Light a CANDLE. An Innovative Burnup Strategy of Nuclear Reactors. Hiroshi Sekimoto

Transcription

1 Liht a CANDLE A Iovative Burup Stratey of Nuclear Reactors Hiroshi Sekimoto

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5 Liht a CANDLE A Iovative Burup Stratey of Nuclear Reactors Hiroshi Sekimoto Research Laboratory for Nuclear Reactors Tokyo Istitute of Techoloy O-okayama, Meuro-ku, Tokyo JAPAN hsekimot@r.titech.ac.jp The 21st Cetury Ceter of Excellece Proram Iovative Nuclear Eery Systems for Sustaiable Developmet of the World (COE-INES) Tokyo Istitute of Techoloy URL:

6 Copyriht 2005 The 21st Cetury Ceter of Excellece Proram Iovative Nuclear Eery Systems for Sustaiable Developmet of the World (COE-INES) Tokyo Istitute of Techoloy All rihts reserved ISBN C3058

7 Preface This world is created i a orderly fashio. With the advacemet of sciece, it is becomi icreasily clear what the purpose behid this order is. It almost appears as if the world is created i a orderly fashio for the beefit of humakid. Nuclear fissio provides a ood example of this. The eutros eerated i the process of uclear fissio ca be used to trier succeedi uclear fissios or to create further fissile material. Very few eutros are left over i this process. How should we use these remaii eutros? The Creator of this world has preseted us with this very iteresti questio ad seems to be woderi what solutios we come up with. CANDLE burup is oe solutio. CANDLE is a ew burup stratey for uclear reactors. The acroym stads for Costat Axial Shape of Neutro Flux, Nuclide Desities ad Power Shape Duri Life of Eery Productio, but also represets the cadle-like burup. Whe this burup stratey is adopted, althouh the fuel is fixed i a reactor core, the buri reio moves, at a speed proportioate to the power output, alo the directio of the core axis without chai the spatial distributio of the umber desity of the uclides, eutro flux, ad power desity. The reactivity ad reactor characteristics do ot chae. Most siificatly, whe usi this stratey it is ot ecessary to use cotrol rods for the cotrol of the burup. A CANDLE uclear reactor is hece safer, ad just as importatly, makes us feel safer. CANDLE burup has various other roud-breaki merits. Whe this burup is used i a fast reactor that has excellet eutro ecoomy, excellet performace is obtaied. It is possible to use atural uraium or depleted uraium as fuel ad about 40% of the fuel will bur. A lare amout of depleted uraium is already available, ad hece if we are able to use it as fuel, we ca cotiue to use uclear eery for almost a milleium without further uraium mii, erichmet, ad reprocessi. I additio, the amout of spet fuel is reatly reduced. While there are reat advataes i usi CANDLE burup, umerous

8 techoloical developmets are ecessary before it ca be used. However, for block-fuel hih-temperature as-cooled reactors, curretly uder developmet i several coutries, CANDLE burup ca be applied without additioal techoloical developmet. I this booklet, the specific applicatio of CANDLE burup to a hih-temperature as-cooled reactor ad a fast reactor with excellet eutro ecoomy are described. Whe the former Nuclear Reulatory Commissio Chairma Dr. Meserve lectured o the curret status of uclear eery, he cited a Chiese proverb to brihte the preset dark status. I remember he said, Better to liht a cadle tha curse the darkess. Thus, I have ive the booklet the title: Liht a CANDLE. I hope that this booklet will cotribute to the briht future of uclear eery. I have avoided riorous discussios i this booklet so that it ca be read i a relaxed maer. If this makes it difficult for experts to uderstad, the please forive me. I recommed that iterested experts should read the refereces. Eve thouh umerous papers coceri CANDLE burup have bee published, they are ot tareted to the eeral audiece, ad therefore I have ot listed may refereces. Althouh I tried ot to use equatios, I had o optio i the explaatio of the aalysis method, ad differetial equatios had to be icluded, thouh I used oly the most basic equatios from uclear reactor theory. Those who have studied the subject will easily uderstad these equatios, however, those readers who are ot ood at mathematics ca skip that chapter. This booklet is writte so that eve those readers ca uderstad the rest of the chapters. I have received ecouraemet from umerous people i prepari this booklet. Professor Thomas H. Piford, my Ph.D. thesis adviser, is chief amost them. He has a iterest i the importat role of the combiatio of eutro trasport ad burup, which was the topic of my Ph.D. thesis, ad ave me reat ecouraemet i my research. Professor Ehud Greespa assisted with cosiderable discussios coceri CANDLE burup. It was he who iformed me of similar research coducted by Dr. Edward Teller. I am also rateful to the umerous other researchers for ivi me advice ad ecouraemet. Althouh I do ot kow Dr. Alvi M. Weiber persoally, I oce set him a

9 paper, as he had bee promoti the developmet of iheretly safe reactors ad I thouht that he would be iterested i CANDLE burup. Dr. Weiber showed a iterest i the paper ad set me a letter of ecouraemet. I heard that he cotacted Dr. Teller. Some time later I saw Dr. Teller s obituary i the ewspaper. I would have liked to have kow what he thouht of CANDLE burup. The Japaese Miister of Educatio, Culture, Sports, Sciece ad Techoloy bea 21st Cetury COE (Ceter of Excellece) Proram i fiscal 2002 for selecti excellet research istitutes of uiversities ad formi iteratioally competitive research bases. Academic disciplies from humaities ad social scieces to atural scieces are divided ito te cateories. A proposal from Tokyo Istitute of Techoloy Iovative Nuclear Eery Systems for Sustaiable Developmet of the World (COE-INES) was adopted i the cateory of Mechaical, civil, architectural ad other fields of eieeri. It is the oly oe COE i the uclear eieeri field. CANDLE burup is oe of the most importat research topics i COE-INES. The research described i this booklet was coducted by Dr. Kouichi Ryu, Mr. Ketaro Taaka, Mr. Takashi Takada, Dr. Yasuori Ohoka, Mr. Yutaka Udaawa, Mr. Ke Tomita, ad Mr. Makoto Yamasaki, raduate studets of my research laboratory. I am very rateful to them, ad also rateful to Associate Professor Tohru Obara for his fruitful discussios. Tokyo November 2005 Hiroshi Sekimoto

