I have been asked to give a definition of the emergy
unit. I would like to do a little more and define emergy itself as well as
emergy efficiency. Further, I will give some examples as they apply to special
cases.
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 – T_{o}S], the Helmholtz availability
function [U  T_{o}S], and entropy are given in Appendix I, Fundamentals of
Thermodynamics, where the symbols and technical terms employed in this
paragraph are explained. [T_{o} 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 sunlightbased 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, singlephase, 60 Hz, 110volt alternating
current is taken to be standard electricity.
Definition (Emergy Unit). My arbitrary – but
welldefined – choice for one unit of emergy (1 MU) is 1.0 kilowatthours 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
kilowatthours. 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 kilowatthours 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 kilowatthours. This is an electricitybased transformity, the
units of which are emergy units per kilowatthour.
Definition (Emergy). The embodied energy or emergy of a
primary fuel is the Gibbs availability of the fuel in kilowatthours multiplied
by the electricitybased 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 byproducts 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 electricitybased 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/MarkIIBalance.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/MarkIIEROI.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 byproducts, 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

λ_{R}

electricitybased
transformity of fuel produced

MR

emergy
of fuel produced by process = λ_{R} · ER

MI

the
algebraic sum of all of the emergy inputs (except for MN) minus the
byproducts

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)

λ_{N}

the
electricitybased transformity of the energy supplied by Nature

MN

emergy
of energy from Nature = λ_{N} · EN

β

Energy
returned over energy invested minus 1 (ERoEI1) = ER/EI = MR/MI

EP

the
Gibbs availability of primary energy in Type 2 conversions

λ_{P}

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 productequivalent 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 ERoEI1 is a good measure of the
effectiveness of the process. (See http://www.dematerialism.net/MarkIIEROI.html.)
[An example of an indirect cost is the prorata 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 wellknown
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 λ_{N}, the value we compute, is greater than λ_{N*}, 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 λ_{N} should be considered for a new value of
the transformity of the energy supplied by Nature.
Case 2. If λ_{N}
is less than λ_{N*}, 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
wellestablished value of the transformity of the energy supplied by Nature is
accepted and the transformity of the product is computed from it. Call it λ_{R'}. If λ_{R'} is less than λ_{R}, the true value, we should revert to Case 1 and recalculate the
transformity of the natural energy. If λ_{R'} is greater than λ_{R}, then the efficiency is λ_{R} over λ_{R'}. This is in agreement with Equation 2 above.
Let us imagine the process in the
configuration illustrated by Figure 2.
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 λ_{P*}) minus the emergies of any useful byproducts 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 suboptimal and the efficiency, η, is
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 wellknown 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 2. If λ_{P}
is less than λ_{P*}, 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
wellestablished value of the transformity of the energy supplied by Nature is
accepted and the transformity of the product is computed from it. Call it
λ_{R'}. If λ_{R'} is less than λ_{R}, the true value, we should revert to Case 1 and recalculate the
transformity of the natural energy. If λ_{R'} is greater than λ_{R}, then
the efficiency is λ_{R} over λ_{R'}. This is
in agreement with Equation 2 above.
Let us imagine the process in the
configuration illustrated by Figure 2.
Type 3 Conversion. The third type of conversion is the manufacture of nonenergy goods. The manufacturing process has inputs of energy, material goods, transportation, labor, taxes, etc., and outputs that include a principal product, one or more byproducts, and waste heat. This is best illustrated with a diagram such as Figure 4.
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 λ_{P*}) minus
the emergies of any useful byproducts 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 suboptimal and the efficiency,
η, is
_{}_{}
and, the transformity of the product we would compute from
_{}
is higher than the true value λ_{R}. 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.
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 byproduct

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 kilowatthour 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 nonenergy 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
byproduct 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 byproducts are present, the emergies of
the byproducts and the principal project must be apportioned in a canonical
manner that should be determined by the analyst on a casebycase basis.
If the emergy of a byproduct 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 nonmarket 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. ERoEI1 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.
Houston, Texas
Friday, October 27, 2006
If someone who reads this has some idea about what I need to do to get Blogger to render MS Word's subscripts so that they look like subscripts rather than the monsters one sees in this article, I would be most appreciative.
ReplyDeleteAs soon as I get a chance I plan to rewrite this article so as to calculate ERoEI rather than ERoEI  1.0.
ReplyDelete