ML101540176

Updated Safety Analysis Report, Revision 23, Section 9.1A, Fuel Storage Rack Analysis

ML101540176
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Site:	Wolf Creek
Issue date:	03/11/2010
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WOLF CREEK APPENDIX 9.2A FUEL STORAGE RACK ANALYSIS 9.1A.1 THE HIGH DENSITY RACK (MDR) DESIGN CONCEPT 9.1A.1.l Introduction Historically, spent fuel rack designs have been based on conservative assumptions that could easily be accommodated since it was not planned to store large numbers of high exposure spent fuel assemblies on-site. Previously it was anticipated that only small amounts of high exposure fuel assemblies (1/4 to 1/2 of a full core load) would normally be stored in the spent fuel pool at any one time. Additionally it was anticipated that occasionally (e.g., for inservice inspection of the reactor vessel internals) the entire core would be unloaded and temporarily stored in the initial spent fuel pool. Therefore, the spent fuel storage rack design was based on the conservative assumption that all fuel rack storage positions would be occupied by fresh unirradiated fuel assemblies of the highest initial enrichment that was foreseen as being usable in that facility.The penalty in achievable fuel storage density associated with this conservative design assumption was relatively small under the circumstances anticipated and easily accommodated by a conservative fuel rack design. The potential penalty associated with this conservative design basis is no longer small when long-term on-site storage of spent fuel is a necessity.

There is no situation where more than one full core load of fresh unirradiated fuel assemblies is to be stored in the fuel storage pool. Therefore, it is unnecessary and wasteful to base the entire fuel storage rack design on the assumption of fresh unirradiated fuel of the highest initial enrichment.

In the previous maximum density rack (MNR) design concept utilized by Wolf Creek, the spent fuel pool was divided into two separate and distinct regions which, for the purpose of criticality'considerations may be considered as separate pools. Suitability of this design assumption regarding pool separability was assured through appropriate design restrictions at the boundaries between Region 1 and Region 2. The smaller region, Region 1, of the pool was designed on the basis of accepted conservative criteria which allowed for the safe storage of a number of fresh unirradiated fuel assemblies (including a full core loading if that should prove necessary).

The larger region of the pool, Region 2, was designed to store irradiated fuel assemblies.

The change in criteria was the recognition of actual fuel and fission product inventory, accompanied by a system for checking fuel prior to moving any fuel assembly from Region -.l to Region 2.In the HDR design concept., currently utilized by Wolf Crook, the rack modules for the fuel storage pool are designed for storage of both new fuel and spent fuel,. Spent fuel storage is designated into Regions based upon initial enrichment and accumulated bur4up. (b)(4)(b)(4)9. lA-IRev. 14 WOLF CREEK 9. IA.1.2 (b)(4)Design Bases Moderator is unborated water at a temperature that results in the highest reactivity (4 0 C, corresponding to the maximum possible moderator density).No soluble poison or control rods are assumed to be present for normal, operations, although the additional margin due to the presence of soluble boron is identified.

The effective multiplication factor of an infinite radial array of fuel assemblies was used except for the assessment of peripheral effects and certain abnormal/accident conditions where neutron leakage is inherent.Neutron absorption in minor structural members is conservatively i.e., spacer grids are replaced by water.Depletion calculations assume conservative operating conditions; and moderator temperature and an allowance for the soluble boron during incore operation.(b)(4)neglected, highest fuel concentrations 9.]1A-2 Rev. 14 WOLF CREEK 9.lA.1.3 Design Description (b)(4)9. 1A-3 Rev. 14 WOLF CREEK I(b)(4)9. IA-4 Rev. 14 WOLF CREEK (b)(4)9. 1A-5 Rev. 14 WOLF CREEK'(b)(4)9. 1A-6 Rev. 14 WOLF CREEK--.. ...........9.]3A-7 Rev. 14 WOLF CREEK (b)(4)9.1A.2.2.3.1 iFuel Burnup Calculations and Uncertainties CASMO-3 was used for burnup calculations in the hot operating condition.

CASMO-3 has been extensively benchmarked (References 7 and 9) against cold, clean, critical experiments (including plutonium-bearing fuel.), Monte Carlo calculations, reactor operations, and heavy element concentrations in irradiated fuel. In addition to burnup calculations, CASMO-3 was used for evaluating the small reactivity increments (by differential calculations) associated with manufacturing tolerances and for determining temperature effects.9. IA-8 Rev. 14 WOLF CREEK In the CASMO-3 geometri6 model, each fuel rod and its cladding were described explicitly and reflective boundary conditions were used at*the centerline of the Boral and steel plates between storage cells. These boundary conditions have the effect of. creating an infinite array of storage cells in the X-Y plane and provide a conservative estimate of the uncertainties in reactivity attributed to manufacturing tolerances.(b)(4)9.1A.2.2.3.2 Effect of Axial Burnup Distribution Initially, fuel loaded into the reactor will burn with a slightly skewed cosine power distribution.

As burnup progresses, the burnup distribution wili tend to flatten, becoming more highly burned in the central regions than in the upper and lower regions. At high burnup, the more reactive fuel near the ends of the fuel assembly (less than average burnup) occurs in regions of high neutron leakage. Consequently, it is expected that over most of the burnup history, fuel assemblies with distributed burnups will exhibit a slightly lower reactivity than that calculated for the uniform average burnup. As burnup progresses, the distribution, to some extent, tends to be self-regulating as controlled by the axial. power distribution, precluding the existence of large regions of significantly reduced burnup. Among others, Turner (Reference 20)has provided generic analytic results of the axial burnup effect based upon calculated and measured axial burnup distributions.

These analyses confirm the minor and generally negative reactivity effect of the axially distributed burnup.9. 1A-9 Rev. 14 WOLF CREEK (b)(4)9.1A.2.2.4 Criticality Analyses Uncertainties and Tolerances A number of tolerances result in reactivity uncertainties which must be considered in the criticality analyses.9.1A.2.2.4.1 Nominal Design (b)(4)9.1A.2.2.4.2 Uncertainties Due to Manufacturing Tolerances The uncertainties due to manufacturing tolerances are summarized in Table 9.1A-5 and discussed below.9.1A.2.2.4.2.1 Boron Loading Tolerances The Boral absorber panels are manufactured with a tolerance limit in B-10 content which ass3res that at any point, the minimum B-10 areal density will not be ) ess thanDI _(4) ...............(b)(4)9. IA-10 Rev. .14 WOLF CREEK 9.IA.2.2.4.2.2 Boral Width T'olerance The differential[(b)(4) calculated reactivity uncertainty is +/-0.0010 Ak, when the reference stdiage cell design has the minimum tolerance for Bora.l panel thickness.

