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2013-10-24T20:02:15Z

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In [[statistics]], the '''quartile coefficient of dispersion''' is a descriptive statistic which measures [[Statistical dispersion|dispersion]] and which is used to make comparisons within and between data sets.

The statistic is easily computed using the first (''Q''1) and third (''Q''3) [[quartile]]s for each data set. The quartile coefficient of dispersion is:<ref>{{cite doi|10.1016/j.csda.2005.05.007}}</ref>

: <math>{Q_3 - Q_1 \over Q_3 + Q_1}.</math>

Consider the following two data sets:

: Data set A: 2, 4, 6, 8, 10, 12, 14.

:: ''n'' = 7, range = 12, mean = 8, median = 8, ''Q''1 = 4, ''Q''3 = 12

:: coefficient of dispersion = 0.5

: Data set B: 1.8, 2, 2.1, 2.4, 2.6, 2.9, 3

:: ''n'' = 7, range = 1.2, mean = 2.4, median = 2.4, ''Q''1 = 2, ''Q''3 = 2.9

:: coefficient of dispersion = 0.18

The quartile coefficient of dispersion of data set A is 2.7 times as great (0.5 / 0.18) as that of data set B.

==References==
{{reflist}}

{{DEFAULTSORT:Quartile Coefficient Of Dispersion}}
[[Category:Statistical deviation and dispersion]]
[[Category:Statistical ratios]]

{{statistics-stub}}

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2013-08-23T22:12:24Z

94.174.69.42: Minor edit: Corrected typos (topolocically)

{{TOC right}}
In [[physics]], [[energy economics]] and [[energetics|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.<ref name='mh2010'>{{cite journal
|title=Year in review EROI or energy return on (energy) invested
|last=Murphy |first= D.J.
|last2= Hall |first2= C.A.S.
|year=2010
|journal=Annals of the New York Academy of Sciences
|volume= 1185
|pages=102–118
|doi= 10.1111/j.1749-6632.2009.05282.x |ref=harv}}</ref><ref name="eo">{{cite web
|url= http://www.eoearth.org/article/Energy_return_on_investment_(EROI)
|title=Energy return on investment (EROI)
|first= Cleveland
|last= Cutler
|publisher=The Encyclopedia of Earth
|date=2011-08-30
|accessdate=2011-09-02}}</ref> 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 energy|primary]] source of energy.

: <math> EROEI = \frac{\hbox{Usable Acquired Energy}}{\hbox{Energy Expended}}</math>

== 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.

== Relationship to net energy gain ==
EROEI 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 EROEI measures the ratio or efficiency of the process. They are related simply by

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

or

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

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.

== Oil sands ==
Because much of the energy required for producing oil from [[oil sands|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]] {{Brandt|2013}} "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." <ref name="Brandt2013">{{Cite doi|10.1016/j.energy.2013.03.080}} "Current oil sands operations have mine mouth NERs (net energy returns) of about 6 GJ output per GJ of energy consumed and point of use energy returns of about 3 GJ/GJ."</ref>

== Economic influence of EROEI ==
[[File:EROI - Ratio of Energy Returned on Energy Invested - USA.svg|thumb|450px|EROI — Ratio of Energy Returned on Energy Invested. {{harvnb|Murphy|Hall|2010}}]]

{| class="wikitable sortable" style="float:right; clear: right;"
|-
! EROI (for US)
! width=300 | Fuel
|-
| 1.3
| Biodiesel
|-
| 3.0
| Bitumen tar sands
|-
| 80.0
| Coal
|-
| 1.3
| Ethanol corn
|-
| 5.0
| Ethanol sugarcane
|-
| 100.0
| Hydro
|-
| 35.0
| Oil imports 1990
|-
| 18.0
| Oil imports 2005
|-
| 12.0
| Oil imports 2007
|-
| 8.0
| Oil discoveries
|-
| 20.0
| Oil production
|-
| 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
|-
| 6.8
| Photovoltaic
|-
| 5.0
| Shale oil
|-
| 1.6
| Solar collector
|-
| 1.9
| Solar flat plate
|-
| 18.0
| Wind
|-
| 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).{{Citation needed|date=November 2008}} <ref>{{cite web
|url=http://www.esf.edu/efb/hall/talks/EROI6a.ppt
|title=EROI: definition, history and future implications
|first=Charles A.S. |last=Hall |format=PowerPoint
|accessdate=2009-07-08
}}</ref>
Currently (2006) according to the Danish Wind Energy Association, the EROEI of wind energy in North America and Europe is about 20:1.<ref>
{{cite web
|url=http://www.windpowerwiki.dk/index.php?title=Energy_balance
|title=Energy Payback Period for Wind Turbines
|publisher=Danish Wind Energy Association
|accessdate=2010-08-18
}}</ref>

