Energy and Emission Matrix
The present work is a revision of basic concepts necessary for facing technological forecast, with emphasis on energy. For accomplishing the proposed goal, we define technique as a set of procedures and materials used for producing goods; technology is the systematic study of techniques based on scientific principles. In the current language, technology is also used to express a set of techniques, including knowledge, materials and the equipment used in production.
The first demonstration of technical capacity would have been the fabrication of artifacts by combining natural utensils such as the stone, the club and the silex knife. The combination of a stone and a club would have originated the hammer as well as the combination of a club and silex originated the axe and the spear. Technology would be contained in the act of generalizing the technique of fixing the stone or the knife to the club, allowing for the fabrication of other instruments by the same process.
For the Greek thinkers, Science, which is concerned with knowledge of Nature, differentiates itself from workmanship and craft whose objective would be to manipulate Nature. Prigogine (1) points out the common origin of machine, mechanics and engineer, linked to technical activities and therefore to the manipulation of Nature (by means of artifices, tricks and stratagems). In the Greek culture, the activity of a scientist was predominantly rational that is, reason was considered as an excellent form of knowledge while experience (sensorial) would be a subaltern form, and on this difference was based the hierarchy of knowledge.
The approximation between science and technique proposed by Roger Bacon (13th century) got new momentum in the Renaissance when Galileu’s experimental method (16th century) was established as scientific method. It interesting to emphasize that the methodological divergences among rationalism (pure reasoning), empiricism (observation without intervention) and experimentalism (observation in controlled conditions) and between science and technique are reflected until now in the attitude of man vis-à-vis Nature, stressing the view of supporters and enthusiasts of technology as well as that of their opponents.
Presently, it seems that Science has lost part of its characteristics of free speculation about Nature, linking itself more and more to the economic and social needs. The advances of Science yield co-products of secondary importance in what regards speculation but of practical application. Therefore, when one observes the evolution of those needs and the accomplishments of Science in the near past it is possible to undertake an evaluation of the general direction of the advance of technology.
Several economy and society evolution scholars such as Odum (2), Rifkin (3) and Ayres (4) list the needs of technology development vis-à-vis the scarcity of the available energy (the fraction of energy that in some way can be converted to mechanical energy). Thus the change in man’s feeding base would have been forced by insufficient energy, since fruit gathering in competition with other species and also with other human individuals demanded the displacement of the gatherer to larger distances making deficient the energy balance. The hunting of large animals, a more profitable activity, demanded the organization of groups, the exchange of information and the fabrication of weapons since it is a team activity. The basic characteristics of technology are thereby organization and information, requirements for adaptation of society to the changes in the environment.
Technology prospecting is nowadays a component of planning since the needs of investments grows with the population and with the evolution of the production environment.
The exploration of natural resources privileges those of better quality, so the production continuity demands growing energy inputs to transport to larger distances and processing raw materials with lower concentration of wanted substances, etc. These requirements, that can be evaluated in physical terms, are added to those that are more subjective such as manpower qualification, administration of a productive complex, the updating of scientific knowledge, etc. In these conditions, to know the trend of social demand of product and of service facilitates the identification of investment opportunities and makes savings in the long term. The prospecting model presented here permits to know the kinetics of development of a technique already introduced in the market. The qualitative identification, that is, the prevision of the nature of techniques is still a challenge to the specialists on the subject.
Once the utility of a technique is demonstrated, such as the organization for hunting, it can be copied by other individuals or groups that are mature for that, in other words, that are motivated and are prepared to absorb the novelty. The dissemination velocity can be established from premises by the probabilistic reasoning that follows.
The diagram below represents a symbolic space known in Statistical Mechanics as “phase space”. The n dimensions of this space correspond to the variables that describe the phenomenon. In this space the elements that know the technique are represented by red circles and those that ignore it by yellow ones. The area of each circle represents the aptitude to transmit or receive the new technique, meaning that the phenomenon occurs only if the participants have a minimum “distance” in the phase space (the areas are not necessarily equal since the aptitude for transmitting is not necessarily equivalent to the aptitude for receiving).
