Energy return on investment

2025-10-03T11:06:30Z

188.69.137.116: /* Oil liquids */ Wording fixed (a state after decline could hardly bee called a "plateau")

{{Short description|Ratio of usable energy from a resource}}
{{Distinguish|Net energy gain}}
In [[energy economics]] and [[energy flow (ecology)|ecological energetics]], '''energy return on investment''' ('''EROI'''), also sometimes called '''energy returned on energy invested''' ('''ERoEI'''), 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.<ref name='mh2010'>{{cite journal
|title=Year in review EROI or energy return on (energy) invested
|last1=Murphy |first1= D.J.
|last2= Hall |first2= C.A.S.
|year=2010
|journal=Annals of the New York Academy of Sciences
|volume= 1185
|issue=1 |pages=102–118
|doi= 10.1111/j.1749-6632.2009.05282.x |pmid=20146764 |bibcode=2010NYASA1185..102M|s2cid=6433639 }}</ref>

Arithmetically, the EROI can be defined as:
: <math> EROI = \frac{\hbox{Energy Delivered}}{\hbox{Energy Required to Deliver that Energy}}</math>.<ref name="Hall CA 2013" />

When the EROI of a source of energy 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. A related measure, called '''energy stored on energy invested''' ('''ESOEI'''), is used to analyse storage systems.<ref>{{cite web|url=http://energystoragereport.info/eroi-energy-return-on-investment-energy-storage/|title=Why energy storage is a dead-end industry - Energy Storage Report|date=15 October 2014}}</ref><ref name=c3e>{{cite journal |first1=Charles J. |last1=Barnhart |first2=Michael |last2=Dale |first3=Adam R. |last3=Brandt |first4=Sally M. |last4=Benson |doi=10.1039/c3ee41973h |url=http://pubs.rsc.org/en/content/articlepdf/2013/ee/c3ee41973h |title=The energetic implications of curtailing versus storing solar- and wind-generated electricity |journal=Energy Environ. Sci. |date=2013 |volume=6|issue=10 |pages=2804–10|doi-access=free |bibcode=2013EnEnS...6.2804B }}</ref>

To be considered viable as a prominent fuel or energy source, a fuel or energy must have an EROI ratio of at least 3:1.<ref>{{cite journal
| last1 = Atlason | first1 = R
| last2 = Unnthorsson | first2 = R
| year = 2014
| title = Ideal EROI (energy return on investment) deepens the understanding of energy systems
| journal = Energy
| volume = 67
| pages = 241–45
| doi = 10.1016/j.energy.2014.01.096
| bibcode = 2014Ene....67..241A
}}</ref><ref name="Hall CA 2013">{{cite journal
| last1 = Hall | first1 = CA
| last2 = Lambert | first2 = JG
| last3 = Balogh | first3 = SB
| year = 2013
| title = EROI of different fuels and the implications for society
| journal = Energy Policy
| volume = 64
| pages = 141–52
| doi = 10.1016/j.enpol.2013.05.049
| doi-access = free
}}</ref>

== History ==
{{See also|Ecological economics}}
The energy analysis field of study is credited with being popularised by [[Charles A. S. Hall]], a [[systems ecology]] and [[biophysical economics]] professor at the [[State University of New York]]. Hall applied the biological methodology developed at an Ecosystems Marine Biological Laboratory, and then adapted that method to research human industrial civilisation. The concept would have its greatest exposure in 1984, with a paper by Hall that appeared on the cover of the journal ''Science''.<ref>{{Cite web | url=https://www.scientificamerican.com/article/eroi-charles-hall-will-fossil-fuels-maintain-economic-growth/ | title=Will Fossil Fuels be Able to Maintain Economic Growth? A Q&A with Charles Hall| website=[[Scientific American]]| date=April 2013}}</ref><ref>[https://www.nytimes.com/gwire/2009/10/23/23greenwire-new-school-of-thought-brings-energy-to-the-dis-63367.html?pagewanted=all N.Y. Times article featuring Hall Retrieved November-3-09]</ref>

== Application to various technologies ==
=== Photovoltaic ===
{{See also|Cadmium telluride photovoltaics}}
{{Pie chart
| thumb = right
| caption =Global [[Growth of photovoltaics|PV market]] by technology in 2013.<ref name=Pie-Chart-Fraunhofer-PR-2014>
{{cite web
|title=Photovoltaics Report
|url=http://www.ise.fraunhofer.de/en/downloads-englisch/pdf-files-englisch/photovoltaics-report-slides.pdf
|publisher=Fraunhofer ISE
|access-date=August 31, 2014
|archive-url=https://web.archive.org/web/20140725125239/http://www.ise.fraunhofer.de/en/downloads-englisch/pdf-files-englisch/photovoltaics-report-slides.pdf
|archive-date=July 25, 2014
|url-status=live
|date=July 28, 2014
}}</ref>{{rp|18,19}}
| other =
| label1 =[[Polycrystalline silicon|multi-Si]]
| value1 =54.9
| color1 =#3366CC
| label2 =[[Monocrystalline silicon|mono-Si]]
| value2 =36.0
| color2 =#660099
| label3 =[[Cadmium telluride photovoltaics|CdTe]]
| value3 =5.1
| color3 =#de2821
| label4 =[[Amorphous silicon|a-Si]]
| value4 =2.0
| color4 =#00CC00
| label5 =[[Copper indium gallium selenide solar cell|CIGS]]
| value5 =2.0
| color5 =yellow
}}

