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Kyle Paaren
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NE 4497: Nuclear System Design II Nuclear Narwhals’ Nuclear Reactor Final Report Submitted by: K. Paaren, M. Jones, G. Jones, B. Adams, J. Rhodes, K. Sponsler, A. Tedeschi, B. Gibson, P. Garavaglia, M. Smith, N. Takcas, S. Rohan Submitted: May 6, 2016 Submitted To: Dr. Joshua Schlegel and Dr. Ayodeji Alajo Senior Design Department of Mining and Nuclear Engineering Missouri University of Science and technology Rolla, Missouri
I. Executive Summary NuclearNarwhals’Mobile LeadCooledFastReactorwill provideaGenIV leadcooledfastreactorto any coastal country,city,or province,whowouldwantasteadyandstable supplyof nuclearenergy offshore.Thisis importantbecause developingcitiesneedpowertoexpandwithoutthe needforusing any land.The size of the reactor will be 1000 MWt and 400 MWe assuminga forty percentefficiency[1]. It will be composedof atwo-loopsystem.The primaryloopwill be the liquidlead-bismutheutecticpool and the secondaryloopwill be supercritical carbondioxide.Inthe secondaryloop,heatenergywill be transferredoutof the systemto a watertreatmentfacilityaboardthe vesselafterexitingthe turbine. The excessenergyafterthe desalinationplantwillbe dissipatedintothe ocean.Eachshipwill be usedto provide portable,stablepowertogrowingcoastal areasalongwithbeingable tohelpwithrebuilding coastal areas where natural disastershave takenplace. Major changeshave beenmade to the designand final calculationshave beenmade.The majorchanges to the designinclude changingthe layoutof the reactorcore for a betterburnupandlongerfuel lifetime,andthe natural convectionflow will be pumpassisted.These changeswere made because it will have apositive impactonthe lifetime,heattransfer,andefficiencyof the entire system. Calculationsthathave beenmade thusfarinclude DisplacementsPerAtom(DPA) forall materialsinthe primarypool usingSRIM, conceptsrelatingtoreactorphysics,andtemperaturesandstatesof the secondaryside.Modeling wasdone forthe reactor core’scritical fuel lattice andassemblyusingSTAR- CCM + and for radiationshieldingusingMCNP.Reactorphysicsconceptsinclude the size of the core,the keff of the finite core withandwithoutcontrol rods,criticalitydue topromptneutrons,control rod worths,andthe burnup forthe reactorcore.
Table of Contents I. Executive Summary..........................................................................................................................2 II. List of Figures..................................................................................................................................5 III. Introduction ..................................................................................................................................6 IV. Conceptual Design and Description.................................................................................................9 1 Licensability .............................................................................................................................15 1.1 Reactor Design Considerations ...........................................................................................15 1.2 Radiation Safety.................................................................................................................17 1.3 Accident Scenarios and Safety Analysis ...............................................................................18 1.4 Structural Integrity.............................................................................................................19 1.5 Emergency Planning...........................................................................................................19 2 Economic Analysis ....................................................................................................................21 2.1 Capital Cost.......................................................................................................................21 2.1.1 Fuel Cost....................................................................................................................21 2.1.2 Raw Materials ............................................................................................................22 2.1.3 Major Components.....................................................................................................22 2.1.4 ShipAnalysis ..............................................................................................................23 2.2 Reoccurring Cost................................................................................................................25 2.3 Personnel and Operations Cost...........................................................................................27 2.4 Revenue............................................................................................................................29 3 Technical Feasibility..................................................................................................................31 3.1 Criticality...........................................................................................................................31 3.2 Radiation Transport...........................................................................................................35 3.2.1 Reactor Pool Modeling................................................................................................35
3.2.2 Polonium Off-gas system.............................................................................................40 3.2.3 Spent Fuel Storage......................................................................................................42 3.2.4 Dose Calculations .......................................................................................................42 3.3 Heat Transfer and Fluid Flow..............................................................................................44 3.3.1 Primary Side...............................................................................................................44 3.3.2 Secondary Side...........................................................................................................55 3.3.3 Water Desalination.....................................................................................................59 3.4 Materials...........................................................................................................................61 3.4.1 ShipAnalysis ..............................................................................................................61 3.4.2 DPA Considerations ....................................................................................................62 3.4.3 Corrosion...................................................................................................................62 3.4.4 Support Structure.......................................................................................................64 4 Humanitarian Benefit and Environmental Impact .......................................................................67 4.1 Nonproliferation................................................................................................................67 4.2 Pollution............................................................................................................................68 4.3 Public Concern and Safety..................................................................................................70 4.4 Water Desalination............................................................................................................71 4.5 Mobility ............................................................................................................................72 V. Conclusions..............................................................................................................................74 VI. References..............................................................................................................................75 VII. Appendix..............................................................................................................................79 i. Appendix A: MCNP Input File..................................................................................................79
II. List of Figures Figure 2.1.4.1: Handymax Hull Layout [37] .........................................................................................24 Figure 2.1.4.2: Handymax Hull TopView[37] .....................................................................................24 Figure 2.1.4.3: Cargo Hatch Diagram [37] ...........................................................................................25 Figure 2.1.4.1: Staffing and Employment Time Scheduling...................................................................28 Figure 3.2.1.1: Initial Sketch of Pool Lid..............................................................................................36 Figure 3.2.1.2: Extrusion of "Lip" of Lid with Off Gas System Hole........................................................37 Figure 3.2.1.3: Extrusion of the Pool Wall...........................................................................................38 Figure 3.2.1.4: Displacement of the Lid by Gravity ..............................................................................39 Figure 3.2.1.5: Displacement of the Lid by Gravity and 200 Lb Person..................................................39 Figure 3.3.2.1.3: Cross Section of Critical Fuel Pin...............................................................................49 Figure 3.3.2.1.4: Critical Fuel Pin Outlet Temperature.........................................................................49 Figure 3.3.2.1.5: Critical Fuel Pin OutletVelocity.................................................................................50 Figure 3.3.2.16: Critical Fuel Pin Inlet Temperature.............................................................................50 Figure 3.3.2.1.7: Critical Fuel Pin InletVelocity ...................................................................................51 Figure 3.3.2.1: Secondary Cycle Layout ..............................................................................................56 Figure 3.3.2.2: Secondary Cycle States ...............................................................................................56 Figure 3.3.2.3: Secondary Cycle State Diagram ...................................................................................57 Figure 3.4.4.1: Support Structure.......................................................................................................64 Figure 3.4.4.2: Safety Factor of Support Structure...............................................................................65 Figure 3.4.4.3: Minimum Factor of Safety...........................................................................................66 Figure 3.4.4.4: Support Structure Displacement (mm).........................................................................67
III. Introduction Whenthe opportunitycame todecide how to implementareactor,the distributionroute wasthe main choice.NuclearNarwhals’MobileLeadCooledFastreactorwasimplementedtospreadnuclear poweredenergyacrossthe globe togrowingcoastal citiesandprovinces.Itcanalsobe usedfor assisting the humanrelief effortindevelopingcountriesorplacesaffectedbynatural disasters.There have been manygrowingcitiesandcountriesthathave physicallyrunoutof room, and theirenergydemandsare not beingmet.One place thathas notbeentakenintoconsiderationisbuildingontopof the water.This will allowcitiestoexpandwithoutusingupvaluable land.Onthe opposite endof the spectrumare cities and countriesplaguedbynatural disastersthatneedhelprebuilding.Havingaportable reactorsystem will significantlyhelpshortenthe amountof time forthe rebuildingprocess.Thisisimportantbecauseit isofferingcleanenergyaroundthe world.Itisadvancingthe nuclearindustrybyhavingnuclearreactor plantsable tomove on oceans,ratherthan beingconfinedtothe same areaof landtheywere builton. The reactor systemswill be builtonsite inthe USA to ensure qualitycontrol,andthenexportedto coastal countriesthatneedthem.Thisis creatinga new global view onnuclearenergyandpushingthe industry’sprogressforward. The portable reactorsystemwill provide power andcleanwatertogrowingcitiesorplacesthat are underdevelopedorinneedof rebuildingafternatural disasters. The reactorsystemisdesignedto produce maximumpowerinthe mostefficientwayatthe lowestpossible cost.The goal isto provide enoughenergyata reasonable investmentcost.The systemwill make itsmoneybackaftera period aroundtwenty-one yearsassuming$0.1 perkWh.Ideally,all internationallawsare beingaddressedand takenintoconsiderationwhensellingandtransportingthe portable reactorsystem.The idealgoal isto have one kilowatt-hourcosttencentsto produce afterstartupand initial investmentcostsare taken intoconsideration.
These benefitswillcontributetothe purpose of the designbybringingacompact reactorto people in developingcountries,areassufferingfromnatural disasters,andgrowingnationsorcities.The system accomplishesthisbybuildingareactoroff the shore,thenrunningpowerlinestothe mainland.The systemisdriventothe location,andthenanchored inlike anoilrig.Itwill remaininthatlocationforthe life cycle of the plantthenwill be movedafteritslife cycle isover.Afteritisdriven off site,itcanthen be storedin a containment zone where radiationlevelsmay decrease until theyreachbackground. In the nuclearindustrytoday,the currentstate-of-the-artare GenIV nuclearreactors[2]. The Gen IV reactorsinclude the VeryHighTemperature Reactor(VHTR),Gas-cooledFastReactor(GFR), Supercritical-Water-cooledReactor(SCWR),Sodium-cooledFastReactor(SFR),Lead-cooledFastReactor (LFR),and the MoltenSaltReactor (MSR).These reactorsall focuson simplifyingthe design,improving passive safetysystems,andgeneratinghighertemperaturestoreacha higherefficiency.Outof the six, the one most similartothe designinthisreportisthe LFR. The LFR isdesignedtohave passive decay heatremoval andto have a closedfuel cycle.Italsohasnatural convectiontocool the core alongwith beingproliferationresistantandhasa safe economical design.The Narwhals’leadcooledfastreactor has similarfeatures,butalsoincorporatesotherbenefitsthe currentGenIV LFR doesnot,such as a desalinationplant. The main difference separatingthe twoisthe Narwhals’reactorwill be apool reactor.Most LFRs being designed are muchlike aPWR,where there isno large pool of coolant.Thislarge pool helpswiththe heattransferinthe primarypool andallowsthe reactorto dumpheat whenshuttingdown.The Narwhals’reactoremployspassive safetysystemssuchashavingavacuum outside of the primarypool wall to helpcontainthe heatinside the reactorpool andhavingthe core relyon natural convectionfor
cooling.Bothhelpwithkeepingthe heatinsidethe reactorpool andutilizingitinpowerconversion withoutthe need forpumpsonthe primaryside upto 200 MWt. On the secondaryside of the system withinthe powerloop,there isadesalinationplanttouse the excessheatfromthe systemtoproduce cleanwater.Thisis beneficial because itproducescleanwaterwhile increasingthe difference in temperature onthe secondaryside,improvingsystemefficiency.The secondaryside willbe composed of supercritical CO2.Thiswillallow the secondaryside tohave agreaterchange in temperature while maintainingaverysmall size relative toaRankine cycle.The overall size of the designisfairlysmall, operatingaround5 m3 [3].
IV. Conceptual Design and Description The portable reactorsystemhas twoloops,the primaryloopbeingthe pool of liquidlead-bismuth. Withinthe primarypool,the reactorcore containscontrol rodsand fuel rodsconsistingof 19.75 percent enrichedalphauraniummetal [4].Aroundthe core, there will be fourheatexchangerstoextractheat energyandtransferitto the secondaryloop.These heatexchangeswill be made of 316 stainlesssteel. The heat exchangerswillbe inacircular array aroundthe edge of the pool wall tohelpwithnatural convectionflowthatwill be circulatingthroughoutthe entirepool.Pipeswill helpgetthe hotLBE from the core to the heatexchangersformaximumheattransfer.Outsidethe pool wall,avacuumedout space helpstominimize heattransferandtoserve asa passive safetysystembybeingable tofloodwith waterto decrease shutdowntime. Above the primarypool,thermoelectricgeneratorsrelyonthe excessheatcomingoff the reactorpool. Thiswouldboostthe overall systemefficiencyanduse the energyproducedtoheatthe primarypool wall.Thiswill helpthe coolantmeltif the reactorwere toshutdown[5].The electricityfromthe thermoelectricgeneratorsmay be usedtosupplyenergytothe shipaswell.
The secondaryloopconsistsof a supercritical carbondioxideBraytoncycle thatwill take heatenergyout of the primarycoolantpool byforced convection [6].Whenthe CO2 leaves the heatexchanger,itwill be Figure IV: Primary Pool Reactor Pool Color Coding Control Rods Reactor Core Core Support FlowGuide Heat Exchanger InertGas – (Above the liquidlead) Reactor Pool Wall ShieldingMaterials
a supercritical fluidandfedintothe turbine [3]. The CO2 will thenrotate the turbine togenerate electricity, andthenthe CO2 will leave the turbinetobe passedthrougha desalinationplantwherethe waste heatenergywill be dumped[7].The desalinationplanttakesthe excess heatenergyfromthe CO2 and usesitto boil saltwaterto freshwater.The CO2 iscompressedthenpumpedback tothe mainheat exchangersinthe primarypool where the cycle will beginagain[8].There are four heatexchangers and twocompressorsinthe powerproducingside of the system.Theyare neededtobettertransferheat and to make the systemmore efficient.The excessheatfromthe desalinationplantwillbe transferred to the ocean. The temperature of the reactorpool will be operatingbetween150Β°C and 650Β° C. Thiswill cause creep, fatigue,andswellingof mostmetalsif placedinthese temperatures.Pressure exertedfromthe coolant on the interiorpool wall fromthe weightof the coolantisthe onlypressure concern.Since thisisafast neutronreactor,highradiationdamage inside the reactorcore andpool isexpected[9].HT9 has been chosenforthe material inthe core,as itis resistanttoradiationdamage [10].The lead-bismuthcoolant will alsobecome highlyradioactive,asitisnaturallyflowingthroughthe core.The radiationproducedby the reactor will contribute toadose rate outside of the pool.The coolantandpool wall will needto shieldradiationenoughtoallow workerstobe inthe containmentvessel all yearandnotexceedadose of five rem.Lead-bismuthwill domostof the shieldingasithas a highdensity[11].Corrosionthatwill occur is mostlydue tofluidflowof the lead-bismuthcoolant.All the materialshave factorsof safetyof 2.5 or 3.5 to insure minimumfatigue,creep,andelongation. The fuel will be alphauraniummetal cylindersenrichedto19.75 percent,andthe flux profilewas generatedinMCNP[13]. Alphauraniumwaschosen due toits thermal conductivityproperties,easy machinability,andmaintainsphase structure [13].There isconcernwith flatteningthe fluxprofile,so
burnable poisonsare used.Itisunknownhow the poisonswill reactina lead-bismutheutectic[14]. Reactivitycoefficients wereaddressedbecausesafetywas the mainconcern andtheyaffectcriticality. The reactor was designedtokeepall of these coefficientsnegative.Online refueling wascomparedto the CANDU reactor,but the reactor systembeingdesignedhasthe control rodsrunningverticallyinthe core [4].Multiple ideas were consideredonhow to supportthe possible refueling,butendedupbeing not feasible[15].The core geometry isa hexagonal lattice putinahexagonal array[16]. Radiationsafety andshieldingisahuge concernina nuclearreactorsystem[17].Since thissystemis beingtransportedacrossthe ocean,manydifferentthreats weretakenintoconsideration.Firstisthe securityof the mobile LFRawayat seaand wheninport. Havingan escort to accompanythe system alongwithplacingarmedguardsat entrances isbeingimplemented[18].Natural disasters,sinking, and terrorismare lookedatas worst case scenariosandare currentlyindiscussiononhow tobe dealtwith inthe reactorsystem[19] [20] [21]. Meltdown,lossof coolant,total powerfailure,control rodfailure, vacuumfailure,andleaksinthe reactorpool are designconcerns.Since the reactorsystemis liquid metal cooled, eachaccidentscenarioishandled isspecifictothissystem[22].Materialsand componentsinthe reactorare shielded tomaintainminimumdose requirements [14].Placementof detectorsishard to decide onbecause the reactorsystemneedstobe monitored atall times,butwhen isenoughdetectorsenough;thisisforemployeesandinside the reactorpool.Detectorsinthe pool are ina circulararray betweenthe heatexchangersandthe reactorcore. The reactor system isdesignedto keepexposure low,even duringextreme situations;ALARA will alwaysbe practiced. The goal forthis reactorsystemis to make it as efficientaspossible,whichpertainsprimarilytohowthe overall reactorsystemisdesigned,andhow heatandenergyistransferredinit.The heatfrom the reactor istransferredtothe liquidlead-bismutheutectic,thentoheatexchangers.The layoutof the
heatexchangersisa circulararray around the pool.The numberof heatexchangersneededonthe secondaryside isfour,witheachof them transferring380 MWt of heat energyaway.Thisandthe natural convectioncalculationsdeterminedhow strongandfastthe natural convective andforcedflow will be movingthroughthe reactorcore [23] [24] [25]. The speedat whichthe secondarygasispumped throughwill alsoplaya role inthe rate at whichheatleavesthe system.The speedatwhichthe fluid flowsalsoaffectsthe amountof force createdbythe momentumof the fluidandthe numberof oscillationsitwill create.Partof the secondloop’s energywill be transferredtoadesalinationplantto boil saltwater[26]. The amount of energyrequiredfordesalination wasdeterminedandassessedfor the quantitywantedforpurification.Afterthe twoloops,the amountof leftoverheatenergy was determinedand maybe transferredintothe oceanwithoutcausingharmto the environment[8]. Economicsplaya huge role inany product,especiallyinthe nuclearindustrybecause the investment requiredfora reactorpowerfacilityisinthe billions.Costforupkeepandmaintenance wasdetermined alongwithcorrosioncostsversusmaterial costs, cleaningof the ship,andthe upkeepof the crew.The wage of the workers,costof the shipitself [27],andall otherexpensesare includedinthe costs to determine the returnoninvestment.Where tosell thissystemisabigfactoras energydemandsof largercitiesare greaterthan energydemandsof thirdworldcountries;biggercitiesleadtogreater profits[28]. Social and regulatoryissuesdealwiththe publicimage andtie inwithradiationshieldingandprotection. If the reactorsystemand ship were toroll overand flip,the effectsinside the reactorpool are unknown but are assumed that the reactor core wouldbe exposeddue tothe lead-bismuthcoolantspillingover the sidesof the reactor pool.If the coolantcontaminatesthe seawater,thisisaconcernfor the environmentbecause of the radioactivityof the coolant,and leadmaybe absorbedintoliving
organisms.Itisunsure howto extractthe coolantfromsaltwater if it doesnot solidifyinlarge clumps. The radioactivityof waterdue to the coolantalsohas to be below the DACinwaterset bythe International Committee of Radiological Protection[29].Safeguardandnon-proliferationconcerns are addressedaswell tokeepthe general publicsafe.Whowill staff the mobile LFRisa bigconcernas their backgroundand intentisnotas well known asradiationsafetyworkersinthe UnitedStates.
1 Licensability 1.1 Reactor Design Considerations The most importantpart of a nuclearpowerplantisthe reactorcore, andseveral considerations must be made for thisdesign.Thisinvolvessignificantuse of MCNPcalculationsforcriticalitypurposes. Section3.1 focusesonthose calculationsindetail. Thiscore isbeingdesignedforamaximumthermal powerof 1000 megawatts(MWt).The core of this reactor ismade up of 90 fuel assembliesarrangedinahexagonal lattice.Eachassemblyhas217 fuel pins arrangedin theirownhexagonal lattice,andare 5.5 cm on eachside.The fuel pinsare 0.2 cm inradius, and are made of metallicuranium.The claddingismade of HT9 and is0.05 cm thick,withaninnerradius of 0.24 cm and an outerradiusof 0.29 cm. The fuel pinitself is1.5m tall,while the claddingis3m tall. Surroundingthe fuel pinwithinthe claddingisleadbismuthcoolant,andacompressibleheliumplenum. The core has 31 control rods made of 1 cm thick gadoliniumwithaB10 carbide interiortoensure effectiveabsorption atfastneutronenergiesaswell asforlower neutron energies.Eachof these control rods hasa total radiusof 3.5 cm. The core isapproximately1.4m in diameter,allowingforcompact designthatcan be easilytransportedacrossthe world. For the fuel,the metallicuraniumhasanenrichmentof 19.75% byweightof U235 .This enrichmentwas choseninorderto maximize the amountof fissile material inthe core withoutmakingthe core largeror goingto high-enricheduranium.Alloyingthe fuel with anothermaterialwasconsidered; zirconiumat 10% byweightbeingthe mostlikelycandidate due tohavingdesirablematerialpropertiessuchasa highermeltingtemperature.Thiswasrejectedinordertokeepthe amountof fissilematerialthe same withoutincreasingenrichmentorexpandingthe core.InMCNP,addingthe zirconiumdecreasedthe
amountof fissilematerial inthe core tothe pointsuchthat in orderto maintainthe desiredfuel cycle length,eitherthe uraniumwouldhave tobe highlyenriched,orthe core wouldhave tobe expanded. Both optionswere undesirable because of proliferationconcerns,andthe core size neededtobe as small as possible fortransportation. At the givenenrichment,the maximumKeff the core can achieve is1.16074 inMCNP. That value then allowsforan excessreactivityvalue of 13.84% Ξ”k/k.Thisvalue as well asthe enrichmentmustbe consideredforlicensingtodetermine the safetyof the reactorand whatregulationswill apply.By findingthe Keff usingonly promptneutrons,the Ξ²eff was calculated,whichhasa value of 0.44% Ξ”k/k.The burnupwas calculated inMNCPforthis enrichment,whichalsogivesthe fuellifetime.The core may last about1.5 yearsbefore becomingsubcritical.Thisisthe time spaninwhichroughlyhalf orthe fissile material inthe core is usedup.In the future,thismaybe improved upon. The control rodshave beenplacedintofive groupsbasedondistance fromthe core.Group1 consistsof the centercontrol rod, witha reactivityworthof 2.34% Ξ”k/k. Thisisthe highestrodworthinthe core. The nextsix rodsare two lattice spacesawayandare group 2. These eachhave a reactivityworthof 2.11% Ξ”k/k.Group 3 has six rodsas well,andare locatedoutside of group2, offsetby60 degrees.Each rod has a reactivityworthof 1.68% Ξ”k/k. The rods ingroup 4 are roughlythe same distance fromthe core as group3, butare offsetby60 degreesfromgroup3, placingthemslightlyfurtherfromthe center.Each of these rodshasa reactivityworthof 1.47% Ξ”k/k.The group5 rods are the furthestout, and consistof 12 rods placedinpairs. Each of these rodshas a reactivityworthof 1.03% Ξ”k/k. By adding all of these rodworthvaluestogetherfromeveryrodinthe core,the total rod worth is foundto be 46.4% Ξ”k/k.By subtractingthe excessreactivityandthe reactivityworthof the centerrod,the shutdownmarginwas foundtobe 30.2% Ξ”k/k.
One concernin relationtothe control rods isthat the reactivityworthmaybe too highinorder to make finerpoweradjustments.Eventhe slightestmovementsof the rodsmaycause the core to have too small of a period,whichhasbeenchosentonot exceed80secondsforstandard powerincreases.An alternative design forcontrol rods consistsof solidgadolinium of the same dimensions.However,the reactivityeffectsonthe core withthese rodsstill requiresstudyatthistime. 1.2 Radiation Safety Nuclearreactorsmust properlyshieldradiationfromthe peoplewhoworkatthe powerplant.Licensing a nuclearreactor requiresthatworkersandthe environmentwillnotreceive aharmful dose.The NRC published10CFR 20 to regulate anylicensee sothat radiationdoesnotexceedthe standardsforsafety [1].The publicmayonlyreceive adose of 0.1 remper year from radiationemittedfroma powerplant. Furthermore,the dose islimitedto0.002 remin anyone hour. For a plantworker,the total effective dose isallowedtobe five remperyear.The reactor must properly shieldradiation suchthatthese conditionsare metwhile beingable tomonitorthe reactoronsite [1]. The reactor systemmustalsomeetcriteriaforradiationexposure tothe environment.Forthisseafaring design,the surroundingenvironmentisthe ocean.There are at thistime nolimitstothe amount of radiationthatcan be transfered intothe ocean.However,itisunlikely thatpublicopinionwill supporta reactor designthatpollutesthe oceanwithradiation.Fromalicensingviewpoint,there isnolimitation. The limitof radiationreleasedintothe environmentwillbe determinedbythe distance fromshore and local regulationsregardingradiationsafety.
1.3 Accident Scenarios and SafetyAnalysis A nuclearreactor’sresponse toaccidentscenarioswillbe consideredwhenapplyingforanoperating license.The worstcase scenariosforanyreactor wouldinclude afuel meltdownandalossof coolant.In a liquidcooledreactor,there are twoprimarythermal considerationsforthe core.The liquidcoolant mustnot boil andthe fuel centerlinetemperature shouldnotreachthe fuel meltingtemperature.To preventanaccidentfromoccurring,the harshestconditionsmustbe met.Inthe core, the hottestfuel elementmustnotfail.If the fuel elementexposedthe harshestconditionsisnotexpectedtofail,it reasonsthat nootherfuel elementshouldfail. The fuel centerlinetemperature isthe hottesttemperature inthe reactor.The fuel centerline isthe first place where the fuel willmelt.Toensure thatthe fuel centerlinetemperature doesnotreachthe fuel meltingtemperature,ahot-channelanalysiswas performed.Inthe hot-channel analysis,the hottest fuel elementwasdeterminedfromthe flux profile.The flux ishigherwhere the mostfissionevents occur. More fissioneventscause more heattobe produced,whichinturn generatesahigher temperature.The volumetricheatgenerationandcenterline temperature are the assumedconditions for the hot-channel analysis. For safetyandproperfunction,aliquidcooledreactor’scoolantcannotchange phase.If the coolant shouldchange fromliquidphase tothe gaseousphase,there wouldbe adramaticreductioninheat transferfromthe fuel.The gaseousphase of LBE doesnot conductheatas well asthe liquidphase.A gaseouscoolantwouldcause agreaterincrease infuel temperature andcouldresultinameltdown scenario.Therefore,ahot-channel analysisisperformedfor the coolanttoverifythatthe coolant will not boil.If the coolantinthe hottestchannel doesnotboil, thenthe coolantinall the otherchannels will be belowboilingaswell.
