In physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, energy economics
Energy economics
Energy economics is a broad scientific subject area which includes topics related to supply and use of energy in societies. Due to diversity of issues and methods applied and shared with a number of academic disciplines, energy economics does not present itself as a self contained academic...

 and ecological energetics
Energetics is the study of energy under transformation. Because energy flows at all scales, from the quantum level to the biosphere and cosmos, energetics is a very broad discipline, encompassing for example thermodynamics, chemistry, biological energetics, biochemistry and ecological energetics...

, energy returned on energy invested (EROEI or ERoEI); or energy return on investment (EROI), is the ratio
In mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second In mathematics, a ratio is...

 of the amount of usable energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

 acquired from a particular energy resource to the amount of energy expended to obtain that energy resource. When the EROEI of a resource is less than or equal to one, that energy source becomes an "energy sink", and can no longer be used as a primary
Primary energy
Primary energy is an energy form found in nature that has not been subjected to any conversion or transformation process. It is energy contained in raw fuels, and other forms of energy received as input to a system...

 source of energy.

Non-manmade energy inputs

The natural or original sources of energy are not usually included in the calculation of energy invested, only the human-applied sources.
For example in the case of biofuels the solar insolation driving photosynthesis
Photosynthesis is a chemical process that converts carbon dioxide into organic compounds, especially sugars, using the energy from sunlight. Photosynthesis occurs in plants, algae, and many species of bacteria, but not in archaea. Photosynthetic organisms are called photoautotrophs, since they can...

 is not included, and the energy used in the stellar synthesis of fissile
In nuclear engineering, a fissile material is one that is capable of sustaining a chain reaction of nuclear fission. By definition, fissile materials can sustain a chain reaction with neutrons of any energy. The predominant neutron energy may be typified by either slow neutrons or fast neutrons...

 elements is not included for nuclear fission
Nuclear fission
In nuclear physics and nuclear chemistry, nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts , often producing free neutrons and photons , and releasing a tremendous amount of energy...

. The energy returned includes usable energy and not wastes such as heat.

Because much of the energy required for producing oil from oil or tar sands (bitumen) comes from low value fractions separated out by the upgrading process, there are two ways to calculate EROEI, the higher value given by considering only the external energy inputs and the lower by considering all energy inputs, including self generated. See: Oil sands#Input energy

Relationship to net energy gain

EROEI and Net energy (gain)
Net energy gain
Net Energy Gain is a concept used in energy economics that refers to the difference between the energy expended to harvest an energy source and the amount of energy gained from that harvest. The net energy gain, which can be expressed in joules, differs from the net financial gain that may result...

measure the same quality of an energy source
Energy quality
Energy quality is the contrast between different forms of energy, the different trophic levels in ecological systems and the propensity of energy to convert from one form to another. The concept refers to the empirical experience of the characteristics, or qualia, of different energy forms as they...

 or sink in numerically different ways. Net energy describes the amounts, while EROEI measures the ratio or efficiency of the process. They are related simply by


For example given a process with an EROEI of 5, expending 1 unit of energy yields a net energy gain of 4 units. The break-even point
happens with an EROEI of 1 or a net energy gain of 0.

The economic influence of EROEI

High per-capita energy use has been considered desirable as it is associated with a high standard of living based on energy-intensive machines. A society will generally exploit the highest available EROEI energy sources first, as these provide the most energy for the least effort. With non-renewable sources, progressively lower EROEI sources are then used as the higher-quality ones are exhausted.

For example, when oil was originally discovered, it took on average one barrel of oil to find, extract, and process about 100 barrels of oil. That ratio has declined steadily over the last century to about three barrels gained for one barrel used up in the U.S. (and about ten for one in Saudi Arabia).
Currently (2006) the EROEI of wind energy in North America and Europe is about 20:1 which has driven its adoption.

Although many qualities of an energy source matter (for example oil is energy-dense and transportable, while wind is variable), when the EROEI of the main sources of energy for an economy fall energy becomes more difficult to obtain and its value rises relative to other resources and goods.
Therefore the EROEI gains importance when comparing energy alternatives. Since expenditure of energy to obtain energy requires productive effort, as the EROEI falls an increasing proportion of the economy has to be devoted to obtaining the same amount of net energy.