9.lA.2.2.4.2.3 Tolerances in Cell Lattice Spacing The differentiali(bj))

calculations determine an uncertainty of +/-0.0016 Ak in the calculated reactivity when the minimum manufacturing tolerance on the inner box dimension is used. The minimum manufacturing tolerance on the inner box dimension directly affects the storage cell lattice spacing between fuel assemblies.

9.1A.2.2.4.2.4 Stainless Steel Thickness Tolerances The nominal stainless steel thickness for the stainless steel box also has an impact on the calculation of reactivity.

The reactivity uncertainty of the expected stainless steel thickness tolerances was calculated with (b)(4)------

[b)(4)-- -.9.lA.2.2.4.2.5 Fuel Enrichment and Density Tolerances r .... .... ...... ...... ............

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...........

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constitutes a neutron flux-trap for the storage cells of facing racks.(b)(4) were made with the referencel(b)(4)

Ito determine the uncertaintyassociated with a water-gap tolerance.---Due to the asymmetries in the MZTR pool configuration, the effect of the horizontal and vertical water gaps (see F-igure_9.lA-l) -were calculated separately, ~)(~_b ) ............

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..... ... .-- ........ .... ........ .. ... ... ........ ....... ......... .... .. ..... ... ..... .... ....(b)(4) The racks are constructed with the base plate extending beyond the edge-of the cells which assures that the minimum spacing between storage modules is maintained under all credible conditions.

9.1A.2.2.4.4 Eccentric Fuel Positioning The fuel assembly is assumed to be centered in the storage rack cell.Calculations were made using KEN05a assuming the fuel assemblies were. located in th'e corners of the storage rack cells (four-assembly clusters at the closest possible approach).

These calculations indicated that the reactivity effect is small and negative.

Therefore, the reference case in which the fuel assemblies are centered is controlling and no uncertainty for eccentricity is necessary.

9.]A-11 Rev. ]14 WOLF CREEK 9.1A.2.2.5 Abnormal and Accident Conditions The reactivity Table 9.1A-3.9.1A.2.2.5.1 effects of abnormal and accident conditions are summarized in Temperature and Water Density Effects (b)(4)9.IA.2.2.5.2 Lateral Rack Movement The possibility of reductions in the rack-to-rack gaps and the resulting criticality consequences have also been reviewed.

Criticality evaluations are sensitive to these gap dimensions, since the inter-rack gaps provide a flux trap which reduces the reactivity.

Rack-to-rack gap reductions are a concern subsequent to dynamic events which are severe enough to displace the racks laterally or produce fuel-to-rack cell, wall. impacts of sufficient magnitude to exceed cell wall material yield strength (i.e., produce plastic deformation).(b)(4)9. IA-12 Rev. 14 WOLF CREEK (b)(4)9. I.A-13 Rev. 1 4 WOLF CREEK 9.1A.2.2.5.5 (b)(4)9.1A.2.2.6 Dropped Fuel Assembly Benchmark.

Calculations The methodologies for determining criticality safety have been verified by comparison with critical experiment data for configurations that impose a stringent test of the capability of the analytical methodologies.

These benchmark calculations have been made on selected critical experiment, chosen, in so far as possible to bound the range of variables in fuel storage rack designs, including the Wolf Creek high density racks.9.1A.2.2.6.1 Summary Two independent methods of analysis were used i.n performing the Wolf Creek fuel storage rack criticality safety analyses.

These two methods differ in cross ,section librar.4es and in the treatment of the cross sections (b ..4...is a continuous energy Monte Carlo code and](b)(4)

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.. a ] a s'(b)( uses groupsdependent cross sections.

For the (b)(4) .ar'.alyses reported liere, the 238-group library was chosen, processed' through the NITAWL- ]1 (b)(4) programto create a working library and no account for resonance self-shielding in uranium-238 (Nordheim integral treatment).

The 238-group library was chosen to avoid or minimize the errors (trends) that have been reported (e.g., References 1.9-21 ) for calculations with collapsed cross section sets. Small but observable trends (errors) have beenzreported for calculations with the ..... j.-. ...... These errors are probably due to the use of a single collapsing spectrum whe'F the spectrum should be different for the various cases analyzed, as evidenced by the spectrum indices.9.1-A-14 Rev. 14 WOLF CREEK (b)(4)Table 9.1A-7 summarizes results of the ,benchmark calculations for al.l, cases selected and analyzed, as referenced in the table. The effect of the major variables are discussed in subsequent sections below. It is important to note that there is obviously considerable overlap in parameters since it is not possible to vary a single parameter and maintain criticality; some other parameter or parameters must be concurrently varied to maintain criticality.(b)(4).'igur.es 9.1A-7 and 9.1A-8 show the calculated for the .benchmark critical (b)(4) respectively (U0 2"'fuel only). The scatter in the data (even for comparatively minor variation in critical parameters) represents experimental error in performing the critical experiments within each laboratory, as well as between the various testing laboratories.

A classical example of experimental error is the corrected enrichment in the PNL experiments, first as an addendum to the initial report and, secondly, by. revised values in subsequent reports for the same fuel rods.The B&W critical experiments show a larger experimental error than the PNL criticals.

This would be expected since the B&W criticals encompass a greater range of critical parameters than the PNL criticals.(b)(4)9. 1A-15 Rev. 1 4 WOLF CREEK (.)(4)9. 1.A-1 6 Rev. 14 WOLF CREEK b ) 4 ).. .. ...................................................

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....... .... ... ...... -- ----- --(b)(4)9.1A.2.2.6.4 Miscellaneous and Minor Parameters 9,1A.2.2.6.4.1 Reflector Material and Spacings PNL has performed a number of critical experiments with thick steel and lead reflectors.

Analysis of these critical experiments are listed in Table 9.IA-]l (subset of data in Table 9.1A-7) .There appears to be a small tendency toward over prediction of ket at the lower spacing, although there are an insufficient number of data points in each series to allow a quantitative determination of any trends. The tendency toward over prediction at close spacing means that the rack calculations may be slightly more conservative than otherwise.