Evenwiththe precautionsdescribedabove,itisnecessarytounderstandthe reactor’sresponse toan accidentscenario.Inthe eventof a complete meltdown,the fuel will mix withthe coolant.Mixingthe fuel andcoolantwill decrease the criticalityof the reactor.Ina complete meltdown,the reactorshould become subcritical.The dispersionof fuel will greatlydecrease the numberof neutronscreatingnew fissionevents.Atthispointinthe project,the analysisof accidentscenarioshasbeentheoretical.The previousdescriptionsare whatisexpectedtooccur inan accidentscenario. 1.4 StructuralIntegrity The supportstructure for the core mustwithstandthe stressplacedonitfrom the core. Metals tendto become weakerwhenheated.The elevatedtemperature thatthe reactorproduces inthe reactor pool will affectthe supportstructure design.The maximumservice temperatureof SS316 is 750Β° C [2].Since the highesttemperature we expecttosee in the core is650Β° C, thisshouldnotbe an issue.Usinga yield strengthof 170 MPa and a safetyfactor of 3, tensupportcolumnsof radius10 cm will supportthe core. The baseplate will alsoneedtobe analyzed similarlytoestablishitsstructural integrityatelevated temperatures. However,because itisconstructedfrom516 Gr 70 stainlesssteel,the standardfor reactorsof thistype,itis assumedthatthe material will meet the structural requirements [3]. 1.5 Emergency Planning Accidentresponse andemergencyplanning isakeyaspectof maintainingalicense tooperate forthe mobile LFR.A fewlogisticconsiderationswere made toensure the designiseffective andmaintains a highlevel of securityandsafety.Some of these considerations were made toaccommodate severe
weather,releaseof radioactive material,andfacilitydefensive measures.Instancesof severe weather will be dealtwithinafewwaysdependingonthe event. A ten-mileevacuationzone hasbeendeemednecessaryduringanysevere weatherevent,whichisfive timesgreaterthanwhat the NRCregulatesforemergency evacuationzones [4].Thisistoensure the safetyof anyone inthe vicinityfromapossible release of radiation.Hurricanesandmajorstormswill warrant a plantshutdowntoensure the safetyof the surroundingareas.Thisshutdownwill be basedon a report froma local weatheragencythatthe mobile LFRsystemresides in.The shutdown will begin well before the stormapproaches.Lightningwill be verycommonduringthesetypesof stormsandthe vessel willbe equippedwithsurge arrestersandalightningrod/groundingsystemtopreventdamage to electroniccomponents. Inthe eventof atsunami,the plantcan be simplymovedinhopesof avoiding the wave.The needtoactuallymove the mobile LFRsystemdue toa tsunami isdrasticallyreducedthe fartherthe systemisplacedawayfrom shore.The mobile LFRsystemalsohas beendesignedtoprevent the release of anyradioactive materialsintothe environment.Radiationmonitoringsystemswill be in place inboth the primaryand secondaryloopstoensure noabnormal radiationlevelsarise inthe plant systems. If aneventoccurs inthe plant,guidelinesinplace will aimtoacquire AsLow As Reasonably Achievable(ALARA) doses.Thiswouldincuronlynecessary exposure forreactoroperators.If severe enough,atotal plantshutdown will be initiateduntilapropercleanupcan be arranged. Two otherscenariosthatare accommodatedinthe mobile LFRdesignare the lossof heatexchangers and lossof coolantaccident(LOCA).Asinmanyof the designfeaturesof thisnuclearreactorsystem, a highfactor of safetyhas beenbuilt intoall components.The extractionof heatfromthe reactorpool is no differentandcanbe accomplishedby three heatexchangers.If noheatsinksare available to dissipate heatinthe primaryloop,the pool itself shouldbe able toalleviatethe heat.If secondaryside
heattransferfluidislost,the primarycoolantwill be able toabsorbthe excessdecayheatfora marginal time periodduringandafterthe shutdownperioduntil the properrepairscanbe made.Withthe coolantbeinga liquidmetal,itwill solidifyatnormal atmosphericconditions if itleaks.Defensive measuresare neededtoprotectthe mobile LFR,andwill be similartowhatcurrent nuclearpower plantsdo alongwithaddedmeasuresdue tobeingonthe ocean.Exclusionzones cannotbe enforced witha fence,sopatrol boats are usedinstead.Securitystaff will be presentonthe vessel toprotectit fromexternal threats. 2 Economic Analysis 2.1 Capital Cost 2.1.1 Fuel Cost To determine the capital costof the fuel fabricationforthe project, manyfactorsmustbe considered otherthan the price of the raw U3O8,such as the cost of conversiontoUF6,the furtherenrichmentto 19.75% U235 , and the price of fabricating intothe final shape.Raw U3O8 can be purchasedfor $97 per kg, and thenbe convertedtoUF6 for $16 per kg [5].Calculationsusingthe price perSWU andcurrent costs for UF6 have beenusedtofindthe cheapesttailstoenrichthe uraniumto19.75%. This wasdone calculatingthe massof feedperkg of product neededfordifferentvaluesof Xt usingEquation 2.1.1.1. M𝑓 = ( X 𝑝 βˆ’ X 𝑑 X 𝑓 βˆ’ X 𝑑 ) 2.1.1.1 The SWU was thencalculatedwithEquation 2.1.1.2[6]. SWU = M 𝑝(VX 𝑝 βˆ’ VX 𝑑 ) βˆ’ M𝑓VX 𝑓 2.1.1.2 It isfoundthat the cheapesttailsis 0.185%, and the cheapestprice of fuel before fabricationis approximately$6758. The total price is foundbyaddingthe cost of the raw uranium, the costof conversion,the price of enrichment,andthe costof fuel fabrication,whichisfoundtobe approxi mately
$7058/kg of 19.75% enrichedU235 .These calculationswere preformedtogive anestimationwhen purchasing19.75% enriched U235 .The total amountof fuel neededtorunthe reactor is 7031 kg. With the fuel costing$7058/kg, an entire fuel cycle’s worthof fuel wouldcost $4,962,715. 2.1.2 Raw Materials Many materialswill significantlyaddtothe cost of the reactor system.The price of these materialswill directlyaffectthe capital costof the reactor. Equation2.1.2.1 showsthe methodusedto obtainthe total cost. πΆπ‘œπ‘ π‘‘ = ( π‘ƒπ‘Ÿπ‘–π‘π‘’ π‘π‘’π‘Ÿ π‘˜π‘–π‘™π‘œπ‘”π‘Ÿπ‘Žπ‘š) βˆ— (πΈπ‘ π‘‘π‘–π‘šπ‘Žπ‘‘π‘’π‘‘ π‘€π‘Žπ‘ π‘  𝑛𝑒𝑒𝑑𝑒𝑑) 2.1.2.1 HT9 is$5.00 per kg and2716 kg are required;thismaterial costs$13,580 [5]. The price for 316L SSis $2.47 perkg, of whichwe will need30 millionkgforatotal cost of $74,100,000 [5].Productionof the steel increasesthe price byroughly53%. LBE costs $10.81 per kgand 14.8 millionkgisrequiredtofill the pool [7] [8].This meansthatthe LBE usedcosts $160 million.The baseplate,made of SS516 G70 costs $0.80 per kg, and with1000 kg needed, the total forthismaterial comesto $800 [5]. Manufacturingof thismaterial increasesthe price to $0.85 per kg, makingthe total $850. Gadoliniumis the control rod material andcosts $55 per kg [33]. 6920 kg of it are neededandthe total cost is $381,000 for Gadolinium.Productionof eachrodisestimatedtobe $1350. Approximately$234.5 millionforrawmaterialsisneededtofabricate the components tobuildthe reactor. 2.1.3 Major Components The cost of the turbines,generators,andothermajorcomponentsare alarge part of the overall project cost.
Table 2.1.3.1: MW Output and Cost Shaft Output Average MW Cost 300.00 $214,688,425.30 400.00 $280,721,772.70 500.00 $345,966,649.02 600.00 $410,616,682.52 700.00 $474,793,116.05 Global Energyand InfinityTurbineLLCprovidedthe informationonthe price of theirsupercritical CO2 turbines. Theirapplicationswereforlow powerbetween50kilowattsand2 megawatts. Extrapolating theirnumbers,alongwiththe expectedefficiencyof secondaryside, the estimateforaturbine is between$2.8millionto$4.1 million. 2.1.4 Ship Analysis Whenselectingthe ship,earlycalculationsfoundthatitwouldneed toholdatleast14,000 tonnes. Addingthe additional weightof the staff,fuel,waterballasts,heat exchangers,turbines, electromagneticpumps,andpiping,the weightthe shipis requiredto supportisapproximately29,000 tonnes.Withthis weightrequirement,the Ultramax bulkcarrieristhe bestshiptodesignwith. The ship is200 m long,32 m wide, hasa 13 m draft,and the deadweighttonnage (DWT) of the shipis63,000 tonnes[37]. This allowsforanavailable capacityof approximately34,000 tonnes. Shipsinthisclassbuilt around2012 cost $30 to $35 millionnew [38].Currentpricesfora new vessel were notgivenfromthe manufacturer. Accountingforinflation,these shipstodaycouldcost $32 to $37 million. The variationin price isin partlydue to loadcapacity as well as gearequippedonthe ship.β€œGeared”shipsare vessels, whichhave cranesabove eachcargo hatch to loadand unloadsupplies.Thisisanoptional feature thatis alreadyfiguredintosome of the pricesforthese ships.If all of the cranesequippedare not deemed
necessary,theycanbe removedfromthe buildsheetreducingthe overall costof the ship. Figures 2.1.4.1 and 2.1.4.2 showsome genericdiagramsof an Ultramax dry bulkcarrier. Figure 2.1.4.1: Handymax Hull Layout [9] Figure 2.1.4.2: Handymax Hull Top View [9] In Figure 2.1.4.2, fourindividual cargobinscanbe seen.Typical shipshave fourtofive separate cargo bins,a double reinforcedfloor,anda crane above each hatch.The cargo hatchesare all automatedand are operatedbyexternallymountedhydrauliccylinders.A diagramof thissystemisshowninFigure 2.1.4.3 [37].
Figure 2.1.4.3: Cargo Hatch Diagram [9] Withthe planto modifyapre-builtship,there will needtobe manymodifications.Thisincludes structuresto holdadded components,piping toconnectmajorcomponents,addedshieldingtoprotect workers,andany otherneededsystems. Estimatingthe costof modifyingthe shipisverydifficult withouthavinganexactplan,and couldvaryfrom a few milliondollarstomore thanthe original costof the ship. 2.2 Reoccurring Cost Refuelingthe reactorisone of the majorrecurringcosts inthe mobile LFR.Accordingtothe burnup calculationsdone inMCNP,the reactorfuel hasa lifetime of only18months.Thismeansthat every18 months,the reactorhas to be shutdownand the fuel mustbe replaced.Whenthe reactorrefuels,7031
kg of fuel mustbe purchasedeachtime at $7058/kg, costing$4,962,715 infuel alone. Othermaterials associatedwithanoutage are the cladding,fuel,andgapmaterial.Total costsassociatedhere are $1,297,692.65 at currentmaterial prices,notincludingthe costtomanufacture the core to specified dimensions.Thisisthe costto replace the entire core asa solidpiece.Inaddition,the supporting structure of the core will have tobe re-examinedwitheachcycle.Thiswill added50% to the total refuelingcostandshouldonlyoccur once everyfifteenyears. In the reactor pool,316 stainlesssteel mustbe removedbecause of the severecorrosionitexperiences while incontactwithLBE. By replacingthismaterial withT-91martensiticsteel,we willexperience a longerlifetime. Equation 2.2.1 describeshow the oxide scale thicknessonthe T-91 pipingwill develop overtime as a functionof temperature. 𝛿( 𝑑, 𝑇) = (βˆ’0.98 + (2.54 Γ— 10βˆ’3) βˆ— 𝑇) βˆ— √ 𝑑 2.2.1 𝛿( 𝑑, 𝑇) = π‘œπ‘₯𝑖𝑑𝑒 π‘ π‘π‘Žπ‘™π‘’ π‘‘β„Žπ‘–π‘π‘˜π‘›π‘’π‘ π‘  (πœ‡π‘š) 𝑑 = π‘‘π‘–π‘šπ‘’(β„Žπ‘œπ‘’π‘Ÿπ‘ ) 𝑇 = π‘‘π‘’π‘šπ‘π‘’π‘Ÿπ‘Žπ‘‘π‘’π‘Ÿπ‘’ (℃) [10] Equation2.2.1 isonly ratedfor temperaturesranging from420Β° C to 550Β° C and flow rateslowerthan 2m/s, butgive a goodapproximationof whattoexpect.Overthe course of 3 years,the pipingwill experience ascale growthgreaterthan68 Β΅m. After6 years,thisscale isgreaterthan96 Β΅m and after9 years,the scale will reacha thicknessgreaterthan118 Β΅m. By 15 years,the scale build-uponthe piping will reacha thicknessof 197 Β΅m. It isat thispointthat the heatexchangerswill have tobe removedand replacedtoprovide adequate heattransferfromthe reactorcore.
The recurringcost relatingtothe coolantwill be frommaintainingoxygenlevels,flowingacovergas above the reactor pool,andfilteringpoloniumproducedinthe coolant. Thiswillkeepthe oxidationof the coolantto a minimum allowingforitscontinual use. Duringeach outage,the HT9 claddingwill needtobe replaced.There are 90 fuel assembliesinthe core and eachassemblyhas217 fuel pins.Itwas calculatedthateachfuel pincontains0.195 kg of HT9, which meansduringeachoutage there will be 3812.74 kg of HT9 replaced.At$5 perkg, the total cost of HT9 peroutage comesto $19,063.69 [33]. Basedon a presentationfrom OpCost,the costtomaintainthe mobile LFRwouldbe approximately $6,472 per day. There are several waystodeal withthiscost,the easiestbeingtodepositanestimate maintenance amountinafundwithsome interestrate andmake appropriate withdrawalsonasemi- annual basis. The outage cost can increase if there are anyproblemsthatwoulddelaythe process because eachday the reactor isnot makingelectricity,the mobile LFRislosingprofits. 2.3 Personnel and Operations Cost Personnel costscanmake up a significantportionof the recurringcost tokeepa reactor running. Because of the safetyconcernsnuclearreactorscreate,itis importanttokeepthe reactor facilitystaffed at all times.All essential staff wouldwork10 hoursa day on a 5-3, 5-4, 5-3 work schedule [11].This methodof 24/7 staffingrequires5staffedteams, eachof which workfive dayson,thenthree off,then five dayson,thenfouroff,thenfive dayson, thenthree daysoff.The cycle then repeats.Each team averagesa 42 hourwork week.
Figure 2.1.41: Staffing and Employment Time Scheduling Essential staff includespeoplesuchassecuritypersonnel,reactoroperators,andseniorreactor operators.Fromthe NRC’sregulationslinedoutin10 CFR50.54, itwas determinedthatthe minimum numberof operatorsnecessaryatall timesfora single operatingreactoristwoseniorreactoroperators and tworeactor operators. [12] Since there isa minimumof 5 teamsof 2 reactor operatorsand2 senior reactor operators,atleast10 reactor operatorsandseniorreactoroperatorswouldhave tobe hired. The average salaryfor a reactor operatoris$65,080, and fora seniorreactoroperatoris$76,020 [11]. Because the employeesare workingshiftwork, abonuspay incentiveof 30% will be added. Payingout benefitsandtaxesnormallycostsacompany1.4 timesthe employee’ssalarytoemploythem.This makesthe cost to hire the bare minimumnumberof operatorsdenotedbythe NRC$2,398,700/year. πΆπ‘œπ‘ π‘‘ = 1.4(10(65080 + 76020)) + .3(10(65080 + 76020)) 2.3.1 Ideally,the numberof securitypersonnel onstaff wouldnominallybe tenatall times. Securityisan importantconcernforthe project because the design istobe implementedinforeignareas.If ten securityguardsworkper team,thena minimumof 50 on site guardswouldneedtobe hired to workthe same 5-3, 5-4, 5-3 work shifts.If each nuclearsecurityofficermakesasalaryof $52,237, thenit would cost approximately$4,231,197/year.
2.4 Revenue The revenue andbreak-evenpointscanbe determinedbytakingthe total costof the projectoverthe projectedtime.Thiscaneasilybe visualizedby equation2.4.1. π΅π‘Ÿπ‘’π‘Žπ‘˜ 𝐸𝑣𝑒𝑛 πΆπ‘œπ‘ π‘‘ ( $ π‘˜π‘Šβ„Ž ) = π‘‡π‘œπ‘‘π‘Žπ‘™ πΆπ‘œπ‘ π‘‘ π‘œπ‘“ π‘ƒπ‘Ÿπ‘œπ‘—π‘’π‘π‘‘ π‘˜π‘Šβ„Ž π‘ƒπ‘Ÿπ‘œπ‘‘π‘’π‘π‘’π‘‘ 2.4.1 To findthe breakevenpointforprice to sell powerintime,equation2.4.2can be used. π΅π‘Ÿπ‘’π‘Žπ‘˜ 𝐸𝑣𝑒𝑛 π‘ƒπ‘œπ‘–π‘›π‘‘ ( π‘¦π‘’π‘Žπ‘Ÿπ‘ ) = π‘‡π‘œπ‘‘π‘Žπ‘™ πΆπ‘œπ‘ π‘‘ π‘œπ‘“ π‘ƒπ‘Ÿπ‘œπ‘—π‘’π‘π‘‘ βˆ— π‘˜π‘Šβ„Ž π‘π‘Ÿπ‘œπ‘‘π‘’π‘π‘’π‘‘ π‘π‘’π‘Ÿ π‘¦π‘’π‘Žπ‘Ÿ πΆπ‘œπ‘ π‘‘ π‘œπ‘“ π‘ƒπ‘œπ‘€π‘’π‘Ÿ 2.4.2 For the mobile LFR,the original break-evencostof powerproductionwascalculatedfor10 years. This was the project’soriginal goal forreturnoninterest.Forthe break-evencost,the total capital costof the projectwas totaledto$998 million,andthe recurringcostsaveragedat$31 million/year,or$310 millionover10years. Powerwouldhave tobe soldat $0.165 perkWh to breakevenin10 years.If poweriscontinuedtobe soldat $0.165 per kWh,the profitmarginafterbreakingevenisapproximately $99million/yearwhichcanbe seeninFigure 2.4.1.
Figure 2.4.1: ROI for $0.16 per kWh To calculate the time neededtobreakevensellingpoweratthe $0.10 per kWh,the time to breakeven and start makingprofitis21.1 years.Afterbreakingevenafter21.1 years,the projectwouldbe making approximately$59million/yearinprofit. Figure 2.4.2: ROI for $0.1 per kWh
3 Technical Feasibility 3.1 Criticality For thisdesign,determiningthe technicalfeasibilityfromacriticalitystandpointinvolvedextensiveuse of MCNPwithcollaborationfromthe STARmodel forthe correct temperature outputs.The methodfor designingthe core wasto start witha unitcell andworkoutwardto developthe whole core.A unitcell was developedbasedonthe choice of fuel materials,coolantandcladding,representingasingle fuel pin inFigure 3.1.1. Dark blue representsthe fuelpin,whichisUranium metal enrichedto19.75 percent U235 .The green representsHT9,whichisthe claddingmaterial.The lightblue isthe lead-bismutheutectic.Notice that there isleadbismutheutecticinside the cladding.Thisallowsbetterheattransferbetweenthe fueland the cladding. The claddingthicknessis0.05 cm.Fuel pinis1.5 m tall,while the space inside the cladding is3 m tall.This allowsfora 1.5 m compressible heliumplenum, which allowsforfuel expansiondue to fissionproductbuildupaswell ascatchingfissionproductsshouldtheyfindtheirwayoutof the fuel. These pinsare thengroupedintobundlescalledfuel assemblies.Inside the assemblies,the pinsare Figure 3.1.1: Single Fuel Pin
arrangedin a hexagonal lattice withapitchof 0.714 cm.Each assemblycontains217 fuel pins,withthe longestrowcontaining17 pinsform cornerto corner. Figure 3.1.2: Fuel Assembly These assembliesare thenarranged intotheirownhexagonallattice inthe core.However,some of the lattice locationswillinsteadhave control rodsinsteadof fuel assemblies.These control rodsare 3.5 cm inradius and made of gadoliniumcylinders1cm thick.The interiorof each cylinderisthenfilledwith boroncarbide powder.The boronwill be enrichedin B10 .These control rodsare placedingroupsbased on distance fromthe centerof the core, as describedinsection1.1.Inthe followingfigures,the boron carbide isin red,and the gadoliniumisinyellow:
Figure 3.1.3: Control Rod Figure 3.1.4: Whole Core In orderto calculate the reactivityworthof eachcontrol rod, the one twelfth symmetryof the core allowedfordeterminingthe rodworth(RW) for everyrodwhile onlyperformingthe MCNPcalculations one rod fromeach of the five groups.The keff of the core was foundwithoutanyrodsinserted:1.16074. Then,by findingthe keff of the core withonlythe rod to be testedinserted,the reactivity(ρ) of that control rod can be foundusingthe followingequation: π‘…π‘Š = 𝜌 π‘Ÿπ‘œπ‘‘ π‘œπ‘’π‘‘ βˆ’ 𝜌 π‘Ÿπ‘œπ‘‘ 𝑖𝑛 3.1.1 However,reactivityiscalculatedfromkeff fromthe followingequation: 𝜌 = π‘˜ 𝑒𝑓𝑓 βˆ’ 1 π‘˜ 𝑒𝑓𝑓 3.1.2 By substitutingequation3.1.2intoequation3.1.1 withthe appropriate keff for eachterm, the following equationemerges: π‘…π‘Š = π‘˜ π‘Ÿπ‘œπ‘‘ π‘œπ‘’π‘‘ βˆ’ 1 π‘˜ π‘Ÿπ‘œπ‘‘ π‘œπ‘’π‘‘ βˆ’ π‘˜ π‘Ÿπ‘œπ‘‘ 𝑖𝑛 βˆ’ 1 π‘˜ π‘Ÿπ‘œπ‘‘ 𝑖𝑛 3.1.3
Placingeachtermover the commondenominator(krod out)*(krod in) andthencombininglike termsresults inthe following: π‘…π‘Š = π‘˜ π‘Ÿπ‘œπ‘‘ π‘œπ‘’π‘‘ βˆ’ π‘˜ π‘Ÿπ‘œπ‘‘ 𝑖𝑛 π‘˜ π‘Ÿπ‘œπ‘‘ π‘œπ‘’π‘‘ βˆ— π‘˜ π‘Ÿπ‘œπ‘‘ 𝑖𝑛 3.1.4 Thisequationallowedforcalculatingthe rodworthforeveryrodin the core,givingthe followingtable: Table 3.1.1: Rod Worth of Each Control Rod by Group Rod Group Keff w/ 1 rod in Rod Worth (Ξ”k/k) group1 1.12999 0.023444208 group2 1.13294 0.0211399 group3 1.1385 0.016829329 group4 1.14118 0.014766574 group5 1.14693 0.010373416 no rods 1.16074 As shown,the group1 rod, consistingof the centerrodin the core,is the rod withthe highestrod worth.Multiplyingeachrod worthbythe numberof rodsin the respective groupresultsinfindingthe rod worthof eachrod in the core.The sumof these valuesgivesthe total rodworthinthe core.This allowsforcalculatingshutdownmargin(SDM) usingthe followingequation: 𝑆𝐷𝑀 = π‘…π‘Šπ‘‘π‘œπ‘‘π‘Žπ‘™ βˆ’ π‘…π‘Šmax𝑖𝑛 π‘π‘œπ‘Ÿπ‘’ βˆ’ πœŒπ‘’π‘₯𝑐𝑒𝑠𝑠 3.1.5 Excessreactivity(ρexcess) canbe foundby usingthe maximumkeff (1.16074) andequation3.1.2. That and equation3.1.5 resultinthe followingtable: Table 3.1.2: Total Rod Worth, Excess Reactivity, and Shutdown Margin Total RW (Ξ”k/k) Ξ‘excess (Ξ”k/k) SDM (Ξ”k/k) 0.464340025 0.138480624 0.302415193
Witha shutdownmarginof over30% Ξ”k/k, the reactorcan be shutdown easily.However,forcontrol, anotherimportantvalue isthe delayedneutronfractionΞ²eff.Thiscan be calculatedusingthe following equation: 𝛽𝑒𝑓𝑓 = 1 βˆ’ π‘˜ π‘π‘Ÿπ‘œπ‘šπ‘π‘‘ π‘˜ 𝑒𝑓𝑓 3.1.6 For thisequation,kprompt isthe keff calculatedusingonlypromptneutronsinMCNP.Thiscalculation resultsina value of Ξ²eff = 0.44% Ξ”k/k. 3.2 Radiation Transport 3.2.1 Reactor Pool Modeling Once it wasdecidedthatthisdesignwasgoingto be cooledbyLBE, it wasapparentthat a strong, stable pool wouldneedtobe createdthat couldnotonlywithstandthe relativelyhightemperatures,butalso the highradiationdoses of the reactor environment. Assuch,the reactorpool andliddesign incorporatesseveral importantparameters. The pool wall thickness wasfound toensure thatthe hydrostaticpressure fromthe moltenleaddidnotcause fracturingof the pool wall.ByusingEquation 3.2.1.1 and Equation3.2.1.2, the minimumthicknessatthe bottomof the pool (includingafactorof safety of 3.5) was found [13]. π‘ƒπ‘Ÿπ‘’π‘ π‘ π‘’π‘Ÿπ‘’ = πœŒπ‘”β„Ž 3.2.1.1 π‘‡β„Žπ‘–π‘π‘˜π‘›π‘’π‘ π‘  = π‘ƒπ‘Ÿπ‘’π‘ π‘ π‘’π‘Ÿπ‘’ βˆ— π‘Ÿπ‘Žπ‘‘π‘–π‘’π‘  β„Žπ‘œπ‘œπ‘ 𝑦𝑖𝑒𝑙𝑑 π‘ π‘‘π‘Ÿπ‘’π‘ π‘  3.2.1.2 Withan assumedpool radiusof 4.5 m and a depthof 8 m, the minimumthicknessof the pool wall was foundto be 8 cm.
