ERoEI* as a Measure of Sustainability

Thomas L Wayburn, PhD in chemical engineering


The Autonomous Alternative Energy District

It is essential to realize that energy is the life blood of a society.  Sustainability amounts to providing a sustainable renewable energy technology, a technology that harvests energy (corrected for entropy) from the sun in real time and that returns more energy than is consumed to install it, operate it, maintain it, maintain its storehouses of natural material capital, prevent or repair environmental damage including aesthetic damage, and support the community that serves the renewable energy installation both directly and indirectly.

If we wish to define a ratio of Energy Returned over Energy Invested (ERoEI*) that will indicate a sustainable alternative energy technology if and only if it is greater than 1.0, we must begin to think of society as a system the purpose of which is to maintain the flow of high-grade renewable energy.  Let us begin with a thought experiment that will make perfectly clear what should be included in the energy investment term (EI*) in ERoEI* = ER/EI*.  Suppose that a group of people representing all of the trades and professions wishes to support itself completely by relying on a single alternative, renewable energy technology for all of its energy needs. Let us suppose further that all of the natural resources necessary to do this are available within the AAED [and the repositories of such natural resources can be retained at steady state from the detritus of the AAED including superannuated installations of the technology].  Nothing is imported from outside the District whereas energy and only energy is exported. If a man needs a car to drive from his home (in the District) to his job (in the District), the car is built, maintained, and fueled in the District. If his wife is sick, the doctor in the District will treat her with medicine made in the District from chemicals produced there from raw materials mined there and subsequently recycled aggressively. The ERoEI of the new energy technology is the total energy produced, ER, divided by the quantity ER minus the quantity EX, where EX is the energy exported; i. e., EX = ER – EI*.   If the District is able to export any energy at all the ERoEI ratio exceeds one and the technology is sustainable – at least.

The actual situation in a self-contained US economy would be virtually identical to that of the AAED if the economy were to run exclusively on the alternative, renewable energy technology under investigation and there were precisely as many physicians, for example, as are needed to supply the needs of those whose purpose in life is to provide energy. Thus, every ancillary and indirect expense of producing energy including the support of the workers and their dependents must be counted in computing energy invested if the ERoEI methodology is to be used to determine sustainability.  In the broader economy, the pro-rated share of each workers energy budget that should be charged to energy invested is easily determined from the pro-rated share of his working hours and the consumption stratum to which he belongs. If more than one technology is employed and the matching problem discussed in Chapter 2 of On the Preservation of Species has been solved, it is not necessary to convert one form of energy to another; therefore, a transformity of unity can be assigned to each form of energy produced. Since, in addition, the fraction of personal energy and work-related energy served by each technology is usually known, this methodology can be extended easily to the more general situation. Let us call this ratio ERoEI* (pronounced E-R-O-E-I star) to distinguish it from the superscripted ERoEIs in “Energy in a Mark II Economy” and to indicate its importance as the only ERoEI that determines sustainability.

Heretofore, I have used the terms “feasible’ and “sustainable” interchangeably.  I think it may be useful to draw distinctions between sustainability and feasibility – and to define a new concept, namely, quasi-sustainability: 

An energy technology is sustainable if and only if ERoEI* (E-R-O-E-I star) is no less than 1.0.  An entire society is sustainable if and only if the compound ERoEI* of its entire mix of energy technologies is no less than 1.0.   Early on, recognizing that a community can persist for quite a long time if most of the characteristics of ERoEI* are satisfied, we considered quasi-sustainability; that is, during a transition period between fossil fuels and renewable energy, we must tolerate some slight environmental destruction and diminution of our storehouses of essential natural resources because of the large proportion of the energy investment for most renewable energy technologies that must be paid before any energy is returned.

Let us agree that a renewable energy technology is feasible if no more characteristics of ERoEI* are relaxed than are consistent with the community standards and laws of the land currently. 