9.!A.2.2.6.4.2 Fuel Pellet Diameter and Lattice Pitch"'he critical experiments selected for analiysis cover a rango of fuel pellet..... .................

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........ ....................(b)(4)(b)(4) Ifo BWR fuel.Thus, the critical experiments analyzed provide a reasonable representation of power reactor fuel. Based on the data in Table 9.]A-7, there does not appear to be any observable trend with. either fuel pellet diameter or lattice pitch, at least over the range of the critical experiments applicable to rack designs.9.lA-17 Rev. 14 WOLF CREEK 9.lA.2.2.6.4.3 Soluble Boron Concentration Effects Various soluble boron concentrations were used in the B&W series of critical rments and in one Pexpexperiment, with boron concentrations ranging up to (b)(4)show a tendency to slightly over predict reactivity for the three experiments I (J4) In turn, this would suggest that. the eval uation of the racks with higher soluble boron concentrations could be slightly conservative.(jb)(4)9. IA. 3 THERMAL AND HYDRAULIC ANALYSES The Wolf Creek reracked fuel. storage pool (spent fuel pool. and cask loading pool with fuel storage racks installed) and the Fuel Pool Cooling and Cleanup System (FPCCS) comply with the provisions of Section III of the USNRC "OT Position Paper for Review and Acceptance of Spent Fuei Storage and Handling Applications", (April 14, 1978). The methods, models, analyses, and numerical results are summarized below.The thermal-hydraulic qualification analyses for the rack arrays fall into the following categories:

1. Evaluation of the maximum decay heat load limit as a function of the bulk temperature limit for the postulated discharge scenario.2, Evaluation of the postulated loss-of-forced cooling scenarios to establish that pool boiling will not occur, 3. Determination of the maximum temperature difference between the pool local temperature and the bulk pool temperature at the instant when the bulk temperature reaches its maximum value.4. Evaluation of the maximum temperature difference between the fuel rod cladding temperature and the local pool. water temperature to establish that nucleate boiling at any location around the fuel is not possible with forced cooling available.

9. IA-18 Rev. 14 WOLF CREEK Because the thermal and hydraulic analyses bound both the Callaway and Wolf Creek fuel storage pools, the pool water volume is conservatively based on the minimum east-west and north-south dimensions of the two pools. This conservatism results in a lower bound thermal inertia and outer periphery downcomer dimension in the thermal-hydraulic calculations.

FPCCS at Wolf Creek is described in Section 9.1.3. ib4..........

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T h e d e c a y heat generated by the stored fuel in the poolis transferred from"The fuel pool cooling t. ......... Normal makeup water to the fuel storage pool is supplied by the reactor makeup water system., An alternate source of makeup water is the RWST via the fuel pool cleanup pumps. Emergency makeup water is supplied from the Essential Service Water system. Boron addition to the fuel storage pooe is normally accomplished by supplying borated water from the boric acid tanks via the boric acid blending tee. Boron may also be added by using the RWST as the source of makeup water to the fuel storage pool. Isolation of non-safety related portions of the FPCCS is a manual action.The fuel pool cleanup system provides the capability for purification of the water in the spent fuel pool, the cask loading pool, the transfer canal, the refueling pool, and the RWST. The cleanup system is an essential adjunct to the FPCCS system to maintain clarity and water chemistry control in the fuel storage pool.Consistent with the current plant practice, two discharge scenarios are postulated when considering fuel storage pool cooling: partial core offload ii. full-core offload In lieu of prescribing a batch size and cooling period for the partial core offload, the maximum pool heat load is determined for a scenario of only one cooling train operating and a limit on the steady state bulk pool temperature (b)(4)Similarly, the full core offload scenario is required to be executed so that the maximum pool heat load will not allow for bulk pool boiling at the[ib(b!4--(b)(4) .....More specifically, the bulk water temperature is_____ .. after two hours of pool heat-up in the absence of all forced cooling pathss...Evaluation of these two scenarios provides maximum flexibility in batch sizes and cooling periods prior to offload into the pool. In both scenarios, the component cooling water (CCW), used to remove heat from the fuel pool cooler, is assumed to be at its maximum design temperature.

During the partial core offload scenario CCW flow is assumed to be at its nominal rate. During full core offload conditions, CCW flow is assumed to be at its design basis flow rate. With the thermal effectiveness of the fuel pool cooler thus fixed, the requirement of the ceiling on the bulk pool temperature essentially translates into a limit on the total heat generation rate in the pool.Finally an evaluation is performed for a loss of cooling accident occurring some time after restart. This evaluation considers a four hour long loss of forced cooling in the FPCCS followed by a twenty hour long period with cooling provided at one-half the normal coolant flow rate. Under this scenario, the fuel ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 1 po l d e o e c h ....b l b i i g e p r t r

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]fuel, pool does not reach the bulk boiling temperature1(b)(4)

For this evaluation, the component cooling.water to the heat exchFan~ge-r is assumed to be at an elevated temperature and reduced flow rate.9. 1A- 1,9 Rev. 14 WOLF CREEK 9.IA.3.1 Decay Heat Load Limit.The heat load imposed on the pool is from the decay heat generated by fuel assemblies discharged into the pool., The primary safety function of the FPCCS is to adequately transport this heat load to the CCW system and thereby maintain the bulk pool temperature within specified limits. Compliance with the limiting heat load will be ensured through adjustments to the cooling system performance and/or adjustments to the fuel. offload rate. Commonly used decay heat calculation methods based upon ASB 9-2, ANS 5. 1, or ORIGEN2 are used to provide conservative estimates of decay heat values for specific fuel pool inventories.

9.1A.3.1.1, Decay Heat Load Calculations and Conservatisms The following conservatisms are applied in the decay heat load limit calculations." FPCCS heat exchanger thermal performance is based on the design maximum fouling and plugging level. This will conservatively minimize the heat rejection capability of the FPCCS," Thermal inertia induced transient effects resulting in a lag in bulk pool temperature response are neglected, This conservatively lowers the calculated decay heat load limit by forcing the peak decay heat load to coincide with the peak pool temperature.,* In calculating the fuel storage pool evaporation heat losses, the.bul.. din i nt fuel storage pool <b)(4).I(b)(4)humidity.