Next,the pool andpool lidwere bothmodeledinAutodeskInventor.The pool lidwasmodeledfirstat9 m indiameter.Fourholes, 60.96 cm in diameter, were extrudedfromthe lidtoallow forpipingfrom twoheat exchangers,andtwo15.24 cm holeswere extrudedtoallow forthe off-gassystemforgasified Poloniumremoval.Initially,25holeswithdiametersof 7 cm were extrudedforthe control rods. However,thiswill needtobe updatedforthe new control rodconfigurationobtainedrecently.See Figure 3.3.1.1 forthe initial sketchof the pool lid. Figure 3.2.1.1: Initial Sketch of Pool Lid Afterfinishingthe original9m in diametersketch of the topof the pool lid,a889.71 cm indiameter circle wasinscribedonthe lowersurface.Thiscircle wasthenusedtoextrude a16 cm thickprotrusion on the bottomof the lidinorderto allow the lidto sit atop the pool wall.Figure 3.3.1.2 below showsa close-upof thisprotrusion,aswell asone of the extrudedoff-gassystemholes.
Figure 3.2.1.2: Extrusion of "Lip" of Lid with Off Gas System Hole Next,the pool wall wasextruded8m downwardusingthe profileof the protrudingedge of the lidas shownabove inFigure 3.2.2. The cylinderisshowninFigure 3.3.1.3.
Figure 3.2.1.3: Extrusion of the Pool Wall To finishthe model,the profile of half of the extrudedpool wasrevolvedaroundthe centerpointof the model.Thisresultedinthe hemisphere shapeof the bottomof the pool,whichensuresthat there is evenpressure alongthe bottom of the pool. Several stressand strainsimulationswere performedon the pool lidpriorto modelingthe restof the pool.Byselectingthe StainlessSteel material forthe lid, parametersforthe strengthand toughnessof the material were automaticallyloadedbyInventor.Two mainsimulationswerecompletedsuccessfully:asingle force of gravitydownwardonthe lid andthe force of gravityplusthe weightof a 200 poundpersonstandinginthe middle of the lid.These simulationsbothresultedinextremelysmall deformationsconsideringthe diameter-to-thicknessratio. Please note thatinFigure 3.2.1.4 and3.2.1.5 that the deformationof eachisnotto scale;the displacement’sscale alongthe lidisshowninthe left-handportionof the figure inmillimeters.
Figure 3.2.1.4: Displacement of the Lid by Gravity Figure 3.2.1.5: Displacement of the Lid by Gravity and 200 Lb Person Overall,thismodel will be usedfordisplayandstress analysisof the design.Asthe designevolves,this model will be updatedtoreflectthe mostrecentchangesof the system.
3.2.2 Polonium Off-gas system The lead bismutheutecticcoolantwill be exposedtoaneutronflux.Bi209 thatispresentinthe coolant will absorbneutronstoconvertintoPo210 .Thisconcernsthe safetyof reactorpersonnel because Po210 is an alphaemitter[14].PoloniumcanthenbondwithLead to formLead-Polonide.Mostof these moleculeswill stayinthe eutectic,butwiththe elevatedtemperaturesinthe reactor,some cangasify [15]. Equation3.2.2.1 showsthe methodusedtofindthe absorptionrate. π΄π‘π‘ π‘œπ‘Ÿπ‘π‘‘π‘–π‘œπ‘› π‘Ÿπ‘Žπ‘‘π‘’ ( π‘Žπ‘π‘ π‘œπ‘Ÿπ‘π‘‘π‘–π‘œπ‘›π‘  π‘π‘’π‘Ÿ π‘ π‘’π‘π‘œπ‘›π‘‘) = πœ™ βˆ— βˆ‘ π‘Ž βˆ— 𝑉 3.2.2.1 A thermal flux of πœ™ =1015 neutronspersquare centimeterpersecondwasassumed.The macroscopic absorptioncrosssectionforBismuthis βˆ‘ π‘Ž =0.0009319 cm-1 . The volume usedis55% of the coolant channels volume toaccountforthe coolantbeing55% bismuth.Afterfindingthe absorptionrate,the total numberof absorptionsina yearwere calculated.The worst-case scenarioiscomplete gasification of Polonium.Approximately10kg of poloniumisproduced peryearof operation. Thisgaswill collectin the heliumthatsitsontop of the reactor pool.The gas will contain2247 cubicfeet of helium. A pump will move thisgas inand outof the pool viatwo six-inchdiameterpipes,asseeninfigure 3.2.2.1.These pipescango to one of twopotential systems forPoloniumcapture.The firstsystemisarare earth filtrationsystemwhere the gaswill travel toastainlesssteelbox.Thisbox contains screens electroplatedwitharare earth metal.These screens hold10,000 strandselectroplatedwith Praseodymium.While thistypeof system ispredicted tohave a highefficiency,thisremoval systemhas not beenextensivelytested [15].Anefficiencyof 25% was assumedfor extraction, meaning40 kgof Praseodymiumwill be neededtoreactwithPoloniumperyearof operation. A 0.1 micronthicklayerwill plate the screenwires.If these screenshave anareaof five square meters,fivethousandof themwill have to be stackedto filterenoughpolonium.The raw cost of Praseodymiumtocoatthese screens wouldrunover$100,000 a year[16]. Thiscan be expectedtolargelyincrease aftermanufacturingcosts
are added.Due to thiscost andthe factthat a manufacturingsystemforthisdesign hasnotbeen establishedyet,asecondoptionwasalsocreated. Figure 3.2.2.1: Pool Off-gas System The secondoptionwouldbe torun the pipesfromthe pool to a tank or seriesof tankswhere the helium gas, saturatedwithpolonium,wouldsit.The containerswouldsitforfive years,overtenhalf livesof Po210 ,toallowforfull decay.Thiswouldrequire the gastobe replacedeverytime the core istobe opened.The benefitwouldbe alesscomplicatedsystemthatwouldcostlessthan$100 forthe helium inthisoff-gassystem.
3.2.3 SpentFuel Storage A spentfuel pool willneedtobe considereddue tothe shortnessof the fuel’slifetime.Anoff-site pool couldbe used,butthis posesmanyproblems.Findingpoolsavailableforouruse and shippingthe spent fuel tosuch siteswouldaddextracostsand effort.Anotheroptionwouldtobe tobuilda spentfuel pool on our vessel.If we move forwardwiththis option, the pool will be astandard40 feetdeep.Onlyabout 20 feetisneededtokeepradiationatacceptable levelsbutthiswill provide uswithafactorof safety. Thisassumptionisbasedoff PWRdesigns [17].The waterwill be kept at roughly35o C to ensure adequate coolingof the fuel.The storage rackswithinthe pool will alsoneedtobe made of a high neutronabsorbingmaterial suchasB10 .This will helpshieldworkersandmaterialsfromradiationaswell as maintainingsub-criticality.Radiolysisisaconcernwithspentfuel poolsaswatermay be converted intohydrogen gas,whichcan accumulate above the pool.The airwithinthe roomwill needtobe monitoredperiodicallyandtreatedif necessary.The biggestriskforspentfuel poolsis afailure inthe coolingsystem.Thiscancause the waterto boil andcause radioactive materialstobecome present withinthe air.Planswill needtobe made if sucha situation occursor a failsafe will needtobe putin place,suchas a cap overthe pool to filteroutharmful materials. 3.2.4 Dose Calculations Determiningthe neutronandgammaflux at the reactorpool boundariesprove tobe a difficulttaskand furtherresearch isneeded toobtainmore exactresults.Preliminaryresultsforneutronsbeingfound outside ourreactorpool lidwas extremelysmall,suchthatMCNPreturneda value of zero.Tallyvalues fromMCNP gave a dose of 191 remper hourfor everysquare meterof the reactorpool wall,whichis immenselyhigh.Tomanage thisproblem, boratedpolyethylene will be addedaroundthe reactorpool wall to lowerthe dose AsLowAs ReasonablyAchievable.MCNPwill be utilizedagaintocalculate the correct thicknessof the plasticandboronconcentration.DatafromMCNP concludedthatgamma rays
of anyspectrumwill be statisticallyabsentfromthe boundariesof the pool wall andlid.The bottomof the reactor pool will receiveasignificantdose of radiation due toneutronsandgammarays. Significant shieldingwillhave tobe addedtothisarea in the formsof borate polyethylene andlead.Thisareaisof leastimportance though,due tono one beinglocatedoractivelyworkingunderneaththe reactorpool. Table 3.2.4.1: MCNP Dose Values per Square Meter Tally# Surface # Surface Location Particle Dose (rem/hr)/m^2 2 25 Pool Wall neutron 191.2352998 12 26 Pool Cap neutron 0 22 27 Pool Bottom neutron 10423327.07 32 25 Pool Wall photon 0 42 26 Pool Cap photon 0 52 27 Pool Bottom photon 915904.1144 Thisconcludesthatthe current shieldingdesignof the mobile LFRwill be adequate inattenuation, thickness,andstoppingpower.Byadequate,there will be anextremelyhighprobabilitythatminimal dose wouldbe receivedbyworkersstandingnexttothe reactorpool once shieldingmodificationshave beenmade.One caveatthoughisthat coolantactivationanalysiswasnotperformed.The mobile LFR designaccommodatesforpoloniumproductionthroughthe off-gassystem.Otheractivatedisotopes and fissionproductscouldpotentially enterthe mainpool coolant.Furtherindepthanalysisof the productionandmobilityof these particleswouldhave tobe conductedtoadequatelyperformrealistic dose calculations outsidethe reactorpool.Mitigatingthispotential problemcouldbe fixedbysuppling additional shieldingmaterialsto the reactorpool wall suchas lead,boratedpolymer,andpotentially more steel.
3.3 Heat Transfer and Fluid Flow 3.3.1 Primary Side 3.3.1.1 Single Fuel Element Heat Transfer Analysis In orderto obtainimportantsystemparametersaswell astoverifythe safetyof the fuel,ananalytical solutionforthe radial heattransferequationwasfound.Since the maximumfuel temperature isknown, the equationsbelow were usedtofindthe surface temperature of asingle fuel element.Accordingto Incroperaand DeWitt,the steadystate heatconductionequationwithheatgenerationisEquation 3.3.1.1.1 [18]. 1 π‘Ÿ 𝑑 π‘‘π‘Ÿ ( π‘Ÿ 𝑑𝑇 π‘‘π‘Ÿ ) + π‘žβ€²β€²β€² π‘˜ = 0 3.3.1.1.1 By assumingsteadystate operationinone dimension(radius,r) and integrating,Equation3.3.1.1.2was obtained. 𝑇( π‘Ÿ) = βˆ’ π‘žβ€²β€²β€² π‘Ÿ2 4π‘˜ + 𝐢1 ln( π‘Ÿ) + 𝐢2 3.3.1.1.2 Thisequationisonlyapplicableforaradiusbetween0and the outerradiusof the fuel elementR1.This outerradiuscorrespondstothe surface boundarybetweenthe fuelandthe leadgap.Assuch, the boundaryconditionsbelowwere usedtofindconstantsC1 and C2. 𝐡𝐢1: 𝐴𝑑 π‘Ÿ = 0, 𝑑𝑇 π‘‘π‘Ÿ = 0 => 𝐢1 = 0 3.3.1.1.3 𝐡𝐢2: 𝐴𝑑 π‘Ÿ = 𝑅1, 𝑇( 𝑅1) = 𝑇𝑠 => 𝐢2 = 𝑇𝑠 + π‘žβ€²β€²β€² 𝑅1 2 4π‘˜ 3.3.1.1.4 Afterapplyingthese twoboundaryconditions,the general heattransferequationforthe fuel element can be expressedbyEquation3.3.1.1.5. 𝑇( π‘Ÿ) = βˆ’ π‘žβ€²β€²β€² π‘Ÿ2 4π‘˜ + 𝑇𝑠 + π‘žβ€²β€²β€² 𝑅1 2 4π‘˜ 𝑇1,𝐻 βˆ’ 𝑇1,𝐢 𝑇2,𝐻 βˆ’ 𝑇2,𝐢 = πœ‚ 3.3.1.1.5
By usingthisequationwiththe correctvaluesof T(0),q’’’,andk, one can obtainthe temperature atthe edge of the fuel pin.Due to the highthermal conductivityof the metallicfuelpin,thissurface temperature wascalculatedtobe almostexactlythe temperature of the fuel pin center.Assuminga temperature of 823o K, the edge of the fuel pinwasfoundto be approximately822.9o K. Thissame approach was alsousedtoderive equationsforthe heatconductionacrossthe lead-filledgap and cladding.Byusingthe temperature obtainedinthe previousstep,the temperaturesateachof the otherboundaries(gap-to-claddingandcladding-to-pool)were obtained.Eachtemperature wasonly reducedbyslightlyless thanatenthof a degree Kelvin due tothe unique propertiesof ourfuel,gap, cladding,andoverall fuel pindimensions. However,duringthe lifetime of the reactor’sfuel,the fuel will expanddue toradiationswelling.Inmost reactors,the fuel will expandtoclose the gapbetweenthe fuel andcladding,whichcanresultin mechanical failure of the rod.Assuch,an analytical solutionfordirectfuel-to-claddinginteractionwas found.AccordingtoKruper,the fully-derivedequationsforthe fuel elementandcladdingare representedasEquation3.3.1.1.6 andEquation3.3.1.1.7 respectively [19].The subscriptsβ€œf”and β€œc” denote fuel andcladding;the subscriptsβ€œ1”andβ€œ2” denote the fuel-claddingandcladding-pool radiiof the fuel element;β€œh”denotesthe convective heattransfercoefficient. 𝑇( π‘Ÿ) = βˆ’ π‘žβ€²β€²β€² π‘Ÿ2 4π‘˜ 𝑓 βˆ’ π‘žβ€²β€²β€² 𝑅1 2 2π‘˜ 𝑐 ln( 𝑅1) + π‘žβ€²β€²β€² 𝑅1 2 2β„Žπ‘…2 + π‘žβ€²β€²β€² 𝑅1 2 2π‘˜ 𝑐 ln( 𝑅2)+ 𝑇𝑠 + π‘žβ€²β€²β€² 𝑅1 2 4π‘˜ 𝑓 3.3.1.1.6 𝑇( π‘Ÿ) = π‘žβ€²β€²β€² 𝑅1 2 2π‘˜ 𝑐 ln( π‘Ÿ) + π‘žβ€²β€²β€² 𝑅1 2 2β„Žπ‘…2 + π‘žβ€²β€²β€² 𝑅1 2 2π‘˜ 𝑐 ln( 𝑅2)+ 𝑇𝑠 3.3.1.1.7
Once the linearheatrate of the hottestfuel elementisfoundusingMCNP,these equationscanbe used to determine the temperatureof the centerof the fuel.Inthisway,itcan be verifiedthatwiththe given core parameters,the fuel will not exceeditsmeltingtemperature. 3.3.1.2 STAR Modeling Due to the reactorsystemhavinga pool design,modelsneededtobe createdto calculate the heat transferandfluidflowsince valuescannotbe obtained analytically.The modelscreatedtoshow these propertiesstartedinSolidWorks,thenwereimportedintoSTAR-CCM+.Three modelshave been createdthusfar. The three modelsinclude acoarse model of the primarypool,areactor assembly,and a critical fuel pinlattice. The coarse primarypool wascreated first,as it hadthe simplestgeometryandboundaryconditions. Thismodel includessmallcylinderinside alarge cylinder,whichrepresentsthe reactorcore inside the primarypool.The pool isnine metersindiameterandeightmeterstall.The base size forthe meshused was 0.1 m. No problemsoccurredwhenthe meshwasgenerated.Asforthe boundaryconditions,a velocityof 1.435 m/swas specifiedthroughthe core andan entrance and exittemperatureof the LBE throughthe core. All surfacesinthismodel were assumedtobe insulated.The purpose of thismodel was to determinehownatural convectionwouldworkinthe core andhow heatwouldbe distributed. Boundaryconditionsstill needtobe specifiedbefore anyiterationsare ran. The fuel assembly has217 fuel pinsinsidethe hexagonal lattice.Eachof the sidesof the hexagonare 5.5 cm, and the radiusof each fuel pinis0.29 cm. The pitch forthe fuel pinsis0.714 cm, andthe heightof the assemblyis1.5 m. The base size usedforthismodel was one millimeter.Suchasmall base side was usedforthe meshingbecause of the amountof detail thatneedstobe obtainedfromthe model.No
problemsoccurredwhenthe meshingwasgenerated.Forthe boundaryconditions,the outside surfaces of the assemblywere setasreflective since otherfuelassemblieswill be borderingit.The fuel rods inside the assemblywillhave the heatflux specifiedonthe walls.The fluidvelocityatthe entrance to the fuel assemblywasspecifiedas1.435 m/sso the velocity profileinside the core isgenerated.The purpose of thismodel isto findflowandheattransferthroughthe assemblyandto identifythe fuel lattice withthe highestoutputtemperature. Figure 3.3.1.2.1: STAR CCM Model of an Entire Fuel Element The critical fuel pinisa triangularlattice composedof three fuel pinsinsideanassembly.The geometry was createdbydrawingan equilateraltriangleusingthe pitchasthe side length,thensubtractingthe area fromthe fuel pins.The base size usedinthismodel was0.1 mm. Sucha small base side wasused for the meshingbecause of the amountof detail thatneedstobe obtainedfromthe model.The boundaryconditionssetonthe fuel pinshave aheatflux of 2.09 X 107 W/m2 .The straightwallswill have a reflective boundaryappliedtothemtosimulate otherchannelsnexttoit.A constantvelocityof 1.435 m/swas assumedat the inletof the fuel channel.Thismodelwascreatedtofindthe maximum temperature inthe pool,andtomake sure the fuel will notmeltandthe coolantwill notboil.
Figure 3.3.1.2.2: STAR CCM Model of a Single Coolant Channel The critical fuel pinwentthrough500 iterationsandconvergedafterthe first50. The fuel pindidnot exceed1027Β° C,whichis belowthe 1135Β° C meltingtemperature of the fuel [13].The LBE inthe fuel channel hadan inlettemperature of 150Β° C and an outlettemperatureof 877Β° C.The outlet temperature of the fuel channel wasbelow the 1670Β° C boilingtemperature of LBE[32]. The velocity enteredthe fuel channelat1.435 m/s and leftthe fuel channel at1.64 m/s. Thermal expansionof the coolantcausedthe velocitytoincrease by0.21 m/s.These resultsare seeninfigures3.3.1.2.3,3.3.1.2.4, 3.3.1.2.5, 3.3.1.2.6, and 3.3.1.2.7.
Figure 3.3.1.2.3: Cross Section of Critical Fuel Pin Figure 3.3.1.2.4: Critical Fuel Pin Outlet Temperature
Figure 3.3.1.2.5: Critical Fuel Pin Outlet Velocity Figure 3.3.1.2.6: Critical Fuel Pin Inlet Temperature
Figure 3.3.1.2.7: Critical Fuel Pin Inlet Velocity 3.3.1.3 Natural Convection Because pipeswere addedlinking the reactortothe heatexchangers,thentothe primarypool,natural convectionequationswere usedtodetermineif natural convection issufficienttosupply1000 MWt of power.The followingequationswereusedinfindingthe total change inpressure toprovide 1000 MWt of power: Δ𝑃 = πœŒπ‘‰π‘Ÿ 2 2 (βˆ‘[ 𝑓 βˆ— 𝐿 𝐷 + βˆ‘ 𝐾] βˆ— 𝐴 π‘Ÿ 𝐴 𝑖 𝑖 ) 3.3.1.3.1 𝑓 = 0.316 𝑅𝑒0.25 3.3.1.3.2 𝑅𝑒 = πœŒπ‘£π· πœ‡ βˆ— 𝐴 π‘Ÿ 𝐴 𝑖 3.3.1.3.3 π·β„Ž = 4𝐴 𝑃 3.3.1.3.4 Δ𝑃 = Δ𝑝𝑔Δ𝑇 (for natural convection) 3.3.1.3.5 π‘ƒπ‘œπ‘€π‘’π‘Ÿ = πœŒπ‘‰π΄πΆ 𝑝Δ𝑇 3.3.1.3.6
By usingthese equations,itwasdeterminedthatapressure differenceof 28.4 kPa wasprovidedby natural convection,buta pressure difference of 491.7 kPa wasneededtoachieve the powerof 1000 MWt. Losseswere consideredforthe powercalculation,but notfornatural convection.Because the pressure differenceneededisgreaterthanwhatnatural convectioncouldprovide,forcedflow will be neededtoachieve apowerpast200 MWt. These calculationswere done assumingconservative loss coefficientsforenteringandexitingpipesalongwithelbowbends.Foroperationat1000 MWt, forced convectionwill be usedprimarilyandnatural convectionwillassist.The massflow rate movingthrough the core is14410.4 kg persecond. Withnatural convection,the systemwouldbe able toproduce 200 MWt. To achieve the 1000 MWt desiredforthe design,the LBEcoolantwouldhave tobe pushedthroughthe core at a velocityof 1.435 m/s.To achieve thisvelocity,the decisionwasmade touse an electromagneticpump.Whenlookingfor pumps,several modelswere found,butpricingforthese modelscouldnotbe located.Shownbelowin Figure 3.3.1.3.1 isa back-uppumpusedinthe RussianBN-800 reactor [53]. Figure 3.3.1.3.1: TsLIN 4/26
Thispumpdraws 14 kW and has a flowrate of 26.1 m3 /h[53]. The other pumpinoperationatthe RussianBN-800 is a TsLIN 1.5/430. Thispump draws66.4 kW and has a flow rate of 429 m3 /h [53].By locatingthese pumps, the teamdeterminedthatthe pumpsrequiredforthe applicationexistandall that isneededisto determine the cost.Takingpricesfromsmallerelectromagneticpumpsavailable, the teamextrapolatedthe datatodetermine the price andpoweruse of the requiredpump.Thisdatacan be seenbelowin Table 3.3.1.3.1. At 1.435 m/s the pumpwoulddraw 21.53 kW of powerandcost approximately$190,400. Table 3.3.1.3.1: Electromagnetic Pump Pricing 3.3.1.4 Heat Exchangers For the heatexchangerdesign,the paperβ€œThermal-hydraulicperformanceof heavyliquidmetal in straight-tube andU-tube heatexchangers”wasusedbecause itgave dataon possible LBEheat exchanger[20].The one chosenwas the straighttube type because itdoesnot exhibitthe corrosion problemsof the U-bendstyle.Equationsgivenbythe paperwere inputtedintoanexcel spreadsheet withthe ultimate goal of finding q.Currentdesigncallsforaone meterouterpipe diameteranda three meterlongpipe. Table 3.3.1.4.1 containsthe expectedtemperatures. Extrapolated Price Power Use (kW) Linear Linear RΒ² = 0.9949 RΒ² = 0.9882 1.371 $180,964.50 21.41 1.389 $183,323.70 21.44 1.407 $185,682.90 21.47 1.426 $188,042.10 21.50 1.444 $190,401.30 21.53 1.462 $192,760.50 21.56 1.480 $195,119.70 21.59 1.498 $197,478.90 21.62 1.516 $199,838.10 21.65 Fluid Velocity (m/sec)
Table 3.3.1.4.1: Expected Temperatures in the Heat Exchanger Location Temperature(K) T-hot-L 923 T-cold-O 423 T-hot-L 900 T-cold-O 305 Picturedbelowisadiagramof the heatexchangerfromthe paper β€œThermal-hydraulicperformance of heavyliquidmetal instraight-tubeandU-tube heatexchangers”, summarizingthe basisforthe ones usedinthisreactor [20]. Figure 3.3.1.4.1: Straight Tube Heat Exchanger Convective transfercoefficientsweregiveninthe paperandusedinthisanalysis.The paperalso providedequationsusedtosolve forsome keyfactorsinthe designof aheat exchangerof thistype. Belowisa table of the factors, includingpressure losses,frictionfactor,and Reynoldsnumber:
Table 3.3.1.4.2: Table of Heat Transfer Factors for Heat Exchangers Factor Value Units Reynolds Number 45444 NA Ξ”P 0.933 NA f 0.0014 NA U(overall heattransfer) 1.11E+05 W/(m2 *K) q 3.80E+08 W Ξ”T-log mean 546 K The main factorin thisanalysis,q,indicatesthe heatexchangerwillmove 380 MWt overitslength.This meansat leastthree heatexchangerswillhave tobe placedaroundthe reactor pool inorderto handle the heat loadfromthe reactor. 3.3.2 Secondary Side The purpose of the secondarycycle isto extractenergyfromthe core and turn itintousable electricity. To do this,a systemof compressors,turbines,andregeneratorsare usedtoextractheatfromthe core usingsupercritical carbondioxide.Inreal life,the componentsinthe secondaryside have setefficiencies and thermal limits.Indesigningthiscycle,assumptionsregardingthe capabilitiesof the machineryare giveninTable 3.3.2.1. Table 3.3.2.1: Assumed Machine Efficiencies for Secondary Cycle Component Assumed Efficiency (%) Flow Coming From LTR (%) Turbine 0.95 Compressor 1 0.90 0.65 Compressor 2 0.90 0.35 High Regenerator 0.98 Low Regenerator 0.92 Generator/Alternator
Figure 3.3.2.1: Secondary Cycle Layout Figure 3.3.2.2: Secondary Cycle States
Figure 3.3.2.3: Secondary Cycle State Diagram To quantifyeachstate inthe cycle,the followingequations fromaheattransfertest were used [18]. π‘‡β„Žπ‘–π‘”β„Ž π‘‡π‘™π‘œπ‘€ = ( π‘ƒβ„Žπ‘–π‘”β„Ž π‘ƒπ‘™π‘œπ‘€ ) (π›Ύβˆ’1) 𝛾 3.3.2.1 𝛾 = 𝑐 𝑝 𝑐 𝑣 3.3.2.2 πœ‚ π‘‘β„Žπ‘’π‘Ÿπ‘šπ‘Žπ‘™ = π‘Šπ‘›π‘’π‘‘ 𝑄 π‘Žπ‘‘π‘‘π‘’π‘‘ 3.3.2.3 T is the temperature inKelvin.Pisthe pressure inMPa.Gamma, 𝛾, isthe heatcapacityratio.Cp is the heatcapacity at constantpressure.Cv is the heatcapacity at constantvolume. πœ‚ representsthe efficiency. 3.3.2.isusedwhencomparingthe statesinand outof a compressoror turbine.Thisequation isusedfor determiningstate 2from state 1, state 6 from state 5, and state 8 fromstate 4. Calculations were startedwiththe assumptionof the hottestfluidtemperature andlowest fluidtemperature.At state 1, itis assumedthatthe supercritical CO2 leavesthe core at923Β° K at a pressure of 20 MPa. The lowtemperature,atstate 5, is 305Β° K and isat a pressure of 7.7 MPa. From the assumedstate 1,
Equation3.3.2.1 wasusedto findstate 2. From the assumedstate 5, Equation3.3.2.1 was usedtofind state 6, whichneededtohave apressure of 20 MPa. To determine state 9,a simple weightedaverage of the temperaturesof state 7 and state 8 withrespecttomass flow rate isall that isrequired.Inthe regenerators,anotherequationwas usedtofindthe outletstates. 𝑇1,𝐻 βˆ’ 𝑇1,𝐢 𝑇2,𝐻 βˆ’ 𝑇2,𝐢 = πœ‚ 3.3.2.4 The efficienciesof the regeneratorsisassumedtobe 98% forthe hightemperature regeneratorand 92% forthe lowtemperature regenerator.Knowingonlythree of the fourstates,the fourthstate canbe determined.Withall otherstatesnowdefined,states 3and 4 have nostrictlydefinedvalue.Thisimplies that the amountof heattransferredthroughthe regeneratorsisnotsetandcan be manipulatedto achieve amore efficientcycle.Bymodifyingthese state temperatures,amaximumcycle efficiencycan be determined.Tofindthe overall cycle efficiency,the followingequationsare used. π‘Š = (π‘‡β„Žπ‘–π‘”β„Ž βˆ’ π‘‡π‘™π‘œπ‘€)(πœ‚ π‘π‘œπ‘šπ‘π‘œπ‘›π‘’π‘›π‘‘) 3.3.2.5 πœ‚ π‘‘β„Žπ‘’π‘Ÿπ‘šπ‘Žπ‘™ = π‘Šπ‘›π‘’π‘‘ 𝑄 π‘Žπ‘‘π‘‘π‘’π‘‘ 3.3.2.6 πœ‚ π‘‘β„Žπ‘’π‘Ÿπ‘›π‘Žπ‘™ = π‘Šπ‘‘π‘’π‘Ÿπ‘π‘– 𝑛 𝑒 βˆ’ π‘Šπ‘π‘œπ‘šπ‘π‘Ÿπ‘’π‘ π‘ π‘œπ‘Ÿ 1 βˆ’ π‘Šπ‘π‘œπ‘šπ‘π‘Ÿπ‘’π‘ π‘ π‘œπ‘Ÿ 2 𝑄 π‘Žπ‘‘π‘‘π‘’π‘‘ 3.3.2.7 Where W is the workthrougha turbine orcompressorandQ is the amountof heataddedto the system. The bestefficiencyachievable isthe Carnotefficiencyandcan be calculatedwith Equation3.3.2.8. 𝑇𝐻 βˆ’ 𝑇𝑐 𝑇𝐻 Γ— 100% 3.3.2.8 For the system,the hottestandcoldesttemperaturesare 923 and305Β°K, respectively.Thisgivesa Carnot efficiencyof 66.96%. Usingthe actual worktaken out fromthe system, we have a cycle efficiency of 45.5%. Thisseemstobe reasonable whencomparedtosimilarpowerplantcycles.Thisefficiencyis greaterthan manytraditional PWRcycles.
