Reaktör Sonrası Nükleer Yakı t Çevriminin
Ekonomik Analizi
Ali Erkan Soyer
Subm itted in Partial F u lfillm en t o f the R equirem ents for the Degree of
M aster of Science
in the Field of N uclear E ngineering
Hacettepe University
To the In stitu te for G raduate Studies in Pure and A pplied Sciences,
This work has been approved by the G raduate C om m ittee as partial fu lfillm en t of the requirem ents for then degree of M aster of Science in the field of Nuclear E ngineering
Graduate Committee
Head _____________________________________________
Assoc. Prof. H. Okan Zabunoğ lu
M e m b e r___________________________________________
Prof. Osman Kemal K adiroğ lu
M e m b e r___________________________________________
A ssist. Prof. Erol Çubukçu
APPROVED
This thesis has been approved on / / 1998 by the G raduate C om m ittee established by the Board o f the Institute
/ / 1998
Prof. Dr. G ültekin GÜNAY
HEAD OF THE INSTITUTE FOR GRADUATE STUDIES IN PURE AND APPLIED SCIENCES
ABSTRACT
Closing the nuclear fuel cycle has certain indisputable advantages: it increases utilization of resources by allowing reuse of valuable nuclear fuel materials and makes a significant contribution to environmental protection by making it possible to reduce waste volumes and to process waste into safer final forms for disposal. Closing the cycle would certainly be preferable if it does not have any significant economical drawbacks.
Taking a typical LWR (Light Water Reactor) cycle as the reference cycle, for different uranium prices and reprocessing and MOX (Mixed Oxide) fabrication costs, closed cycles in which spent MOX is disposed of or reprocessed is economically compared to the open cycle. Unit process costs obtained from literature is used and a computer program based on simplex method is written for cost calculations.
Break-even reprocessing costs which equal the cost of each closed cycle considered to that of the open cycle is determined for different price/cost conditions. Besides, shares and effects of unit process costs in and on the total fuel cycle cost is investigated.
ÖZET
Kapaly nükleer yakyt çevriminin avantaj lary arasynda deöerli nükleer yakyt maddelerinin tekrar kullanymyny saölayarak kaynak israfyny önlemesi ve atyklaryn düŞük hacimde güvenli Şekilde tasfiyesine imkan vererek çevresel korumaya önemli bir katky saölamasy sayylabilir. Bu avantajlara ekonomik avantaj da eklenebilirse açyk çevrime göre tercih edilmesi kaçynylmaz olacaktyr.
Tipik bir LWR (Hafif-Su Reaktörü) yakyt çevrimi referans alynarak; farkly uranyum fiyatlary ve yeniden imleme ve MOX (KaryŞyk Oksid) yakyt fabrikasyon maliyetleri için, kullanylmyŞ MOX'un tasfiye edildiöi ve yeniden iŞlendiöi kapaly çevrimlerin açyk çevrim ile ekonomik mukayesesi yapylmyŞtyr. Maliyet hesaplamalary için literatürden saölanan birim iŞlem maliyetleri kullanylmyŞ ve simplex metoduna dayanan bir bilgisayar programy hazyrlanmyŞtyr.
DeöiŞik fiyat/maliyet durumlary için kapaly çevrim maliyetini açyk çevrim maliyetine eŞit kylan yeniden imleme maliyetleri hesaplanmyŞ ve bunun uranyum fiyatlary ve MOX fabrikasyon maliyetleri ile olan ilişkisi belirlenmiştir. Ayryca yakyt çevriminde yer alan işlemlerin toplam maliyetteki paylary ve etkileri incelenmiştir.
ACKNOWLEDGMENTS
I am grateful to my advisor, Assoc. Prof. Okan Zabunoğlu, for his initiation of this study, his constant and patient guidance, understanding and confidence, and his inspiring stimulation throughout my study. I am also sincerely thankful for his careful review of this manuscript.
I extend special thanks to my family, my wife, and all of my friends. Without their love and encouragement this thesis would not have come into existence.
CONTENTS
ABSTRACT... iv ÖZET... v ACKNOWLEDGMENTS... vi CONTENTS... vii LIST OF FIGURES... ix LIST OF TABLES... x 1. INTRODUCTION... 12. THE NUCLEAR FUEL CYCLE... 2
2.1. Front End of the Nuclear Fuel Cycle... 3
2.1.1. Uranium Mining, Milling and Refining... 3
2.1.2. Uranium Conversion and Enrichment... 3
2.1.3. Fuel Fabrication... 3
2.2. Back End of the Nuclear Fuel Cycle... 4
2.2.1. Spent Fuel Storage... 4
2.2.2. Reprocessing of Spent Fuel... 5
2.2.3. W astes... 6
2.2.4. Disposal of Spent Fuel and/or High Level W aste... 7
2.3. Recycling... 8
2.3.1. Recycle Uranium... 9
2.3.2. Mixed-Oxide Fuel (MOX)... 10
3. THE REFERENCE AND ALTERNATIVE FUEL CYCLES...17
3.1. Once Through Cycle... 17
3.2. Closed Cycles... 18
3.2.1. MOX Disposal Cycle (MOXD)... 18
3.2.2. MOX-1 Cycle (MOX1)... 20
3.2.3. MOX-3 Cycle (MOX3)... 22
4.1. Purpose of the Study... 24
4.2. Linear Programming and Simplex Method... 25
4.3. Notation and Symbols Used... 27
4.4. Fuel Cycle Balance Equations... 29
4.5. Constraint Equations... 30
4.6. Unit Costs... 31
4.7. Minimization of Fuel Cycle Costs... 33
4.8. Summary of Input List... 34
4.8.1. Reactor Data... 34
4.8.2. Fuel Data and Fuel Cycle Parameters... 34
5. RESULTS AND DISCUSSION... 36
5.1. Once Through Fuel Cycle... 37
5.2. MOX Disposal Fuel Cycle (MOXD)... 38
5.3. MOX-1 Cycle (MOX1)... 40
5.4. MOX-3 Cycle (MOX3)... 42
5.5. Discussion and Recommendations for Further Study... 44
6. APPENDIX... 46
6.1. Computer Program and Input Description... 46
6.2. Sample Input... 49
6.3. Calculation of aPUM, aPU, aMPU, aU... 51
6.4. Optimum Tails Assay Calculation... 52
6.5. Unit Costs... 53
LIST OF FIGURES
Figure 2.1. Generalized nuclear fuel cycle...2
Figure 3.1. Once through cycle...17
Figure 3.2. MOX disposal cycle...18
Figure 3.3. MOX1 cycle... 20
Figure 3.4. MOX3 cycle... 22
Figure 5.1. Shares of process costs...37
Figure 5.2. Ratio of MOXD/once through fuel cycle cost (MOX fab.=300 $/kgHM)38 Figure 5.3. Break-even reprocessing costs for MOXD...39
Figure 5.4. Shares of process costs for MOXD (MOX fab.= 300$/kgHM)...39
Figure 5.5. Ratio of MOX1/once through fuel cycle cost (MOX fab.=300 $/kgHM)40 Figure 5.6. Break-even reprocessing costs for MOX1...41
Figure 5.7. Shares of process costs for MOX1 (MOX fab.=300$/kgHM)...41
Figure 5.8. Ratio of MOX3/once through fuel cycle cost (MOX fab.=300 $/kgHM)42 Figure 5.9. Break-even reprocessing costs for MOX3...43
Figure 5.10. Shares of process costs for MOX3 (MOX fab.=300$/kgHM)... 43
Figure 5.11. Break-even reprocessing cost (MOX fab.=300 $/kgHM)... 44
Figure 5.12. Break-even reprocessing cost (MOX fab.=600 $/kgHM)... 44
Figure 5.13. Break-even reprocessing cost (MOX fab.=900 $/kgHM)... 45
LIST OF TABLES
Table 2.2. Values of important neutronic parameters for 235U and 239P u ... 12
Table 2.3. Enrichments of fissile Pu fuel rods within the same assembly ... 13
Table 4.1. Indices for fuel cycle processes and nuclear materials... 27
Table 4.2. Symbols... 28
Table 4.3. Unit costs... 32
Table 4.4. Reactor data... 34
Table 4.5. Fuel data and fuel cycle parameters... 34
Table 5.1. Effect of 20% increase in unit process costs... 37
Table 5.2. Effect of 20% increase in unit process costs (for 60$/kgU)... 39
Table 5.3. Effect of 20% increase in unit process costs (for 60$/kgU)...41
Table 5.4. Effect of 20% increase in unit process costs (for 60$/kgU)...43
Table 5.5. Effect of 20% increase in unit process costs (MOX fab.=300$/kgHM)... 45
1. INTRODUCTION
A nuclear fuel cycle includes all processes starting from exploring and mining uranium and ending with permanent disposal of wastes. All processes taking place before irradiation in a reactor form the "front end of the cycle", which supply the fuel to reactors. The other part which includes processes after the fuel is removed from the reactor is named "back end of the cycle". The processes involved in the back end categorize the fuel cycle either as "open" or "closed". When the spent fuel is reprocessed and recovered materials are recycled, the cycle becomes "closed". Without reprocessing, the cycle is "open", in which it is planned to dispose of spent fuel permanently.
