122.812 NUCLEAR ENERGY ECONOMICS POLICY ANALYSIS S’04ClassnoteThe Economics of the Nuclear Fuel Cycle: (1) Once-Through Fuel Cycle1. Introduction• A complex cycle of industrial operations is required to prepare andmanufacture fresh fuel for nuclear power reactors and to manage ‘spent’(irradiated) fuel after it is discharged. The particular characteristics of thenuclear fuel cycle depend on the type of reactor that is being supported. Herewe will concentrate mainly on the fuel cycle for light water reactors (LWRs)• One of the objectives of this module is to develop a simple model forestimating the contribution of the nuclear fuel cycle to the overall cost ofnuclear energy. We will not discuss each of the stages of the cycle in greatdetail, but in each case we will provide some background on current costsand likely trends.• The basic flowsheet for the LWR fuel cycle is shown below:• A key distinction is between ‘open’ and ‘closed’ fuel cycles. In the open oronce-through fuel cycle, the spent fuel discharged from the reactor istreated as waste. In the closed fuel cycle, the spent fuel is reprocessed,and the products are partitioned into uranium, plutonium, and the residualmaterial, mostly fission products, which is treated as high level waste.Deutsch, John, Ernest Moniz et al. "The Future of Nuclear Power: An Interdisciplinary MIT Study." Massachusetts Institute of Technology, 2003 (ISBN 0-615-12420-8). Available at http://web.mit.edu/nuclearpower/. p. 101.2• We begin by considering the once-through fuel cycle.2. Stages of the nuclear fuel cycle• The nuclear fuel cycle can be divided into three stages: the front-end, whichextends from the mining of uranium ore to the delivery of fabricated fuelassemblies to the reactor; at-reactor; and the back-end, which starts wiith theshipping of spent fuel offsite and ends with the disposal of high level waste.Mining:• Uranium mining is the first stage of the fuel cycle. Uranium ore deposits arefound in many parts of the world. The main producing nations today are theUnited States, Australia, South Africa, Canada, Russia, and other nations ofthe former Soviet Union.• Large deposits of uranium ore typically contain only a few tenths of a percentof uranium, although a few very rich deposits in Canada and Australia contain10-20% uranium. The ore is processed in a uranium mill to produce‘yellowcake’, a concentrate containing 85-90% by weight of uranium oxide(U3O8). The mill is typically located close to the mine site in order to minimizethe cost of transporting the ore. The non-uraniferous material whichconstitutes the vast bulk of the ore is rejected at the mill. This material,known as the mill tailings, contains most of the radioactive daughter productsof uranium that were present in the ore, and must be stabilized to prevent therelease of these radioisotopes (including radon gas) into the environment.• Conversion and Enrichment• In the next stage of the cycle, the yellowcake is purified and converted touranium hexafluoride (UF6), the only stable compound of uranium that isvolatile at temperatures close to ambient. UF6 is the feed material for theuranium enrichment stage, in which the weight fraction of the fissile isotope235U is increased from 0.711% up to about several percent -- the fissileconcentration needed for LWR fuel. Different isotopes of the same elementexhibit identical chemical behavior, so considerable ingenuity is needed todevise physical separation means. The isotopic enrichment of uranium isone of the most technically challenging stages of the fuel cycle.• The two main enrichment technologies in commercial use today are gaseousdiffusion and the gas centrifuge process. For several decades gaseousdiffusion plants produced almost all of the enriched uranium used in nuclearpower reactors, and still today account for most of the world’s enrichmentcapacity. The process relies on the slight (less than 1%) mass differencebetween molecules of 235UF6 and 238UF6. Gaseous UF6 is pumped underpressure across a semi-porous diffusion barrier. The lighter 235UF6 moleculeshave a slightly higher probability of diffusing through the barrier, and the gas3on the downstream side is thus slightly enriched in the fissile isotope, whilethe undiffused gas is slightly depleted (see Figure 1).High pressurefeed stream,xFLow pressureLow pressureEnriched stream,xPDepleted stream,xWDiffusionbarrier Figure 1: Schematic of a gaseous diffusion stage• The ratio of U-235 to U-238 in the downstream gas rises only by a very smallamount, and more than 1000 stages are needed to achieve a U-235enrichment of 3%.• The performance of each enrichment stage is described by the separationfactor, a, given by the expression: a=xP1 - xPxW1- xWwhere xP and xW are the weight fractions of U-235 in the enriched anddepleted product streams respectively. The stage separation factor for agaseous diffusion stage is 1.00429. (An analogous separation factor is usedto characterize other isotope separation processes too.)• The stages are arranged in a ‘cascade’, in which the enriched product fromone stage becomes the feed to the next highest stage, while the depletedproduct becomes the feed to the next lowest one. The feed stream is4introduced into a central stage of the cascade, while the enriched product anddepleted ‘tails’ streams are withdrawn from each end (see Figure 2).Enriched product, P kgxpFeed, F kgxFTails, W kgxxFigure 2: An enrichment cascadeAn overall material balance on the cascade yields:F = P + W eq. (1)and a material balance on the U-235 isotope leads toFxF = PxP + Wxweq. (2)where F, P, and W are the masses of uranium in the feed, product, and tailsstreams respectively, and xF, xP, and xw are the weight fractions of U-235 in thethree streams.In these equations, P and xP are determined by the in-core fuel managementscheme; xF is given by the U-235 content of natural uranium (0.711%); and xW isset to optimize enrichment plant operations. Thus we have two equations in twounknowns (F and W). Solving for F, we get that:5F = Pxp- xWxF- xWÈ Î Í ˘ ˚ ˙ Example: For a cascade enriching natural uranium to 3% in U-235 at a tailsassay, xw, of 0.2%, solving equations (1) and (2) gives: F = PxP- xWxF- xWÊ Ë Á ˆ ¯ ˜ = 5.48Pi.e., to produce one kilogram of 3% enriched uranium product requires about 5.5kilograms of natural uranium feed.• Gaseous diffusion plants are extremely