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How many nuclear plants does it take to meet the world's energy needs?

Several weeks ago Joshua Pearce at Clarion University in Pennsylvania released a study titled “Thermodynamic limitations to nuclear energy deployment as a greenhouse gas mitigation technology.” In the study he stated...
nuclear energy production would have to increase by 10.5% per year from 2010 to 2050 to both replace fossil-fuel-energy use and meet the future energy demands.
This line, of course, made the headlines and has been picked up by several outlets and blogs. When looking into his calculations for this statement, he made one assumption error that overstated the above sentence by nearly a factor of three.

Page 121, Section 4.1 of the study states:
Richard Smalley pointed out that in 2004, the global economy consumed the equivalent of 220 million barrels of oil per day, which converted into electricity terms is the equivalent of 14.5 TeraWatts (TW), or 14,500,000 MegaWatts (MW) (2005). … With a nuclear plant having about 1000 MW (1 GW) of capacity, we would need 14,500 nuclear power plants to power the entire world.
The first sentence is correct; the last sentence contains his false assumption. The 14.5 TW of power he calculates are referring to thermal energy. The 1,000 MW nuclear capacity assumption he makes is referring to electric energy. A 1,000 MWe nuclear plant provides about 3,000 MW of thermal energy. When using the correct assumption of 3,000 MWt instead of 1,000 MWe, the number of nuclear plants that can provide the amount of energy equivalent to daily world energy consumption is about 5,300 and not 14,500. I’ll explain further.

Energy and Heat
When you think of energy, think of it as heat. The energy we consume is really how much heat we consume. The kicker is how efficient we can turn heat into usable energy. A typical car engine is only 20% efficient and a typical steam power plant (used primarily by coal and nuclear plants) is only 33% efficient. This means that only a fraction of the heat created is turned into usable energy. Thermal energy is the total energy created and electric energy is the usable energy after efficiency losses.

Heat Rates
A heat rate is “a measurement used in the energy industry to calculate how efficiently a generator uses heat energy.” The average nuclear plant heat rate is about 10,000 Btus/kWh. But only 3,412 Btus are needed to generate one kWh of electricity. Thus, for every kWh generated by a nuclear plant, 6,600 Btus are not used. What happens to all those Btus? It is dissipated through cooling towers, lakes, rivers or oceans as steam or hot water.

Daily Electricity Generation and World Energy Consumption
In one day, a nuclear plant operating at 100% power will provide 24,000 megawatt-hours (1,000 megawatts each hour for 24 hours). With a heat rate of 10,000 Btus/kWh, a nuclear plant thus produces 240 x 10^9 Btus each day. In 2005, world primary energy consumption was 462.798 quadrillion Btus. Thus, daily world energy consumption was 1.27 x 10^15 Btus. To put the energy consumption in the context of Mr. Pearce’s study, we need to convert Btus to barrels of oil equivalent - one barrel of oil contains 5.8 x 10^6 Btus. Therefore, in 2005, the daily energy consumption was 219 million barrels of oil equivalent. Mr. Pearce’s study cites 220 million barrels of oil equivalent per day in 2004. Close enough.

Here’s how we calculate the mistake in the study. If we divide the world daily primary energy consumption of 1.27 x 10^15 Btus by the daily Btu production from one average nuclear plant (240 x 10^9), we find the world consumed the equivalent amount of energy from about 5,300 nuclear plants each day in 2005; not Pearce's calculation of 14,500 in 2004. In reality, the total number of nuclear plants is more like 6,000 because they are not always operating at 100% power every day.

How many nuclear plants are needed by 2050?
According to page 121 of Pearce’s study, world energy consumption is projected to double by 2050. If we double the calculated number of nuclear plants from today’s rate, the world will consume the equivalent amount of energy from 11,000-12,000 nuclear plants by 2050. Pearce’s study first calculated 33,000 but then says only 26,000 nuclear plants are needed to replace fossil-fuels while meeting the world's growing demands. The other 7,000 plants are supposed to be met by other non-emitting sources.