Actually, energy returned might be confused with net energy returned, denoted ER – EI in my papers except for; therefore, we should be referring to the energy produced. Also, and this is more important, in, I defined EROI so that it is the same as EROI - 1 in and

In a community that can subsidize a renewable energy technology with fossil fuel, it is especially important to use ERoEI* as discussed at because the lifestyles of the participants can be supported by fossil fuel. Thus, the alternative energy technology might be able to produce energy, but the total amount of fossil fuel used by the community would be increased rather than diminished. And, no one might ever know – until it’s too late.

The price of energy should reflect the cost of preventing or repairing any changes to the environment that diminish the quality of life of mankind and other species or that compromise the sustainability of the relevant ecosystems including the magnitude of the storehouses of natural resources. The quality of life depends upon aesthetics as well as pure material circumstances.

The energy-invested term should have an energy contribution corresponding to every monetary item that affects the price even if this reduces ERoEI* to less than 1.0. Research should continue until technologies with ERoEI* greater than 1.0 are found. This approach is mathematically rigorous as opposed to other approaches that merely state that an ERoEI must be greater than some unsupported number such as 3.0 to support the operations of civilization.


Comment on Computing ER and EI

It's easy to compute the quantity of energy (really availability, which is energy corrected for entropy) we expect to be produced over the life of the project for any energy production installation we wish to investigate - in particular, to determine whether or not it produces more than it consumes. We consider energy spent to prevent or repair environmental damage caused by the installation, embodied and direct energy purchased with money paid to the stakeholders in the system, and the many other direct and indirect energy costs discussed in eroeistar.htm all to be part of the energy consumed by the process over the life of the installation. The energy produced is denoted ER for Energy Returned and the energy consumed to produce it is EI for Energy Invested. Clearly, if ER/EI < 1.0 (ER < EI), the installation should not be built. In a fossil-fuel economy, if the installation is built - usually because subsidies hide its true nature from analysts who go by monetary costs - it will result in the combustion of more fossil fuel not less. Thus, the computation of ERoEI* should be done before the installation is built using our best estimates of things like the amount of energy required to hold the supply of materials in steady state, the energy costs to rehabilitate the plant site to a pristine condition if the plant becomes obsolete, demographics change, or for some other reason the installation abandons the planned plant site, etc. If you do this computation for any given nuclear plant taking proper account of every negative effect, you will probably determine that ERoEI* for nuclear is less than 1.0. If it is less than 1.0 for solar, it shows that more research should be done, as we have not reached our goal yet of a sustainable renewable energy technology. But, we must eventually succeed and we will.


Why We Need the Concept of Emergy

The input to the production facility that produces solar cells and their ancillary equipment consists of energy (availability), material streams, and human effort.  The embodied energy or emergy of the material inputs must be added to the Energy Invested term.  Thus, a definition of renewable (sustainable) energy must employ the concept of emergy. 


Definition of Emergy 

This paper is too long to enter here.  Serious readers should download the paper or read it on-line.  Definition of Emergy


Missing Components of ERoEI 

Let us recall once more that, in a sustainable society, the store houses of natural resources with which the earth and our species are blessed must be retained at more or less steady-state accumulations.  The atmosphere and the land are natural resources as well as the repositories of iron and other metals, the nutrients in the soil, and the atmosphere itself.  This means air and water quality and the infrastructure of primary and recycle processes must be maintained.  Therefore, let us add to the list of energy expenses that must be met to achieve sustainability. 

1) Sequester carbon, in case fossil fuels are involved in the process - even if only in the start-up phase.  But, in the case of shale oil and gas, the energy costs of carbon sequestration that must be borne by the consumer should be added to the energy-invested term to calculate ERoEI.  Probably, under present-day economic conditions, this can be thought of as a tax, which should be levied.

2) Maintain storehouses of materials that are used to build and maintain the principal process and the secondary processes such a tax preparation, healthcare, etc.

3) Mothball process equipment at the end of its life and restore the plant site to the pristine conditions in which we found it.  Let us maintain Earth as a garden.

4) Desalinate sea water to replace the fresh water used and decontaminate such water as the process renders unfit to drink.

