Modelling market clearing price and
global uranium bank effect in the
nuclear energy market
Aris Auzans
Institute of Physics, University of Tartu Ostwaldi street 1, EE-50411
Tartu, Estonia
October 27, Coimbra, Portugal, 2016
1
Overview
• Uranium (U) mining and
enrichment are steps in the front
end of the nuclear fuel cycle
(NFC)
• Competitive markets exist for
these services
• They provide enriched U fuel to
nuclear reactors, whose demand
for fuel is nearly inelastic in the
short run
European Nuclear Society
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Overview
• We are using a market-clearing model that evaluates the
evolution of these markets through 2030:
• primary uranium from mines,
• secondary uranium from e.g. depleted uranium (DU) upgrading or
highly enriched uranium (HEU) down blending
• conversion to uranium hexafluoride (UF6),
• enrichment to 4-5% 235U, as required by most reactors.
• The model is not used to predict prices, but rather to
evaluate policy measures affecting the front end markets,
while taking a stochastic approach to account for
uncertainties
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Outline
• Importance
• Ensure supply security
Source www.iaea.org
• Limit nuclear material proliferation
• Methodology
• Underlying databases
• Depiction of supply and demand & assumptions
• Coupling between markets
• Uranium bank module
• Test case
• Test case to prove the concept
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Supply databases
• Primary uranium (CSM):
• contains more than 350 uranium properties at various stages
of development, representing reserves and resources of over
7 million tonnes U (tU).
• Secondary uranium (UT-Austin):
• includes inventories of excess HEU, DU, other governmentand utility-held U stocks, and excess weapons grade
plutonium (WGPu)
• Enrichment (UT-Austin)
• Existing capacity as well as announced and planned
expansions through 2018; growth assumed thereafter
*CSM - Colorado School of Mines
** UT - Austin - University of Texas at Austin
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Supply curve construction
Total supply curve
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Demand curve construction
• Demand curves are calculated as the locus of points
that minimise cost, C [$], to the consumer:
PU, PC, PSWU = market prices of U, conversion, enrichment [$/kg or $/SWU]
Ud, SWUd, NUd = amount [kg or SWU] of U or SWU
Each term is a function of the DU ‘tails’ U-235 enrichment, xw
(and the reactor fuel and natural uranium enrichments xp and xf).
• Constraints:
• Demand for reactor fuel (fixed in the short run) must be
satisfied
• PU treated as free, PSWU = f(SWUd) obtained from clearing
enrichment market at each trial xw
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Market price calculation
• All uranium mines can
potentially produce in a
given time period if the
price is high enough
Supply and demand curve example
8
Interplay between markets
• It would take many years for a reactor (at large cost) to modify its
demand for fuel
• But utilities can substitute uranium for enrichment services
• so the uranium and enrichment demand curves exhibit
considerable short run price elasticity
enrichment services
are measured in
separative work units,
SWU
The substitution is
achieved by adjusting
the amount of U-235
left in the depleted
uranium “tails”
Interplay between enrichment market and natural uranium suppliers
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Uranium mines operation strategy
• The supply curve for
each individual mine
is also the same in
every time period
• Production decision is
determined based on
the short-run market
price
• Mines can produce
between E1 and E2
• Time delay
Cost curves for a single uranium mine
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The Global uranium bank
Core module
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The Global uranium bank
The global uranium bank algorithm
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Test case
U mine
Total Reserves&
Resources tU
Reference Annual
Extraction Rate
tU/year
Year Available
Reference
Cost
$/kg U
A
150,000
15,000
2009
75
B
300,000
15,000
2009
100
C
200,000
20,000
2009
120
D
150,000
15,000
2018
60
E
10,000,000
26,000
2009
50
• Different P and Q
coefficients
• Changing the slope of
supply curve
• Each next produced unit will
cost more
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Test case results
Amount supplied per period with coefficients Q=0.7,
P=0.5
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Test case results
U market clearing price
Reference model market clearing price
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Conclusions
• The global uranium bank assure constant U supply
in cases of supply shortage
• The decisions were based upon the economic theory
of individual firms
• The next logical step is to limit global uranium bank
capacity
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Thanks for attention!
“This research was supported by European Social Fund’s Doctoral Studies and Internationalisation
Programme DoRa”.
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