Uranium Stocks in Slovenia for Nuclear Power Plant NEK

Seminar

Uranium Stocks in Slovenia for Nuclear Power Plant NEK

Author: Matic Suhodolčan Supervisor: dr. Andrej Trkov

March 2, 2011

Abstract In this seminar we try to demonstrate how it would be possible for the Slovenian mine Rudnik Urana Žirovski Vrh (RUŽV) to supply Slovenian power plant NEK and that reopening would make sense. We try to calculate the years of operating NEK only with uranium ore that is at disposal in RUŽV. We would also like to expand this calculated period by doing some calculations for reprocessing fuel.

Uranium Stocks in Slovenia for Slovenian Nuclear Power Plant NEK

Matic Suhodolčan FMF

Contents 1. Introduction _________________________________________________3 2. Uranium ore in Slovenia _______________________________________3 2.1.

Formation of find-spot in RUŽV ___________________________________________ 3

2.2.

Recasting of uranium ore into yellowcake ____________________________________ 4

2.3.

Process of making UF6 from U3O8 for enrichment purposes _____________________ 4

2.4.

Uranium enrichment methods _____________________________________________ 5

2.4.1. 2.4.2. 2.4.3.

2.5.

Gaseous Diffusion _______________________________________________________________ 5 AVLIS and MLIS separation ______________________________________________________ 6 Gas Centrifuge__________________________________________________________________ 6

Final processes of making fuel for pressurized light water reactors_______________ 7

3. Estimation of the stocks of Triuranium octoxide (U3O8) in RUŽV ______7 4. Estimation of operating years (in concern of estimated Slovenian stocks of uranium) of Power Plant NEK _____________________________________8 4.1.

Estimation of operating years without fuel reprocessing ________________________ 8

4.2.

Conditions for reprocessing fuel____________________________________________ 9

4.3.

Estimation of operating years with reprocessing fuel__________________________ 13

4.2.1. 4.2.2.

Fission and absorption cross sections and factor η _____________________________________ 9 Mass of fuel and fission material __________________________________________________ 11

5. Conclusion _________________________________________________14 6. References _________________________________________________15

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1. Introduction Nowadays uranium ore is one of the most perspective ores on the planet. Many new nuclear power plants are growing every year and so the prices of uranium ore rise. Because of these reasons and because in Slovenia we have our own uranium ore mine, an in-depth discussion has to be done. The purpose of this seminar is to present some facts about how uranium ore was formatted, how a recasting of uranium ore into usable (for nuclear power plants) yellowcake is done, how we can enrich the very low-enriched ore, what are the most important conditions for reprocessing uranium… The most important part of the seminar is to summary of the stocks of uranium ore in Slovenian Rudnik Urana Žirovski Vrh (RUŽV) and the estimation of the period of time when Slovenian nuclear power plant NEK could run only on Slovenian fuel.

2. Uranium ore in Slovenia 2.1. Formation of find-spot in RUŽV The formation of uranium ore is definitely in close relation to processes of sedimentation. Water from surface brought a lot of grain and vegetable waste. Hardening and formation of hard rock soon began. Results of these chemical processes were change of colour and disposal of many materials such as uranium ore, tailings and many other sulfide minerals [1]. Processes in clastic rocks happened (in diagenesis) very close to the surface and at relatively low pressure and temperature. Where sandstones were protected from oxidation with vegetable waste, reductive environment was produced. Anaerobic bacteria played an important role, under which influence significant amount of H2S was produced. Alkaline groundwater brought a lot of uranium into reductive center in shapes of two- or tri-carbonate ion complexes. They were unstable in that kind of environment and so uranyl ions (UO2)2+ were eliminated out of the solution. Silicon dioxide (SiO2) was also eliminated because of huge amounts of chert in groundwater [2]. Because of constant sinking of those layers there was not even a chance that reoxidation of groundwater would ever happen again, not even that uranium would be dissolved and extracted again. But after a while (in retrograde epigenesist) tectonic plates motion became a crucial part in the process. That is the reason why layers with uranium ore came closer to the surface and also the reason why stones cracked and secondary porosity resulted. At that stage uranium minerals and sulfides were transferred. Some of the tailings also 3