5) To the energy costs of 1 - 4, add the energy budgets of the employees and the appropriate pro-rata portions of those whose services must be charged to the process such as the health services that keep the workers healthy.  If there are stockholders or venture capitalists who take profits from the process, an appropriate portion of their energy budgets must be charged to the energy-invested term (EI).  Recall that every item that adds to the (monetary) price the consumer must pay for the product has an associated energy cost.  Clearly, salaries, fees, profits, and taxes add to the price.  All computations of ERoEI and/or emergy must be carried out just as they would have been carried out if government subsidies had not existed.  Quite frankly government subsidies are not the best way to defeat market intransigence and they make our job as analysts harder. Quite possibly there is an energy cost associated with subsidies that should be added to EI.

6) If there is an energy cost due to withdrawal of the land from other uses, it should be added to EI.  I am not quite certain how to calculate this term if, for some reason, the value of the insolation on that is not acceptable.  Perhaps the reader has some ideas.  If you do, please write to me at (It should be noted that setting the value of the land equal to the value of the insolation intercepted by it accounts for the disqualification of ownership of land.  Rental only is permitted, as the total insolation in perpetuity is infinite.)

Additional objections are as follows:

ERoEI in even the sound form that Wayburn has promoted does no more than provide a measure of the effectiveness of an energy supply process. It does not take into account

1.    Whether the energy supplied is used for a useful purpose or otherwise. Is all the fuel used by cars serving a useful purpose?

2.    That the supply process produces waste material that has caused such deleterious consequences as climate change and the accumulation of stores of radioactive materials

3.    That the supply process irreversibly divests limited natural material resources, including fossil fuels and uranium

Here are my comments on these three points:

1.    How the energy is used is not the business of the analyst and it should not be.  Can you imagine what most people would say if I told them that the energy they use to conduct their lives or businesses is wasted because I do not approve of what they are doing?

2.    This is included in the energy-invested term by including the cost of sequestration.  Even the loss of space to sequestration can be given an energy value by counting the insolation that might have been harvested but could not be because the space was otherwise occupied.

3.    If the process does consume material resources, the energy-invested term can be increased by the energy cost to recycle not consume, which is always possible except for an insignificant trace amount.  In some cases, this expense is unbearable and must be avoided by choosing different technology. 

Additional Concerns about Recycling

In Item 2 of "Some Important Components of the Energy-Invested Term that Are Generally Neglected" (, Dec. 6), I imply without proof or explanation that the repositories of materials needed for the main process under investigation and the essential ancillary processes can be maintained at their original levels. I wrote as though the recycle problem had been solved and a steady state could be achieved without further ado. That is not the case. Recycling the material in the infrastructure is a tricky business. More research is needed. Here is what I wrote to the critic who raised that point and, in addition, was concerned about the effects of friction:

Friction is not a problem. In general, the principal effect of friction is overcome by pushing harder. Let us weigh an engine with serious friction, like the gas turbine on a 747, when it’s brand new and after it is ready to be replaced. I would be surprised if the two weighings gave very different results, that is, I am under the impression that the slight loss of material will not affect sustainability.

In other cases, the problem should be categorized thusly: (a) Separate the materials that we need to carry out the activities we consider important to our civilization, i. e., the materials we need to produce food and clothing, maintain shelter, render health care, and provide art, music, literature and a few luxuries to take the drudgery out of life, e. g., computers; divide the useful materials into two categories: (b1) the materials that can be recycled and devise the most energy efficient techniques to recycle them; (b2) find substitutes for the materials that cannot be recycled in any way, shape, or manner. (Remember that, even if only the elemental species can be recovered, with enough energy the original substance can be synthesized at the expense of our supply of available energy (enthalpy minus the lowest temperature reservoir to which waste heat can be rejected times the entropy).)

I expected that you might nail me on recycling pharmaceuticals. I gave it a lot of thought. For now, I am satisfied that pissing on the ground might have to be forbidden. This was done by the Freemen on Frank Herbert’s Dune, a desert planet. Useful chemicals can be extracted from sewage by chromatography for example. Materials that are deemed essential and cannot be recycled for one reason or another will remain a challenge for the time being.


