Nuclear Energy

Nuclear energy actually describes two different types of energy, fission and fusion. Nuclear fission is the form already in use, while no nuclear fusion power plants yet exist. Nuclear fission is the process of splitting heavy atomic nuclei, such as uranium, plutonium, or thorium into lighter products, turning a small amount of the mass into energy in the process (associated with the nuclear binding energy of the nuclei). Nuclear fusion involves combining lighter atomic nuclei into heavier ones, retrieving a small amount of the mass as energy once again. As a general rule, fission releases energy for nuclei much larger than iron, while fusion releases energy for nuclei much smaller than iron.

Energy Potential

Nuclear energy is unlike most sources of energy that are considered renewable, because in any given year we are able to extract as much energy from it as we choose to use in fuel. Nuclear energy isn't limited by the amount of solar radiation falling on the surface, the speed the winds blow, or the amount of rain that falls. The limiting factor is the amount of material available to be used in nuclear reactions.

Fission

Uranium

Uranium has two isotopes currently used to produce energy from nuclear fission. The first of these, uranium-235 makes up only about 0.7% of worldwide uranium, but can be used much more easily. The second isotope of uranium, U-238, can be turned into plutonium-239 within fast breeder reactors, which can then extract about 60 times as much energy from the same amount of uranium ore.

Uranium is currently mined from uranium ores. There are presently about 4.7*10^9 kilograms of uranium stored in these ores, enough at our present rate of use of just nuclear energy to last us a mere 85 more years according to the International Atomic Energy Agency. If we started exclusively using fast breeder reactors however, this same supply of uranium could provide the same power output for over 2500 years.

Much more uranium is stored in phosphates; an estimated 3.5*10^10 kilograms. Accessing this would come at a few times the cost of mining uranium ore, but since the cost of the fuel is such a tiny fraction of the cost of running a nuclear power plant, fuel extraction costs can afford to increase several times without causing a significant increase in the price of the electricity we receive.

The vast majority of the world's known uranium is stored in the oceans however. A total of 4.5*10^12 kilograms exists dissolved in our sea water, enough, if used in combination with fast breeder technology to continue current nuclear energy production for nearly 2.4 million years. Extracting uranium from sea water has been done in the past; however, never on an industrial scale, most likely due to the lack of economic incentive at current uranium prices.

Nuclear energy only accounts for 5.8% of the world's present energy supply. If we wished to replace the energy from all sources with energy produced from fast breeder reactors, the world's known uranium resources could last roughly 140,000 years.

Thorium

The other major fuel currently used in fission reactors is thorium. Thorium reactors are similar to fast breeder reactors, but rather than turning uranium-238 into fissile plutonium-239 they turn thorium-232 into the fissile uranium-233. Known worldwide thorium reserves which are easily recoverable amount to 2.6*10^9 kilograms. Using this easily recoverable thorium with current reactor technology, this could supply all world energy demand for roughly 66,000 years.

Fusion

Fusion is the form of energy that powers our sun. Currently fusion reactions have been done in lab conditions on earth, and energy has been gathered from these reactions, but the energy put into starting these reactions has always been greater than the energy recovered. In 2008 construction began on an international project, ITER, that hopes to be able to sustain a fusion reaction with an output of 500 million watts (Joules per second) for at least 1000 seconds at a time with an energy input of only a tenth of this amount. ITER plans to react deuterium and tritium creating helium and energy as its product.

Deuterium is a naturally occurring isotope of hydrogen, and about 33 grams of deuterium can be found in every ton of water. Tritium does not occur in large quantities naturally, but is made from lithium. The amount of lithium is the limiting factor in this reaction, so we will investigate its total potential.

According to the USGS, “The identified lithium resources total 760,000 tons in the United States and more than 13 million tons in other countries.” This is much less than the estimated 230 billion tonnes that are dissolved in our oceans. A reasonable estimate for energy gained per kilogram of lithium would be around 8*10^12 Joules. Assuming this technology pans out, this would mean nearly 2*10^27 Joules of potential energy, or enough to replace earth's current supply for 3.7 million years.

