1.6 fuel cycle coursera calculations presentation
TRANSCRIPT
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Nuclear Engineering Program
A Look at Nuclear Science and Technology
Larry Foulke
Module 1.6 Grand Tour of the Nuclear Fuel Cycle – Supplemental File of Calculations
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Calculate the mass of U-235 per metric ton (t) of uranium ore assuming the total uranium is 1 wt% of the ore.
(Note: U has 0.711wt % U-235)
Mass and Energy Calculations
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Calculate the mass of U-235 per metric ton (t) of uranium ore assuming the total uranium is 1 wt% of the
ore. (Note: U has 0.711wt % U-235)
Answer:
1000 kg of ore x (0.01 kg U/kg ore) = 10 kg U U-235 is 0.711 wt% of U so mass of U-235 = 0.00711 x 10
kg U = 0.0711 kg or 71.1 grams
Mass and Energy Calculations
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• Let n represent the number of moles • A mole is the number of atoms or
molecules of a substance or element equal to 6.022 x 1023 (Avogadro's number, NAV).
For example: a mole of uranium is roughly 6.022 x 1023 uranium atoms.
Concept of a Mole
Image Source: See Note 1
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• The number of moles, n, of a mass, m, of material is given by:
n moles = mass of material, m, in grams divided by the molecular mass M (gm/mole)
• M – molecular mass (weight) in gm/mole – For uranium, MU ≈ 238 gm/mole
– For oxygen, MO ≈ 16 gm/mole
– The molecular mass of an isotope is just its atomic weight
Concept of a Mole and Molecular Mass
nmoles= m (grams)
M grams / mole( )
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• What is the molecular mass of MU3O8 ? • We combine 3 moles of uranium with 8 moles of
oxygen to get:
• So the molecular mass of U3O8 is 842 gm/mole
Concept of a Mole
3moles( ) U gm /mole( )+ 8moles( ) Ogm /mole( )= 3( ) 238( )+ 8( ) 16( ) = 842gm /mole
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Uranium when mined is often in the form of Uranium Oxide, U3O8. How many kg of Uranium is in 100 kg
of U3O8?
Answer: We just created the molecular mass of U3O8
We took 3 parts of uranium at (3 moles)(238 gms/mole)= 714 grams
We took 8 parts of oxygen at (8 moles)(16 gms/mole)= 128 grams
To get a total of 714+128=842 gms
So the weight fraction of U in the U3O8 is (714 gms/842 gms)=0.848
So if we have 100 kg of U3O8 we have (0.848)(100 kg)=84.8 kg U
Mass and Energy Calculations
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• Presume the total weight of UO2 fuel in a PWR is 150 metric tons (1 metric ton = 1,000 kg). If the enrichment of U is 4 wt% U-235, how many tons of uranium ore (with 0.711 wt% U-235) must be mined if the total uranium in the ore is 0.5 wt%? (This is kind of involved, so think through the steps carefully).
• Choices for answers
a) 150MT
b) 170 MT
c) 750 MT
d) 150,000 MT
Mass and Energy Calculations
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• Presume the total weight of UO2 fuel in a PWR is 150 metric tons (1 metric ton = 1,000 kg). If the enrichment of U is 4 wt% U-235, how many tons of uranium ore (with 0.711 wt% U-235) must be mined if the total uranium in the ore is 0.5 wt%? (This is kind of involved, so think through the steps carefully)
• Answer: about 148,776 MT of ore (or 150,000 metric tons ore)
How did we get that?
Mass and Energy Calculations
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• What is the molecular mass of MUO2 ? • We combine one mole of uranium with two moles of
oxygen to get:
• So the molecular mass of UO2 is 270 gm/mole and the fraction of the mass that is U is (238/270)=0.881
• So there is (0.881)(150 MT)= 132 MT of U in the UO2
Concept of a Mole
1moles( )U gm / mole( )+ 2moles( )O gm / mole( )= 1( )238( )+ 2( )16( )= 270 gm / mole
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• As implied in the problem statement – kind of involved. Let’s look at the solution.
• Consider 132 metric tons (MT) of U in 150 MT of UO2.
• So the 132 MT U is enriched to 4 wt% in U-235.
• So the amount of U-235 in the core is • (0.04)(132.23 MT) = 5.29 MT U-235.
Mass and Energy Calculations
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• How much natural uranium must be mined to get 5.29 MT U-235?
• Natural uranium consists of 0.711 wt% U-235; hence, to get 5.29 MT of U-235 we must mine enough ore to give (5.29 kg/0.00711 MT U-235 per kg of Unatural) = 743.87 MT Unatural.
