Energy 32 (2007) 115

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Consumption of resources and discharge of wastes are

used at a rate that allows their re-formation (sustainable

money) on a common basis, the joule of solar (equivalent)energy. Solar energy is the ow that created, helpeddevelop and maintains life in the biosphere; all biophysical

tion of natural goods is to draw up a balance of all the

take into account, in its original formulation (e.g. [11]1),

used directly and indirectly to make a product. Its unit is the

emjoule (ej) [7], and its physical dimensions are those ofenergy ([ML2T2]). Solar emjoules (sej) are the solar

ARTICLE IN PRESSenergy equivalents ([ML2T2solar]) required (directly or

0360-5442/$ - see front matter r 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.energy.2006.08.009

Corresponding author. Tel.: +390577 234358; fax: +39 0577 234177.E-mail address: bastianoni@unisi.it (S. Bastianoni). 1In [11], emergy was still called embodied energy.yield) [2]. This principle implies the use of indicatorsbased on thermodynamics, where the Second Law (dealingwith quality) has at least the same relevance as the FirstLaw (dealing with quantity) [36].Emergy evaluation [7] is a method based on thermo-

dynamic principles; it provides indicators that can be usedto assess the sustainability of systems. The emergy functioncan be used to describe any ow of matter, energy (or even

the limitations imposed by the Second Law because it isonly based on the thermodynamic function energy and thuson the First Law (see for example [12]). In practice, theSecond Law is seen as a consequence of the First, sincethrough the heat sink only high entropy ows aredispersed [7]. However, it is not difcult to reformulate theemergy function denition to include the Second Law:Emergy is the available energy of single kind previouslyexceeds the carrying capacity of the Earth. Sustainabilityhas become a fundamental policy issue, and achieving it isa matter of endless debate. Bruntlands denition thatSustainable development is development that meets theneeds of the present without compromising the ability offuture generations to meet their own needs [1] has beeninterpreted and misused. The confusion between compa-tible and sustainable development is claried in HermanDalys rst principle of sustainability: resources should be

process, since emergy ows represent what nature invested(as solar energy) to make this resource available. This is adonor-referenced concept rather than a receiver-referencedone [8]. Emergy measures the convergence of sourceenergies at system boundaries into processes or productsobtained within the system. This is sometimes referred to asenergy memory [9]it is the embodiment or enfolding inprocesses or products of energy from different sources [10].According to some criticisms, this function does notpresently proceeding at a rate which in some instances solar energy ows going into all resources used during aEmergy as a fu

S. Bastianoni, A. Facc

Department of Chemical and Biosystems Sciences, U

Received 1

Abstract

This paper aims to clarify some aspects of the discussion betwe

differences between energy-based emergy and exergy-based eme

equivalent of solar energy as scale factor. In the second part, we sho

alone, in particular of partial efciencies of the processes involv

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Emergy; Exergy; Energy-based emergy; Exergy-based emergy

1. Introduction81162

tion of exergy

ni, L. Susani, E. Tiezzi

ersity of Siena, Via A. Moro 2, 53100 Siena, Italy

arch 2006

emergists and exergists. First, we address the problem of the

: we show that the two are proportional, having the exergetic

hat emergy and transformity can be written as a function of exergy

in a production system, from solar energy to the nal product.

processes on earth function by virtue of this high-qualityenergy ow. A convenient way to estimate the consump-

www.elsevier.com/locate/energy

This paper wants to build a (part of a) bridge betweenemergy and exergy, more focusing the attention on whatcan be common than using the microscope to highlight thedifferences. The rst step is to write emergy as a function ofexergy. In this way emergy would benet of a strongerscientic basis, since exergys roots are in classicalthermodynamics.Some questions arise when we tackle the problem of

exergy-based emergy:

Is the exergy-based emergy different from the energy-based emergy?

Is it possible to express emergy only as a function ofexergy?

what is the consequence of this possibility/impossibilityboth on emergy and on exergy analyses?