3.3.3 Water Desalination Water desalinationisthe processof removingimpuritiesof awater source.The goal is to produce pure H2O. There are many methodsof waterdesalination,suchasdistillation,membrane processes,andion exchange.Thisdesignwill be usingdistillationbecause itusesexcessheatfrompowergenerationloop. Thisextraheat wouldotherwise be dumpedintothe environment.Inthisway,we are lesseningthe powerplant’sthermal footprintwhileprovidinganothercommodity,water,whichcanbe soldfora profit. The plant will extractdrinkable water outof the seawaterthroughmultiple-effectdistillation.The basic principle of waterdistillationisasfollows.Waterisheatedtoitsboilingpoint.More heatisaddedto change the phase of waterintovapor.A coolersurface to the boilingcontainercondensesthe waterand divertsthe condensationtoanotherholdingtank.The boiled-off watershouldbe nearlypure,asthe contaminantsshouldnotboil attemperaturesaslow asthe water.Multiple effectdistillationusesa numberof stagesto distill water.The name comesfromeachstage beingcalledanβ€˜effect’.The stages differintemperature andpressure.Onthe inside of atube,wateriscondensed,andonthe outside of the tube,a thinwaterfilmisvaporized [21]. Multiple effectdistillationonlyrequiresexternalheatingatthe firststage.Thisstage has the highest pressure.Because the boilingtemperature of waterdecreaseswithdecreasingpressure,the vapor createdinthe previousstage canbe usedto boil water inthe nextstage [22]. Thisdesalinationsystem doesnothave definite temperaturesandpressuressetforeachstage.The informationprovidedby Warsinger’sworkondesalinationmethod detailsthe overall efficienciesof variousdesalinationmethods [23]. It isexpectedthatwe will have arecoveryratiogreaterthan40%, whichmeansthat at least40% of
inputwaterwill become drinkable.The heattransferintodesalinationisknown.There isanamountof heat,q, fromthe secondaryCO2 that needstobe disposedfromthe system.Thisqwill gointothe desalinationsystem.UsingefficienciesfoundinWarsinger’spaper,we have come tothe conclusionthat we can produce approximately1.15 milliongallonsof waterperday(or4.3 millionlitersperday). It isimportantto note that notall the seawaterthatgoesthroughthe systemwill become drinkable water.Asseawaterprogressesfromstage tostage,itbecomesincreasinglydifficulttodistill.The amountof impuritiesremainthe same while the amountof solvent,water,decreases.Thismeansthat the outputwateris more of a brine thanthe inputwater.The brine mustbe dischargedbackintothe ocean.This is a forma pollutionandmustbe monitored.However,the brine shouldbe dilutedbythe oceanto a negligibleconcentration.The mostimportantpollutantswill come fromcleaningagentsused for maintenance andmetalsdissolvedfromthe pipesandtanks [24]. Multiple effectdistillationcanbe reasonablyachievedonaseafaringvessel forareasonable cost.The onlymovingpartsinthe designare the low pressure pumps.The stagescanbe constructedout of cheap materials,like aluminum.The processoperatesat a relativelylow temperature,whichreducesscaling. It isan economical choice because ithasverylow maintenance costsanddoesnotneedmuch supervisionwhile operating.Multipleeffectdistillationusesverylittle electrical powercomparedto multi stage flashdistillationormembrane processeslikereverse osmosis [25].Additionally,there are alreadycompanies,like EntropieVeolia,thatmanufacture modulardesigns.The instillation wouldbe easilyperformedwithourshipdesign.Therewould,however,be achange inthe designto accommodate CO2 as the heatingfluidinsteadof water.
3.4 Materials 3.4.1 Ship Analysis An importantaspectof the mobile LFRdesignis thatthe shipthat contains the entire facility. Conservative preliminarycalculationsregardingthe size of the shipwere made usingthe weightof the lead-bismutheutecticcoolantpool.The weightof the core and coolantpool were doubledbecause the powerconversionsystemsandothersmallercomponentswere notincludedinthe measurements.The calculatedminimumvolume of the ship,includingthe safetyfactorof 2.5, was36,011.6 m3 .In a traditionallydesignedrectangularship,itwouldbe aminimumof 70 m long,35m wide,and15m draft. A fewshipsthatmetthe requirementsforsize forthe projectwere the Hbulkcarrier,the Handymax bulkcarrier,and the ClassB bulkcarrier.The Handymax bulkcarrieristhe shipthatwill mostlikelybe usedas the reactor systemsvessel.The Handymax BulkCarrieris200 m long,has a 32 m beam, and has a 19 m draft.It has a DWT (DeadweightTon) measurementof 46,000, meaningthatitcan carry 46,000 tonsof cargo, not includingthe ship’sweight.The Handymax isalsoagearedship,meaningthatithas cranesoverheadof the shipdeckavailable to liftandlowerpartsintothe vessel.The reasonthe Handymax isbeingchosenisthatit islarge enoughto holdthe reactor components,house the power conversionsystems,apossible spentfuel storage pool,andpotentialhousingforreactoremployees. Afterthe shiphasbeenpurchasedand before itisreadyto house the nuclearreactor,the shiphas to be retrofitted.Several systemsnotcurrentlyonboardthe shipwouldhave tobe installed, suchasa power conversionsystem, the desalinationsystem, andthe reactorsystemitself.Before systemssuchasthese can be installedonthe vessel,safetyandsupportsystemsmustbe installed.Afterthe necessarysupport and safetystructuresforthe reactor systemshave beendesigned,the designforthe renovationof the shipcan be completed.
3.4.2 DPA Considerations The main considerationforradiationdamage tothe reactoristhe fuel cladding.Due tothe highvolume of liquidmetal surrounding the core,pool materialswill receiveafractionof the dose that the cladding does.Due to this,if the cladding isshowntobe safe,the core can said to be safe under operation conditions. Several assumptionswere made toallow foramore straightforward DPA calculation. The crosssection of ourmaterial was assumed constantat all energies.Thisisvalidbecausethe energyspectrumgivenby criticalityisrelativelynarrowandthe crosssectionchangesbyonlya few barns.Damage was caused entirely byIronatoms wasalso assumed.Of which,the claddingcontainsmore than80%.SRIM simulations withatomsatappropriate percentagesactuallyshow lessdamage thanthe entirelyIron assumption,makingthe estimate conservative whilestreamliningthe calculation. Usingthe Displacements/Ionoutputfromthe SRIMcode,DPA is calculatedforHT-9 as 18.8 DPA overa periodof 2.5 years.Giventhe incubation periodof HT-9is 100-200 DPA,core materialshave an estimatedlifetimeof 25 yearsunderthislevel of radiationdamage.Thisestimate,whichutilizesprimary knock-onatomsas the source of damage,overestimatesthe actual damage thatcore materialswill suffer.Fromthis,itcan be shownthat chemical andmechanical stressesare the primaryfactorsinthe material degradation. 3.4.3 Corrosion One of the majorconcernswhenlookingatthe lifetimeof reactormaterials iscorrosion.Lead-bismuth eutectic(LBE) isa corrosive material,especiallyatelevatedtemperatures(T> 500Β° C) [39]. Oxygenlevels
inthe reactormust be closelymonitoredinordertoallow protective oxide layerstoformonreactor materialswhilepreventingthe LBEcoolantfrom formingprecipitates. Withoxygenlevelstoolow,the dissolutionof metal alloyswill beginandthe structureswill starttodegrade.Withoxygenlevelstoo high,rapidoxidationof inpool supportstructureswill occurand PbOprecipitateswill begintoformin the coolant.These factorswill endupcausinglowerheattransferrates.Usingthe equationsbelow,the teamhas foundthat the optimal range duringoperatingconditions (T=600o C) fallsbetween 3.617 X 10-3 and 3.35 X 10-8 weightpercentoxygen. Oxygenupperlimit: π‘™π‘œπ‘”(𝐢 π‘œ βˆ— ( 𝑀𝑑%)) = 2.25 βˆ’ 4125 𝑇( 𝐾) 3.4.3.1 OxygenLowerLimit: log(𝐢 π‘œmin( 𝑀𝑑%)) = βˆ’ 3 4 log( 𝐢 𝐹𝑒( 𝑀𝑑%))+ 2.28 βˆ’ 10456 𝑇( 𝐾) 3.4.3.2 log 𝐢 𝐹𝑒 𝑆 ( 𝑀𝑑%) = 2.01 βˆ’ 4380 𝑇( 𝐾) 3.4.3.3 Whenlookingatspecificmaterials,the 316L stainlesssteel pipingusedforthe heatexchangersended up beingaproblematicchoice. Atlowertemperatures,T< 500o C, 316L formsa thinoxide layerthatis sufficientinprotectingthe material.Astemperaturesincrease,T> 500o C, thisoxide layerbeginstoget thickerandproducesmore defects.The defectsinthe protectiveoxidelayerare permeable tothe LBE coolantand dissolutionof metal willoccur.Thispreventsadditional oxidesfromformingand studies have shownthat these materialscanfail asearlyas 4000 hoursintoservice [10].Surface alloyingor diffusionalloyingof aluminumorsiliconintothe stainlesssteel canaidinoxide formationandextend the lifetimeof the material.However, studieshave shownmartensiticsteel alloyT91 to be a better candidate forthese applications.The additional chromium contentinthissteel causesathickoxide layer
to format highertemperaturesandprovide betterprotectioninthe LBE environment.TestsusingT91in a LBE environmenthave beenperformedforover20,000 hours withoutthe material failing.Toincrease the corrosionprotection of T91 evenfurther, aluminumorsiliconcanbe alloyedintothe surface to provide additional oxide protection.One othermethodof corrosionprotectionwouldbe toadd corrosioninhibitors(likezirconiumandtitanium) tothe coolant(concentration<10-3 wt. %) allowing protective oxidestoformonthe steel surfaces [10]. 3.4.4 Support Structure The supportstructure for the reactor was modeledusinga1000 kN load.The supportstructure ismade out of 13 supportlegsmeasuring4 cm by 4 cm andare 1 meterlong.The baseplate is140 cm across, 6 cm thick,and has holesinthe baseplate toallow forfluidflow. Figure 3.4.4.1: Support Structure Whenmodelingthe structure,itwasdeterminedthatthe majorityof the structure hada safetyfactor greaterthan 5 witha minimumof 3.09 on the inside cornerof the outerlegswhere theymeetthe
baseplate.The simulationresultscanbe seeninFigure 3.4.4.2 withthe area havingthe smallestfactor of safetyshowninFigure 3.4.4.3. Figure 3.4.4.2: Safety Factor of Support Structure
Figure 3.4.4.3: Minimum Factor of Safety The simulationalsoshowedthatthe greatestdisplacementexperiencedbythe structure isonly0.3885 mm.This displacementoccursonthe outeredge of the baseplate inbetweenthe supportlegs.These resultscanbe seeninFigure 3.4.4.4.
Figure 3.4.4.4: Support Structure Displacement (mm) From the preliminaryanalysisandthe structure simulationdoneonAutoDeskInventor,the teamhas determinedthatthe above designedsupportstructure willbe sufficienttosupportthe reactorcore underoperatingconditions. 4 Humanitarian Benefit and Environmental Impact 4.1 Nonproliferation Witheverybranchof the nuclear powerindustry,proliferationisaconcernand the mobile LFRisno exception.Tohelpcombatthe spreadof nuclear arms, enricheduraniumandspentfuel must be closely monitored.Withthe use of the mobile LFR, there are several builtinnonproliferationfeaturesthatare intrinsictothe design.Forexample,the spentfuel of the reactorwill be storedonsite andwill be too radioactive todirectlyhandle,renderingmostif notall attemptsof acquiringthe spentfuel useless.This aspect,while commoninthe nuclearindustry,hasbeentime testedandprovenandwill be keytothe mobile LFRdesign.
The mobile LFRwill have alimitedamountof potential buyersandwill be regulatedtothe private industriesandcountriesthatare preapprovedbythe United Nations.Thiswill helpreduce the fuelor spentfuel frommakingitswayto anyindividualswithmaliciousintent.Inaddition,the spreadof nucleartechnologywillbe regulatedwhile helpingpromote the nuclearpowerindustry. The mobileLFR will be securelyoperatedandmaintainedbyexperiencedindividualsthathave passedbackground checksand auspiciouswith regardtokeepingthe mobile LFRsafe fromharm. The ship’sdesignswillbe keptstrictlyconfidential.Thisistohelppreventanyopportunityfor terrorist partiesand organizationsfromacquiringthe meanstocause damage to the vessel andendangeringthe surroundingpeople. 4.2 Pollution The operationof a nuclearreactor involvesthe riskof leakingpotential pollutantsintothe environment. In the case of thisdesign,the mainconcerninthisarea isleakingpollutantsintoseawater.There are three mainformsof pollutionassociatedwiththisdesign:lead,heat,andradioactivity.Eachformhas beenresearchedtofindacceptable quantitiesof pollutionandthe decontaminationprocedures associatedwitheach. The primaryconcern withthe operationof thisreactordesignislead.Leadinwater(especiallydrinking water) can cause a numberof ill effectsonlivingthings.The mostsevere formof leadpoisoninginvolves the replacementof calciumionsinthe nervoussystem,therebydegradingneuronal functioning[26]. Thankfully,thissystemisdesignedtobe usedinsaltwaterbodies,meaningthatchronicexposure to leadthroughdrinkingwaterisnotof concern.However,leadcanstill affectaquaticlife.Guidelineshave beenimposedbythe UnitedStatesEnvironmentalProtectionAgency(EPA)toprotectaquaticlife.These
seawaterguidelinesstate thatacute dose concentrationsforleadshouldbe below 210 microgramsper liter,andthat chronicdose concentrationsshouldstaybelow8.1microgramsper liter[27].Since water desalinationisplannedforthisreactorsystem, the maximumconcentrationshave alsobeenobtained for freshwater.Theseguidelinesare stricterat65 and 2.5 microgramsperliterfor acute and chronic dosesrespectively [27].Inthe case of contamination,eitherphysical orinactivation(chemical) decontaminationprocesseswillbe usedtodispose of the contaminatedmaterials[28]. Overall,itisnot expectedthatthisdesignwill require adischarge of leadintoanybodyof water.Evenso, precautions will be takentokeepleadpollutionaslow asreasonablyachievable. Heat pollutionis anotherconcernforthisdesign.Duringoperation,the reactorwill needawayto dispose of excessprocessheatatthe back endof the cycle.This designwillrejectexcessprocessheatto the seawateraroundthe vessel.Atthistime,there are nointernational regulationsconcerningheat pollutionof the ocean,since the oceanisconsideredaninfinite heatsink.However,thisdoesnot necessarilymeanthatheatpollutionnearthe inletoroutletof a smallerbodyof water(suchas a river, lake,or port) isnot of concern.Since the reactor will be anchoredsomewhatclose toland,heat pollutionof the local areawill be monitored.Inthe case of local heatpollution,guidelinescreatedby the country’senvironmental agencieswill be followed.Whetherthe reactorislocatedinan oceanor otherbodyof water,the contaminationof heatwill be keptaslow asreasonablyachievable.Inthe case of β€œcontamination”,there are nospecificdecontaminationproceduresthatcanbe followed.The only course of action wouldbe to stopthe dumpingof excessheatintothe bodyof water(reactor shutdown). Radiationleakage intothe environmentisanissue thateveryreactordesignhastoconsider.According to the NuclearRegulatoryCommission(NRC),equivalentradiationdosestothe general publicmustbe
keptunder100 mrem peryear[29]. There are special circumstancesinwhichthatequivalentdose limit may be exceeded(suchasthe onsite visitingof anindividualof the public) [29].However,itisnot expectedthatthe reactordesignwill releaseanyradiationtothe publicduringnormal operation.As withthe otherformsof pollution,the amountof radiationreleasedintothe environmentwill be keptas lowas reasonablyachievable. 4.3 Public Concern and Safety The publicimage of any industryisvastlyimportantasitdeterminesonhow acceptable itisinthe world.Forthe nuclearindustry,thishasbeenachallenge toovercome due toatomicwarfare,nuclear accidents,andthe publicnotunderstandingradiation.Because of these threeobstacles,the nuclear industryhasto clearthembefore theyare acceptedbysocietyandare able to succeed.Forthe mobile LFR, the systemmustshowitis safe forthe general public,workers,andpractice ALARA. A potential concernandcriticismfromthe public isbasedonreactionstosimilarnuclearprojects deemedtohave environmentalimpact [30].Thishoweverprovidesanumberof benefitsforthe reactor systemandthe public.Bythe reactorsystembeing400 m offshore minimum, the general publicwillnot be exposedtoanyradiation.Thisisbecause the discharge waterwill be releasedunderthe vessel.By doingthis,the excessheatandradiationwill be dilutedfromthe oceantoundetectable concentrations [29]. Thisis accomplishedbythe oceanbeinganinfinite medium.The amountof radiationreleasedwill be comparable to a typical PWRand ALARA will be practiced,reducingconcentrationsevenfurther.The waterreleasedintothe oceanwill be below the DACvalue forwatersetbythe International Committee of Radiological Protection [31]. For workersinand onthe reactorsystem, UnitedStatesNuclearRegulatoryCommissionpublications will be practicedandapplicable [32].Thisgoesforlicensingpurposesandforworkerregulations.
Workerswill be preventedfromaccumulatingan annual dose greaterthanfive rem.All workerswillbe issuedafilmbadge,whichwill recordthe amountof radiationreceived.A healthphysicistonsite will monitoreachfilmbadge.The reactorstaff will handle accidentsthatoccuron site andALARA principles will be inpractice. The Worst-case scenarioforthe reactorsysteminvolvesthe vessel sinkingorrollingover.Ineithercase, if the shipstarts to roll or tippast a certainpoint,the reactor will immediatelySCRAM.The coolantwill thensolidifyaroundthe core,encasingthe core andshieldingthe radiationfromthe outside.Thiswill keepthe radiationfromenteringthe oceanwaterandcausinganotherFukushima.Thisdoesprovetobe an environmental hazarddue tothe leadbeingexposedtothe ocean.However,there are no international regulationsinregardstoleadpollutioninoceanwaters[49].Instead,the reactorsystem will followEPA regulationssince thereare regulationsforleadconcentrationsinthe UnitedStates. Multiple nuclearsubmarineshave sunkinthe oceanbefore,andnoknownlongtermeffectshave come fromthem.If the vessel sinks40m off shore,itwill goto a depthof at least1000 m.This claimmaybe made since the average depthof the oceanis 2.3 km[33]. At thisdepth,the vessel maysafelyrestatthe bottomof the ocean. 4.4 Water Desalination From the onsetof thisproject,a goal of thisdesignhasbeentoprovide humanitarianaidforadisaster area.Providingfreshwaterthroughdesalinationisone waytomake progresstowardsthisgoal.Clean wateris a necessityforhumancivilizationanditssupplymaybe diminishedinthe wake of anatural disaster.The freshwaterprovidedbythisdesigncanhelprelieve the immediate watershortagesaftera disasterandstill provide waterforthe communityasitrecovers andcontinuesnormal operations.This sectionwill detailthe effectsthatour1.1 milliongallondesalinationplantcanhave on a community.
Water isneededforhumansurvival.Onaverage,anadultneeds3.2litersof waterperday [34]. Assumingwaterfromthe desalinationplantcanbe distributedwell,the 4.16millionlitersof watercould sustain1.3 millionpeople.Thisestimate,however,doesnotconsiderthe real-worlddifficultiesof disasterreliefefforts. Survival (drinkingandfood) waterneedsare accompaniedbybasichygiene and cookingneedswithwater.Dependingonthe social andcultural environment,thisbasicwaternecessity raisesto 15 litersperpersonperday [35].Thismeans that the desalinationplantcanreasonablysupply 277,000 people inthe aftermathof adisaster.Toput that intoperspective,thatisapproximatelythe populationof Lincoln,Nebraska. Afterinitial disasterrelief effortsare taken,the communitywillneedwaterformore diverse purposes than justsurvival.Inthe recoveringcommunity,waterwill be usedforpersonal washing,homecleaning, agriculture,sanitation,indoorplumbing,andanumberof otheruses.For intermediate uses,itcanbe expectedthatthe desalinationplantcansustain170,000 people inrelativecomfort.That’s approximatelythe size of Springfield,Missouri.Inthe longterm, waterdemandswill continue to increase.The average UnitedStatescitizencanconsume nearly90gallonsof waterperday [36].The desalinationplantcouldprovidefor13,000 people if waterdemandreachesthishigh. 4.5 Mobility The topic of mobilitypresentsconcernforthe design.Nuclearreactorsingeneral have trouble inthe publiceye,andhavingamobile reactorwill be nodifferent.However,the currentdesignhasseveral safetyfeatures,andthese will helpcounteranypotentialmobile concern.Since the shipwill utilize similarsecuritymethodsthatcurrentnuclearpower plantshave,anymanmade threatsshouldbe reduced, if noteliminated.Also,anynatural disasterthreatswill be analyzed, andif needed,the shipwill
take necessaryprecautionstoreduce riskof damage to the vessel anditscrew.Usingthe ship'smobi lity will allowforevadingpredictable natural disastersandwill adhere toanywarningsissuedbylocal or national organizations(i.e.the National OceanicandAtmosphericAdministration).Mobilityalsoeases the manufacturingof the shipsince itcan be builtinthe mostefficientlocation thenmovedtoits destination.Thiscanreduce costandeffortinbuildingthe mobile LFR.
V. Conclusions The nuclearreactor systemiscomposedof a two-loopcycle,whichhasanefficiencyof forty-five percentandprovidesenoughenergytopowerthe systemitselfalongwithadesalinationplantonsite. The designincludescalculationsevaluatingthe progressof the systemand modelstobackuphand calculations. Calculationsperformedthusfarinclude the following: ο‚· Control rod worth ο‚· Burnupfor fuel ο‚· Natural convectionVs.Forcedconvection ο‚· STAR-CCM+ models ο‚· Secondarycycle efficiency ο‚· DPA rates formaterials ο‚· Productionandpersonnel costs ο‚· Dose rates outside reactorpool Currentworkto furtherimprove the systemincludesoptimizingthe secondarycycle,reactingmore detailedmodelsof the primarypool inSTAR-CCM+, MCNP,and SolidWorks,finalizing the final costof the system,findingoutthe activationtime of the coolant,andmakingsure all modelsmeshwithone another.All of the currentwork will tie togethertofinalizethe NuclearNarwhals’reactordesign.
