16O 83Kr 93Nb 94Zr 95Mo 99Tc 103Rh 105Rh 106Ru 109Ag 126Sn 135I 131Xe 135Xe 133Cs 134Cs 135Cs 137Cs 143Pr 144Ce 143Nd 145Nd 146Nd 147Nd 147Pm 148Pm 149Pm 148Nd 147Sm 149Sm 150Sm 151Sm 152Sm 151Eu 153Eu 154Eu 155Eu 152Gd 154Gd 155Gd 156Gd 157Gd 158Gd 160Gd 244Cm Table 19: ADDNUX=2 (30 additional nuclides for a total of 94) 91Zr 93Zr 95Zr 96Zr 95Nb 97Mo 98Mo 99Mo 100Mo 101Ru 102Ru 103Ru 104Ru 105Pd 107Pd 108Pd 113Cd 115In 127I 129I 133Xe 139La 140Ba 141Ce 32 142Ce 143Ce 141Pr 144Nd 153Sm 156Eu Table 20: ADDNUX=3 (136 additional nuclides for a total of 230) 72Ge 73Ge 74Ge 76Ge 75As 79Br 76Se 77Se 78Se 80Se 82Se 81Br 80Kr 82Kr 84Kr 85Kr 86Kr 85Rb 86Rb 87Rb 84Sr 86Sr 87Sr 88Sr 89Sr 90Sr 89Y 90Y 91Y 90Zr 92Zr 92Mo 94Mo 96Mo 94Nb 96Ru 98Ru 99Ru 100Ru 105Ru 102Pd 104Pd 106Pd 110Pd 107Ag 111Ag 106Cd 108Cd 110Cd 111Cd 112Cd 114Cd 115mCd 116Cd 140Ce 113In 140La 112Sn 114Sn 115Sn 116Sn 117Sn 118Sn 119Sn 120Sn 122Sn 123Sn 124Sn 125Sn 121Sb 123Sb 124Sb 125Sb 126Sb 120Te 122Te 123Te 124Te 125Te 126Te 127mTe 128Te 129mTe 130Te 132Te 130I 131I 124Xe 126Xe 128Xe 129Xe 130Xe 132Xe 134Xe 136Xe 134Ba 135Ba 136Ba 137Ba 138Ba 136Cs 142Pr 142Nd 150Nd 151Pm 144Sm 148Sm 154Sm 152Eu 157Eu 232U 233U 159Tb 160Tb 160Dy 161Dy 162Dy 163Dy 164Dy 165Ho 166Er 167Er 175Lu 176Lu 181Ta 182W 183W 184W 186W 185Re 187Re 197Au 231Pa 233Pa 230Th 232Th Table 21: ADDNUX=4 (158 additional nuclides for a total of 388) 2H 3H 3He 4He 6Li 7Li 7Be 9Be 15N 17O 19F 23Na 24Mg 25Mg 26Mg 27Al 28Si 29Si 30Si 31P 32S 33S 34S 36S 35Cl 37Cl 36Ar 38Ar 40Ar 39K 40K 41K 40Ca 42Ca 43Ca 44Ca 46Ca 48Ca 45Sc 46Ti 47Ti 48Ti 49Ti 50Ti 50Cr 52Cr 53Cr 54Cr 55Mn 54Fe 56Fe 57Fe 58Fe 58Co 58mCo 59Co 58Ni 59Ni 60Ni 61Ni 62Ni 64Ni 63Cu 65Cu 70Ge 69Ga 71Ga 74As 74Se 79Se 78Kr 110mAg 113Sn 123Xe 130Ba 132Ba 133Ba 136Ce 138Ce 139Ce 138La 148mPm 153Gd 156Dy 158Dy 166mHo 162Er 164Er 168Er 170Er 174Hf 176Hf 177Hf 178Hf 179Hf 180Hf 182Ta 191Ir 193Ir 196Hg 198Hg 199Hg 200Hg 201Hg 202Hg 204Hg 204Pb 206Pb 207Pb 208Pb 209Bi 223Ra 224Ra 225Ra 225Ac 226Ac 227Ac 226Ra 227Th 228Th 229Th 233Th 234Th 232Pa 235Np 236Np 238Np 239Np 237U 239U 240U 241U 236Pu 237U 243Pu 244Pu 246Pu 242mAm 244Am 244mAm 241Cm 245Cm 246Cm 247Cm 248Cm 249Cm 250Cm 249Bk 250Bk 249Cf 250Cf 251Cf 33 252Cf 253Cf 254Cf 253Es 254Es 255Es Burnup calculations were performed for all of the six possible cases. Results in terms of keff are shown in Table 22 and are plotted on Figure 11. Table 22: kef variation with ADDNUX parameters Step Number addnux=0 addnux=1 addnux=-2 addnux=2 addnux=3 addnux=4 0 1.24661 1.24635 1.24556 1.24556 1.24612 1.24612 1 1.22804 1.23621 1.18385 1.18373 1.18291 1.18247 2 1.18933 1.20412 1.13843 1.13699 1.13717 1.13669 3 1.14683 1.17426 1.09819 1.09554 1.09383 1.09267 4 1.09668 1.14574 1.06155 1.05727 1.05522 1.05488 5 1.03823 1.11888 1.02733 1.02068 1.02057 1.01947 6 0.97279 1.09105 0.99525 0.98837 0.98814 0.98633 7 0.89764 1.06465 0.9652 0.95765 0.95558 0.95444 8 0.81068 1.04089 0.93724 0.93013 0.92863 0.92663 9 0.71169 1.01571 0.91046 0.90215 0.90167 0.90022 There is one step for each cross-section processing on the burnup calculations on TRITON. Because three libraries for each burnup cycle were created, nine calculation steps are performed. Step number zero is the first cross-section processing and is performed at the burnup time equal zero, i.e. beginning of life. Figure 12: kef variation with ADDNUX parameters 0.71 0.81 0.91 1.01 1.11 1.21 0246810 Neutron Multiplication Factor Time Step Number TRITON/KENO-VI depletion sequence - ADDNUX cases add0 add1 add-2 add2 add4 34 VII.2 TIMETABLE Block This block allows modification of material properties such as temperature and density during a depletion calculation. In this specific case, soluble boron dissolution on the moderator is to be taken into account. At each time step, the boron concentration in the moderator is modified by a multiplication factor and TRITON applies linear