10 Cotets 1. Excess Neutros Does Istability Mea More Stability? Nuclear Fissio Chai Reactio ad Cotrol of Criticality Burup ad Burup Cotrol Use of Excess Neutros 8 2. What is the CANDLE Burup Stratey? Cocept of the Burup Stratey Advataes ad Issues i the Burup Stratey Mathematical Explaatio ad Aalysis Method Block-fuel Hih-temperature Gas-cooled Reactor Priciple Advataes Aalysis Results Natural Uraium (or Depleted Uraium) Loaded Fast Reactor Priciple Aalysis Results Advataes ad Issues Supplemetary Issues Issues Coceri the Iitial Core Issues i Hih Burup Summary 38

11 Refereces 40 Techical Terms 42

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13 1. Excess Neutros 1.1. Does Istability Mea More Stability? Whe I was a studet, I believed that a eutral state was more stable tha a state i which positive ad eative chares were separated. Therefore, whe I leared that the eutro is ustable ad the proto stable, I thouht it was very strae. However, I was impressed with the mechaism of ature after I realized that the istability of the eutro is absolutely ecessary for our existece i the uiverse. A eutro i isolatio ca exist for oly a short time, ad breaks dow to a heavy, positively chared proto ad a liht, eatively chared electro by the process kow as β-decay. However, a eutro ca be stable whe it is boded to a proto. A suitable umber of protos ad eutros boded toether form a positively chared ucleus. The traditioal imae of a atom is of a ucleus circled by eatively chared liht electros. Iterestily, the state i which electros circle aroud oly oe ucleus is ot ecessarily the most stable state. This istability leads to the formatio of molecules, with further iteratio leadi to polymers, maki possible livi matter, ad evetually leadi, as the deree of complexity icreases, to huma beis. Most iteresti is the fact that the mass of a eutro is oly 0.08% larer tha the sum of the masses of a proto ad a electro. As a result of this, the half-life of a eutro is 10.4 miutes. It is assumed that whe the uiverse was created with the Bi Ba, approximately the same umber of protos ad eutros were created. However, these eutros bea coverti ito protos. Yet, the half-life of a eutro was sufficiet for deutero to be formed by the bodi of eutros to protos before the eutros disappeared, ad subsequetly for helium to be formed. If the half-life of a eutro was ay shorter, very little helium would have bee formed ad heavier atoms would ot have bee created. Accordily, itelliet life costructed from complicated molecules would have ever bee created. O the other had, if the half-life was loer, eutros would be more stable ad eutro stars would have bee easily created. I this case, shii stars would ot have bee created, maki coditios for the creatio of itelliet life very difficult.

14 The allowable istability rae of the eutro is extremely arrow for the birth of itelliet life. It may be possible to explai the mechaism by which this value was selected based o more basic laws ad costats. However, this leads ito a edless cycle of searchi for the orii of the basic laws ad costats. Oe miht almost be iclied to cocede that God himself selected the exact istability of the eutro. Whatever its orii, the istability of the eutro is thus exquisite Nuclear Fissio As described above, a ucleus cosists of protos ad eutros. Therefore, protos ad eutros are called ucleos. Liht atomic uclei have ood symmetry ad cosist of approximately the same umber of protos ad eutros. However, as the size of the ucleus icreases, the electric repulsio due to the positive chares of the protos makes the ucleus ustable. However, atomic uclei with a larer umber of eutros tha protos become stable aai. The larest atomic ucleus existet o the earth is uraium-238 ( 238 U), which has 146 eutros compared to 92 protos. Nuclear reactios betwee atomic uclei are very difficult to achieve because the stro electric repulsio due to the positive chare of uclei hiders their approach to each other. However, sice eutros have o chare, they ca easily cause uclear reactios. A eutro with low eery is more likely to cause a uclear reactio because of the quatum effect. Whe a eutro with low eery hits a ucleus, eutro absorptio usually takes place. Whe a eutro is absorbed by a ucleus, the ewly created ucleus usually ais excess eery. The excess eery icreases the iteral kietic eery of the ucleus ad it becomes ustable. I most cases the excess eery is evetually released as hih eery electromaetic waves (γ rays) ad the ucleus becomes stable. However, whe a eutro hits uraium-235 ( 235 U), the ucleus ais a lare amout of excess eery, ad sice it cosists of may ucleos, it starts vibrati like a liquid drop, evetually breaki ito two uclei of a similar size with very hih probability. This uclear reactio is called uclear fissio ad the two eerated uclei are called fissio products. I uclear reactors, fast-traveli eutros collide with liht uclei, loweri the eery of the eutros. By repeated collisios the eutros are rapidly moderated ad

15 reach a fial eery equivalet to the kietic eery of the collisio taret, amely, the thermal eery of the medium. Hece, moderated eutros are called thermal eutros. If a thermal eutro is absorbed by 235 U, uclear fissio takes place. Uraium-238 ( 238 U) o the other had does ot udero uclear fissio by eutro absorptio, due to the fact that a ucleus with a eve umber of eutros ad of protos is more stable tha oe with a odd umber of eutros or protos. That is, the eutro umber of 235 U is 143, which is odd, but becomes 144, which is eve, after absorbi a eutro. The eutro umber of 238 U however becomes odd after absorbi a eutro. Because of this differece, the excess eery aied by eutro absorptio is larer for 235 U tha 238 U, ad accordily, uclear fissio takes place for 235 U but does ot for 238 U. A uclide that fissios after absorbi a thermal eutro is called a fissile material, ad a uclide that does ot fissio but becomes a fissile material is called a fertile material. As metioed above, a heavy ucleus has more eutros relative to the umber of protos tha a liht ucleus. I uclear fissio, a heavy ucleus is coverted ito two uclei each of approximately half the weiht of the paret ucleus. As a result, the umber of eutros is i excess of that required for uclear stability, ad hece two to three eutros are usually released per uclear fissio. This umber of emitted eutros, averai aroud 2.5, will be very importat i the rest of this booklet. It is less tha the umber of eutros expected from the excess eutros of the two dauhter uclei. Not all the excess eutros are released; the majority of them are retaied i the fissio products. These uclei are ustable, but are radually stabilized by the decay of the excess eutros ito protos. It should be oted thouh that a small fractio of uclei are stabilized by releasi eutros. Neutros released i this way are called delayed eutros. Delayed eutros play a importat role i the operatio of a uclear reactor; however, the explaatio of this role will be omitted here. Eve for stable uclei, some uclei have hih stability ad some have low stability. The peak of stability is located aroud iro; uclei heavier ad lihter tha iro are less stable tha iro. Uraium is located at the heaviest ed. It is itrisically ustable ad chaes very slowly ito a lihter ucleus by successively releasi α- ad β- particles. Throuh uclear fissio a very ustable ucleus is coverted ito stable uclei i oe reactio. Eery is released whe a ustable state chaes to a