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Final Report

  • 1. NE 4497: Nuclear System Design II Nuclear Narwhals’ Nuclear Reactor Final Report Submitted by: K. Paaren, M. Jones, G. Jones, B. Adams, J. Rhodes, K. Sponsler, A. Tedeschi, B. Gibson, P. Garavaglia, M. Smith, N. Takcas, S. Rohan Submitted: May 6, 2016 Submitted To: Dr. Joshua Schlegel and Dr. Ayodeji Alajo Senior Design Department of Mining and Nuclear Engineering Missouri University of Science and technology Rolla, Missouri
  • 2. I. Executive Summary NuclearNarwhals’Mobile LeadCooledFastReactorwill provideaGenIV leadcooledfastreactorto any coastal country,city,or province,whowouldwantasteadyandstable supplyof nuclearenergy offshore.Thisis importantbecause developingcitiesneedpowertoexpandwithoutthe needforusing any land.The size of the reactor will be 1000 MWt and 400 MWe assuminga forty percentefficiency[1]. It will be composedof atwo-loopsystem.The primaryloopwill be the liquidlead-bismutheutecticpool and the secondaryloopwill be supercritical carbondioxide.Inthe secondaryloop,heatenergywill be transferredoutof the systemto a watertreatmentfacilityaboardthe vesselafterexitingthe turbine. The excessenergyafterthe desalinationplantwillbe dissipatedintothe ocean.Eachshipwill be usedto provide portable,stablepowertogrowingcoastal areasalongwithbeingable tohelpwithrebuilding coastal areas where natural disastershave takenplace. Major changeshave beenmade to the designand final calculationshave beenmade.The majorchanges to the designinclude changingthe layoutof the reactorcore for a betterburnupandlongerfuel lifetime,andthe natural convectionflow will be pumpassisted.These changeswere made because it will have apositive impactonthe lifetime,heattransfer,andefficiencyof the entire system. Calculationsthathave beenmade thusfarinclude DisplacementsPerAtom(DPA) forall materialsinthe primarypool usingSRIM, conceptsrelatingtoreactorphysics,andtemperaturesandstatesof the secondaryside.Modeling wasdone forthe reactor core’scritical fuel lattice andassemblyusingSTAR- CCM + and for radiationshieldingusingMCNP.Reactorphysicsconceptsinclude the size of the core,the keff of the finite core withandwithoutcontrol rods,criticalitydue topromptneutrons,control rod worths,andthe burnup forthe reactorcore.
  • 3. Table of Contents I. Executive Summary..........................................................................................................................2 II. List of Figures..................................................................................................................................5 III. Introduction ..................................................................................................................................6 IV. Conceptual Design and Description.................................................................................................9 1 Licensability .............................................................................................................................15 1.1 Reactor Design Considerations ...........................................................................................15 1.2 Radiation Safety.................................................................................................................17 1.3 Accident Scenarios and Safety Analysis ...............................................................................18 1.4 Structural Integrity.............................................................................................................19 1.5 Emergency Planning...........................................................................................................19 2 Economic Analysis ....................................................................................................................21 2.1 Capital Cost.......................................................................................................................21 2.1.1 Fuel Cost....................................................................................................................21 2.1.2 Raw Materials ............................................................................................................22 2.1.3 Major Components.....................................................................................................22 2.1.4 ShipAnalysis ..............................................................................................................23 2.2 Reoccurring Cost................................................................................................................25 2.3 Personnel and Operations Cost...........................................................................................27 2.4 Revenue............................................................................................................................29 3 Technical Feasibility..................................................................................................................31 3.1 Criticality...........................................................................................................................31 3.2 Radiation Transport...........................................................................................................35 3.2.1 Reactor Pool Modeling................................................................................................35
  • 4. 3.2.2 Polonium Off-gas system.............................................................................................40 3.2.3 Spent Fuel Storage......................................................................................................42 3.2.4 Dose Calculations .......................................................................................................42 3.3 Heat Transfer and Fluid Flow..............................................................................................44 3.3.1 Primary Side...............................................................................................................44 3.3.2 Secondary Side...........................................................................................................55 3.3.3 Water Desalination.....................................................................................................59 3.4 Materials...........................................................................................................................61 3.4.1 ShipAnalysis ..............................................................................................................61 3.4.2 DPA Considerations ....................................................................................................62 3.4.3 Corrosion...................................................................................................................62 3.4.4 Support Structure.......................................................................................................64 4 Humanitarian Benefit and Environmental Impact .......................................................................67 4.1 Nonproliferation................................................................................................................67 4.2 Pollution............................................................................................................................68 4.3 Public Concern and Safety..................................................................................................70 4.4 Water Desalination............................................................................................................71 4.5 Mobility ............................................................................................................................72 V. Conclusions..............................................................................................................................74 VI. References..............................................................................................................................75 VII. Appendix..............................................................................................................................79 i. Appendix A: MCNP Input File..................................................................................................79
  • 5. II. List of Figures Figure 2.1.4.1: Handymax Hull Layout [37] .........................................................................................24 Figure 2.1.4.2: Handymax Hull TopView[37] .....................................................................................24 Figure 2.1.4.3: Cargo Hatch Diagram [37] ...........................................................................................25 Figure 2.1.4.1: Staffing and Employment Time Scheduling...................................................................28 Figure 3.2.1.1: Initial Sketch of Pool Lid..............................................................................................36 Figure 3.2.1.2: Extrusion of "Lip" of Lid with Off Gas System Hole........................................................37 Figure 3.2.1.3: Extrusion of the Pool Wall...........................................................................................38 Figure 3.2.1.4: Displacement of the Lid by Gravity ..............................................................................39 Figure 3.2.1.5: Displacement of the Lid by Gravity and 200 Lb Person..................................................39 Figure 3.3.2.1.3: Cross Section of Critical Fuel Pin...............................................................................49 Figure 3.3.2.1.4: Critical Fuel Pin Outlet Temperature.........................................................................49 Figure 3.3.2.1.5: Critical Fuel Pin OutletVelocity.................................................................................50 Figure 3.3.2.16: Critical Fuel Pin Inlet Temperature.............................................................................50 Figure 3.3.2.1.7: Critical Fuel Pin InletVelocity ...................................................................................51 Figure 3.3.2.1: Secondary Cycle Layout ..............................................................................................56 Figure 3.3.2.2: Secondary Cycle States ...............................................................................................56 Figure 3.3.2.3: Secondary Cycle State Diagram ...................................................................................57 Figure 3.4.4.1: Support Structure.......................................................................................................64 Figure 3.4.4.2: Safety Factor of Support Structure...............................................................................65 Figure 3.4.4.3: Minimum Factor of Safety...........................................................................................66 Figure 3.4.4.4: Support Structure Displacement (mm).........................................................................67
  • 6. III. Introduction Whenthe opportunitycame todecide how to implementareactor,the distributionroute wasthe main choice.NuclearNarwhals’MobileLeadCooledFastreactorwasimplementedtospreadnuclear poweredenergyacrossthe globe togrowingcoastal citiesandprovinces.Itcanalsobe usedfor assisting the humanrelief effortindevelopingcountriesorplacesaffectedbynatural disasters.There have been manygrowingcitiesandcountriesthathave physicallyrunoutof room, and theirenergydemandsare not beingmet.One place thathas notbeentakenintoconsiderationisbuildingontopof the water.This will allowcitiestoexpandwithoutusingupvaluable land.Onthe opposite endof the spectrumare cities and countriesplaguedbynatural disastersthatneedhelprebuilding.Havingaportable reactorsystem will significantlyhelpshortenthe amountof time forthe rebuildingprocess.Thisisimportantbecauseit isofferingcleanenergyaroundthe world.Itisadvancingthe nuclearindustrybyhavingnuclearreactor plantsable tomove on oceans,ratherthan beingconfinedtothe same areaof landtheywere builton. The reactor systemswill be builtonsite inthe USA to ensure qualitycontrol,andthenexportedto coastal countriesthatneedthem.Thisis creatinga new global view onnuclearenergyandpushingthe industry’sprogressforward. The portable reactorsystemwill provide power andcleanwatertogrowingcitiesorplacesthat are underdevelopedorinneedof rebuildingafternatural disasters. The reactorsystemisdesignedto produce maximumpowerinthe mostefficientwayatthe lowestpossible cost.The goal isto provide enoughenergyata reasonable investmentcost.The systemwill make itsmoneybackaftera period aroundtwenty-one yearsassuming$0.1 perkWh.Ideally,all internationallawsare beingaddressedand takenintoconsiderationwhensellingandtransportingthe portable reactorsystem.The idealgoal isto have one kilowatt-hourcosttencentsto produce afterstartupand initial investmentcostsare taken intoconsideration.
  • 7. These benefitswillcontributetothe purpose of the designbybringingacompact reactorto people in developingcountries,areassufferingfromnatural disasters,andgrowingnationsorcities.The system accomplishesthisbybuildingareactoroff the shore,thenrunningpowerlinestothe mainland.The systemisdriventothe location,andthenanchored inlike anoilrig.Itwill remaininthatlocationforthe life cycle of the plantthenwill be movedafteritslife cycle isover.Afteritisdriven off site,itcanthen be storedin a containment zone where radiationlevelsmay decrease until theyreachbackground. In the nuclearindustrytoday,the currentstate-of-the-artare GenIV nuclearreactors[2]. The Gen IV reactorsinclude the VeryHighTemperature Reactor(VHTR),Gas-cooledFastReactor(GFR), Supercritical-Water-cooledReactor(SCWR),Sodium-cooledFastReactor(SFR),Lead-cooledFastReactor (LFR),and the MoltenSaltReactor (MSR).These reactorsall focuson simplifyingthe design,improving passive safetysystems,andgeneratinghighertemperaturestoreacha higherefficiency.Outof the six, the one most similartothe designinthisreportisthe LFR. The LFR isdesignedtohave passive decay heatremoval andto have a closedfuel cycle.Italsohasnatural convectiontocool the core alongwith beingproliferationresistantandhasa safe economical design.The Narwhals’leadcooledfastreactor has similarfeatures,butalsoincorporatesotherbenefitsthe currentGenIV LFR doesnot,such as a desalinationplant. The main difference separatingthe twoisthe Narwhals’reactorwill be apool reactor.Most LFRs being designed are muchlike aPWR,where there isno large pool of coolant.Thislarge pool helpswiththe heattransferinthe primarypool andallowsthe reactorto dumpheat whenshuttingdown.The Narwhals’reactoremployspassive safetysystemssuchashavingavacuum outside of the primarypool wall to helpcontainthe heatinside the reactorpool andhavingthe core relyon natural convectionfor
  • 8. cooling.Bothhelpwithkeepingthe heatinsidethe reactorpool andutilizingitinpowerconversion withoutthe need forpumpsonthe primaryside upto 200 MWt. On the secondaryside of the system withinthe powerloop,there isadesalinationplanttouse the excessheatfromthe systemtoproduce cleanwater.Thisis beneficial because itproducescleanwaterwhile increasingthe difference in temperature onthe secondaryside,improvingsystemefficiency.The secondaryside willbe composed of supercritical CO2.Thiswillallow the secondaryside tohave agreaterchange in temperature while maintainingaverysmall size relative toaRankine cycle.The overall size of the designisfairlysmall, operatingaround5 m3 [3].
  • 9. IV. Conceptual Design and Description The portable reactorsystemhas twoloops,the primaryloopbeingthe pool of liquidlead-bismuth. Withinthe primarypool,the reactorcore containscontrol rodsand fuel rodsconsistingof 19.75 percent enrichedalphauraniummetal [4].Aroundthe core, there will be fourheatexchangerstoextractheat energyandtransferitto the secondaryloop.These heatexchangeswill be made of 316 stainlesssteel. The heat exchangerswillbe inacircular array aroundthe edge of the pool wall tohelpwithnatural convectionflowthatwill be circulatingthroughoutthe entirepool.Pipeswill helpgetthe hotLBE from the core to the heatexchangersformaximumheattransfer.Outsidethe pool wall,avacuumedout space helpstominimize heattransferandtoserve asa passive safetysystembybeingable tofloodwith waterto decrease shutdowntime. Above the primarypool,thermoelectricgeneratorsrelyonthe excessheatcomingoff the reactorpool. Thiswouldboostthe overall systemefficiencyanduse the energyproducedtoheatthe primarypool wall.Thiswill helpthe coolantmeltif the reactorwere toshutdown[5].The electricityfromthe thermoelectricgeneratorsmay be usedtosupplyenergytothe shipaswell.
  • 10. The secondaryloopconsistsof a supercritical carbondioxideBraytoncycle thatwill take heatenergyout of the primarycoolantpool byforced convection [6].Whenthe CO2 leaves the heatexchanger,itwill be Figure IV: Primary Pool Reactor Pool Color Coding Control Rods Reactor Core Core Support FlowGuide Heat Exchanger InertGas – (Above the liquidlead) Reactor Pool Wall ShieldingMaterials
  • 11. a supercritical fluidandfedintothe turbine [3]. The CO2 will thenrotate the turbine togenerate electricity, andthenthe CO2 will leave the turbinetobe passedthrougha desalinationplantwherethe waste heatenergywill be dumped[7].The desalinationplanttakesthe excess heatenergyfromthe CO2 and usesitto boil saltwaterto freshwater.The CO2 iscompressedthenpumpedback tothe mainheat exchangersinthe primarypool where the cycle will beginagain[8].There are four heatexchangers and twocompressorsinthe powerproducingside of the system.Theyare neededtobettertransferheat and to make the systemmore efficient.The excessheatfromthe desalinationplantwillbe transferred to the ocean. The temperature of the reactorpool will be operatingbetween150Β°C and 650Β° C. Thiswill cause creep, fatigue,andswellingof mostmetalsif placedinthese temperatures.Pressure exertedfromthe coolant on the interiorpool wall fromthe weightof the coolantisthe onlypressure concern.Since thisisafast neutronreactor,highradiationdamage inside the reactorcore andpool isexpected[9].HT9 has been chosenforthe material inthe core,as itis resistanttoradiationdamage [10].The lead-bismuthcoolant will alsobecome highlyradioactive,asitisnaturallyflowingthroughthe core.The radiationproducedby the reactor will contribute toadose rate outside of the pool.The coolantandpool wall will needto shieldradiationenoughtoallow workerstobe inthe containmentvessel all yearandnotexceedadose of five rem.Lead-bismuthwill domostof the shieldingasithas a highdensity[11].Corrosionthatwill occur is mostlydue tofluidflowof the lead-bismuthcoolant.All the materialshave factorsof safetyof 2.5 or 3.5 to insure minimumfatigue,creep,andelongation. The fuel will be alphauraniummetal cylindersenrichedto19.75 percent,andthe flux profilewas generatedinMCNP[13]. Alphauraniumwaschosen due toits thermal conductivityproperties,easy machinability,andmaintainsphase structure [13].There isconcernwith flatteningthe fluxprofile,so
  • 12. burnable poisonsare used.Itisunknownhow the poisonswill reactina lead-bismutheutectic[14]. Reactivitycoefficients wereaddressedbecausesafetywas the mainconcern andtheyaffectcriticality. The reactor was designedtokeepall of these coefficientsnegative.Online refueling wascomparedto the CANDU reactor,but the reactor systembeingdesignedhasthe control rodsrunningverticallyinthe core [4].Multiple ideas were consideredonhow to supportthe possible refueling,butendedupbeing not feasible[15].The core geometry isa hexagonal lattice putinahexagonal array[16]. Radiationsafety andshieldingisahuge concernina nuclearreactorsystem[17].Since thissystemis beingtransportedacrossthe ocean,manydifferentthreats weretakenintoconsideration.Firstisthe securityof the mobile LFRawayat seaand wheninport. Havingan escort to accompanythe system alongwithplacingarmedguardsat entrances isbeingimplemented[18].Natural disasters,sinking, and terrorismare lookedatas worst case scenariosandare currentlyindiscussiononhow tobe dealtwith inthe reactorsystem[19] [20] [21]. Meltdown,lossof coolant,total powerfailure,control rodfailure, vacuumfailure,andleaksinthe reactorpool are designconcerns.Since the reactorsystemis liquid metal cooled, eachaccidentscenarioishandled isspecifictothissystem[22].Materialsand componentsinthe reactorare shielded tomaintainminimumdose requirements [14].Placementof detectorsishard to decide onbecause the reactorsystemneedstobe monitored atall times,butwhen isenoughdetectorsenough;thisisforemployeesandinside the reactorpool.Detectorsinthe pool are ina circulararray betweenthe heatexchangersandthe reactorcore. The reactor system isdesignedto keepexposure low,even duringextreme situations;ALARA will alwaysbe practiced. The goal forthis reactorsystemis to make it as efficientaspossible,whichpertainsprimarilytohowthe overall reactorsystemisdesigned,andhow heatandenergyistransferredinit.The heatfrom the reactor istransferredtothe liquidlead-bismutheutectic,thentoheatexchangers.The layoutof the
  • 13. heatexchangersisa circulararray around the pool.The numberof heatexchangersneededonthe secondaryside isfour,witheachof them transferring380 MWt of heat energyaway.Thisandthe natural convectioncalculationsdeterminedhow strongandfastthe natural convective andforcedflow will be movingthroughthe reactorcore [23] [24] [25]. The speedat whichthe secondarygasispumped throughwill alsoplaya role inthe rate at whichheatleavesthe system.The speedatwhichthe fluid flowsalsoaffectsthe amountof force createdbythe momentumof the fluidandthe numberof oscillationsitwill create.Partof the secondloop’s energywill be transferredtoadesalinationplantto boil saltwater[26]. The amount of energyrequiredfordesalination wasdeterminedandassessedfor the quantitywantedforpurification.Afterthe twoloops,the amountof leftoverheatenergy was determinedand maybe transferredintothe oceanwithoutcausingharmto the environment[8]. Economicsplaya huge role inany product,especiallyinthe nuclearindustrybecause the investment requiredfora reactorpowerfacilityisinthe billions.Costforupkeepandmaintenance wasdetermined alongwithcorrosioncostsversusmaterial costs, cleaningof the ship,andthe upkeepof the crew.The wage of the workers,costof the shipitself [27],andall otherexpensesare includedinthe costs to determine the returnoninvestment.Where tosell thissystemisabigfactoras energydemandsof largercitiesare greaterthan energydemandsof thirdworldcountries;biggercitiesleadtogreater profits[28]. Social and regulatoryissuesdealwiththe publicimage andtie inwithradiationshieldingandprotection. If the reactorsystemand ship were toroll overand flip,the effectsinside the reactorpool are unknown but are assumed that the reactor core wouldbe exposeddue tothe lead-bismuthcoolantspillingover the sidesof the reactor pool.If the coolantcontaminatesthe seawater,thisisaconcernfor the environmentbecause of the radioactivityof the coolant,and leadmaybe absorbedintoliving
  • 14. organisms.Itisunsure howto extractthe coolantfromsaltwater if it doesnot solidifyinlarge clumps. The radioactivityof waterdue to the coolantalsohas to be below the DACinwaterset bythe International Committee of Radiological Protection[29].Safeguardandnon-proliferationconcerns are addressedaswell tokeepthe general publicsafe.Whowill staff the mobile LFRisa bigconcernas their backgroundand intentisnotas well known asradiationsafetyworkersinthe UnitedStates.
  • 15. 1 Licensability 1.1 Reactor Design Considerations The most importantpart of a nuclearpowerplantisthe reactorcore, andseveral considerations must be made for thisdesign.Thisinvolvessignificantuse of MCNPcalculationsforcriticalitypurposes. Section3.1 focusesonthose calculationsindetail. Thiscore isbeingdesignedforamaximumthermal powerof 1000 megawatts(MWt).The core of this reactor ismade up of 90 fuel assembliesarrangedinahexagonal lattice.Eachassemblyhas217 fuel pins arrangedin theirownhexagonal lattice,andare 5.5 cm on eachside.The fuel pinsare 0.2 cm inradius, and are made of metallicuranium.The claddingismade of HT9 and is0.05 cm thick,withaninnerradius of 0.24 cm and an outerradiusof 0.29 cm. The fuel pinitself is1.5m tall,while the claddingis3m tall. Surroundingthe fuel pinwithinthe claddingisleadbismuthcoolant,andacompressibleheliumplenum. The core has 31 control rods made of 1 cm thick gadoliniumwithaB10 carbide interiortoensure effectiveabsorption atfastneutronenergiesaswell asforlower neutron energies.Eachof these control rods hasa total radiusof 3.5 cm. The core isapproximately1.4m in diameter,allowingforcompact designthatcan be easilytransportedacrossthe world. For the fuel,the metallicuraniumhasanenrichmentof 19.75% byweightof U235 .This enrichmentwas choseninorderto maximize the amountof fissile material inthe core withoutmakingthe core largeror goingto high-enricheduranium.Alloyingthe fuel with anothermaterialwasconsidered; zirconiumat 10% byweightbeingthe mostlikelycandidate due tohavingdesirablematerialpropertiessuchasa highermeltingtemperature.Thiswasrejectedinordertokeepthe amountof fissilematerialthe same withoutincreasingenrichmentorexpandingthe core.InMCNP,addingthe zirconiumdecreasedthe
  • 16. amountof fissilematerial inthe core tothe pointsuchthat in orderto maintainthe desiredfuel cycle length,eitherthe uraniumwouldhave tobe highlyenriched,orthe core wouldhave tobe expanded. Both optionswere undesirable because of proliferationconcerns,andthe core size neededtobe as small as possible fortransportation. At the givenenrichment,the maximumKeff the core can achieve is1.16074 inMCNP. That value then allowsforan excessreactivityvalue of 13.84% Ξ”k/k.Thisvalue as well asthe enrichmentmustbe consideredforlicensingtodetermine the safetyof the reactorand whatregulationswill apply.By findingthe Keff usingonly promptneutrons,the Ξ²eff was calculated,whichhasa value of 0.44% Ξ”k/k.The burnupwas calculated inMNCPforthis enrichment,whichalsogivesthe fuellifetime.The core may last about1.5 yearsbefore becomingsubcritical.Thisisthe time spaninwhichroughlyhalf orthe fissile material inthe core is usedup.In the future,thismaybe improved upon. The control rodshave beenplacedintofive groupsbasedondistance fromthe core.Group1 consistsof the centercontrol rod, witha reactivityworthof 2.34% Ξ”k/k. Thisisthe highestrodworthinthe core. The nextsix rodsare two lattice spacesawayandare group 2. These eachhave a reactivityworthof 2.11% Ξ”k/k.Group 3 has six rodsas well,andare locatedoutside of group2, offsetby60 degrees.Each rod has a reactivityworthof 1.68% Ξ”k/k. The rods ingroup 4 are roughlythe same distance fromthe core as group3, butare offsetby60 degreesfromgroup3, placingthemslightlyfurtherfromthe center.Each of these rodshasa reactivityworthof 1.47% Ξ”k/k.The group5 rods are the furthestout, and consistof 12 rods placedinpairs. Each of these rodshas a reactivityworthof 1.03% Ξ”k/k. By adding all of these rodworthvaluestogetherfromeveryrodinthe core,the total rod worth is foundto be 46.4% Ξ”k/k.By subtractingthe excessreactivityandthe reactivityworthof the centerrod,the shutdownmarginwas foundtobe 30.2% Ξ”k/k.
  • 17. One concernin relationtothe control rods isthat the reactivityworthmaybe too highinorder to make finerpoweradjustments.Eventhe slightestmovementsof the rodsmaycause the core to have too small of a period,whichhasbeenchosentonot exceed80secondsforstandard powerincreases.An alternative design forcontrol rods consistsof solidgadolinium of the same dimensions.However,the reactivityeffectsonthe core withthese rodsstill requiresstudyatthistime. 1.2 Radiation Safety Nuclearreactorsmust properlyshieldradiationfromthe peoplewhoworkatthe powerplant.Licensing a nuclearreactor requiresthatworkersandthe environmentwillnotreceive aharmful dose.The NRC published10CFR 20 to regulate anylicensee sothat radiationdoesnotexceedthe standardsforsafety [1].The publicmayonlyreceive adose of 0.1 remper year from radiationemittedfroma powerplant. Furthermore,the dose islimitedto0.002 remin anyone hour. For a plantworker,the total effective dose isallowedtobe five remperyear.The reactor must properly shieldradiation suchthatthese conditionsare metwhile beingable tomonitorthe reactoronsite [1]. The reactor systemmustalsomeetcriteriaforradiationexposure tothe environment.Forthisseafaring design,the surroundingenvironmentisthe ocean.There are at thistime nolimitstothe amount of radiationthatcan be transfered intothe ocean.However,itisunlikely thatpublicopinionwill supporta reactor designthatpollutesthe oceanwithradiation.Fromalicensingviewpoint,there isnolimitation. The limitof radiationreleasedintothe environmentwillbe determinedbythe distance fromshore and local regulationsregardingradiationsafety.
  • 18. 1.3 Accident Scenarios and SafetyAnalysis A nuclearreactor’sresponse toaccidentscenarioswillbe consideredwhenapplyingforanoperating license.The worstcase scenariosforanyreactor wouldinclude afuel meltdownandalossof coolant.In a liquidcooledreactor,there are twoprimarythermal considerationsforthe core.The liquidcoolant mustnot boil andthe fuel centerlinetemperature shouldnotreachthe fuel meltingtemperature.To preventanaccidentfromoccurring,the harshestconditionsmustbe met.Inthe core, the hottestfuel elementmustnotfail.If the fuel elementexposedthe harshestconditionsisnotexpectedtofail,it reasonsthat nootherfuel elementshouldfail. The fuel centerlinetemperature isthe hottesttemperature inthe reactor.The fuel centerline isthe first place where the fuel willmelt.Toensure thatthe fuel centerlinetemperature doesnotreachthe fuel meltingtemperature,ahot-channelanalysiswas performed.Inthe hot-channel analysis,the hottest fuel elementwasdeterminedfromthe flux profile.The flux ishigherwhere the mostfissionevents occur. More fissioneventscause more heattobe produced,whichinturn generatesahigher temperature.The volumetricheatgenerationandcenterline temperature are the assumedconditions for the hot-channel analysis. For safetyandproperfunction,aliquidcooledreactor’scoolantcannotchange phase.If the coolant shouldchange fromliquidphase tothe gaseousphase,there wouldbe adramaticreductioninheat transferfromthe fuel.The gaseousphase of LBE doesnot conductheatas well asthe liquidphase.A gaseouscoolantwouldcause agreaterincrease infuel temperature andcouldresultinameltdown scenario.Therefore,ahot-channel analysisisperformedfor the coolanttoverifythatthe coolant will not boil.If the coolantinthe hottestchannel doesnotboil, thenthe coolantinall the otherchannels will be belowboilingaswell.