crystallized and during the oxidation processes new secondary uranium minerals arose [2]. 2.2. Recasting of uranium ore into yellowcake In Rudnik Urana Žirovski Vrh (RUŽV) the technology of mechanical crushing, classification and grinding the uranium ore had been in use. For the production of uranium technical concentrate they used an acidic hydrometallurgical process. This production method was developed in connection with the well-known Institute Jožef Stefan from Ljubljana and will also be suitable for today recasting of uranium ore into uranium concentrate in RUŽV. There are lots of nonpermeable rocks in the area of RUŽV and so the normally used method of leaching was not and would not be appropriate in RUŽV [2]. The technological procedure for recasting uranium ore is compounded of many crucial operations we are going to describe in details. First ore is put into a crumbling machine, and then it is transported into processing operation, where it is wet melded with rod mills. In the next process melded ore is leached – diluted sulfuric acid and oxidants are added. Leach separates from tailings with filtration. Uranium is then extracted from leach in solvent extraction. That process happens in huge mixers and in separators with liquid ionic exchangers. It is then separated from other ions [3]. From pure uranium solution precipitation with ammonia is done. These products are then put into a huge drier. The final product represents a technical concentrate of uranium and is called ammonium diuranate, from witch they than extract the uranium concentrate powder, better known as yellowcake, named for its colour. The quantity of U3O8 in produced yellowcake is from 65 to 80% [2]. 2.3. Process of making UF6 from U3O8 for enrichment purposes We have already discussed in chapter 2.2 how yellowcake is produced. The next process we want to be familiar with is how fuel for pressurized light water reactors (such as NEK) is produced. First yellowcake is purified with chemical processes. Then it is dissolved in nitric acid. The solution that comes out of this procedure is put into process with a chemical solvent. Uranyl nitrate transforms back into oxide and then into uranium hexafluoride (UF6), which is suitable for the processes of enrichment [2]. We use uranium in the shape of UF6 because it is extremely beneficial for storage, we can change its states of matter with just small modification of pressure or temperature and most of all, its boiling point is extremely low (for 4



example – boiling point for the pure uranium is 4131°C but for the UF6 is only 56.5°C) [3]. 2.4. Uranium enrichment methods 2.4.1. Gaseous Diffusion

One of the first successful enrichment methods created is the gaseous diffusion. It works on the principle that (on average) lighter gas molecules travel faster than heavier ones and so consequently tend to collide more often with the porous barrier material. The lighter molecules will thus hit the walls more often than the heavier ones, so the probability of hitting a pore in the barrier is higher. Because there is a pressure difference between the two sides of the barrier, on the flow of gas through the pores in the opposite direction is smaller, so the gas on the other side of the barrier will be slightly enriched with the lighter molecules (figure 1) [4]. For UF6 the difference in velocities between molecules containing 235U and 238U is small and so the amount of separation achieved by a single stage of gaseous diffusion is almost imperceptible – this method increases enrichment by less than 1% [4]. Therefore, many cascade stages are required to achieve a detectable difference [5].

Figure 1: Basic diagram of a gaseous diffuser. It works on the principle that lighter molecules travel faster than heavier ones and tend to collide more often with the porous barrier material. There is a pressure difference between the two sides of the barrier and so the gas will be slightly enriched on one side of the barrier with the lighter molecules [4].

This method for enriching uranium is unlikely to be the preferred technology due to difficulties associated with making and maintaining a suitable barrier, long equilibrium times and especially large energy consumption. The gas must be re-compressed after each stage of the process, which leads to compression heating. It must then be cooled before entering the next diffuser [4]. 5



