--- title: "ChEn 433 Nuclear" date: Class 16-17 lang: en-US slideNumber: false width: 1600 height: 1000 transition: fade css: ../assets/style.css theme: simple title-slide-attributes: data-background-image: "https://www.iaea.org/sites/default/files/styles/full_page_width_landscape_16_9/public/nuclear_fuel_cycle_1.jpg?itok=L6c6WxFF" data-background-opacity: "1.0" verticator: enable: true menu: enable: true chalkboard: enable: false --- # Nuclear What are the major issues associated with nuclear power? ::: incremental * No GHG emissions (CO$_2$) * Environmental concerns * Safety concerns * Proliferation * Waste storage * Fuel resources * Regulation * Public perception ::: # Nuclear timeline
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# U.S. nuclear power by year image ## U.S. nuclear plant locations image ## U.S. nuclear plant stats ::: {.cols2} ::: {.col2-l} * [20% of U.S. electricity from nuclear](https://www.eia.gov/tools/faqs/faq.php?id=427&t=3) * First plant in U.S. in 1958 * 2021 stats * 94 reactors, ~1 GW each (avg) * 56 plants * 28 states * Average age is 39 years * Oldest plant is Nine Mile Point (NY), Dec. 1969, 52 years * Newest is [Vogtle Unit 4, 2023](https://www.georgiapower.com/company/news-hub/press-releases/vogtle-unit-4-enters-commercial-operation.html), Georgia ::: ::: {.col2-v} image

*Shippingport Power Station, Pennsylvania*

::: ::: ## U.S. nuclear plants timeline image ::: notes bar chart of US nuclear power capacity additions, by year of initial operation (1970-2023), GW, includes Vogtle 3 unit ::: ## World nuclear plants image * ~156 plants in service (> 1000 MW) * Google "list of nuclear reactors" --> people also ask... ## World nuclear plants image # Exercise: World Electricity as Nuclear ::: {.cols2} ::: {.col2-l} * Look up the world total electricity production. Energy Institute * Convert this to CMO * If run continuosly over the year, find the power in GW * What is the largest nuclear power plant, and it's power? * What is the average size nuclear power plant > 1000 MW? * How many of the largest and average size plants are needed? * If one plant is built per week, how many years are needed? ::: ::: {.col2-v} image ::: ::: ## Exercise: World Electricity as Nuclear ::: incremental * BP: 26823 TWh $\cdot$ 3600 s/h = 9.65628E19 J (per year) * 1.6E20 J/CMO $\rightarrow$ 0.6 CMO * 9.65628E19 J/yr $\cdot$ yr/(3600 $\cdot$ 24 $\cdot$ 365 s) $\cdot$ GW/1E9 W = 3062 GW * Largest plant is the [Kashiwazaki-Kariwa (K-K) Plant](https://en.wikipedia.org/wiki/Kashiwazaki-Kariwa_Nuclear_Power_Plant) in Japan * 7965 MW * Avg size plant = 2382 MW (for plants over 1000 MW) * 155 plants over 1000 MW * \# K-K plants = 3062/7.965/0.92 = 418 * with a [92% capacity factor](https://www.energy.gov/ne/articles/what-generation-capacity#:~:text=Nuclear%20has%20the%20highest%20capacity,and%20solar%20(25%25)%20plants.) * 1 plant per week for 8 years * \# avg plants = 3062/2.382/0.92 = 1397 * 1 plant per week for 27 years ::: # Isotope binding energy Isotope Binding Energy image ## Stardust [Genesis 3:19](https://www.churchofjesuschrist.org/study/scriptures/ot/gen/3?lang=eng) ...for dust thou art, and unto dust shalt thou return ["It is totally 100% true: nearly all the elements in the human body were made in a star and many have come through several supernovas."](https://www.nhm.ac.uk/discover/are-we-really-made-of-stardust.html) image ## Emission/Decay * $\alpha$ (helium nucleus), e.g., * $^{238}_{92}\text{U} \rightarrow ^{234}_{90}\!