interpolation between each pair (step, density multiplier). The user-specified density multipliers were obtained from previous works using the SAS2H burnup sequence on SCALE5.1, which also worked as motivation and comparison basis of such calculations. Table 23 provides the data used for specifying the applied density multipliers along with the time steps, in days, on which these factors were applied. On Figure 12 the concentration values on TRITON and SAS2H for the isotope b-10 are plotted. Table 23: Boron letdown timetable applied to the calculations Time Step Number Time Step [Days] Density Multiplier 0 0 1.75 1 61 1.6 2 183 1 3 304 0.4 4 441 1.6 5 563 1 6 684 0.4 7 821 1.6 8 943 1 9 1064 0.4 Figure 13: Boron letdown curve applied to the calculations As expected the curves from TRITON and SAS2H are identical. One must be aware that 2.00E-06 3.00E-06 4.00E-06 5.00E-06 6.00E-06 7.00E-06 8.00E-06 9.00E-06 1.00E-05 1.10E-05 1.20E-05 1.30E-05 1.40E-05 0 2 4 6 8 10 Number Density [atoms/b-cm] Time Step Boron B-10 Letdown Curve SAS2H TRITON 35 VII.3 TIMETABLE and ADDNUX Analysis Taking into account both of the previous analyses, calculations using the boron letdown curve from SAS2H and the ADDNUX cases were carried out. The results for KENO-VI and NEWT are shown on Table 25 and Table 26, and plotted on Figure 13 and Figure 15. On these charts, addnux=N stands for the ADDNUX set used (N=0, 1, -2, 2, 3, 4), while sas2h are the results for the case run by SAS2H on SCALE5.1. Because SAS2H automatically adds a set of nuclides in the neutron transport calculations, as depicted on Table 24, another set of nuclides was manually included on TRITON calculations, using addnux=0 and specified as part of the fuel composition at trace quantities (1.0E–20 atoms/b-cm) so as to match the nuclides included by SAS2H. This case is labeled atoms and follows in Table 25, Table 26, Figure 14 and Figure 15 as well. Table 24: List of fuel nuclides automatically included by SAS2H in neutron transport calculation Xe-135 Pu-240 Cs-133 Pu-241 U-234 Pu-242 U-235 Am-241 U-236 Am-242m U-238 Am-243 Np-237 Cm-242 Pu-238 Cm-243 Pu-239 Cm-244 Table 25: kef variation for ADDNUX cases with boron letdown with KENO-VI Step sas2h addnux=0 addnux=1 addnux=-2 addnux=2 addnux=3 addnux=4 atoms 0 1.1738 1.16905 1.17 1.16907 1.16907 1.17047 1.16866 1.16962 1 1.149 1.1645 1.17689 1.13067 1.12833 1.12796 1.12747 1.14345 2 1.1792 1.18909 1.20726 1.14006 1.13732 1.13795 1.13617 1.16992 3 1.2114 1.22896 1.23898 1.15292 1.14785 1.14958 1.1464 1.19704 4 1.0645 1.01975 1.09035 1.01509 1.01084 1.00992 1.00848 1.06028 5 1.0945 1.03994 1.11966 1.02866 1.02303 1.02192 1.02063 1.0845 6 1.1281 1.07478 1.15391 1.04473 1.03701 1.03648 1.03553 1.11572 7 0.9854 0.81506 1.0112 0.91985 0.91545 0.91482 0.91374 0.98316 8 1.0171 0.81209 1.04321 0.93923 0.93099 0.93061 0.92713 1.01352 9 1.0518 0.81646 1.07722 0.95846 0.94783 0.94733 0.94534 1.04447 Table 26: kef variation for ADDNUX cases with boron letdown with NEWT Step sas2h addnux=0 addnux=1 addnux=-2 addnux=2 addnux=3 addnux=4 atoms 0 1.1738 1.16903226 1.16903226 1.16898883 1.16898883 1.16902082 1.16902082 1.16902506 1 1.149 1.16327576 1.17622196 1.12856301 1.12762808 1.12748105 1.12729322 1.14318741 2 1.1792 1.18880893 1.20647047 1.13968718 1.13748727 1.137396 1.13635958 1.16994937 3 1.2114 1.22948941 1.23824729 1.15279661 1.14921763 1.14891842 1.1473277 1.19782099 4 1.0645 1.01992009 1.08855119 1.01381778 1.00978741 1.00938198 1.00779951 1.05896905 5 1.0945 1.03918419 1.11959408 1.02794796 1.02262386 1.02192783 1.02001667 1.08560343 6 1.1281 1.07277066 1.15380981 1.04502006 1.03827685 1.03731281 1.03519194 1.11611967 7 0.9854 0.81501232 1.00898428 0.92131243 0.9147382 0.91360215 0.91212162 0.98319424 8 1.0171 0.81165139 1.042596 0.93882438 0.93093432 0.92963771 0.92782854 1.01239853 9 1.0518 0.8155127 1.07828142 0.95801608 0.94863821 0.94716444 