• If the Unatural content of the ore is 0.5 wt%, we must mine 743.87 MT/0.005 = 148,773 MT of ore.
Mass and Energy Calculations
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Now we are in a position to calculate the number of atoms in a mass of material.
Here is a formula that is used often:
Or
Number of Atoms Or Number Density
N (atoms / volume) = ρ gm
cm3
⎛
⎝⎜⎞
⎠⎟x 1
Mmolegm
⎛
⎝⎜⎞
⎠⎟x N AV
atomsmole
⎛
⎝⎜⎞
⎠⎟
N (atoms) = m gm( )x 1
Mmolegm
⎛
⎝⎜⎞
⎠⎟x N AV
atomsmole
⎛
⎝⎜⎞
⎠⎟
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Presume that a volume of pure U-235 is the size of a Tootsie Pop. How many atoms of U-235 will there be in the Tootsie Pop?
(We will use this result In a future problem)
Here are the steps that you need to go through:
• Estimate the volume of the Tootsie Pop (Volume =
• Calculate the mass assuming the density of pure uranium metal
• Calculate the number of atoms in the uranium mass
Mass and Energy Calculations
Volume = 43π r( )3 where r = radius
Get the density of uranium metal off the web as 19.1 gm/cm3
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• Estimate the volume of the Tootsie Pop (Volume =
Presume r = 2.8 cm/2 = 1.4 cm so
• Calculate the mass assuming the density of pure uranium metal
So the mass of a Tootsie Pop’s volume of pure uranium-235 is
Mass and Energy Calculations
Volume = 43π 1.4cm( )3 = 4
3(3.14) 2.744( )=11.5 cm3
Get the density of uranium metal off the web as 19.1 gm/cm3
mass = 19.1 gm
cm3
⎛
⎝⎜⎞
⎠⎟11.5cm3( )≅ 219.5gms U − 235
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Now the final step using our formula
• Calculate the number of atoms in the uranium mass
Mass and Energy Calculations
N (#) = 220 gmsU − 235
235gmsmole
x 6.022x1023( ) #mole
⎛
⎝⎜⎞
⎠⎟= 5.63x1023 atoms
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• Let’s do one more problem to calculate the cost of nuclear fuel.
Fuel Cost Impact
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• Fuel cost is a minor factor for nuclear power. • Increasing the price of uranium would have little effect
on the overall cost of nuclear power
• Doubling the cost of natural uranium would increase the total cost of nuclear generated electricity by about 5 percent.
• If the cost of natural gas were doubled, the cost of gas-fired electricity would increase by about 60 percent.
Fuel Cost Impact
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Image Source: See Note 2
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Estimate the cost of 1 kg of 3 wt% enriched uranium.
Yellowcake (U3O8 cost) = Conversion cost = Enrichment SWU’s required=
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Estimate the cost of 1 kg of 3 wt% enriched uranium.
Image Source: See Note 3
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http://www.uxc.com/review/uxc_PriceChart.aspx?chart=spot-u3o8-full
Image Source: See Note 4
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Estimate the current cost of 1 kg of 3 wt% enriched uranium.
Yellowcake (U3O8 cost) = $62.50/lb U3O8= (2.2 lb/kg)($62.50) = $137.50/kg U3O8 Conversion cost = Enrichment SWU’s required=
See Segment 1.6 Fuel cycle cost calculator. xlsx
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http://www.uxc.com/review/uxc_g_2yr-price.html
Image Source: See Note 4
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Estimate the current cost of 1 kg of 3 wt% enriched uranium.
Yellowcake (U3O8 cost) = $62.50/lb U3O8= (2.2 lb/kg)($62.50) = $137.50/kg U3O8= Conversion cost = $12.50/kg U as UF6 Enrichment SWU’s and feed required = (See Knief, Table 17-3 and assume 0.2% tails)
=3( ) 238( )+ 8( ) 16( )⎡⎣ ⎤⎦kg U3O8
3( ) 238( )kg Ux$137.50kg U3O8 = $162.15 / kg U
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Enrichment Requirements (From Table 17-3 of Knief)
Image Source: See Note 5
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Eq.17 − 4M f
M p
=p − tf − t
=3.0 − 0.20.711− 0.2
= 5.479
Eq.17 − 5SWU =V (p)+V (t)(F −1)−V ( f )F
Eq.17 − 6
V (χ ) = (2χ −1)ln χ1− χ
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3% enriched
0.2% tails Mf/Mp=5.479
SWU = 4.306 kgSWU/kg product
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Estimate the current cost of 1 kg of 3 wt% enriched uranium.