The whole point of Mr. Pearce’s study was to “demand modesty in claims of ‘emission-free nuclear energy’ as a panacea for global climate destabilization.” I agree with only part of this statement. Contrary to Pearce, I think it is clearly appropriate to call nuclear energy emission-free. Nuclear plants do not emit greenhouse gases while producing electricity and that’s what counts. The antis have tried to discount this truth by holding nuclear accountable for the emissions of fossil-fuels during nuclear’s lifecycle. Yet, even if we play by the anti’s game, numerous studies have shown that nuclear’s lifecycle emissions are equivalent to other non-emitting sources of energy.

Nuclear energy can and should increase much greater than 6% of the world’s energy needs. I do agree with Pearce, though, that we need to be “modest” for how much nuclear can contribute. It is impractical to think nuclear energy (nor any energy) should be the only source of energy used in the world. The diversity of energy sources is the best choice because it provides flexibility, sustainability and reliability, and nuclear definitely adds to that diversity.


Eric McErlain said…
Great work, Dave. Keep it up.
David Bradish said…
Thanks. Good to see you in the comments.
DV8 2XL said…
"It is impractical to think nuclear energy (nor any energy) should be the only source of energy used in the world."

It's all well and good to say this, and it may well be true in the broad sense, however if the cost of diversity for its own sake means that funds and efforts are being wasted on sources that cannot ever hope to meet a fraction of the projected demand, its benefits become moot.

Solar and wind have started to make noises that suggest that they are trying to hitch their wagon to nuclear's rising star, but still maintain the illusion that they can become significant contributers to the energy mix. This will never be the case. If the energy sector wishes to look to diversity it should demand that thorium cycle reactors and other breeders be developed to the point where they can be deployed, rather than become involved with generating schemes that have no long term value.
Luke said…
Further to David's above conclusion, we note that whilst one typical nuclear reactor might have a power output of around 1000 MWe, many nuclear power plants have two, three or more reactor units - therefore, the number of nuclear power plants needed is correspondingly smaller again.
JC said…
Hi there, interesting but may be a distinction without a difference. There are approximately 440 reactors operating today. Construction times can be between 4-8 years (although the Bruce units in Ontario seem to be having some difficulty in this regard) and the expertise required limits the number that can be built simultaneously. Even if it were possible to be working on 200 new facilities at a time that would require (best case scenario (6000-440)/(200/4=) 111.2 years. Admittedly more engineers would be trained but there is still a considerable lag involved. There would still be a limit in the number of personnel available as you can't drag in just anybody off the street. Ukrainians understand the consequences of putting neophytes at the helm of a nuclear facility. Our energy and environmental crisises will have manifested themselves long before the requisite number of plants could be built therefore the adaptations (as unpleasant as they may be) in consumption will already have been forced upon us.

Twenty times more reactors would probably mean more than twenty times the likelihood of an accident as the talent pool would be stretched thinner. If an accident were to occur it would undoubtedly slow construction progress. Unless virtually all of these proposed facilities were of the new breed, immediate fuel supply becomes an issue. The devotion required, in terms of money and political will, would also test the limits of our capabilities.

Because of these limitations (and others), it is almost certain that nuclear power will not be the technology to meet our energy needs in short or long term. We must find solutions that require less energy overall. Considering the probable timeline, efficiency and conservation are presently the only tools at our disposal that can mitigate the worst of the looming energy shortfall. 6000 or 14500 really makes no difference at all.
David Bradish said…

I could agree with some of your first two paragraphs but I think your third paragraph is off.

Because of these limitations (and others), it is almost certain that nuclear power will not be the technology to meet our energy needs in short or long term.

In the short term (next 10 years) natural gas will meet our energy needs. Natural gas also has been meeting our energy needs for the past 15 years. As a result of this reliance, gas prices have more than tripled since the '90s. High gas prices especially have hurt the chemical manufacturing sector by sending over 100,000 jobs overseas over the past few years.

How is nuclear not a long-term solution? A new nuclear plant hasn't come online for over a decade. Yet, in 2007, the US nuclear fleet broke its previous record for electricity generation. Also, the next nuclear plant to retire won't be until 2029. To me, an energy source that will run for at least 60 years IS a long-term solution.

We must find solutions that require less energy overall.