2.4.2. AVLIS and MLIS separation

LIS is an acronym which stands for Laser Isotope Separation. The first consonants AV in AVLIS represents Atomic Vapor, the consonant M in MLIS represents Molecule. The main principle is based on absorption frequencies of 235 U and 238U. They slightly differ due to the hyperfine structure of the isotopes – absorption peak for 238U is 502.74nm and for 235U is 502.73nm [6, 7]. The 235U atom absorbs the laser light and its electrons are excited to a higher energy state. When the absorption is great enough a 235U atom will eject an electron and become a positively charged ion. The 238U atoms remain neutral. The 235U ions may then be deflected by an electrostatic field to a product collector [7]. AVLIS uses a two-stage tunable pulsed dye laser usually pumped by a copper vapor laser. The laser can be set so that only 235U absorbs photons and undergoes photoionization [7]. The principal advantages of the MLIS method are its low power consumption and the use of UF6. First UF6 is irradiated by an infrared laser system, which excites the 235UF6, leaving the 238UF6 unexcited. Secondary photons from a second laser system dissociate the excited 235UF6 to form 235UF5 and fluorine (F) atoms [5]. The 235UF5 formed from the dissociation precipitates from the gas as a powder that can be filtered from the gas stream. In each stage conversion of the enriched UF5 back to UF6 is done, so that further enrichment can be proceeded [8]. These two methods are still in research, but the estimations of energy efficiency have already been done and the energy efficiencies of those methods are comparable to the method Gas Centrifuge. The researchers also estimated that this method would be able to increases enrichment by far the most [7]. 2.4.3. Gas Centrifuge

The gas centrifuge enrichment method is based on the principles of centripetal force which accelerates molecules. A fast centrifuge creates a strong centrifugal force (about 104 - 105 stronger than the gravitational force), which pulls the heavier molecules to the wall of the centrifuge and the lighter ones remain close to the center (figure 2). The gas is then heated to create a thermal gradient in a direction by keeping the top of the rotating column cool and the bottom hot. Convection current then carries the lighter molecules (235U) to the top while the heavier ones (238U) settle at the bottom from where they can be disposed [9, 10]. This method increases enrichment up to 30% [10]. Centrifuges are about 4 to 5 meters tall (some even up to 12 meters), measure 20 cm in diameter and rotate at about 50000-70000 rpm [5]. 6



Figure 2: Basic diagram of a gas centrifuge. A fast centrifuge creates a strong centrifugal force, which pulls the heavier molecules to the wall of the centrifuge and the lighter ones remain closer to the center. Afterwards a thermal gradient is established (bottom of column hot and top cool) and convection current then carries the lighter molecules to the top while the heavier ones settle at the bottom and can be disposed [11].

2.5. Final processes of making fuel for pressurized light water reactors First the conversion of enriched solid uranium hexafluoride (UF6) into powdered uranium dioxide (UO2) is done. Next the process of pressing UO2 powder into pellets is performed. Pellets are then thermally processed (sintering) and put into round zircaloy rods. Rods are filled with inert gas and hermetically sealed [2]. They are assembled into fuel elements, which consists of a 16x16 array of fuel rods (sometimes called fuel pins) and are about 3.6 m long [12].

3. Estimation of the stocks of Triuranium octoxide (U3O8) in RUŽV In the mine RUŽV researchers separated the whole field into two areas, depending on how much research has already been done. The name of the first area was extracting area, the second was the research area. The first one was on the northwest side of the hill and measured around 1800 m in length [2]. It had lot of shafts for transportation and ventilation. That part had already been used for excavating ore and was divided into four parts. The part with class number 1 had already been dug, parts 2 and 5 were ready for workers to begin digging, in part number 4 the researches had just begun. Well researched stocks of ore were divided into two groups with codes B and C1, while those, which were not as 7



well researched as previously mentioned, were divided into groups C2 and D1 (table 1) [2]. More to the northwest and also southeast of the extracting area, the research area continued. In northern part of research area all they found was a small amount of very poor ore and so they decided that no additional research would ever be done in that part of the mine. On the other hand in parts on southern side of research area they found almost the same quality of ore as the one in primary discussed area [2]. We have to mention that research area was not ready for excavating ore (and still is not), because none of the shafts was dug and none of the preparation work was done yet. We can see the final estimation of stocks of U3O8 in RUŽV in table 1: Estimated stocks Researched Promising Not enough researched Expected Sum

B C1

457696 1425148

Content of yellowcake in ore [kg U3O8 /t] 1.431 1.429

C2

8183624

1.402

11477

D1

1268994

1.183

1502 15671

Categories Quantity of of stocks ore [t]

U3O8 [t] 655 2037

Table 1: In the table we find final estimation of stocks of U3O8 in RUŽV. Well researched stocks of ore were divided into two groups with codes B and C1, while not as well researched fields were divided into groups C2 and D1 [2].