The issue is still the subject of numerous studies, 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 from 2013.<ref>{{cite journal | last1 = Dale, M. | display-authors = 1 | last2 = and Benson, S.M. | year = 2013 | title = ''Energy balance of the global photovoltaic (PV) industry – is the PV industry a net electricity producer?''. In | journal = Environmental Science and Technology | volume = 47 | issue = 7 | pages = 3482–3489 | doi = 10.1021/es3038824 | pmid = 23441588| bibcode = 2013EnST...47.3482D }}</ref>

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 cells produce electricity, while the invested energy may be lower grade [[primary energy]].

A 2015 review in [[Renewable and Sustainable Energy Reviews]] assessed the energy payback time and EROI of a variety of PV module technologies. In this study, which uses an insolation of 1700 kWh/m2/yr and a system lifetime of 30 years, mean harmonised EROIs between 8.7 and 34.2 were found. Mean harmonised energy payback time varied from 1.0 to 4.1 years.<ref>{{cite journal | last1 = Bhandari | display-authors = et al | year = 2015 | title = ''Energy payback time (EPBT) and energy return on energy invested (EROI) of solar photovoltaic systems: A systematic review and meta-analysis''. In | journal = [[Renewable and Sustainable Energy Reviews]] | volume = 47 | pages = 133–141 | doi = 10.1016/j.rser.2015.02.057 | bibcode = 2015RSERv..47..133B }}</ref>{{better source needed|date=January 2019}}
In 2021, the [[Fraunhofer Society|Fraunhofer]] Institute for Solar Energy Systems calculated an energy payback time of around 1 year for European PV installations (0.9 years for Catania in Southern Italy, 1.1 years for Brussels) with wafer-based silicon [[Crystalline silicon#PERC solar cell|PERC]] cells.<ref>Fraunhofer Institut (2022), ''Photovoltaics Report'', page 37, https://www.ise.fraunhofer.de/content/dam/ise/de/documents/publications/studies/Photovoltaics-Report.pdf</ref>

=== Wind turbines ===
In the scientific literature EROIs wind turbines is around 16 unbuffered and 4 buffered.<ref>{{cite web|url=https://festkoerper-kernphysik.de/Weissbach_EROI_preprint.pdf|title=Energy intensities, EROIs, and energy payback times of electricity generating power plants|website=Festkoerper-kernphysik.de|access-date=July 26, 2022}}</ref> Data collected in 2018 found that the EROI of operational wind turbines averaged 19.8 with high variability depending on wind conditions and wind turbine size.<ref>{{Cite web|url=https://www.researchgate.net/publication/222703134|title=Meta-Analysis of Net Energy Return for Wind Power Systems|website=Researchgate.net}}</ref>
EROIs tend to be higher for recent wind turbines compared to older technology wind turbines.
Vestas reports an EROI of 31 for its V150 model wind turbine.<ref>{{Cite web |url=https://www.vestas.com/~/media/vestas/about/sustainability/pdfs/lca%20of%20electricity%20production%20from%20an%20onshore%20v15042mw%20wind%20plantfinal.pdf |title=Archived copy |access-date=2020-10-20 |archive-date=2020-10-21 |archive-url=https://web.archive.org/web/20201021122004/https://www.vestas.com/~/media/vestas/about/sustainability/pdfs/lca%20of%20electricity%20production%20from%20an%20onshore%20v15042mw%20wind%20plantfinal.pdf |url-status=dead }} {{Title missing|date=September 2025}}</ref>

=== Hydropower plants ===
The EROI for hydropower plants averages about 110 when it is run for about 100 years.<ref>{{Cite journal| doi = 10.1016/j.renene.2013.12.029| issn = 0960-1481| volume = 66| pages = 364–370| last1 = Atlason| first1 = R. S.| last2 = Unnthorsson| first2 = R.| title = Energy return on investment of hydroelectric power generation calculated using a standardised methodology| journal = Renewable Energy| access-date = 2024-02-27| date = 2014-06-01| bibcode = 2014REne...66..364A| url = https://www.sciencedirect.com/science/article/pii/S0960148113007064| url-access = subscription}}</ref>