What Is the Energy Cost of Pollution? 

This is an easy question to answer:  The energy cost of pollution is the energy cost of whatever has to be done to prevent pollution whether it be (i) the alteration of the process to avoid the pollution step, (ii) the decontamination and temperature normalization of process water for recycle or discharge, where the discharge of fresh water effluent to the  environment must be accompanied by the transport and desalination of sea water, (iii) the treatment of gas phase effluent to remove all contaminants such that only air and water at normal temperature is discharged.  The discharged air may be oxygen-rich provided it does NOT contain ozone, and (iv) whatever else must be done to prevent air, earth, and water pollution. 

In cases where the process pollutes, the fine shall be sufficiently great that it is cheaper to prevent pollution than to pay the fine.  The fine shall be used to further the agenda of the most sincere environmentalists and to partly compensate the victims. Someone should implement some sort of plan to make it uneconomical to cheat.  Photovoltaic cells do not pollute, but the factory that makes them does.  It is the responsibility of the purveyors of solar energy installations to make certain that their vendors and suppliers do not pollute and/or add the cost of the appropriate process equipment or the principal of the fine to the energy-invested term. 


Time Delay and Distance between Production Facility and Consumers for ERoEI 

It strikes me as too arbitrary to piggy-back the time value of energy on the current time value of money. We would much rather use something with a physical basis that would remain constant throughout most periods of interest. Suppose that the consumer of the Energy Returned has to wait 24 hours for the delivery even though he is obliged to consume energy constantly at the rate contracted for. The value of the Energy Invested over the life of the project should be increased by the value of the energy from the best available replacement technology adjusted by the appropriate transformity as discussed at; however, the life of the project must be increased by one day. Suppose that a crucial part in an energy installation like an electric turbine generator is not available until one year after the time it was needed by the builder of a wind power installation. The Energy Invested should be increased by the value of the substitute energy just as in the previous example with the life of the project extended by one year. Presumably, the energy cost per unit of energy recovered of the substitute technology exceeds the energy cost for the planned technology, which is why the new technology is contemplated provided they are both renewable. Other similar cases require similar consideration; however, nothing relieves the analyst from the intelligent and judicious application of the principles of his craft. The fundamental principle of dealing with all departures from ideality, such as intervals in space separating the locations where the energy is produced and consumed or emission of greenhouse gases, is adding all energy costs of such additional equipment as would restore ideality. It is clear that the energy embedded in any material that must be considered in any analysis can be computed properly by making as many adjustments as are required to the straightforward cost of production by the method of judicious substitutions.

Renewable Energy 

Here is a letter to Energy Resources:

An appreciable number of people on the Yahoo! Energy Resources (Peak Oil) forum do not want to admit that solar and wind energy either are renewable or would be if it were not for the ridiculous energy cost of supporting a market economy*.  In a debate with Dave Kimble of Running on Empty Oz, who argued that the front-loaded investment costs of photovoltaic solar installations disqualify PV solar as a way to mitigate the effects of Peak Oil even in Australia, I conceived of a plan to bootstrap solar by purchasing abroad solar energy equipment to start up with.  Now, renewable energy technologies came into a world dominated by coal, oil, natural gas, and nuclear fission; so, it is understandable that the first front-loaded energy invested in “renewables” probably came from fossil fuel and nuclear, but possibly hydroelectric.  Let us assume, though, that the solar installations purchased abroad to get started in a solar economy were produced without the application of any energy that could not be termed “renewable”.  Then, the first wave of solar energy installations slated for Australia would be completely renewable.  That is, they would produce enough stored energy such that no fossil fuel at all need be used to maintain the infrastructure and build replacements for it when they were needed, to maintain the stockpiles of materials used in the maintenance and the construction of replacements – and, for that matter, to restore such portions of the earth as were occupied by solar installations to Earth-as-a-Garden ideality.  If the ratio ERoEI*, as defined at and, in greater detail, on my new blog at, is greater than 1.0, this can be done, although ERoEIs very close to 1.0 will be poor investment risks because of long payback times and because a very slight change in circumstances could render them infeasible or because ERoEI* is actually less than 1.0 except for minor computational inaccuracies.  In the spreadsheet analysis done by Dave Kimble and me, we used an ERoEI equal to 3.0.  I assumed that ERoEI*PV = 3.0.  Both Dave and I included construction, maintenance, and eventual replacement energy costs in perpetuity in EI.  In any case, if solar and wind are not strictly renewable, a competent energy analyst would compute ERoEI* < 1.0 and be forewarned.  See