16 stable state. The eery released per uclear fissio is about 200 MeV ( ev). I cotrast, the buri of fossil fuel is a chemical reactio, where the heat value per chemical reactio is measured i ev. From the compariso we ca see that the heat value of uclear fissio is extremely lare. Eve for stable uclei, some uclei have hih stability ad some have low stability. The peak of stability is located aroud iro; uclei heavier ad lihter tha iro are less stable tha iro. Uraium is located at the heaviest ed. It is itrisically ustable ad chaes very slowly ito a lihter ucleus by successively releasi α- ad β- particles. Throuh uclear fissio a very ustable ucleus is coverted ito stable uclei i oe reactio. Eery is released whe a ustable state chaes to a stable state. The eery released per uclear fissio is about 200 MeV ( ev). I cotrast, the buri of fossil fuel is a chemical reactio, where the heat value per chemical reactio is measured i ev. From the compariso we ca see that the heat value of uclear fissio is extremely lare. produced eery:200mev/fissio mea umber of emitted eutros: ν 2.5 eutro fissile ucleus fissio product(fp) (fissio framet) Fiure 1 Characteristics of uclear fissio. The characteristics of uclear fissio are summarized i Fiure 1.

17 1.3 Chai Reactio ad Cotrol of Criticality As metioed, if a fissile material absorbs a eutro, uclear fissio takes place at a hih probability ad two to three eutros are released. This leads to the possibility of the ewly eerated eutros iduci successive uclear fissios. A stri of such succeedi uclear fissios iduced by the eerated eutros is called a chai reactio, show i Fiure 2. fissio capture leak Fiure 2 Nuclear fissio chai reactio. The umber of eutros i the system may icrease or decrease with time, or it may stay the same. This is very importat for uclear reactors ad is ecapsulated by the eutro multiplicatio factor. A uclear fissio chai reactio proresses from oe

18 eeratio of uclear fissio to the succeedi eeratio of uclear fissio. The eutro multiplicatio factor is defied as the ratio of the umber of eutros i oe eeratio divided by the umber of eutros i the precedi eeratio: Neutro multiplicatio factor = Number of eutros i oe eeratio Number of eutros i the precedi eeratio Whe this value is equal to uity, the umber of eutros does ot chae with time ad the system is i what we call a critical state. Whe the value is larer tha uity, the umber of eutros icreases with time, ivi a supercritical state. Whe the value is smaller tha uity, the umber of eutros decreases with time, ivi a subcritical state. I a uclear reactor operati at costat power, the umber of eutros is costat ad the eutro multiplicatio factor is uity. I order to stop the operatio of the reactor, we make the eutro multiplicatio factor sufficietly smaller tha uity. This is accomplished by iserti a eutro absorber ito the core (the fuel reio of the uclear reactor). I this way, eutros eerated by uclear fissio are absorbed by the eutro absorber by the time of the succeedi eeratio of uclear fissio. Thus, the eutro multiplicatio factor becomes less tha uity. A eutro absorber is usually formed ito a rod shape ad therefore is called a cotrol rod. The eutro multiplicatio factor will also chae depedi upo operatioal circumstaces. For example, a chae of core temperature alters the multiplicatio factor. It is a serious problem if the eutro multiplicatio factor icreases with a icrease i temperature. I this case, eve if the iitial state is critical (i.e., the eutro multiplicatio factor is uity), as the uclear fissio causes a icrease i temperature, the umber of uclear fissios icreases (i.e., the eutro multiplicatio factor icreases to reater tha uity). This causes the temperature to icrease further, resulti i a further icrease i the umber of uclear fissios. I this way, the uclear reactor will eter a vicious cycle leadi to a ruaway reactio. Hece, it is ecessary to desi a uclear reactor so that the eutro multiplicatio factor decreases with a icrease i temperature. I a reactor desied i this way, whe the temperature icreases as a result of a icrease i uclear fissio (i.e., whe the eutro multiplicatio factor is reater tha

19 uity), the eutro multiplicatio factor decreases ad evetually coveres to uity. That is, the uclear reactor respods to exteral disturbaces due to temperature chae, elimiati the effect ad stabilizi the operatio Burup ad Burup Cotrol Nuclear reactors differ from fossil fuel reactors i the way the fuel is used. I a fossil fuel reactor, a lare amout of fuel must be cotiuously supplied to the furace. I a uclear reactor, however, oce fuel has bee put ito the uclear reactor, it ca be kept i the reactor for years. Hece it is said that a uclear reactor has hih eery security. It ca cotiue to operate eve whe the supply of fuel is suspeded. Both reactors however cosume their fuel, ad by aaloy with fossil fuel power eeratio, the cosumptio of fuel by a uclear reactor is called burup. What happes i a uclear reactor i a critical state whe burup proresses? I widely operated liht-water reactors, fissile material decreases ad fissio products accumulate. The reactor is iitially put i a critical state by adjusti the eutro multiplicatio factor to be uity. However, the multiplicatio factor becomes less tha uity after the proressio of burup, ad if othi is doe, the reactor will become subcritical. I order to solve this problem, the followi method is eerally adopted. A excess of eutro absorber is iitially placed i the reactor. As the eutro multiplicatio factor decreases, due to the chae of the fuel compoets with burup, the amout of eutro absorber i the reactor is decreased so that the multiplicatio factor returs to uity. As a method for decreasi the eutro absorber, a eutro absorber that chaes due to burup ca be used, i additio to a method i which a operator withdraws the eutro absorber, as described i the precedi sectio. I this case, a eutro absorber is selected that is coverted to a material with smaller eutro absorptio as it absorbs eutros. The adjustmet of the coversio rate, however, is a importat desi challee. A eutro absorber used i this way is called burable poiso. It is difficult to maitai a uclear reactor i a exact critical state with oly burable poiso ad it is ecessary to iclude a huma-operated cotrol mechaism. Nevertheless, the load of the huma-operated cotrol mechaism ca be cosiderably decreased by the use of burable poiso.