Do you have any ideas? I have one: it's a nuclear plant. Did you know one uranium fuel pellet (the size of your fingertip) contains the same amount of energy as a ton of coal, three barrels of oil or 17,000 cubic feet of gas?

Considering the probable timeline, efficiency and conservation are presently the only tools at our disposal that can mitigate the worst of the looming energy shortfall.

In theory conservation and efficiency sound good. If you go the conservation route, though, you're basically starving people of energy. It is well documented that an increase in electricity consumption increases quality of life.

Ever heard of Jevon's paradox? It says increases in efficiency will decrease prices. A decrease in prices will thus result in an increase in the quantity demanded. While some may think efficiency will reduce our demand, it will do the opposite - increase our energy consumption.

6000 or 14500 really makes no difference at all.

Maybe to you. But to me the error completely obscures how much energy we consume.
David Bradish said…

I included this post in an email to the author of the study, Dr. Pearce, and below is his courteous response back to me.

"I made the assumption that the usable energy coming from a nuclear power plant was only electrical because this is the current practice in the nuclear energy industry. Nuclear power plants create thermal energy, but nuclear energy is rarely used in co-generation (heat + electricity) systems and thus roughly 2/3rds of all the energy (heat) produced by a nuclear plant is currently wasted. Your analysis would be correct IF we actually used that heat – but we do not and thus you ended up grossly underestimating the number of plants needed to provide for world energy needs. Energy we use is for transportation and heating dwarfs the energy currently used in the form of electricity. Thus, if we were to make a large scale move from fossil fuels to nuclear energy using current practices – the energy would be delivered as electricity (e.g. used for space heating, charging batteries, etc.) and my assumption was largely correct. If the 'waste' heat from nuclear power plants was actually used, which I strongly encourage in the article, a significantly smaller armada of power plants would be needed as you suggest. To be absolutely correct I should have used the direct thermal energy for the fraction of global energy use from electricity. All that said, it is impossible (and some would say foolish) to predict the future – the exact growth rate for energy use could be negative or much higher than current projections based on a number of factors that are very hard to predict (e.g. recessions, war, new technologies, rapid third world development, etc). This was not the main point of my article.

The main point of the article was that we must take into account the life cycle energy and emissions from nuclear power plants. This is also true of any other energy system, but I was asked to focus on the nuclear energy industry. What I showed is that for the nuclear energy industry during rapid growth a need is created for energy that uses (or cannibalizes) the energy of existing power plants. Thus during rapid growth the nuclear industry as a whole produces no net energy because new energy is used to fuel the embodied energy of future power plants. If the growth rate is pushed even higher the nuclear energy industry can actually become an energy user rather than a source! Others can argue about what exactly that growth rate is where the break even point is reached - but that exact number is relatively unimportant. To offset a large fraction of fossil fuel energy the nuclear industry will have to grow very fast – and that growth will cannibalize a massive amount of the energy (and thus emission reduction mitigation) from the whole of nuclear plants. This drastically limits nuclear energy's ability to help us out of the current energy crisis we find ourselves in – namely we must rapidly eliminate greenhouse gas emissions from fossil fuel energy use as soon as possible without devastating the world economy.

I agree with you that using a diversity of energy sources is the best choice because it provides flexibility, sustainability and reliability – and I would also argue we should push energy efficiency as far as we can. That said, I strongly disagree with the continued use of "emission free" as a descriptor for nuclear power. The fact that nuclear plants do not emit greenhouse gases while producing electricity directly is immaterial. What matters is the amount of emissions per unit energy produced. As you point out, other energy sources have the same problem. This is absolutely true – but we thus should not ignore the effect, all energy technologies must be held accountable for the emissions from fossil-fuels during their life cycle. When it comes to climate change, we actually have physical limits to the amount of greenhouse gases we can emit. As current practices stand in the U.S. the nuclear energy life cycle is responsible for substantial emissions and must be improved. It is simply too inefficient to be taken seriously as a large scale source of emission reductions if we are really going to try to eliminate fossil fuels AND keep rapidly expanding energy use. I made several suggestions for improving that efficiency and I would like to explore them in more depth in future articles to inform policy on the best investments for climate change mitigation."

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