The Energy Return on Energy Invested (ERoEI or EROI) of any energy gathering system is a measure of that system’s efficiency. The concept was originally derived in ecology and has been transferred to analyse human industrial society. In today’s energy mix, hydroelectric power ± nuclear power have values > 50. At the other end of the scale, solar PV and biofuels have values <5.
It is assumed that ERoEI >5 to 7 is required for modern society to function. This marks the edge of The Net Energy Cliff and it is clear that new Green technologies designed to save humanity from CO2 may kill humanity through energy starvation instead. Fossil fuels remain comfortably away from the cliff edge but march closer to it for every year that passes. The Cheetah symbolises an energy system living on the edge.
I first came across the concept of Energy Return on Energy Invested (ERoEI) several years ago in Richard Heinberg’s book The Party’s Over . I had never contemplated the concept before and I was immediately struck by its importance. If we used more energy to get the energy we need to survive then we will surely perish.
Shortly thereafter I joined The Oil Drum crew and had the great pleasure of meeting Professor Charles Hall, the Godfather of ERoEI analysis who developed the concept during his PhD studies and first published the term in 1977. ERoEI would become a point of focus for Oil Drum posts. Nate Hagens and David Murphy, both Oil Drum crew, have now completed PhDs on ERoEI analysis aided and abetted by the conversation that the Oil Drum enabled.
But recently I have received this via email from Nate:
10 years on the same questions and issues are being addressed – (and maybe 40 years on for Charlie). A new tier of people are aware of EROI but it is still very fringe idea?
Are we wrong to believe that ERoEI is a fundamentally important metric of energy acquisition or is it simply that the work done to date is not sufficiently rigorous or presented in a way that economists and policy makers can understand. At this point I will cast out a bold idea that money was invented as a proxy for energy because ERoEI was too complex to fathom.
And I have this via email from my friend Luis de Sousa who did not like the Ferroni and Hopkirk paper  nor my post reviewing it:
On the grand scheme of things: PV ERoEI estimates range from 30 down to 0.8. Before asking the IEA (or whomever) to start using ERoEI, the community producing these estimates must come down to a common, accepted methodology for its assessment. As it stands now, EROEI is not far from useless to energy policy.
And while I disagree with Luis on a number of issues, on this statement I totally concur. So what has gone wrong? Professor Hall points out that it is not the concept that is at fault but non-rigorous application of certain rules that must be followed in the analysis. In this post I will endeavour to review the main issues and uncertainties, and while it is labelled “for Beginners”, I will flirt with an intermediate level of complexity.
What is ERoEI?
ERoEI is simply the ratio of energy gathered to the amount of energy used to gather the energy (the energy invested):
ERoEI = energy gathered / energy invested
Note that in common vernacular the term energy production is used. But in fact humans produce very little energy, but what distinguishes us from other species is that we have become very efficient at gathering energy that already exists and building machines that can convert the energy to goods (motor cars, televisions and computers) and services (heat and light and mobility) that collectively define our wealth.
This began by gathering fire wood and food and progressed to gathering coal, oil and natural gas. This led to gathering U and Th and learning how to convert this to enormous amounts of thermal and electrical energy. And now we attempt to gather solar energy through photovoltaics, wind turbines and liquid biofuels.
The prosperity of humanity depends upon the efficiency with which we gather energy. 100 years ago and 50 years ago we hit several jackpots in the form of vast coal, oil and gas deposits. These were so rich and large that energy virtually spewed out of them for next to no energy or financial investment. Examples include the Black Thunder coal field (USA), the Ghawar oil field (Saudi Arabia) and the Urengoy gas field (Russia) to name but a few. But these supergiant deposits are now to varying degrees used up. And as global population has grown together with expectations of prosperity that are founded on energy gathering activities, humanity has had to expand its energy gathering horizons to nuclear power, solar power and energy from waste. And it is known that some of the strategies deployed have very low ERoEI, for example corn ethanol is around 1 to 2  and solar PV between 1 and 5 [2,3] depending upon where it is sited and the boundaries used to estimate energy costs. Consider that an ERoEI greater than 5 to 7 is deemed necessary to sustain the society we know (see below) then it is apparent that we may be committing energy and economic suicide by deliberately moving away from fossil fuels.
