Beyond Fear: The Nuclear Fuel Cycle In regard to energy production and byproducts

I've decided to publish this work on my site because it's a topic near and dear to my heart- it's a bit lengthy but I hope you might consider it a topic worth understanding.


ABSTRACT: Within the United States, energy in the form of electricity is produced predominately through means such as fossil fuels, nuclear power, and renewable energy resources. Among these current electricity sources, Nuclear Energy continues to be such a point of supply that allows the country and states to produce enormous amounts of energy with a minimal amount of pollutants being produced in the process. The powering mechanisms of nuclear fuel consist of fuel rods that contain approximately 2-3% uranium-235 oxide (235UO2) for nuclear fission. Upon fission, used nuclear fuel cells still contain roughly 1% of the original 235UO2.1 Recycling this uranium for future use is of importance due to the environmental protection aspects as well as market demand for the uranium oxide fuel used in the nuclear reactors.2 However, the established method employed by used nuclear fuel (UNF) reprocessing facilities to reclaim still feasible material, the PUREX process, releases fission products such as 129I, 85Kr, 14C, 3H and multiple Xe isotopes as an off-gas composition.3 These byproducts of nuclear waste reprocessing require serious attention, given the harm that these volatile radionuclides pose to both the public and the environment.4 Such precautions to these volatile radionuclides have inclined other nuclear states, such as France, to seek ways to effectively contain these radioactive particles using various methods of absorption, adsorption, cryogenic distillation, and other immobilization techniques.

The economic function of energy demand in the United States is in a continuous state of inflation as our national population continues to increase. As our country continues the search for new methods of meeting the American demand for energy, nuclear power continues to be an option that is cost effective, low risk, and economically favorable. Yet, due to the perception of energy production through nuclear power being less than favorable in the eyes of the American public, the idea of expanding our nation’s nuclear capabilities continues to suffer in the court of public opinion. An instinct of fear towards nuclear power has been established in the minds of the electorate. The goal of this publication is to offer an explanation to the nuclear process, in terms of energy production and waste management, in a method that is both simple to understand yet thorough in explanation. Hopefully, upon conclusion, one might be able to hold an understanding of both the benefits and the risks in their proper contexts, so that a more informed consensus can be established.
Energy Production: The Nuclear Process
The theory behind nuclear energy at an atomic level is fairly straightforward. A collision between the atom of a fission reactant, or fuel, and a supplied neutron will generate fission products and subsequent neutrons. These ensuing neutrons can henceforth continue the nuclear fission process through interactions with other fission reactants within the nuclear fuel cell crystal lattice.  For example, a single 235U atom can be struck by a supplied neutron which, due to the instability of the 236U isotope, will cause the Uranium nucleus to split into the fission products of the krypton isotope 91Kr, the barium isotope 142Ba, and three subsequent neutrons.These three neutrons can then move forward, further progressing the fission reaction by interacting with other 235U atoms within the uranium oxide crystal lattice.
            This process of Uranium fission generates energy firstly relative to the difference in masses between the associated particles.  In this case, the masses of the following particles are given:         
Where the differences in rest mass can be calculated via:

And through utilization of Einstein’s mass-energy equivalence formula…

…. the energy released through the fission reaction can be quantified with respect to the rest-mass.
 Now it’s important to recognize that in this example we’re neglecting all association with the kinetic energies of the particles. However, incorporating those kinetic energies via relativistic principles will allow one to calculate the total energy released via the nuclear fission process, via changes in both kinetic and rest-mass related potential. 
To note, if the particle velocity is appropriately small compared to the speed of light (less than approximately 6000 kilometers per second), using binomial theorem to expand the radial and truncating the expression after the first set of terms, and finally reducing the equation, will yield an appropriate kinetic energy term of the following form:7
Even though the process of producing energy from nuclear reactions is straightforward, it’s important to recognize that the fundamental consequences of nuclear power aren’t strictly a function of the reaction per se, but more so a function of the products.