Closing the cycle has certain indisputable advantages: (1) it increases utilization of resources by allowing reuse of valuable nuclear fuel materials, (2) it makes a significant contribution to environmental protection by making it possible to reduce waste volumes and to process waste into safer final forms for disposal. Despite these two important advantages, a clear uncertainty exists in the economics of closing the nuclear fuel cycle, which seems to be a drawback at least for today.
This study is concerned with economical analysis of the back end of the nuclear fuel cycle; more specifically, estimating a break-even reprocessing cost (at which a closed cycle will cost the same as once through cycle) for several recycling options and price/cost conditions.
It is intended to find out a break-even reprocessing cost and its relation with other significant price/cost items (such as uranium price and mixed-oxide (MOX) fabrication cost) in the nuclear fuel cycle for certain recycling alternatives without getting into the detailed economics of each process in the back end of the nuclear fuel cycle.
2. THE NUCLEAR FUEL CYCLE
The nuclear fuel cycle starts with uranium exploration and ends with final disposal of the materials used and generated during the cycle. For practical reasons the cycle has been further subdivided into the front-end and the back-end. The front- end of the cycle occurs before irradiation and the back-end begins with the discharge of spent fuel from the reactor.
Figure 2.1 exhibits a general flow diagram of the nuclear fuel cycle; in which the closed cycle is shown by thick lines.
2.1. Front End of the Nuclear Fuel Cycle
2.1.1. Uranium Mining, Milling and Refining
Uranium is mined by conventional methods (either open pit or underground). Uranium ores usually contain 0.1 to 0.2% U3O8 (1 to 2 kg/t) although higher grades have been found in several cases [1]. The ores are processed to produce concentrates with a content of 70% U3O8 or higher. Commercial grade uranium concentrates are dissolved in nitric acid, purified by solvent extraction and precipitated as a nuclear grade material, usually ammonium diuranate.
2.1.2. Uranium Conversion and Enrichment
Light water reactors use slightly enriched uranium as fuel and the enrichment processes currently in use (gaseous diffusion and centrifugation) require uranium hexafluoride as feed material. Uranium hexafluoride is produced from the dioxide in two main steps: uraniumdioxide is converted to uranium tetrafluoride by hydrofluorination and the tetrafluoride is then converted to hexafluoride by fluorination with elemental fluorine. New enrichment processes like laser isotopic separation are being developed but have not yet reached the stage of industrial application.
2.1.3. Fuel Fabrication
Enriched uranium hexafluoride is reconverted to ceramic grade uranium dioxide which is then used to manufacture fuel for light water reactors. Ceramic grade uranium dioxide powder (either natural or enriched ) is cold pressed into pellets. These ‘green’ pellets are then sintered at high temperature (between 1400 oC and 2000 oC) under vacuum or in a controlled atmosphere. The sintered pellets are rectified to precise dimensions, washed, dried and clad in metal tubing (Zircaloy, stainless steel or aluminum) to form fuel pins. The pins are filled with helium under pressure, sealed and arranged into fuel assemblies ready to be introduced into reactors.
2.2.
Back End of the Nuclear Fuel Cycle
2.2.1. Spent Fuel Storage
A spent fuel storage facility can be described by a combination of the following characteristics: heat transfer medium (wet or dry); location(at or away from the reactor); and size (the number of power stations that the facility can support).
A 1000 MW(e) light water reactor will discharge every year about 30 to 35 tones of spent fuel. When this spent fuel is removed from the reactor it is highly radioactive and generates a considerable amount of heat, of the order of 10 kW/t of heavy metal[2]. The fuel must be stored in water pools at the reactor site for a minimum cooling period of 150 days or more, depending on the degree of burnup. Water serves as shielding and as a cooling medium to dissipate the heat released by the fuel elements. While in storage at the plant, the short lived fission products decay rapidly and the heat output decreases correspondingly. With LWR fuel, for example, the heat from a fuel assembly (0.46 tU, 33000 MWd/tU) is 17 kW after one month, 4 kW after one year and 0.8 kW after five years from the time of discharge from the reactor [3].
Spent fuels are transferred from the cooling ponds at the reactor site to interim storage facilities away from the reactor site and stored there for some time before reprocessing (in the closed-cycle approach) or conditioning prior to disposal (in the once through cycle approach). The necessity for the interim storage and the length of the storage period is determined by the capacity of the storage facilities at the reactor and the availability of the reprocessing capacity or of the disposal facility.
Various approaches have been developed for fuel storage. In wet storage approaches, the fuel assemblies are stored in ponds where they are cooled by water which has excellent heat removal characteristics, along with its good radiation shielding properties and optical transparency. Most LWR fuel storage pools are of similar design, rectangular in horizontal cross-section and 12-13 m deep. Fuel assemblies are placed in storage racks or baskets located at the bottom of the pool. The racks hold the assemblies in a vertical position and maintain the prescribed
spacing between assemblies to prevent criticality. The assemblies are normally inserted or removed vertically from above the racks, using mechanical handling systems. LWR fuel assemblies remain submerged during all fuel handling operations. The minimum shielding requirement is about 3 m of water. Generally, LWR rack depths are about 4.5 m, therefore 12-13 m of water is ample for fuel insertion into stationary racks. Radiation levels at the pool surface from all stored fuel are very low because a total of about 8m of water shielding is usually available. [4,5,6]
In other approaches, the fuel assemblies can be safely held in dry storage where cooling is accomplished using either air or inert gases with natural or forced circulation. Dry storage is complementary to wet storage since it requires initial cooling of the spent fuel in a pool prior to storage. Dry storage technology has been developed for the following design concepts: metal cask; concrete cask or silo; vault; and dry well. [5]
2.2.2. Reprocessing of Spent Fuel
A reprocessing operation consists of the following major steps : (1) mechanically chop the spent fuel assemblies into small pieces, (2) dissolve these parts in nitric acid, (3) use solvent extraction to separate into streams containing the products of interest and the wastes and (4) handle the wastes and products. The details of carrying out the various processes differ from plant to plant, but the general flow of the operation is based on these four steps listed above. As far as it is known, all reprocessing plants in the world employ variations of the Purex(Pu-U-Recovery- Extraction) process.
