How much "property" does the earth have left? Let's do the math｜International Clean Energy Day

Today is World Clean Energy Day. There are many kinds of clean energy on Earth that have the potential to be used, such as solar energy, wind energy, geothermal energy, methane hydrate, natural gas, nuclear fission energy, and nuclear fusion energy that humans have not yet found a good way to use. In this article, we mainly discuss those non-renewable energy sources, that is, the energy stored in the earth itself in approximately fixed reserves. For comparison, the reserves of those "unclean" non-renewable energy sources will also be discussed. How many non-renewable energy sources does the earth "itself" have? Today, we will do the math for the earth and ourselves.

01 What is the earth ’s “ own ” non-renewable energy ?

The "non-renewable energy" we are discussing here refers specifically to the energy stored in the earth itself, and does not include energy that can be obtained on the earth but actually comes from outside the earth, such as solar energy, wind energy, tidal energy, etc.

For energy from mineral resources in the lithosphere, we will discuss it based on proven reserves. On the one hand, due to the extreme difficulty of exploring deeper underground conditions, the mineral resources that humans have discovered so far only account for a small part of the total mineral resources in the earth's crust. And how much of a certain mineral is in the earth's crust? It is impossible to fully know with current technical means. On the other hand, not all proven mineral resources can be mined with existing technology. Generally speaking, technically recoverable reserves are generally a fraction of proven reserves, while total geological reserves may be dozens of times or even higher than proven reserves. One thing that needs to be explained is that these proportions will vary greatly with specific geological conditions.

For energy from substances in seawater, since seawater is a flowing liquid, it is relatively easy to survey the composition in deep water, and the composition in different parts of the ocean does not differ much, so this article will directly calculate the total amount based on the average concentration and the total volume or total mass of the ocean.

02Chemical Energy

The chemical energy on Earth is mainly stored in fossil fuels , including natural gas, oil, coal and methane hydrate. Strictly speaking, it also includes biomass, but biomass is rapidly renewable (plant photosynthesis), so in the long run, the total available energy of biomass on Earth depends on how long the material cycle of the Earth's biosphere can be maintained. Although fossil fuels can also be regenerated slowly (biomass is buried by geological movements and undergoes chemical changes underground), their regeneration rate is too slow, so their stock can be considered stable as long as human civilization lasts. In summary, we only calculate the total energy from the combustion of fossil fuels.

natural gas

The world's proven natural gas reserves are approximately 188,074,220,000,000 cubic meters. [1] (2020 data)

In the General Rules for Calculation of Comprehensive Energy Consumption (GB/T 2589-2020), the average low calorific value of natural gas is recommended to be 3.22 to 3.89×10^7 joules/cubic meter[2]. Here we take an intermediate value: 3.5×107 joules/cubic meter.

Then, the total energy of proven natural gas is about 6.58×10^ 21 joules .

oil

The world's proven oil reserves are approximately 236,294,750,000 tons, or 2.36×10^14 kilograms. [3] (2020 data)

The average low calorific value of crude oil still comes from GB/T 2589-2020, which is 4.19×10^7 joules/kilogram.

So, the total energy of proven oil is about 9.888×10^ 21 joules .

coal

The world's proven coal reserves are approximately 1,074,108,000,000 tons, or 1.074×10^15 kilograms. [4] (2020 data)

In the "General Rules for Calculation of Comprehensive Energy Consumption" (GB/T 2589-2020), the average low calorific value of raw coal is about 2.09×10^7 joules/kilogram.

So, the total energy of proven coal is about 2.2447×10^ 22 joules .

Methane hydrate

The situation of methane hydrate is more complicated. Since methane hydrate is mainly distributed in the underground permafrost in cold regions and under the deep seabed , it is very difficult to investigate the reserves of methane hydrate, and therefore data is very scarce. In different studies, the total amount of natural gas contained in methane hydrate (note: not the proven reserves, but the total geological reserves) varies greatly, ranging from 10^15 cubic meters to 10^18 cubic meters. [5][6]

According to the conservative estimate of 1×10^16 cubic meters of reserves, if the average low calorific value is still 3.5×10^7 joules/cubic meter, the total energy of methane hydrate estimated worldwide is about 3.5×10^ 23 joules . Once again, unlike the other resources above, this is not proven reserves, but estimated total geological reserves.