20 1.5. Use of Excess Neutros The oly fissile material existet i ature is 235 U, ad its half life is shorter tha that of 238 U. Both have bee preset i the earth from its creatio, but 235 U decays faster tha 238 U ad hece atural uraium cotais at preset oly 0.7% 235 U, with the rest bei 238 U. Thus, may of the eutros eerated by uclear fissio i atural uraium are absorbed by 238 U, ad a chai reactio caot be maitaied. However, the reactivity of 235 U with thermal eutros is much larer tha that of 238 U. By applyi the characteristics of uclear fissio, Fermi succeeded i maki the first uclear reactor. I order to moderate the eutros, he mixed atural uraium with pure raphite i a heteroeeous structure. I order to lesse the leak of eutros, the assembly had to be hue. This eed for size demostrates how difficult it is to achieve criticality ad how few eutros are available for our use. η (E) Neutro eery, E (ev) Fiure 3 Value of η for typical fissile materials.

21 Recall that the umber of eutros eerated by uclear fissio is two to three. However, a fissile uclide does ot always fissio after the absorptio of eutros; it may remai a heavy ucleus after absorbi a eutro. Therefore, i the discussio of criticality ad the effective use of eutros, the umber of eerated eutros per eutro absorptio is more pertiet tha the umber of eerated eutros per uclear fissio. This value is called η (the Greek letter, read eta ). As show i Fiure 3, the value of η chaes depedi upo the uclide ad the eery of the absorbed eutros. Plutoium-239 ( 239 Pu) shows larer values of η tha 235 U, ad the value icreases drastically with a icrease i eutro eery from aroud 10 kev. If we allow 238 U to absorb a eutro, it ca covert ito the fissile material 239 Pu. This is why 238 U is called a fertile material. I the uclear fissio of 239 Pu iduced by a eutro, more eutros are eerated tha for 235 U, especially for hih eery icidet eutros. Thus, 239 Pu ca be eerated by allowi 238 U to absorb excess eutros, ad criticality of a uclear reactor ca the be achieved by a chai reactio of uclear fissio of maily 239 Pu. I this way, more 239 Pu ca be eerated tha is lost. If this ca be achieved, atural uraium ca be used i uclear fissio. (Of course, ot all atural uraium ca be used sice some plutoium may be mixed ito the waste at the time of plutoium recovery from the spet fuel. It is reasoable to say that about 70% ca be utilized. Eve i this case, we ca use 100 times more tha i the preset method i which oly about 0.7% of atural uraium is usable.) I a uclear reactor, a lare amout of radioactive material is produced. If there are excess eutros, it is possible to covert the radioactive waste ito harmless stable material by uclear reactios. If the eutros are used for uclear fissio ad the eeratio of fissile uclides, the umber of excess eutros available for this purpose will be less tha oe. I reality, the amout of excess eutros available is marial whe we take ito accout wasteful eutro absorptio ad leakae. However, realizi the applicatio of stabilizi the radioactive waste of uclear power is potetially epoch-maki. Thus, the very iteresti challee of How will it be doe? has bee preseted to us. Oe solutio is CANDLE burup.

22 2. What is the CANDLE Burup Stratey? 2.1. Cocept of the Burup Stratey spet fuel spet fuel buri reio burup buri reio fresh fuel fresh fuel Fiure 4 CANDLE burup stratey. (Note that the movi directio ca be the opposite of that illustrated. The core heiht is illustrated here to be extremely lo to make the explaatio easy.) CANDLE stads for Costat Axial Shape of Neutro Flux, Nuclide Desities ad Power Shape Duri Life of Eery Productio [1]. The abbreviatio also represets the cadle-like burup. As show i Fiure 4, whe this burup stratey is used, the buri reio moves at a speed proportioate to the power output alo the directio of the core axis without chai the spatial distributios of the uclide desities, eutro flux, or power desity. What is siificat is that eve thouh the fuel is fixed i the core, it is ot ecessary to use movable devices to cotrol the burup, such as cotrol rods ad reflector cotrol, as is the case i covetioal reactor desi. Note that the core heiht has bee illustrated as bei extremely lo to make it easy to show the characteristics of the burup stratey. I a ormal core however, the

23 combied leth of the spet fuel ad fresh fuel reios is much shorter tha that of the buri reio. Fiure 7, preseted later, better illustrates a actual reactor; thouh eve i Fiure 7, the movi distace is show as bei lo. Note also that althouh i Fiure 4 the buri reio is show as movi from the top to the bottom, it is possible to have the reio move from the bottom to the top. CANDLE burup is possible i a core desied so that the ifiite medium eutro multiplicatio factor k (the eutro multiplicatio factor cosideri the reactor to be of ifiite size) of the fuel chaes with burup specifically as show i Fiure 5. I the fiure, the eutro fluece is plotted o the abscissa, which is obtaied by iterati the eutro flux with respect to time. This value is cosidered to be proportioal to the burup. The ifiite medium eutro multiplicatio factor k of fresh CANDLE fuel is less tha uity. However, it icreases with the burup ad evetually becomes reater tha uity. After reachi a maximum, k decreases ad becomes less tha uity. Ifiite Medium Neutro Multiplicatio Factor, k E+00 1.E+24 2.E+24 3.E+24 4.E+24 Neutro Fluece (/cm 2 ) Fiure 5 Ifiite medium eutro multiplicatio factor k of fuel, with eutro fluece plotted o the abscissa.

