Energy Returned over Energy Invested

The importance of the ratio of Energy Returned over Energy Invested cannot be overstated; however, different researchers have included different items in the energy invested term. This may be satisfactory depending upon the use to which the concept is to placed; but, only the method recommended on this blog results in a ratio that can be used to determine sustainability of the technology*.

 

* To establish feasibility, it is necessary to include some items in the energy invested term that are normally not thought of as investments. For example, the cost of sequestering such carbon dioxide as will be produced by the energy technology under investigation should be added to the energy invested term because feasibility requires that our society be sustainable (until astronomical events intervene). In this thought experiment, the support of an alternative energy technology would be the sole concern of every citizen. 

Introductory Material

This website must necessarily serve only as a gateway to net energy analysis, principally by me but possibly by others who have embraced the concepts of sustainability, quasi-sustainability, and feasibility in a sensible manner, which, as far as I am concerned, is the way I have done it.  The next entry in the blog http://eroei.blogspot.com/ - where I spend the majority of my net time – will explain these three terms.   In the meantime, here are the links to my other work and other interests regardless of their relevance to net energy.

Net Energy

Energy Returned over Energy Invested

Energy Returned over Energy Invested (blog)

mailto:wayburn@eroei.net

 

Most of my work on net energy preceded the net energy blog.   Some of that work was incorporated in the blog and most of the rest is hyperlinked to it. 

Dematerialism and Energy (with a short section on education)

                   Dematerialism and Energy

                   The section on education in the above

                   Dematerialism (wiki)

                   Dematerialism (old blog)

mailto:wayburn@dematerialism.net

Music

Jazz and Classical Music

Jazz and Classical Music (blog)

Jazz and Classical Music (wiki)

mailto:wayburn@jazzandclassical.net

Modeling

Model Railroading

Railroad Modeling, Track Plans, and Model Railroad Photography

mailto:wayburn@modrr.net

Miscellaneous Unlinked

Dropbox, WordPress, Google, the Houston Chronicle, the Wikipedia, SBC Global, and especially Just Passin’ Thru have generously supplied web space for my interests.  I cannot afford the time and effort it would take to keep up with all of them.

 

ERoEI* (pronounced ERoEI star) as a Measure of Feasibility

Currently, I am trying to convince Charles Hall, Tom Robertson, and the rest of the world that I have solved the problem of computing the ratio of energy returned to energy invested, i. e., ER/EI or ERoEI or EROI, depending upon who is writing the term. My latest effort to state the solution concisely is posted at http://dematerialism.net/eroistar.htm, which has hyperlinks to longer discussions elsewhere. The notion of the autonomous alternative energy district (AAED) originated in a section of “Energy in a Mark II Economy” that was posted at http://dematerialism.net/remarks.htm. In “Energy in a Mark II Economy”, I computed a series of subscripted ERoEIs beginning with the direct production expenses of the manufacturer in the energy-invested term and with each successive ERoEIi including more components. The last is very close to the composition of the energy-invested term for ERoEI* in the AAED that determines feasibility. (Overwhelming sentiment dictated that I change EROI back to EROEI or ERoEI – regardless of the similarity of that term to EIEIO in the lyrics of Old MacDonald’s Farm.)

Note. Actually, energy returned might be confused with net energy returned, denoted ER – EI in my papers except for http://dematerialism.net/emergyunit.htm; therefore, we should be referring to the energy produced. The correct ratio to determine feasibility would be EPoEI; but, please, let’s not get into that. Also, and this is more important, in http://dematerialism.net/emergyunit.htm, I defined EROI so that it is the same as EROI - 1 in http://dematerialism.net/Mark-II-EROI.html and http://dematerialism.net/Mark-II-Balance.html.

In a community that can subsidize a renewable energy technology with fossil fuel, it is especially important to use ERoEI* as discussed at http://dematerialism.net/eroistar.htm 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.

Before I ask you to read “ERoEI* as a Measure of Feasibility” copied from http://dematerialism.net/eroistar.htm (with EROI changed to ERoEI), I need to emphasize a few key points:

·    One of the correspondents claimed that ERoEI does not account for quality or convenience. That is not true, provided that transformity is applied to the final product accounting for quality and for time and place of production to compute the emergy of the product in terms of a well-defined standard as I have done in my papers on emergy and ERoEI. It is essential to combine emergy analysis with the computation of ERoEI to determine the feasibility and sustainability of the process under investigation.

·   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.