The deuterium-tritium reaction is not the only one which has been proposed. Deuterium-deuterium is a reaction that has been thoroughly tested in the past although also not yet implemented. For this reaction energy output is roughly 3.5*10^14 Joules per kilogram of deuterium. With about 2.4*10^16 kilograms of deuterium in our oceans, this would mean roughly 8.3*10^30 Joules, or enough to replace our current rate of supply for 16 billion years. This is longer than the current age of the universe and well past the anticipated death of our sun. We can only assume we will be able to harness a fraction of this energy, but this is an energy source with billions of years of potential in any case.

Dangers

Meltdown

Much public fear exists over the potential for a nuclear meltdown. This public fear isn't entirely misplaced as a full scale nuclear meltdown has happened in the past in Chernobyl,Ukraine, and another near meltdown at Three Mile Island in Pennsylvania.

Chernobyl

Fission reactors generate large amounts of heat even when they are not producing electricity, and the Chernobyl nuclear facility required coolant to be flowing at all times even when not generating electricity. In the case of a power outage, three generators would come online in order to keep coolant flowing. Starting these generators up took 15 seconds, and they took an additional 60-75 seconds to reach their full operating capacity. This was thought to be unacceptable, and thus it was proposed that the energy remaining in the plant's steam turbines could be used to power the coolant pumps for roughly 45 seconds while the generators started up. The reactor went online in 1983 without this system being tested successfully.

On April 25, 1986 conditions were planned to run the test at last. The day shift had been instructed on how the test was going to proceed, and the reactor had reduced its power output in the early morning on April 26. However, another power plant unexpectedly went offline that day and the Chernobyl reactor was ordered to return to full output. At around 11PM, the reactor was allowed to reduce its power output once again. The day shift had long since departed at this point, and the night shift was given little opportunity to prepare before being thrust into this test.

The reactor was supposed to be turned down to 700 million watts of power, but the production of neutron absorbing xenon in the reactor core caused the power to continue to fall down to roughly 500 million watts. The senior engineer overseeing the experiment then inserted the control rods into the reactor core much too far causing the power to drop to a mere 30 million watts.

When the control room finally decided to restore power, it took several minutes for power generation to begin to rise again, and it stabilized at roughly 200 million watts of output due to the amount of xenon that had accumulated during this time. At this point the control rods had been maximally withdrawn from the reactor core.

After the reactor power had stabilized near 200 million watts for some time the engineers decided to increase water flow through the reactor as part of the test, despite this being well below the intended test conditions. Increasing water flow dropped the power output of the reactor once again, causing the controllers to manually remove control rods from the reactor in an attempt to restore power.

It was under these conditions that the test began. Steam to the turbines was shut off and the water coolant was pumped using the energy remaining in the generator. As the generator slowed however the coolant began to flow more slowly, allowing more of it to boil and decreasing its ability to cool the reactor causing the reactor to heat more and boil more of the coolant.

The system handled this situation quite well actually, reinserting control rods to handle the increase in temperature. As the test was winding down, the emergency shutdown for the reactor was manually initiated, possibly as an attempt to turn off the reactor after the experiment. The system took several seconds to fully insert the rods however, which were poorly designed with graphite tips, causing them to displace coolant before inserting the neutron absorbing material.

As this happened the core power spiked, with none of the usual control rods in, little to no coolant flowing and steam already decreasing the efficacy of the coolant. Under high pressure steam exploded, fracturing some of the control rods and preventing others from inserting properly. A few seconds later a full nuclear meltdown occurred exploding a significant portion of the facility and causing the remainder to burn for several days.

In addition to having gone online without the proper safety tests having been conducted, the facility was in non-compliance with numerous standards of the time for nuclear facilities, most importantly the positive feedback the steam had on the core temperature, and the improper design of the control rods.

This full scale meltdown occurred at one of the world's largest nuclear facilities and represents the worst possible scenario for any nuclear power malfunction. In addition to the 57 direct deaths as a result of the accident, it is estimated that the total number of deaths attributable to this incident could amount to several thousand.

Several thousand deaths is a tragedy without a doubt, but it is on par with estimates for the deaths attributable to the pollution emitted from coal power plants alone every single year. In relation to power output, nearly all estimates put nuclear energy as one of the safest energy sources regarding its cost in human lives.

