Energy Analysis: a primer

by David Crane, consultant on information technology

Energy analysis is a technique for looking at physical activity within an economy. The main principles were developed in the 1970s following the 1974 oil crisis and a sudden awareness of the importance of fossil fuels in nearly every aspect of our lives (or, at least, our lifestyles). Similar issues look to be coming up again, with the recent debates in the US about whether to open up new oil reserves in environmentally-sensitive areas, and even a reconsideration of nuclear power, long out of favour, as a viable alternative.

The ECCO model uses energy analysis theory as one of its main tools, and many of the variables in the model are expressed in energy terms. This article lays out the fundamental concepts of energy analysis.

In discussing energy analysis, it is important first of all to define energy. Energy is an abstraction, designed to account for the outstanding difference between the initial and final state of a system to which some change has occurred. We call this difference the energy content of the system. Energy exists in several different forms, and, when effecting change to a physical system, will generally shift between these forms. Kinetic energy is energy as applied in moving physical objects. Electromagnetic energy is applied to the vibrating modes of sub-atomic particles, and can be experienced as radio waves, visible light, x-rays, electric current, etc. Potential energy refers to energy stored in some form, capable of being released. A nickel-cadmium battery possesses chemical potential energy, capable of being released as electricity. Finally, heat is a form of energy, the form to which all other types of energy eventually degrade. Energy is governed by a set of physical laws, expressed last century in the discipline of thermodynamics. These are discussed briefly below.


The First Law of Thermodynamics states that energy can neither be created nor destroyed, within a closed system (defined as a system in which no energy or mass may enter or leave). Energy cannot be thrown away. In applying this law to an economic analysis, we must determine the extent to which the system of study is closed.

For example, the global economy is far from a closed system. There is a significant exchange of both matter and energy between it and the natural world. Even if we treat the economy and environment as a single system, there is a sizeable exchange of energy, mainly influx of solar radiation and re-emission of heat to space. Meteorites represent a small, arguably insignificant, transfer of matter between this system and its environment.

At a national level, the system is even more open. That is, the size of the matter and energy transfers is greater, relative to the overall system size. Nonetheless, the First Law contains important consequences for economic systems, providing an absolute physical limit on the availability of energy to a system, and the assimilation of "waste" energy and products. Of course, other more pressing limits, whether physical or social in origin, may impinge more directly on the system, meaning that those imposed by the First Law may not be reached.


The Second Law of Thermodynamics is more directly concerned with the process of transformation, rather than the natures of the initial and final states. As such, the consequences that it has upon an economic system are more pressing than those of the First Law.

The Second Law raises the question of energy quality. Energy cannot be created or destroyed, but it can be made more, or less, useful. That is, the work (in a rigorous physical sense) that can be done by that energy is more than simply a function of the energy content. In order to be able to discuss this, a second abstraction, called entropy, was developed.

Entropy is a measure of the degree of disorder in a system. For example, salt, with its highly regular lattice arrangement of atoms, has much less entropy than the same salt dissolved in water. A house has less entropy before the roof falls in than after. A marching band has less entropy when all dressed in uniform and marching in time than when relaxing in their homes afterwards. As a system's entropy increases, its degree of order, or information content, will decrease. This will not necessarily alter the energy content of the system, and hence a closed system may undergo changes in entropy content.

The Second Law states that, in effecting any change to a system, the overall level of entropy in the system will always increase. It is only possible to reduce the entropy of any part of a system by effecting a greater increase in the entropy elsewhere. For example, a rotting house may spontaneously collapse, but a reversal of the process (i.e. rebuilding the house) requires an external input of an energy resource, the entropy content of which is increased.

Some of the forms of energy discussed above are more entropic than others (that is, they are less ordered). Of these, heat has the highest entropy, and it is for this reason that all other forms of energy eventually disperse as heat. No transfer of energy is totally efficient, and the "lost" energy is usually dispersed as heat. Labelling the energy as "lost" is simply a value judgement. The energy is not destroyed, but is transformed into a form where it either cannot be, or simply is not, used by the economy. Of course, this distinction is essential in an economic analysis.

Examples of energy "loss" include the heating of machine parts through friction as they rub together, the heating up of electrical transmission wires, or the heat generated by a human, or animal, during physical exertion.


It has been calculated that the energy required to heat a bathtub of water from room temperature to 60 Centigrade is equivalent to the work exerted by a lumberjack working for approximately 19.5 hours (Slesser 1978). This comparison is made here in order to highlight the notion of energy quality. The hot bathtub consists of high entropy energy, the lumberjack's work of low entropy energy. Although the lumberjack and bathtub have equivalent energy contents, the lumberjack may use his/her energy to effect a larger amount of work.

Energy quality is reflected in the perceived economic value of the energy. In rugged pioneer country, offering to pay a lumberjack for a long day's work with a bathtub full of hot water would be poorly appreciated. To look at the situation the other way around, though, if one desired a hot bath, one would hardly go about it by hiring a lumberjack to stir the water for 19.5 hours. High quality energy is not necessarily more valuable than low quality energy in the economic context, but, in general, low quality energy is suited to a smaller number of uses.