A Thought Experiment

If we wish to define an ERoEI that will indicate a feasible alternative energy technology if it is greater than 1.0, we must begin to think of society as a system the purpose of which is to keep high-grade energy flowing. 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 http://dematerialism.net/emergyunit.htm. 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. It will not be necessary to take advantage of the distinction between personal emergy budget and work-related emergy budget until we begin to furlough people whose work is unnecessary to the well-being of the community. At this point we may employ the notion of the Autonomous Alternative Energy District (AAED):

Let us 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 agressively. 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 feasible – at least. In the case of a single energy technology, the energy produced by each technology can be assigned a transformity of unity and the value of emergy is quantitatively the same as the Gibbs availability, which, at room temperature, is the Gibbs free energy. I prefer to report emergy values in units of emquads rather than quads, emjoules rather than joules, etc. Thus, the units of transformity are emquads per quad, for example.

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 feasibility.

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. 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 feasibility, let us call it ERoEI*.

Emergy (with an M)

The input to the production facility that produces solar cells and their ancillary equipment consists of energy corrected for entropy and material streams and human effort.  The embodied energy or emergy of the material imputs must be added to the Energy Invested term.  Thus, a blog on ERoEI must discuss the concept of emergy.

Definition (Availability).  Availability (or available energy) is energy [enthalpy, H, or internal energy, U] corrected for entropy, S.  Rigorous definitions of the Gibbs availability function [H – ToS], the Helmholtz availability function [U - ToS], and entropy are given in Appendix I, Fundamentals of Thermodynamics, where the symbols and technical terms employed in this paragraph are explained.  [To is  the  temperature of the environment, usually taken to be the temperature of the coldest body of water or the atmosphere into which the waste heat of a heat engine can be discharged.  For Earth, 300 K will do.  The effect of entropy on the availability function of sunlight is to reduce it by the ratio of the temperature of Earth to the temperature of the Sun – a factor of  about 19/20.  Since the enthalpy of a proton is 4/3 times the energy, the Gibbs availability of sunlight is about 76/60 times the energy.]

Odum’s original definition of emergy.  Odum defined emergy, measured in emjoules, to be the Gibbs availability of the sunlight, measured in joules, required to produce, by an optimal process, (1) fuels; (2) other energy sources such as wind or fresh water in mountain lakes; (3) natural resources such as grass and trees, (4) manufactured objects, (5) human resources; (6) information; and (7) any other objects of economic interest that can be associated with an identifiable quantity of sunlight.  This is a sunlight-based emergy.  It leads to large numbers for the emergies of primary fuels that are known only approximately; therefore, we shall modify the definition slightly to give common industrial energy products emergies that are known precisely and that are close to 1.0 in magnitude.

Definition (Standard Electricity).  In this paper, single-phase, 60 Hz, 110-volt alternating current is taken to be standard electricity.

Definition (Emergy Unit).  My arbitrary – but well-defined – choice for one unit of emergy (1 MU) is 1.0 kilowatt-hours of standard electricity.  Although electrical current carries a small amount of entropy manifest in difference currents, for all practical purposes, that is, for engineering purposes, electricity is pure work.  The availability of electricity is equal to its energy; and, with this choice of emergy unit, the emergy of electrical current is numerically equal to its energy in kilowatt-hours.  The transformity of sunlight, wind, biomass, and other energy products will be less than – but close to – 1.0.

Definition (Transformity).  The transformity of a primary fuel is the number of kilowatt-hours of standard electricity one can obtain from 1 kWhr of the primary fuel by an efficient process, the tradition of reporting the availability of fuels in BTUs per pound or kilocalories per gram mole notwithstanding.  Any unit of energy can be converted to kilowatt-hours.  This is an electricity-based transformity, the units of which are emergy units per kilowatt-hour.

Definition (Emergy).  The embodied energy or emergy of a primary fuel is the Gibbs availability of the fuel in kilowatt-hours multiplied by the electricity-based transformity.  The emergy of anything else is the sum of all the emergy that went into producing it by an efficient process minus the emergies of any by-products formed.  The emergy of an activity is the average rate of expenditure of emergy times the time.  These definitions are easily extended to include the dependence of emergy on location and time.  The concept of nemergy or negative emergy can be introduced to aid in the discussion of environmental damage.

Definition (Emergy efficiency).  Emergy efficiency is emergy out divided by emergy in.  This efficiency is 1.0 for an optimal process because the emergy of the output is defined to be the emergy of the inputs.  For a less than optimal process, the emergy efficiency is the emergy of the inputs to an optimal process over the emergy of the inputs to the process under investigation.  Emergy efficiency lies between zero and one.

The transformity of any fuel can be determined by using it to generate standard electricity by an efficient process.  The most efficient process might be a fuel cell.  Therefore, the emergy of any fuel is the Gibbs availability of the fuel multiplied by the electricity-based transformity.