4. Estimation of operating years (in concern of estimated Slovenian stocks of uranium) of Power Plant NEK The first calculation we are going to do is to calculate how many years NEK would operate if we would produce fuel just from our estimated stocks of uranium in RUŽV. Secondly we would like to estimate how much longer it would be possible for NEK to operate if we would reprocess used fuel elements and put reprocessed fuel back into NEK core. 4.1. Estimation of operating years without fuel reprocessing We know that in NEK on average 36.7 fuel elements are exchanged every year [2]. We are also familiar with the weight of whole 121 fuel elements – it is 48.7 tons [12]. The enrichment of natural uranium is well known to be 0.72% [13], 8



but NEK needs enriched uranium of 4.87% [2]. Now we can easily calculate the number of years of operating NEK: mG 

G m G

(1)

ΔG represents exchanged fuel elements per year, G stands for the number of all fuel elements in the NEK core and m for the whole mass of fuel in the core [14]. ΔmΔG is in our case 14.8 tons. Next we calculate the weight of natural uranium that must be used (to enrich uranium to the mentioned stage) with this simple equation, where we assume that in the processes of enrichment there will remain waste not containing 235U at all [14]: mnatural  mG

0.0487 0.0072

(2)

The mass of the used natural uranium every year to power our nuclear power plant NEK is 99.9 tons. We have to consider the errors we have because of processes in production of fuel elements. Errors around 1% must be considered because of loss when rebuilding uranium pellets, 1% because of conversion of uranium into UF6, up to 5% because of the averaging the quantity of U3O8 in produced yellowcake and around 2% because of the averaging of the content of yellowcake in ore. We would take the approximate number of 110 tons and quite easily calculate that all natural uranium we got from RUŽV would be spent in 142 years. 4.2. Conditions for reprocessing fuel When we are thinking of reprocessing fuel we cannot overlook the conditions that we must fulfil: - η (number of neutrons produced in each fission reaction per neutron absorbed in the fuel nuclei – see section 4.2.1.) for new fuel must be the same as η for reprocessed one [14]. - Quantity of fission material available must be the same for new fuel rods as for reprocessed one. - Mass of new fuel must be the same as mass of reprocessed fuel. 4.2.1. Fission and absorption cross sections and factor η

Let us start with the first condition. To come to any results we have to start with cross sections. If we want to calculate the macroscopic cross sections we must 9



know the number density of every nuclide in the mixture, and first we have to know the microscopic cross sections for our nuclides (table 2): Nuclides 235

U U 239 Pu 238

σscattering

σcapture(γ)

σfission(f)

15.0 8.2 9.5

101 2.7 274

577.0 0 740.6

[barn]

[barn]

[barn]

Table 2: Microscopic cross sections for the most important nuclides in power plants: 235U, 238 U and 239Pu [15].

Equation for number density is defined as: ni 

N A mi VM i

(3)

Where NA is the Avogadro constant, mi is the mass of the nuclides in the mixture, V stands for the whole volume of fuel in one fuel element and Mi is the molar mass of the chosen nuclide [14]. The densities of new fuel elements (for NEK) are: n238Unew = 2.055*1022 cm-3 and n235Unew = 1.065*1021 cm-3. From now on we will use mark 238 for isotope 238U, mark 235 for isotope 235U and 239 for isotope 239Pu. All further equations are simplified assuming the single-group approximation. We must be aware that the spectrum (fission spectrum, spectrum change due to radiative capture…) slightly changes during the fuel cycle and that it changes even more if we use the reprocessed fuel elements. We can hardly estimate how the number densities change and we have to consider that approximation in further treatment. We can now use the calculated number densities in the new equation for macroscopic absorption and macroscopic fission cross sections. We have to remember that absorption cross section is compounded from microscopic fission cross section, microscopic radiative capture cross section and other minor reactions:  a   ni  i   fi   i 