Yellowcake (U3O8 cost) = $62.50/lb U3O8= (2.2 lb/kg)($62.50) = $137.50/kg U3O8= Conversion cost = $12.50/kg U as UF6 Enrichment SWU’s and feed required = (See Knief, Table 17-3 and assume 0.2% tails) Natural U feed required = 5.479 kg SWU required = 4.306 kg SWU
=3( ) 238( )+ 8( ) 16( )⎡⎣ ⎤⎦kg U3O8
3( ) 238( )kg Ux$137.50kg U3O8 = $162.15 / kg U
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http://www.uxc.com/review/uxc_PriceChart.aspx?chart=spot-u3o8-full
Image Source: See Note 4
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Estimate the current cost of 1 kg of 3 wt% enriched uranium. Yellowcake (U3O8 cost) = $62.50/lb U3O8= (2.2 lb/kg)($62.50) = $137.50/kg U3O8= Conversion cost = $12.50/kg U as UF6 Yellowcake + Conversion to UF6=$162.15+$12.50=$174.65/kgU Enrichment SWU’s and feed required = (See Knief, Table 17-3 and assume 0.2% tails) Natural U feed required = 5.479 kg SWU required = 4.306 kg SWU Cost of UF6 = (5.479 kg)($174.65/kg) = $956.91 Cost of enrichment = (4.306 kg SWU)($155) = $667.43 Total Cost = $956.91 + $667.43 = $1624.34
=3( ) 238( )+ 8( ) 16( )⎡⎣ ⎤⎦kg U3O8
3( ) 238( )kg Ux$137.50kg U3O8 = $162.15 / kg U
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Estimate the current cost of 1 kg of 3 wt% enriched uranium. Yellowcake (U3O8 cost) = $62.50/lb U3O8= (2.2 lb/kg)($62.50) = $137.50/kg U3O8 Conversion cost = $12.50/kg U as UF6
Yellowcake + Conversion to UF6=$162.15+$12.50=$174.65/kgU Enrichment SWU’s and feed required = (See Knief, Table 17-3 and assume 0.2% tails) Natural U feed required = 5.479 kg SWU required = 4.306 kg SWU Cost of UF6 = (5.479 kg)($174.65/kg) = $956.91/kg Cost of enrichment = (4.306 kg SWU)($155) = $667.43 Total Cost = $956.91 + $667.43 = $1,624.34 Plus cost of fuel fabrication of $460/kg for total cost of $1,624.34 + $460 = $2,084.34 for 1 kg of 3 wt% U-235
=3( ) 238( )+ 8( ) 16( )⎡⎣ ⎤⎦kg U3O8
3( ) 238( )kg Ux$137.50kg U3O8 = $162.15 / kg U
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Image Source: See Note 6
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Image Source: See Note 6 Image Source: See Note 4
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Presume that a volume of pure U-235 is the size of a Tootsie Pop. If the average annual energy consumption for a U.S. residential utility customer is approximately 11,496 kw-hrs*
per year, how many years would this amount of U-235 power the average home if all the U-235 atoms were fissioned and converted to electricity? Assume 180 MeV of recoverable
energy per fission and a conversion efficiency of 0.33 (thermal energy to electrical energy).
In this hypothetical case, what would be the approximate volume of
waste produced after all the U-235 is fissioned?
*In 2010, the average annual electricity consumption for a U.S. residential utility customer was 11,496 kWh, an average of 958 kilowatt hours (kWh) per month. See http://www.eia.gov/tools/faqs/faq.cfm?id=97&t=3
Mass and Energy Calculations
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1. Public domain: http://en.wikipedia.org/wiki/File:Avogadro_Amedeo.jpg
2. Reprinted with permission from World Nuclear Organization. http://www.world-nuclear.org/info/Economic-Aspects/Economics-of-Nuclear-Power/#.UWh_Q0rSl4c
3. Reprinted with permission from Ux Consulting. http://www.uxc.com/review/uxc_prices.aspx
4. Reprinted with permission from Ux Consulting. http://www.uxc.com/review/uxc_PriceChart.aspx?chart=spot-conv-ful
Image Source Notes
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5. Reprinted with permission from the American Nuclear Society. Nuclear Engineering – Theory and Technology of Commercial Nuclear Power by Ronald Allen Knief, 2nd Edition, American Nuclear Society. Copyright 2008 by the American Nuclear Society, La Grange Park, Illinois. Table 17-3.
6. WISE Uranium Project. Free for non-commercial use. http://www.wise-uranium.org/nfcc.html
Image Source Notes