=== Oil sands ===
Because much of the [[Oil sands#Energy balance|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 EROI, the higher value given by considering only the external energy inputs and the lower by considering all energy inputs, including self generated. One study found that in 1970, oil sand net energy returns were about 1.0, but by 2010 had increased to about 5.23.<ref name="Brandt20132">{{Cite journal|last1=Brandt|first1=A. R.|last2=Englander|first2=J.|last3=Bharadwaj|first3=S.|year=2013|title=The energy efficiency of oil sands extraction: Energy return ratios from 1970 to 2010|journal=Energy|volume=55|pages=693–702|doi=10.1016/j.energy.2013.03.080|bibcode=2013Ene....55..693B }}</ref>{{Clarify|reason=the text leads in saying there are two ways. This remaining text has one set of numbers. I removed some other text with some other numbers because it was insufficiently explained to make sense.|date=January 2019}}

=== Conventional oil ===
Conventional sources of oil have a rather large variation depending on various geologic factors. The EROI for refined fuel from conventional oil sources varies from around 18 to 43.<ref name=":0">{{Cite web|url=https://westernresourceadvocates.org/publications/assessment-of-energy-roi-of-oil-shale/|title=An Assessment of Energy Return on Investment of Oil Shale|website=Western Resource Advocates|language=en-US|access-date=2020-04-21}}</ref>

=== Oil Shale ===
Due to the process heat input requirements for oil shale harvesting, the EROI is low. Typically, natural gas is used, either directly combusted for process heat or used to power an electricity-generating turbine, which then uses electrical heating elements to heat the underground layers of shale to produce oil from the kerogen. The resulting EROI is typically around 1.4–1.5.<ref name=":0" /> Economically, oil shale might be viable due to the effectively free natural gas on site used for heating the kerogen, but opponents have debated that the natural gas could be extracted directly and used for relatively inexpensive transportation fuel rather than heating shale for a lower EROI and higher carbon emissions.

=== Oil liquids ===
The weighted average standard EROI of all oil liquids (including coal-to-liquids, gas-to-liquids, biofuels, etc.) is expected to decrease from 44.4 in 1950 to 6.7 in 2050.<ref>{{Cite journal|last1=Delannoy|first1=Louis|last2=Longaretti|first2=Pierre-Yves|last3=Murphy|first3=David J.|last4=Prados|first4=Emmanuel|date=December 2021|title=Peak oil and the low-carbon energy transition: A net-energy perspective|journal=Applied Energy|language=en|volume=304|article-number=117843|doi=10.1016/j.apenergy.2021.117843|bibcode=2021ApEn..30417843D |s2cid=240530798|doi-access=free}}</ref>

=== Natural gas ===
The standard EROI for natural gas is estimated to decrease from 141.5 in 1950 to an apparent plateau of 16.8 in 2050.<ref>{{Cite journal|last1=Delannoy|first1=Louis|last2=Longaretti|first2=Pierre-Yves|last3=Murphy|first3=David J.|last4=Prados|first4=Emmanuel|date=January 2021|title=Assessing Global Long-Term EROI of Gas: A Net-Energy Perspective on the Energy Transition|journal=Energies|language=en|volume=14|issue=16|pages=5112|doi=10.3390/en14165112|doi-access=free}}</ref>

=== Nuclear plants ===
The EROI for nuclear plants ranges from 20<ref>{{Cite journal| title = Energy Return on Investment of Major Energy Carriers: Review and Harmonization | date = 2022 | doi = 10.3390/su14127098 | doi-access = free | last1 = Murphy | first1 = David J. | last2 = Raugei | first2 = Marco | last3 = Carbajales-Dale | first3 = Michael | last4 = Rubio Estrada | first4 = Brenda | journal = Sustainability | volume = 14 | issue = 12 | page = 7098 | bibcode = 2022Sust...14.7098M }}</ref> to 81.<ref>{{Cite web| title = Energy Return on Investment - World Nuclear Association| access-date = 2024-02-27| url = https://world-nuclear.org/information-library/energy-and-the-environment/energy-return-on-investment.aspx}}</ref>

== Non-manmade energy inputs ==
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, and in practice it is often excluded in EROI analysis of energy sources.{{clarify|reason = Well why not? If it weren't for formerly waste heat being converted to useful heat in these applications, other energy would have to be supplied from some other system. To my mind, this distinction makes as much sense as not counting power from PV just because it runs a fridge instead of an air conditioner. This also needs a reference.|date=January 2019}}

== Competing methodology ==
In a 2010 paper by Murphy and Hall, a proposed extended ["Ext"] boundary protocol, for all future research on EROI, was detailed, to produce what they consider to be a more realistic assessment and to generate greater consistency in comparisons than what Hall and others view as the "weak points" in competing methodology.<ref name="sciencedirect.com">{{Cite journal |doi = 10.1016/j.enpol.2016.03.034|title = Energy Return on Energy Invested (ERoEI) for photovoltaic solar systems in regions of moderate insolation|journal = Energy Policy|volume = 94|pages = 336–344|year = 2016|last1 = Ferroni|first1 = Ferruccio|last2 = Hopkirk|first2 = Robert J.|doi-access = free| bibcode=2016EnPol..94..336F }}</ref> In more recent years, however, a source of continued controversy is the creation of a different methodology endorsed by certain members of the [[International Energy Agency|IEA]] which for example most notably in the case of [[solar photovoltaics|photovoltaic solar panel]]s, controversially generates more favorable values.<ref name="spectrum.ieee.org">{{Cite journal|url=https://spectrum.ieee.org/argument-over-the-value-of-solar-focuses-on-spain|title=Argument Over the Value of Solar Focuses on Spain: Analysts disagree on whether the energy returned from solar is worth the energy invested |first=Peter |last=Fairley|journal=IEEE Spectrum: Technology, Engineering, and Science News |date=30 August 2012}}</ref><ref name="JPROC 2014">{{Cite journal | doi=10.1109/JPROC.2014.2332092| title=Energy return on energy invested (EROI): A quintessential but possibly inadequate metric for sustainability in a solar-powered world? [point of view]| journal=Proceedings of the IEEE| volume=102| issue=8| pages=1118–1122| year=2014| last1=Pickard| first1=William F.| doi-access=free}}</ref>