This minimizes the evaporative heat ioss component, maximizing the heat duty burden on the pool cooling system......... .....9, 1A-20 Rev. .1.4 WOLF CREEK (b)(4)9. 1A-21 Rev. 14 WOLF CREEK (b)(4)9. 1 A-22 Rev. 1.4 WOLF CREEK (b)(4)9.1A.3.3 Local Pool Water Temperature A single conservative evaluation for a bounding amalgam of conditions was performed to evaluate the local pool water temperature.

The result of the single evaluation is a bounding temperature difference between the maximum local water temperature and the bulk pool temperature.

In order to determine an upper bound on the maximum local water temperature, a series of conservative assumptions are made. The most important of these assumptions are: 9. 1A-23 Rev. 11 WOLF CREEK" With a full core discharged into the racks farthest from the coolant water inlet, the remaining cells in the spent fuel pool are postulated to be occupied with previously discharged fuel.* The hottest assemblies, located together in the pool, are assumed to be located in "pedestal" cells of the racks. These cells have a reduced water entrance area, caused by the pedestal blocking the basep]ate hole, and a correspondingly increased hydraulic resistance." The cool*ant water inlet temperature, and therefore the bulk pool temperature, is mininized to conservatively maximize the fluid viscosity.

This assumption will maximize the head losses for water flowing through the fuel racks and fuel assemblies.

• No downcomer flow is assumed to exist between the rack modules.(b)(4)9.1 A.3.3. 1 Local Temperature Evaluation Methodoloja The inlet piping which returns cooled pool water from the FPCCS terminates above the level of the fuel racks. To demonstrate adequate cooling of hot fuel in the pool, it is necessary to rigorously quantify the velocity field in the pool created by the interaction of buoyancy driven flows and water injection/egress.

A Computational Fluid Dynamics (CFD) analysis for this demonstration is required.

The objective of this study is to demonstrate that the principal thermal-hydraulic criteria of ensuring local subcooled conditions in the pool is met for all postulated fuel discharge/cooling alignment scenarios.

The local thermal-hydraulic analysis is performed such that partial cell blockage and slight fuel assembly variations are bounded. An outline of the CFD approach is described in the following.

9. IA-24 Rev. 14 WOLF CREEK (b)(4)The fuel storage pool geometry required an adequate portrayal of large scale and small scale features, spatially distributed heat sources in the fuel storage racks and water inlet/outlet configuration.

Relatively cooler bulk pool water normally flows down between the fuel rack outline and pool wall liner clearance known as the downcomer.

Near the bottom of the racks, the flow turns from a vertical to horizontal direction into the bottom plenum supplying cooling water to the rack cells. Heated water issuing out of the top of the racks mixes with the bulk pool water. An adequate modeling of these features on the CFD program involves meshing the large scale bulk pool region and small scale downcomer and bottom plenum regions with sufficient number of computational cells to capture the bulk and local features of the flow field.The distributed heat sources in the fuel storage pool racks are modeled by identifying distinct heat generation zones considering full-core discharge, bounding peak effects, and presence of background decay heat from old discharges.

Three heat generating zones were modeled. The first consists of background fuel from previous discharges, the remaining two zones consist of fuel from a bounding full-core-discharge scenario.

The two full. core discharge zones are differentiated by one zone with higher than average decay heat generation and the other with less than average decay heat generation.

The background decay heat load is determined such that the total decay heat load in the pool is equal to the calculated decay heat load limit. This is a conservative model, since all of the fuel with higher than average decay heat is placed in a contiguous area. A uniformly distributed heat generation rate was applied throughout each distinct zone.9. ]A-25 Rev. 14 WOLF CREEK (b)(4)9. 1A-26 Rev, 14 WOLF CREEK 9.1A.3.3.2 Local Water and Fuel Cladding Temperatures Consistent with the approach to make conservative assessments of temperature, the local water temperature calculations are performed for a pool with decay heat generation equal to the maximum calculated decay heat load limit. Thus, the local water temperature evaluation is a calculation of the temperature increment over the theoretical spatially uniform value due to local hot spots (due to the presence of a highly heat emissive fuel bundle).The CFD study has analyzed a single bounding local thermal-hydraulic scenario.In this scenario, a bounding full-core discharge is considered in which the 193 assemblies are located in the pool, farthest from the cooled water inlet, while the balance of the rack cells are postulated to be occupied by fuel from old discharges.(b) (4)9. IA-27e Rev. 14 WOLF CREEK (b)(4)9. ]A-28 Rev. 1 4 WOLF CREEK 9.1A.3.5 Decay Heat Load Limits The calculated decay heat load limit is summarized in Table 9.lA-17. Because all transient effects were excluded from the evaluations, this decay heat load corresponds to the invariant heat load which results in a steady-state bulk pool temperature which will not exceed the temperature limit for either the partial core or full core offload scenario.This calculated decay heat load limit is not based on any specific discharge conditions, but is a mathematically derived quantity.

Any conservative decay heat calculation used to determine the operational limits (i.e. in-core hold time requirement) necessary to avoid exceeding this decay heat load provides conservative operational limits. The operational limits are determined based on the decay heat load limit in Table 9.1A-17. Based on this limit, the fuel storage pool cooling system will remain in compliance.

9.1A.4 STRUCTURAL AND SEISMIC CONSIDERATIONS The structural adequacy of the high density spent fuel racks are considered under all loadings postulated for normal, seismic, and accident conditions.

The fuel storage racks must remain fully functional during and after a seismic disturbance.

The seismic adequacy is demonstrated in response to both a Safe Shutdown Earthquake (SSE) and the Operational Design Basis Earthquake (OBE).The analyses undertaken to confirm the structural integrity of the racks are performed in compliance with the USNRC Standard Review Plan (Reference

42) and the OT Position Paper (Reference 13).(b)(4)(b )(4 ) ..................................

S om e un iq u e attributes of rack dynamic behavior include a large fraction of the total structural mass in a confined rattling motion, friction support of rack pedestals against lateral motion, and large fluid coupling effects due to deep submergence and independent motion of closely spaced adjacent structures.

Whole Pool Multi-Rack (WPMR) analysis simulates the dynamic behavior of the storage rack ..t r. tur.. ..W4 ..... ..........(b)(4)9.1A.4. 1 Analysis Methodology An accurate simulation is obtained by direct integration of the nonlinear equations of motion with three pool slab acceleration time-histories applied as the forcing functions acting simultaneously.