The reason investors are bailing out of renewables is that they have become convinced by investment bankers that the ERoEI for shale plays is greater than 1.0 if, in fact, they know what ERoEI is or should be.  To their sorrow, they are about to find out that ERoEI for shale is less than 1.0 even if operators neglect their responsibilities toward Earth.  When the shale bubble bursts, there will be much gnashing of teeth here in Texas. I feel sorry for all the new Houston citizens who are about to be left high and dry except for submergence in unmanageable credit card debt based upon false hopes for a prosperous future.  It’s too bad that they didn’t invest their futures in solar and wind and political change.  

By the way, Denis Frith has been most helpful by suggesting various concrete problem areas in energy production that have to be addressed to calculate ERoEI*.  The difficulty of finding a new recycling methodology or a substitute material resource in case a material is encountered with no known substitute for which recycling is impractical remains a tough nut to crack; however, we shall cross that bridge when we come to it – and perhaps we never will, as, in contradistinction to the Second Law of Thermodynamics that provides an absolute upper bound for energy efficiency, we have the Conservation of Matter governing material balances.  I am certain he will continue to be of service by suggesting problem areas in establishing renewable energy technology.  It is, of course, the component of energy input that comes from the sun that suggested the term “renewable” to earlier workers.  Although we intend to “pay” Mother Earth, we have no such intention to “pay” Papa Sun.

The Fundamental Principle of Ecology 

The fundamental principle of ecology ought to be "Leave it alone".  It is not necessary to solve systems of equations to manage an eco-region; i. e., a connected area of the face of the earth all of which drains into a large body of water – usually an ocean – with no part of the drainage region omitted, although systems of millions of equations of all types, even, can be solved if necessary. What is really needed is a general powering down, i. e., much less economic activity and a much smaller population.

Mankind has discovered that he may harvest energy, as well as fruits, vegetables, nuts, and berries, from Nature.  He presumes that he is entitled to exploit these resources with no thought of paying Nature, putting anything back, or cleaning up. Now, he is in a bind.  His life is filled with feverish activity.  He knows that he has much too great an impact on the environment.  But he can't stop.  He has credit card debt.  He just barely avoided the last big lay-off at his job.  His wife has been bugging him to earn more money, in keeping with the normal measure of worth in his society, usually referred to as status.  He has a brokerage account; but, he has been unable to earn extra money by trading stocks, options, and other securities.  This man's troubles will be recognized as instances of the modes in which capitalist economies achieve the economic growth they require.

But, all of this activity, from which capitalism will not let up but demands more of the same is in violation of the Fundamental Principle of Ecology (now promoted to initial caps).  Thus, capitalism's route to inevitable collapse is the greatest evil in the world today.


Thomas Wayburn, Houston, Texas

* The following three papers go a long way towards disqualifying market economies:  (In addition, as shown by David Delaney <>, market economies usually have a number of characteristics that necessitate economic growth whereas economic shrinkage (or de-growth) is necessary for sustainability.)


Let us begin by defining consumption in terms of emergy with an M. For those who wish to know what I mean by emergy see Thus, every citizen can be characterized by the community according to how much emergy he or she consumes strictly because he is employed, e. g., commuting costs, clothing costs, and meals away from home, and how much emergy he consumes otherwise.  Suppose, for the sake of analysis, that these quantities can be replaced by the average values in a few discrete strata. Then, the system I used in Chapter 2 of On the Preservation of Species can be resurrected mutatis mutandis for our purposes.