  • 19. Evenwiththe precautionsdescribedabove,itisnecessarytounderstandthe reactor’sresponse toan accidentscenario.Inthe eventof a complete meltdown,the fuel will mix withthe coolant.Mixingthe fuel andcoolantwill decrease the criticalityof the reactor.Ina complete meltdown,the reactorshould become subcritical.The dispersionof fuel will greatlydecrease the numberof neutronscreatingnew fissionevents.Atthispointinthe project,the analysisof accidentscenarioshasbeentheoretical.The previousdescriptionsare whatisexpectedtooccur inan accidentscenario. 1.4 StructuralIntegrity The supportstructure for the core mustwithstandthe stressplacedonitfrom the core. Metals tendto become weakerwhenheated.The elevatedtemperature thatthe reactorproduces inthe reactor pool will affectthe supportstructure design.The maximumservice temperatureof SS316 is 750Β° C [2].Since the highesttemperature we expecttosee in the core is650Β° C, thisshouldnotbe an issue.Usinga yield strengthof 170 MPa and a safetyfactor of 3, tensupportcolumnsof radius10 cm will supportthe core. The baseplate will alsoneedtobe analyzed similarlytoestablishitsstructural integrityatelevated temperatures. However,because itisconstructedfrom516 Gr 70 stainlesssteel,the standardfor reactorsof thistype,itis assumedthatthe material will meet the structural requirements [3]. 1.5 Emergency Planning Accidentresponse andemergencyplanning isakeyaspectof maintainingalicense tooperate forthe mobile LFR.A fewlogisticconsiderationswere made toensure the designiseffective andmaintains a highlevel of securityandsafety.Some of these considerations were made toaccommodate severe
  • 20. weather,releaseof radioactive material,andfacilitydefensive measures.Instancesof severe weather will be dealtwithinafewwaysdependingonthe event. A ten-mileevacuationzone hasbeendeemednecessaryduringanysevere weatherevent,whichisfive timesgreaterthanwhat the NRCregulatesforemergency evacuationzones [4].Thisistoensure the safetyof anyone inthe vicinityfromapossible release of radiation.Hurricanesandmajorstormswill warrant a plantshutdowntoensure the safetyof the surroundingareas.Thisshutdownwill be basedon a report froma local weatheragencythatthe mobile LFRsystemresides in.The shutdown will begin well before the stormapproaches.Lightningwill be verycommonduringthesetypesof stormsandthe vessel willbe equippedwithsurge arrestersandalightningrod/groundingsystemtopreventdamage to electroniccomponents. Inthe eventof atsunami,the plantcan be simplymovedinhopesof avoiding the wave.The needtoactuallymove the mobile LFRsystemdue toa tsunami isdrasticallyreducedthe fartherthe systemisplacedawayfrom shore.The mobile LFRsystemalsohas beendesignedtoprevent the release of anyradioactive materialsintothe environment.Radiationmonitoringsystemswill be in place inboth the primaryand secondaryloopstoensure noabnormal radiationlevelsarise inthe plant systems. If aneventoccurs inthe plant,guidelinesinplace will aimtoacquire AsLow As Reasonably Achievable(ALARA) doses.Thiswouldincuronlynecessary exposure forreactoroperators.If severe enough,atotal plantshutdown will be initiateduntilapropercleanupcan be arranged. Two otherscenariosthatare accommodatedinthe mobile LFRdesignare the lossof heatexchangers and lossof coolantaccident(LOCA).Asinmanyof the designfeaturesof thisnuclearreactorsystem, a highfactor of safetyhas beenbuilt intoall components.The extractionof heatfromthe reactorpool is no differentandcanbe accomplishedby three heatexchangers.If noheatsinksare available to dissipate heatinthe primaryloop,the pool itself shouldbe able toalleviatethe heat.If secondaryside
  • 21. heattransferfluidislost,the primarycoolantwill be able toabsorbthe excessdecayheatfora marginal time periodduringandafterthe shutdownperioduntil the properrepairscanbe made.Withthe coolantbeinga liquidmetal,itwill solidifyatnormal atmosphericconditions if itleaks.Defensive measuresare neededtoprotectthe mobile LFR,andwill be similartowhatcurrent nuclearpower plantsdo alongwithaddedmeasuresdue tobeingonthe ocean.Exclusionzones cannotbe enforced witha fence,sopatrol boats are usedinstead.Securitystaff will be presentonthe vessel toprotectit fromexternal threats. 2 Economic Analysis 2.1 Capital Cost 2.1.1 Fuel Cost To determine the capital costof the fuel fabricationforthe project, manyfactorsmustbe considered otherthan the price of the raw U3O8,such as the cost of conversiontoUF6,the furtherenrichmentto 19.75% U235 , and the price of fabricating intothe final shape.Raw U3O8 can be purchasedfor $97 per kg, and thenbe convertedtoUF6 for $16 per kg [5].Calculationsusingthe price perSWU andcurrent costs for UF6 have beenusedtofindthe cheapesttailstoenrichthe uraniumto19.75%. This wasdone calculatingthe massof feedperkg of product neededfordifferentvaluesof Xt usingEquation 2.1.1.1. M𝑓 = ( X 𝑝 βˆ’ X 𝑑 X 𝑓 βˆ’ X 𝑑 ) 2.1.1.1 The SWU was thencalculatedwithEquation 2.1.1.2[6]. SWU = M 𝑝(VX 𝑝 βˆ’ VX 𝑑 ) βˆ’ M𝑓VX 𝑓 2.1.1.2 It isfoundthat the cheapesttailsis 0.185%, and the cheapestprice of fuel before fabricationis approximately$6758. The total price is foundbyaddingthe cost of the raw uranium, the costof conversion,the price of enrichment,andthe costof fuel fabrication,whichisfoundtobe approxi mately
  • 22. $7058/kg of 19.75% enrichedU235 .These calculationswere preformedtogive anestimationwhen purchasing19.75% enriched U235 .The total amountof fuel neededtorunthe reactor is 7031 kg. With the fuel costing$7058/kg, an entire fuel cycle’s worthof fuel wouldcost $4,962,715. 2.1.2 Raw Materials Many materialswill significantlyaddtothe cost of the reactor system.The price of these materialswill directlyaffectthe capital costof the reactor. Equation2.1.2.1 showsthe methodusedto obtainthe total cost. πΆπ‘œπ‘ π‘‘ = ( π‘ƒπ‘Ÿπ‘–π‘π‘’ π‘π‘’π‘Ÿ π‘˜π‘–π‘™π‘œπ‘”π‘Ÿπ‘Žπ‘š) βˆ— (πΈπ‘ π‘‘π‘–π‘šπ‘Žπ‘‘π‘’π‘‘ π‘€π‘Žπ‘ π‘  𝑛𝑒𝑒𝑑𝑒𝑑) 2.1.2.1 HT9 is$5.00 per kg and2716 kg are required;thismaterial costs$13,580 [5]. The price for 316L SSis $2.47 perkg, of whichwe will need30 millionkgforatotal cost of $74,100,000 [5].Productionof the steel increasesthe price byroughly53%. LBE costs $10.81 per kgand 14.8 millionkgisrequiredtofill the pool [7] [8].This meansthatthe LBE usedcosts $160 million.The baseplate,made of SS516 G70 costs $0.80 per kg, and with1000 kg needed, the total forthismaterial comesto $800 [5]. Manufacturingof thismaterial increasesthe price to $0.85 per kg, makingthe total $850. Gadoliniumis the control rod material andcosts $55 per kg [33]. 6920 kg of it are neededandthe total cost is $381,000 for Gadolinium.Productionof eachrodisestimatedtobe $1350. Approximately$234.5 millionforrawmaterialsisneededtofabricate the components tobuildthe reactor. 2.1.3 Major Components The cost of the turbines,generators,andothermajorcomponentsare alarge part of the overall project cost.
  • 23. Table 2.1.3.1: MW Output and Cost Shaft Output Average MW Cost 300.00 $214,688,425.30 400.00 $280,721,772.70 500.00 $345,966,649.02 600.00 $410,616,682.52 700.00 $474,793,116.05 Global Energyand InfinityTurbineLLCprovidedthe informationonthe price of theirsupercritical CO2 turbines. Theirapplicationswereforlow powerbetween50kilowattsand2 megawatts. Extrapolating theirnumbers,alongwiththe expectedefficiencyof secondaryside, the estimateforaturbine is between$2.8millionto$4.1 million. 2.1.4 Ship Analysis Whenselectingthe ship,earlycalculationsfoundthatitwouldneed toholdatleast14,000 tonnes. Addingthe additional weightof the staff,fuel,waterballasts,heat exchangers,turbines, electromagneticpumps,andpiping,the weightthe shipis requiredto supportisapproximately29,000 tonnes.Withthis weightrequirement,the Ultramax bulkcarrieristhe bestshiptodesignwith. The ship is200 m long,32 m wide, hasa 13 m draft,and the deadweighttonnage (DWT) of the shipis63,000 tonnes[37]. This allowsforanavailable capacityof approximately34,000 tonnes. Shipsinthisclassbuilt around2012 cost $30 to $35 millionnew [38].Currentpricesfora new vessel were notgivenfromthe manufacturer. Accountingforinflation,these shipstodaycouldcost $32 to $37 million. The variationin price isin partlydue to loadcapacity as well as gearequippedonthe ship.β€œGeared”shipsare vessels, whichhave cranesabove eachcargo hatch to loadand unloadsupplies.Thisisanoptional feature thatis alreadyfiguredintosome of the pricesforthese ships.If all of the cranesequippedare not deemed
  • 24. necessary,theycanbe removedfromthe buildsheetreducingthe overall costof the ship. Figures 2.1.4.1 and 2.1.4.2 showsome genericdiagramsof an Ultramax dry bulkcarrier. Figure 2.1.4.1: Handymax Hull Layout [9] Figure 2.1.4.2: Handymax Hull Top View [9] In Figure 2.1.4.2, fourindividual cargobinscanbe seen.Typical shipshave fourtofive separate cargo bins,a double reinforcedfloor,anda crane above each hatch.The cargo hatchesare all automatedand are operatedbyexternallymountedhydrauliccylinders.A diagramof thissystemisshowninFigure 2.1.4.3 [37].
  • 25. Figure 2.1.4.3: Cargo Hatch Diagram [9] Withthe planto modifyapre-builtship,there will needtobe manymodifications.Thisincludes structuresto holdadded components,piping toconnectmajorcomponents,addedshieldingtoprotect workers,andany otherneededsystems. Estimatingthe costof modifyingthe shipisverydifficult withouthavinganexactplan,and couldvaryfrom a few milliondollarstomore thanthe original costof the ship. 2.2 Reoccurring Cost Refuelingthe reactorisone of the majorrecurringcosts inthe mobile LFR.Accordingtothe burnup calculationsdone inMCNP,the reactorfuel hasa lifetime of only18months.Thismeansthat every18 months,the reactorhas to be shutdownand the fuel mustbe replaced.Whenthe reactorrefuels,7031
  • 26. kg of fuel mustbe purchasedeachtime at $7058/kg, costing$4,962,715 infuel alone. Othermaterials associatedwithanoutage are the cladding,fuel,andgapmaterial.Total costsassociatedhere are $1,297,692.65 at currentmaterial prices,notincludingthe costtomanufacture the core to specified dimensions.Thisisthe costto replace the entire core asa solidpiece.Inaddition,the supporting structure of the core will have tobe re-examinedwitheachcycle.Thiswill added50% to the total refuelingcostandshouldonlyoccur once everyfifteenyears. In the reactor pool,316 stainlesssteel mustbe removedbecause of the severecorrosionitexperiences while incontactwithLBE. By replacingthismaterial withT-91martensiticsteel,we willexperience a longerlifetime. Equation 2.2.1 describeshow the oxide scale thicknessonthe T-91 pipingwill develop overtime as a functionof temperature. 𝛿( 𝑑, 𝑇) = (βˆ’0.98 + (2.54 Γ— 10βˆ’3) βˆ— 𝑇) βˆ— √ 𝑑 2.2.1 𝛿( 𝑑, 𝑇) = π‘œπ‘₯𝑖𝑑𝑒 π‘ π‘π‘Žπ‘™π‘’ π‘‘β„Žπ‘–π‘π‘˜π‘›π‘’π‘ π‘  (πœ‡π‘š) 𝑑 = π‘‘π‘–π‘šπ‘’(β„Žπ‘œπ‘’π‘Ÿπ‘ ) 𝑇 = π‘‘π‘’π‘šπ‘π‘’π‘Ÿπ‘Žπ‘‘π‘’π‘Ÿπ‘’ (℃) [10] Equation2.2.1 isonly ratedfor temperaturesranging from420Β° C to 550Β° C and flow rateslowerthan 2m/s, butgive a goodapproximationof whattoexpect.Overthe course of 3 years,the pipingwill experience ascale growthgreaterthan68 Β΅m. After6 years,thisscale isgreaterthan96 Β΅m and after9 years,the scale will reacha thicknessgreaterthan118 Β΅m. By 15 years,the scale build-uponthe piping will reacha thicknessof 197 Β΅m. It isat thispointthat the heatexchangerswill have tobe removedand replacedtoprovide adequate heattransferfromthe reactorcore.
  • 27. The recurringcost relatingtothe coolantwill be frommaintainingoxygenlevels,flowingacovergas above the reactor pool,andfilteringpoloniumproducedinthe coolant. Thiswillkeepthe oxidationof the coolantto a minimum allowingforitscontinual use. Duringeach outage,the HT9 claddingwill needtobe replaced.There are 90 fuel assembliesinthe core and eachassemblyhas217 fuel pins.Itwas calculatedthateachfuel pincontains0.195 kg of HT9, which meansduringeachoutage there will be 3812.74 kg of HT9 replaced.At$5 perkg, the total cost of HT9 peroutage comesto $19,063.69 [33]. Basedon a presentationfrom OpCost,the costtomaintainthe mobile LFRwouldbe approximately $6,472 per day. There are several waystodeal withthiscost,the easiestbeingtodepositanestimate maintenance amountinafundwithsome interestrate andmake appropriate withdrawalsonasemi- annual basis. The outage cost can increase if there are anyproblemsthatwoulddelaythe process because eachday the reactor isnot makingelectricity,the mobile LFRislosingprofits. 2.3 Personnel and Operations Cost Personnel costscanmake up a significantportionof the recurringcost tokeepa reactor running. Because of the safetyconcernsnuclearreactorscreate,itis importanttokeepthe reactor facilitystaffed at all times.All essential staff wouldwork10 hoursa day on a 5-3, 5-4, 5-3 work schedule [11].This methodof 24/7 staffingrequires5staffedteams, eachof which workfive dayson,thenthree off,then five dayson,thenfouroff,thenfive dayson, thenthree daysoff.The cycle then repeats.Each team averagesa 42 hourwork week.
  • 28. Figure 2.1.41: Staffing and Employment Time Scheduling Essential staff includespeoplesuchassecuritypersonnel,reactoroperators,andseniorreactor operators.Fromthe NRC’sregulationslinedoutin10 CFR50.54, itwas determinedthatthe minimum numberof operatorsnecessaryatall timesfora single operatingreactoristwoseniorreactoroperators and tworeactor operators. [12] Since there isa minimumof 5 teamsof 2 reactor operatorsand2 senior reactor operators,atleast10 reactor operatorsandseniorreactoroperatorswouldhave tobe hired. The average salaryfor a reactor operatoris$65,080, and fora seniorreactoroperatoris$76,020 [11]. Because the employeesare workingshiftwork, abonuspay incentiveof 30% will be added. Payingout benefitsandtaxesnormallycostsacompany1.4 timesthe employee’ssalarytoemploythem.This makesthe cost to hire the bare minimumnumberof operatorsdenotedbythe NRC$2,398,700/year. πΆπ‘œπ‘ π‘‘ = 1.4(10(65080 + 76020)) + .3(10(65080 + 76020)) 2.3.1 Ideally,the numberof securitypersonnel onstaff wouldnominallybe tenatall times. Securityisan importantconcernforthe project because the design istobe implementedinforeignareas.If ten securityguardsworkper team,thena minimumof 50 on site guardswouldneedtobe hired to workthe same 5-3, 5-4, 5-3 work shifts.If each nuclearsecurityofficermakesasalaryof $52,237, thenit would cost approximately$4,231,197/year.
  • 29. 2.4 Revenue The revenue andbreak-evenpointscanbe determinedbytakingthe total costof the projectoverthe projectedtime.Thiscaneasilybe visualizedby equation2.4.1. π΅π‘Ÿπ‘’π‘Žπ‘˜ 𝐸𝑣𝑒𝑛 πΆπ‘œπ‘ π‘‘ ( $ π‘˜π‘Šβ„Ž ) = π‘‡π‘œπ‘‘π‘Žπ‘™ πΆπ‘œπ‘ π‘‘ π‘œπ‘“ π‘ƒπ‘Ÿπ‘œπ‘—π‘’π‘π‘‘ π‘˜π‘Šβ„Ž π‘ƒπ‘Ÿπ‘œπ‘‘π‘’π‘π‘’π‘‘ 2.4.1 To findthe breakevenpointforprice to sell powerintime,equation2.4.2can be used. π΅π‘Ÿπ‘’π‘Žπ‘˜ 𝐸𝑣𝑒𝑛 π‘ƒπ‘œπ‘–π‘›π‘‘ ( π‘¦π‘’π‘Žπ‘Ÿπ‘ ) = π‘‡π‘œπ‘‘π‘Žπ‘™ πΆπ‘œπ‘ π‘‘ π‘œπ‘“ π‘ƒπ‘Ÿπ‘œπ‘—π‘’π‘π‘‘ βˆ— π‘˜π‘Šβ„Ž π‘π‘Ÿπ‘œπ‘‘π‘’π‘π‘’π‘‘ π‘π‘’π‘Ÿ π‘¦π‘’π‘Žπ‘Ÿ πΆπ‘œπ‘ π‘‘ π‘œπ‘“ π‘ƒπ‘œπ‘€π‘’π‘Ÿ 2.4.2 For the mobile LFR,the original break-evencostof powerproductionwascalculatedfor10 years. This was the project’soriginal goal forreturnoninterest.Forthe break-evencost,the total capital costof the projectwas totaledto$998 million,andthe recurringcostsaveragedat$31 million/year,or$310 millionover10years. Powerwouldhave tobe soldat $0.165 perkWh to breakevenin10 years.If poweriscontinuedtobe soldat $0.165 per kWh,the profitmarginafterbreakingevenisapproximately $99million/yearwhichcanbe seeninFigure 2.4.1.
  • 30. Figure 2.4.1: ROI for $0.16 per kWh To calculate the time neededtobreakevensellingpoweratthe $0.10 per kWh,the time to breakeven and start makingprofitis21.1 years.Afterbreakingevenafter21.1 years,the projectwouldbe making approximately$59million/yearinprofit. Figure 2.4.2: ROI for $0.1 per kWh
  • 31. 3 Technical Feasibility 3.1 Criticality For thisdesign,determiningthe technicalfeasibilityfromacriticalitystandpointinvolvedextensiveuse of MCNPwithcollaborationfromthe STARmodel forthe correct temperature outputs.The methodfor designingthe core wasto start witha unitcell andworkoutwardto developthe whole core.A unitcell was developedbasedonthe choice of fuel materials,coolantandcladding,representingasingle fuel pin inFigure 3.1.1. Dark blue representsthe fuelpin,whichisUranium metal enrichedto19.75 percent U235 .The green representsHT9,whichisthe claddingmaterial.The lightblue isthe lead-bismutheutectic.Notice that there isleadbismutheutecticinside the cladding.Thisallowsbetterheattransferbetweenthe fueland the cladding. The claddingthicknessis0.05 cm.Fuel pinis1.5 m tall,while the space inside the cladding is3 m tall.This allowsfora 1.5 m compressible heliumplenum, which allowsforfuel expansiondue to fissionproductbuildupaswell ascatchingfissionproductsshouldtheyfindtheirwayoutof the fuel. These pinsare thengroupedintobundlescalledfuel assemblies.Inside the assemblies,the pinsare Figure 3.1.1: Single Fuel Pin
  • 32. arrangedin a hexagonal lattice withapitchof 0.714 cm.Each assemblycontains217 fuel pins,withthe longestrowcontaining17 pinsform cornerto corner. Figure 3.1.2: Fuel Assembly These assembliesare thenarranged intotheirownhexagonallattice inthe core.However,some of the lattice locationswillinsteadhave control rodsinsteadof fuel assemblies.These control rodsare 3.5 cm inradius and made of gadoliniumcylinders1cm thick.The interiorof each cylinderisthenfilledwith boroncarbide powder.The boronwill be enrichedin B10 .These control rodsare placedingroupsbased on distance fromthe centerof the core, as describedinsection1.1.Inthe followingfigures,the boron carbide isin red,and the gadoliniumisinyellow:
  • 33. Figure 3.1.3: Control Rod Figure 3.1.4: Whole Core In orderto calculate the reactivityworthof eachcontrol rod, the one twelfth symmetryof the core allowedfordeterminingthe rodworth(RW) for everyrodwhile onlyperformingthe MCNPcalculations one rod fromeach of the five groups.The keff of the core was foundwithoutanyrodsinserted:1.16074. Then,by findingthe keff of the core withonlythe rod to be testedinserted,the reactivity(ρ) of that control rod can be foundusingthe followingequation: π‘…π‘Š = 𝜌 π‘Ÿπ‘œπ‘‘ π‘œπ‘’π‘‘ βˆ’ 𝜌 π‘Ÿπ‘œπ‘‘ 𝑖𝑛 3.1.1 However,reactivityiscalculatedfromkeff fromthe followingequation: 𝜌 = π‘˜ 𝑒𝑓𝑓 βˆ’ 1 π‘˜ 𝑒𝑓𝑓 3.1.2 By substitutingequation3.1.2intoequation3.1.1 withthe appropriate keff for eachterm, the following equationemerges: π‘…π‘Š = π‘˜ π‘Ÿπ‘œπ‘‘ π‘œπ‘’π‘‘ βˆ’ 1 π‘˜ π‘Ÿπ‘œπ‘‘ π‘œπ‘’π‘‘ βˆ’ π‘˜ π‘Ÿπ‘œπ‘‘ 𝑖𝑛 βˆ’ 1 π‘˜ π‘Ÿπ‘œπ‘‘ 𝑖𝑛 3.1.3
  • 34. Placingeachtermover the commondenominator(krod out)*(krod in) andthencombininglike termsresults inthe following: π‘…π‘Š = π‘˜ π‘Ÿπ‘œπ‘‘ π‘œπ‘’π‘‘ βˆ’ π‘˜ π‘Ÿπ‘œπ‘‘ 𝑖𝑛 π‘˜ π‘Ÿπ‘œπ‘‘ π‘œπ‘’π‘‘ βˆ— π‘˜ π‘Ÿπ‘œπ‘‘ 𝑖𝑛 3.1.4 Thisequationallowedforcalculatingthe rodworthforeveryrodin the core,givingthe followingtable: Table 3.1.1: Rod Worth of Each Control Rod by Group Rod Group Keff w/ 1 rod in Rod Worth (Ξ”k/k) group1 1.12999 0.023444208 group2 1.13294 0.0211399 group3 1.1385 0.016829329 group4 1.14118 0.014766574 group5 1.14693 0.010373416 no rods 1.16074 As shown,the group1 rod, consistingof the centerrodin the core,is the rod withthe highestrod worth.Multiplyingeachrod worthbythe numberof rodsin the respective groupresultsinfindingthe rod worthof eachrod in the core.The sumof these valuesgivesthe total rodworthinthe core.This allowsforcalculatingshutdownmargin(SDM) usingthe followingequation: 𝑆𝐷𝑀 = π‘…π‘Šπ‘‘π‘œπ‘‘π‘Žπ‘™ βˆ’ π‘…π‘Šmax𝑖𝑛 π‘π‘œπ‘Ÿπ‘’ βˆ’ πœŒπ‘’π‘₯𝑐𝑒𝑠𝑠 3.1.5 Excessreactivity(ρexcess) canbe foundby usingthe maximumkeff (1.16074) andequation3.1.2. That and equation3.1.5 resultinthe followingtable: Table 3.1.2: Total Rod Worth, Excess Reactivity, and Shutdown Margin Total RW (Ξ”k/k) Ξ‘excess (Ξ”k/k) SDM (Ξ”k/k) 0.464340025 0.138480624 0.302415193
  • 35. Witha shutdownmarginof over30% Ξ”k/k, the reactorcan be shutdown easily.However,forcontrol, anotherimportantvalue isthe delayedneutronfractionΞ²eff.Thiscan be calculatedusingthe following equation: 𝛽𝑒𝑓𝑓 = 1 βˆ’ π‘˜ π‘π‘Ÿπ‘œπ‘šπ‘π‘‘ π‘˜ 𝑒𝑓𝑓 3.1.6 For thisequation,kprompt isthe keff calculatedusingonlypromptneutronsinMCNP.Thiscalculation resultsina value of Ξ²eff = 0.44% Ξ”k/k. 3.2 Radiation Transport 3.2.1 Reactor Pool Modeling Once it wasdecidedthatthisdesignwasgoingto be cooledbyLBE, it wasapparentthat a strong, stable pool wouldneedtobe createdthat couldnotonlywithstandthe relativelyhightemperatures,butalso the highradiationdoses of the reactor environment. Assuch,the reactorpool andliddesign incorporatesseveral importantparameters. The pool wall thickness wasfound toensure thatthe hydrostaticpressure fromthe moltenleaddidnotcause fracturingof the pool wall.ByusingEquation 3.2.1.1 and Equation3.2.1.2, the minimumthicknessatthe bottomof the pool (includingafactorof safety of 3.5) was found [13]. π‘ƒπ‘Ÿπ‘’π‘ π‘ π‘’π‘Ÿπ‘’ = πœŒπ‘”β„Ž 3.2.1.1 π‘‡β„Žπ‘–π‘π‘˜π‘›π‘’π‘ π‘  = π‘ƒπ‘Ÿπ‘’π‘ π‘ π‘’π‘Ÿπ‘’ βˆ— π‘Ÿπ‘Žπ‘‘π‘–π‘’π‘  β„Žπ‘œπ‘œπ‘ 𝑦𝑖𝑒𝑙𝑑 π‘ π‘‘π‘Ÿπ‘’π‘ π‘  3.2.1.2 Withan assumedpool radiusof 4.5 m and a depthof 8 m, the minimumthicknessof the pool wall was foundto be 8 cm.
