Economic Viability of Metallic Sodium-Cooled Fast Reactor Fuel in Korea

Table 7

Equations for the direct disposal cost.

Recharge interval	𝑅𝑖=𝐶𝑠𝑁𝑏×BUMWt×𝐶𝑓×365 (Unit: year)
Generation cost	𝐶=𝐹𝑐+𝑉𝑐=𝐶uc⋅𝑅𝑇⋅𝑈𝑟⋅1−𝐼𝑐+NFCC
Quantity of fabrication	𝐶Qf(𝑡)=^𝑠𝑁𝑏,𝑡=batch
Quantity of enrichment	Qe(𝑡)=𝑉(EL)+EL−𝑇𝑎NAT−𝑇𝑎−1⋅𝑉𝑇𝑎−EL−𝑇𝑎NAT−𝑇𝑎𝑉(NAT)Qf(𝑡)(1+LF)
Quantity of conversion	Qc(𝑡)=EL−𝑇𝑎NAT−𝑇𝑎Qf(𝑡)(1+LF)
Quantity of uranium	Qu(𝑡)=Qc(𝑡)(1+LF)
Spent fuel generation	Qsf(𝑡)=𝑃365𝐶𝑓𝜀BU
Cost of uranium	Cu=∑𝑡Qu(𝑡)⋅UCu⋅(1+𝐸U)^𝐿(𝑡)−LEDu−YRc(1+𝐷)^𝐿(𝑡)−LEDu−YRp
Cost of conversion	Cc=∑𝑡Qc(𝑡)⋅UCc⋅(1+𝐸𝑐)^𝐿(𝑡)−LEDc−YRc(1+𝐷)^𝐿(𝑡)−LEDc−YRp
Cost of enrichment	Ce=∑𝑡Qe(𝑡)⋅UCe⋅(1+𝐸𝑒)^𝐿(𝑡)−LEDe−YRc(1+𝐷)^𝐿(𝑡)−LEDe−YRp
Cost of fabrication	Cf=∑𝑡Qf(𝑡)⋅UCf⋅(1+𝐸𝑓)^𝐿(𝑡)−LEDf−YRc(1+𝐷)^𝐿(𝑡)−LEDf−YRp
Cost of transportation; applied LAG time	Ct=∑𝑡Qsf(𝑡)⋅UCt⋅(1+𝐸𝑡)^𝐷(𝑡)+LAGt−YRc(1+𝐷)^𝐷(𝑡)+LAGt−YRp
Cost of storage	Cs=∑𝑡Qsf(𝑡)⋅UCs⋅(1+𝐸𝑠)^𝐷(𝑡)+LAGs−YRc(1+𝐷)^𝐷(𝑡)+LAGs−YRp
Cost of disposal	Cd=∑𝑡Qsf(𝑡)⋅UCd⋅(1+𝐸𝑑)^𝐷(𝑡)+LAGd−YRc(1+𝐷)^𝐷(𝑡)+LAGd−YRp
Total cost of direct disposal option	TC𝐷=Cu(𝑡)+Cc(𝑡)+Ce(𝑡)+Cf(𝑡)+Ct(𝑡)+Cs(𝑡)+Cd(𝑡)

𝑅_𝑖: recharge interval, 𝐶_𝑠: core size, 𝑁_𝑏: total number of batches, BU: burn up, MWt: thermal power, 𝐶_𝑓: load (Capacity) factor, 𝐿(t): loading time, 𝐷(t): discharging time, LED: lead times, LAG: lag times, 𝐹_𝑐: fixed unit cost, 𝑉_𝑐: variable unit cost, 𝐶_uc: construction unit cost ($/kW), 𝑅: fixed charge rate, 𝑇: 8760 (=365 days × 24 hours), 𝐼_𝑐: consumption rate in power plant, NFCC: nuclear fuel cycle cost, EL: enrichment of equilibrium core, NAT: enrichment of natural uranium, 𝑇_𝑎: tail assay, LF: loss rate factor, 𝑉(𝑥)=(2𝑥−1)ln(𝑥/(1−𝑥)), Cu: cost of uranium, Qu(t): quantity of uranium, 𝑃: capacity (MWe), ε: thermodynamic efficiency (MWe/MWt), UC: unit cost, UCu: unit cost of uranium, Eu: escalation rate of uranium, 𝐷: discount rate, YRt: base year, Qsf(t): quantity of spent fuel, TC_𝐷(t): total cost of direct disposal option, Cu(t): uranium cost, Cc(t): conversion cost, Ce(t): enrichment cost, Cf(t): fabrication cost, Ct(t): transportation cost, Cs(t): storage cost, Cd(t): disposal cost, t: years.