Reliable assessment of the stress field and kinematic behavior of the rack modules incorporates key attributes of the actual structure in a conservative dynamic model.. The model must have the capability to execute the concurrent motion forms compatible with the free-standing installation of the modules.Calculations must incorporate momentum transfers due to the rattling of fuel assemblies inside storage cells; the lift-off and subsequent impact of support pedestals with the pool liner (or bearing pad); and quanti.fcation of fluid coupling due to water mass in the interstitial spaces around rack modules. In short, there are a large number of parameters with potential influence on the rack kinematics.

The comprehensive structural evaluation must deal with all of these without sacrificing conservatism.

9. 1A-29 Rev. 14 WOLF CREEK The model must be capable of effecting momentum transfers which occur due to rattling of fuel assemblies inside storage cells and the capability to simulate lift-off and subsequent impact of support pedestals with the pool liner (or bearing pad). The contribution of the water mass in the interstitial spaces around the rack modules and within the storage cells must be modeled in an accurate manner. During dynamic rack motion, hydraulic energy is either drawn from or added to the moving rack, modifying its submerged motion in a significant manner. Therefore, the dynamics of one rack affects the motion of all others in the pool.(b)(4)9. 1A-30 Rev. 14 WOLF CREEK I(b)(4)9.1A.4.1.2 Synthetic Time-Histories The synthetic time-histories in three orthogonal directions (N-S, E-W, and vertical) are generated in accordance with the provisions of SRP 3.7.1 (Reference 48). A preferred criterion for the synthetic time-histories in SRP 3.7.1 calls for both the response spectrum and the power spectral density corresponding to the generated acceleration time-history to envelope their target (design basis) counterparts with only finite enveloping infractions.

The time-histories for the pools have been generated to satisfy this preferred (and more rigorous) criterion.

The seismic files also satisfy the requirements of statistical independence mandated by SRP 3.7.1.Figures 9.1A-12 through 9.1A-16 provide Plots of the time-history accelerograms

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.... ....i ...... .i .. i i i i i i i i i i i i ii i i iii i .........II I I respective..y.

These artificial time-hisLories are used in all non-linear dynamic simulations of the racks, Results of the correlation function of the three time-histories are given in Table 9.1A-19. Absolute values of the correlation coefficients are shown to be less than 0.15, i ndicat:i.ng the slat~ist ical independence of the three data sets.9.1A.4.2 WPMR Methodology The WPMR methodology incorporates both stress and displacement criteria.

The following summarizes the sequence steps undertaken for model development:

a. Suitable 3-D dynamic models for a time-history analysis of the new maximum density racks are prepared.

These models include the assemblage of all rack modules in each pool. Include all fluid coupling interactions and mechanical coupling appropriate to performing an accurate non-linear simulation.

This 3-D simulation is referred to as a, Whole Pool Mul]ti-Rack model.9.1IA-31 Rev. 19 1 WOLF CREEK b. 3-D dynamic analyses are performed on various physical conditions (such as coefficient of friction and extent of cells containing fuel assemblies).

Appropriate displacement and load outputs from the dynamic model for post-processing are archived.c. A stress analysis of high stress areas for the limiting case of all the rack dynamic analysis is performed to demonstrate compliance with ASME Code Section III, Subsection NF limits on stress and displacement.(b)(4)9. 1A-32 Rev. 14 WOLF CREEK (b)(4) ..................................................

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.....(b) (4 9. 1A-39 Rev. 14 WOLF CREEK'(b)(4)9. 1A-40 Rev. ].4 WOLF CREEK (b)(4)9. IA-4 1 Rev. 1 4 WOLF CREEK (b)(4)9. 1A-42 Rev. 14 WOLF CREEK (b)(4)9. 1A-43 Rev. 1.4 WOLF CREEK.(b)(4) --. ... .9. vA-44 Rev. 14 WOLF CREEK (b)(4)9.1IA-45 Rev. 14 WOLF CREEK The time-varying lateral (horizontal) and vertical forces on the extremities of the support pedestals produce stresses at the root of the pedestals in the manner of an end-loaded cantilever.

The stress field in the cellular region of the rack is quite complex, with its maximum values located in the region closest to the pedestal.

The maximum magnitude of the stresses depends on the severity of the pedestal end loads and on the geometry of the pedestal/rack baseplate region.Alternating stresses in metals produce metal fatigue if the amplitude of the stress cycles is sufficienLly large. In high density racks designed for sites with moderate to high postulated seismic action, the stress intensity amplitudes frequently reach values above the material endurance limit, leading to expenditure of the fatigue "usage" reserve in the material.Because the locations of maximum stress (viz., the pedestal/rack baseplate junction) and the close placement of racks, a post-earthquake inspection of the high stressed regions in the racks is not feasible.

Therefore, the racks are engineered to withstand multiple earthquakes without reliance of nondestructive inspections for post-earthquake integrity assessment.

The fatigue life evaluation of racks is an integral aspect of a sound design.A time-history analysis was performed to provide the means to obtain a complete cycle history of the stress .intensities in the highly stressed regions of the rack.I(b)(4)9.IA.4.3.5.5 Weld Stresses Weld locations subjected to significant seismic loading are at the bottom of the rack at the baseplate-to-cell connection, at the top of the pedestal support at the baseplate connection, and at cell-to-cell connections.

Bounding values of resultant loads are used to qualify the connections.

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9. 1A-46 Rev. 14 WOLF CREEK b. Baseplate-to-Pedestal Welds The weld between the baseplate and the support pedestal is checked using finite element analysis to determine the maximum stress under a Level B or Level D event. The calculated stress values are below the allowable values.c. Cell-to-Cell Welds Cell-to-cell connections aie by a series of connecting welds along the cell height. Stresses in storage cell to cell welds develop due to fuel assembly impacts with the cell wall.. These weld stresses are conservatively calculated by assuming that fuel assemblies in adjacent cells are moving out of phase with one another so that impact loads in two adjacent cells are in opposite directions; this tends to separate the two cells from each other at the weld. Table 9.1A-20 gives results for the maximum allowable load that can be transferred by these welds based on the available weld area. An upper bound on the load required to be transferred is also given in 'Fable 9.1A-20 and is much lower than the allowable load. This upper bound value is very conservatively obtained by applying the bounding rack-to-fuel.

impact load from any simulation in two orthogonal directions simultaneously, and multiplying the result by 2 to account for the simultareous impact of two assemblies.

An equilibrium analysis at the connection then yields the upper bound load to be transferred.