24 Fiure 6 shows the same data as Fiure 5 with the core axis (Z axis) plotted o the abscissa. O the left is the fresh fuel side ad o the riht is the spet fuel side. O the left side of the peak, k icreases with burup, ad o the riht side it decreases. Accordily, the peak shifts to the left side, amely, to the fresh fuel side. The peak of the eutro flux is located i the viciity of the k peak. At locatios away from the peak, k takes smaller values ad is less tha uity ad the eutro flux approaches zero. As a result, burup does ot take place ad k shows a costat value at the left ad riht eds. I a equilibrium state, the spatial distributio of k does ot chae with time, it oly shifts to the fresh fuel side. It is ot difficult to eerate the k chae show i Fiure 5. The specific methods vary depedi upo the uclear reactor ad will be explaied later. Ifiite Medium Neutro Multiplicatio Factor, k Axial Positio (cm) Fiure 6 Ifiite medium eutro multiplicatio factor of fuel plotted aaist the cetral axis (Z axis). Arrows idicate the directios of chae with burup. I will add here the followi poits. Eve if the power level is chaed, the relative shape of the power distributio does ot chae ad oly the absolute values of the power distributio chae. The movi speed of the buri reio is proportioal

25 to the power level, the priciple of which I will explai i Sectio 3, Mathematical Explaatio ad Aalysis Method. I reality, the core heiht is fiite. Whe the buri reio reaches the ed of the core, the fuel should be chaed, as show i Fiure 7. Whe the buri reio reaches the ed of the core, the spet fuel reio is removed ad fresh fuel is added i the directio of burup. I this way CANDLE burup ca be cotiued. buri reio fresh fuel burup spet fuel buri reio refueli buri reio fresh fuel burup spet fuel buri reio Fiure 7 Refueli i the CANDLE burup stratey. Oce the iitial core is successfully prepared, the secod ad later cores are easily prepared. However, short life radioactive materials located i the buri reio i the steady state caot be used i the iitial core preparatio process, ad hece it miht be difficult to fabricate the buri reio of the iitial core usi oly easily obtaied materials. Cotrol rods miht be ecessary i the case where a ideal iitial core could ot be prepared ad a lare variatio i excess reactivity is caused with burup. If this happes, it may be more appropriate to build a special reactor oly for the first several cores, with cotrol rods istalled to cotrol the excess burup reactivity. Whe the first several cores are bured, fuel for the remaii core is produced with a compositio close to that of a ideal CANDLE core. This ew core is the trasferred to a ormal CANDLE reactor, which has o mechaism of cotrolli the excess burup reactivity. Thus, may iitial CANDLE cores ca be produced usi the oe uclear reactor. Presetly, research ito the makeup of the buri reio of the iitial core is i proress. With curret techoloy it is possible to prepare a iitial core that has little chae i excess reactivity, usi oly eriched uraium ad atural elemets. A example is ive Sectio 6.1. We are aii cofidece that a uclear reactor dedicated for prepari the iitial core will ot be ecessary.

26 2.2. Advataes ad Issues i the Burup Stratey I should explai how the k chae show i Fiure 5 ca be accomplished ad leads to CANDLE burup. However, the specific methods vary depedi upo the uclear reactor type. Therefore, I will explai this later whe I detail the differet reactors. Istead I will first explai what advataes are eerally expected whe this type of burup becomes possible. From eeral cosideratios, the followi advataes are expected. 1) No cotrol mechaism is required for the burup. I presetly used eeral uclear reactors, operatio is cotiued for a fixed period betwee refuelis. As the operatio is cotiued with fuel i the core, fissile material is cosumed ad fissio products, which waste eutros, accumulate. As a result, the characteristics of criticality deteriorate. To make the iterval betwee refuelis lo eouh, it is ecessary to make the reactivity (defied as (1-k)/k where k is the eutro multiplicatio factor of the core) sufficietly positive after the refueli. This causes the reactor to become supercritical, ad it must be adjusted so that it becomes critical by the isertio of cotrol rods. However, this leads to a bi waste of eutros, ad i additio the malfuctio of cotrol rods ad operatioal error may lead to serious accidets. I CANDLE burup, cotrol rods for the adjustmet of burup reactivity are ot ecessary, ad hece the followi advataes are expected. There is o waste of eutros. This is hihly desirable sice the umber of excess eutros is few, as metioed i Chapter 1. The operatio is simple ad easy sice burup cotrol is ot ecessary. The isertio of cotrol rods ito the core causes cosiderable distortio to the power distributio, which varies reatly with the burup. This effect suppresses the averae power desity ad deteriorates the ecoomy. This does ot take place i CANDLE burup. Accidets due to withdrawal errors of cotrol rods caot take place. Cotrol rods kept cotiuously i a uclear reactor lose their eutro absorptio capability. I CANDLE burup it is ot ecessary to have a