In the case of photovoltaic solar panels, the IEA method tends to focus on the energy used in the factory process alone. In 2016, Hall observed that much of the published work in this field is produced by advocates or persons with a connection to business interests among the competing technologies, and that government agencies had not yet provided adequate funding for rigorous analysis by more neutral observers.<ref>{{Cite web|url=https://www.resilience.org/stories/2016-05-27/the-real-eroi-of-photovoltaic-systems-professor-hall-weighs-in/|title=The Real EROI of Photovoltaic Systems: Professor Hall Weighs in|date=May 27, 2016|website=Resilience}}</ref><ref>{{cite web |last1=Hall |first1=Charles |title=The real EROI of photovoltaic systems: professor Hall weighs in|url=https://cassandralegacy.blogspot.com/2016/05/the-real-eroi-of-photovoltaic-systems.html |website=Cassandra's Legacy |publisher=Ugo Bardi|date=2016-05-26 }}</ref>

== Relationship to net energy gain ==
EROI and ''[[Net energy gain|Net energy (gain)]]'' measure the [[Energy quality|same quality of an energy source]] or sink in numerically different ways. Net energy describes the amounts, while EROI measures the ratio or efficiency of the process. They are related simply by

: <math> \hbox{GrossEnergyYield} \div \hbox{EnergyExpended} = EROI </math>

or

: <math>(\hbox{NetEnergy} \div \hbox{EnergyExpended} ) + 1 = EROI </math>

For example, given a process with an EROI of 5, expending 1 unit of energy yields a net energy gain of 4 units. The break-even point happens with an EROI of 1 or a net energy gain of 0. The [[Payback period|time]] to reach this break-even point is called energy payback period (EPP) or [[Crystalline silicon#Energy payback time|energy payback time]] (EPBT).<ref>
{{cite web
|url = http://www.bnl.gov/pv/files/pdf/241_Raugei_EROI_EP_revised_II_2012-03_VMF.pdf
|title = The Energy Return on Energy Investment (EROI) of Photovoltaics: Methodology and Comparisons with Fossil Fuel Life Cycles
|author1=Marco Raugei |author2=Pere Fullana-i-Palmer |author3=Vasilis Fthenakis
|website = Brookhaven National Laboratory
|date = March 2012
|archive-url = https://web.archive.org/web/20160308235118/https://www.bnl.gov/pv/files/pdf/241_Raugei_EROI_EP_revised_II_2012-03_VMF.pdf
|archive-date = 8 March 2016
|url-status = live
}}</ref><ref name=Galarraga>{{cite book|url= https://books.google.com/books?id=N6rVrxV2ujMC&q=Energy+payback+period |title=Handbook of Sustainable Energy |author=Ibon Galarraga, M. González-Eguino, Anil Markandya |page=37|date=1 January 2011|publisher=Edward Elgar Publishing|access-date=9 May 2017|via=Google Books |isbn=978-0857936387}}</ref>

== Economic influence ==
Although many qualities of an energy source matter (for example, oil is energy-dense and transportable, while wind is variable), when the EROI of the main sources of energy for an economy fall, that energy becomes more difficult to obtain and its [[relative price]] may increase.

With 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.<ref name="Hall CA 2013" />

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 EROI) energy sources, which is related to the concept of [[energy slave]]s. [[Thomas Homer-Dixon]]<ref>{{cite book |last=Homer-Dixon |first=Thomas |author-link=Thomas Homer-Dixon |title=The Upside of Down; Catastrophe, Creativity and the Renewal of Civilisation |year=2007 |publisher=Island Press |isbn=978-1-59726-630-7 |url=https://books.google.com/books?id=rvk6tsE4UDcC}}</ref> argues that a falling EROI 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 EROI 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, based on about 2,500–3,000 [[calorie]]s per day per person. It comes out roughly equal to the area of food production at its height. But [[Environmental degradation|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 EROI 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 [[Maya civilization|Maya]]n and Cambodian collapse too. [[Joseph Tainter]]<ref>{{cite book |last=Tainter |first=Joseph |author-link=Joseph Tainter |title=The Collapse of Complex Societies |publisher=[[Cambridge University Press]] |year=1990 |url=https://books.google.com/books?id=M4H-02d9oE0C |isbn=978-0521386739}}</ref> suggests that diminishing returns of the EROI is a chief cause of the collapse of complex societies, which has been suggested as caused by [[peak wood]] in early societies. Falling EROI 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.<ref>{{cite book |last=Morgan |first=Tim |date=2013 |title=Life After Growth |location=Petersfield, UK|publisher=Harriman House |isbn=9780857193391}}</ref>

