# Future World Energy

L. David Roperarts.bev.net/RoperLDavid/

Slide Show for this web page

I have also done a detailed calculation of global warming due to fossil-fuels burning.

## Introduction

The purpose of this article is to show the energy deficit in future years by extrapolating world energy consumption and coal, crude-oil, natural-gas and uranium extraction into future years.

A calculation of energy produced by nuclear reactors is shown to be rather small compared to the projected energy consumption and the energy available from the three fossil fuels. Therefore, the only way to fill the energy deficit beyond fossil-fuels energy is by renewable energy, such as solar and wind.

It is then shown that a reasonable growth rate for three renewable energy sources (wind, photovoltaics and biofuels) can meet an assumed asymptotic energy per capita of 60x106 BTU/year/person.

"Energy" here refers to the total energy available in the fuel, often called "primary energy", not the energy actually converted into useful work or electricity.

Of course, energy consumption by humans cannot grow indefinitely, because there is a limit to the amount of energy that can be captured from the Sun. The graph below shows the world energy-consumption data and a hyperbolic-tangent-function fit to the data in order to extrapolate into the future with an eventual asymptotic consumption amount of 350x106 BTU/year/person (~12 kW/person), for an assumed final asymptotic population of about 8.3x109. This is about the per-capita consumption of the United States now. This amounts to a consumption asymptote of about 2900x1015 BTU/year [2900 quad/year or (2900*1055)x1015 joules/year=3.06x1021 J/yr=9.69x1010 kilowatts=8.50x1014 kWh/year]:

Currently the U.S. uses about 350x106 BTU/person/year (~12 kW/person), industrialized countries average about 200x106 BTU/person/year (~6.5 kW/person), developing countries average about 35x106 BTU/person/year (~1.2 kW/person) and the world average is about 75x106 BTU/person/year (~2.5 kW/person). The leveling off assumes that renewable energy sources will be developed in time to make the transition from the peaked fossil-fuels extraction curve to the smoothly rising energy-consumption curve.

## Energy from Fossil Fuels

The main sources of energy for the world are coal, crude oil and natural gas. The following constants are needed to calculate the amount of energy that can be obtained from these three fossil fuels:

• 1 ton (2000 lbs) of coal yields about 25.2 MBTU.
• 1 barrel (42 gallons) of crude oil yields about 5.8 MBTU.
• 1 mcf (103 ft3) of natural gas yields about 1 MBTU.

The graph below shows the energy obtainable from fossil fuels as a function of time, using these constants and the depletion curves of coal, crude oil and natural gas and assuming that 75% of fossil-fuels extraction amount is burned for energy in the year they are extracted:

(The 75% assumption is a rough approximation. Surely, each fossil fuel has a different fraction that is burned for energy and the fractions undoubtedly vary with time.)

The graph below compares the world energy consumption to the total energy supplied by fossil fuels:

As should be the case, other energy sources besides fossil fuels supply some of the energy consumption. There is a huge energy deficit relative to fossil-fuels energy to meet the 350 MBTU/person/year asymptote.

## Energy from Uranium

An interesting next question to ask is how much primary energy is supplied by "burning" uranium in nuclear reactors? The best analysis of energy produced by nuclear reactors I have found gives the following constants needed to do this calculation:

• The fraction of natural uranium in U3O8 ore is 0.846.
• The amount of electrical energy delivered by nuclear reactors is about 151.8 Tjoules/tonne of natural uranium = 144 109MBTU/tonne.
• The factor to convert electrical energy into thermal energy for nuclear reactors is about 2.6, which corresponds to a conversion efficiency of 1/2.6 = 0.38.

The amount of nuclear thermal energy produced by reactors as a function of time, assuming a very optimistic amount of nuclear resources, is shown in the following graph:

The red curve is a fit where the amount to eventually be extracted is double the amount of the blue curve, an extremely optimistic case.

It was assumed that all uranium mined is eventually used to extract energy. Of course, much of it was used and will be used to make nuclear weapons; however, some weapons were dismantled and their uranium used to extract energy. So this calculation is extremely optimistic for useful electrical energy that can be gotten from uranium.

The graph below compares the world energy consumption to the total energy supplied by the fossil fuels and uranium:

Doubling the total uranium finally extracted has very little effect. The conclusion is that uranium will never supply very much energy for humans to use.

The amount of energy that must be supplied by sources other than fossil fuels and uranium are shown in the graph below:

It is possible that the decline in extraction of fossil fuels will cause a population collapse. This would surely cause the world energy consumption to also fall to some new asymptote. In that case the amount of energy that must be supplied by other than fossil fuels and uranium would be less than shown above.