Purex process uses a solvent called TBP (tri-n-butyl phosphate) and liquid- liquid extraction principles, combined with oxidation-reduction chemical reactions. After the fuel is chopped, it is dissolved into nitric acid. The heavy elements go into solution, leaving behind the cladding. The nitric acid solution, which contains the uranium, plutonium, fission products and transuranium elements is processed through a solvent extraction system that separates fission products and transuranium elements from the uranium and plutonium. After that, uranium and plutonium are separated by using a chemical that reduces plutonium to an organic-insoluble state
while keeping the uranium in organic phase. The uranium is first recovered as uranyl nitrate (UO2(NO3)2.6H2O), which is subsequently converted into UF6 if it is to be sent to an enrichment plant. Plutonium is recovered first as nitrate (Pu(NO3)4), which is later converted into oxide (PuO2).
When the fuel is dissolved in nitric acid, gases such as tritium, krypton, xenon, iodine , CO2, nitrogen oxides, and steam are released. The gases are directed to a gas- treatment system where some are stored for later treatment and/or release, and others are recycled (nitric acid being formed from nitrogen oxides). Tritium containment is still questionable [7]. It should be mentioned that a reprocessing plant has an elaborate ventilation system and operates under negative pressure.
2.2.3. Wastes
During operations at the reprocessing plant, several separate categories of radioactive wastes are produced.
The liquid wastes generated from the solvent extraction system constitute high level waste (HLW). The high-level liquid waste contains more than 99 per cent of the non-gaseous fission products, together with traces of plutonium and other actinides. This waste may be concentrated by evaporation and stored in stainless steel tanks, which are water-cooled, double-walled, and situated in shielded facilities or calcined into nonstoichiometric oxides and stored in that form. The amount of liquid waste from a 1000 MWe PWR will typically be about 4 m3/year [3]. The rate of radioactive decay and the decrease in heat generation of the liquid waste is at first comparable to that of the spent fuel, as the radioactivity is dominated in both cases by the fission products. After some time, the plutonium nuclides and their daughter products come to dominate the decay of the spent fuel, and the decay of liquid waste then becomes more rapid.
Intermediate-level liquid wastes are usually contaminated with alpha-emitting radionuclides. The wastes can be processed to concentrate their radioactive content, which can be added to the high-level waste stream, or alternatively immobilized into a solid matrix such as concrete, bitumen, or resin. Low-level liquid wastes contain
very little radioactivity and are disposed of after appropriate treatment or discharged under carefully controlled conditions.
Solid wastes include the cladding removed from the spent fuel, filters, resins and other materials used during the reprocessing operation, and contaminated plant equipment. These wastes are radioactive to various degrees and most of them are contaminated with alpha emitters. After possible volume reduction by incineration, compaction or shredding, the wastes are immobilized into a solid matrix such as concrete or metal for disposal.
Gaseous wastes are produced during the chopping up of the spent fuel. After removing radioactive particulate materials by filtering and then removing some gaseous wastes by chemical processes, the remaining gases (H3, I2, Xe, Kr, C14..) are discharged under carefully controlled conditions to the atmosphere [7,3].
2.2.4. Disposal of Spent Fuel and/or High Level Waste
When reprocessing option is not adopted, spent fuel itself is considered as high level waste. Before final disposal of spent fuel conditioning techniques which include various embedding and encapsulation processes are to be employed. As for liquid HLW, a solidification (glassification or calcination) process is to be employed. Most commonly accepted solid form of HLW is glass. Waste oxides and glass melt are poured into metal canisters and canisters are surrounded by an overpack before disposal. In either case, spent fuel or HLW, metal cylinders of different sizes are the final form of waste to be disposed of permanently.
The only disposal method considered at present is geological disposal, where appropriately packaged wastes will be disposed of in repositories which will be constructed between several hundred and one thousand meter underground [8]. The repository for disposal of radioactive waste must provide a high isolation capability and be adequately stable. The repository design has to be optimized for each site,
bearing in mind the type of waste, the type of host rock, site specific conditions and so on.
The siting of such a repository requires special geological and seismic conditions in order to provide a physically and chemically stable environment preventing eventual migration of actinides and fission products into the environment. Several geological formations are under investigation for underground repository siting, including granite, salt deposits, basalt and tuff.
A geologic repository will look, on the surface, like a mine. A region of 2000 acres will form the exclusion area within which the main on-surface facilities will be built. Underneath, at a depth of between 600 to 1200 m, the spent fuel and/or HLW will be placed in excavated tunnels called “waste emplacement rooms” [9,10,11]. The waste, either spent fuel or HLW vitrified and contained in a metal canister, will be deposited in these rooms or in holes drilled in the rock. After the operation of the repository has been confirmed to be as designed, the rooms will be backfilled with the excavated rock. The backfilling provides an extra barrier between the wastes and the environment and also reinforces the structural integrity of the mined geologic medium.
At present there is no operating final repository for nuclear reactor fuel, although several are under study. The fuel is at present kept in at-reactor pools or in monitored and retrievable interim spent fuel storage, basically awaiting better technologies or eventual reuse of fissile material by means of reprocessing. The rate of progress in science and technology in the past few decades gives reason for optimism that a satisfactory solution of this problem will be found [2].
2.3. Recycling
Recycling of nuclear materials in the nuclear fuel cycle has been a main objective since the early 1970s. This objective has been given added stimulus by the desire to reprocess spent fuel, both as a means of waste management and to utilize further the recycled products (plutonium and uranium), thus closing the fuel cycle. Recycling of fissile materials from spent fuels is also identified as a contribution
towards ensuring the peaceful use of the material by incineration in reactors. However, recycling is unlikely to take place unless a net economic benefit is foreseen. Some of the difficulties involved in the enrichment of recycled uranium are examined, as well as the economic benefits arising when uranium recycling is undertaken.
2.3.1. Recycle Uranium
The value of reprocessed uranium will become increasingly important as material becomes available from reprocessing plants, even if the cost of natural uranium remains static.
Reprocessed uranium will differ significantly from natural uranium. The principal differences between reprocessed uranium and natural uranium are as follows[12].
The isotope U, which does not occur naturally, is present in recycled uranium and it is strongly radioactive relative to U. The U decay chain includes a number of gamma emitters, notably 208Tl, which is a strong emitter. Thus, the gamma activity of reprocessed uranium is higher than that of natural uranium and steadily increases, reaching an equilibrium value after about 10 years.
The isotope U is a naturally occurring alpha emitter. It is enriched in the fuel before irradiation and is only partly burnt out; hence, there is a higher concentration in the reprocessed uranium. As a result, the alpha activity of reprocessed uranium is also higher than that of natural uranium.
235
The concentration of U, the fissile isotope, is likely to be in the range 0.6 to 1.25w/o. The actual concentration in a delivery of UF6 for enrichment will not only depend on the initial enrichment and burnup of the original fuel, but also on its subsequent processing and blending through the reprocessing and conversion plants.