27 coutermeasure for this situatio. 2) There is o chae i the core characteristics duri the proress of burup. I a covetioal uclear reactor, the power desity peaki factor ad the power coefficiet of reactivity chae duri the proress of burup. Therefore, these effects should be fully take ito accout i the cotrol method. I CANDLE burup, these parameters are costat throuhout the burup. As a result, the operatio does ot chae, ad it is very simple ad reliable. The calculatio precisio i reactor physics (of the criticality characteristics, power distributio, power coefficiet of reactivity, etc.) is hih. This is due ot oly to the precisio of the data ad calculatio methods used, but is also the result of umerous criticality experimets. However, calculatios i reactor physics are difficult to verify experimetally whe burup has proressed, ad errors are lare compared with calculatios for fresh fuel. Therefore, it has bee ecessary i covetioal reactors to iclude lare safety maris i the power desity peaki factors ad power coefficiet of reactivity due to burup. This type of cosideratio is less importat for CANDLE burup. 3) It is ot ecessary to adjust the flow rate with orifices duri the proress of burup. I ordiary uclear reactors, the power distributio chaes with the proress of burup i a plae perpedicular to the axis. Therefore, eve if the flow rate of coolat is adjusted at the start of the burup, so that the exit temperature of the coolat is costat (for flow parallel to the core axis), the flow rate chaes with the proress of burup. If the chae is too bi, it is ecessary to readjust the flow rate throuh the coolat chael of the core. For example, a lo life reactor usi the out-i burup stratey has bee proposed, where the power peak moves from the outside to the ceter. I order to optimize its cooli, the outside of the orifice is iitially kept ope ad the later arrowed. At the ceter, it is iitially arrowed ad the opeed. I CANDLE burup, the axial iterated power distributio i the plae perpedicular to the axis does ot chae duri the proress of burup. Therefore, it is ot ecessary to adjust the flow rate duri burup. As a result, the operatio is easy ad operatioal errors ca be reduced.

28 4) Hih-level optimizatio of the radial power distributio is possible. As described above, i covetioal reactors, the power distributio exhibits complicated chae duri the proress of burup. A optimum distributio at oe time poit may chae to a cosiderably deviated distributio at aother time poit. Therefore, it is ecessary to optimize the distributio as a whole, cosideri the total lifetime of the core. I CANDLE burup, oce the power distributio is optimized, it ca be maitaied throuhout the lifetime of the core, ad hih-level assured optimizatio is possible. 5) The lifetime of a uclear reactor ca be easily letheed by icreasi the heiht of the core. I the case of a liht-water reactor, the core lifetime is letheed by icreasi the erichmet of fresh fuel ad icreasi the burup. The lifetime is simply determied by the material iterity ad allowable excess reactivity. If we wat to lethe the lifetime more tha allowed by this process, we have to decrease the power desity. Thus, eve for the same burup, the umber of years of operatio ca be letheed. I this case, if we wat to icrease the lifetime of the core by a factor of M without chai the total power, the volume should be made M times larer. If we wat to exted the lifetime of a CANDLE core, the core heiht should be letheed, icreasi the volume. If the distace the buri reio moves i the oriial desi is D, the a leth (M-1) D should be added to the core heiht i order to icrease the lifetime by a factor of M. I the case of the power desity stratey the volume must be icreased by a multiplicative factor, whereas i case of the CANDLE stratey, the volume must be icreased by a additive factor. Thus, the required icrease i volume is eerally smaller i the CANDLE stratey tha i the power desity stratey. The larer M is, the larer the differece betwee the two strateies. However, eve i the CANDLE stratey, if D is lare, the required chae i volume is expected to be lare, thouh D is eerally extremely small. The advataes of CANDLE burup because of this assumptio are listed below. The movi speed of the buri reio is eerally very slow. As a result, it is easy to desi a super lo-life reactor.

29 The core life ca be easily altered by chai the core heiht. Oce a small lo-life reactor is realized, a uclear reactor ca be produced at a factory, trasferred ad istalled at the site, operated for a lo time without chai fuel, ad trasferred back to the factory (for replacemet with a ew uclear reactor). Thus, the followi additioal advataes are expected: Refueli is the most difficult of the ormal operatios for a uclear reactor. Hece, whe a reactor is operated at a locatio where hih-level techoloy may ot be available, ot requiri refueli is a bi advatae. A uclear reactor that has fuel semi-permaetly eclosed i the core has hih uclear proliferatio resistace. 6) k of fresh fuel i a exchaed core is less tha uity. As show i Fiure 5, a importat feature of CANDLE burup is that k of fresh fuel is less tha uity (thouh depedi upo its desi, it ca slihtly exceed uity). From the viewpoit of safety, it is hihly desirable that k of fresh fuel be less tha uity. Eve whe a lare amout of fresh fuel is athered toether, the possibility of it becomi critical is very small. Thus, the trasportatio ad storae of fresh fuel is simple ad safe. O the other had, CANDLE burup has the followi issues. 1) The core teds to be axially lo ad the pressure loss of coolat teds to become lare. If a lo-life reactor is desired, a axially lo core should be prepared, which requires that the chael leth of the coolat also becomes lo. As a result, the pressure loss becomes lare, ad it is ecessary to use a powerful pump. However, as lo as the core is ot extremely lo, this is ot a problem. If the movi speed of the buri reio is very slow, a lo lifetime ca be achieved without usi a very lo core. For example, the movi speed i a lare fast reactor is typically about 4 cm/year, or 40 cm i 10 years ad 80 cm i

30 20 years. These leths are i a rae that eve a ormal pump will ot be affected by a icrease i pressure loss. 2) The adjustmet freedom i the axial power desity distributio is small. A axial power distributio is iheret to CANDLE burup. However, the radial power distributio ca be reatly optimized, as metioed above i advatae 4. O the whole, the total power distributio is cosidered to be quite ood. 3) The preparatio of the iitial core is difficult. The preparatio of exchae fuel is simple. However, for the iitial core, fuel that ca stimulate the buri reio effectively must be prepared. Sice there is cosiderable radioactive material i the buri reio, it is difficult to stimulate it with easily available materials. The requiremets are as follows. The effective eutro multiplicatio factor of the core i a equilibrium state should be uity. The chae of the effective eutro multiplicatio factor should be small util a equilibrium state of the core is reached. The CANDLE core should be swiftly brouht to equilibrium. It may be ecessary to istall cotrol equipmet if the chae of the effective eutro multiplicatio factor of the iitial core is lare. I this case, as metioed i Sectio 2.1, oe solutio is to make a special uclear reactor for the preparatio of the fuel of the equilibrium core. Various solutios have bee proposed to address these issues. I will ot o ito further detail here, thouh I will describe oe example i Sectio 6.1. Hopefully the above explaatio has show you that CANDLE burup is a excellet burup stratey. There are otable advataes for each type of reactor employi CANDLE burup, as will be explaied later as each reactor type is aalyzed. I the followi sectios, calculatio results will be preseted for the applicatio of the burup stratey i a block-fuel hih-temperature as-cooled reactor ad a lead-bismuth-eutectic (LBE) cooled metallic fuel fast reactor. Before that, however, I will briefly touch o a aalysis method for CANDLE burup.