  • 36. Next,the pool andpool lidwere bothmodeledinAutodeskInventor.The pool lidwasmodeledfirstat9 m indiameter.Fourholes, 60.96 cm in diameter, were extrudedfromthe lidtoallow forpipingfrom twoheat exchangers,andtwo15.24 cm holeswere extrudedtoallow forthe off-gassystemforgasified Poloniumremoval.Initially,25holeswithdiametersof 7 cm were extrudedforthe control rods. However,thiswill needtobe updatedforthe new control rodconfigurationobtainedrecently.See Figure 3.3.1.1 forthe initial sketchof the pool lid. Figure 3.2.1.1: Initial Sketch of Pool Lid Afterfinishingthe original9m in diametersketch of the topof the pool lid,a889.71 cm indiameter circle wasinscribedonthe lowersurface.Thiscircle wasthenusedtoextrude a16 cm thickprotrusion on the bottomof the lidinorderto allow the lidto sit atop the pool wall.Figure 3.3.1.2 below showsa close-upof thisprotrusion,aswell asone of the extrudedoff-gassystemholes.
  • 37. Figure 3.2.1.2: Extrusion of "Lip" of Lid with Off Gas System Hole Next,the pool wall wasextruded8m downwardusingthe profileof the protrudingedge of the lidas shownabove inFigure 3.2.2. The cylinderisshowninFigure 3.3.1.3.
  • 38. Figure 3.2.1.3: Extrusion of the Pool Wall To finishthe model,the profile of half of the extrudedpool wasrevolvedaroundthe centerpointof the model.Thisresultedinthe hemisphere shapeof the bottomof the pool,whichensuresthat there is evenpressure alongthe bottom of the pool. Several stressand strainsimulationswere performedon the pool lidpriorto modelingthe restof the pool.Byselectingthe StainlessSteel material forthe lid, parametersforthe strengthand toughnessof the material were automaticallyloadedbyInventor.Two mainsimulationswerecompletedsuccessfully:asingle force of gravitydownwardonthe lid andthe force of gravityplusthe weightof a 200 poundpersonstandinginthe middle of the lid.These simulationsbothresultedinextremelysmall deformationsconsideringthe diameter-to-thicknessratio. Please note thatinFigure 3.2.1.4 and3.2.1.5 that the deformationof eachisnotto scale;the displacement’sscale alongthe lidisshowninthe left-handportionof the figure inmillimeters.
  • 39. Figure 3.2.1.4: Displacement of the Lid by Gravity Figure 3.2.1.5: Displacement of the Lid by Gravity and 200 Lb Person Overall,thismodel will be usedfordisplayandstress analysisof the design.Asthe designevolves,this model will be updatedtoreflectthe mostrecentchangesof the system.
  • 40. 3.2.2 Polonium Off-gas system The lead bismutheutecticcoolantwill be exposedtoaneutronflux.Bi209 thatispresentinthe coolant will absorbneutronstoconvertintoPo210 .Thisconcernsthe safetyof reactorpersonnel because Po210 is an alphaemitter[14].PoloniumcanthenbondwithLead to formLead-Polonide.Mostof these moleculeswill stayinthe eutectic,butwiththe elevatedtemperaturesinthe reactor,some cangasify [15]. Equation3.2.2.1 showsthe methodusedtofindthe absorptionrate. π΄π‘π‘ π‘œπ‘Ÿπ‘π‘‘π‘–π‘œπ‘› π‘Ÿπ‘Žπ‘‘π‘’ ( π‘Žπ‘π‘ π‘œπ‘Ÿπ‘π‘‘π‘–π‘œπ‘›π‘  π‘π‘’π‘Ÿ π‘ π‘’π‘π‘œπ‘›π‘‘) = πœ™ βˆ— βˆ‘ π‘Ž βˆ— 𝑉 3.2.2.1 A thermal flux of πœ™ =1015 neutronspersquare centimeterpersecondwasassumed.The macroscopic absorptioncrosssectionforBismuthis βˆ‘ π‘Ž =0.0009319 cm-1 . The volume usedis55% of the coolant channels volume toaccountforthe coolantbeing55% bismuth.Afterfindingthe absorptionrate,the total numberof absorptionsina yearwere calculated.The worst-case scenarioiscomplete gasification of Polonium.Approximately10kg of poloniumisproduced peryearof operation. Thisgaswill collectin the heliumthatsitsontop of the reactor pool.The gas will contain2247 cubicfeet of helium. A pump will move thisgas inand outof the pool viatwo six-inchdiameterpipes,asseeninfigure 3.2.2.1.These pipescango to one of twopotential systems forPoloniumcapture.The firstsystemisarare earth filtrationsystemwhere the gaswill travel toastainlesssteelbox.Thisbox contains screens electroplatedwitharare earth metal.These screens hold10,000 strandselectroplatedwith Praseodymium.While thistypeof system ispredicted tohave a highefficiency,thisremoval systemhas not beenextensivelytested [15].Anefficiencyof 25% was assumedfor extraction, meaning40 kgof Praseodymiumwill be neededtoreactwithPoloniumperyearof operation. A 0.1 micronthicklayerwill plate the screenwires.If these screenshave anareaof five square meters,fivethousandof themwill have to be stackedto filterenoughpolonium.The raw cost of Praseodymiumtocoatthese screens wouldrunover$100,000 a year[16]. Thiscan be expectedtolargelyincrease aftermanufacturingcosts
  • 41. are added.Due to thiscost andthe factthat a manufacturingsystemforthisdesign hasnotbeen establishedyet,asecondoptionwasalsocreated. Figure 3.2.2.1: Pool Off-gas System The secondoptionwouldbe torun the pipesfromthe pool to a tank or seriesof tankswhere the helium gas, saturatedwithpolonium,wouldsit.The containerswouldsitforfive years,overtenhalf livesof Po210 ,toallowforfull decay.Thiswouldrequire the gastobe replacedeverytime the core istobe opened.The benefitwouldbe alesscomplicatedsystemthatwouldcostlessthan$100 forthe helium inthisoff-gassystem.
  • 42. 3.2.3 SpentFuel Storage A spentfuel pool willneedtobe considereddue tothe shortnessof the fuel’slifetime.Anoff-site pool couldbe used,butthis posesmanyproblems.Findingpoolsavailableforouruse and shippingthe spent fuel tosuch siteswouldaddextracostsand effort.Anotheroptionwouldtobe tobuilda spentfuel pool on our vessel.If we move forwardwiththis option, the pool will be astandard40 feetdeep.Onlyabout 20 feetisneededtokeepradiationatacceptable levelsbutthiswill provide uswithafactorof safety. Thisassumptionisbasedoff PWRdesigns [17].The waterwill be kept at roughly35o C to ensure adequate coolingof the fuel.The storage rackswithinthe pool will alsoneedtobe made of a high neutronabsorbingmaterial suchasB10 .This will helpshieldworkersandmaterialsfromradiationaswell as maintainingsub-criticality.Radiolysisisaconcernwithspentfuel poolsaswatermay be converted intohydrogen gas,whichcan accumulate above the pool.The airwithinthe roomwill needtobe monitoredperiodicallyandtreatedif necessary.The biggestriskforspentfuel poolsis afailure inthe coolingsystem.Thiscancause the waterto boil andcause radioactive materialstobecome present withinthe air.Planswill needtobe made if sucha situation occursor a failsafe will needtobe putin place,suchas a cap overthe pool to filteroutharmful materials. 3.2.4 Dose Calculations Determiningthe neutronandgammaflux at the reactorpool boundariesprove tobe a difficulttaskand furtherresearch isneeded toobtainmore exactresults.Preliminaryresultsforneutronsbeingfound outside ourreactorpool lidwas extremelysmall,suchthatMCNPreturneda value of zero.Tallyvalues fromMCNP gave a dose of 191 remper hourfor everysquare meterof the reactorpool wall,whichis immenselyhigh.Tomanage thisproblem, boratedpolyethylene will be addedaroundthe reactorpool wall to lowerthe dose AsLowAs ReasonablyAchievable.MCNPwill be utilizedagaintocalculate the correct thicknessof the plasticandboronconcentration.DatafromMCNP concludedthatgamma rays
  • 43. of anyspectrumwill be statisticallyabsentfromthe boundariesof the pool wall andlid.The bottomof the reactor pool will receiveasignificantdose of radiation due toneutronsandgammarays. Significant shieldingwillhave tobe addedtothisarea in the formsof borate polyethylene andlead.Thisareaisof leastimportance though,due tono one beinglocatedoractivelyworkingunderneaththe reactorpool. Table 3.2.4.1: MCNP Dose Values per Square Meter Tally# Surface # Surface Location Particle Dose (rem/hr)/m^2 2 25 Pool Wall neutron 191.2352998 12 26 Pool Cap neutron 0 22 27 Pool Bottom neutron 10423327.07 32 25 Pool Wall photon 0 42 26 Pool Cap photon 0 52 27 Pool Bottom photon 915904.1144 Thisconcludesthatthe current shieldingdesignof the mobile LFRwill be adequate inattenuation, thickness,andstoppingpower.Byadequate,there will be anextremelyhighprobabilitythatminimal dose wouldbe receivedbyworkersstandingnexttothe reactorpool once shieldingmodificationshave beenmade.One caveatthoughisthat coolantactivationanalysiswasnotperformed.The mobile LFR designaccommodatesforpoloniumproductionthroughthe off-gassystem.Otheractivatedisotopes and fissionproductscouldpotentially enterthe mainpool coolant.Furtherindepthanalysisof the productionandmobilityof these particleswouldhave tobe conductedtoadequatelyperformrealistic dose calculations outsidethe reactorpool.Mitigatingthispotential problemcouldbe fixedbysuppling additional shieldingmaterialsto the reactorpool wall suchas lead,boratedpolymer,andpotentially more steel.
  • 44. 3.3 Heat Transfer and Fluid Flow 3.3.1 Primary Side 3.3.1.1 Single Fuel Element Heat Transfer Analysis In orderto obtainimportantsystemparametersaswell astoverifythe safetyof the fuel,ananalytical solutionforthe radial heattransferequationwasfound.Since the maximumfuel temperature isknown, the equationsbelow were usedtofindthe surface temperature of asingle fuel element.Accordingto Incroperaand DeWitt,the steadystate heatconductionequationwithheatgenerationisEquation 3.3.1.1.1 [18]. 1 π‘Ÿ 𝑑 π‘‘π‘Ÿ ( π‘Ÿ 𝑑𝑇 π‘‘π‘Ÿ ) + π‘žβ€²β€²β€² π‘˜ = 0 3.3.1.1.1 By assumingsteadystate operationinone dimension(radius,r) and integrating,Equation3.3.1.1.2was obtained. 𝑇( π‘Ÿ) = βˆ’ π‘žβ€²β€²β€² π‘Ÿ2 4π‘˜ + 𝐢1 ln( π‘Ÿ) + 𝐢2 3.3.1.1.2 Thisequationisonlyapplicableforaradiusbetween0and the outerradiusof the fuel elementR1.This outerradiuscorrespondstothe surface boundarybetweenthe fuelandthe leadgap.Assuch, the boundaryconditionsbelowwere usedtofindconstantsC1 and C2. 𝐡𝐢1: 𝐴𝑑 π‘Ÿ = 0, 𝑑𝑇 π‘‘π‘Ÿ = 0 => 𝐢1 = 0 3.3.1.1.3 𝐡𝐢2: 𝐴𝑑 π‘Ÿ = 𝑅1, 𝑇( 𝑅1) = 𝑇𝑠 => 𝐢2 = 𝑇𝑠 + π‘žβ€²β€²β€² 𝑅1 2 4π‘˜ 3.3.1.1.4 Afterapplyingthese twoboundaryconditions,the general heattransferequationforthe fuel element can be expressedbyEquation3.3.1.1.5. 𝑇( π‘Ÿ) = βˆ’ π‘žβ€²β€²β€² π‘Ÿ2 4π‘˜ + 𝑇𝑠 + π‘žβ€²β€²β€² 𝑅1 2 4π‘˜ 𝑇1,𝐻 βˆ’ 𝑇1,𝐢 𝑇2,𝐻 βˆ’ 𝑇2,𝐢 = πœ‚ 3.3.1.1.5
  • 45. By usingthisequationwiththe correctvaluesof T(0),q’’’,andk, one can obtainthe temperature atthe edge of the fuel pin.Due to the highthermal conductivityof the metallicfuelpin,thissurface temperature wascalculatedtobe almostexactlythe temperature of the fuel pin center.Assuminga temperature of 823o K, the edge of the fuel pinwasfoundto be approximately822.9o K. Thissame approach was alsousedtoderive equationsforthe heatconductionacrossthe lead-filledgap and cladding.Byusingthe temperature obtainedinthe previousstep,the temperaturesateachof the otherboundaries(gap-to-claddingandcladding-to-pool)were obtained.Eachtemperature wasonly reducedbyslightlyless thanatenthof a degree Kelvin due tothe unique propertiesof ourfuel,gap, cladding,andoverall fuel pindimensions. However,duringthe lifetime of the reactor’sfuel,the fuel will expanddue toradiationswelling.Inmost reactors,the fuel will expandtoclose the gapbetweenthe fuel andcladding,whichcanresultin mechanical failure of the rod.Assuch,an analytical solutionfordirectfuel-to-claddinginteractionwas found.AccordingtoKruper,the fully-derivedequationsforthe fuel elementandcladdingare representedasEquation3.3.1.1.6 andEquation3.3.1.1.7 respectively [19].The subscriptsβ€œf”and β€œc” denote fuel andcladding;the subscriptsβ€œ1”andβ€œ2” denote the fuel-claddingandcladding-pool radiiof the fuel element;β€œh”denotesthe convective heattransfercoefficient. 𝑇( π‘Ÿ) = βˆ’ π‘žβ€²β€²β€² π‘Ÿ2 4π‘˜ 𝑓 βˆ’ π‘žβ€²β€²β€² 𝑅1 2 2π‘˜ 𝑐 ln( 𝑅1) + π‘žβ€²β€²β€² 𝑅1 2 2β„Žπ‘…2 + π‘žβ€²β€²β€² 𝑅1 2 2π‘˜ 𝑐 ln( 𝑅2)+ 𝑇𝑠 + π‘žβ€²β€²β€² 𝑅1 2 4π‘˜ 𝑓 3.3.1.1.6 𝑇( π‘Ÿ) = π‘žβ€²β€²β€² 𝑅1 2 2π‘˜ 𝑐 ln( π‘Ÿ) + π‘žβ€²β€²β€² 𝑅1 2 2β„Žπ‘…2 + π‘žβ€²β€²β€² 𝑅1 2 2π‘˜ 𝑐 ln( 𝑅2)+ 𝑇𝑠 3.3.1.1.7
  • 46. Once the linearheatrate of the hottestfuel elementisfoundusingMCNP,these equationscanbe used to determine the temperatureof the centerof the fuel.Inthisway,itcan be verifiedthatwiththe given core parameters,the fuel will not exceeditsmeltingtemperature. 3.3.1.2 STAR Modeling Due to the reactorsystemhavinga pool design,modelsneededtobe createdto calculate the heat transferandfluidflowsince valuescannotbe obtained analytically.The modelscreatedtoshow these propertiesstartedinSolidWorks,thenwereimportedintoSTAR-CCM+.Three modelshave been createdthusfar. The three modelsinclude acoarse model of the primarypool,areactor assembly,and a critical fuel pinlattice. The coarse primarypool wascreated first,as it hadthe simplestgeometryandboundaryconditions. Thismodel includessmallcylinderinside alarge cylinder,whichrepresentsthe reactorcore inside the primarypool.The pool isnine metersindiameterandeightmeterstall.The base size forthe meshused was 0.1 m. No problemsoccurredwhenthe meshwasgenerated.Asforthe boundaryconditions,a velocityof 1.435 m/swas specifiedthroughthe core andan entrance and exittemperatureof the LBE throughthe core. All surfacesinthismodel were assumedtobe insulated.The purpose of thismodel was to determinehownatural convectionwouldworkinthe core andhow heatwouldbe distributed. Boundaryconditionsstill needtobe specifiedbefore anyiterationsare ran. The fuel assembly has217 fuel pinsinsidethe hexagonal lattice.Eachof the sidesof the hexagonare 5.5 cm, and the radiusof each fuel pinis0.29 cm. The pitch forthe fuel pinsis0.714 cm, andthe heightof the assemblyis1.5 m. The base size usedforthismodel was one millimeter.Suchasmall base side was usedforthe meshingbecause of the amountof detail thatneedstobe obtainedfromthe model.No
  • 47. problemsoccurredwhenthe meshingwasgenerated.Forthe boundaryconditions,the outside surfaces of the assemblywere setasreflective since otherfuelassemblieswill be borderingit.The fuel rods inside the assemblywillhave the heatflux specifiedonthe walls.The fluidvelocityatthe entrance to the fuel assemblywasspecifiedas1.435 m/sso the velocity profileinside the core isgenerated.The purpose of thismodel isto findflowandheattransferthroughthe assemblyandto identifythe fuel lattice withthe highestoutputtemperature. Figure 3.3.1.2.1: STAR CCM Model of an Entire Fuel Element The critical fuel pinisa triangularlattice composedof three fuel pinsinsideanassembly.The geometry was createdbydrawingan equilateraltriangleusingthe pitchasthe side length,thensubtractingthe area fromthe fuel pins.The base size usedinthismodel was0.1 mm. Sucha small base side wasused for the meshingbecause of the amountof detail thatneedstobe obtainedfromthe model.The boundaryconditionssetonthe fuel pinshave aheatflux of 2.09 X 107 W/m2 .The straightwallswill have a reflective boundaryappliedtothemtosimulate otherchannelsnexttoit.A constantvelocityof 1.435 m/swas assumedat the inletof the fuel channel.Thismodelwascreatedtofindthe maximum temperature inthe pool,andtomake sure the fuel will notmeltandthe coolantwill notboil.
  • 48. Figure 3.3.1.2.2: STAR CCM Model of a Single Coolant Channel The critical fuel pinwentthrough500 iterationsandconvergedafterthe first50. The fuel pindidnot exceed1027Β° C,whichis belowthe 1135Β° C meltingtemperature of the fuel [13].The LBE inthe fuel channel hadan inlettemperature of 150Β° C and an outlettemperatureof 877Β° C.The outlet temperature of the fuel channel wasbelow the 1670Β° C boilingtemperature of LBE[32]. The velocity enteredthe fuel channelat1.435 m/s and leftthe fuel channel at1.64 m/s. Thermal expansionof the coolantcausedthe velocitytoincrease by0.21 m/s.These resultsare seeninfigures3.3.1.2.3,3.3.1.2.4, 3.3.1.2.5, 3.3.1.2.6, and 3.3.1.2.7.
  • 49. Figure 3.3.1.2.3: Cross Section of Critical Fuel Pin Figure 3.3.1.2.4: Critical Fuel Pin Outlet Temperature
  • 50. Figure 3.3.1.2.5: Critical Fuel Pin Outlet Velocity Figure 3.3.1.2.6: Critical Fuel Pin Inlet Temperature
  • 51. Figure 3.3.1.2.7: Critical Fuel Pin Inlet Velocity 3.3.1.3 Natural Convection Because pipeswere addedlinking the reactortothe heatexchangers,thentothe primarypool,natural convectionequationswere usedtodetermineif natural convection issufficienttosupply1000 MWt of power.The followingequationswereusedinfindingthe total change inpressure toprovide 1000 MWt of power: Δ𝑃 = πœŒπ‘‰π‘Ÿ 2 2 (βˆ‘[ 𝑓 βˆ— 𝐿 𝐷 + βˆ‘ 𝐾] βˆ— 𝐴 π‘Ÿ 𝐴 𝑖 𝑖 ) 3.3.1.3.1 𝑓 = 0.316 𝑅𝑒0.25 3.3.1.3.2 𝑅𝑒 = πœŒπ‘£π· πœ‡ βˆ— 𝐴 π‘Ÿ 𝐴 𝑖 3.3.1.3.3 π·β„Ž = 4𝐴 𝑃 3.3.1.3.4 Δ𝑃 = Δ𝑝𝑔Δ𝑇 (for natural convection) 3.3.1.3.5 π‘ƒπ‘œπ‘€π‘’π‘Ÿ = πœŒπ‘‰π΄πΆ 𝑝Δ𝑇 3.3.1.3.6
  • 52. By usingthese equations,itwasdeterminedthatapressure differenceof 28.4 kPa wasprovidedby natural convection,buta pressure difference of 491.7 kPa wasneededtoachieve the powerof 1000 MWt. Losseswere consideredforthe powercalculation,but notfornatural convection.Because the pressure differenceneededisgreaterthanwhatnatural convectioncouldprovide,forcedflow will be neededtoachieve apowerpast200 MWt. These calculationswere done assumingconservative loss coefficientsforenteringandexitingpipesalongwithelbowbends.Foroperationat1000 MWt, forced convectionwill be usedprimarilyandnatural convectionwillassist.The massflow rate movingthrough the core is14410.4 kg persecond. Withnatural convection,the systemwouldbe able toproduce 200 MWt. To achieve the 1000 MWt desiredforthe design,the LBEcoolantwouldhave tobe pushedthroughthe core at a velocityof 1.435 m/s.To achieve thisvelocity,the decisionwasmade touse an electromagneticpump.Whenlookingfor pumps,several modelswere found,butpricingforthese modelscouldnotbe located.Shownbelowin Figure 3.3.1.3.1 isa back-uppumpusedinthe RussianBN-800 reactor [53]. Figure 3.3.1.3.1: TsLIN 4/26
  • 53. Thispumpdraws 14 kW and has a flowrate of 26.1 m3 /h[53]. The other pumpinoperationatthe RussianBN-800 is a TsLIN 1.5/430. Thispump draws66.4 kW and has a flow rate of 429 m3 /h [53].By locatingthese pumps, the teamdeterminedthatthe pumpsrequiredforthe applicationexistandall that isneededisto determine the cost.Takingpricesfromsmallerelectromagneticpumpsavailable, the teamextrapolatedthe datatodetermine the price andpoweruse of the requiredpump.Thisdatacan be seenbelowin Table 3.3.1.3.1. At 1.435 m/s the pumpwoulddraw 21.53 kW of powerandcost approximately$190,400. Table 3.3.1.3.1: Electromagnetic Pump Pricing 3.3.1.4 Heat Exchangers For the heatexchangerdesign,the paperβ€œThermal-hydraulicperformanceof heavyliquidmetal in straight-tube andU-tube heatexchangers”wasusedbecause itgave dataon possible LBEheat exchanger[20].The one chosenwas the straighttube type because itdoesnot exhibitthe corrosion problemsof the U-bendstyle.Equationsgivenbythe paperwere inputtedintoanexcel spreadsheet withthe ultimate goal of finding q.Currentdesigncallsforaone meterouterpipe diameteranda three meterlongpipe. Table 3.3.1.4.1 containsthe expectedtemperatures. Extrapolated Price Power Use (kW) Linear Linear RΒ² = 0.9949 RΒ² = 0.9882 1.371 $180,964.50 21.41 1.389 $183,323.70 21.44 1.407 $185,682.90 21.47 1.426 $188,042.10 21.50 1.444 $190,401.30 21.53 1.462 $192,760.50 21.56 1.480 $195,119.70 21.59 1.498 $197,478.90 21.62 1.516 $199,838.10 21.65 Fluid Velocity (m/sec)
  • 54. Table 3.3.1.4.1: Expected Temperatures in the Heat Exchanger Location Temperature(K) T-hot-L 923 T-cold-O 423 T-hot-L 900 T-cold-O 305 Picturedbelowisadiagramof the heatexchangerfromthe paper β€œThermal-hydraulicperformance of heavyliquidmetal instraight-tubeandU-tube heatexchangers”, summarizingthe basisforthe ones usedinthisreactor [20]. Figure 3.3.1.4.1: Straight Tube Heat Exchanger Convective transfercoefficientsweregiveninthe paperandusedinthisanalysis.The paperalso providedequationsusedtosolve forsome keyfactorsinthe designof aheat exchangerof thistype. Belowisa table of the factors, includingpressure losses,frictionfactor,and Reynoldsnumber:
  • 55. Table 3.3.1.4.2: Table of Heat Transfer Factors for Heat Exchangers Factor Value Units Reynolds Number 45444 NA Ξ”P 0.933 NA f 0.0014 NA U(overall heattransfer) 1.11E+05 W/(m2 *K) q 3.80E+08 W Ξ”T-log mean 546 K The main factorin thisanalysis,q,indicatesthe heatexchangerwillmove 380 MWt overitslength.This meansat leastthree heatexchangerswillhave tobe placedaroundthe reactor pool inorderto handle the heat loadfromthe reactor. 3.3.2 Secondary Side The purpose of the secondarycycle isto extractenergyfromthe core and turn itintousable electricity. To do this,a systemof compressors,turbines,andregeneratorsare usedtoextractheatfromthe core usingsupercritical carbondioxide.Inreal life,the componentsinthe secondaryside have setefficiencies and thermal limits.Indesigningthiscycle,assumptionsregardingthe capabilitiesof the machineryare giveninTable 3.3.2.1. Table 3.3.2.1: Assumed Machine Efficiencies for Secondary Cycle Component Assumed Efficiency (%) Flow Coming From LTR (%) Turbine 0.95 Compressor 1 0.90 0.65 Compressor 2 0.90 0.35 High Regenerator 0.98 Low Regenerator 0.92 Generator/Alternator
  • 56. Figure 3.3.2.1: Secondary Cycle Layout Figure 3.3.2.2: Secondary Cycle States
  • 57. Figure 3.3.2.3: Secondary Cycle State Diagram To quantifyeachstate inthe cycle,the followingequations fromaheattransfertest were used [18]. π‘‡β„Žπ‘–π‘”β„Ž π‘‡π‘™π‘œπ‘€ = ( π‘ƒβ„Žπ‘–π‘”β„Ž π‘ƒπ‘™π‘œπ‘€ ) (π›Ύβˆ’1) 𝛾 3.3.2.1 𝛾 = 𝑐 𝑝 𝑐 𝑣 3.3.2.2 πœ‚ π‘‘β„Žπ‘’π‘Ÿπ‘šπ‘Žπ‘™ = π‘Šπ‘›π‘’π‘‘ 𝑄 π‘Žπ‘‘π‘‘π‘’π‘‘ 3.3.2.3 T is the temperature inKelvin.Pisthe pressure inMPa.Gamma, 𝛾, isthe heatcapacityratio.Cp is the heatcapacity at constantpressure.Cv is the heatcapacity at constantvolume. πœ‚ representsthe efficiency. 3.3.2.isusedwhencomparingthe statesinand outof a compressoror turbine.Thisequation isusedfor determiningstate 2from state 1, state 6 from state 5, and state 8 fromstate 4. Calculations were startedwiththe assumptionof the hottestfluidtemperature andlowest fluidtemperature.At state 1, itis assumedthatthe supercritical CO2 leavesthe core at923Β° K at a pressure of 20 MPa. The lowtemperature,atstate 5, is 305Β° K and isat a pressure of 7.7 MPa. From the assumedstate 1,
  • 58. Equation3.3.2.1 wasusedto findstate 2. From the assumedstate 5, Equation3.3.2.1 was usedtofind state 6, whichneededtohave apressure of 20 MPa. To determine state 9,a simple weightedaverage of the temperaturesof state 7 and state 8 withrespecttomass flow rate isall that isrequired.Inthe regenerators,anotherequationwas usedtofindthe outletstates. 𝑇1,𝐻 βˆ’ 𝑇1,𝐢 𝑇2,𝐻 βˆ’ 𝑇2,𝐢 = πœ‚ 3.3.2.4 The efficienciesof the regeneratorsisassumedtobe 98% forthe hightemperature regeneratorand 92% forthe lowtemperature regenerator.Knowingonlythree of the fourstates,the fourthstate canbe determined.Withall otherstatesnowdefined,states 3and 4 have nostrictlydefinedvalue.Thisimplies that the amountof heattransferredthroughthe regeneratorsisnotsetandcan be manipulatedto achieve amore efficientcycle.Bymodifyingthese state temperatures,amaximumcycle efficiencycan be determined.Tofindthe overall cycle efficiency,the followingequationsare used. π‘Š = (π‘‡β„Žπ‘–π‘”β„Ž βˆ’ π‘‡π‘™π‘œπ‘€)(πœ‚ π‘π‘œπ‘šπ‘π‘œπ‘›π‘’π‘›π‘‘) 3.3.2.5 πœ‚ π‘‘β„Žπ‘’π‘Ÿπ‘šπ‘Žπ‘™ = π‘Šπ‘›π‘’π‘‘ 𝑄 π‘Žπ‘‘π‘‘π‘’π‘‘ 3.3.2.6 πœ‚ π‘‘β„Žπ‘’π‘Ÿπ‘›π‘Žπ‘™ = π‘Šπ‘‘π‘’π‘Ÿπ‘π‘– 𝑛 𝑒 βˆ’ π‘Šπ‘π‘œπ‘šπ‘π‘Ÿπ‘’π‘ π‘ π‘œπ‘Ÿ 1 βˆ’ π‘Šπ‘π‘œπ‘šπ‘π‘Ÿπ‘’π‘ π‘ π‘œπ‘Ÿ 2 𝑄 π‘Žπ‘‘π‘‘π‘’π‘‘ 3.3.2.7 Where W is the workthrougha turbine orcompressorandQ is the amountof heataddedto the system. The bestefficiencyachievable isthe Carnotefficiencyandcan be calculatedwith Equation3.3.2.8. 𝑇𝐻 βˆ’ 𝑇𝑐 𝑇𝐻 Γ— 100% 3.3.2.8 For the system,the hottestandcoldesttemperaturesare 923 and305Β°K, respectively.Thisgivesa Carnot efficiencyof 66.96%. Usingthe actual worktaken out fromthe system, we have a cycle efficiency of 45.5%. Thisseemstobe reasonable whencomparedtosimilarpowerplantcycles.Thisefficiencyis greaterthan manytraditional PWRcycles.