2. Energy- versus exergy-based emergy

Let us consider a product (Oa), obtained from two inputss1 and s2 (see Fig. 1a). For energy-based emergy we can

ARTICLE IN PRESSergy 32 (2007) 11581162 1159indirectly) to make a product (with energy content([ML2T2product]) [10]. The intensive function ofemergy, calculated by dividing the emergy content by theenergy of the product (or by dividing the empower by theenergy ow produced), is called transformity, a dimension-less function expressed in sej/J.In assuming the concept of available energy (universally

expressed by the exergy function) in the emergyfunction, we can formulate emergy on the basis of thethermodynamic function exergy.Exergy is the maximum work that can be obtained from

a system when the system is brought from its present stateto the state of thermal, mechanical and chemical equili-brium with the surrounding environment. Exergy can bewritten as the weighted sum of (at least) three gradients ofintensive variables, where the weight is the correspondingextensive variable:

dEx S dT V dpXi

Ni dmi, (1)

where S is entropy, V is volume and Ni are number ofmoles of the ith species are extensive variables and dT anddp and dmi are gradients of intensive variables (tempera-ture, pressure and chemical potential of the ith species)between the system and the environment.Several papers have discussed the relations between

emergy evaluation and exergy (or also embodied energy)analysis e.g. [6,1215]. Especially the Sciubba and Ulgiati[12] and Brown and Herendeen [14] papers are paradig-matic of a debate that is difcult to be solved: both thepapers are discussed in which each author writes a part ofthe paper and try to convince the audience that his ownthesis is stronger than the co-authors one. Few agreementsare reached, and they are on differences. One is that thetwo analyses have different goals: emergy evaluationintends to trace back the solar energy embodied in aproduct, while exergy assesses the amount of primaryresources of any kind that went into that product(Szarguts Cumulative Exergy Cost [16]). Furthermore,the boundaries of the reference state differ substantially: inemergy, the system encompasses the entire biosphere,whose external surface is crossed by the basic input, i.e.solar energy; in exergy analysis, the control volume isdened by the analyst, according to the aim of the study.Main points of discussion are the criteria of allocation,

the use of splits and co-products, the calculation offeedback ows. On these aspects the debate is still strongand positions are quite far from being reconciled.Nevertheless, in time, what were almost ideological

differences, are now, more correctly, reduced to a debateon the self-consistency and efcacy of the methods. Also,one of the newest developments in the exergy analysisfamily, e.g. extended exergy analysis [17], uses some ofthe features of emergy evaluation to enlarge the ability of

S. Bastianoni et al. / Enexergy to consider all the inputs to a system, includingmoney ows and manpower.Fig. 1. The three basic congurations. (a) Both inputs are solar energy. (b)On

The input has a different origin, but originates from a type (a) system. (c)

e most general system, where both inputs are non-solar.

ARTICLE IN PRESSergwrite

EmEOa t^s1Es1 t^s2Es2 (2)while for the exergy-based emergy we can write

EmExOa ts1Exs1 ts2Exs2, (3)where Em(E) and Em(Ex) are, respectively, the energy-basedemergy and the exergy based emergy; E and Ex are theenergy and exergy content of the inputs s1 and s2,respectively; t^ (t) is the transformity of the inputsdened as the solar energy (exergy) directly and indirectlyrequired to obtain an energy (exergy) unit of the product.The units of transformity are in both cases sej/J [18]. Boththe energy- and exergy-based transformities of sunlight areby denition, equal to 1 sej/J:

t^solar tsolar 1 sej=J.Furthermore,

t^s1 Esolars1Es1

and t^s2 Esolars2Es2

,

while

ts1 Exsolars1Exs1

and ts2 Exsolars2Exs2

,

where Esolar( ) and Exsolar( ) are the solar energy andexergy (respectively) directly necessary to obtain a productwith energy and exergy content (respectively) of E and Ex.Thus

EmEOa Esolars1 Esolars2,EmExOa Exsolars1 Exsolars2.