\!\text{Th} + ^4_2\!\text{He}$ * $\beta^-$ (emitted electron) * $n \rightarrow p + e^- + v_e$ * $\beta^+$ (positron, ~ a positively charged electron) * $p \rightarrow n + e^+ + v_e$ * $\gamma$ (high energy photon) * often occurs from an excited daughter nucleus after $\alpha$ or $\beta$ decay ::: notes $\beta^+$ and $\beta^-$ emission occur in nuclei not bare $p$ or $n$ ::: ## Table of Nuclides ## Half life ::: {.cols2} ::: {.col2-l} **Equation for radiactive decay?** ::: incremental * Radioactive decay is governed by $\frac{dN}{dt} = -N/\tau$, $N(0) = N_0$. * Here, $\tau$ is the characteristic decay time. * The analytic solution is
$$N = N_0e^{-t/\tau}$$
* Relate this to the half-life: $\frac{N}{N_0} = \frac{1}{2} = e^{-t_{1/2}/\tau}\rightarrow \tau = -t_{1/2}/\ln(1/2)$ $$\tau = t_{1/2}/\ln(2)$$ $$t_{1/2} = \tau\ln(2)$$

$$N = N_0\left(\frac{1}{2}\right)^{t/t_{1/2}}$$

::: ::: ::: {.col2-v} ::: fragment image ::: ::: ::: ## Radiation penetration image * $\alpha$ stopped by paper, dead outer layer of skin (dangerous if injested) * Polonium-210 [poisoning of Alexander Litvinenko](https://en.wikipedia.org/wiki/Poisoning_of_Alexander_Litvinenko#Illness_and_poisoning) * $\beta$ stopped by aluminum foil, can penetrate ~1/2 inch into skin * $\gamma$ stopped by lead, thick concrete ## Radiation penetration ## Ionization demonstration # U-235 Fission ::: {.cols2} ::: {.col2-vp} * $^{235}U + n \rightarrow [^{236}U] \rightarrow ^{144}Ba + ^{89}Kr + 3n$ * typical * 1n $\rightarrow$ 2.5n *daughter* neutrons * *prompt* neutrons are fast: * ~2 MeV = 19.5 million m/s (7% of light). image ::: ::: {.col2-v} image ::: ::: ## Chain reaction ::: {.cols2} ::: {.col2-l} ::: incremental * Neutron fate: * Fission * Absorbed (e.g., by U-238) * Escape * (bare n is unstable $\rightarrow$ p+$e^-$) * half life ~ 10 minutes. * [Chain reaction](https://en.wikipedia.org/wiki/Nuclear_chain_reaction) * 1 fission creates $\ge$ 1 fission * Energy from mass: $$\Delta m = m_\text{reactants} - m_\text{products}$$ $$\Delta m = \frac{E}{c^2}$$ * mass difference as kinetic energy of fission products $\rightarrow$ slows $\rightarrow$ heat. * Neutrons + protons are conserved, electrons are not (formed). * Energy released as more stable nuclei are formed (sounds familiar) ::: ::: ::: {.col2-v} image ::: ::: ## Exercise: mass $\rightarrow$ energy How much mass converted fully to energy equivalent to 1 CMO? ::: incremental * 1 CMO = 1.6E20 J * $E = mc^2$ $\rightarrow$ $m = E/c^2$ * c = 299792458 m/s * m = 1780 kg * ~ 2 m$^3$ of oil (@ 890 kg/m$^3$) * Volume is 9 billion times less than 1 CMO ::: ::: fragment *Of course, nuclear reactions never approach full mass conversion.