Spent Fuel

The radiation from the fuel itself isn't the main concern when dealing with spent nuclear fuel. The fuel was mined out of the earth in the first place and it would be hardly any effort to dilute it down to its original concentration and dispose of it underground. The main concern is the radiation from shorter lived isotopes created as products of the fission reaction. If uranium-238 with a half life of 4.5 billion years is split into two smaller isotopes each with half lives of 4.5 million years, then the expected rate of decay at present will have increased 2000 fold (although the type of radiation emitted may have changed). Many of the fission products have much shorter half lives, and once spent fuel has been allowed to cool for a few decades only a tiny fraction of the original radioactivity remains.



Within roughly a thousand years, the radioactivity of the spent fuel is no higher than that of the original ore.

Conclusions

Nuclear energy is by far the cheapest energy source with the potential to replace fossil fuels in the long term. It also has the ability to keep up with a growing population and an increasing standard of living. If we wish to make nuclear power last in the long term, more sustainable fast breeder technologies will need to be adopted on a large scale, but eventually nuclear fusion technology will need to be explored. Current projects such as ITER and its proposed successor DEMO show a great deal of promise, but have yet to become realities. If these technologies pan out as hoped, we may finally have found a solution to long term energy independence.

Additional Reading

Sustainable Energy — without the hot air

Combustible Renewables and Waste – Biomass

This category of our energy supply describes a huge array of different energy sources, which makes putting figures on their potential growth more difficult. The International Energy Agency describes this category of being composed of liquids from biomass, industrial wastes, municipal wastes, and solid biomass and animal products.

Liquids from Biomass

This category includes landfill gas, gasses from sewage and animal slurries (manure lagoons), as well as the much hyped ethanol.

Landfill, Sewage, and Slurry Gasses

All of these gasses involve the capture of methane produced by anaerobic bacteria feeding in these conditions and then burning this methane to produce energy. According to the EPA total methane emissions into the atmosphere from all sources amount to 5.66*10^11 kilograms per year. Combustion of methane releases roughly 5.55*10^7 Joules per kilogram burned. This means even if we were able to capture all of the methane leaking into the atmosphere around the world this would amount to 3.1*10^19 Joules per year, or 6.2% of the world demand. Capturing methane might make sense in some situations, but it does not have large scale potential.

Ethanol

Ethanol is the same alcohol found in the alcoholic beverages we consume. It is produced from the fermentation of a number of foods, primarily corn, but also sugarcane, other cereals, and more recently even cellulose. These plants gather energy from the sun, so in a sense ethanol production is an inefficient, but convenient form of solar power collection.

Measuring the energy gained from producing ethanol is very difficult to determine due to all the factors that go into producing it: energy to use the farm equipment, energy to produce fertilizers, energy to transport crops, energy to refine the ethanol. Partially due to the large extent the United States has been pushing ethanol fuels, a great deal of effort has been put into calculating this energy gained from ethanol.

Early studies on producing ethanol from corn were unclear as to whether there was any net benefit, putting it somewhere between a couple times more energy produced, down to significantly less energy gained than originally used to produce the ethanol. It now appears that producing ethanol from corn has a marginal benefit of somewhere between 6% and 67% more energy extracted from the ethanol than was used to produce it. One study on biofuels soberly put the case as, “The picture for ethanol from corn is particularly depressing. The entire global harvest of corn (700 million tons) converted to ethanol with current technology would yield enough transportation fuels to supply only 6% of the global gasoline and diesel demand.” Gasoline and diesel for transport being only a fraction of the world's overall energy use.

The outlook for producing ethanol from sugarcane has a much better outlook than corn, producing somewhere in the range of 8-10 times as much energy as is used to produce it. Nonetheless, our overall potential from all ethanol fuels is still quite small as the previous biofuels study notes, “Converting 100% of the global harvest of corn, sugarcane, soy and palm oil into liquid fuels, using the current technology, would provide fuel energy of 3% of global primary energy from fossil fuel combustion and net energy (after subtracting the energy required to produce the fuels) of 1.2% of the global primary energy from fossil fuel combustion.” Converting all of our major food crops into ethanol still only has the potential to replace a small fraction of our fossil fuel dependence.

Industrial and Municipal Wastes

Both of these are comprised of burning the solid and liquid wastes which would otherwise be thrown away. If we assume that municipal trash in Denmark is fairly typical of the energy content of wastes around the world then incineration of waste yields roughly 1.05*10^7 Joules per kilogram.