== Criticism of EROI ==
[[File:Hydro_quebec_meter.JPG|thumb|Measuring energy output is a solved problem; measuring the input remains highly debated.]]
EROI is calculated by dividing the energy output by the energy input. Measuring total energy output is often easy, especially in the case of an electrical output, where some appropriate [[electricity meter]] can be used. However, researchers disagree on how to determine energy input accurately and therefore arrive at different numbers for the same source of energy.<ref>Mason Inman. [https://www.scientificamerican.com/article/eroi-behind-numbers-energy-return-investment/ Behind the Numbers on Energy Return on Investment]. ''Scientific American'', April 1, 2013. [https://web.archive.org/web/20171223202459/https://www.scientificamerican.com/article/eroi-behind-numbers-energy-return-investment/ Archive]</ref>

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 amortised? 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 steelworkers' breakfasts? These are complex questions evading simple answers.<ref>{{cite journal |title=Does a Change in Price of Fuel Affect GDP Growth? An Examination of the US Data from 1950–2013 |first1=Michael |last1=Richards |first2= Charles |last2=Hall |year=2014 |journal=Energies |volume=7 |issue=10 |pages=6558–6570 |doi=10.3390/en7106558 |doi-access=free }}</ref> A full accounting would require considerations of [[opportunity cost]]s 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. It is in part for these fully encompassed systems reasons, that in the conclusions of Murphy and Hall's paper in 2010, an EROI of 5 by their extended methodology is considered necessary to reach the minimum threshold of sustainability,<ref name="sciencedirect.com"/> while a value of 12–13 by Hall's methodology is considered the minimum value necessary for technological progress and a society supporting high art.<ref name="spectrum.ieee.org"/><ref name="JPROC 2014"/>

Richards and Watt propose an ''Energy Yield Ratio'' for photovoltaic systems as an alternative to EROI (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.<ref>
{{cite journal |title=Permanently dispelling a myth of photovoltaics via the adoption of a new net energy indicator |first1=B.S. |last1=Richards |first2= M.E. |last2=Watt |year=2006 |journal=Renewable and Sustainable Energy Reviews |doi=10.1016/j.rser.2004.09.015 |url=http://www.inference.phy.cam.ac.uk/sustainable/refs/solar/Myth.pdf |volume=11 |pages=162–172}}
</ref>

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. 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 EROI of less than one, but could still be desirable due to the benefits of liquid fuels (assuming the latter are not used in the processes of extraction and transformation).

== Additional EROI calculations ==
There are three prominent expanded EROI calculations: point of use, extended, and societal. Point of Use EROI 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 processes, EROI will decrease.<ref name="Hall CA 2013"/> Extended EROI provides point of use expansions, as well as the cost of creating the infrastructure needed for transportation of the energy or fuel once refined.<ref>Hall CA, Lambert JG, Balogh SB. 2013. EROEI of different fuels and the implications for society. Energy Policy. 141–52</ref> Societal EROI is the sum of all the EROIs 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 are done by summing all of the EROIs 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.<ref>Lambert JG, Hall CA, Balogh S, Gupta A, Arnold M. 2014. Energy, EROI and quality of life. Energy Policy.</ref> According to this calculation, the amount of energy a society has available to it 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.<ref>Lambert JG, Hall CA, Balogh S, Gupta A, Arnold M. 2014. Energy, EROI and quality of life. Energy Policy. 153–67 & Arvesen A, Hertwich EG. 2014. More caution is needed when using life cycle assessment to determine energy return on investment (EROI). Energy Policy. 1–6</ref> This is to say that societal EROI and overall quality of life are very closely linked.

== EROI and payback periods of some types of power plants ==
The following table is a compilation of sources of energy.<ref>[[:de:Erntefaktor#Erntefaktoren und Amortisationszeiten einiger Kraftwerkstypen|German Wikipedia]].</ref> The minimum requirement is a breakdown of the cumulative energy expenses according to material data. Frequently in literature, harvest factors are reported, for which the origin of the values is not completely transparent. These are not included in this table.