(4)

i

Where ni is the number density of the nuclide in the material, σ is microscopic cross section for every reaction and the sum is done over all nuclides we have in mixture [15]. We will do a minor approximation and include only fission reactions and radiative capture due to the fact that other minor reactions are almost not detectable. Macroscopic fission cross section is calculated with a similar equation, just that it includes only microscopic fission cross section [14]: 10



 f   ni fi

(5)

i

The key parameter in processes in reactors (for fission chain reaction) is the number of neutrons produced in each fission reaction per neutron absorbed in the fuel nuclei defined as written below [14]:

    i

i f

(6)

i

i a

i

Where ν represents the average number of neutrons released per fission (table 3) and sum is done over all nuclides we have in the mixture. Nuclide 235 U 238 U 239 Pu

νthermal neutrons 2.43 0 2.90

Table 3: The average number of neutrons released per fission for the most important nuclides in power plants: 235U, 238U and 239Pu [14].

We can write the equation of parameter η for new fuel element as:  new 

 235 n235  f 235 new

n 235new ( f 235    235 )  n238 ( f 238    238 )

(7)

And ηnew must be exactly the same as ηrep of reprocessed fuel, because our condition is to generate the same power out of our power plant NEK:  rep 

 235 n 235

funal

 f 235   239 n 239  f 239 rep

n 235 funal ( f 235    235 )  n238 ( f 238    238 )  n 239rep ( f 239    239 )

(8)

4.2.2. Mass of fuel and fission material

We know that the core in NEK contains 48.7 tons of fuel [2]. Each fuel element weighs 402.5 kg when new and must weigh the same when we put reprocessed fuel back in. Because we use 4.87 % enriched uranium, there is 19.6 kg of 235U (of fission material that can be used) and 382.9 kg of 238U when we use new fuel. When an atom of 238U is exposed to neutron radiative capture, the nucleus will capture a neutron, changing it to 239U. The 239U then undergoes two beta 11



decays. After the 238U absorbs a neutron to become 239U it then emits an electron and an anti-neutrino by beta decay to become 239Np. 239Np then emits another electron and anti-neutrino by a second beta decay to become 239Pu. So now we want to calculate how much 239Pu is produced and expended during the cycle in the NEK core, while the most important figure for us would be the quantity of the remains of 239Pu in the fuel element at the end of the cycle. Let us start by solving the differential equation for expending of 235U in the core: n 235   a 235 n235 t

(9)

Where n235 is the number density of 235U, σa235 is the microscopic absorption cross section for 235U and is the flux of neutrons in the core [14]. The flux of neutrons is calculated with a simple equation: 

P cV f

(10)

Where P is the power of the reactor, V stands for the whole volume of the fuel, Σf is macroscopic fission cross section and c represents the amount of energy that is relieved in the processes of fission and is 3.1*10-11J [15]. Now we can go back to our differential equation (equation 9) and solve the problem. We will mix variables and continue with integrating: n235 final

t final

n235 new

0

 n235 n235     a 235t

 n235 final ln  n 235 new 

    a 235t final  

n 235 final  n 235new e

(11)

 a 235t final

As we mentioned above, we must calculate the quantity of 239Pu that has been produced and also expended in the same cycle. This figure can be solved with differential equation, where we use the approximation and ignore the half-life of 239 U and 239Np because they are so small (approximate 2 days) in comparison to the length of the whole fuel cycle and can therefore be neglected: n 239   a 238 n238   a 239 n 239 t

(12)

12



Where n239 is the number density of 239Pu, σa238 is microscopic absorption cross section for 238U and σa239 is microscopic absorption cross section for 239Pu [14]. Again we will mix variables, introduce the new variable x = n238σa238 – n239σa239 and continue with integrating: n 239    a 238 n 238   a 239 n 239 t n239 final



n239 new



n239   a 238 n238   a 239 n239

1

n238 a 238  n239 final  a 239

 a 239

n 239 final 



n238 a 238



n 238 a 238 1  e  a 239

t final

 t 0

(13)