Since the discovery of fire, humans have increasingly used exogenous sources of energy to multiply human muscle-power and improve living standards.
Some historians have attributed our improved quality of life since then largely to more easily exploited (i.e. higher EROEI) energy sources, which is related to the concept of energy slaves
Energy Slave
An Energy Slave is that quantity of energy which, when used to construct and drive non-human infrastructure replaces a unit of human labour...

. Thomas Homer-Dixon
Thomas Homer-Dixon
Thomas Homer-Dixon holds the Centre for International Governance Innovation Chair of Global Systems at the Balsillie School of International Affairs in Waterloo, Ontario, and is a Professor in the Centre for Environment and Business in the Faculty of Environment, University of Waterloo...

  demonstrates that a falling EROEI in the Later Roman Empire was one of the reasons for the collapse of the Western Empire in the fifth century CE. In "The Upside of Down" he suggests that EROEI analysis provides a basis for the analysis of the rise and fall of civilisations. Looking at the maximum extent of the Roman Empire
Roman Empire
The Roman Empire was the post-Republican period of the ancient Roman civilization, characterised by an autocratic form of government and large territorial holdings in Europe and around the Mediterranean....

, (60 million) and its technological base the agrarian base of Rome was about 1:12 per hectare for wheat and 1:27 for alfalfa (giving a 1:2.7 production for oxen). One can then use this to calculate the population of the Roman Empire required at its height, on the basis of about 2,500-3,000 calories per day per person. It comes out roughly equal to the area of food production at its height. But ecological damage (deforestation
Deforestation is the removal of a forest or stand of trees where the land is thereafter converted to a nonforest use. Examples of deforestation include conversion of forestland to farms, ranches, or urban use....

, soil fertility loss particularly in southern Spain, southern Italy, Sicily and especially north Africa) saw a collapse in the system beginning in the 2nd century, as EROEI began to fall. It bottomed in 1084 when Rome's population, which had peaked under Trajan
Trajan , was Roman Emperor from 98 to 117 AD. Born into a non-patrician family in the province of Hispania Baetica, in Spain Trajan rose to prominence during the reign of emperor Domitian. Serving as a legatus legionis in Hispania Tarraconensis, in Spain, in 89 Trajan supported the emperor against...

 at 1.5 million, was only 15,000. Evidence also fits the cycle of Maya
Maya civilization
The Maya is a Mesoamerican civilization, noted for the only known fully developed written language of the pre-Columbian Americas, as well as for its art, architecture, and mathematical and astronomical systems. Initially established during the Pre-Classic period The Maya is a Mesoamerican...

n and Cambodian collapse too. Joseph Tainter
Joseph Tainter
Joseph A. Tainter is a U.S. anthropologist and historian.Tainter studied anthropology at the University of California and Northwestern University, where he received his Ph.D. in 1975. He is currently a professor in the Department of Environment and Society at Utah State University...

 suggests that diminishing returns of the EROEI is a chief cause of the collapse of complex societies. Falling EROEI due to depletion of non-renewable resources also poses a difficult challenge for industrial economies.

Criticism of EROEI

Measuring the EROEI of a single physical process is unambiguous, but there is no agreed standard on which activities should be included in measuring the EROEI of an economic process. In addition, the form of energy of the input can be completely different from the output. For example, energy in the form of coal could be used in the production of ethanol. This might have an EROEI of less than one, but could still be desirable due to the benefits of liquid fuels.

How deep should the probing in the supply chain of the tools being used to generate energy go? For example, if steel is being used to drill for oil or construct a nuclear power plant, should the energy input of the steel be taken into account, should the energy input into building the factory being used to construct the steel be taken into account and amortized? Should the energy input of the roads which are used to ferry the goods be taken into account? What about the energy used to cook the steelworker's breakfasts? These are complex questions evading simple answers. A full accounting would require considerations of opportunity costs and comparing total energy expenditures in the presence and absence of this economic activity.

However, when comparing two energy sources a standard practice for the supply chain energy input can be adopted. For example, consider the steel, but don't consider the energy invested in factories deeper than the first level in the supply chain.

Energy return on energy invested does not take into account the factor of time. Energy invested in creating a solar panel may have consumed energy from a high power source like coal, but the return happens very slowly, i.e. over many years. If energy is increasing in relative value this should favour delayed returns. Some believe this means the EROEI measure should be refined further.