The bold numbers are those given in the respective literature source; the normal printed ones are derived (see Mathematical Description).
{| class="wikitable"
|- class="hintergrundfarbe6"
! rowspan="2" | Type !! style="padding: 0.5em 1em" rowspan="2" | EROI !! rowspan="2" style="padding: 0.5em 1em" | Amortization period !! colspan="2" | Amortisation period compared to an 'ideal' power station
|-
|- class="hintergrundfarbe6"
! style="padding: 0.5em 1em" | EROI !! style="padding: 0.5em 1em" | Amortization period
|-
| colspan="5" align="center" | [[Nuclear power]] (a)
|-
| [[Pressurized water reactor|Pressurised water reactor]], 100% {{ill|Centrifuge enrichment|de|Uran-Anreicherung#Anreicherung durch Gaszentrifugen|vertical-align=sup}} || style="text-align:right" | '''106''' || style="text-align:right" | '''2 Months'''{{Failed verification|date=June 2021}} || style="text-align:right" | 315{{Failed verification|date=June 2021}} || style="text-align:right" | 17 Days{{Failed verification|date=June 2021}}
|-
| [[Pressurized water reactor|Pressurised water reactor]], 83% {{ill|Centrifuge enrichment|de|Uran-Anreicherung#Anreicherung durch Gaszentrifugen|vertical-align=sup}} || style="text-align:right" | '''75''' || style="text-align:right" | '''2 Months'''{{Failed verification|date=June 2021}}|| style="text-align:right" | 220{{Failed verification|date=June 2021}} || style="text-align:right" | 17 Days{{Failed verification|date=June 2021}}
|-
| colspan="5" align="center" | [[Fossil fuel|Fossil energy]] (a)
|-
| [[Coal-fired|Brown coal]], Open-cast || style="text-align:right" | '''31''' || style="text-align:right" | '''2 Months'''{{Failed verification|date=June 2021}}|| style="text-align:right" | 90{{Failed verification|date=June 2021}} || style="text-align:right" | 23 Days{{Failed verification|date=June 2021}}
|-
| [[Coal-fired|Black coal]], underground mining without coal transportation|| style="text-align:right" |'''29''' || style="text-align:right" | '''2 Months'''{{Failed verification|date=June 2021}}|| style="text-align:right" | 84{{Failed verification|date=June 2021}}|| style="text-align:right" | 19 Days{{Failed verification|date=June 2021}}
|-
| [[Combined cycle power plant|Gas (CCGT)]], Natural gas || style="text-align:right" | '''28''' || style="text-align:right" | '''9 Days'''{{Failed verification|date=June 2021}}|| style="text-align:right" | 81{{Failed verification|date=June 2021}}|| style="text-align:right" | 3 Days{{Failed verification|date=June 2021}}
|-
| [[Combined cycle power plant|Gas (CCGT)]], Bio gas || style="text-align:right" | '''3.5''' || style="text-align:right" | '''12 Days'''{{Failed verification|date=June 2021}}|| style="text-align:right" | 10{{Failed verification|date=June 2021}}|| style="text-align:right" | 3 Days{{Failed verification|date=June 2021}}
|-
| colspan="5" align="center" | [[Hydropower]]
|-
| [[Run-of-the-river hydroelectricity|River hydroelectric]] || style="text-align:right" | '''50''' || style="text-align:right" | '''1 Year'''{{Failed verification|date=June 2021}}|| style="text-align:right" | 150{{Failed verification|date=June 2021}}|| style="text-align:right" | 8 Months{{Failed verification|date=June 2021}}
|-
| colspan="5" align="center" | [[Concentrated solar power|Solar thermal]] (b)
|-
| Desert, parabolic troughs + phenyl compounds medium|| style="text-align:right" |'''21''' || style="text-align:right" | '''1.1 Years'''{{Failed verification|date=June 2021}}|| style="text-align:right" | 62{{Failed verification|date=June 2021}}|| style="text-align:right" | 4 Months{{Failed verification|date=June 2021}}
|-
| colspan="5" align="center" | [[Wind power|Wind energy]] (b)
|-
| 1,5 MW ({{ill|Enercon E-66|lt=E-66|de|Liste der Windkraftanlagentypen von Enercon#E-66|vertical-align=sup}}), 2000 {{ill|Full load hours VLh|de|Volllaststunde|vertical-align=sup}} (German coast)|| style="text-align:right" |'''16''' || style="text-align:right" | '''1.2 Years'''{{Failed verification|date=June 2021}}|| style="text-align:right" | 48{{Failed verification|date=June 2021}}|| style="text-align:right" | 5 Months{{Failed verification|date=June 2021}}