Since they are of the same kind (solar) they can be added:

EmExOa a EmEOa, (4)

where a is the exergetic equivalent of solar energy (E0.93)that expresses the percentage of available energy (exergy)that can be extracted from a solar energy ow [19].Statement (4) is a focal point and we will show it has a

more general validity for the two ways of calculatingemergy. As shown in Eq. (4) Em(Ex) can be written as

EmExs1 aEsolars1,EmExs2 aEsolars2. 5

It is now important to prove that the exergetic equivalenta remains constant even if more complex input patterns areconsidered. In Fig. 1 three production processes are shownwith increasing level of complexity from Fig. 1a to c. In therst example (Fig. 1a), where s1 and s2 are both solarenergy ows, then the statement (4) is trivial.In the second example (Fig. 1b), one of the inputs is not

a direct solar energy ow, but it can be produced by

S. Bastianoni et al. / En1160two direct solar energy inputs sa; sb as the product Oa(Fig. 1a). Then N1 ow can be expressed as the sum of thetwo emergy ows that give rise to it:

EmExN1 EmExsa EmExsb aEmEsa EmEsb. 6

The emergy of the total output Ob of the process inFig. 1b can thus be written as

EmExOb EmExs1 EmExsa EmExsb aEmEs1 EmEsa

EmEsb aEmEOb. 7Also in this case Eq. (4) is conrmed. Fig. 1c shows the

more general case, in which none of the inputs arise directlyfrom solar energy. In this case, output O3 can be expressedas the sum of energy-based emergy ows multiplied by theexergetic equivalent of solar energy. As shown in Eq. (8)this value, as is perfectly consistent with Eq. (4):

EmExOc EmExs1 EmExs2 EmExs3 EmExs4 aEmEs1 EmEs4 aEmEOc. 8

Thus, Eq. (4) remains valid for complex topologies and,except for a scale constant which multiplies all ows,emergy takes the same values whether based on the energyor the exergy function.The same does not hold for transformities, which a have

different hierarchy in the two cases. According to Odum,when an item is the result of a suitable process of selection(e.g. natural selection), the transformity of that itemrepresents the quality of that item in nature [18]. Interest-ingly, if the entropy aspects considered in exergy (with respectto energy) are included some low exergy types of energy (likelow temperature heat) rise in hierarchy. This seems counter-intuitive but is due to the fact that the lower the transformityof a product, the higher its efciency in converting direct andindirect solar energy into nal output. Exergy of course ratesproducts according to their work potential.

3. Emergy as a function of exergy

In general terms, emergy (Em) can be written as afunction of exergy (Ex) as follows:

Em Xi

ti Exi, (9)

where t is the transformity and i the i-th input.If Ex and t are the exergy and the transformity,

respectively, of the output of the process, by sensitivityanalysis of the emergy and transformity of the output wecan write

@Em

@ti Exi and

@t@ti

@@ti

Em

Ex Exi

Ex oi,

where oi is the reciprocal of the partial efciency of the

y 32 (2007) 11581162ith input to obtain the output and is dened only as afunction of exergies. Therefore transformity can be dened

as a sum of reciprocals of partial efciencies weighted byprevious step transformities, through the relation

t Xi

tioi. (10)

Iterating the procedure from the nal product back tosolar energy, through the inputs involved in the wholechain of processes needed, we obtain

t Xi

oiXj

o1i;jXk

o2i;j;k . . .Xs

ozi;j;k;...;s

! ! !

(11)

which is only a function of the reciprocals of the partialefciencies oi, calculated as ratios of exergy ows. Thenumber of indices increases with the number of steps fromsolar energy to the nal product, following the routesthrough each input. In the nal steps of the backwardcalculations of oi, when each input is converted to solarenergy, the transformity is 1 sej/J; therefore the transfor-mity is not explicitly present in Eq. (7). In conclusion,transformity can be expressed in terms of exergy alone, andemergy as well, since emergy is expressed by Eq. (5).This notation, albeit correct, is not readily understood

and applied. We therefore generalize the formula to makeit easier, though less economic. We consider only two