31 3. Mathematical Explaatio ad Aalysis Method Some priciples of CANDLE burup are easy to uderstad if they are mathematically explaied. I fact, the explaatio of the aalysis method is difficult without usi some equatios. Here the mathematical explaatio ad aalysis method for CANDLE burup are described. Readers who do ot like mathematics ca skip this chapter sice the other chapters ca be uderstood without readi this chapter. It is ot easy to directly solve the equatios for a CANDLE burup reactor. It is also difficult to cofirm if the core is i a equilibrium state i the true sese. Sice the power distributio shifts with time, a lo coordiate axis is ecessary ad the determiatio of coverece is difficult. A detailed explaatio of these is omitted ad oly the priciples of how to solve the problem of equilibrium will be explaied. See referece [1] for further details. First, the eutro trasport equatio ad uclide trasformatio equatio must be solved. For the deree of precisio presetly uder cosideratio, the eutro diffusio equatio is sufficiet istead of the eutro trasport equatio. I order to simplify the equatio, cylidrical coordiates are used for the equatio. Note that this does ot mea that the diffusio equatio is suitable for CANDLE burup reactor aalysis, thouh the strict trasport equatio ca be trasformed i a similar way. Eve whe space is treated three-dimesioally, a similar expasio is possible. --- (1) Here the terms for short time trasiets such as the time derivative of the eutro flux ad delayed eutro cotributios are omitted. The uclide trasformatio equatio is expressed i the ext equatio. + + R N N z D z r rd r r 1 1,,, 1 φ σ φ σ φ φ 0 ' ' ',, = + F eff N k φ νσ χ + + R N N z D z r rd r r 1 1,,, 1 φ σ φ σ φ φ 0 ' ' ',, = + F eff N k φ νσ χ

32 --- (2) These equatios are the most basic i uclear reactor theory. The symbols used for the variables are those eerally used, ad therefore a explaatio of them is omitted. Ufamiliar readers should cosult textbooks o uclear reactor theory. The solutio is obtaied by solvi these equatios simultaeously. This aalysis is much the same as covetioal uclear reactor aalysis. However, there are very differet characteristics, which I will describe. I ordiary uclear reactor aalysis, the uclide desity distributio i the uclear reactor is ive as a calculatio coditio, ad the power desity ad criticality are solved for this ive uclide desity distributio. I the case of a CANDLE reactor, the situatio is differet ad the locatio of the buri reio is ot certai. Uder ideal coditios ive for the ifiite-leth core, the buri reio moves from ifiity i oe directio, to ifiity i the other directio. The buri reio has a spread, but it is difficult to determie. The power distributio, which is usually costraied by boudary coditios (ad eutro source coditios i some other cases) i ordiary uclear reactor aalysis, caot be fixed with coordiates i the aalysis of a CANDLE reactor. Nevertheless, the power distributio udeiably exists. The difficulty i calculatio is related to the ucertaity i the positio of the buri reio ad because of the movemet of the buri reio. I order to address this difficulty, we ca cosider a coordiate system that moves alo with the buri reio. I this case, eve as burup proresses, the buri reio does ot move. The trasformatio to this type of coordiate system is the Galilea trasformatio. Uder this trasformatio, the eutro diffusio equatio ad uclide trasformatio equatio become as follows. --- (3) = ' ', ' ' ' ',, A N N N t N φ σ λ φ σ λ + + R N N z D z r rd r r 1 1,,, 1 φ σ φ σ φ φ 0 ' ' ',, = + F eff N k φ νσ χ + + R N N z D z r rd r r 1 1,,, 1 φ σ φ σ φ φ 0 ' ' ',, = + F eff N k φ νσ χ

33 --- (4) Here V stads for the movi speed of the buri reio. Sice V is a ukow, it is ecessary to determie it. These equatios are solved by iteratio, but the details will be omitted. Please see referece [1]. Equatio (3) does ot chae uder the Galilea trasformatio, ad is the same as equatio (1). The importat fact is that the time variable has disappeared i equatios (3) ad (4). Thus, the calculatio becomes very simple ad coverece becomes certai. The eutro trasport equatio correspodi to equatio (3) would also ot chae uder the Galilea trasformatio eve if the strict trasport equatio was cosidered istead of the diffusio equatio. Several characteristics ca be derived from the obtaied equatios ad here a few of the most importat aspects are described. I equatio (4), there are two kids of uclear trasformatio, eutro iduced reactio ad radioactive decay; however, radioactive decay ca be eerally iored. If V / = φ Φ is used istead of φ, V is removed from equatios (3) ad (4). Φ + Φ Φ + Φ R N N z D z r rd r r 1 1,,, 1 σ σ 0 ' ' ',, = Φ + F eff N k νσ χ 0 ', ' ',, = Φ + Φ A N N z N σ σ This idicates the followi. If the eutro flux, amely the power, is icreased by a factor of m, the movi speed of the buri reio also icreases by m. Eve the absolute value of the power becomes m times reater, thouh the relative shape does ot chae. That is, whe the power is chaed, the movi speed of the buri reio ad the absolute value of the power desity chae, however, the power desity distributio does ot chae. These results, however, do ot hold whe radioactive 0 ' ' ', ' ' ' ',, = A N N N z N V φ σ λ φ σ λ

34 decay caot be iored. I this case, a chae i the eutro multiplicatio factor poses a bier problem tha a chae i the power distributio. The relatioship betwee the movi speed of the buri reio, burup of spet fuel, ad total power is more directly expressed by the followi equatio, which has o approximatio. ' N σ φ dz = V N σ dt F,, ' ' F,, ' φ ' ' Here the left side is the total umber of uclear fissios iterated alo the axis at a certai radial positio. The iteral o the riht side is proportioal to the burup of the spet fuel at the same radial positio.