|-
| 1,5 MW ({{ill|Enercon E-66|lt=E-66|de|Liste_der_Windkraftanlagentypen_von_Enercon#E-66|vertical-align=sup}}), 2700 {{ill|Full load hours VLh|de|Volllaststunde|vertical-align=sup}} (German coast), shore)<ref name="pick">E. Pick, [[Hermann-Josef Wagner]]: ''Beitrag zum kumulierten Energieaufwand ausgewählter Windenergiekonverter''. Arbeitsbericht des Instituts für ökologisch verträgliche Energiewirtschaft, Universität Essen, 1998.</ref>|| style="text-align:right" | 21{{Failed verification|date=June 2021}}|| style="text-align:right" | 0.9 Years{{Failed verification|date=June 2021}}|| style="text-align:right" | '''63'''{{Failed verification|date=June 2021}}|| style="text-align:right" | '''3.7 Months'''{{Failed verification|date=June 2021}}
|-
| 2,3 MW ({{ill|Enercon E-82|lt=E-82|de|Liste der Windkraftanlagentypen von Enercon#E-82 E2 / 2,3 MW/ 2,3 MW|vertical-align=sup}}), 3200 {{ill|Full load hours VLh|de|Volllaststunde|vertical-align=sup}} (German coast), shore)<ref name="vdi">[http://www.vdi-nachrichten.com/artikel/Mehr-Windkraft-an-Land-rueckt-Oekologie-ins-Blickfeld/54733/1 ''Mehr Windkraft an Land rückt Ökologie ins Blickfeld''] {{Webarchive|url=https://web.archive.org/web/20111009121207/http://www.vdi-nachrichten.com/artikel/Mehr-Windkraft-an-Land-rueckt-Oekologie-ins-Blickfeld/54733/1 |date=2011-10-09 }}. In: ''vdi Nachrichten.'' 2 September 2011. Retrieved 17 September 2011.</ref><ref>[http://www.enercon.de/p/downloads/Windblatt_04_11_de_web.pdf ''Enercon Windblatt 4/2011''] {{Webarchive|url=https://web.archive.org/web/20120112135725/http://www.enercon.de/p/downloads/Windblatt_04_11_de_web.pdf |date=2012-01-12 }} (PDF; 1,2 MB). Internetseite von Enercon. Retrieved 10 January 2012.</ref> (c) || style="text-align:right" |'''51'''{{Failed verification|date=June 2021}}|| style="text-align:right" | '''4.7 Months'''{{Failed verification|date=June 2021}}|| style="text-align:right" | 150{{Failed verification|date=June 2021}}|| style="text-align:right" | 1.6 Months{{Failed verification|date=June 2021}}
|-
| 200 MW park (5 MW installation), 4400 {{ill|Full load hours VLh|de|Volllaststunde|vertical-align=sup}} (offshore)<ref name="Tryfonidou-Wagner">Rodoula Tryfonidou, Hermann-Josef Wagner: ''Offshore-Windkraft – Technikauswahl und aggregierte Ergebnisdarstellung.'' ([http://www.ier.uni-stuttgart.de/forschung/projektwebsites/lci_bmwi/ergebnisse/offshore-windkraft.pdf Kurzfassung] {{Webarchive|url=https://web.archive.org/web/20070208080903/http://www.ier.uni-stuttgart.de/forschung/projektwebsites/lci_bmwi/ergebnisse/offshore-windkraft.pdf |date=2007-02-08 }}, PDF-Datei, 109 kB) Lehrstuhl für Energiesysteme und Energiewirtschaft, Ruhr-Universität, Bochum 2004.</ref>|| style="text-align:right" | 16 || style="text-align:right" | 1.2 Years{{Failed verification|date=June 2021}}|| style="text-align:right" | 48{{Failed verification|date=June 2021}}|| style="text-align:right" | '''5 Months'''{{Failed verification|date=June 2021}}
|-
| colspan="5" align="center" | [[Photovoltaics]] (b)
|-
| Poly-silicon, roof installation, 1000 {{ill|Full load hours VLh|de|Volllaststunde|vertical-align=sup}} (South Germany)|| style="text-align:right" |'''4.0''' || style="text-align:right" | '''6 Years'''{{Failed verification|date=June 2021}} || style="text-align:right" | 12{{Failed verification|date=June 2021}}|| style="text-align:right" | 2 Years{{Failed verification|date=June 2021}}
|-
| Poly-silicon, roof installation, 1800 {{ill|Full load hours VLh|de|Volllaststunde|vertical-align=sup}} (South Europe)<ref name="Scholten">Mariska de Wild-Scholten: [https://smartgreenscans.nl/publications/deWildScholten-2011-Environmental-profile-of-PV-mass-production--presentation.pdf ''Environmental profile of PV mass production: globalization.''] (PDF; 1,8 MB) 2011.</ref>|| style="text-align:right" | 7.0 || style="text-align:right" | 3.3 Years{{Failed verification|date=June 2021}}|| style="text-align:right" | 21{{Failed verification|date=June 2021}}|| style="text-align:right" | '''1.1 Years'''{{Failed verification|date=June 2021}}
|}

