Economy & Energy
Year III - No 12 Jauary/February 1999

ollaoro.gif (978 bytes) Main Page
ollaoro.gif (978 bytes)Brazilian Energy Matrix
ollaoro.gif (978 bytes)Optimism in Times of Crises
ollaoro.gif (978 bytes)Exegertic Analysis of  Agriculture
ollaoro.gif (978 bytes)e&e links
Following the Brazilian Economy:
ollaoro.gif (978 bytes)Brazilian Public Debt
ollaoro.gif (978 bytes)Brazilian
ollaoro.gif (978 bytes)Internationl Reserves
Graphical Edition:
Editoração Eletrônic
Friday, 11 July 2003.


Omar Campos Ferreira
Associate Researcher - FAPEMIG
undercon.gif (1131 bytes)English Version
Frida Eidelman

Production systems in general are classified as open thermodynamic systems. The input is constituted of natural resources transformed by production operations on articles for human consumption. From the energy point of view the agricultural production system may be interpreted as the conversion of solar radiation into food energy, with the intervention of water, carbonic gas and semi-elaborated products such as fuel, fertilizers, pesticides, seeds, etc. One of the basic inputs is production technology which, in analogy with capital, results from the accumulation of production surplus over consumption and is transferred to another production way that we call technology development.

Rudimentary subsistence agriculture uses only natural resources such as solar rays, rain water, carbon from natural cycle and human labor, besides those that characterize the quality of natural soil. Once exhausted the potential production of a settlement area, the primitive land cultivator simply moved to another area, starting again the production cycle. Since there was abundant land, the exhausted area was allowed to recompose the productive potential through natural mechanisms and eventually be used in another production cycle. Along civilization’s development, the investments made in the settlement infrastructure such as houses, paths, systems for water adduction, etc. became too valuable to be abandoned and the land rotation system, known as ALQUEIVE, became anti-economic. But the re-composition of the land by artificial processes demanded the introduction of extra-human energy and the use , at the beginning, of domesticated animals for driving rudimentary machines that were progressively perfected in order to improve yield. In a general way, the process of making use of the land may be described as the partial substitution of one production factor (land’s fertility) by another one, namely energy.

The introduction of steam machines, of internal combustion engines and of the electric motors emphasized the use of energy in progressively sophisticated forms, in the sense of being more manageable. With the development of other production systems, such as the chemical industry, agriculture became assisted also by the energy contained in fertilizers, pesticides, fuels, whose production was facilitated by the existence of other natural resources, such as nitrates, phosphates, etc. But all natural resources outside the photosynthesis cycle are exhaustible in historical periods and, like the primitive agriculture from Mesopotamia, Egypt, China and other regions that once were essentially agriculturist, the European countries have seen decrease their production potential, requiring increasingly quantities of energy in order to maintain the growing population. It is predictable that the same evolution sequence will be followed by the Brazilian agriculture in which energy demand is growing faster that that of industry.

While energy resources are abundant, we repeat with them the land exploration cycle; once one resource is exhausted we explore another one, preferably using the same conversion technology and the observed limitation in primitive agriculture will be repeated in converting energy. When combined, the two exhausting processes represent an insurmountable hindrance for further development of civilization. In the case of energy, there still is a fundamental mistake, namely evaluating resources as if they were equivalent in the conversion to driving energy, the conversion final product, which results in ignoring fundamentally the limitation of conversion efficiency imposed by the Entropy Law, still considered even in the technical circles, as an unnecessary complication in energy analysis. Therefore, the energy accounting is presently based on the Energy Conversion Law and the generalized belief is that there will always be energy convertible into driving energy at constant cost. The deep impact of the petroleum prices chock of the seventies on the political and economical organization of society suggests the need of refining the methods of energy analysis so that it will be possible to use better the natural resources and to evaluate the environmental impacts of the energy-intensive processes.

The methodology we propose to be introduced in the analysis of agricultural production systems originated in Europe at the end of last century and it was ignored in the specialized literature until the petroleum crisis. The fright caused by the crisis shook up the technical- scientific circle and as a consequence there was an avalanche of articles on the thermodynamic function called energy availability, ESSERGY, EXERGY and, more recently, EMERG (H.T. Odum, in "Environmental Accounting"). In Brazil, there are groups working on the concept of EXERGY in USP, UNICAMP, EFEI, IPT, UFMG e UFV ( Prof. Delly Oliveira Filho and his Post-graduation group) aiming at different ends ( analysis of internal combustion motors, waste recycling systems, energy planning, co-generation systems, combined cycles, etc.) but the methodology of EXERGETIC analysis is still ignored by most specialists. In the CETEC, in a project financed by FAPEMIG, it is being implemented as an instrument for ecological analysis, energy planning and the study of the mechanism of soil destabilization. In partnership with EMBRAPA and EPAMIG, a project for analysis of irrigation systems performance is being defined, and this is the reason why a contract is being established.