The space is always filled with circles, assuming that at the beginning there is at least one transmitter, since the model does not intend to explain the singularity that resulted in the technique under study. If the agent is placed at random in the space the probability that it is at a minimum transmission distance is measured by the ratio between the area of the yellow circles and the total phase space (that includes the area associated with the agent). If there are N agents and (N*–N) receptors in the instant t, where N* represents the total number of circles that fill the space, the probability of occurring an interaction is proportional to:
p = m N (N*-N), (1)
where m is a constant that takes into account the differences of areas or of requirements for transmitting and receiving the total number of agents and receptors, N*. Once the conditions for interaction are satisfied, we admit, as in the model that interprets radioactive disintegration, that the probability of occurring an interaction in the set of the participating elements in the time interval dt is proportional to dt. Therefore, the probable number of interactions in the interval dt is given by the equation :
dI = a N (N*-N) dt.
rate of conversion of receptors into transmitters will be
dN/dt = a N(N*-N). (2)
This differential equation, assigned to Verhulst, was established for analyzing Malthus’ proposition regarding the exponential growth of the human population.
It should be noticed that the y(N) = dN/dt function is the equation of a symmetric parabola relative to the straight line N=N*/2; as a function of t , the curve is bell shaped and it looks like the Gauss normal distribution curve. As an example we show below the annual distribution of publications about the exergy thermodynamic function obtained in the www.exergia.se site.
The integrated form of the Verhulst equation is:
N(t)/N* = 1 / (1+ ke-aN*t ) (3)
The law described by this equation is called logistic or sigmoid due to the elongated S form of the corresponding curve and represents the accumulated value of publications on the same subject until the year t.
Making F = N/N*, one can have equation 3 in the linear form
ln (F/1-F) = a N* t +ln k, (4)
which is simpler for representing and for fitting.
The steps for obtaining the logistic projection consist of extracting from the historical data series the rate dN/dt. Generally the average rate for three or five years is used, according to the extension of the series. By fitting a parabola to the rate series, its maximum value may be determined, since…
d/dt (dN/dt) = a(N*-2N) dN/dt vanishes for N=N*/2.
We should observe that the point N=N*/2, the maximum point of the parabola, is an inflexion point of the logistic curve, that is, it is the point where the curvature changes its direction.
From the N* point on, the linear form (eq. 4) is used completing the determination of the kinetics of the phenomena evolution. In the case of publications about exergia, the graphic suggests that within two decades this function, that is hardly known today, will be incorporated to the practice of Engineering.
The complete form of the equation contains a term corresponding to the mortality of the users of the technique under analysis. Assuming a constant mortality rate λ, the equation will be:
dN/dt = a N (N*-N) – λN = a N [(N*- λ/a) - N]
Prigogine and Stengers (1) suggest that a and λ can be adjusted (by a biological species) to permit survival in a changing environment. In the case of technological development, it is reasonable to suppose that the shortening of the information transmission time (increase of a) and conservation of information (decrease of λ ) are the survival mechanism of technology. We will verify that these hypotheses are compatible with the interpretation of occurrences of development pulses.
The following figures show the sequence for studying the evolution of publications. The first one shows the evolution of the publication rate (publication/year). From this graphic one can have the maximum number of publications as being the abscissa point of maximum rate. The second one shows the linear form of the logistic function, which is the base for calculating the number of future publications. The third one is the result of the model application where one can see the good agreement between the observed and the projected number of publications. The quality of the agreement depends on the extension of the historical data series and naturally on their reliability. For energy demand, generally recorded with good precision, relatively short series lead to satisfactory results. Marchetti (5) used a series of 20 years for petroleum consumption (1900-1920) and projected the demand for the following 50 years with good precision.
The methodology above described has been used in the study of a large number of phenomena of different natures, such as the propagation of epidemics and habits, the introduction of innovations in the market, the construction of gothic cathedrals and of colonial churches in Minas Gerais, Brazil, intellectual production (arts and science) and others.
The same methodology can now be used to describe two species competing in a niche. It is sufficient to observe that in the previous case 1–F represents the fraction of the niche occupied by the only species under examination. Whenever there are two species N1 and N2, the fraction not occupied by N1 is occupied by N2. Therefore, it is sufficient to make F= N1/N2 and apply the methodology as described. The graphic below shows the competition between vegetal coal (N1) and mineral coal + coke (N2) in Brazilian metallurgy. The graphic permits to extrapolate the participation of vegetal coal, assuming that the price ratio of the two competitors is maintained.
The competition among three or more species requires the solution of the differential equation using numerical methods and will not be considered in the present introduction.
A new event such as the discovery of a new natural resource or of a new form of using resources already known can start a family of techniques whose objective is to use the resources as much as possible. Thus, the discovery of petroleum in the United States, coupled with a surge of industrialization in the country started the evolution of the Otto cycle engine (spark ignition), proposed by Beau de Rochas in France and developed by N. Otto, who kept in the glory of the deed, in Germany.