* 1 CMO requires about 2000 tons of U-235 fission ::: ::: notes U235 + n --> Ba-144 + Kr-189 + 3n mU = 235.043928 amu mn = 1.008664916 amu mBa = 143.922955 amu mKr = 88.907835 amu dM = mReact - mProd = 0.195808 amu dM/mU = 0.000833 = rest mass change per mass of U-235 So, if 1 cmo = 1780 kg, then 1780/0.000833 is the mass of U235 fission for 1 CMO = 2.1368E6 kg = 2355 tons CMO book p 130 quotes "about 2000 tons of U235 can release as much energy as burning 4.2 billion tons of oil (which is 1 CMO)." ::: ## Cross section ::: {.cols2} ::: {.col2-l} * [Cross section](https://www.nuclear-power.com/nuclear-power/reactor-physics/nuclear-engineering-fundamentals/neutron-nuclear-reactions/microscopic-cross-section/) is an area of interaction of a target particle * May be bigger or smaller than the geometrical area * In this sense it's *like* a probability of interation * Units: 1 **barn** = 10$^{-28}$ m$^3$ * as in "you couldn't hit the broad side of a barn" * Depends on the nucleus and the neutron energy * Fast (prompt) neutrons are released during fusion ([0.1 - 10 MeV](https://www.nuclear-power.com/nuclear-power/fission/prompt-neutrons/prompt-neutrons-and-delayed-neutrons/)). * These have low fission cross sections though, so they are slowed down to "thermal" by neutron interactions with a *moderator*. * Thermal neutrons (0.025 eV at 17 $^o$C, ~2.2 km/s=4900 mph) ::: ::: {.col2-v} image ::: ::: ## Cross section image [nuclear-power.com](https://www.nuclear-power.com/nuclear-power/reactor-physics/nuclear-engineering-fundamentals/neutron-nuclear-reactions/microscopic-cross-section/) ## Neutron moderator ::: {.cols2} ::: {.col2-l}
* Fast (prompt) neutrons are released during fusion ([0.1 - 10 MeV](https://www.nuclear-power.com/nuclear-power/fission/prompt-neutrons/prompt-neutrons-and-delayed-neutrons/)). * These have low fission cross sections though, so they are slowed down to "thermal" by neutron interactions with a [*moderator*.](https://www.nuclear-power.com/neutron-moderator/) * Thermal neutrons (0.025 eV at 17 $^o$C, ~2.2 km/s=4900 mph) ::: fragment **Question: how to slow the neutrons down?** ::: ::: fragment Collide with masses similar to the mass of a neutron. Recall [elastic collisions](https://en.wikipedia.org/wiki/Elastic_collision). So, what to use? ::: ::: fragment Hydrogen (water) ::: ::: fragment Also consider absorption cross section. Graphite, heavy water... :::
::: ::: {.col2-v} image ::: ::: # Uranium ::: {.cols2} ::: {.col2-l} * U-235 * 0.72% abundance * Only natural fissile isotope * half life of 703.8 million years * $\rho=19.1$ g/cm$^3$ (lead is 11.3) ::: ::: {.col2} * U-238 * 99.27% abundance * [non-fissile](https://en.wikipedia.org/wiki/Fissile_material#Fissile_vs_fissionable) * half life of 4.468 billion years * can form Pu-239 ::: ::: image     image ## Uranium deposits ::: {.cols2} ::: {.col2-l} * 40 times more common than silver, 500 times more common than gold. * Found everywhere. * Highest grade deposits in [Canada](https://en.wikipedia.org/wiki/Athabasca_Basin#Uranium_mines) ::: ::: {.col2-v} image ::: ::: ## US Uranium sources image image ## Uranium processing ::: {.cols2} ::: {.col2-l}
* Uranium oxide, dissolved with acid, then precipitated as U$_3$O$_8$ (yellowcake) * Mined where concentration 0.5-5% * Mining type * underground * open pit * gold and phosphorus tailings. * [In-situ leach (ISL) mining](https://world-nuclear.org/information-library/nuclear-fuel-cycle/mining-of-uranium/in-situ-leach-mining-of-uranium.aspx) (57%) * sulfuric acid or sodium bicarbonate * Enrichment * Reaction to UF$_6$ (gas, liquid, solid). * reacts with water to form HF, corrosive! * [Ultracentrifuge](https://energyeducation.ca/encyclopedia/Gas_centrifuge_for_uranium_enrichment) to separate $^{238}UF_6$ from $^{235}UF_6$ based on density differences. * MW = 349, 352 (0.8% different). * ~100,000 RPM