t final

x   t x 0 t final a 239



Here enters the important condition that mass of fission material that can be used in core must be the same – when fuel elements are new and when we put into the core reprocessed ones. 4.3. Estimation of operating years with reprocessing fuel We will reprocess fuel elements after three cycles in core. One cycle is approximately 300 days long, and we can calculate how much 235U would be left after those three cycles in NEK core (equations 11). The number density is n235final = 4.04*1020 cm-3. The enrichment of uranium in fuel elements is 1.9%. We can also calculate the quantity of 239Pu and it is n239final = 4.2*1019 cm-3 (equations 13). From these quantities (n235final and n239final) we can now estimate the mass of fuel we need to add, to get new fuel elements. Here enters the important condition mentioned above, that the mass of fission material that can be used in the core must be the same – when fuel elements are new and when we put into the core reprocessed ones. We have to remember that the new fuel element weighted 402.5 kg, we use the approximation that the quantity of 238U is still the same as when new, but the mass of 235U has dropped from 19.6 kg to 7.44 kg. That means that we have to add 12.16 kg of 235U or 239Pu in each fuel element to satisfy these conditions. If we want to use our produced 239Pu we have to figure out how much of it has been left in the fuel elements after the mentioned three cycles in the core. From the number density we calculate that the mass of it is 0.79 kg (in each fuel element) and that means that we can take all fuel elements out of the core and 13



make new elements from used ones, but we will be able to make one new fuel element out of 15.6 old elements. For adding fission material we would be using only the self produced 239Pu. At this point we have to be sure that the parameters η are the same for new and for reprocessed fuel. And if we have a look at the numbers we can see that we found out, that they are in maximum deviation of 3%, ηnew = 1.92 and ηrep = 1.98. In further calculation we found out, that we have gained on fuel for another 10 years of operating of NEK. What we have found out is something extremely important. If we do an effective fuel reprocessing, we can gain more than another 10 years (or we can say another 7%) of operating of such a huge power plant as NEK, and that is a massive result.

5. Conclusion There remains the fact that we ourselves have enough ore to power our power plant NEK for more than 152 years, so we are very well supplied. We have found out that an effective fuel reprocessing is essential and must not be overlooked. It is true that there are still prices of uranium out in the world that are at such a level that the reopening of RUŽV would not be economically appropriate, but the more the trend of rising prices and building new power plants is growing the more we can be sure that some day RUŽV could live another more successful life. It must be emphasized that the present analysis is based exclusively on the existing technology. New Generation-IV reactor designs are under investigation, which will allow the utilisation and recycling of all actinides including thorium, which is about five times more abundant in nature than uranium. This would increase our potential reserves of nuclear fuel practically indefinitely.

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6. References [1] J. W. Clegg, D. D. Foley, Uranium Ore Processing (Addison – Wesley publishing company, U.S.A., 1958) [2] Ž. Sternad, F. Čadež, M. Kromar, B. Likar, B. Lahajnar, Ocena zalog uranove rude v Republiki Sloveniji (Krško, 2010) [3] http://web.ead.anl.gov/uranium/guide/prodhand/index.cfm (12.11.2010) [4] http://www.globalsecurity.org/wmd/intro/u-gaseous.htm (12.11.2010) [5] S. Manojlović, Uranium enrichment methods, Seminar 4 (Ljubljana, 2010). Found 10.11.1010 on web address http://mafija.fmf.unilj.si/seminar/files/2009_2010/Seminar16052010.pdf [6] http://en.wikipedia.org/wiki/AVLIS (19.12.2010) [7] http://www.globalsecurity.org/wmd/intro/u-laser.htm (12.11.2010) [8] http://en.wikipedia.org/wiki/Molecular_laser_isotope_separation (19.12.2010) [9] http://en.wikipedia.org/wiki/Gas_centrifuge (22.12.2010) [10] http://www.globalsecurity.org/wmd/intro/u-centrifuge.htm (12.11.2010) [11] http://www.euronuclear.org/info/encyclopedia/images/gascentrifuge.jpg (10.1.2011) [12] http://www.nek.si/sl/ (10.12.2010) [13] http://en.wikipedia.org/wiki/Natural_uranium (10.1.2011) [14] J. J. Duderstadt, L. J. Hamilton, Nuclear Reactor Analysis (John Wiley & Sons, Canada, 1976) [15] M. Ravnik, L. Snoj, Reaktorska in radiacijska fizika, Vaje (Ljubljana, 2007)

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