Balance Equations.  Sholto Maud suggested working out energy, availability, and emergy balance equations for simple extraction and conversion processes.  Writing balance equations for extraction and Type 1 conversion helped me to understand what must be included in the definition of emergy and what may not be included without encountering inconsistencies.  Many other people can improve their understandings by studying the balance equations discussed at http://www.dematerialism.net/Mark-II-Balance.html.

Extraction.  An example of extraction is the production of petroleum from the well to the refinery.  Extraction is discussed in http://www.dematerialism.net/Mark-II-EROI.html.

Type 1 Conversion.  The first type of conversion is the production of primary energy from energy supplied by Nature for which we do not compensate Nature.  This is a sustainable process provided the energy from Nature (natural energy) comes from a source that is continuously renewed by the Moon or by the Sun shining on the Earth.  The input to such a process includes other types of energy, material goods, transportation, labor, taxes, etc.  The output includes the principal product, one or more by-products, waste heat, and pollution.  Normally, pollution is not considered; however, the concept of nemergy (negative emergy) should be employed to account for pollution of every type even, for example, the extent to which animals are deprived of habitat by the mere existence of the energy production facility.  Examples of Type 1 conversion are the production of electricity by windpower and solar power.  The emergy balance equation for a Type 1 process will be discussed next:

 

Figure 1.  Emergy Balance for Type 1 Conversion

 

Let us define some symbols to be used in connection with Figure 1:

Table of symbols used in this discussion

ER

Gibbs availability of fuel produced by process

λR

electricity-based transformity of fuel produced

MR

emergy of fuel produced by process = λR · ER

MI

the algebraic sum of all of the emergy inputs (except for MN) minus the by-products

EI

Gibbs availability of stream MI

μ

ratio of EN per unit mass to ER per unit mass

EN

Gibbs availability of energy from Nature = μ · (ER + EI)

λN

the electricity-based transformity of the energy supplied by Nature

MN

emergy of energy from Nature = λN · EN

β

Energy returned over energy invested minus 1 (ERoEI-1) = ER/EI = MR/MI

EP

the Gibbs availability of primary energy in Type 2 conversions

λP

the transformity of the primary energy source in Type 2 conversions

MP

the emergy of the primary energy supply in Type 2 conversions

 

Each of the input emergies, except the emergy supplied by Nature, is to be transformed into a product-equivalent emergy.  Then, the emergy invested, MI, is imagined to have been produced by the same process that produced the fuel.  In this way, it will be apparent immediately if the process consumes more emergy than it produces.  All indirect energy expenses should be included in the MI term, in which case ERoEI-1 is a good measure of the effectiveness of the process.  (See http://www.dematerialism.net/Mark-II-EROI.html.)  [An example of an indirect cost is the pro-rata share of the commuting costs of the tax consultant (A) that should be charged to the worker (B) who maintains a windpower installation because the man (C) who serves B lunch had his taxes done by A.]

Then, since 

 

 

and,

 

In the first approach, the transformity of the product is determined by the generation of standard electricity with a well-known efficient process and the transformity of the energy from Nature, whether it be from the tides, from biomass, from wind, from sunlight itself, or from some other natural source, is determined from the emergy balance.  Normally, this transformity is well established.  Therefore, two separate cases obtain:

Case 1.  If λN, the value we compute, is greater than λN*, the accepted value of the transformity of the natural energy, then we should report that our process is part of a more efficient route to standard electricity, and λN should be considered for a new value of the transformity of the energy supplied by Nature.

Case 2.  If λN is less than λN*, then our process is less efficient than the process that established the larger value and we must report an efficiency, η, for our process because we could have generated more emergy with the same quantity of natural energy if we had used the standard process.  The reader should remember that the energy from Nature is “free”, but the area of the solar collector or the size of the windmill is not.

 

In the second approach, the well-established value of the transformity of the energy supplied by Nature is accepted and the transformity of the product is computed from it.  Call it λR'.  If λR' is less than λR, the true value, we should revert to Case 1 and recalculate the transformity of the natural energy.  If λR' is greater than λR, then the efficiency is λR over λR'.  This is in agreement with Equation 2 above.

Let us imagine the process in the configuration illustrated by Figure 2.

 

Figure 2.  Alternative Diagram for Type 1 Conversion

 

If the algebraic sum of the emergy inputs to a process minus the emergy supplied by Nature exceeds the emergy of the product, that is, if MI > MR, then the process is wasting energy resources.  This is the case for some alternative energy projects that seek venture capital, government subsidies, donations, or unwary buyers.  If they were not subsidized by fossil fuel, they would not work.