The 236U isotope is only present in reprocessed uranium. It is a strong neutron absorber and reduces the reactivity of the reprocessed uranium. Enrichment of reprocessed uranium is also more complicated than that of natural uranium because of the presence of U. The problems associated with U in the reprocessed
uranium are twofold. First, the isotope is a neutron absorber which effectively 235 reduces the reactivity of the material, i.e. it effectively reduces the U concentration. This necessitates additional 235U enrichment to compensate and it has been suggested that the compensation factor (i.e. the amount of additional U concentration required per unit of 236U concentration) for LWRs will be in the range 0.15 to 0.25 [12]. This will lead to a need for some 10 to 20% extra separative work. This is roughly equivalent to the separative work already contained in the reprocessed uranium, because the U assay is normally greater than that occurring in natural uranium. Second, the 236U present in the reprocessed uranium will be enriched. This will consume separative power and will increase the cost of enrichment by about 1%.
The transuranic elements neptunium and plutonium are also not present in natural uranium but result from the irradiation of the fuel assemblies. These elements are alpha emitters. In addition, fission products such as 106Ru and 99Tc will be present in reprocessed uranium and will contribute towards the gamma and beta activity of the material.
These differences between natural and reprocessed uranium require that modifications which include protection against radiation and compensation for the U- 236 neutron absorption effect should be made in the standard enrichment process of natural uranium in order to enrich reprocessed uranium.
It should also be noted that when spent uranium is stored as part of a strategic stockpile its value is likely to reduce with time because of the extra processing costs that will be needed due to the increasing activity of the material.
2.3.2. Mixed-Oxide Fuel (MOX)
Since the earliest days of the commercial utilization of nuclear power, it has been recognized that plutonium from reprocessing is best used in FBR’s. In the 1950’s, the general opinion was that reprocessing capacities in excess of the requirements for feeding FBR prototypes would be available. Most forecasts predicted that the excess plutonium would have to be utilized in LWRs during an intermediate period of 10 to 20 years. [13]
2.3.2.1. Behavior of MOX Fuel in LWR's
Behavior of MOX fuel in LWR's can be summarized as follows [13].
a- MOX fuel rods behave in a way similar to UO2 rods, with integrity as good as that of UO2 fuels. Pelletized and alternative vibrocompacted fuels perform similarly;
b- Excellent neutronic prediction can be achieved in power and burnup calculations in PWRs ;
c- Although an increase in fission gas release is noticed in MOX fuel rods, this effect is important only if the fuel operates close to the thermal instability threshold which is never reached in normal operation conditions;
d- MOX fuel shows a lower fuel clad mechanical interaction than UO2 rods;
2.3.2.2. Nuclear Characteristics of MOX
When a fraction of an LWR core, normally fueled with UO2, is replaced by MOX fuel, many characteristics of the core will change because of the different physical, chemical, and neutronic properties of the MOX fuel relative to UO2.
In general, the results of test assemblies irradiated in LWRs or in fast reactors show that mixtures of UO2 and PuO2 behave in much the same way, physically and chemically, as pure UO2. The potential differences are minimized by replacing only a fraction of the UO2 with MOX fuel. Much closer attention, however, must be paid to the neutronic differences between UO2 and MOX fuels.
There are two reasons for the neutronic differences. One is that the MOX fuel contains not one but many plutonium isotopes with relative concentrations that depend on the origin of the plutonium (recycled from LWR fuel or recovered from an FBR blanket), the time period during which the plutonium was stored, and whether or not the plutonium was recycled one or more times. For example, the relative concentrations of plutonium that was burned to 33000 MWD/MTHM, was reprocessed 3 yr. after discharge, and was stored for 2 yr. are 1.8w/o 238Pu, 58.3w/o
239Pu, 23.3w/o 240Pu, 11w/o 241Pu, and 5.6w/o 242Pu [14]. If it is burned in a subsequent cycle, again to 33000 MWD/MTHM, this discharged fuel would have the
following approximate composition: 2w/o 238Pu, 46.4w/o 239Pu, 27.4w/o 240Pu, 16.3w/o 241Pu, 7.9w/o 242Pu. Notice that the fraction of fissile plutonium (239Pu plus 241
Pu) is 69.3w/o in LWR-reprocessed fuel, but it becomes 62.7w/o after it is irradiated one more time. Obviously, for LWRs only the two fissile isotopes are useful; the others act as neutron poisons. This reduction of fissile plutonium, as irradiation increases, is well known from weapons production and is one of the obstacles that makes the civilian nuclear fuel cycle proliferation-resistant.
The second reason for the differences between UO2 and MOX fuel comes from the values of important neutron parameters like cross sections, neutrons emitted per fission. Table 2.2 provides the values of the most important parameters for core neutron physics. As a result of the larger absorption cross section of 239Pu in the thermal region, the reactivity worth of the control rods and of dissolved boron (in PWRs) is reduced. To improve this effect, one should place MOX rods away from control rods. The higher fission cross section of 239Pu will tend to produce power peaks. One way to avoid this effect is to place the MOX rods away from the water gap (where the thermal flux is high).
235 239
Table 2.2. Values of important neutronic parameters for U and Pu
Parameter 235U 239Pu
Ga (2200 m/s) 682 b 1019 b
Gf (2200 m/s) 584 b 748 b
n (2200 m/s) 2.07 2.11
P (delayed neutron fraction) 0.0065 0.0021
l (neutron lifetime) 47 p,s 27 |is
239 235
The fact that the average value of n is less for Pu than for U makes the former worth less (in the neutronic sense) than the latter. The existence of many resonances in Pu cross sections causes larger reactivity changes, due to the temperature-caused Doppler effect, than those of 235U. Both of these effects would require more fissile plutonium mass than with UO2 fuel to obtain the same excess reactivity in the core. Owing to neutron gamma reactions in competition with the fission reactions, the various plutonium isotopes are transmuted in plutonium
isotopes of higher atomic mass. This coupled chain, containing two fissile isotopes separated by a fertile isotope, results in a slower reduction of reactivity with burnup for MOX fuel than for UO2 fuel; as a result, the reactivity of a core containing MOX fuel assemblies decreases less rapidly with burnup than that of a core containing initially only UO2 fuel, providing an easier increase of reactivity lifetime.
Luckily, the reactivity decrease with burnup is slower in MOX fuel than in UO2. In fact, the difference is such that, to achieve the same burnup, one needs less excess reactivity with MOX than with UO2 fuel.
The lower value of the delayed neutron fraction P is of concern in case of accidents. A lower value for P means that it takes less reactivity to reach prompt criticality. The main method of alleviating this problem is to limit the amount of MOX in the core. The difference in prompt neutron lifetimes causes similar kinetics concerns.
In France, it has been reported that the decision has been made (1) to restrict the amount of MOX in the core to no more than 30% to ensure kinetics safety and (2) to place the MOX rods, within an assembly, in two or three zones with different enrichments. These zones and enrichments are shown in Table 2.3. This type of zoning results in the flattening of the power distribution.
Table 2.3. Enrichments of fissile Pu fuel rods within the same assembly [13]
Zone Enrichment Fissile Plutonium(%) Total Plutonium(%) Exterior 3.60 5.2 Intermediate 5.05 7.3 Central 6.50 9.40
The variation of the cross-sections of plutonium isotopes with energy is more complex than for the uranium isotopes since :(1) Absorption cross-sections of the main isotopes ( Pu, Pu) are about twice as important as for U in the thermal energy spectrum, resulting in relatively smaller reactive values for the control rod worth or for the boric acid in a UO2 - PuO2 lattice; (2) Absorption cross-sections of plutonium isotopes are characterized by absorption resonances more numerous and much higher in the epithermal energy range (0.3 to 1.5 eV) than those of the uranium
isotopes; moderator and fuel temperature coefficients are therefore more negative for MOX fuel than for UO2 fuel [13]. A LWR core loaded with MOX fuel assemblies is therefore more stable than a core containing only UO2 fuel and presents better reactor cycle stretch-out capabilities.