            Subcritical, Critical, and Supercritical
            If you observe the fission reaction previously listed, it’s firstly important to note that the ratio of neutrons consumed by the reaction with respect to the number of neutrons produced by the reaction is 1:3. This demonstrates that the reaction rate of 235U has the potential to increase on an exponential timescale. I.E. one 235U atom causes three 235U atoms to react, which causes nine 235U atoms to react, which causes 27 subsequent reactions, 81, 243, etc. At 50 iterative steps, the number of reactions per iteration goes to a magnitude of 1023. At 500 iterative steps, that magnitude goes to a factor of 10238.
This process of exponential growth is what’s referred to as a supercritical reaction. For the previously demonstrated case, the multiplication factor k, the ratio of the number of neutrons in the next iterative step with respect to the preceding iteration, is equated to the value of three. Or, for every one reaction, there is a 100% probability for three subsequent reactions to occur. Any process where the k factor is greater than one is considered a supercritical reaction process, and as such is a reaction process that is uncontrollable. To achieve a steady-state fission reaction of a nuclear fuel cell, the fission reaction must be what is considered critical, where the k factor for the fission process is exactly equal to the value of 1, where one fission reaction causes only one subsequent fission reaction. Finally, any k factor that is less than one renders the fission process to be that of subcritical, and as such the reaction output asymptotically approaches zero. nuclear reactor operations are optimized at the critical point.
With respect to the iterations, integrating the functional models and normalizing their values to Avogadro’s constant demonstrates the number of iterative steps it requires to react 1 mole of material. Or, in this case, how many iterative steps it takes to release our previously calculated Rest-Energy value if these models depicted the fission reaction of 235U.
The resulting integration processes demonstrate that, in case of model a(x), it would take 550 iterative steps to react 1 mole of 235U, for model b(x), 6.022x1023 steps, and in the case of model c(x), no amount of iterations would produce the desired energy. For perspective, if each iterative step has a time equivalence of an attosecond, model a(x) would output the calculated rest-energy in approximately ½ of a femtosecond (10-15 sec), and model b(x) would output the same energy amount in approximately a week.
Radioactive Byproducts
Another fundamental consequence of nuclear fission is the production of unstable radioactive byproducts. If one were to map out a spectrum of stable atomic isotopes, neutron number with respect to atomic number, they would observe that a function mapping the spectrum would have a non-constant derivative of the form n.xn-1, where n was greater than 1. Or in other terms, maintaining stability as you increase in atomic number requires more neutrons per proton as you reach higher and higher proton quantities.

The number of nucleons (summation of protons and neutrons) is constant throughout a fission process. Therefore, the consequence is that the fission byproducts will most likely be unstable, and as time progresses the fission products themselves will undergo radioactive decay until they reach a stable state. For example, the barium isotope 142Ba is unstable and would undergo four sets of  beta-minus decay to generate the stable neodymium-142 isotope.
It’ll be important to touch on the concept of half-life with respect to radioactive decay before continuing on to the topic of current nuclear capacities of the United States. Although it is currently theoretically impossible to predict exactly when an isolated particle will decay, the statistical analysis of a large cluster of identical particles is on the other hand is quite simple to model. Radioactive decay is a first-order rate reaction, with a solution of the following, for some material “a” with a given concentration C:
Through the experimental examination of concentrations for various materials with respect to time, one can determine the constant of proportionality associated with a given decay cycle. Using such, the half-life of a material (the time it takes for a given concentration to decay to half of the initial concentration) can be calculated.
The State of the Union: current capacities and protocols.