At the beginning, the engine was fed with benzene that endured small compression without detonation. It was followed by various formulations of gasoline that permitted increasing the compression ratio and consequently a better efficiency of the engine, and the development of engine components such as piston rings, ignition distribution electric system, fuel injector system, electronic system for combustion control and valve driving system, constituting a family of techniques with a common purpose.
The Diesel cycle engine (compression ignition) had a similar story and the difference lies in the fact that the fuel used must ignite by increasing the temperature of its mixture with air, which requires physical-chemical properties different from those of gasoline, which must endure compression without ignition. Therefore, the development of fuels and engines must be treated as synergetic items. Both type of engines are treated here as belonging to the same family, namely, internal combustion engines. The engine technical evolution is very appropriately described by efficiency whose evolution is shown in the graphics that follow (6).
The maximum efficiency foreseen by the model is 67%, in good agreement with the Carnot cycle with a temperature of 650 0 C for the hot source (metallurgical limit for cast iron or steel engines), which is 68%. It is verified that there still is room for efficiency gain, and it is predicted a competition between the advanced engine and the fuel cell, a subject to be examined in another Technical Note.
Sequence of technique families.
In the technical literature it is observed a trend for correlating the start of a new technique family, such as that of the internal combustion engines, with the exploration of new energy resources. Although the correlation is justified on physical basis only for techniques regarding fuel conversion, it is possible that the hypothesis is also valid for other techniques where energy has a dominant role.
Aiming at systematizing the study of the development process regarding techniques from discoveries related to scientific research, Marchetti (5) has developed a correlation series for families of energy converters and industrial processes, grouping them in development pulses of inventions and innovations. According to the author, inventions are discoveries, generally of a scientific nature, that yield products accepted by the market, the so-called innovations.
The grouping method considers three pulses associated with the primary energy source in ascension, that of 1802 (mineral coal), that of 1857 (petroleum) and that of 1920 (natural gas), years that correspond to the centers of the logistic functions average point. For each one of them it was constructed the logistic function regarding inventions and innovations and each one of them is characterized by a center (the maximum point of the parabola associated to the pulse’s kinetic) and a time constant (time necessary for the niche fraction occupied by the invention/innovation to vary from 5 to 95%).
The graphics below summarize the method used for treating the data, where one can see , for each invention pulse, a logistic curve for inventions and one for innovations; the center of each logistic curve, the corresponding time constants, the pulse center and the year when occurred the maximum participation of a primary form of energy (firewood, hay, mineral coal, petroleum and natural gas) that preceded the ascending source during the drive are indicated.
The main conclusions regarding the analysis of the first three pulses examined are:
· The interval between the innovation pulses measured between the centers of the respective logistic graphics is about 55 years, a value that reasonably coincides with the duration of the economic cycle postulated by Kondratieff (1792-1850, 1850-1896, 1896-1940). It is interesting to observe that the economic development pulse that started with the implementation of the Marshall Plan for the economic recovery of Europe between 1945 and 1948 is completing 1 kondra (economic time unit, according to Marchetti), what suggests an economic recession in the present days, a fact indicated by the saturation already observed in the steel, aluminum, cars, etc. markets.
Based on the identified regularities, Marchetti foresees a next pulse of innovations, coinciding with the incoming of nuclear energy in the market, based on the invention pulse centered in 1968 (semiconductors, microelectronics, fine chemistry, genetic engineering ). The last graphic consolidates the pulses already observed and the next three pulses (that of nuclear fission energy, that of fusion nuclear energy and that of elementary particle called μ-sion, a combination of the generic designation of particles (muons) with the process of fission-fusion conversion, not yet identified by the author).
Finally, Marchetti observes that the prices of primary energy sources goes through peaks that coincide with the average points of the pulse (graphic below) and suggested in 1981 that petroleum prices would drop in the following years, what really happened in 1986.
The progressive shortening of the inventions and innovations pulse’s time constants seems to corroborate the interpretations of Prigogine and Stengers, previously mentioned regarding a biologic system, relative to the adaptation of the technological system to the production environment in which the quantity and quality of the natural resources (raw material and primary energy) develop in a direction that is unfavorable to the economic production of goods and services. Ayres (4) considers that technological development has compensated the impoverishment of natural resources and proposes an interpretation regarding the interaction of the economic and technological systems from the point of view of the Entropy Law that considers the technology development as an item of capital accumulation. Ayres also discusses the limitation of technology development as a solution to the exhaustion of natural resources (neo-Malthusianism), a topic also discussed by Rifkin (3) under the title “decreasing returns of technology” that recalls the Marxist hypothesis about the decreasing return of capital revenue. The consolidation of these interpretations seems feasible since they do not contradict but only consider the question from different points of view.