No worldwide figures exist for total garbage production, but the United States Environmental Protection Agency estimates that 2.3*10^11 kilograms of garbage is thrown away in the United States each year. Considering both the proportion of greenhouse gas emissions that come from the United States and the percentage of the world's population that lives there, I think a reasonable estimate for the world total would be 10-20 times the US total. Taking the most optimistic of all our assumptions, this still yields a maximum energy potential from burning wastes of about 4*10^19 Joules or less than 10% of the world's current demand.

Environmental Impact

The incineration of municipal and industrial wastes used to contribute a significant number of pollutants into the environment. Newer standards for cleaning the flue gasses combined with newer technologies have turned incineration from one of the dirtiest energy forms to one of the cleanest. The United States Environmental Protection Agency estimates that dioxin emissions from incineration are 1/1000 of their levels in 1987. Emissions of many other pollutants have also decreased by upwards of 90%.

Solid Biomass and Animal Products

This category involves the direct burning wood or other plant matter for fuel or turning it into another form before burning it for fuel. Also included in this category is the burning of animal products or wastes; although this is not a significant source of energy. At present, the burning of wood and other plant materials is still a significant source of heat for warmth as well as cooking especially in developing countries.

Burning these fuels directly is much dirtier than turning it into cleaner fuels such as ethanol, and it has little more energy potential at this stage.

Powering Our Future

Concern over the environmental impact of energy production has been rightfully high in recent years. In deciding how we are going to provide energy in the future, we need to consider how much energy we are going to be able to provide and at what cost it is going to come, cost being both environmental and financial.

The Present Situation

As our population has continued to grow and we adopt wealthier standards of living over time worldwide energy consumption has continued to increase accordingly. As of 2008 worldwide energy production was 5.1*10^20 Joules (4.9*10^17 Btu). For those of you not familiar with these units, a typical 60 Watt light bulb uses 60 Joules of energy every second. This world total does not include only electrical energy, but also energy used to drive our cars, heat our homes or perform any number of other tasks. As of 2008 Oil accounted for 33.2% of our energy production, Coal 27.0%, and Natural Gas an additional 21.1%. The next largest source of energy production comes from the combustion of biomass (wood and other plant materials) and other wastes both municipal and industrial, accounting for 10.0% of energy production. Next we have Nuclear energy accounting for 5.8% of production and Hydroelectric energy accounting for another 2.2%. The remaining 0.7% of our production is the amount currently produced by all of the other methods we currently hear about; the sum total of all our efforts for renewable energy.



Check out the International Energy Agency's 2010 Key World Energy Statistics report for additional information on our present situation.

Future Challenges

Our three main energy sources at present are problematic for a number of reasons. Most obviously, they are all finite and at present use rates are each going to run out between a few decades and a few millennia from present. Extracting each of them will become increasingly difficult in the future as the more easily accessible sources of each become depleted.

More importantly perhaps, each of these make a huge contribution to anthropogenic global warming. Our atmosphere is transparent in the visible and near-visible parts of the electromagnetic spectrum. Our sun emits electromagnetic radiation including the light we see because it has a temperature. At it's surface temperature of roughly 5800K most of the light it emits is in the part of the spectrum where our atmosphere is transparent. The earth's surface temperature of roughly 300K emits virtually all of its energy as radiation in the infrared portion of the spectrum. Carbon dioxide and other greenhouse gasses are opaque in the infrared portion of the electromagnetic spectrum and thus absorb a great deal of radiated energy from the earth's surface once again. The burning of each of our three main fuel sources is the largest anthropogenic source of carbon dioxide.

Finally, the burning of coal in particular emits quite a large amount of particulate matter and a number of other pollutants into the atmosphere which can be detrimental to health in excess.

Replacing these means replacing the energy they provide. Not merely the electrical energy generated from these sources, but we need to be able to replace the energy used to drive our cars, heat our homes, fuel our stoves, build our products, and transport our goods as well, which largely comes from these three main sources.

There are a number of energy alternatives to these three main sources which have been proposed. A great deal of effort has been put into making many of these a reality, but they still have seen little success in replacing our present system of production. Some of them, such as cold fusion or perpetual motion are nothing other than magical thinking, but many others have actual potential for energy generation and have even been put into place to some extent. This post is going to attempt to look at the several most realistic of these sources in particular assessing both their potential costs and their potential for energy generation.