Low ERoEI is expected to correlate with high cost and in the normal run of events investors should steer clear of such poor investment returns. But the global energy system is now dictated by climate concern, and any scheme that portends to produce energy with no CO2 is embraced by policymakers everywhere and financial arrangements are put in place to enable deployment, regardless of the ERoEI.
Net energy is the close cousin of ERoEI being the surplus energy made available to society from our energy gathering activities. It is defined simply as:
net energy = ERoEI-1
If we have ERoEI = 1, then the net energy is zero. We use as much energy to gather energy as energy gathered. The “1” always represents the energy invested. If ERoEI falls below 1 we end up with an energy sink. Low ERoEI systems are effectively energy conversions where it may be convenient or politically expedient for us to convert one energy carrier into another with little or no energy gain. Corn ethanol is a good example where fertiliser, natural gas, diesel, electricity, land, water and labour gets converted into ethanol, a liquid fuel that can go in our cars. But it does leave the question why we don’t just use liquefied natural gas as a transport fuel in the first place and save on all the bother that creating corn ethanol involves?
The Net Energy Cliff
Many years ago during a late night blogging session on The Oil Drum, and following a post by Nate Hagens, I came up with a way of plotting ERoEI that for many provided an instantaneous understanding of its importance. The graph has become known as the net energy cliff, following nomenclature of Nate and others.
Figure 1 The Net Energy Cliff shows how with declining ERoEI society must commit ever larger amounts of available energy to energy gathering activities. Below ERoEI = 5 to 7 such large numbers of people would be working for the energy industries that there would not be enough people left to fill all the other positions our current altruistic society offers.
The graph plots net energy as a % of ERoEI and shows how energy for society (in blue) varies with ERoEI. In red is the balance being the energy used to gather energy.
It is the shape of the boundary between blue and red that is of interest. If we start at 50 and work our way down the ERoEI scale moving to the right, we see that energy invested (red) increases very slowly from 2% at ERoEI=50 to 10% at ERoEI=10. But beyond 10, the energy invested increases exponentially to 20% at ERoEI=5 and to 50% at ERoEI=2. At ERoEI = 1, 100% of the energy used is spent gathering energy and we are left with zero gain.
This is important because it is the blue segment that is available for society to use. This pays for infrastructure, capital projects, mining and manufacturing, agriculture, food processing and retailing, education, healthcare and welfare, defence and government. In fact it is the amount of net energy that powers everything in society as we know it today. The net energy from past energy gathering has accumulated to create what we identify as capital and wealth. Nothing could be more important, and yet the concept remains on the fringe of energy policy and public awareness. One of the problems is that measuring ERoEI consistently is difficult to do. One problem is retaining objectivity. If you manufacture PV modules you are unlikely to claim that the ERoEI is less than 5, and there are a multitude of variables that can be adjusted to provide whatever answer is deemed to be good.
This depiction of Net Energy is also useful in defining that all energy and labour can be divided into energy and labour used in the energy industries and the industries that support them and energy and labour used by society that consumes the surpluses produced by the energy industries. More on this later.
It has been assumed by many that ERoEI > 7 was required for the industrial society we live in to function although the source of this assertion remains elusive. But the blue-red boundary provides a clear visual picture of why this may be so. Below 7 and humanity falls off the net energy cliff where a too large portion of our human resources and capital need to be invested in simply staying alive to the detriment of the services provided by net energy such as health care, education and pensions.
One of the main uncertainties in ERoEI analysis is where to set the system boundaries. I have not found a simple text or graphic that adequately explains this vital concept.
Figure 2 A simplified scheme for an energy system divided into construction, operation and decommissioning with accumulated inputs and outputs. Graphic from this excellent presentation by Prieto and Hall
Figure 2 provides an illustration of the life cycle of an energy system divided into three stages 1) construction, 2) operation and 3) decommissioning. Energy inputs occur at each stage but energy outputs will normally only occur during the operational phase. It should be straight forward to account for all the energy inputs and outputs to calculate ERoEI but it isn’t. For example many / most of our energy systems today are still operational. We do not yet have final numbers for oil produced from single fields. And the decommissioning energy costs are not yet known. Most wind turbines ever built are still operational, producing energy and the ultimate energy produced will depend upon how long they last. And then perhaps some turbines are offered a new lease of life via refurbishment etc.