The systematization proposed by Marchetti is still in the initial stage and seems promising, in spite of the small number of pulses that were analyzed.
It should be stressed that its application refers to the world industrial system, it is not apparently applicable to separate national economies, since the latter have different development rhythms. It is possible that the so called globalization of the economy, which makes the national economies behavior uniform, will permit the particularization of the methodology to these economies.
Diminishing Returns Law
In the previous item we have mentioned the analogy among chemical system, studied by Stengers, biological system (mentioned by those authors as analogous to a self-catalytic chemical system) and system of techniques development. With some restrictions , the behavior of these systems and of others that we intend to discuss in the present work, can be described by the logistic law.
One of the interesting applications, considering the world economic moment, is the diminishing returns of capital or, if we prefer, of the capital productivity. We have shown in a previous e&e work (“ Capital accumulation in the Brazilian economy”, e&e n0 9, 1998) , following Ayres’ suggestion (4), that capital accumulation in Brazil followed the logistic law until 1970 when it occurred the so called “Brazilian miracle”, the ”hurried” industrialization, whose results can be interpreted today as dissipation of resources in the thermodynamic sense. According to the results shown in the mentioned article, the capital accumulation foreseen by the logistic law would have reached the accumulation achieved around 1998, with the difference that the growth potential, represented by the tangent to the logistic curve, would be higher than that corresponding to the real path.
Since the objective of the present work is not to identify irreversible phenomena that concurrently with the petroleum crisis have led our economy to its present situation, in the present analysis we will limit ourselves to the saturation of the financial capital that makes speculators transfer their resources from one country to the other, depending on the trouble of the moment.
In the logistic law equation:
dN/dt= a N(N*-N)
N can be identified as the capital stock , N* as a quantity of natural resources (ore, forest, hydraulic potential, etc.) that the capital transforms into more capital (as in a self-catalytic reaction where the catalyst makes the reaction happen without itself being changed) and dN is the net result of the process that transforms resources into capital.
In order to apply this law to an economical system it is necessary to adequate the equation to the social accounting methodology that collects the economic movements in annual balances. When we pass from a differential equation to a finite one that approximates the model to the facto situation, there are differences of values that Carlos Feu et al (7) have verified to be negligible relative to the expected incertitude of economic studies. So, the equivalent finite equation would be;
DN/N = a (N* - N) Dt
where Dt is the interval of economic result collection, considered as constant. The first member of the equation represents the capital productivity that diminishes as the stock comes near to the maximum value N* (or N*- λ/a, considering mortality a irreversible phenomenon par excellence and whose effect is reflected in the diminishing of stock of resources on which production is based). In the case of the “miracle” , the fitting of the capital growth to the logistic function was only moderate, detonating the occurrence of other irreversible phenomena besides the natural one (wear, obsolescence, attack from natural agents, etc.). Therefore the space for growth shrank due to the irreversibility induced by the desire of ... growing.
So it seems demonstrable the diminishing returns law. Simplifications introduced in the present exercise will be considered in future works.
“Si non é vero,...”
Technological forecasting in the energy area for the Brazilian conditions
In the prospecting to be elaborated for the development of technology in Brazil, whose historical series are relatively short and whose economy is relatively closed, it does not seem convenient to try to generalize. However, the evaluation of horizons for techniques already implemented can profitably be made for singular techniques, as input for recurrent discussions about competition between renewable and fossil energy sources. In the case of alcohol fuel, the analysis of the efficiency evolution of internal combustion engines, mentioned as example of application of the methodology, indicates that there still is space to be gained which, coupled with potential gains in the productivity of sugarcane plantation and the use of bagasse in co-generation of electricity and process vapor, can substantially change the perspectives of the Sugar-Alcohol Sector. It seems also interesting, among others to be identified, the following cases in the energy area:
Finally, a survey of the state of the art in the development of fuel cells would permit to aggregate useful information for orienting the investment policy regarding R&D in the energy area.
In all cases, the work starts with the identification of the parameter to be modeled, in general the conversion efficiency or the productivity of energy use. It is followed by a test of the historical data series to verify the applicability of the logistic methodology and, in the positive case, the elaboration of previsions about the existing margin for development.
- Prigogine, I e Stengers, I – “A Nova Aliança” – Ed. UnB (1984).
 In the chemical system, it is assumed the thermal and mechanical balance; in the biological system, it is accepted that there is no competition among species; in the techniques development system, it is supposed that the market, or the consumer’s preference, preserves certain techniques and discards others.
Graphic Edition/Edição Gráfica:
Tuesday, 11 November 2008.