35 4. Block-fuel Hih-temperature Gas-cooled Reactor 4.1. Priciple The hih-temperature as-cooled reactor [2] has attracted a rowi iterest ad various applicatios based o its use of hih temperature as are evisioed. Lately, the hih safety of the reactor has attracted attetio ad its excellet ecoomy has bee recoized. As a result, the costructio of commercial reactors is plaed. A further advatae of this reactor is that the iterity of coated fuel particles i the reactor ca be maitaied up to hih burup, ad thus the reactor has attracted attetio as a suitable reactor for the elimiatio of plutoium ad mior actiides. For details see the explaatio i referece [2]. coolat flow fuel flow cotrol rod reflector core reflector core (a) Block-fuel type (b) Pebble-bed type Fiure 8 Schematic diarams of hih-temperature as-cooled reactors. Hih-temperature as-cooled reactors ca be maily classified ito the block-fuel type ad pebble-bed type. Schematic diarams of the two types are show i Fiure 8.

36 Keep i mid however that the leth ratios i these illustratios are very differet from the actual leth ratios; for example, the pebbles (fuel spheres) i the pebble-bed reactor are of teis ball size. The size of the pressure vessel i these uclear reactors is ot very differet from that of a lare liht-water reactor. The drivi mechaism for the cotrol rods is illustrated oly for the block-fuel reactor. For the pebble-bed reactor, oly a cotrol rod drivi mechaism for start-ad-stop cotrol is ecessary; cotrol rods are ot ecessary for burup cotrol. Althouh the pebble-bed reactor has a advatae i that refueli is possible duri operatio, it has some techoloical complicatios. For the applicatio of CANDLE burup, the block-fuel hih-temperature as-cooled reactor is the most suitable uclear reactor amost presetly operated uclear reactors sice o drastic desi chaes are ecessary.[3] Burup ad refueli i this reactor are show i Fiure 9. I this fiure, chaes i uclide desity of importat uclides ad eutro flux (speed weihted averae umber desity of eutros) alo the core axis are show. 1.0E E+13 uclide desity (#/cm 3 ) 1.0E E E E E U 157 Gd fissio products (icludi Gd) eutro flux 2.5E E E E E+12 eutro flux (#/cm 2 s) 1.0E axial positio (cm) 0.0E+00 Fiure 9 CANDLE burup i a block-fuel hih-temperature as-cooled reactor.

37 I a thermal reactor, CANDLE burup is realized by addi burable poiso to the fuel. I Fiure 9 adoliium (Gd) is employed. Whe the microscopic absorptio cross sectio of the burable poiso is sufficietly larer tha that of the fissile material, the burable poiso will absorb eutros leaki from the buri reio to the fresh fuel reio ad will quickly disappear, as show i Fiure 9. I the fiure it does ot decrease to zero because it is repleished by fissios. Thus, fissile material remais i the fresh fuel reio ad the buri reio ca move ito this reio, realizi CANDLE burup. Burable poiso is presetly used i ordiary uclear reactors for suppressi excess reactivity duri burup. Thus, the self-shieldi effect, which adjusts the eutro absorptio rate, is coveietly utilized. However, i CANDLE burup, the burable poiso ideally disappears as soo as possible. Thus, it is thily mixed ito a raphite matrix to decrease self-shieldi. As is clear from Fiure 7, CANDLE-type refueli is possible for block fuel without drastic desi chae, ulike pi-type fuel i liht-water reactors. Note that i this fiure, to emphasize the characteristics of CANDLE, the movi distace of the buri reio is show to be lo. Hece, the fiure is quite differet from the actual desi as it shows the exchae sectio as bei lare. I reality, oe block of spet fuel is removed ad oe block of fresh fuel loaded. Eve i this case, the lifetime of a operatio cycle is usually a few years Advataes Applyi CANDLE burup to a block-fuel hih-temperature as-cooled reactor has the followi advataes. 1) It shares the major advataes of the pebble-bed reactor. Cotrol rods for burup cotrol are ot ecessary. This is very importat from a safety viewpoit, so I will explai it further. I a hih-temperature as-cooled reactor, the coolat helium pressure is hih, aroud 70 atmospheres. Therefore, there is a possibility that the drivi mechaism of the cotrol rods, which rus throuh the pressure vessel, may jump out. If this happes, the reactivity of the uclear reactor

38 suddely icreases reatly ad the power may ru out of cotrol. I a CANDLE reactor, there are o cotrol rods for burup cotrol. Other cotrol rods used i the reactor do ot cause bi reactivity icreases ad the daer of reactivity accidets coveres eve if they should jump out. The characteristics of the uclear reactor do ot chae with time. Operatio is simple ad hihly reliable. 2) It has more advataes tha the pebble-bed reactor. Complicated equipmet used for o-power refueli is ot ecessary. I the pebble-bed reactor, the burup history of each pebble is radomly differet; thus, it is ucotrollable ad upredictable. I a CANDLE core, the burup of each elemet of fuel is cotrollable ad predictable. I the pebble-bed reactor, the fuel pebbles pile up ad move. Therefore, they may et damaed. This does ot occur i a block fuel reactor. 3) The maximum fuel temperature ca be lowered by chaeli the coolat i the opposite directio of the movemet of the buri reio. The power distributio shifts i the directio of the movemet of the buri reio ad expoetially decreases i the opposite directio. For such a power distributio, the maximum fuel temperature ca be lowered by chaeli the coolat i the opposite directio of the movemet of the buri reio. The other advataes described i Sectio 2.2 ca also be achieved Aalysis Results The desi parameters for a example block-fuel hih-temperature as-cooled reactor are show i Table 1. As burable poiso, atural adoliium is used. For the thermal output ad core shape, the values for the Hih Temperature Eieeri Test Reactor (HTTR), operated at JAERI, were mostly adopted. HTTR is a experimetal reactor ad the thermal output is extremely small. Thus, the desi is ot suitable for a commercial reactor. However, the values for this reactor were adopted sice the desi data are easily available. For the calculatio, a four-roup diffusio equatio, which is ofte used for the