Energy inputs can normally be divided as follows :
- On site energy consumption
- Energy embedded in materials used
- Energy consumed by labour
- Auxiliary services
Moving from 1 to 4 may be considered expansion of the ERoEI boundary where energy embedded in materials and energy consumed by labour are added to on-site energy consumption. There follows some examples of ambiguity that remains in deciding what to include and what to leave out. These examples are given for purely illustrative purposes.
No one should question that the electricity used by a PV factory should be included. But do you include electricity / energy used to heat or cool the factory? Or just the electricity used to run the machines? Including heating or cooling introduces a site specific variable which will mean that the energy inputs to a PV panel may vary according to where it was manufactured. There are many such site specific variables like transport, energy costs, labour energy costs, health and safety energy costs etc, which when combined in our globalised market has made China the lowest energy cost centre for PV manufacturing today.
It is clear to me that the energy cost of all materials used in the energy production process must be included. And this should include materials consumed at the construction, operational and decommissioning stages. In the oil industry this will include the materials in the oil platform, the helicopter and the onshore office. In the solar PV industry this will include all the materials in the panels, in the factory, and in the support gantries and inverter. As a general rule of thumb, massive energy gathering systems that contain a huge amount of materials will have reduced ERoEI because of the energy embedded in those materials.
It is also clear to me that the energy cost of all labour should be included in the ERoEI analysis for construction, operation and decommissioning. But it is far less clear how it should be calculated. The energy consumed by labourers varies greatly from country to country and with time. Should we just include the energy consumed by a labourer on his/her 8 hour shift? Or should we include the full 24/7? Should the energy consumed by labourers getting to and from work be included? – of course it should. Should the energy consumed on vacations be included? – not so clear. And how can any of this be calculated in the first place?
The standard way to calculate the energy cost of labour is to examine the energy intensity of GDP. For most countries, the total amount of primary energy consumed is roughly known and the total GDP is known. This provides a means of converting MJ to $ and we can then look at the $ earnings of a labourer to get a rough handle on the notional energy use that may be attributed to his salary scale. This is far from perfect but is currently the only practical method available.
Auxiliary services become even more difficult to differentiate. Some argue that the energy cost of the highway network, power distribution network and services like schools and hospitals should be pro-rated into new energy production systems. My own preference is to generally exclude these items from an ERoEI analysis unless there are good reasons for not doing so. I think it is useful to go back to the question are we expending energy on energy gathering or are we expending energy on society and most of the infrastructure upon which new energy systems depend was built using prior surpluses allocated to society. In my view it becomes too complex to pro-rate these into an ERoEI calculation. The power grid delivering power to the PV factory already existed. But if a new power line needs to be built to export renewable electricity then that should be accounted for.
One might imagine that measuring the energy output would be more straightforward, but it is not so. Many earlier studies on the ERoEI of oil set a boundary at the well head or on site tank farm. And it is relatively straightforward to measure the oil production from a field like Forties in the North Sea. But crude oil itself is rarely used directly as a fuel. It is the refined products that are used. To actually use the oil we need to ship or pipe it to shore and then on to a refinery. The energy cost of transport may add 10% to energy inputs and refining may add yet another 10%. It has been suggested that one approach is to calculate ERoEI at Point of Use. Crude oil on an offshore platform is of no use to anyone. Gasoline in a filling station is what we want and all the energy inputs involved in getting the gasoline to the forecourt need to be counted.
But here we meet another dilemma. The refinery may produce paraffin and gasoline. The ERoEI of both are likely to be similar at the refinery gate. But the gasoline is burned in an engine to produce kinetic energy used for transport and in so doing about 70% of the energy is lost as waste heat. The paraffin may be burned in a stove with near 100% conversion efficiency to space heating. Do we reduce the ERoEI of gasoline by 70% to reflect energy losses during use?
This introduces the concept of energy quality where we know that final energy conversions are in three main forms 1) heat 2) motion and 3) electricity that has a myriad of different uses. Is it really possible to compare these very different energy outputs using the single umbrella of ERoEI? The routine followed by ERoEI analysts to date is to adjust ERoEI for energy quality though I’m unsure how that is done . Another option that I like is to hypothetically normalise all outputs to a single datum, for example MWh of electricity (see below). But this again gets to a level of complexity that is beyond this blog post.