Type 2 Conversion.  The second type of conversion is the production of secondary energy from primary energy.  The production of hydrogen from methane or from electrolysis of water is an example of Type 2 conversion.  Figure 2 is the same as Figure 1 except that MP, the primary energy, is substituted for MN:

 

Figure 3.  Emergy Balance for Type 2 Conversion

 

In the first approach, the transformity of the product is determined by the generation of standard electricity by a well-known efficient process and the transformity of the primary energy is computed from the emergy balance equation just as we did in the case of a Type 1 conversion, mutatis mutandis:

 

Case 1.  If λP, the value we compute, is greater than λP*, the accepted value of the transformity of the primary energy, then we should report that our process is part of a more efficient route to standard electricity, and λP should be considered for a new value of the transformity

Case 2.  If λP is less than λP*, then our process is less efficient than the process that established the larger value and we must report an efficiency, η, for our process because we could have generated more emergy with the same quantity of primary energy if we had used the standard process.

 

 

In the second approach, the well-established value of the transformity of the primary energy is accepted and the transformity of the product is computed from it.  Call it λR'.  If λR' is less than λR, the true value, we should revert to Case 1 and recalculate the transformity of the natural energy.  If λR' is greater than λR, then the efficiency is λR over λR'.  This is in agreement with Equation 3 above.  These results are worth deriving in a different way:

If a fuel the emergy of which is known is produced by the process under investigation and the sum of all of the emergy costs – both direct and indirect – that go into the process (computed with the true transformity λP*) minus the emergies of any useful by-products is greater than the algebraic sum of the emergy inputs for the process that determined the known emergy of the energy product, the process under investigation is sub-optimal and the efficiency, η, is

 

and, the transformity of the product we would compute from 

 

 

is higher than the true value λR.  The only justification for the process is that we cannot do without the product and there is no other way to get it, which is not the case when electricity is used to produce hot water (discussed below) since hot water can be produced with less emergy by burning fuel under normal circumstances.  Nevertheless, the process may be needed in extraordinary circumstances where the burning of fuel is prohibited, e. g., in a space capsule.

If the algebraic sum of the emergy inputs for the process under investigation is less than that of the older process, the transformity of the primary energy should be recalculated.  It may not be expedient to discontinue production by the older process immediately because of compelling reasons not to shut down the older facilities – not the least of which is the time delay before new facilities can be built.  The emergy efficiency of the older process is now less than 1.0.

Type 3 Conversion.  The third type of conversion is the manufacture of non-energy goods.  The manufacturing process has inputs of energy, material goods, transportation, labor, taxes, etc., and outputs that include a principal product, one or more by-products, and waste heat.  This is best illustrated with a diagram such as Figure 4.

 

Figure 4.  Emergy Balance for Manufacturing Process

Table of symbols for Figure 4

MI

emergy of direct energy supplies

MX

emergy of inputs of material, transportation, labor, taxes, etc.

MA

emergy of principal product

MB

emergy of by-product

MW

emergy of waste heat stream

 

The emergy, MW, of the waste heat stream is its availability times the number of kilowatts of standard electricity that can be generated efficiently by one kilowatt-hour of waste heat.  The emergy of the sum total of all direct energy inputs to the process is determined in the usual way.  The emergy of the sum total of all non-energy inputs must be available from past studies or must be determined during the analysis.  It may include contributions from pollution etc. in which case negative emergy in the output is added to the input.  Unlike the case of energy production, the transformities of the inputs cannot be influenced by the process.  The emergy of the principal product and the by-product must equal the emergy of the inputs minus the emergy of the waste heat.  In the case of a principal product as the sole output, the determination is trivial.  However, when one or more by-products are present, the emergies of the by-products and the principal project must be apportioned in a canonical manner that should be determined by the analyst on a case-by-case basis.

If the emergy of a by-product is known in some other way, it may be appropriate to use the known value.  In a case where the emergies must be distributed equitably, the relation between market price, either instantaneous or averaged over time, and energy or emergy may be useful.  See “The Relation of Energy to Money”.  Thus, the emergy is apportioned according to market value.  This is a singular intrusion of money into the physical realm of emergy analysis and may not be advisable.  In a non-market economy, some combination of energy, labor, capital expenditures, product mass or heat of fusion (even) might be of use.  In any case, the sum of the emergies of the products must close the emergy balance.  The consumer may find it expedient to compare the emergy of any given product with the emergy of a comparable product to minimize his impact upon the environment.

Note.  ERoEI-1 is one less than the usual ERoEI which equals (MR + MI)/MI.  The reader should realize that the terms Type 1, Type 2, and Type 3 Conversion have no currency outside of this paper. 

Please proceed to http://eroei.blogspot.com/.