It is seen from the results in Table 9.1A-20 that the calculated load is well below the allowable, (b)(4)9.1A,4.3.5.7 Level A Evaluation The Level A condition is not a governing condition for spent fuel racks since the general level of loading is far less than Level B loading. To illustrate this, the heaviest spent fuel rack is considered under the dead weight load. It is shown below that the maximum pedestal load is low and that further stress evaluations are unnecessary.

9. IA-4 7 Rev. 1 4 WOLF CREEK (b)(4)9.1 A-48 Rev. 1.4 WOLF CREEK 9.1,A.4.4 Fuel Pool Structure Integrity The Wolf Creek fuel storage pool is a safety related, seismic category 1, reinforced concrete structure.

Spent fuel is to be placed within storage racks located in the fuel storage pool. The fuel storage pool includes the spent fuel pool and the cask loading pool with fuel storage racks installed.

The area is collectively referred to in this section as the fuel pool structure.

An analysis was performed to demonstrate the structural adequacy of the pool structure, as required by Section IV of the USNRC OT Position Paper (Reference 63).The fuel storage pool regions are analyzed using the finite element- method.Results for individual load components are combined using factored load combinations mandated by SRP 3.8.4 (Reference

64) based on the "ultimate strength" design method. It is demonstrated that for the critical bounding factored load combinations, structural integrity is maintained when the pools are assumed to be fully loaded with spent fuel racks, as shown in Figure 9.1-2 with all storage locations occupied by fuel assemblies.

The regions examined in for the fuel storage pool include the floor slabs and the highly loaded wall sections adjoining the slabs. Both moment and shear capabilities are checked for concrete structural integrity.

Local punching and bearing integrity of the slab in the vicinity of a rack module support pedestal pad is evaluated.

All structural capacity calculations are made using design formulas meeting the requirements of the American Concrete Institute (ACI).(b)(4)9. lA4 9 Rv. 1 9. 1A-49 Rev. 14 WOLF CREEK 4. The Cask Handling Crane and Spent Fuel. Handling Machine (Refueling Platform) are designed to move along the N-S direction.

The dead weight and the rated lift weight of these cranes are considered as dead load and live load, respectively.

5. The hydrostatic water pressure.9.1A.4.4.2.2 Seismic Induced Loads 1. Vertical loads transmitted by the rack support pedestals to the slab during a SSE or OBE seismic event.2. Hydrodynamic inertia loads due to the contained water mass and sloshing loads (considered in accordance with.(Reference 66)) which arise during a seismic event.3. Hydrodynamic pressures between racks and pool walls caused by rack motion in the pool during a seismic event.4. Seismic inertia force of the walls and slab.9.1A.4.4.2.3 Thermal Loading Thermal loading is defined by the temperature existing at the faces of the pool concrete walls and slabs. Two thermal loading conditions are evaluated:

The normal operating temperature and the accident temperature.

The effect of gamma heating on the concrete was also considered and requires the implementation of administrative controls to maintain concrete temperatures within acceptable ranges, as discussed in section 9.IA.4.4.5.

9.lA.4.4.2.4 Pool Water Loading The loadings described above were considered for two possible scenarios:

one considers the Cask Loading Pool full of water and the other considers the Cask Loading Pool empty.9.]A.4.4.3 Analysis Methodology 9.1A.4.4.3.1 Finite Element Analysis Mode]The finite element model encompasses the entire Spent Fuel. Pool and three other reinforced concrete structures located immediately adjacent to the Spent Fuel Pool (the Cask Loading Pool, the Transfer Canal and the Cask Washdown Pit).The interaction with the rest of the Fuel Building reinforced concrete, which is not included in the finite-element model, is simulated by imposing appropriate boundary conditions.

The structural area of interest for the fuel storage pool includes only two, the spent fuel pool and the cask loading pool.However, by augmenting these areas of interest with the addition of the Transfer Canal and the Cask Washdown Pit, the constructed finite-element model and numerical investigation are enhanced because the perturbation induced by the boundary conditions on the stress field distribution for the area of interest is minimized.

9. lA-50 Rev. 14 WOLF CREEK.(b)(4)To simulate the interaction between the modeled region and the rest of the Fuel Building a number of boundary restraints were imposed upon the described finite-element model.The behavior of the reinforced concrete existing in the structural elements (walls, slab and mat:) is considered elastic and isotropic.

The elastic characteristics of the concrete are independent of the reinforcement contained in each structural element for the case when the un-cracked cross-section is assumed. This assumption is valid for all load cases with the exception of the thermal loads, where for a more realistic description of the reinforced concrete cross-section including the assumption of cracked concrete i.s used.To simulate the variation and the degree of cracking patterns, the original elastic modulus of the concrete is modified in accordance with Reference (Reference 65).9.lA.4.4.3.2 Analysis Technique The structural region isolated from the Fuel Building and comprised of four pools (the Spent Fuel Pool, the Cask Loading Pool, the Transfer Canal and the Cask Washdown Pit) is numerically investigated using the finite element method.The pool walls and their supporting reinforced concrete mat are represented by a 3-D finite-element model.The individual loads considered in the analysis are grouped in five categories:

dead load (weight of the pool structure, dead weight of the rack modules and stored fuel, dead weight of the reinforced concrete Fuel Building upper structure, the dead weight. of the Cask Handling Crane (CHC).and the Spent Fuel Handling Mach:ine (SFHM), and the hydro-static pressure of the contained water), live loads (CHC and SFHM suspended loads), thermal loads (the thermal gradient through the pool walls and slab for normal operating and accident conditions) and the seismic induced forces (structural seismic forces, interaction forces between the rack modules and the pool slab, seismic loads due to self-excitation of the pool structural elements and contained water, and seismic hydro-dynamic interact:ion forces between the rack modules and the pool walls for boLh OBE and SSE conditions).

The dead and thermal loads are considered static acting loads, while the seismic induced loads are time-dependent.

The material behavior uýnder all. type of loading conditions is described as elastic and isotropic representing the un-cracked characteristics of the structural elements cross-secLion, with the exception of the thermal load cases where the material elasticity modulus is reduced in order to simulate the variation and the degree of the crack patterns.

This approach (Reference 65)acknowledges the self-relieving nature of the thermal loads. The degree of reduction of the elastic modulus is calculated based on the average ultimate capacity of the particular structural element.9. 1A-5]Rev. I1I WOLF CREEK (b)(4).................