03Geothermal Energy

Geothermal heat may come from many sources - the release of gravitational potential energy from meteorites and dust that gathered to form the Earth when the Earth was first formed; frictional heating from the deformation of the Earth caused by the tides of the Sun and the Moon; and heat released from the decay of radioactive materials inside the Earth.

The total amount of heat energy contained in the earth is about 12.6×10^ 7 joules , of which 5.4×10^ 24 joules are in the earth's crust, and the total power of natural heat dissipation from the earth's interior to the outside is about 4.2×10^ 13 watts . [] However, as far as the current level of human technology is concerned, geothermal energy can only be utilized in areas with more intense geological activities and a large amount of magma/hydrothermal fluids entering shallower strata. Although the earth contains a huge amount of heat energy, most of it is in the mantle and core that humans cannot reach .

Figure 3: Geothermal utilization suitability map calculated by the maximum entropy model . Darker colors represent areas that are more suitable for building geothermal power plants.

Image source:

https://www.sciencedirect.com/science/article/pii/S0959652620319211

04 Nuclear Energy

4.1 Fission Energy

The most common fissile nuclide on Earth is uranium-235. However, uranium-235 is extremely rare, accounting for only 0.72% of natural uranium. [8] However, two other more abundant nuclides can be converted into fissile nuclides: uranium-238 (99.27% ​​of natural uranium) and thorium-232 (99.98% of natural thorium). [9]

Thorium Ore

The estimated reserves of thorium ore known worldwide (note that this is not the proven reserves) are about 6.212×10^9 kg (2019 data)[10]. This reserve is lower than the proven reserves of uranium, but the content of thorium in the earth's crust (13 mg/kg) is much higher than that of uranium (2.5 mg/kg)[11]. Therefore, the reason why the currently known reserves of thorium ore are less than those of uranium ore is more likely because thorium is rarely used in industry, so its exploration is not deep.

After absorbing a neutron, thorium 232 turns into thorium 233, which then decays into uranium 233 through several steps. Uranium 233 can absorb a neutron and then fission, releasing energy and more neutrons, allowing the cycle to continue.[12] During this process, each kilogram of thorium 232 releases 7.94×10^13 joules of energy.[13]

Figure 1 Thorium fuel cycle

Image source:

https://energyeducation.ca/encyclopedia/Thorium_fuel_cycle

In summary, the total energy of thorium in discovered thorium ores is approximately 4.93×10^ 23 joules .

Uranium resources

Uranium has two relatively stable isotopes: uranium-235 (0.72%) and uranium-238 (99.27%).

Among them, uranium 235 is relatively easy to fission. It can directly fission after absorbing a neutron. The fission of each atomic nucleus releases 193.4 mega-electron-volts of energy, which is 7.939×10^13 joules of energy per kilogram[14].

On land, the proven reserves of uranium are about 1.067×10^10 kg (data from 2022)[15]. Based on a 0.72% concentration, this includes about 7.68×10^7 kg of uranium-235.

Then, the total energy of uranium 235 in the proven uranium ore is about 6.097×10^ 21 joules . This energy is about the same as the total energy of proven natural gas.

However, the vast majority of uranium in nature is the isotope uranium-238, which can also release nuclear energy, but it is a little more complicated. Uranium-238 first absorbs a fast neutron and becomes uranium-239, which then decays into plutonium-239. Plutonium-239 then absorbs a neutron and fissions, releasing energy and more neutrons, allowing the cycle to continue. [16] In this process, each kilogram of uranium-238 releases about 8.06×10^13 joules of energy. [17]

Figure 2 Uranium fuel proliferation

Image source:

https://www.nuclear-power.com/glossary/nuclear-breeding/

Then, taking into account the proliferation of uranium 238 fuel , the total energy of the proven uranium in the world's terrestrial uranium mines is approximately 8.536×10^ 23 joules .

In the ocean, uranium exists mainly in the form of uranyl tricarbonate ions ([UO2(CO3)]^4+)[18], with an average uranium content of about 3.3 micrograms per liter of seawater[19]. The total volume of the world's oceans is about 1.3324×10^9 cubic kilometers[20]. Therefore, the total amount of uranium in seawater is about 4.3969×10^12 kilograms. Although uranium resources in seawater are abundant, uranium mining in seawater is not currently mainstream due to the high cost of extraction.

Then, taking into account the proliferation of uranium 238, the total energy of uranium in seawater is about 3.5175×10^ 26 joules .

