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 (the exergy) delivered from a particular energy resource to the amount of exergy used to obtain that energy resource. It is a distinct measure from energy efficiency as it does not measure the primary energy inputs to the system, only usable energy.
Arithmetically the EROEI can be written as:
When the EROEI of a resource is less than or equal to one, that energy source becomes a net "energy sink", and can no longer be used as a source of energy, but depending on the system might be useful for energy storage (for example a battery). A related measure Energy Store On Energy Invested (ESOEI) is used to analyse storage systems.
The natural or primary energy sources are not 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 only human usable energy and not wastes such as waste heat.
Nevertheless, heat of any form can be counted where it is actually used for heating. However the use of waste heat in district heating and water desalination in cogeneration plants is rare, globally, and in practical terms it is often excluded in EROEI analysis of energy sources.
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. The time to reach this break-even point is called energy payback period (EPP) or energy payback time (EPBT).
The issue is still subject of numerous studies, giving wildly different answers, and prompting academic argument. That's mainly because the "energy invested" critically depends on technology, methodology, and system boundary assumptions, resulting in a range from a maximum of 2000 kWh/m² of module area down to a minimum of 300 kWh/m² with a median value of 585 kWh/m² according to a meta-study.
Regarding output, it obviously depends on the local insolation, not just the system itself, so assumptions have to be made.
Some studies (see below) include in their analysis that photovoltaic produce electricity, while the invested energy may be lower grade primary energy.
Most importantly, even the most pessimist studies conclude in a greater than 1 EROEI (or, in payback time, a shorter than average lifetime) for an installation.
A 2015 review in Renewable and Sustainable Energy Reviews assessed the energy payback time and EROI of solar photovoltaics. In this study, which uses an insolation of 1700/kWh/m²/yr and a system lifetime of 30 years, mean harmonized EROIs between 8.7 and 34.2 were found. Mean harmonized energy payback time varied from 1.0 to 4.1 years. A review Pickard reports EROEI estimates for monocrystalline silicon photovoltaics by four groups in the range of 2.2 to 8.8. Raugei, Fullana-i-Palmer and Fthenakis found EROEI in the range of 5.9 to 11.8 and 19 to 39 for the major commercial PV types in South European installations. The low range assumes that primary energy and electricity are of the same quality, whereas the high range (19-39) is calculated by converting the electricity output of PV to primary energy as recommended by the IEA PVPS Task 12 LCA Methodology Guidelines they contributed to write. Furthermore, Fthenakis determined the EROEI to be as high as 60 for the least energy consuming thin-film PV technology installations in the U.S. Southwest.
|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|
|Oil shale (surface mining/ex situ)|
|2.4–15.8 (electric, external)
1.2–1.6 (electric, net)
6–7 (thermal, external)
|Oil shale (in situ)|
|105||Nuclear (Centrifugal enrichment)|
|10.0||Nuclear (with diffusion enrichment – Obsolete)|
|2000 (estimate)||Dual fluid molten salt – molten lead nuclear|
|30.0||Oil and gas 1970|
|14.5||Oil and gas 2005|
|1.9||Solar flat plate|
|9.5||Geothermal (without hot water heating)|
|32.4||Geothermal (with hot water heating)|
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. This is an example of David Ricardo's best-first principle. Then progressively lower quality ores or energy resources are used as the higher-quality ones are either exhausted or in use, for example, wind turbines positioned in the windiest areas.
In regard to fossil fuels, when oil was originally discovered, it took on average one barrel of oil to find, extract, and process about 100 barrels of oil. The ratio, for discovery of fossil fuels in the United States, has declined steadily over the last century from about 1000:1 in 1919 to only 5:1 in the 2010s.
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 that energy becomes more difficult to obtain and its relative price increases. 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 argues 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, this has been suggested as caused by peak wood in early societies. Falling EROEI due to depletion of high quality fossil fuel resources also poses a difficult challenge for industrial economies, and could potentially lead to declining economic output and challenge the concept (which is very recent when considered from a historical perspective) of perpetual economic growth.
Tim Garrett links EROEI and inflation directly, based on a thermodynamic analysis of historical world energy consumption (Watts) and accumulated global wealth (US dollars). This economic growth model indicates that global EROEI is the inverse of global inflation over a given time interval. Because the model aggregates supply chains globally, local EROEI is outside its scope.
Because much of the energy required for producing oil from oil 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 "utilized detailed energy production and consumption data reported by oil sands producers from 1970 to 2010 to examine trends in historical energy returns from oil sands extraction. " They argued that by 2010, NERs (net energy returns) from oil sands mining and in situ operations had become significantly more energy efficient since 1970 although the NER remained significantly less efficient than conventional oil production. NERs from the oil sands, grew from "1.0 GJ/GJ in 1970 (entirely from the Suncor mining operation) to 2.95 GJ/GJ in 1990 and then to 5.23 GJ/GJ in 2010." 
The EROEI is calculated by dividing the energy output by the energy input, however researchers disagree on how to determine energy input accurately and therefore come with different numbers for the same source of energy. 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 (assuming the latters are not used in the processes of extraction and transformation).
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[weasel words] 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.
Another issue with EROI that many studies attempt to tackle is that the energy returned can be in different forms, and these forms can have different utility. For example, electricity can be converted more efficiently than thermal energy into motion, due to electricity's lower entropy.
There are three prominent expanded EROEI calculations, they are point of use, extended and societal. Point of Use EROEI expands the calculation to include the cost of refining and transporting the fuel during the refining process. Since this expands the bounds of the calculation to include more production process EROEI will decrease. Extended EROEI includes point of use expansions as well as including the cost of creating the infrastructure needed for transportation of the energy or fuel once refined. Societal EROI is a sum of all the EROEIs of all the fuels used in a society or nation. A societal EROI has never been calculated and researchers believe it may currently be impossible to know all variables necessary to complete the calculation, but attempted estimates have been made for some nations. Calculations done by summing all of the EROEIs for domestically produced and imported fuels and comparing the result to the Human Development Index (HDI), a tool often used to understand well-being in a society. According to this calculation, the amount of energy a society has available to them increases the quality of life for the people living in that country and countries with less energy available also have a harder time satisfying citizens’ basic needs. This is to say that societal EROI and overall quality of life are very closely linked.
ESOEI (or ESOIe) is used when EROEI is below 1. "ESOIe is the ratio of electrical energy stored over the lifetime of a storage device to the amount of embodied electrical energy required to build the device."
|Lead acid battery||5|
|Zinc bromide battery||9|
|Vanadium redox battery||10|
|Lithium ion battery||32|
|Pumped hydroelectric storage||704|
|Compressed air energy storage||792|
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. In practice, nuclear breeder reactors are the only large scale breeders that have been constructed as of 2014, with the 600 MWe BN-600 and 800 MWe BN-800 reactor, the two largest in operation.