Energy returned on energy invested
In physics, energy economics and ecological energetics, energy returned on energy invested (EROEI or ERoEI); or energy return on investment (EROI), is the ratio of the amount of usable energy 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 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 is not included, and the energy used in the stellar synthesis of fissile elements is not included for nuclear fission. 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) measure the same quality of an energy source 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.
Economic influence of EROEI 
|EROI (for US)||Fuel|
|3.0||Bitumen tar sands|
|35.0||Oil imports 1990|
|18.0||Oil imports 2005|
|12.0||Oil imports 2007|
|10.0||Natural gas 2005|
|10.0||Nuclear (with diffusion enrichment)|
|50.0||Nuclear (with centrifuge enrichment, with fast reactor or thorium reactor)|
|30.0||Oil and gas 1970|
|14.5||Oil and gas 2005|
|1.9||Solar flat plate|
|35.0||World oil production|
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) according to the Danish Wind Energy Association, the EROEI of wind energy in North America and Europe is about 20:1.
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 invention of agriculture, humans have increasingly used exogenous sources of energy to multiply human muscle-power. Some historians have attributed this largely to more easily exploited (i.e. higher EROEI) energy sources, which is related to the concept of energy slaves. Thomas Homer-Dixon  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, (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, 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 at 1.5 million, was only 15,000. Evidence also fits the cycle of Mayan and Cambodian collapse too. Joseph Tainter 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 
|This section does not cite any references or sources. (May 2010)|
Measuring the EROEI of a single physical process is unambiguous, but there is no agreed-upon 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), decrease of greenhouse gas emissions (including carbon dioxide and others), 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.
Richards and Watt propose an Energy Yield Ratio for photovoltaic systems as an alternative to EROEI (which they refer to as Energy Return Factor). The difference is that it uses the design lifetime of the system, which is known in advance, rather than the actual lifetime. This also means that it can be adapted to multi-component systems where the components have different lifetimes.
EROEI under rapid growth 
A related recent concern is energy cannibalism 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 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. The solar module processing plant at Frederick, Maryland was originally planned as such a solar breeder. In 2009 the Sahara Solar Breeder Project was proposed by the Science Council of Japan as a cooperation between Japan and Algeria with the highly ambitious goal of creating hundreds of GW of capacity within 30 years. Theoretically breeders of any kind can be developed.
See also 
- Embodied energy
- Energy balance
- Energy cannibalism
- Jevon's paradox 1880s observation of the efficiency effect multiplier
- Khazzoom-Brookes Postulate 1980s updating of Jevon's paradox
- Net energy gain
- Levelized cost of energy
- Murphy, D.J.; Hall, C.A.S. (2010). "Year in review EROI or energy return on (energy) invested". Annals of the New York Academy of Sciences 1185: 102–118. doi:10.1111/j.1749-6632.2009.05282.x.
- Cutler, Cleveland (2011-08-30). "Energy return on investment (EROI)". The Encyclopedia of Earth. Retrieved 2011-09-02.
- Hall, Charles A.S. "EROI: definition, history and future implications" (PowerPoint). Retrieved 2009-07-08.
- "Energy Payback Period for Wind Turbines". Danish Wind Energy Association. Retrieved 2010-08-18.
- Homer-Dixon, Thomas (2007). The Upside of Down; Catastrophe, Creativity and the Renewal of Civilisation. Island Press.
- Tainter, Joseph (1990). The Collapse of Complex Societies. Cambridge University Press.
- Richards, B.S.; Watt, M.E. (2006). Renewable and Sustainable Energy Reviews. doi:10.1016/j.rser.2004.09.015 http://www.inference.phy.cam.ac.uk/sustainable/refs/solar/Myth.pdf
|url=missing title (help). Text "Permanently dispelling a myth of photovoltaics via the adoption of a new net energy indicator" ignored (help)
- Pearce, J.M. (2008). "Limitations of Greenhouse Gas Mitigation Technologies Set by Rapid Growth and Energy Cannibalism". Klima. Retrieved 2011-04-06.
- "The Azimuth Project: Solar Breeder". Retrieved 2011-04-06.
- Lindmayer, Joseph (1978). "The solar breeder". Proceedings, Photovoltaic Solar Energy Conference, Luxembourg, September 27–30, 1977. Dordrecht: D. Reidel Publishing. pp. 825–835. Retrieved 2011-04-06.
- Lindmayer, Joseph (1977). The Solar Breeder. NASA. Unknown parameter
- "The BP Solarex Facility Tour in Frederick, MD". Sustainable Cooperative for Organic Development. Retrieved 28 February 2013.
- Koinuma, H.; Kanazawa, I.; Karaki, H.; Kitazawa, K. (Mar. 26, 2009), Sahara solar breeder plan directed toward global clean energy superhighway, G8+5 Academies' meeting in Rome, Science Council of Japan
Further reading 
- Heinberg, Richard (2003). The Party's Over: Oil, War, and the Fate of Industrial Societies. Gabriola, BC: New Society Publishers. ISBN 0-86571-482-7.
- Gupta, Ajay K; Hall, Charles A.S (2011). "A Review of the Past and Current State of EROI Data". Sustainability 3 (10): 1796–1809. doi:10.3390/su3101796. Retrieved 25 March 2012.
- World-Nuclear.org, World Nuclear Association study on EROEI with assumptions listed.
- Web.archive.org, Wayback Archive of OilAnalytics.org, "EROI as a Measure of Energy Availability"
- Dematerialism.net, "Energy in a Mark II Economy".
- EOearth.org, Energy return on investment (EROI)
- EOearth.org, Net energy analysis
- H2-pv.us, Essay on H2-PV Breeder Synergies
- explanation of EROI and peak oil