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.

Mistake
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.

Wrap-Up
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.