The United States currently has within its electrical infrastructure 99 fully operational Nuclear Reactors, that generate approximately 805k gigawatt-hours of electricity, or the equivalent of 19.74% of the national annual power load produced.5 As a result, nuclear output discharges spent nuclear fuel at a rate of 2,200 metric tons per year.8 The United States at the federal level currently doesn’t have a nationalized program for storing or reprocessing waste. In 1977, then-President Jimmy Carter announced that the United States would indefinitely suspend any efforts in the reprocessing of Used Nuclear Fuel.9 Following in the footsteps of Carter’s Nuclear Waste Policy Act, the proceeding president, Ronald Reagan, directed the federal government to establish a national repository site for nuclear waste at the Yucca Mountain, 100 miles northeast of Las Vegas, Nevada.  In the late 2000’s however, the plans for that national depository locale were abandoned, and no replacement locale for a national depository site was established.4 As it currently stands, most used nuclear fuel cells removed from the reactor cores are stockpiled on-site, where over 60 years of accumulated nuclear waste currently sit in temporary storage.10
 To note though, it should be considered a misnomer to refer to used nuclear fuel cells as “nuclear waste”. Conservative figures state that used nuclear fuel cells contain roughly 95% of the original energy capacity from fission, with more liberal estimates of the recoverable fission reactants being placed at a percentage value closer to that of 97%.11,12 Given such, the current model for handling used nuclear fuel in the United States is considerably shortsighted and potentially hazardous, least of all environmentally unfriendly.
Given the state of American misconduct with respect to used nuclear fuel, it’s appropriate to explore the various venues of Used Nuclear Fuel reprocessing and radioactive waste treatment. Regarding the nuclear fuel process, there are many various fission byproducts to consider. For the sake of simplicity within this initial report however, we will be focusing on the two isotopes in the decay process that have been identified as the most significant in terms of radiation exposure to large populations: Krypton-85 and Iodine-129.13, 14 In regard to these radioactive isotopes, 85Kr has a half-life of 10.7 years, and 129I has a half-life of 1.57x107 years.14, 17
Current United States Regulations of Krypton-85 and Iodine-129
In terms of Federal Regulations, Nuclear Waste as a function of radioactivity is strictly regulated by the Environmental Protection Agency, via the United States Code of Federal Regulations. 40 CFR 190.10 regulates public exposure of dosage equivalents to that of 0.25mSv/yr for the whole body, 0.75mSv/yr in terms of exposure to the thyroid, and 0.25 mSv/yr for all other organs. In terms of energy production, emissions per gigawatt-year are <50,000 Ci for 85Kr, and <5mCi for 129I. 15
In order to meet such regulatory requirements within the context of nuclear fuel reprocessing, special care is required regarding if and how radionuclides are volatilized during the reprocessing procedure, and where such contaminants are deposited.
Used Nuclear Fuel Reprocessing: the PUREX process  
As it currently stands, the most prominent methodology employed at a global scale for nuclear fuel reprocessing is through a process called PUREX (Plutonium Uranium Extraction).16 The standard procedure for PUREX implementation is as follows (From Dr. Carlos H Castano’s Publication titled “Nuclear Fuel Reprocessing” in the Nuclear Energy Encyclopedia):
“Fuel is decladded using either mechanical (shearing, chopping, sawing) or chemical means (mostly for aluminum-uranium fuel elements) to expose the fuel to the dissolving agent. The broken fuel and cladding are mixed with hot nitric acid to dissolve the fuel while leaving the cladding (steel or Zircaloy) mostly untouched. Depending on local government regulations of the plant, radiokrypton, xenon, 14 C, tritium, and other volatile products (iodine, etc.) are either released or collected for disposal. Collection processes might include oxidization, adsorption, absorption, voloxidation, or scrubbing with water. The aqueous solution at this point usually requires some pretreatment, which might include pH adjustment (pH 2.5), cooling, clarification, or valence adjustment of Pu ions in solution to (IV) by nitrogen peroxide. The cladding husks are washed with water and removed for waste storage. Uranium and plutonium are separated from the fission products by solvent extraction with a solution of 30% (by volume) TBP in a hydrocarbon diluent (e.g., n-dodecane). This step removes about 99% of the fission products from the U and Pu in the solution. Pu is extracted (from the TBP phase) by reducing the Pu to the trivalent state without reducing the uranium. The reducing agent could be ferrous sulfamate, tetravalent uranium ions, hydroxylamine, or cathodic reduction. Once the plutonium and uranium are separated (different streams), they are treated to precipitate the uranium and the plutonium from their respective phases. Both plutonium and uranium are (usually) further purified by additional cycles of solvent extraction. Plutonium nitrate is converted to PuO2 by evaporation, calcination, or precipitation with oxalate or a peroxide, followed by calcination. The uranyl nitrate solution is evaporated and then calcinated obtaining UO3. Nitric acid vapors are condensed and reused. High level wastes are solidified and disposed of (e.g., in a geological repository).” 16
There are multiple variations to the PUREX process so to advance alternate objectives during the reprocessing of used nuclear fuel, such as UREX to reduce the chance of proliferation through UNF reprocessing, SANEX to allow for lanthanide and actinide separation, et al. 16
Major components of the PUREX process involve liquid solutions of high level waste, which can be appropriately dealt with through solidification and disposal via geological repository. However, PUREX also introduces within the reprocessing method the variable that is the volatilization of radionuclides. These radionuclides are released from the PUREX process as an off-gas, and due to their radioactive nature must be dealt with in some form or another.