  • 59. 3.3.3 Water Desalination Water desalinationisthe processof removingimpuritiesof awater source.The goal is to produce pure H2O. There are many methodsof waterdesalination,suchasdistillation,membrane processes,andion exchange.Thisdesignwill be usingdistillationbecause itusesexcessheatfrompowergenerationloop. Thisextraheat wouldotherwise be dumpedintothe environment.Inthisway,we are lesseningthe powerplant’sthermal footprintwhileprovidinganothercommodity,water,whichcanbe soldfora profit. The plant will extractdrinkable water outof the seawaterthroughmultiple-effectdistillation.The basic principle of waterdistillationisasfollows.Waterisheatedtoitsboilingpoint.More heatisaddedto change the phase of waterintovapor.A coolersurface to the boilingcontainercondensesthe waterand divertsthe condensationtoanotherholdingtank.The boiled-off watershouldbe nearlypure,asthe contaminantsshouldnotboil attemperaturesaslow asthe water.Multiple effectdistillationusesa numberof stagesto distill water.The name comesfromeachstage beingcalledanβ€˜effect’.The stages differintemperature andpressure.Onthe inside of atube,wateriscondensed,andonthe outside of the tube,a thinwaterfilmisvaporized [21]. Multiple effectdistillationonlyrequiresexternalheatingatthe firststage.Thisstage has the highest pressure.Because the boilingtemperature of waterdecreaseswithdecreasingpressure,the vapor createdinthe previousstage canbe usedto boil water inthe nextstage [22]. Thisdesalinationsystem doesnothave definite temperaturesandpressuressetforeachstage.The informationprovidedby Warsinger’sworkondesalinationmethod detailsthe overall efficienciesof variousdesalinationmethods [23]. It isexpectedthatwe will have arecoveryratiogreaterthan40%, whichmeansthat at least40% of
  • 60. inputwaterwill become drinkable.The heattransferintodesalinationisknown.There isanamountof heat,q, fromthe secondaryCO2 that needstobe disposedfromthe system.Thisqwill gointothe desalinationsystem.UsingefficienciesfoundinWarsinger’spaper,we have come tothe conclusionthat we can produce approximately1.15 milliongallonsof waterperday(or4.3 millionlitersperday). It isimportantto note that notall the seawaterthatgoesthroughthe systemwill become drinkable water.Asseawaterprogressesfromstage tostage,itbecomesincreasinglydifficulttodistill.The amountof impuritiesremainthe same while the amountof solvent,water,decreases.Thismeansthat the outputwateris more of a brine thanthe inputwater.The brine mustbe dischargedbackintothe ocean.This is a forma pollutionandmustbe monitored.However,the brine shouldbe dilutedbythe oceanto a negligibleconcentration.The mostimportantpollutantswill come fromcleaningagentsused for maintenance andmetalsdissolvedfromthe pipesandtanks [24]. Multiple effectdistillationcanbe reasonablyachievedonaseafaringvessel forareasonable cost.The onlymovingpartsinthe designare the low pressure pumps.The stagescanbe constructedout of cheap materials,like aluminum.The processoperatesat a relativelylow temperature,whichreducesscaling. It isan economical choice because ithasverylow maintenance costsanddoesnotneedmuch supervisionwhile operating.Multipleeffectdistillationusesverylittle electrical powercomparedto multi stage flashdistillationormembrane processeslikereverse osmosis [25].Additionally,there are alreadycompanies,like EntropieVeolia,thatmanufacture modulardesigns.The instillation wouldbe easilyperformedwithourshipdesign.Therewould,however,be achange inthe designto accommodate CO2 as the heatingfluidinsteadof water.
  • 61. 3.4 Materials 3.4.1 Ship Analysis An importantaspectof the mobile LFRdesignis thatthe shipthat contains the entire facility. Conservative preliminarycalculationsregardingthe size of the shipwere made usingthe weightof the lead-bismutheutecticcoolantpool.The weightof the core and coolantpool were doubledbecause the powerconversionsystemsandothersmallercomponentswere notincludedinthe measurements.The calculatedminimumvolume of the ship,includingthe safetyfactorof 2.5, was36,011.6 m3 .In a traditionallydesignedrectangularship,itwouldbe aminimumof 70 m long,35m wide,and15m draft. A fewshipsthatmetthe requirementsforsize forthe projectwere the Hbulkcarrier,the Handymax bulkcarrier,and the ClassB bulkcarrier.The Handymax bulkcarrieristhe shipthatwill mostlikelybe usedas the reactor systemsvessel.The Handymax BulkCarrieris200 m long,has a 32 m beam, and has a 19 m draft.It has a DWT (DeadweightTon) measurementof 46,000, meaningthatitcan carry 46,000 tonsof cargo, not includingthe ship’sweight.The Handymax isalsoagearedship,meaningthatithas cranesoverheadof the shipdeckavailable to liftandlowerpartsintothe vessel.The reasonthe Handymax isbeingchosenisthatit islarge enoughto holdthe reactor components,house the power conversionsystems,apossible spentfuel storage pool,andpotentialhousingforreactoremployees. Afterthe shiphasbeenpurchasedand before itisreadyto house the nuclearreactor,the shiphas to be retrofitted.Several systemsnotcurrentlyonboardthe shipwouldhave tobe installed, suchasa power conversionsystem, the desalinationsystem, andthe reactorsystemitself.Before systemssuchasthese can be installedonthe vessel,safetyandsupportsystemsmustbe installed.Afterthe necessarysupport and safetystructuresforthe reactor systemshave beendesigned,the designforthe renovationof the shipcan be completed.
  • 62. 3.4.2 DPA Considerations The main considerationforradiationdamage tothe reactoristhe fuel cladding.Due tothe highvolume of liquidmetal surrounding the core,pool materialswill receiveafractionof the dose that the cladding does.Due to this,if the cladding isshowntobe safe,the core can said to be safe under operation conditions. Several assumptionswere made toallow foramore straightforward DPA calculation. The crosssection of ourmaterial was assumed constantat all energies.Thisisvalidbecausethe energyspectrumgivenby criticalityisrelativelynarrowandthe crosssectionchangesbyonlya few barns.Damage was caused entirely byIronatoms wasalso assumed.Of which,the claddingcontainsmore than80%.SRIM simulations withatomsatappropriate percentagesactuallyshow lessdamage thanthe entirelyIron assumption,makingthe estimate conservative whilestreamliningthe calculation. Usingthe Displacements/Ionoutputfromthe SRIMcode,DPA is calculatedforHT-9 as 18.8 DPA overa periodof 2.5 years.Giventhe incubation periodof HT-9is 100-200 DPA,core materialshave an estimatedlifetimeof 25 yearsunderthislevel of radiationdamage.Thisestimate,whichutilizesprimary knock-onatomsas the source of damage,overestimatesthe actual damage thatcore materialswill suffer.Fromthis,itcan be shownthat chemical andmechanical stressesare the primaryfactorsinthe material degradation. 3.4.3 Corrosion One of the majorconcernswhenlookingatthe lifetimeof reactormaterials iscorrosion.Lead-bismuth eutectic(LBE) isa corrosive material,especiallyatelevatedtemperatures(T> 500Β° C) [39]. Oxygenlevels
  • 63. inthe reactormust be closelymonitoredinordertoallow protective oxide layerstoformonreactor materialswhilepreventingthe LBEcoolantfrom formingprecipitates. Withoxygenlevelstoolow,the dissolutionof metal alloyswill beginandthe structureswill starttodegrade.Withoxygenlevelstoo high,rapidoxidationof inpool supportstructureswill occurand PbOprecipitateswill begintoformin the coolant.These factorswill endupcausinglowerheattransferrates.Usingthe equationsbelow,the teamhas foundthat the optimal range duringoperatingconditions (T=600o C) fallsbetween 3.617 X 10-3 and 3.35 X 10-8 weightpercentoxygen. Oxygenupperlimit: π‘™π‘œπ‘”(𝐢 π‘œ βˆ— ( 𝑀𝑑%)) = 2.25 βˆ’ 4125 𝑇( 𝐾) 3.4.3.1 OxygenLowerLimit: log(𝐢 π‘œmin( 𝑀𝑑%)) = βˆ’ 3 4 log( 𝐢 𝐹𝑒( 𝑀𝑑%))+ 2.28 βˆ’ 10456 𝑇( 𝐾) 3.4.3.2 log 𝐢 𝐹𝑒 𝑆 ( 𝑀𝑑%) = 2.01 βˆ’ 4380 𝑇( 𝐾) 3.4.3.3 Whenlookingatspecificmaterials,the 316L stainlesssteel pipingusedforthe heatexchangersended up beingaproblematicchoice. Atlowertemperatures,T< 500o C, 316L formsa thinoxide layerthatis sufficientinprotectingthe material.Astemperaturesincrease,T> 500o C, thisoxide layerbeginstoget thickerandproducesmore defects.The defectsinthe protectiveoxidelayerare permeable tothe LBE coolantand dissolutionof metal willoccur.Thispreventsadditional oxidesfromformingand studies have shownthat these materialscanfail asearlyas 4000 hoursintoservice [10].Surface alloyingor diffusionalloyingof aluminumorsiliconintothe stainlesssteel canaidinoxide formationandextend the lifetimeof the material.However, studieshave shownmartensiticsteel alloyT91 to be a better candidate forthese applications.The additional chromium contentinthissteel causesathickoxide layer
  • 64. to format highertemperaturesandprovide betterprotectioninthe LBE environment.TestsusingT91in a LBE environmenthave beenperformedforover20,000 hours withoutthe material failing.Toincrease the corrosionprotection of T91 evenfurther, aluminumorsiliconcanbe alloyedintothe surface to provide additional oxide protection.One othermethodof corrosionprotectionwouldbe toadd corrosioninhibitors(likezirconiumandtitanium) tothe coolant(concentration<10-3 wt. %) allowing protective oxidestoformonthe steel surfaces [10]. 3.4.4 Support Structure The supportstructure for the reactor was modeledusinga1000 kN load.The supportstructure ismade out of 13 supportlegsmeasuring4 cm by 4 cm andare 1 meterlong.The baseplate is140 cm across, 6 cm thick,and has holesinthe baseplate toallow forfluidflow. Figure 3.4.4.1: Support Structure Whenmodelingthe structure,itwasdeterminedthatthe majorityof the structure hada safetyfactor greaterthan 5 witha minimumof 3.09 on the inside cornerof the outerlegswhere theymeetthe
  • 65. baseplate.The simulationresultscanbe seeninFigure 3.4.4.2 withthe area havingthe smallestfactor of safetyshowninFigure 3.4.4.3. Figure 3.4.4.2: Safety Factor of Support Structure
  • 66. Figure 3.4.4.3: Minimum Factor of Safety The simulationalsoshowedthatthe greatestdisplacementexperiencedbythe structure isonly0.3885 mm.This displacementoccursonthe outeredge of the baseplate inbetweenthe supportlegs.These resultscanbe seeninFigure 3.4.4.4.
  • 67. Figure 3.4.4.4: Support Structure Displacement (mm) From the preliminaryanalysisandthe structure simulationdoneonAutoDeskInventor,the teamhas determinedthatthe above designedsupportstructure willbe sufficienttosupportthe reactorcore underoperatingconditions. 4 Humanitarian Benefit and Environmental Impact 4.1 Nonproliferation Witheverybranchof the nuclear powerindustry,proliferationisaconcernand the mobile LFRisno exception.Tohelpcombatthe spreadof nuclear arms, enricheduraniumandspentfuel must be closely monitored.Withthe use of the mobile LFR, there are several builtinnonproliferationfeaturesthatare intrinsictothe design.Forexample,the spentfuel of the reactorwill be storedonsite andwill be too radioactive todirectlyhandle,renderingmostif notall attemptsof acquiringthe spentfuel useless.This aspect,while commoninthe nuclearindustry,hasbeentime testedandprovenandwill be keytothe mobile LFRdesign.
  • 68. The mobile LFRwill have alimitedamountof potential buyersandwill be regulatedtothe private industriesandcountriesthatare preapprovedbythe United Nations.Thiswill helpreduce the fuelor spentfuel frommakingitswayto anyindividualswithmaliciousintent.Inaddition,the spreadof nucleartechnologywillbe regulatedwhile helpingpromote the nuclearpowerindustry. The mobileLFR will be securelyoperatedandmaintainedbyexperiencedindividualsthathave passedbackground checksand auspiciouswith regardtokeepingthe mobile LFRsafe fromharm. The ship’sdesignswillbe keptstrictlyconfidential.Thisistohelppreventanyopportunityfor terrorist partiesand organizationsfromacquiringthe meanstocause damage to the vessel andendangeringthe surroundingpeople. 4.2 Pollution The operationof a nuclearreactor involvesthe riskof leakingpotential pollutantsintothe environment. In the case of thisdesign,the mainconcerninthisarea isleakingpollutantsintoseawater.There are three mainformsof pollutionassociatedwiththisdesign:lead,heat,andradioactivity.Eachformhas beenresearchedtofindacceptable quantitiesof pollutionandthe decontaminationprocedures associatedwitheach. The primaryconcern withthe operationof thisreactordesignislead.Leadinwater(especiallydrinking water) can cause a numberof ill effectsonlivingthings.The mostsevere formof leadpoisoninginvolves the replacementof calciumionsinthe nervoussystem,therebydegradingneuronal functioning[26]. Thankfully,thissystemisdesignedtobe usedinsaltwaterbodies,meaningthatchronicexposure to leadthroughdrinkingwaterisnotof concern.However,leadcanstill affectaquaticlife.Guidelineshave beenimposedbythe UnitedStatesEnvironmentalProtectionAgency(EPA)toprotectaquaticlife.These
  • 69. seawaterguidelinesstate thatacute dose concentrationsforleadshouldbe below 210 microgramsper liter,andthat chronicdose concentrationsshouldstaybelow8.1microgramsper liter[27].Since water desalinationisplannedforthisreactorsystem, the maximumconcentrationshave alsobeenobtained for freshwater.Theseguidelinesare stricterat65 and 2.5 microgramsperliterfor acute and chronic dosesrespectively [27].Inthe case of contamination,eitherphysical orinactivation(chemical) decontaminationprocesseswillbe usedtodispose of the contaminatedmaterials[28]. Overall,itisnot expectedthatthisdesignwill require adischarge of leadintoanybodyof water.Evenso, precautions will be takentokeepleadpollutionaslow asreasonablyachievable. Heat pollutionis anotherconcernforthisdesign.Duringoperation,the reactorwill needawayto dispose of excessprocessheatatthe back endof the cycle.This designwillrejectexcessprocessheatto the seawateraroundthe vessel.Atthistime,there are nointernational regulationsconcerningheat pollutionof the ocean,since the oceanisconsideredaninfinite heatsink.However,thisdoesnot necessarilymeanthatheatpollutionnearthe inletoroutletof a smallerbodyof water(suchas a river, lake,or port) isnot of concern.Since the reactor will be anchoredsomewhatclose toland,heat pollutionof the local areawill be monitored.Inthe case of local heatpollution,guidelinescreatedby the country’senvironmental agencieswill be followed.Whetherthe reactorislocatedinan oceanor otherbodyof water,the contaminationof heatwill be keptaslow asreasonablyachievable.Inthe case of β€œcontamination”,there are nospecificdecontaminationproceduresthatcanbe followed.The only course of action wouldbe to stopthe dumpingof excessheatintothe bodyof water(reactor shutdown). Radiationleakage intothe environmentisanissue thateveryreactordesignhastoconsider.According to the NuclearRegulatoryCommission(NRC),equivalentradiationdosestothe general publicmustbe
  • 70. keptunder100 mrem peryear[29]. There are special circumstancesinwhichthatequivalentdose limit may be exceeded(suchasthe onsite visitingof anindividualof the public) [29].However,itisnot expectedthatthe reactordesignwill releaseanyradiationtothe publicduringnormal operation.As withthe otherformsof pollution,the amountof radiationreleasedintothe environmentwill be keptas lowas reasonablyachievable. 4.3 Public Concern and Safety The publicimage of any industryisvastlyimportantasitdeterminesonhow acceptable itisinthe world.Forthe nuclearindustry,thishasbeenachallenge toovercome due toatomicwarfare,nuclear accidents,andthe publicnotunderstandingradiation.Because of these threeobstacles,the nuclear industryhasto clearthembefore theyare acceptedbysocietyandare able to succeed.Forthe mobile LFR, the systemmustshowitis safe forthe general public,workers,andpractice ALARA. A potential concernandcriticismfromthe public isbasedonreactionstosimilarnuclearprojects deemedtohave environmentalimpact [30].Thishoweverprovidesanumberof benefitsforthe reactor systemandthe public.Bythe reactorsystembeing400 m offshore minimum, the general publicwillnot be exposedtoanyradiation.Thisisbecause the discharge waterwill be releasedunderthe vessel.By doingthis,the excessheatandradiationwill be dilutedfromthe oceantoundetectable concentrations [29]. Thisis accomplishedbythe oceanbeinganinfinite medium.The amountof radiationreleasedwill be comparable to a typical PWRand ALARA will be practiced,reducingconcentrationsevenfurther.The waterreleasedintothe oceanwill be below the DACvalue forwatersetbythe International Committee of Radiological Protection [31]. For workersinand onthe reactorsystem, UnitedStatesNuclearRegulatoryCommissionpublications will be practicedandapplicable [32].Thisgoesforlicensingpurposesandforworkerregulations.
  • 71. Workerswill be preventedfromaccumulatingan annual dose greaterthanfive rem.All workerswillbe issuedafilmbadge,whichwill recordthe amountof radiationreceived.A healthphysicistonsite will monitoreachfilmbadge.The reactorstaff will handle accidentsthatoccuron site andALARA principles will be inpractice. The Worst-case scenarioforthe reactorsysteminvolvesthe vessel sinkingorrollingover.Ineithercase, if the shipstarts to roll or tippast a certainpoint,the reactor will immediatelySCRAM.The coolantwill thensolidifyaroundthe core,encasingthe core andshieldingthe radiationfromthe outside.Thiswill keepthe radiationfromenteringthe oceanwaterandcausinganotherFukushima.Thisdoesprovetobe an environmental hazarddue tothe leadbeingexposedtothe ocean.However,there are no international regulationsinregardstoleadpollutioninoceanwaters[49].Instead,the reactorsystem will followEPA regulationssince thereare regulationsforleadconcentrationsinthe UnitedStates. Multiple nuclearsubmarineshave sunkinthe oceanbefore,andnoknownlongtermeffectshave come fromthem.If the vessel sinks40m off shore,itwill goto a depthof at least1000 m.This claimmaybe made since the average depthof the oceanis 2.3 km[33]. At thisdepth,the vessel maysafelyrestatthe bottomof the ocean. 4.4 Water Desalination From the onsetof thisproject,a goal of thisdesignhasbeentoprovide humanitarianaidforadisaster area.Providingfreshwaterthroughdesalinationisone waytomake progresstowardsthisgoal.Clean wateris a necessityforhumancivilizationanditssupplymaybe diminishedinthe wake of anatural disaster.The freshwaterprovidedbythisdesigncanhelprelieve the immediate watershortagesaftera disasterandstill provide waterforthe communityasitrecovers andcontinuesnormal operations.This sectionwill detailthe effectsthatour1.1 milliongallondesalinationplantcanhave on a community.
  • 72. Water isneededforhumansurvival.Onaverage,anadultneeds3.2litersof waterperday [34]. Assumingwaterfromthe desalinationplantcanbe distributedwell,the 4.16millionlitersof watercould sustain1.3 millionpeople.Thisestimate,however,doesnotconsiderthe real-worlddifficultiesof disasterreliefefforts. Survival (drinkingandfood) waterneedsare accompaniedbybasichygiene and cookingneedswithwater.Dependingonthe social andcultural environment,thisbasicwaternecessity raisesto 15 litersperpersonperday [35].Thismeans that the desalinationplantcanreasonablysupply 277,000 people inthe aftermathof adisaster.Toput that intoperspective,thatisapproximatelythe populationof Lincoln,Nebraska. Afterinitial disasterrelief effortsare taken,the communitywillneedwaterformore diverse purposes than justsurvival.Inthe recoveringcommunity,waterwill be usedforpersonal washing,homecleaning, agriculture,sanitation,indoorplumbing,andanumberof otheruses.For intermediate uses,itcanbe expectedthatthe desalinationplantcansustain170,000 people inrelativecomfort.That’s approximatelythe size of Springfield,Missouri.Inthe longterm, waterdemandswill continue to increase.The average UnitedStatescitizencanconsume nearly90gallonsof waterperday [36].The desalinationplantcouldprovidefor13,000 people if waterdemandreachesthishigh. 4.5 Mobility The topic of mobilitypresentsconcernforthe design.Nuclearreactorsingeneral have trouble inthe publiceye,andhavingamobile reactorwill be nodifferent.However,the currentdesignhasseveral safetyfeatures,andthese will helpcounteranypotentialmobile concern.Since the shipwill utilize similarsecuritymethodsthatcurrentnuclearpower plantshave,anymanmade threatsshouldbe reduced, if noteliminated.Also,anynatural disasterthreatswill be analyzed, andif needed,the shipwill
  • 73. take necessaryprecautionstoreduce riskof damage to the vessel anditscrew.Usingthe ship'smobi lity will allowforevadingpredictable natural disastersandwill adhere toanywarningsissuedbylocal or national organizations(i.e.the National OceanicandAtmosphericAdministration).Mobilityalsoeases the manufacturingof the shipsince itcan be builtinthe mostefficientlocation thenmovedtoits destination.Thiscanreduce costandeffortinbuildingthe mobile LFR.
  • 74. V. Conclusions The nuclearreactor systemiscomposedof a two-loopcycle,whichhasanefficiencyof forty-five percentandprovidesenoughenergytopowerthe systemitselfalongwithadesalinationplantonsite. The designincludescalculationsevaluatingthe progressof the systemand modelstobackuphand calculations. Calculationsperformedthusfarinclude the following: ο‚· Control rod worth ο‚· Burnupfor fuel ο‚· Natural convectionVs.Forcedconvection ο‚· STAR-CCM+ models ο‚· Secondarycycle efficiency ο‚· DPA rates formaterials ο‚· Productionandpersonnel costs ο‚· Dose rates outside reactorpool Currentworkto furtherimprove the systemincludesoptimizingthe secondarycycle,reactingmore detailedmodelsof the primarypool inSTAR-CCM+, MCNP,and SolidWorks,finalizing the final costof the system,findingoutthe activationtime of the coolant,andmakingsure all modelsmeshwithone another.All of the currentwork will tie togethertofinalizethe NuclearNarwhals’reactordesign.