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9. IA. ..6 Coric .L5iusinS Regions affected by ]oadinq the fuel pool. completely with high density racks are examined for structural integrity under bending and shearing action. It has been determined that adequate safety margins exist assuming that all racks are fully loaded with a bounding fuel weight and that the factored load combinations are checked against the appropriate structural design strengths.

It is also shown that local loading on the liner does not compromise liner integrity under a postulated fatigue condition and that concrete bearing strength limits are not exceeded.{(b)(4)..............

9. IA ý)4 R v. 1 WOLF CREEK!I I 9.1A.6 REFERENCES

1. Petrie and N. F. Landers, "KENO Va -An Improved Monte Carlo Criticality Program with Supergrouping, " Volume 2, Section F]I from "SCALE: A Modular System for Performing Standardized Computer Analysis for Licensing Evaluation" NUREG/CR-0200, Rev. 4, January 1990.2. J.F. Briesmei:ster, Editor, "MCNP -A General Monte Carlo N-Particle Transport Code, Version 4A, " LA-12625, Los Alamos National.

Laboratory (1993).3. N. M. Greene, L.M. Petrie and R.M. Westfall, 3. "NITAWLIT:

Scale System Module for Performing Shielding and Working Library Production," Volume 1, Section Fl from "SCALE: A Modular System for Performing Standardized Computer Analysis for Licensing Evaluation" NUREG/CR0200, Rev. 4, January 1990.4. M.G. Natrella, Experimental Statistics, National Bureau of Standards Handbook 91, August 1963.5. A. Ahlin, M. Edenius, and H. Haggblom, "CASMO -.A Fuel Assembly Burnup Program", AERF-76-4158, Studsvikreport.

6. A. Ahlin and M. Edenius, "CASMO -A Fast Transport Theory Depletion Code for LWR Analysis", ANS Transactions, Vol. 26, p. 604, ]977.7. M. Edenius, A. Ahlin and B.H. Forssen, "CASMO-3 A Fuel. Assembly Burnup Program User's Manual," Studsvik/NFA-86/7, Studsvik Energitechnik AB, November 1986.8. S. E. Turner, "Waterford Criticality Analysis," HI-961562, 1996.9. M. Edenius and A. Ahlin, "CASMO-3:

New Features, Benchmarking, and Advanced Applications," Nucl. Sc.i. Eng, 100 (1988).10. S. E. Turner, "Uncertainty Analysis -Burnup Distributions", presented at the DOE/SANDIA Technical Meeting on Fuel Burnup Credit, Special Session, ANS/ENS Conference, Washington, D.C., November 2, 1988.11. General. Design Criteria 62, Prevention of Criticality in Fuel Storage and Handli ng.12. USNRC Standard Review Plan, NURFG-0800, Section 9.1 .2, Spent Fuel Storage, Rev. 3 -Jul.y 1981.9.1IA-55 Rev, 14 WOLF CREEK 13. USNRC letter of April 14, 1-978, to all Power Reactor Licensees

-OT Position for Review and Acceptance of Spent Fuel Storage and Handling Applications, including modification letter dated January 18, 1979.14. USNRC Regulatory Guide 1.13, Spent Fuel Storage Facility Design Basis, Rev. 2 (proposed), December 198].15. ANSI ANS-8.17-1984, Criticality Safety Criteria for the Handling, Storage and Transportation of LWR Fuel Outside Reactors.16. ANSI/ANS 8.1 (NI6.1) -Nuclear Criticality Safety in Operations with Fissionable Materials Outside Reactors.17. Briesmeister, Ed., "MCNP4a -A General Monte Carlo N-Particle Transport Code, Version 4A; Los Alamos National Laboratory, LA-12625-M (1993).18. SCALE 4.3, "A Modular Code System for Performing Standardized Computer Analyses for Licensing Evaluation", NUREG-0200 (ORNL-NUREG-CSD-2/U2/R5, Revision 5, Oak Ridge National Laboratory, September 1995.19. DeHart and S.M. Bowman, "Validation of the SCALE Broad Structure 44-G Group ENDF/B-Y Cross-Section Library for Use in Criticality Safety Analyses", NUREG/CR-6102 (ORNI,/TM-12460)

Oak Ridge National Laboratory, September 1994.20. W.C. Jordan et al., "Validation of KENOV.a", CSD/TM-238, Martin Marietta Energy Systems, Inc., Oak Ridge National Laboratory, December 1986.21. O.W. Hermann et al., "Validation of the Scale System for PWR Spent Fuel Isotopic Composition Analysis", ORNL-TM-12667, Oak Ridge National Laboratory, undated.22. R.J. Larsen and M.L. Marx, An Introduction to Mathematical Statistics and its Applications, Prentice-Hal1, 1986.23. M. N. Baldwin et al., Critical Experiments Support~ing Close Proximity Water Storage of Power Reactor Fuel, BAW- 1.484-7, Babcock and Wilcox Company, July 19"79.24. G.S. Hoovier et al., Critical Experiments Supporting Underwater Storage of Tightly Packed Configurations of Spent Fuel Pins, BAW -16454, Babcock& Wilcox Company, November 1991.25. L.W. Newman et al., Urania Gadolinia:

Nuclear Model Development and Critical Experiment Benchmark, BAW-1810, Babcock and Wilcox Company, April 1984.26. J.C. Manaranche et al., "Dissolution and Storage Experimental Program with 4.75 w/o Enriched Uranium-Oxide Rods," Trans. Am. Nucl. Soc. 33: 362-364 (1979).2-7. S.R. Bierman and E.D. Clayton, Criticality Experiments with Subcritical Clusters of 2.35 w/o and 4.31 w/o 235LI Enriched U02 Rods in Water with Steel Reflecting Walls, PNL-3602, Battelle Pacific Northwest Laboratory, April 1981.28. S.R. Bierman et al., Criticality Experiments with Subcritical Clusters of 2.35 w/o and 4.31 w/o 235u Enriched U02 Rods in Water with Uranium or Lead Reflecting Walls, PNL-3926, Battelle Pacific Northwest Laboratory, December, 1981.29. Bierman et al., Critical.