There are some other important energy quality factors. Dispatch for electricity is one. Producing a vast amount of electricity from wind on a stormy Sunday night has little to no value. While the ability to produce electricity on demand at 6 pm on a freezing Wednesday evening in January (NH) is of great value. Curtailed wind should clearly be deducted from wind energy produced in the ERoEI calculation. Just like the oil spilled from the Deep Water Horizon in the Gulf of Mexico should not be counted as oil produced from the Macondo field.
External environmental factors may also have to be considered as part of the energy quality assessment. It is clear that the oil spilled from the Deep Water Horizon had to be cleared up immediately and the energy cost of doing so almost bankrupted BP. But it is less clear that the energy cost of eliminating CO2 emissions needs to be borne by the energy production industries. For example, the cost of carbon capture and storage would fall on the consumer and not the energy producer.
Using energy proxies
In ERoEI analysis direct energy use can normally be measured, for example gas and diesel used on an oil platform or the electricity used in a factory. But the indirect energy consumed by, for example materials and labour, are less easy to measure and are often based on proxies. It is nearly impossible to measure the energy embedded in an offshore oil platform. Instead the mass of steel and the number of man days of labour used in construction can be estimated and from these the energy expended and now embedded in the platform can be estimated.
As already discussed, the standard way of estimating the energy cost of labour is to use the energy intensity of GDP data from the countries in question combined with workers salaries.
For materials Murphy et al  provide this useful summary (Figure 3)
Figure 3 The estimated energy content of common materials 
From this the most striking feature is the vast range within certain materials and between materials. For example aluminium ranges from 100 to 272 GJ/tonne. Steel 9 to 32 GJ/tonne. Part of this will be down to methodological differences in the way the numbers are derived. But part of it may be down to real differences reflecting different energy efficiencies of smelting plants.
ERoEI of Global Fuels and Energy Flows
So what is the current status of ERoEI in the global energy mix? Hall et al 2014  provide the following summary table which is the foundation of the summary graph below.
Figure 4 Summary of the ERoEI for a range of fuels and renewable energies.
Figure 5 Placing main energy sources on The Net Energy Cliff framework shows that hydro-electric power, high altitude kites and perhaps nuclear power have very high ERoEI and embracing these technologies may prevent humanity from falling off the Net Energy Cliff. The new bright Green energies of bio-fuels, solar PV and buffered wind (see below) are already over the cliff edge and if we continue to embrace these technologies human society may perish as we expend too large a portion of our energy endowment simply getting energy. Fossil fuels remain comfortably to the left of the cliff edge but are marching ever closer towards it with every year that passes. Eeq = electricity equivalent (see below).
In order to compare fossil fuels with electricity flows on a single diagram it is essential to reduce all of the energy types to a common datum. Its quite simply not valid to compare the ERoEI of coal at the mine mouth with nuclear power since in converting the coal to electricity, much of the energy is lost. The easiest route is to rebase everything to electricity equivalent (Eeq) where I follow the BP convention and adjust the ERoEI of fossil fuels by a factor of 0.38 to account for energy conversion losses in a modern power station.
In an earlier thread, Owen posted a link to a pre-print by Weisbach et al  who follow similar methodology reporting all data as electricity. To a large extent their numbers are similar to those reported here with the exception of nuclear that is quoted to be 75. Weisbach report values for solar PV and wind that are “buffered” to include the energy cost of intermittency. This reduces the ERoEI for solar PV by about half and wind by a factor of 4. “Buffered” ERoEIs are therefore also included in Figure 6.
The inclusion of high altitude kite is based on a calculation provided by site sponsor KiteGen. I have checked the calculation and am satisfied that the ERoEI is potentially >>50. This will be the subject of another post. But suffice to say here that wind speed at altitude may be double that on the ground and power increases by the cube of wind speed. And the mass of the KiteGen structure is a small fraction of a large wind turbine. Hence it is theoretically straightforward to reach an ERoEI at altitude that is many multiples of the ERoEI of a wind turbine.
Figure 6 At altitude the wind speed may be double that on the ground. Accessing that kinetic energy resource provides potential for a 2 to 4 fold uplift in the power available for wind generation. This calculation does not include further uplift from higher capacity factor and reduced intermittency at altitude.
The key and fundamental observation from Figure 6 is that three energy sources potentially have ERoEI >> 50 making them vastly superior to all others using this metric. These are hydroelectric power, possibly nuclear power (depending upon whose numbers are believed) and possibly high altitude wind power once the technology matures.