Hydroelectric

After biomass and nuclear energy, hydroelectric energy is the only remaining energy source with any significant implementation to date. Hydroelectric energy comes from the potential energy water (or any mass) has when in a gravitational well. This energy can be calculated by multiplying the mass by the force of gravity by the distance the mass is moving in the direction of the gravity force. If we wish to calculate this energy in Joules for a mass on earth we would use 9.8 (m/s/s) as the value for gravity and the distance in meters that the mass of water in kilograms is traveling up or down. Assuming that a typical area of land has 80cm of rain a year falling at a mean altitude of 100 meters, this would equal roughly 1.2*10^20 Joules of energy per year for the entire landmass of the earth, still only a fraction of the supply we need to replace. Additionally, it is obviously unrealistic to expect us to be able to capture every bit of potential energy from when a water drop lands anywhere on land until it reaches sea level. More realistically the best hydroelectric resources have already been utilized and there is only marginal room for growth potential in this area.

Solar

One of the positive aspects about hydroelectric energy was that when water is held behind dams, it can be released to generate electricity as there is demand for it. One problem that comes with adopting solar-heavy energy generation is that we are only able to generate energy as it comes in. This means we need to find ways to store sufficient energy during the day to supply our needs at night and sufficient energy during the summer to supply our needs during the winter as well.

At the earth's distance from the sun, solar radiation amounts to roughly 1367 Watts (Joules per second) for every square meter of surface perpendicular to the direction to the sun. This varies by about 50 Watts per square meter over the course of the year due to the earth's slightly eliptical orbit and by roughly half a Watt per square meter over the course of the 12 year solar cycle.

Not all of this light makes it through our atmosphere and earth, as a rotating sphere, doesn't have all of its surface perpendicular to the direction to the sun. A good area of desert at low latitude can expect somewhere around 300-350 Watts of energy to reach every square meter of surface. Solar power doesn't need to include only solar electrical generation, it is currently used in many areas for heating hot water as well as homes.

When it comes to generating electricity from heat we cannot achieve anywhere near full conversion. The finest solar cells we are able to assemble in labs are able to achieve slightly over 40% conversion efficiency at present. A typical multicrystalline silicon cell someone might install on their roof however would probably be able to achieve between 14% and 19% efficiency. Large solar power generating facilities often use parabolic reflectors to focus light on a single small area which is then usually able to achieve around 35% efficiency.

As of 2008 Solar energy accounted for less than 0.02% of the world's total energy production. This is likely due to the high costs of installing solar cells compared to other technologies and the accordingly higher costs for the electricity generated (usually a few times that of most other technologies Source. Solar energy, however, does at least have the potential to meet the world's present demand for energy if we were able to build the required infrastructure. Assuming we are using 18% efficient solar cells in an area receiving 300 Watts per square meter of energy from the sun, we would need to cover 3*10^11 square meters with these cells in order to meet the world's demand. This is almost exactly equal to the area of the US state of Arizona (and covering their entire state with solar cells sounds about as reasonable as the “birther” and illegal immigration legislation they've passed this year).

Wind

At present, wind power accounts for approximately 0.24% of worldwide energy generation. Wind power is even less reliable than solar, depending entirely on wind conditions to determine the energy it generates. Accordingly if we are going to adopt an electrical grid dependent upon wind power we need to be able to find ways to store energy for possible multiple week periods of calm winds.

A 2005 study from Stanford University attempted to estimate the world potential energy generation from wind power by attempting to measure wind speeds around the world at the height of a modern large wind turbine. Assuming all of the world's windy land or near-land areas were covered with massive 80 meter high, 77 meter diameter wind turbines, the authors estimate wind could provide 2.3*10^21 Joules or roughly 4.5 times the world's current energy needs.

Achieving this potential would require massive engineering well beyond anything ever completed before. Each of these 77 meter diameter wind turbines towers into the air roughly as high as a 38 story building. Most of this potential does not exist on land, but rather offshore where building challenges become much greater and costs also skyrocket.

Geothermal

Roughly 1.4*10^21 Joules of energy flows out through the earth's crust from the mantle each year. This represents roughly 2.7 times the planet's present energy demands. Of this, roughly 2/3 is replaced by radioactive decay. The difference between these two values is due to the huge amount of energy left over from the accretion of our planet.