Separation Between Subcritical Clusters of 4.31 w/o 235U Enriched U02 Rods in Water with Fixed Neutron Poisons, PNL-2615, Battelle Pacific Northwest Laboratory, October 1977.30. R. Bierman, Criticality Experiments with Neutron Flux Traps Containing Voids, PNL-7167, Battelle Pacific Northwest Laboratory, April 1990.31. B.M. Durst et al., Critical Experiments with 4.31 wt % 235U Enriched UO0 Rods in Highly Borated Water Lattices, PNL-4267, Battelle Pacific Northwest Laboratory, August 1982.32. S.R. Bierman, Criticality Experiments with Fast Test Reactor Fuel Pins in Organic Moderator, PNL-5803, Battelle Pacific Northwest Laboratory, December 1981.33. E.G. Taylor et al., Saxton Plutonium Program Critical Experiments for the Saxton Partial Plutonium Core, WCAP-3385-54, Westinghouse Electric Corp., Atomic Power Division, December 1965.9. 1A-56 Rev. 14 WOLF CREEK 34. Natrella, Experimental Statistics, National Bureau of Standards, Handbook 91, August 1963.35. Heat Loss to the Ambient from Spent Fuel Pools: Correlation of Theory with Experiment", Holtec Report HI-90477, Rev. 0, April 3, 1990.36. "An Improved Correlation for Evaporation from Spent Fuel Pools", Holtec Report HI- 971664, Rev. 0.37. Batchelor, G.K., "An Introduction to Fluid Dynamics", Cambridge University Press, 196/.38. Hinze, J.0., "Turbulence", McGraw Hill Publishing Co., New York, NY, 1975.39. Launder, B.E., and Spalding, D.B., "Lectures in Mathematical Models of Turbulence", Academic Press, London, 1972.40. "QA Documentation and Validation of the FLUENT Version 4.32 CFD Analysis Program", Holtec Report HI-961444.

41. Rohsenow, N.M., and Hartnett, J.P., "Handbook of Heat Transfer,", McGraw Hill Book Company, New York, 1973.42. USNRC NUREG-0800, Standard Review Plan, June 1987.43. (USNRC Office of Technology) "OT Position for Review and Acceptance of Spent Fuel Storage and Handling Applications", dated April 14, 1978, and January 18, 1979 amendment thereto.44. Soler, A.I. and Singh, K.P., "Seismic Responses of Free Standing Fuel Rack Constructions to 3-D Motions", Nuclear Engineering and Design, Vol.80, pp. 315-329 (1984).45. Soler, A.I. and Singh, K.P., "Some Results from Simultaneous Seismic Simulations of All Racks in a Fuel Pool.", INNM Spent Fuel Management Seminar X, January, 2.993.46. Singh, K.P. and Soler, A.I., "Seismic Qualification of Free Standing Nuclear Fuel Storage-Racks

-the Chin Shan Experience, Nuclear Engineering International, UK (March 1991).47. Holtec Proprietary Report -HI-961465

-WPMR Analysis User Manual for Pre&Post Processors

& Solver, August, 1997.48. USNRC Standard Review Plan, NUREG-0800 (Section 3.7.1, Rev. 2, 1989).49. Holtec Proprietary Report 111-89364

-Verification and User's Manual for Computer Code GENEQ, January, 1990.50. Rabinowicz, E., "Friction Coefficients of Water Lubricated Stainless Steels for a Spent Fuel Rack Facility," MIT, a report for Boston Edison Company, 1976.51. Singh, K.P. and Soler, A.T., "Dynamic Coupling in a Closely Spaced Two-Body System Vibrating in Liquid Medium: The Case of Fuel Racks," 3rd International Conference on Nuclear Power Safety, Keswick, England, May 1982.52. Fritz,.R.J., "The Effects of Liquids on the Dynamic Motions of Immersed Solids," Journal of Engineering for Industry, Trans. of the ASME, February 1972, pp 167-172.53. Levy, S. and Wilkinson, J.P.D., "The Component Element Method in Dynamics with Application to Earthquake and Vehicle Engineering," McGraw Hill, 1976.54. Paul, B., "Fluid Coupling in Fuel Racks: Correlation of Theory and Experiment", (Proprietary), NUSCO/Holtec Report HI-88243.55. ASME Boiler & Pressure Vessel Code,Section III, Subsection NF, 2.989 Edition.56. ASME Boiler & Pressure Vessel Code,Section III, Appendices, 1989 Edition.57. USNRC Standard Review Plan, NUREG-0800 (Section 3.8.4, Rev. 2, 1989).58. ACI 349-85, Code Requirements for Nuclear Safety Related Concrete Structures, American Concrete Institute, Detroit, Michigan, 1985.59. ACT 318-71, Building Code requirements for Structural Concrete.60. R. W. Westfall and J. H. Knight, "SCALE System Cross-Section Validation with Shipping Cask Critical Experiments", ANS Transactions, Vol. 33, p.368, November 1979.9.]IA-57 Rev. 14 WOLF CREEK 61. Scavuzzo, R. J., Stokey, W. F., and Radke, E. F., "Dynamic Fluid-Structure Coupling of Rectangular Modules in Rectangular Pools", ASME Special Publicatlion, Dynamics at Fluid-Structure Systems in the Energy Industry, PVP-39 June, 1979, pp. '77-86.62. Specification C-175, "Technical Specification for Purchase of Spent Fuel Storage Racks for the Standardized Nuclear Unit Power Plant System (SNUPPS)", Appendix B.63. OT Position for Review and Acceptance of Spent Fuel Handling Applications, by B.K. Grimes, USNRC, Washington, D.C., April 14, 1978.64. NUREG-0800, SRP-3.8.4, Rev. 1., July 1981.65. ACI 349-85, Code Requirements for, Nuclear Safety Related Concrete Structures, American Concrete Institute, Detroit Michigan.66. "Nuclear Reactors and Earthquakes, U.S. Department of Commerce, National Bureau of Standards, National Technical Information Service, Springfield, Virginia (TID 7024).67. STARDYNE User's Manual, Research Engineers, Inc., Rev. 4.4.9. IA-58 Rev. 14 1 WOLF CREEK (b)(4)Rev. 14 1 WOLF CREEK (b)(4)I, Rev. 14 1 WOLF CREEK (b)(4)Rev. 14 WOLF CREEK I (b)(4)1k Rev. 14 WOLF CREEK (b)(4)Rev. 141 WOLF CREEK (b)(4)Rev. 14 WOLF CREEK iR Rev. 14/I¸ WOLF CREEK Rev. 14j WOLF CREEK Rev. i4 H; :,a' .W .* , ........ -ad m j,4fl- 2 Z & *haa, &? ......,,- , ,, -e,5 -:, -

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