2.3.2.3.Reprocessing MOX Fuel
The plutonium recycled in LWRs essentially arises from the reprocessing of spent UO2 fuel. Its isotopic composition is a function of the discharge burnup of the fuel, especially if the plutonium arises from the reprocessing of a fuel which consisted initially of MOX fuel.
Until now, reprocessing of MOX fuel has not been performed on an industrial scale mainly because the priority was given to standard uranium enriched fuel and because the quantity of MOX fuel available for reprocessing was very small. It appears however that with adequate precautions to cope with or to minimize undissolved residues, the reprocessing of MOX fuel could be performed with existing technology.
In most of the reprocessing scenarios envisaged for the future, MOX assemblies are assumed to be dissolved and reprocessed jointly with enriched uranium assemblies.
Assuming a one year cooling time and simultaneous reprocessing of MOX and uranium fuel in the ratio 1:3, the following consequences arise from the difference in fission products (lower activity) and heavy metal (higher activity) composition [13]:
a) MOX fuel assemblies require a dedicated criticality safe dissolver;
b) Larger amounts of plutonium necessitate both a 60% increase in the flow rate of the process stream carrying the reducing agent through the plutonium extraction pulsed columns and an adjustment of the evaporator capacity;
c) Decay heat of high level wastes increases by 25% on account of the higher actinide content;
d) Neutron dose rates are increased by 35%, owing to the increased content of even plutonium isotopes;
e) Resulting collective doses increase by 10 to 20%, depending on decontamination procedures prior to maintenance;
f) The essential difference in airborne activity release consists of a factor of two increase in alpha aerosol emissions.
With due considerations of these factors, one sees that the reprocessing facilities are able to reprocess MOX fuel at no significant extra cost as long as it is diluted with uranium fuel at a ratio directed by the design of reprocessing plant [13].
2.3.2.4.Justification for MOX Fuel Utilization
Cost of Pu storage: The storage of Pu is costly. Beside the storage costs
themselves, some countries take into consideration the value of Pu and therefore the carrying charges of this capital. It is clear that the utilities have the opportunity to put their capital to work rather than store it with no return.
Decay of 241Pu: The Pu progressively loses part of its fissile content owing to
decay of Pu into Am, so that the valuable fissile material is lost for recycling since it is converted into a neutron absorber which, moreover, adds significantly to the radioactivity of the Pu to be handled. When too much Am is accumulated, this Pu needs to be purified. The losses in this process are usually evaluated to be equivalent to the losses due to reprocessing.
Buildup of decay products: As a result of the buildup of decay products
from 236Pu and 241Pu, Pu becomes more and more radioactive, after it has been produced by the reprocessing plant. This process is usually referred to as the ‘aging’ of Pu. As a consequence, Pu must be used for fabrication within a definite period after reprocessing. The length of this period depends on the Pu isotopic composition. For typical LWR fuel irradiated to standard discharge burnups, the Pu produced should be used within 3 years after reprocessing [13].
Plutonium arising: Plutonium arising from the reprocessing of MOX fuel is
uranium fuel. There is therefore no advantage to store either spent LWR fuel or reprocessed Pu for a long period rather than to use the Pu immediately in LWRs.
Plutonium utilization: The progressive incorporation of MOX fuel into
power plants allows for an increase in experience in Pu utilization and prepares in a timely manner for the 21st century when Pu will be one of the major energy resources.
Economy of MOX fuel: The cost of MOX fuel utilization is very
economical. The fabrication cost in the present facility is already satisfactory and will be reduced in the future facilities mainly through the size factor, the planned match of the expanding capacity to needs as well as the adequate adaptation of the processes and equipment to each product [15].
When looking at the Pu value in the present manufacturing context and in the future manufacturing facilities, one should ask whether Pu should not be stored to be fabricated in future manufacturing plants. The cost related to the storage of this Pu must take into account the storage cost itself, the interest charges on the value of Pu, the price of purification when the radioactivity of the Pu becomes too high (typically after about 3 years) and the loss of fissile Pu due to aging during the storage and to the rejects of the purification operation.
In any case, it would be uneconomical to store Pu for 3 years or more with the expectation that the low fabrication cost will lead to a benefit. In fact the benefit from lower fabrication cost is lost in the costs associated with Pu storage and purification. Practically, since the manufacturing capacity will gradually increase and therefore the fabrication price gradually decrease, it is not justified, on economic grounds, to store Pu for more than 1 to 2 years. [13,16]
3. THE REFERENCE AND ALTERNATIVE FUEL
CYCLES
In this study, once through cycle (or open cycle) is taken as the reference cycle and three closed cycles, MOX Disposal (MOXD), MOX-1 (MOX1), MOX-3 (MOX3) cycles are considered as alternatives.
3.1. Once Through Cycle
0.5 w/o Loss
0.3w/o Loss Depleted U
Figure 3.1. Once through cycle
Figure 3.1 shows material flow for the once through cycle. In this cycle slightly enriched uranium fuels are irradiated in the reactor for 3 years after enrichment and fabrication. The time spent for enrichment and fabrication processes is 1 year, each. 0.3w/o(weight percent) loss in enrichment, 0.5w/o in conversion and 0.5w/o in fabrication are assumed. After irradiation in a 1000 MWe LWR for 1100 days, each year one third of the core is removed from the reactor. The spent fuels are cooled for 5 years and then disposed in a geological medium.
3.2. Closed Cycles
3.2.1. MOX Disposal Cycle (MOXD)
0.5 w/o loss
Figure 3.2 shows material flow for MOXD cycle. In this cycle, enriched uranium fuels are irradiated in the reactor for 3 years after enrichment and fabrication. 0.5w/o loss in fabrication, 0.5w/o loss in conversion and 1w/o loss in reprocessing are assumed. The time spent for enrichment and fabrication processes is 1 year, each. The spent fuels removed are reprocessed after cooling for one year in reactor spent fuel pool. The time spent for reprocessing is 1 year. The recovered uranium is enriched to 3.5w/o due to U-236 penalty. After conversion and fabrication processes, the recovered uranium is irradiated in the same reactor with normal uranium fuels.
The recovered plutonium (Pu(U)) is blended with natural uranium to produce MOX fuel with a fissile content of 3.7w/o. MOX fuel is used in the same reactor together with recycling uranium and slightly enriched fresh uranium. Spent MOX fuel after irradiation is cooled for 5 years and then disposed in a geological medium. The resulting HLWs are cooled for 4 years and then disposed in a geological medium.
3.2.2. MOX-1 Cycle (MOX1)
0.5 w/o loss
Figure 3.3 shows material flow for MOX1 cycle. In this cycle, the spent fuels removed are reprocessed after cooling for one year in the reactor spent fuel pool. The recovered uranium is recycled and used in the same reactor. The recovered plutonium is used to produce MOX fuel, then MOX fuel is irradiated in the same reactor with recycling uranium and slightly enriched fresh uranium. The recovered HLWs are cooled for 4 years and disposed in a geological medium. After irradiation, spent MOX is cooled for 1 year and then reprocessed to recover Pu (Pu(MOX)). This Pu(MOX), which contains less fissile Pu (Puf) than Pu(U) obtained from reprocessing spent uranium fuel, is used to produce MOX1 fuel. MOX1 fuel is irradiated in the same reactor together with other fuels. Spent MOX1 is cooled for 5 years and then disposed; so, MOX fuel is recycled only once.