Most of this energy can not be reasonably harnessed. Part of this is because most of the planet is underwater and also because most areas have very small amounts of geothermal energy coming up through the crust. The most optimistic estimates for how much energy we could ever expect to extract from geothermal power is roughly 8.0*10^19 Joules per year or roughly 17% of our worldwide demand. More sober estimates for the potential of geothermal are as low as 2.2% of present worldwide demand.

Wave

Waves are generated by winds blowing across large open bodies of water such as our oceans. The energy in wave power depends upon the square of the wave height and the frequency of the waves.

Estimates from the International Energy Agency for the total energy available in wave power vary widely from 3*10^19 Joules per year to 3*10^20 Joules per year. The World Energy Council estimates the wave resource as at least 6*10^19 Joules per year. Overall these estimates range from 6% to 60% of our present supply. Harnessing all of this resource would mean covering all of our coastline or an equivalent region of open sea entirely with wave collectors.

Tidal

Tidal energy is, in my opinion, the most fascinating of our proposed energy sources. Tides are generated by the gravitational pull from the moon (and partially the sun as well). Water is held to the earth by the earth's gravity, but the slight impact the presence of these celestial bodies has on the gravitational force at the earth's surface creates two small tidal bulges of water following the moon around the sky. Since the earth rotates faster than the moon, the effect of friction from the earth's surface keeps these bulges slightly ahead of the moon's position. This has the effect of pulling the moon forward just slightly sending it into a higher orbit and robbing the earth of a small amount of its angular momentum.

The earth has a gravitational impact upon the moon as well, enough to slightly distort its distribution of mass as it rotates. This is the reason the moon has become “tidally locked” with the earth, always showing the same side to those on the earth's surface.

The earth has quite a bit of energy stored in its rotation, a total of roughly 2.1*10^29 Joules, or enough to supply the world's energy at today's rate of demand for a little over 400 million years. We cannot simply take this angular momentum from our planet at our will however, it depends entirely on the changes in water distribution caused by our moon.

The equation for energy in water works very similarly to our equation for hydroelectric power. If the tides raise the height of water by two meters over a square kilometer area (1,000,000 square meters) then this water with a density of 1000 kg per cubic meter will have a mass of 2*10^9 kg (2 million tonnes). Not all of this water will have two meters it is able to descend however. Only the water at the very top of our column will be able to return a full two meters down, the water in the middle will only be able to descend a single meter and the water at the bottom of the column will have remained at the original sea level. The average distance the water will be descending will be only a single meter. Thus, a 2 meter tide over a square kilometer region has 9.8 (gravity) *2*10^9 or 19.6 billion Joules of energy. There are roughly 700 tides per year so this would mean 1.4*10^13 Joules of energy per year in our hypothetical square kilometer.

Tides in the open ocean are fairly small and much harder to harness. The potential for harnessing tidal power exists mostly in bays and estuaries with large tides. No worldwide estimate exists for the total amount of tidal energy that can be reasonably harnessed; however, estimates have been made for bays and estuaries with at least one bank in England, which has a relatively large coastline and fairly high tides. England is estimated to have roughly 1.8*10^17 Joules per year of useable tidal energy. This represents less than 0.04% of the world's present energy supply. Even if we did scale this up to all of earth's useable bays and estuaries it would be difficult to imagine more than a couple percent of our demand being met by tidal power.

Costs

The United States department of energy has put together a report estimating the costs of most of the energy sources we discuss for the year 2016.


The overall cost is listed in the far right column, one megawatt-hour being equal to 3.6*10^9 Joules.

Most of the energy sources are able to compete fairly closely in terms of price with three exceptions: offshore wind, solar photovoltaics, and solar thermal. The main trouble is that offshore wind and solar were the two energy sources we investigated that actually had the potential to replace our current major energy sources, or even come reasonably close. The good news is that we have yet to look at the two energy sources we ignored at the beginning, biomass and nuclear energy. These two energy sources have the most potential to replace our current energy supply, but are also the most controversial for their perceived risk. Because of this, each of these energy sources will get the attention they deserve in their own future post.

Biomass
Nuclear

Note: If you have trouble verifying any of the numbers in this post feel free to ask in the comments for additional clarification. Most of the calculations are simply changing units to maintain consistency, but occasionally some additional steps were done.