The Economics of the Nuclear Fuel Cycle

March 29, 2004

Enrichment Plant Material Balance

Product: P, x P

Feed: F, x F

T ails: W , x w

Material balance on U: F = P + W Material balance on U-235: Fx F = Px P + Wx W

F  P  x p  x W ˘

  x F  x W  

and for x P = 0.03, x F =0.00711, x W = 0 .002, F/ P = 5 .5

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Source: US Energy Information Agency (http://eia.doe.gov/cneaf/nuclear/page/nuc_reactors/pwr.html)

3/29/04 Nuclear Energy Economics and 15

Policy Analysis

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Source: US Energy Information Agency (http://eia.doe.gov/cneaf/nuclear/page/nuc_reactors/pwr.html)

PWR Batch Refueling Scheme (Batch fraction = 1/3)

C y cl e No. Batc h #

I II III IV

Startup core

V

Discharged after 1 cycle B ~B *

Discharged after 2 cycles

Discharged after 3 cycles

d c

B ~2 B *

B ~3 B *

d c d c

* Useful approximation. In p ractice, nee d to track B d with computer codes

Energy from a fuel batch

If the bat ch fraction is 1/n, under steady state conditions each batch remains in the core for n cycles.

Similarly, at steady state the energy produced by all n batches in the core during o ne cycle is equal to the energy produced by one batch during its total residence time in the core (i.e., n cycles.) .

Thus the total electrical energy produced by a given batch during its in-core lifetime at steady state is:

where:

CF = cycle average capacity f actor (including refueling d owntime) K = plant rating (kwe)

T c = cycle length (yrs) including downtime

We can also write that the energy produced per batch is:

where:

B d = discharge burnup of the f uel (MWD(th)/MT of heavy metal)

 = thermodynamic efficiency (Mwe/MW(th)) P = batch fuel inventory ( M T o f heavy metal)

Also,

T b = n T c B d = n B c

And P, the fuel inventory p e r batch = T otal core inventory/n

Material balance on the front end of the cycle

Assume:

K = 1000 MWe

T c = 1.5 years

CF = 90%

 = 33%

n = 3

In-core fuel inventory = 89.4 M THM

Hence w e can calculate:

• Energy output per batch, E b, (at s teady s tate)

• Mass of fuel (as heavy metal), P, per batch

• D ischarge burnup of spent fuel, B d (MWDth/MTHM)

Approximate Correlation: Initial enrichment (x P ) v s . discharge burnup (B d )

Image removed due to copyright considerations.

where n = number of batches (valid for x p < 20%)

Source: Zhiwen Xu, N ED Doctoral Dissertation, 2003

Materia l balanc e o n th e fron t en d o f th e PW R fue l cycle

(Basis: 1 steady state batch; 1000 MWe PWR; thermal efficiency = 33%; 90% capacity factor; 18-month refueling cycle; batch fraction = 1/3; discharge burnup = 50,000 MWD(th)/MT))