3.2.3. MOX-3 Cycle (MOX3) 0.5w/o loss 0.5w/o loss a
f
■
— Î
- 1--- UO2________ Conversion Natural Natural U 3.3w/o U-235 Recycle UO2 3.5w/o U-235 Uranium Fuel Fabrication Preparation o f MOX MOX3 3.7w/o fissile contentMOX2 3.7w/o fissile content
MOX1 3.7w/o fissile content
MOX 3.7w/o fissile contenf
MOX Fuel Fabrication
Light Water Reactor 1000 MWe Thermal efficiency :0.325 Exposure : 1100 days Burnup : 33000 MWd/t Capacity factor :0.8 Fuel inventory: 81813 kgHM Spent Fuel 95% U 1% Pu 3.5% Fis. Prod. 0.5% Actinides Disposal MOX Spent Fuel Cooling Pu (U) 58w/o Pu-239 11w/o Pu-241 MO MOX1 X2 M OX3 '[____y Spent Fuel Cooling MOX Pu (MOX) Uranium Reprocessing Pu (MOX1) Pu (MOX2) Conversion of Enrichment t Recycle UF6
Uranyl Nitrate Uranyl Nitrate 0.83w/o U-235 ' 0.83w/o U-235
to UF6 Depleted U 0.3w/o Loss
0.3 w/o Loss MOX2 MOX1 MOX3 Disposal MOX Reprocessing HLW Disposal HLW Disposal
Figure 3.4 shows fuel cycle material flow for MOX3 cycle. In this cycle, spent fuels removed are reprocessed after cooling for one year in reactor spent fuel pool. The recovered uranium is recycled and used in the same reactor. The recovered plutonium is used to produce MOX fuel, then MOX fuel is irradiated in the same reactor. The recovered HLWs are cooled 4 years and disposed in a geological medium. After irradiation, spent MOX is cooled for 1 year and then reprocessed to recover Pu(MOX). This Pu(MOX), which contains less fissile Pu than Pu(U), is used to produce MOX1 fuel. MOX1 fuel is irradiated in the same reactor together with other fuels. After irradiation, spent MOX1 is cooled for 1 year and then reprocessed to recover Pu(MOX1). This Pu(MOX1), which contains less fissile Pu than Pu(MOX), is used to produce MOX2 fuel. MOX2 fuel is irradiated in the same reactor together with other fuels. After irradiation, spent MOX2 is cooled for 1 year and then reprocessed to recover Pu(MOX2). This Pu(MOX2), which contains less fissile Pu than Pu(MOX1), is used to produce MOX3 fuel. MOX3 fuel is irradiated in the same reactor together with other fuels. Spent MOX3 is cooled for 5 years and then disposed; so, MOX fuel is recycled three times.
4. METHOD OF CALCULATION
4.1. Purpose of the Study
Closing the nuclear fuel cycle implies using resources more efficiently; however, that does not necessarily make the closed cycle economically more advantageous. Purpose of the study is to investigate the price/cost conditions for which the closed cycle becomes more economical compared to the once through cycle.
For this purpose, it is necessary to obtain reliable price/cost data for each process in the nuclear fuel cycle. Since the processes in the front end are well established, the cost data for those are readily available with little uncertainty. However, for the back end of the nuclear fuel cycle, cost data of the processes reported vary in unacceptably large ranges.
Whether to take the unit cost of a process "constant" or "variable" (in the sense that calculations are to be carried out for different selected values) has been decided by taking into account the contribution of unit cost of that process to the total fuel cycle cost and the relative uncertainty in the reported cost data.
In that respect, cost of reprocessing and cost of MOX fabrication are assumed variable within certain ranges determined by scanning the reported data. Although reliable data are available, U price is also taken as variable in order to observe how a U price change in future would affect the economics of the fuel cycles under investigation.
More specifically, purpose of the study is
• To compare cost of the closed fuel cycles to the cost of the once through fuel cycle for certain U prices, reprocessing cost and MOX fabrication cost,
• To determine break-even reprocessing costs for which the cost of the closed cycle equals that of the once through cycle for certain U prices and MOX fabrication costs,
• To determine the contribution of unit costs of primary processes to the total fuel cycle cost and to observe effect of variations in unit costs on the total cost,
• Finally, to economically compare MOXD, MOX1 and MOX3 closed cycles to the once through cycle and to one another.
4.2. Linear Programming and Simplex Method
The balance and constraint equations are determined to calculate fuel cycle costs. The solution of these fuel cycle equations is reduced to a linear programming problem. This problem is solved by using a computer program which uses simplex method. The procedure for simplex method is mentioned below [17,18].
Linear optimization problem can be written in normal form; that is,
maximize
or minimize
f = ciXi +.... ... +cnxn (4.1)subject to constraints
ai1X1+... ... +ainxn = b1 (4.2) a 21X1 +... ...+ a2nxn = b 2 (4.3) am1X1+... ...+ amnxn = bm (4.4) x i > 0 (i=1,...,n). (4.5)For finding an optimal solution of this problem, we need to consider only the basic feasible solutions, but these are still so many that we have to follow a systematic search procedure. For that purpose an iterative method called the simplex method is used.
In this method, one proceeds stepwise from one basic feasible solution to another in such a way that the objective function f always increases its value until
reaching an optimal solution. Each such transition is accomplished by an exchange in which a right-hand variable becomes a basic variable and vice versa. The method
begins with an initial operation Io in which we find a basic feasible solution to start from.
Initial operation Io
Find any basic feasible solution by dividing the variables x1s...xn into two classes by selecting m variables called
basic variables;
then the other n-m variables are those which must be zero at a basic feasible solution; these are callednonbasic
variables
orright-hand variables
because we shall write them on the right-hand side of our system, which we solve for basic variables. If this method should give a negative value for some of the basic variables, we must try another set of basic variables. Each further step then consists of three operations :Test for optimality
Find out whether all coefficients off , expressed as a function of the present
right-hand variables, are negative or zero. If this optimality criterion is satisfied, then our basic feasible solution is optimal. Indeed, then f cannot increase if we assign
positive values (instead of zero) to the right-hand variables. Hence this condition is sufficient for optimality, and it can be shown that it is also necessary.
Search for a better basic feasible solution
If the basic feasible solution just tested is not optimal, go to a neighboring basic feasible solution for which f is larger, as follows. To go to a neighboring basic
feasible solution means to go to a point at which another xi is zero; that is, we have to make an exchange; the variables xi which will now be zero leaves the set of basic variables, and one other variable becomes a basic variable instead.
Consider a right-hand variable XR that has a positive coefficient in f Keep the
other right-hand variables at zero. Determine the largest increase AXr of XR such that
all the basic variables are still nonnegative; list the corresponding increase Af o f f
Transition to that better solution
Exchange that right-hand variable XR which gave the greatest Af with the basic variable in the equation. Then, solve the system for the new basic variables.
It can happen, however, that a basic feasible solution is not optimal but one cannot increase f by exchanging a single variable without coming into conflict with
the constraints. This situation can occur only for a basic feasible solution for which more than n-m variables are zero. Such a solution is called
a degenerate feasible
solution.
In such a case one exchanges a right-hand variable with a basic variable which is zero for that solution, and then one proceeds as usual. In more complicated cases, one may even have to perform several such additional exchanges.These operations are continued until reaching an optimal solution.
4.3. Notation and Symbols Used
The notation used is based on the processes and materials flowing in or through each process in the fuel cycles shown in Chapter 3. The symbol denotes the annual inventories or amounts of material B flowing in or through the process A. As shown in Table 4.1, A takes process labels (R, C, DIS, REP, PUS) and B takes material labels (FU, RU, U, MOX, PU). For simplicity, enrichment, fabrication and reactor are all taken as a single index, R.