For those initiated in Thermodynamics, the EXERGY function may conceptualized without great efforts, starting with a thermodynamically closed system that does not exchange matter with its surroundings and then generalizing the concept for open systems. For closed systems, the Energy Conservation and no decrease of Entropy equations for an elementary process are:

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Where the symbol d indicates that differences are not exact, that is, work and quantity of heat are dependent on the path of the system in the space of phases p,V (figure) and the subscript refers to the surrounding of the system.

It should be remembered that in non-reversible processes, the system temperature is not unique, which prevents the direct measurement of the heat exchanged. To remove this problem, it is usual to assume that the system exchanges heat with a reservoir situated in the surrounding, with thermal capacity much larger that that of the system and then:

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that allows to obtain

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Using the expression for dQ in the conservation equation, one obtains

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And, since the second member contains only exact differentials, one may write

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The function

E = U - T0 S

is called EXERGY of the system in the state defined by T0 and S.

The work so expressed is the total one effectuated by the system, including the useful work and that of its expansion against the pressure made by its surrounding. If the process considered is reversible, the work is the maximal possible between two thermodynamic states. In this case, calculating W by the variation of EXERGY gives the same result as calculating it by the energy balance. Since the real processes are irreversible, the energy balance presently used as the only method for evaluating efficiency gives unrealistic evaluations in different grades, according to the importance of the irreversibility. There are flagrant cases of inadequacy of balance analysis such as the evaluation of the old electrothermal program of the Federal Government in which electric energy is valued by its thermal equivalence, regarding, for example, heating by thermal waste from motors as equal to heating by electrical energy.

By integrating the elemental work in order to obtain work in a finite process, it appears an integration constant that must be defined so that the analysis is complete. For applications in economy and ecology which involve energy exchange between the system and the biosphere, the thermodynamic state of reference is that which corresponds to equilibrium in the environment. But the biosphere is far from being a system in equilibrium so that it is necessary to idealize a state whose variables have the

average value of temperature, entropy and internal energy of the environment and ascribing to it zero EXERGY. If this is accepted as true, EXERGY of the system is interpreted as the work performed by the system if it is gets in equilibrium with the environment by means of a reversible process. Conversely, EXERGY is the work that must be supplied to the system in order to remove it from the equilibrium state with the environment and take it to the considered state.

From this interpretation stems the usefulness of EXERGETIC analysis:

the EXERGY of the systems measures the potential of interaction with the environment, which in ecological analysis is called environmental impact

the EXERGY measures the minimal work necessary to produce goods or a service which in economical analysis is called added value.

It should be emphasized that the potential of environmental impact is not the effective impact in the same way as minimal work is not the effectively added value. Both are limit values for these parameters when the irreversibility of the process tends to zero, in the same way as the Carnot cycle has the limit efficiency for irreversible real cycles. Therefore, the EXERGETIC analysis is not a panacea for economical or ecological analysis but an improvement of the conventional energy method.

In what regards the added value, for example, of course other production factors must be considered. Nevertheless, in limiting situations in which energy is the critical factor, as it might be expected in case of a new petroleum crisis, which is not unpredictable due to the political situation in the Far East and in Russia, the EXERGETIC analysis allows to predict the directions of the world economy with more assurance than the energy balance. The fundamental difference between these two methods, from our point of view, lies on the comparison of the possible thermodynamics paths and then directing the actions to that which permits extracting the maximal work from a given natural resource characterized by its internal energy. In other words, the EXERGETIC analysis demands the examination of the process’ nature, while the energy balance considers the process as already established. This use of the EXERGETIC analysis opens news perspectives for the rationalization of energy, presently restricted to minimizing the internal energy loss.

For open systems as those of production, the EXERGY expression is slightly different. In order to prevent extending the text more than necessary for a first approximation, we will limit the presentation to open systems operating in permanent regime. Since now there is matter circulation and the corresponding work must be considered as cost, one can demonstrate that the adequate expression of the EXERGY function is:

B = H - T0 S

H being the enthalpy of the system, giving

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The diagram bellow shows a typical production system, the matter and energy exchange and the energy interaction with the environment whose temperature is supposed to be constant and equal to T0.


The important factor for the possible processes is the EXERGETIC efficiency, defined, for production, as the ratio between the products’ EXERGY and that of the inputs. EXERGY tables for the most common substances used in industrial processes and also for some substances contained in food, such as carbohydrates, sugars and proteins, are given in several references.

For ecological analysis purposes there are other definitions that will be opportunely presented.

Since the terms of the EXERGY function are extensive thermodynamic properties, except temperature, which is constant, EXERGY of a mixture of substances is equal to the sum of the EXERGY of the composing substances. In this case it is necessary to take into account the entropy variation associated with the inter-diffusion of the composing substances.

The EXERGETIC efficiency may be used as a criterion for selection of culture types, orienting policies for population feeding, for cost distribution in systems in which one or more inputs have multiple use, such as water, in order to compare production configurations ( for example, traditional agriculture compared to the assisted one), to evaluate effects of input data, etc.