129I and Caustic Scrubbing
Caustic Scrubbing with respect to off-gas treatment from the PUREX process is generally considered to be the first developed methodology for the aqueous processing of volatile iodine from the PUREX off-gas stream. The off-gas is passed through a 1-2 M Sodium Hydroxide solution within a type of fractionating column known as a bubble-cap column. The resulting process yields Sodium Iodine and Sodium Iodate complexes that can either be disposed of or further treated.18,19
129I and the Iodox Process
Another method for solidifying the Iodine waste within the off-gas stream is known as the Iodox process. This process involves feeding the off-gas through solutions of 20-22 M Nitric Acid within a bubble-cap column. This process generates a water-soluble solid iodine product. To convert the solid iodine product from a soluble state to an insoluble one, the material is reacted with Barium Hydroxide to form Barium Iodate [Ba(IO3)2]. Finally, the Barium Iodate compound is deposited in a cement matrix for long-term storage.17
129I and the Mercurex Process
A similar method to Iodox that is utilized in the iodine treatment of off-gas streams is the Mercurex process. The iodine within the Mercurex process is converted both to iodate and mercury complexes via treatment by a 8-12 M Nitric Acid, 0.2-0.4 M Mercuric Nitrate scrubbing solution. The resulting complexes are oxidized to form Mercuric Iodate, which can be metathesized to precipitate out recyclable Mercuric Oxide and aqueous iodate, which then is subsequently exposed to barium hydroxide to form the insoluble Barium Iodate complex. Finally, the resulting compound, like in the Iodox process, is deposited in cement for long-term storage.17,18
129I on Silver-Zeolites
Moving from aqueous treatment processes to solid-state radioiodine treatment, a popular method for iodine capture in off-gas streams over the last few decades has been induced via silver-based sorbents. The off-gas stream is passed through silver-containing zeolite mordenite to form within the zeolite lattice stable silver-iodine complexes.17
129I Physical Adsorption
Other processes regarding effective iodine capture have been explored through developing solid-state materials through which intramolecular forces between particulates induce physical adsorption onto materials as a function of surface area, porosity, et al. Activated Carbons, Metal Oxides, Metal Organic Frameworks, and Titanosilicate derivatives have been used in such manner with a variety of success.19, 20, 21
Analysis of Iodine capture techniques
Regarding the previously mentioned treatment methodologies, each comes with a unique set of pros and cons regarding implementation.