0.94522407 1.04440638 36 Figure 14: kef variation for ADDNUX cases with boron letdown using KENO-VI Figure 15: kef variation for ADDNUX cases with boron letdown using NEWT The inventory obtained from these calculations, after all the burnup cycles, is collected with OPUS and used on a follow-up criticality analysis by CSAS6 performed for the region II of the spent fuel storage pool. Results for TRITON/KENO-VI and TRITON/NEWT depletion are shown on Table 26 and plotted on Figure 16 and Figure 17 Table 27: Criticality analysis for the region II of the spent fuel storage pool Case Kef (KENO-VI) Kef (NEWT) 0.8 0.9 1 1.1 1.2 0 2 4 6 8 10 Neutronic Multiplication Factor Time Step TRITON/KENO-VI burnup sequence - ADDNUX cases with boron letdown sas2h addnux=0 addnux=1 addnux=-2 addnux=2 addnux=3 addnux=4 atoms 0.8 0.9 1 1.1 1.2 0 2 4 6 8 10 Neutronic Multiplication Factor Time Step TRITON/NEWT burnup sequence - ADDNUX cases with boron letdown sas2h addnux=0 addnux=1 addnux=-2 addnux=2 addnux=3 addnux=4 atoms 43 Figure 21: Description of Wilks methodology in order to obtain the most critical burnup profile Thus, since the axial burnup profile notably influences the criticality calculations, it will be necessary to obtain a hypothetical profile, which is able to provide a conservative representation of a fuel element of average burnup and specific enrichment. For this, and taking into account that the application is made for region II of the PWR spent fuel elements pool, the database of axial profiles is available, supplied by the PWR, and reconstructed by the processing computer. From it, the axial profiles have been grouped accordingly to the initial enrichment of the fuel element (1.9%, 2.5%, 3.3%, 3.5%, 3.7%, 3.85%, 3.95%, 4.35% and 4.5%). Following this, they are grouped in burnup ranks, independent from the initial enrichment. The maximum width of each interval has been fixed at 2 GWd/TU, in order to obtain the maximum number of profiles per rank, and so that the previously mentioned profiles, once normalised can be representative of it. That is, by stating the rank [39,41] GWd/TU centred around the mean value of 40 GWd/TU, it can be assumed that the normalised axial profile corresponding to a fuel element with average burnup, for instance of 39.5 GWd/TU is very similar to that of another fuel element with an average burnup within the same rank. In addition, it must also be taken into account that, as the average burnup increases, the normalised burnup at the ends will also increase, with the result that if we were to choose higher ranks for the study of the average burnup (>40 GWd/TU), the kef would be sensibly lower. However, there is a commitment to 44 apply the methodology, which, on one hand, uses the maximum number of profiles, and on the other hand the minimum possible burnup interval band. The width of the established band satisfies both criteria. In order to analyse different profiles with average burnup, for instance, of 40 GWd/TU, a burnup band between 39 and 41 GWd/TU is determined. Then, the corresponding burnup of each axial node (Bi,j) is divided by the average burnup relative to that profile (Bj), and is multiplied by the average burnup under study ( analysis B ), analysis j ji normalised ji B B B B. , , i, axial node, j, number of profile. In contrast with the criticality analyses which take the fresh fuel elements as a starting point, burnup credit needs to consider the operational history of the fuel element, including the axial burnup distribution. VIII.4 Criticality analysis of real profiles Wilks [12] establishes that the maximum value of an average sample of a magnitude measured from a sample of N elements is the single-sided upper tolerance limit, with a  probability and a level of reliability  , of the values of this magnitude. A diagram of Wilks' methodology is shown in the Figure 18. According to Wilks, for