::: ::: {.col2-v} image image image ::: ::: ## Uranium reserves
* [8 million tonnes (2019) uranium metal](https://www.iaea.org/newscenter/pressreleases/worlds-uranium-resources-enough-for-the-foreseeable-future-say-nea-and-iaea-in-new-report) * "Reasonably assured and inferred" resource * Recoverable at market prices 40-260 $US/kgU * *From the "red book"* * [80 years](https://phys.org/news/2011-05-nuclear-power-world-energy.html#:~:text=Uranium%20abundance%3A%20At%20the%20current,for%20less%20than%205%20years.) at current rate of consumption with conventional reactors * Current reactors (in the U.S.) are "once through." * Reprocessing * [Gain 25-30%](https://world-nuclear.org/information-library/nuclear-fuel-cycle/fuel-recycling/processing-of-used-nuclear-fuel.aspx) more energy from the original uranium. * reduce volume of waste * reduce level of radioactivity * Breeder reactors * produce more fuel than they consume * U-238 (forming Pu-239), "fast" reactor * Th-232 (forming U-233) "thermal" reactor * Thorium is 3.5 times as common as uranium. * could raise fuel availability 40-50 times > "It has been estimated that doubling the price of uranium ore, which as mentioned above would increase the cost of the electricity by less than 1 ยข/kWh, would increase the known conventional resources base 10-fold. This increase could easiliy support a much larger (CMO/yr-level) role of nuclear power for several centuries" *--Crane et al., A cubic mile of oil, 2010*.
# Nuclear reactors image

*[world-nuclear.org](https://world-nuclear.org/information-library/nuclear-fuel-cycle/nuclear-power-reactors/nuclear-power-reactors.aspx)*

## Nuclear reactors: PWR ::: {.cols2} ::: {.col2-l} * [Pressurized water reactor](https://world-nuclear.org/information-library/nuclear-fuel-cycle/nuclear-power-reactors/nuclear-power-reactors.aspx) * Pressurized water in contact with fuel * Water transfers heat and moderates the neutrons * Nonboiling (high P) * Heat transfer to separate steam loop * T: 290 $\rightarrow$ 325 $^oC$ * P: 15 MPa (2250 psi) ::: ::: {.col2-v} image ::: ::: ## Nuclear reactors: PWR image     image ## Nuclear reactors: PWR image image ## Nuclear reactors: BWR ::: {.cols2} ::: {.col2-l} * Boiling water reactor * Steam is formed directly in the reactor (*direct cycle*) * No separate heat transfer loop or steam generators needed. * Latent vs sensible heat $\rightarrow$ less water flow. * Water becomes radioactive $\rightarrow$ turbine, pumps, pipes, etc. shielded. * P: 7 MPA (900 psi) * T: 290 $^oC$ * Larger unit for same energy vs. PWR; (BWR lower energy per volume) ::: ::: {.col2-v} image ::: ::: ## Nuclear reactors: PHWR/CANDU ::: {.cols2} ::: {.col2-l}
* Pressurized Heavy Water Reactor/Canadian Deuterium-Uranium * Use natural, unenriched Uranium * Light water absorbs some neutrons requiring enriched U * Deuterium (heavy water) doesn't absorb thermal neutrons. * But less efficient at moderating neutrons $\rightarrow$ longer travel, larger vessel. * Also, unenriched fuel has a lower fissile density $\rightarrow$ larger vessel. * Large pressure vessel is expensive and complex, so the overall reactor is cool, unpressurized, filled with D$_2$O moderator, but penetrated by horizontal [pressure tubes](https://www.researchgate.net/figure/Current-CANDU-reactor-fuel-channel_fig1_267580730) containing the fuel and coolant with a surrounding CO$_2$ shroud. * can be refueled during operation. * P: 8 MPA (1285 psi) * T: [~305 $^oC$](http://large.stanford.edu/courses/2013/ph241/kallman1/docs/nuclear_reactors.pdf) * Indirect steam cycle