Table 4.1. Indices for fuel cycle processes and nuclear materials
Stage Process Index Material Index
U Purchase R FU,MOX
Enrichment R FU,RU
Fuel fabrication R FU,RU,MOX
Reactor R U,MOX
Cooling Pond C U,MOX
Disposal DIS U,MOX
Reprocessing REP U,MOX
Plutonium Storage PUS PU
FU=Fresh Uranium RU=Recycle Uranium U=Uranium Fuel MOX=Mixed Oxide Fuel PU= Plutonium
Table 4.2. Symbols
Symbols
Explanation
a
MPU amount of Puf recovered in reprocessing per 1 kg of loaded MOX fuela
MHLW amount of HLW recovered in reprocessing per 1 kg of loaded MOX fuela
MOX maximum MOX fuel fraction in total reactor fuela
u fraction of U in the spent fuel that will be available for fuel fabrication.a
upu amount of Puf recovered in reprocessing per 1 kg of loaded U fuela
PUM Puf fraction in the fresh MOX fuela
uMox amount of depleted U recovered in repr. per 1 kg of loaded MOX fuela
UHLW amount of HLW recovered in reprocessing per 1 kg of loaded U fuela
pu Pu fraction in MOX fuel.APFIS
fraction of Puf in Pu recovered from reprocessing of U fuelC
R^fu unit cost of fresh U fuel (3.3w/o U-235)
C
R'“'MOX unit cost of fresh MOX fuel (3.736w/o fissile content)
C
R'"/RU unit cost of recycle U fuel (3.5w/o U-235)
Cp unit cost of enriched U
Cf unit cost of natural U
C
SWU unit cost of separative work Cc unit cost of conversionCN
natural U purchase (or natural U unit cost per kg of enriched U)CE
unit cost of enrichmentCC
conversion unit cost per kg of enriched UCFU
unit cost of U fuel fabricationCUM
unit cost of natural U for MOX fuelCFM
unit cost of MOX fuel fabricationCOYI
conversion yieldFAYI
fuel fabrication yieldFISS
fissile fraction of total Pu recovered from repr. of U and MOX fuel.FPUMOX
fraction of Puf in Pu recovered from reprocessing of MOX fuelF
amount of natural U into enrichment.F/P
how much natural U is required to produce 1 kg of enriched productI
fuel residence timeJ
lead time required for recycle U fuel enrichment and fabrication before loading to the reactorK
lead time required for MOX fuel fabrication before loading to the reactor.L
number of cooling pond discharge batchesLoss1
loss in reprocessing and conversion processLoss2
loss in enrichment, conversion and fabrication processLOAD
annual reload fuelP
amount of enriched U from enrichmentPu
f fissile PlutoniumT
amount of tails stream from enrichmentTLOAD
initial charge fuelSymbols
Explanation
XPSPU1
amount of Puf recovered from U fuel reprocessingXPSPU2
amount of Puf recovered from MOX fuel reprocessingXPSPU
total amount of Puf recovered from U and MOX fuel reprocessingXR
^ MOX amount of spent MOX fuel
X
PM fissile content of MOXX
sf U-235 w/o in spent fuelX
ru U-235 w/o in recycle UX
du U-235 w/o in depleted UX
p product assay of enrichmentX
t tails assay of enrichmentX
f feed assay of enrichment4.4. Fuel Cycle Balance Equations
Balance equations for fuel cycles can be written as below.
The annual fuel charge is composed of the fresh uranium Xj^ , recycle
uranium Xj^ and mixed oxide XM OX components
XR u(T) + XR u(T) + XMo x(T) = LOAD(T) (4.6)
The cooling pond inventory balance for irradiated uranium fuels is
XU(T) = XU(T -1 ) + XR u(T - 1) + XR u(T - 1) - XU I S(T) - XUE P(T) (4.7)
and in the case of irradiated mixed oxide,
xMo x(t) = xMo x(t - 1)+xMo x(t - 1) - xMOx(t) - xM E X(t) (4.8)
The amount of recycle uranium is calculated from
XR u(T) = auXUE P(T - J) (4.9)
If the amount of plutonium removed from fuel cycle during the year T is denoted by Xp™ (T), the plutonium inventory XpJ;f(T) is obtained from
Xp U S (T) = XpU S (T -1 ) + au p uXUEP (T -1 ) + a ^ X MOX (T -1 )
- ap u MXM o x(T) - XP U °(T) (4.10)
The amount of depleted uranium produced from MOX fuel reprocessing is
The amount of MOX fuel produced from this Pu material is
XMox = XPUS(T - K)/aPUM (4.12)
The amount of high level waste recovered from reprocessing of spent U is
XHlw(T) = XHlw(T -1) + aUHLWXUEP(T -1) (4.13)
The amount of high level waste recovered from reprocessing of spent MOX is
^^HLW (T ) ^^HLW (t
XMOX (T) _ XMOX ( T " 1) + aMHLW XMOX(T -1)XREP (4.14)
The calculations of au, aPUM, aUPU, aMPU are shown in Appendix 6.3.
4.5. Constraint Equations
The amount of mixed oxide is limited to a certain fraction, aMOX, of the total fuel loading:
XMox(T) < aMoxLOAD(T) (4.15)
There is a minimum cooling time of at least one year before reprocessing. The constraint equations for cooling spent U fuels and spent MOX fuels are as below
XU(T) > XRu(T - 1) + XRu(T - 1) (4.16)
and
XMox(T) > XMox(T - 1) (4.17)
The cooling pond capacity is restricted by
XU(T) + XMox(T )< S lOAD(İ) (4.18)
i_T-I- L
The maximum reprocessing capacity REPR(T) during any given year T is given by
XUEP(T) + XMOX(T) < REPR(T) (4.19)
Spent fuel disposal capacity SFDI(T) during any given year T is given by
If the maximum amount of plutonium that can be annually removed from the cycle is denoted by PUDI(T), then the relevant constraint is given by
XpU°(T) < PUDI(T) (4.21)
4.6. Unit Costs
Since U purchase, enrichment and fabrication are combined as a single process R, the unit costs of natural U based fuel (CFRU), recycle uranium based fuel
(CRRU ) and MOX fuel (CRMOX) should include the relevant expenses. That is why they require a separate treatment.
CRU has 4 components:
CRy = CN + CC + CE + CFU (4.22)
CN = 1 F
COYIxFAYI PCf (4.23)
F = XP - XT
P = XF - XT (4.24)
Note that optimum tails assay (XT) which depends on CF/CSWU ratio and XF, is calculated first, where SWU is separative work unit. The method of calculation is described in Appendix 6.4. F • CC = - CC P C CE = SWU P CSWU SWU=P V(Xp)+ T V(Xt)-F V(Xf) SWU F — = V(Xp ) - V(Xt) - -(V (Xf) - V(Xt)) (4.25) (4.26) (4.27) V(X)=(2X-1) ln(X/(1-X)) (4.28)
CRu has 3 components :
CRu = CC + CE + CFU (4.29)
Calculation of these components are the same, only the equations below are modified.
F = XP - XT
P = XSf - Xt (4.30)
SWU F
— = V(Xp) - V(Xt) - - ( V (xsf) - V(xt)) (4.31)
CMOX has 2 components :
CMOX = CUM + CFM (4.32)
• CUM = (1 - aPU)CF / FAYI (4.33)
• CFM is MOX fuel fabrication cost given in Table 4.3. Note that calculation of aPU is described in Appendix 6.3.