4.2 Nuclear fusion energy

The easiest nuclear fusion reaction with the lowest reaction conditions is the fusion of deuterium and tritium.

Tritium is unstable and almost non-existent in nature, but can be produced by bombarding lithium-6 with neutrons.

Another easier fusion is deuterium-deuterium fusion, which is more difficult than deuterium-tritium fusion, but there is a lot of deuterium in seawater.

But it should be noted that humans currently do not have the technology to effectively utilize the energy of nuclear fusion.

Lithium-6 (source of tritium in deuterium-tritium fusion)

The world's proven reserves of lithium are approximately 2.6×10^10 kg (data from 2022)[21]. 4.85% of lithium is lithium 6[22]. Therefore, the proven reserves of lithium 6 are 1.261×10^9 kg.

Lithium 6 cannot react directly with deuterium, it needs to absorb a neutron first to become tritium:

n+6Li→T+4He (4.8MeV)

Tritium then reacts with deuterium:

D+T→n+4He (17.6MeV)

Both reactions are exergonic. [23] The entire reaction consumes one deuterium atom and one lithium-6 atom and produces 22.4 MeV of energy.

The relative atomic mass of lithium 6 is 6.015. So 1 kg of lithium 6 will release 3.593×10^14 joules of energy after complete reaction with deuterium.

The total energy of the complete reaction of all proven recoverable lithium-6 with deuterium (the total amount of deuterium on Earth is far greater than that of lithium-6) is 4.53×10^ 23 joules .

The total amount of lithium in seawater is approximately 224,000 megatons = 2.24×10^14 kilograms[24], so the total amount of lithium-6 in seawater is approximately 1.0864×10^13 kilograms.

The total energy released after the complete reaction of lithium-6 and deuterium in seawater is about 3.903×10^ 27 joules .

deuterium

The concentration of deuterium in seawater is about 33 g/m3[25]. The total volume of the ocean is about 1.3324×10^9 cubic kilometers. Therefore, the total amount of deuterium in the ocean is about 4.3969×10^16 kilograms.

There are two reactions in deuterium fusion:

(1) D+D→T+p (4.03 MeV)

(2) D+D→3He+n (3.27MeV)

Their products T and 3He will continue to react with D:

D+T→4He+n (17.6MeV)

3He+D→4He+p (18.3 MeV). [26] After the reaction is complete, 6 deuterium atoms are consumed and 43.2 MeV of energy is produced.

One mol of deuterium atoms weighs 2.014 grams[27], so the energy density of the complete deuterium reaction is about 3.449×10^14 joules/kilogram.

In summary, the total energy of deuterium in seawater is about 1.5165×10^ 31 joules .

05 Summary

In comparison, the total energy consumption of human beings in 2023 is about 2.091×10^13 watts[28], the power generation is about 3.365×10^12 watts, and the energy consumption in 2023 is about 6.595×10^20 joules. Let’s see how many times the total amount of these energies is equivalent to the energy consumption of human civilization in 2023.

Natural gas (proven reserves): 6.58×10^21 joules, equivalent to 9.9 times the energy consumption of mankind in 2023.

Oil (proven reserves): 9.888×10^21 joules, 14.9 times.

Coal (proven reserves): 2.2447×10^22 joules, 34 times.

Methane hydrate (estimated total reserves): 3.5×10^23 joules, 530 times.

Thorium (estimated reserves of discovered veins): 4.93×10^23 joules, 747 times.

Uranium 235 (land, proven reserves): 6.097×10^21 joules, 9.245 times.

Uranium (land, proven reserves): 8.536×10^23 joules, 1294 times.

Uranium (ocean, total): 3.5175×10^26 joules, 533,358 times.

Geothermal energy (earth's crust, estimated total amount): 5.4×10^24 joules, 8188 times.

Geothermal energy (entire Earth, estimated total amount): 12.6×10^27 joules, 19,105,382 times.

Lithium 6 (land, proven reserves): 4.53×10^23 joules, 686 times.

Lithium 6 (ocean, total amount): 3.903×10^27 joules, 6918119 times.

Deuterium (total amount): 1.5165×10^31 joules, 22994692949 times.

Author: Kang Yike, undergraduate student majoring in electronic science and technology at Beijing University of Technology

Reviewer: Li Ruixia, Vice President and Researcher of Sinopec New Star (Beijing) New Energy Research Institute, National Geothermal Center

Produced by: Science Popularization China

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