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 Slave|energy slaves]]. [[Thomas Homer-Dixon]] <ref>{{cite book |last=Homer-Dixon |first=Thomas |authorlink=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=http://books.google.com/books?id=rvk6tsE4UDcC}}</ref> 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 [[Maya civilization|Maya]]n and Cambodian collapse too. [[Joseph Tainter]]<ref>{{cite book |last=Tainter |first=Joseph |authorlink=Joseph Tainter |title=The Collapse of Complex Societies |publisher=[[Cambridge University Press]] |location= |year=1990 |url=http://books.google.com/books?id=M4H-02d9oE0C&printsec=frontcover |isbn=052138673X}}</ref> 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-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.<ref>
{{cite paper |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 |format=PDF}}
</ref>

==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 gases#Anthropogenic greenhouse gases|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.<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 |accessdate=2011-04-06 }}</ref>

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.<ref>{{cite web |url=http://www.azimuthproject.org/azimuth/show/Solar+breeder |title=The Azimuth Project: Solar Breeder |accessdate=2011-04-06 }}</ref><ref>{{cite conference |url=http://adsabs.harvard.edu/abs/1978pvse.conf..825L |title=The solar breeder |booktitle=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 |accessdate=2011-04-06 |isbn=9027708894 |oclc=222058767}}</ref> 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.<ref>{{cite book |title=The Solar Breeder |first=Joseph |last=Lindmayer |year=1977 |publisher=NASA |url=http://www.researchgate.net/publication/23885550_Solar_breeder_Energy_payback_time_for_silicon_photovoltaic_systems}}</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|accessdate=28 February 2013}}</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>
{{citation |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=Mar 26, 2009}}
</ref> Theoretically breeders of any kind can be developed.

==See also==
{{Portal|Energy}}
* [[Embodied energy]]
* [[Emergy]]
* [[Energy balance (disambiguation)|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]]
* [[Cost of electricity by source|Levelized cost of energy]]

==References==
{{Reflist|2}}

==Further reading==
* {{cite book | author=[[Heinberg, Richard]] | title=[[The Party's Over: Oil, War, and the Fate of Industrial Societies]] | location=Gabriola, BC | publisher=New Society Publishers | year=2003 | isbn=0-86571-482-7}}
* {{cite journal
|url= http://www.mdpi.com/2071-1050/3/10/1796/
|title= A Review of the Past and Current State of EROI Data
|first=Ajay K
|last=Gupta
|first2=Charles A.S
|last2=Hall
|journal=Sustainability
|volume=3
|issue=10
|pages=1796–1809
|year=2011
|accessdate=25 March 2012
|doi=10.3390/su3101796 }}

==External links==
* [http://www.world-nuclear.org/info/inf11.html World-Nuclear.org], World Nuclear Association study on EROEI with assumptions listed.
* [http://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"
* [http://www.eoearth.org/article/Energy_return_on_investment_(EROI) EOearth.org], Energy return on investment (EROI)
* [http://www.eoearth.org/article/Net_energy_analysis EOearth.org], Net energy analysis
* [http://h2-pv.us/H2/H2-PV_Breeders.html H2-pv.us], Essay on H2-PV Breeder Synergies

{{Bioenergy}}

{{DEFAULTSORT:Eroei}}
[[Category:Peak oil]]
[[Category:Energy economics]]
[[Category:Emergy]]

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2012-09-01T23:31:20Z

94.174.41.218: /* Communication, or locality */ Give Aspect's full name on first mention instead of second (minor)

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