Caustic Scrubbing: caustic scrubbing has a reported retention factor (RF) ranging from 10-103. The treatment process is effective in capturing elemental iodine contaminants, but lacks effectiveness with respect to organic iodide derivatives. Caustic scrubbing techniques are generally required to be paired with a second treatment technique to meet environmental standards regarding iodine removal. Complications can also arise if the Sodium in the fractionating column precipitates via reactions with other off-gas materials in the stream, like C-14 in the form of carbon dioxide.18
Iodox: reported RF values regarding the Iodox process range on the order to 105. The Iodox treatment method is also effective at capturing all Iodine derivatives within the off-gas stream, and is relatively stable regarding other effluents within the gas. However, the Iodox process also introduces hazardous materials within the treatment systems and incurs a high-cost disadvantage.18
Mercurex: Regarding the Mercurex treatment process, RF values are reported in the range from 103 to 104 with respect to laboratory experimentation utilizing a vast array of operation variables. However, the process utilizes mercury solutions which in some instances may pose a greater toxicity danger than the original 129I species.18
Silver-Zeolite: RF values for silver-zeolite treatment methods have been reported on the order of 103. Although the silver-iodine complexes are not completely understood, the process is effective at the removal of all iodine derivatives in the off-gas stream. The disadvantages however are that halogens within the gas interfere with iodine retention. Also, there is yet a developed method for recovering the silver, which is expensive, from the treatment process.18
Physical Adsorption: Being one of the newer methodologies to off-gas treatment, Physical absorption materials are still in their infancy regarding experimentation for off-gas treatment. However, materials that adsorb multiple grams of iodine per gram material have been reported. In addition to potential, physical adsorption techniques host low operational costs with respect to iodine capture.19, 20, 21
85Kr capture through Cryogenic Distillation
Switching over to Krypton studies, the primary methodology for krypton capture in off-gas streams has been cryogenic distillation. Since krypton is chemically inert as a noble gas, physical techniques are required in implementation to separate out the radionuclide from off-gas waste. Using super-cooled systems to induce separation via differences in boiling points is currently the go-to process, as the cryogenic distillation technique is adequate in regard to regulatory levels.1, 17
85Kr capture through Physical Adsorption
Like with Iodine adsorption, Krypton has been another volatile radionuclide that has seen a current upswing in study regarding physical adsorption. Recent reports of Metal Organic Frameworks and Titanosilicates have places absorption loads in the range of 100mmol/kg to that of 1-3 mol/gm for the radionuclide.22
Perspectives: Viva La France
It’s important to note that these previously discussed techniques for nuclear fuel reprocessing are not simply segments of a dialogue only implemented in imagination: although the United States does not currently possess the capability to reprocess used nuclear fuel, other nations of the world have put forth efforts to develop their nuclear energy capabilities, and as such developed their capabilities with varieties of success. For example, the French currently reprocess over 1700 tonnes of nuclear fuel annually at the Le Hague reprocessing plant.24, 25 France is a net exporter of energy, earning over €3 billion euros per year as a result. The French also boast some of the lowest costs for electricity in all of Europe, and because of their nuclear energy infrastructure, the air in France is some of the cleanest air of the industrialized world. France is at the forefront regarding the effective use of nuclear energy. As the New York Times columnist Roger Cohen once put it in 2008, in regard to the future of American energy production, “It’s time to look to the French.”26
Perspectives: Energy Economics and Opportunity Cost
A few final points to consider in the conclusion of these discussions is nuclear energy in terms of potential and opportunity cost. Firstly, current estimates place world energy consumption at approximately 500x1018 kJ/year. Nuclear Power on the other hand has been estimated to hold the full potential of 1021 kJ for power supply. That potential is sufficient to supply the entirety of the earth’s energy needs for roughly 2000 years.23 Secondly, even though there are inherent risks regarding the utilization of energy from nuclear fission, there are also inherent risks that we should not ignore regarding our current methodologies for energy production. While we as a species continue to dump fossil fuel waste into the atmosphere at unprecedented rates, we risk causing damage to the environment at a global scale. Temperatures rise, oceans acidify, and weather fluctuations increase in both frequency and intensity.23 The opportunity cost for these practices, especially with alternatives like nuclear power available, should be considered too great a price to be worth their continued use.
Conclusion: Is this all worth it?
When engaging in the conversation revolving around the risks and benefits of nuclear energy, it’s important to consider the relevant topics within their proper contexts. There are inherent dangers that revolve around utilizing fission to produce consumable energy. But there are also methodologies that have been developed to safeguard against the realization of these hazards. Given the risks, costs, benefits, and alternatives, Nuclear Energy should be seriously considered as a long-term solution to the world’s energy demand.
The conversation revolving around Nuclear Energy, in my opinion, should note be a dialogue marred by speculation based in fear. The power produced through the nuclear cycle is clean, efficient, and if properly handled, safe.


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