non-parametric tolerance limits (only at one end), such that with probability  , at least  per one of the population does not exceed the maximum sampling value, a sample of the following size must be taken: 58 1   ln )(ln N For  equal to 0.95 and  equal to 0.95, the sampling size must be approximately 58. For each rank of average burnups of Wilks’ sampling, the maximum possible number of profiles has been chosen, so that the sampling sizes are always around this value. For our example, the magnitude measured using Wilks' method, is the value of the kef of a normalised real burnup profiles sampling. If we obtain for different average burnup ranks [27,29], [33,35], and [39,41] a GWd/TU with average burnups of 28, 34 and 40 GWd/TU, respectively for each rank, a sample of n=58 fuel elements, the maximum value among all the profiles of the kef sample would be the upper tolerance limit, UL1, which secures a probability and a level of reliability at 95/95. These burnup ranks have been chosen because they are of interest when studying the effect of the axial profiles. 45 The normalised real profile, that has an upper tolerance limit UL1 in the value of the kef for an average burnup analysis is defined as the most critical axial burnup profile. 341.5 / n 1.43 Agua Pastillas de combustible Zircaloy - 4 341.5 / n 1.43 Water Fuel pellets Zircaloy - 4 Figure 22: Model with KENO3D of a burnup node ni of the fuel pellet. The number of burnup nodes (n) is 32. An axial burnup node of the fuel pellet where the different materials, the maximum active length of the node and the pellet passage are shown in Figure 19 whereas in Figure 20, the stack of the different axial nodes to form the complete model of the fuel pellet is given. For all the models, 32 axial burnup nodes have been used. The active length of the pellet was calculated after considering the nominal length of the pellet plus the maximum core fabrication tolerance (341.5 cm.). 46 Figure 23: Model with KENO3D of a fuel pellet of n nodes of 341.5 cm. of maximum active length. The number of burnup nodes is 32. Due to the unfeasibility of obtaining a sample of 58 fuel elements with the same average burnup, at least 58 axial profiles were extracted from the database within the burnup rank with a maximum band of 2 GWd/TU, for all the given enrichments. This part of the work is still to be implemented, with the use of available profiles from the PWR in question. The simplified process to obtain a conservative axial burnup profile would be as follows: The chart depicts the basic steps to find the bounding axial burnup profiles from real profiles as descripted above. 341.5 n1 ni-1 ni ni+1 nn 341.5 n1 ni-1 ni ni+1 nn Database Agroupment of profiles by burnup ranks Normalisation of the profiles Computation of the limitting profiles Combination of profiles 47 IX. CONCLUSIONS AND FUTURE WORKS A burnup credit methodology under development has been studied. Once a conservative bias and its uncertainty is established, the USL was determined, which is the safety limit for a spent fuel storage pool. The recommendations for giving burnup credit to a certain system, specifies that axial burnup is to be considered at high burnup levels. This is a step still in progress and should be analyzed nevertheless. With the USL and axial profile burnup analysis, it will be possible to obtain the loading curve which determines whether a fuel element will be stored in the region I or II. Using the codes TRITON/KENO-VI and CSAS6, different types of PWR operational histories were analyzed. The codes are vastly validated with experimental data and give reliable and accurate nuclear data for this criticality analysis. This study allowed obtaining the closest to reality operational history that remains conservative in terms of criticality. NRC research efforts are currently directed toward developing the technical basis