Other unit costs used are summarized in Table 4.3. Also see Table 6.2 in Appendix 6.5 for the reported data in literature.
Table 4.3. Unit costs
Material
Units
Unit Cost
Natural U ($/kgU) 30,60,90
Conversion ($/kg U) 6
Enrichment ($/kg-SWU) 100
Uranium Fabrication ($/kg U) 250
MOX Fabrication ($/kgHM) 300,600,900
Spent Uranium Fuel Disposal ($/kgHM) 98
Spent MOX Fuel Disposal ($/kgHM) 98
Pu Storage ($/g Puf-year) 1.9
Spent Uranium Fuel Storage ($/kg U) 5
Spent MOX Fuel Storage ($/kgHM) 6
HLW Disposal ($/kgHM) 83
Note that unit cost of MOX reprocessing is assumed to be 20% higher than unit cost of uranium reprocessing.
4.7. Minimization of Fuel Cycle Costs
The fuel cycle equations 4.6 through 4.14 describe the material flow in the cycle. If we assume that the material XA is subject to a particular process with unit
cost CA (T) during or over the year T, then the total cost for this process is
c(T)= CA(T)XA(T) (4.34)
and the annual fuel cycle cost C(T) is then given by
C(T) = X X CA(T)XA(T) (4.35)
A B
Discounting all future costs to the beginning of the planning horizon (T=1) leads to the following
objective function Z
Z = min X C(T)(1 + r)-T (4.36)
T
where r denotes the discount rate.
The system of equations can be expressed in a matrix form
AX < B (4.37)
In this matrix form, the components of the matrix A are the relevant coefficients in the system of equations and the vector B includes the predetermined fuel loadings and capacity restrictions. And, since the components of X refer to material quantities, they should all be non-negative.
X > 0 (4.38)
So, the problem is now reduced to a linear programming problem and solved by simplex method mentioned in section 4.2.
4.8. Summary of Input List
4.8.1. Reactor Data
The reactor chosen is a typical LWR, characteristics of which are shown in Table 4.4.
Table 4.4. Reactor data
Type LWR
Power 1000 MWe
Burnup 33000 MWd/t
Exposure time 1100 days
Capacity factor 0.80
Thermal efficiency 0.325
Total fuel in reactor 81 813 kg U
Beginning of the fuel cycle, year 1995
Ending of the fuel cycle, year 2025
4.8.2. Fuel Data and Fuel Cycle Parameters
All the fuel data and fuel cycle parameters used are presented in Table 4.5. Calculations of aPUM, aPU, aMPU and aU are given in Appendix 6.3 and of optimum tails assay in Appendix 6.4.
Table 4.5. Fuel data and fuel cycle parameters
Parameter
Symbols
Value
U235 w/o in fresh U fuel
X
p 3.300w/oFissile content of MOX fuel
X
p m 3.736w/oU235 w/o in recycle U fuel
X
r u 3.500w/oU235 w/o in natural U
X
f 0.711w/oU235 w/o in spent U fuel
X
s f 0.830w/oU235 w/o in depleted U (U from MOX)
X
d u 0.327w/oUranium-236 Penalty U236 0.200w/o
Conversion yield COYI 99.50w/o
Fabrication yield FAYI 99.50w/o
Gram Puf (fissile) from 1 kg reprocess U-fuel, aUPU aupu 6.218g/kgHM Equilibrium fissile fraction of Pu (from U reprocessing) APFIS 69.645w/o
Maximum MOX-fraction in total fuel loading aMOX 30 w/o
Waste fraction in spent U fuel aUHLW 4.542w/o
Uranium fraction in spent MOX fuel auMOX 91.81w/o
Parameter
Symbols
Value
Initial charge TLOAD 81813kgHM
Annual reload LOAD 27271kgHM
Fuel residence time I 3year
Fuel fabrication lead time K 1year
Reprocessing lead time J 1year
Loss in reprocessing and conversion (Loss1
)
Loss1 5.856w/o Loss in enrichment, conversion and fabrication (Loss2) Loss2 1.3w/o5. RESULTS AND DISCUSSION
Cost calculations have been carried out for each of the cycles (once through, MOXD, MOX1, MOX3) presented in Chapter 3 by running the program Nuclear Fuel Cycle Calculation (NUFCA) given in Appendix 6.1.
Data obtained for each cycle are to be presented as;
• Bar graphs showing "break-even" reprocessing cost for different MOX fabrication and U costs (note that this is not applicable for once through cycle)
• Pie charts showing cost shares of each process for selected U and MOX fabrication costs and tables showing how an increase in the unit cost of a process affects the total cost
5.1. Once Through Fuel Cycle
Total fuel cycle cost is 800 million $ for 30$/kgU, 975 million $ for 60$/kgU, 1.13 billion $ for 90$/kgU. The share of U cost, which includes all front end process costs, in the total cost is 91.5% for 30$/kgU, increases to 93% for 60$/kgU and to 94% for 90$/kgU (Figure 5.1).
Uranium price=30$/kgU Disposal Cooling 8.06% Uranium price=60$/kgU Disposal Cooling 6.60% Uranium price=90$/kgU Cooling Disposal 0.30% 5.66%
Figure 5.1. Shares of process costs
A 20% increase in U cost increases the total cost by 6.73%, while a 20% increase is spent fuel disposal cost increases the total cost by 1.32% when U price is 60$/kgU (Table 5.1).
Table 5.1. Effect of 20% increase in unit process costs Increase
Percent (%)
Effect on total fuel cycle cost
(%) (for 30$/kgU)
Effect on total fuel cycle cost
(%) (for 60$/kgU)
Effect on total fuel cycle cost
(%) (for 90$/kgU)
Uranium 20 4.716 6.73 8.07
Spent Fuel Cooling 20 0.0860 0.0706 0.0598
In bargraphs of Figure 5.2, MOXD/once through fuel cycle cost ratio is presented for several reprocessing costs and U prices with MOX fabrication cost fixed at 300 $/kgHM(Heavy Metal).
Fuel cycle costs were calculated for different U prices (30, 60, 90 $/kgU) and MOX fabrication costs (300, 600 and 900 $/kgHM) and for each case a break-even reprocessing cost was obtained, which is shown in bargraph of Figure 5.3. For the MOXD cycle, break-even reprocessing cost is 51$/kgHM for a U price of 30$/kg and MOX fabrication cost of 900 $/kgHM (the worst case against the MOXD cycle), while it is 290 $/kgHM for a U price of 90 $/kg and MOX fabrication cost of 300 $/kgHM (the best case in favor of the MOXD cycle).
Piecharts showing cost shares of each process for selected U and MOX fabrication costs are given in Figure 5.4. It should be noted that when U cost is changed from 30 to 90$/kgU, U cost component which represents all front end costs increases from 70% to 76%, while reprocessing cost component decreases from about 14% to 11%.
In Table 5.2, effect of an increase process in unit costs on the total cost for different MOX fabrication costs (300, 600, 900$/kgHM) are shown. A 20% increase in U cost, which is the most effective item, increases the total cost by 5.4%, while a 20% increase is reprocessing cost increases the total cost by 2.4% (for MOX fabrication cost is 300$/kgHM).
5.2. MOX Disposal Fuel Cycle (MOXD)
ö
Uranium Price ($/kgU)
□ Reprocess=150$/kgHM □ Reprocess=200$/kgHM □ Reprocess=250$/kgHM □ Reprocess=300$/kgHM
Reprocess=350$/kgHM