indices m 1; . . . ;M and n 1; . . . ;N, which are thenumber of (direct and indirect) inputs to the process andthe maximum number of steps required from solar energyto the nal product, respectively. To clarify further, M isthe total number of inputs required in the transformationfrom solar energy to nal product, and may be large forcomplex processes. For ns requiring fewer transformationsthan N, a number of 1s are added to reach N. Thus weobtain the following formula:

t XMm1

YNn1

onm, (12)

where certain onm have the same value since they connectthe same input to the output.Fig. 2 describes the agricultural production of wheat,

showing some of the inputs that are necessary for theprocess. For the sake of simplicity, we have assumed thatthe inputs are: solar energy, manure, machinery and fuels.The path for the formation of each input is shown, startingfrom solar energy. For manure and oil we assumed verysimple linear transformations; machinery, on the otherhand, is the result of a combination of steel and oil(plastics). Steel, in turn, is obtained from iron and coal, theprecursors of which are iron ore produced by thegeochemical cycle (for iron) and wood and peat (for coal).

ARTICLE IN PRESSS. Bastianoni et al. / Energy 32 (2007) 11581162 1161Fig. 2. Simplied model of wheat production. The model shows all the exergy

of the backward steps to the original solar exergy source.ows directly or indirectly needed for the process and the partial efciencies

ass

caof

[16] Szargut J, Morris DR, Steward FR. Exergy analysis of thermal,

[17

[18

[19

ARTICLE IN PRESSS. Bastianoni et al. / Energy 32 (2007) 115811621162t m1 n1

onm,

where

o21 ::: o71 o52 ::: o72 o63 o73 o45 o56 o57 o67 1

and

o54 o55;o64 o65 o66;o74 ::: o77.

Any complex process can be translated into a schemesimilar to Fig. 2, to obtain a matrix having the samenumber of columns as the number of steps in the longestprocess.

4. Conclusions

Emergy can be reformulated as a function of exergy andtherefore its physical and mathematical validity is the sameas exergys. The main difference is the number of processesinvolved in an emergy calculation, which, in general, ismuch larger. This makes eMergy evaluation intrinsicallyless precise that eXergy evaluation, though when manyprocesses are correctly analyzed, the data set for eMergycalculation becomes more and more reliable.The answers to the three questions arisen in the paper

are:

1. Except for a multiplying constant, emergy has the samevalue whether a purely energy or an exergy approach isused; however, the hierarchy of the transformities isdifferent in the two cases:

2. Emergy can be calculated as a function of the partialexergy efciencies of the transformations of a series ofinputs into an output. The calculation may be compli-cated in certain cases but the formula has a generalvalidity:

3. The main difference between emergy and exergy evalua-tions (considering also extended exergy accounting[12]) is the denition of the system, especially thea1 b1 c1 f1

It can be written, in terms of Eq. (12), as

X7 Y7t eat produced in this hypothetical process can only belculated if all the partial efciencies are known, by meansthe formula

o11 Y4

oa2 Y5

ob3 Y7

oc4 Y7

of 7. (13)repwhTo each one of the steps i in Fig. 2, it is possible toociate a specic partial efciency whose reciprocal oi isorted in Fig. 2 and in Eq. (13). The transformity ofchemical and metallurgical processes. New York: Hemisphere

Publishing Corporation; 1988.

] Sciubba E. Beyond thermoeconomics? the concept of extended exergy

accounting and its application to the analysis and design of thermal

systems. Exergy an Int J 2001;1(2):6884.

] Odum HT. Self-organization, transformity, and information. Science

1988;263:124360.

] Wall G, Gong M. On exergy and sustainable developmentPart 1:

Conditions and concepts. Exergy an Int J 2001;1(3):12845.number of backwards steps considered in the analysis:exergy analysis focuses on the rst step (the exergy of theinputs); emergy analysis considers all direct and indirectinputs to be on the same level, and proceeds backwardsto the original input: solar energy. This should be seenas a point of strength since the two can be used indifferent situations, depending on the type of system andthe aim of the study.

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Emergy as a function of exergyIntroductionEnergy- versus exergy-based emergyEmergy as a function of exergyConclusionsReferences