Conventional economic analysis has no formal accounting rules for the consideration of waste products that are created in the production of the ultimate output. For example, differing economic and energy values placed on the waste products generated in the production of ethanol makes the calculation of this fuel's true EROEI extremely difficult.

EROEI is only one consideration and may not be the most important one in energy policy. Energy independence (reducing international competition for limited natural resources), freedom from pollution (including carbon dioxide and other green house gases
Greenhouse gas
A greenhouse gas is a gas in an atmosphere that absorbs and emits radiation within the thermal infrared range. This process is the fundamental cause of the greenhouse effect. The primary greenhouse gases in the Earth's atmosphere are water vapor, carbon dioxide, methane, nitrous oxide, and ozone...

), and affordability could be more important, particularly when considering secondary energy sources. While a nation's primary energy source is not sustainable unless it has a use rate less than or equal to its replacement rate, the same is not true for secondary energy supplies. Some of the energy surplus from the primary energy source can be used to create the fuel for secondary energy sources, such as for transportation.

EROEI under rapid growth

A related recent concern is energy cannibalism
Energy Cannibalism
Energy cannibalism refers to an effect where rapid growth of an entire energy producing industry creates a need for energy that uses the energy of existing power plants. Thus during rapid growth the industry as a whole produces no energy because new energy is used to fuel the embodied energy of...

 where energy technologies can have a limited growth rate if climate neutrality is demanded. Many energy technologies are capable of replacing significant volumes of fossil fuels and concomitant green house gas emissions. Unfortunately, neither the enormous scale of the current fossil fuel energy system nor the necessary growth rate of these technologies is well understood within the limits imposed by the net energy produced for a growing industry. This technical limitation is known as energy cannibalism
Energy Cannibalism
Energy cannibalism refers to an effect where rapid growth of an entire energy producing industry creates a need for energy that uses the energy of existing power plants. Thus during rapid growth the industry as a whole produces no energy because new energy is used to fuel the embodied energy of...

 and refers to an effect where rapid growth of an entire energy producing or energy efficiency industry creates a need for energy that uses (or cannibalizes) the energy of existing power plants or production plants.

The solar breeder overcomes some of these problems. A solar breeder is a photovoltaic panel manufacturing plant which can be made energy-independent by using energy derived from its own roof using its own panels. Such a plant becomes not only energy self-sufficient but a major supplier of new energy, hence the name solar breeder. Research on the concept was conducted by Centre for Photovoltaic Engineering, University of New South Wales, Australia. The reported investigation establishes certain mathematical relationships for the solar breeder which clearly indicate that a vast amount of net energy is available from such a plant for the indefinite future. BP Solar originally intended its plant in Frederick, Maryland to be such a Solar Breeder, but the project did not develop. Theoretically breeders of any kind can be developed.

See also

  • Embodied energy
    Embodied energy
    Embodied energy is defined as the sum of energy inputs that was used in the work to make any product, from the point of extraction and refining materials, bringing it to market, and disposal / re-purposing of it...

  • Emergy
    Emergy is the available energy of one kind that is used up in transformations directly and indirectly to make a product or service. Emergy accounts for, and in effect, measures quality differences between forms of energy. Emergy is an expression of all the energy used in the work processes that...

  • Energy balance
    Energy balance
    Energy balance may refer to:* First law of thermodynamics, according to which energy cannot be created or destroyed, only modified in form* Energy balance , a measurement of the biological homeostasis of energy in living systems...

  • Energy cannibalism
    Energy Cannibalism
    Energy cannibalism refers to an effect where rapid growth of an entire energy producing industry creates a need for energy that uses the energy of existing power plants. Thus during rapid growth the industry as a whole produces no energy because new energy is used to fuel the embodied energy of...

  • Jevon's paradox 1880s observation of the efficiency effect multiplier
  • Khazzoom-Brookes Postulate
    Khazzoom-Brookes postulate
    In the 1980s, the economists Daniel Khazzoom and Leonard Brookes independently put forward ideas about energy consumption and behavior that argue that increased energy efficiency paradoxically tends to lead to increased energy consumption...

     1980s updating of Jevon's paradox
  • Net energy gain
    Net energy gain
    Net Energy Gain is a concept used in energy economics that refers to the difference between the energy expended to harvest an energy source and the amount of energy gained from that harvest. The net energy gain, which can be expressed in joules, differs from the net financial gain that may result...

External links

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