These primary high ERoEI sources are followed by coal and natural gas which are the most viable and easily accessible energy sources for electricity today. And yet energy policies are dictating that coal be phased out. This will not matter for so long as natural gas remains plentiful at high ERoEI. The high ERoEI group may also include nuclear power depending upon whose ERoEI numbers one believes.
Biofuels are already over the net energy cliff and should never have been pursued in the first place. Solar PV is at best marginal, at worst an energy sink.
There is a vast range in estimates for nuclear power from 5 to 75 [4, 5]and it is difficult to make sense of these numbers. Nuclear power either sits close to the cliff edge or is a high ERoEI low carbon saviour of humanity. Oil will not be used for electricity production and the fact it sits close to the cliff edge today in Eeq form does not matter too much since the energy quality of oil has a special status as an essential transport fuel and this will unlikely change much in the decades ahead.
The concept of ERoEI is vital to understanding the human energy system. 50 years ago, our principal sources of energy – oil, gas and coal – had such high net energy return that no one need bother or worry about ERoEI. Vast amounts of net energy were simply available for all who had the level of technological development to build a power station and a transmission grid. It is part of human nature to “high grade” mineral deposits targeting the richest seams first. In economic terms these return the biggest profit and in energy terms when it comes to oil, gas and coal, they return the highest levels of net energy. An inevitable consequence of this aspect of human nature commonly known as greed is that we have already used up the highest ERoEI fossil fuel resources and as time passes the ERoEI of new resources is steadily falling. This translates to a higher price required to bring on that marginal barrel of oil.
At the present time, our energy web comprises a myriad of different resources. The legacy supergiants – Ghawar, Black Thunder and Urengoy et al – are still there in the mix supplemented by a vast range of lower ERoEI (more expensive) resources. The greatest risk to human society today is the notion that we can somehow replace high ERoEI fossil fuels with new renewable energies like solar PV and biofuels. These exist within the energy web because they are subsidised by the co-existing high ERoEI fossil fuels. The subsidy occurs at multiple levels from fossil fuels used to create the renewable devices and biofuels to fossil fuels providing the load balancing services. Fossil fuels provide the monetary wealth to pay the subsidies. Society is at great risk from Greens promoting the new renewable agenda to politicians and school children whilst ignoring the thermodynamic impossibility of current solar PV technology and biofuels ever being able to power human society unaided. The mass closure of coal fired power stations may prove to be fatal for many should blackouts occur.
Wind power, and in particular high altitude wind power, may be different although in the case of ground-based wind turbines care must be taken in moving offshore to ever larger devices that consume ever larger quantities of energy in their creation. And to be viable, ground based turbines must be able to prove they can deliver dispatchable power without subsidies.
It is proposed that money was invented as a means of exchange for the work energy does on our behalf. If we lived in a society with a single global currency (the EJ) and without taxes or subsidies, then money may represent a fair proxy for ERoEI although distortions would remain from the different efficiencies with which that money (EJ) was spent. However, in the real world, different currencies, interest rates, debts, taxes and subsidies exist that allow the thermodynamic rules of the energy world to be bent, albeit temporarily. We are at risk of exchanging gold for dirt.
The post was much improved by comments provided by Prof Charles Hall.
 Richard Heinberg: The Party’s Over – oil, war and the fate of industrial societies. Pub by Clairview 2003
 David J. Murphy 1,*, Charles A.S. Hall 2, Michael Dale 3 and Cutler Cleveland 4: Order from Chaos: A Preliminary Protocol for Determining the EROI of Fuels (2011): Sustainability 2011, 3, 1888-1907; doi:10.3390/su3101888
 Ferruccio Ferroni and Robert J. Hopkirk 2016: Energy Return on Energy Invested (ERoEI) for photovoltaic solar systems in regions of moderate insolation: Energy Policy 94 (2016) 336–344
 Charles A.S. Hall n, Jessica G. Lambert, Stephen B. Balogh: EROI of different fuels and the implications for society: Energy Policy 64 (2014) 141–152
 D. Weißbacha,b, G. Ruprechta, A. Hukea,c, K. Czerskia,b, S. Gottlieba, A. Husseina,d (Preprint): Energy intensities, EROIs, and energy payback times of electricity generating power plants