## Energy from Renewable Sources

The growth rates for renewable sources have been as follows at the beginning of the 22nd century:

• Wind energy: about 25% per year
• Photovoltaics: about 31% per year
• Biodiesel: about 73% per year

Roughly assume that wind supplies one-half of renewable energy, photovoltaics supplies one-fourth and biofuels (biodiesel and ethanol) supplies one-fourth. A hyperbolic-tangent function is used to represent their growth and their eventually reaching an "asymptote" below the other-sources curve as they were about year 2000. For a hyperbolic-tangent time constant of 20 years and a break-point year of 2015, the result is shown in the graph below:

The renewable-energy growth rates versus time are:

These are achievable growth rates, but will require a massive effort.

An interesting further study would be to calculate how much of the Earth's surface is required to meet these values for energy from photovoltaics and biofuels and whether sufficient wind resources are available to meet these values for wind energy. Possibly the best biofuel is biodiesel and the best source of feedstock for biodiesel is algae.

For a rough calculation, consider that the Sun shines about 5 kWh/m^2/day (1.8x10^7 J/m^2/day or 1.7x10^4 BTU/m^2/day) on the Earth surface. For a Earth land area of about 1.5x10^14 m^2, the total solar energy on the land area is about 9.3x10^20 BTU/year. The asymptotic energy consumption used above is about 3x10^18 BTU/year. So the available solar energy shining on the land is about 310 times that amount that is assumed to be consumed. This implies that the assumed asymptotic consumption is probably higher than possible. Of course, the ocean area is much larger than the land area (71% compared to 21%), so some of the energy could come from the solar energy impinging on the oceans.

The conclusion is that, if the world could level off energy consumption to about 575 quad per year, a continued intensive program of increasing renewable energy sources at a reasonable rate could easily meet the energy needs not met by fossil fuels and uranium.

World Wind

## Coal Moratorium Possibility

Suppose that humans decide to institute a gradual moratorium on burning coal in order to save it for making useful items and to reduce its emitting carbon-dioxide into the atmosphere. For purposes of doing an approximate calculation, assume that the amount of carbon put into the atmosphere by burning coal is modified as a function of time by the factor shown here:

which is a plot of the function . This corresponds to about a hundred-year time interval to institute a coal moratorium.

Then the energy available from fossil fuels would be:

Assume that renewable-energy grows with a hyperbolic-tangent time constant of 20 years and a break-point year of 2015 to an amount corresponding to other non-fossil-fuels sources (e.g., geothermal and hydro) remaining nearly constant with time, as shown in the graph below:

The renewable-energy growth rates versus time with and without a coal moratorium are:

Even with the coal moratorium assumed in this work, the growth is possible.

## Conclusion

The depletion of fossil fuels (coal, crude oil and natural gas) indicate that the time is now for beginning a world intensive program to develop renewable fuel sources (wind, solar and biofuels). In fact, the current rates of growth of renewable-energy sources are more than enough to match the growth in energy consumption and then slow down in growth to make up the difference between the decline of biofuels and a reasonable final per capita use of energy (60x106 BTU/year/person).

Because of depletion, uranium will never be able to supply much energy compared to the need. Precious fossil fuels should be used to develop renewable energy sources rather than more nuclear reactors.

Further study needs to be done as to whether the proposed continued growth of renewable-energy sources is possible on a finite Earth.

I believe that humans will continue to extract and burn fossil-fuels as fast as possible. Fortunately, the peaking of fossil-fuels extraction will put a natural brake on that burning. Unfortunately, the peaking of fossil-fuels extraction will cause massive disruptions in meeting the sustenance needs of nearly 7 billion humans. Also, the increase in temperature in about the year 2100 of about 1.4°C (2.5°F) above the 19th-century temperature will cause great suffering. The current emphasis on cutting back carbon emissions from fossil-fuels burning is needed to reduce global warming, but even more to preserve the fossil fuels for making useful materials and to prepare society for the economic disruptions that will undoubtedly occur when the populace finally realizes that we are on the down side of fossil-fuels depletion.

Probably the best that we can corporately do is to plan for the disruptions that will occur, both from the increase in temperature until 2100, and possibly on into the future if methane clathrates come into play, and the decline of availability of fossil fuels. However, we should strenuously try to use fossil carbon compounds for useful materials instead of burning it for energy.

I have also done a detailed calculation of global warming due to fossil-fuels burning.

## Appendix 1. Fossil-Fuels Extraction and World Population

The asymmetric peaked Verhulst function is used to fit the fossil-fuels extraction data:

where

### World coal extraction

The total amount to be extracted (area under the curve) is 1.5 x 1012 tons for the blue curve and 3 x 1012 tons for the red curve, which is very unlikely..

### World crude-oil extraction

The total amount to be extracted (area under the curve) is 2 x 1012 barrels for the blue curve and 4 x 1012 barrels for the red curve, which is extremely unlikely..

### World natural-gas extraction

The total amount to be extracted (area under the curve) is 15 x 1015 ft 3 = 15 x 1012 mcf for the blue curve and 30 x 1012 mcf for the red curve, which is extremely unlikely.