and information for revising ISG8R2 to allow credit for fission products. The goal is to develop and establish a technically sound validation approach (both depletion and criticality) for SNF criticality safety evaluations based on best-available data and methods, to demonstrate the approach and applicability, and to provide reference bias results. Specifically, for isotopic validation, the planned approach is to use a best estimate Monte Carlo-based method to determine burnup-dependent reactivity bias and bias uncertainty in isotopic predictions via comparisons of isotopic composition predictions and measured isotopic compositions from destructive radiochemical assay, utilizing as much assay data as is available [13]. Future works must include the axial burnup evaluation with nodes discretization with real burnup profiles. Finding the most conservative simulated axial profile for which all of the real profiles are considered safe is a needed step on the progress of this work. Also, assuming ISG8R3 will contemplate the full burnup credit recommendations, the issuance of this guide will allow more details for giving validation and consequent use for this methodology. 48 X. REFERENCES 1. U.S. Nuclear Regulatory Commission Interim Staff Guidance 8 – Revision 2, ‘Burnup Credit in the Criticality Safety Analyses of PWR Spent Fuel in Transport and Storage Casks’. Nuclear Regulatory Commission. 2002 2. J.C. Wagner, M.D. DeHart, ‘Review of Axial Burnup Distribution Considerations for Burnup Credit Calculations’. Oak Ridge National Laboratory. March 2000. 3. A. Machiels, ‘Burnup Credit Methodology - Spent Nuclear Fuel Transportation Applications’. Electric Power Research Institute (EPRI). Report. 2010. 4. C.V. Parks, et. al., ‘Full Burnup Credit in Transport and Storage Casks: Benefits and Implementation’. American Nuclear Society 2006 International High-Level Radioactive Waste Management Conference. April 30 – May 4, 2006. Las Vegas, Nevada. 5. 10 CFR 50.68, ‘Criticality Accident Requirements’. U.S. Nuclear Regulatory Commission 6. NRC memorandum from L. I. Kopp to T. Collins, ‘Guidance on the Regulatory Requirements for Criticality Safety Analysis of the Fuel Storage at Light-Water Reactor Plants’, U. S. Nuclear Regulatory Commission. Agosto 1998. 7. C.V. Parks. ‘Recommendations for PWR Storage and Transportation Casks That Use Burnup Credit’. 2003 International High-Level Radioactive Waste Management Conference, “Progress Through Cooperation”. March 30 – April 2, 2003. Las Vegas, Nevada. 8. M.D. DeHart, S.M. Bowman, ‘Reactor Physics Methods and Analysis Capabilities in SCALE’. Oak Ridge National Laboratory, Nuclear Science and Technology Division. September, 2010. 9. Oak Ridge National Laboratory. ‘SCALE6.1 Electronic Manual'. ORNL/TM. June 2011.. 10. J. J. Lichtenwalter, S. M. Bowman, M. D. DeHart, C. M. Hopper ‘Criticality Benchmark Guide for LightWater Reactor Fuel in Transportation and Storage Packages’, NUREG/CR-6361, ORNL/TM-13211. Oak Ridge National Laboratory, March 1997. 11. UNE 73-501-92. ‘Requisitos de Criticidad para el Diseño de Bastidores de Almacenamiento en Piscinas de Combustible’. 12. M. D. DeHart, S. M. Bowman, ‘Validation of the SCALE Broad Structure 44-Group ENDF/B-V CrossSection Library for Use in Criticality Safety Analyses’, NUREG/CR-6102, ORNL/TM-12460. 49 13. I.C. Gauld, ‘Strategies for Application of Isotopic Uncertainties in Burnup Credit’. Prepared for Division of Systems Analysis and Regulatory Effectiveness Office of Nuclear Regulatory Research. U.S. Nuclear Regulatory Commission 14. S. S. Wilks, ‘Collected papers: Contributions to mathematical statistics’, Ed. John Wiley, 1967. 15. C.V. Parks, et. al., ‘Development of Technical Basis for Burnup Credit Regulatory Guidance in the United States’. 16th International Symposium on the Packaging and Transport of Radioactive Materials, London, 3 - 8 October 2010.