:(a) The cost of fuel transportation is taken into account
:(b) The values refer to the total energy output. The expense for storage power plants, seasonal reserves or conventional load balancing power plants is not taken into account.
:(c) The data for the E-82 come from the manufacturer, but are confirmed by [[TÜV]] Rheinland.{{citation needed|date=March 2021}}

== ESOEI ==
ESOEI (or ESOIe) is used when EROI 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."<ref name=c3e/>

{| class="wikitable sortable"
|-
! Storage Technology !! ESOEI<ref name=c3e/>
|-
| [[Lead–acid battery]] || 5
|-
| [[Zinc–bromide battery]] || 9
|-
| [[Vanadium redox battery]] || 10
|-
| [[Sodium–sulfur battery|NaS battery]] || 20
|-
| [[Lithium-ion battery]] || 32
|-
| [[Pumped hydroelectric storage]] || 704
|-
| [[Compressed-air energy storage]] || 792
|}

One of the notable outcomes of the [[Stanford University]] team's assessment on ESOI was that if pumped storage was not available, the combination of wind energy and the commonly suggested pairing with battery technology, as it presently exists, would not be sufficiently worth the investment, suggesting instead curtailment.<ref>{{Cite web|url=http://energystoragereport.info/eroi-energy-return-on-investment-energy-storage/|title=Why energy storage is a dead-end industry|first=Energy Storage|last=Report|date=October 15, 2014|website=Energy Storage Report}}</ref>

== EROI 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 fuel]]s and concomitant [[Green house gases#Anthropogenic greenhouse gases| greenhouse 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 [[Efficient energy use|energy efficiency]] industry creates a need for energy that uses (or cannibalises) the energy of existing power plants or production plants.<ref>{{cite web|url=http://www.climate2008.net/?a1=pap&cat=1&e=61 |title=Limitations of Greenhouse Gas Mitigation Technologies Set by Rapid Growth and Energy Cannibalism |author=Pearce, J.M. |publisher=Klima |year=2008 |access-date=2011-04-06 |url-status=dead |archive-url=https://web.archive.org/web/20090817071517/http://www.climate2008.net/?a1=pap&cat=1&e=61 |archive-date=2009-08-17 }}</ref>

The {{visible anchor|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.<ref>{{cite web |url=http://www.azimuthproject.org/azimuth/show/Solar+breeder |title=The Azimuth Project: Solar Breeder |access-date=2011-04-06 |archive-date=2013-05-28 |archive-url=https://web.archive.org/web/20130528072547/http://www.azimuthproject.org/azimuth/show/Solar+breeder |url-status=dead }}</ref><ref>{{cite conference |bibcode=1978pvse.conf..825L |title=The solar breeder |work=Proceedings, Photovoltaic Solar Energy Conference, Luxembourg, September 27–30, 1977 |first=Joseph |last=Lindmayer |publisher=D. Reidel Publishing |location=Dordrecht |year=1978 |pages=825–835 |isbn=9027708894 |oclc=222058767}}</ref> The reported investigation establishes certain mathematical relationships for the solar breeder which indicate that a vast amount of net energy is available from such a plant for the indefinite future.<ref>{{cite book |title=The Solar Breeder |first=Joseph |last=Lindmayer |year=1977 |publisher=NASA |url=https://www.researchgate.net/publication/23885550}}</ref> The solar module processing plant at [[Frederick, Maryland]]<ref>{{cite web |title=The BP Solarex Facility Tour in Frederick, MD |url=http://scodpub.wordpress.com/2010/03/29/2003-bp-solarex-tour/ |publisher=Sustainable Cooperative for Organic Development|access-date=28 February 2013|date=2010-03-29 }}</ref> 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.<ref>{{cite conference |first1=H. |last1=Koinuma |first2=I. |last2=Kanazawa |first3=H. |last3=Karaki |first4=K. |last4=Kitazawa|publisher=Science Council of Japan|title=Sahara solar breeder plan directed toward global clean energy superhighway |conference=G8+5 Academies' meeting in Rome|date=March 26, 2009}}</ref>

== See also ==
{{Portal|Energy|Renewable energy|Business and economics|Ecology|Environment}}
* [[Cost of electricity by source]] – levelised cost of energy
* [[Embodied energy]]
* [[Emergy]]
* [[Energy balance (disambiguation)|Energy balance]]
* [[Energy cannibalism]]
* [[Exergy]] – useful energy
* [[Jevons paradox]] – 1880s observation of the efficiency effect multiplier
* [[Khazzoom–Brookes postulate]] – 1980s updating of Jevons paradox
* [[Net energy gain]]
* [[Social metabolism]]
* [[Thermoeconomics]]

== References ==
{{Reflist}}

== External links ==
* [https://www.world-nuclear.org/info/inf11.html World-Nuclear.org] {{Webarchive|url=https://web.archive.org/web/20130215070759/http://www.world-nuclear.org/info/inf11.html |date=2013-02-15 }}, World Nuclear Association study on EROI with assumptions listed.
* [https://web.archive.org/web/20041019220802/http://www.oilanalytics.org/neten/neten.html#measure Web.archive.org], Wayback Archive of OilAnalytics.org, "EROI as a Measure of Energy Availability"
* [https://editors.eol.org/eoearth/wiki/Energy_return_on_investment_(EROI) EOearth.org], Energy return on investment (EROI)
* [https://editors.eol.org/eoearth/wiki/Net_energy_analysis EOearth.org], Net energy analysis
* [https://web.archive.org/web/20090619033511/http://h2-pv.us/H2/H2-PV_Breeders.html H2-pv.us], Essay on H2-PV Breeder Synergies

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Vero - Wikipedia - User contributions [en]

Energy return on investment