::: ::: {.col2-v} image ::: ::: ::: notes * safety: * careful alignment is needed. If tubes overheat, they bend, throwing off the alignment. * add lightwater --> slows reaction as water absorbs neutrons ::: ## Nuclear reactors: PHWR/CANDU ## Nuclear reactors: AGR ::: {.cols2} ::: {.col2-l} * Advanced Gas Reactor * CO$_2$ cooled * non-reactive with fuel or moderator, non-absorbing * not pressurized * [Graphite moderated](https://energyeducation.ca/encyclopedia/Neutron_moderator) * enriched U-235 (2.5-3.5%) * T: 650 $o^C$. * Higher efficiencies: 41% * Indirect steam but heat transfer internal to the reactor vessel. ::: ::: {.col2-v} image ::: ::: ## Nuclear plant tour # Economics * Dominated by capital costs * Fuel costs are around 15% of the cost of the power * Compared to 30% and 70% for coal and NG (~2006) * Time to complete * Gas-fired: 2 years * Coal-fired: 2-4 years * Nuclear: 3-5 or more years * Each nuclear plant is one-of-a-kind * Lack of standardization, contributes to long approval process * Prices of steel and concrete * Headline: "Steel prices are up 219% since early 2020. What to expect next" * [fortune.com](https://fortune.com/2021/08/16/steel-prices-2021-covid-commodities-lumber-costs/) August 16, 2021 ## Economics image
>"The levelized cost of energy (LCOE) is a measure of a power source that allows comparison of different methods of electricity generation on a consistent basis. The LCOE can also be regarded as the minimum constant price at which electricity must be sold in order to break even over the lifetime of the project."
::: notes * [Gas (peaker)](https://en.wikipedia.org/wiki/Peaking_power_plant) are plants that only run on high demand so have a high cost per kWh * This plot will explain some of the increasing wind, solar, and natural gas plants ::: # Radiation exposure: units
* Energy: electron-Volt (eV); 1 eV = 1.60218E-19 J * Decay rate * curie Ci; 1 Ci = 3.7E10 decays per second * becquerel Bq; 1 Bq = 1 decay per second * Ionization producted: roentgen R * 1 electrostatic unit (3.33E-10 coul) of charge of one sign from the interaction of $\gamma$ radiation in 0.001293 g of air (or 1 cm$^3$ of air at 1 atm and O $^oC$) * 1 R = $2.58\times 10^{-4}$ coul/kg. * Absorbed dose * rad (radiation absorbed dose) * 1 rad = 0.01 J/kg = 100 ergs/g * **gray Gy (SI unit)** * 1 Gy = 1 J/kg = 100 rads * Equivalent dose * Absorbed dose is not as useful as how much harm it causes. * Harm depends on: amount of radiation imparted, type of radiation, part of the body exposed * [video](https://www.youtube.com/watch?v=vRYwUPBZ-J4), [video](https://www.youtube.com/watch?v=MpQzhZ0RRDM) * multiply grays by a modification factor. * rem (roentgen equivalent man) * **sievert Sv (SI unit)** * 1 Sv = 100 rem
## Radiation quality factors image $$Sv = Gy \cdot W_R$ ::: notes Q is quality factor (related to $W_R$) ::: ## Radiation dose # Nuclear Regulatory Commission