In all modern economies, the energy exerted by the human workforce is negligible (Slesser 1978). The work equivalent of a lumberjack working for a full day can be purchased in the very high quality form of electricity for about 6 pence. The human workforce, even in "manual" labour, is employed primarily to make decisions rather than for the physical work it actually does.

The bulk of energy utilised by the global economy at present is in the form of three fossil fuels, namely oil, coal and natural gas. The energy qualities (thermodynamic availability) of these three are all very similar. Hence, substitution between them can be calculated accurately with reference only to the energy content. In ECCO this is the "reference energy quality", by which all other energies like electricity (higher quality) or biomass (lower quality) are measured.

For these reasons, a number of practical decisions have been made in the construction of the Irish ECCO model (and other ECCO models). Firstly, fossil fuels are measured solely in terms of energy content, and are assumed to be substitutable (unless explicitly stated otherwise in the model structure). Where we look at substituting fossil fuels and electricity, as in the heat pump or vehicular fuel cell technologies, explicit coefficients for commensurating the two are developed, generally from first principles or the engineering literature.

Secondly, electrical energy is measured separately, and any assumptions made about the substitution between thermal and electrical energy are based on empirical observations, not an equivalence between energy contents. Thirdly, other energy sources, such as nuclear fuels and renewable sources, are treated in terms of fossil fuel equivalents. As these sources are currently used only to generate electricity, that measure is made by equivalencing the inputs required per unit electrical output. These inputs are based on empirical data, i.e. current technological practice. All forms of electricity, generated from whatever source, are, of course, fully substitutable once entered onto the national grid.

These simplifying assumptions present no problem when examining the current technology of energy supply and demand. However, were radical energy policies, involving different qualities of energy carrier, to be explored by the model, the question of energy quality would have to be compiled in terms of the chosen reference qualities mentioned above.


Having provided a definition of energy, it is necessary to establish the reasons for adopting it as the numeraire for the ECCO model. After all, most economic statistics use money, and the adoption of an alternative involves a lot of extra work and inconvenience to the model builder.

Money, like energy, is a human invention, an abstraction designed to represent transactions in the messy real world in a neat, symbolic way. Money is an opinion. Or rather two opinions, that of the seller, and that of the buyer. The price of the good is arrived at by a process that "evenly distributes the disappointment", in the language of traditional economics.

Being an opinion, money has two disadvantages. Firstly, it is subject to change over time as a result of different perceptions of the world, which may or may not be grounded in reality. If they are not, then prediction of these perceptions is very difficult, if only because the cultural world is capable of changing much more rapidly than the physical world, and is harder to quantify.

The second disadvantage of money, as an opinion, is that it has no international standard. Each nation sets up its own currency, and the coefficients relating these (the exchange rates) vary considerably, and quickly. Further, money is applied somewhat arbitrarily to work in most modern economies. In an economic model using money as a numeraire, there is no method for accounting for voluntary or unpaid work, such as childraising and housework, or for work paid in kind (ie work paid for by other work).

Energy is also an abstraction, but one grounded in a more rigorous school of thought. Certainly, more than one unit for energy has enjoyed passing fashion; the calorie has been superseded by the joule over the last twenty or so years. The important distinction, though, is that there are international standards for energy units, due to the precise first-principles methods by which they are defined. Anywhere, at any time, one joule is capable of moving a weight of one Newton by a distance of one metre.

So, the "cost" of goods can be measured by considering the energy that went into their making. Note that this is not a valuation of the good, in that it does not consider the utility of that good to the system. It is simply a measure of the inconvenience that was undergone in the past to create that good, or, more generally, the inconvenience involved in replacing it.

This distinction is perhaps best clarified by illustration. To build an ocean liner would require an energy input of approximately 1.2 PetaJoules using current shipbuilding technologies. In other words, the embodied energy content of the liner would be 1.2 PJ. As a simplifying assumption, let us assume that shipbuilding technology has not altered greatly in the last thirty years, and the estimate of embodied energy is valid over that period.

During the last thirty years, however, air transport has increased in volume, and partially replaced sea transport. Hence, the demand for ocean liners has dropped, and the money-value of the liner has probably dropped too. This decline has not resulted directly from changes in shipbuilding technology, but from wider interactions within the transport sector and in social behaviour.

Hence, the money-value of a good is subject to a wide number of influences. Further, some of these are extremely difficult to quantify. The embodied energy numeraire, in contrast, is relatively unchanging. Thus, for the purposes of the ECCO study, the money numeraire is too unpredictable. For other types of economic analysis, however, this compaction of multiple unknowns into a single value, even through an imperfect market mechanism, may be highly attractive.

Energy, then, is not subject to the wild fluctuations that money experiences. Then again, neither is mass. Why not set up an accounting system based on the mass of goods?

The answer lies with the second law of thermodynamics, and a concept known as substitutability. Only through energy can one material be substituted for another. From the second law of thermodynamics it can be seen that as energy is used in the manufacturing process, in other words making something with a lesser degree of entropy than its constituent parts, the entropy of the energy used increases. Thus it cannot be used again: it is non-renewable.

This is not to say that energy is scarce - the solar flux impinging on the Earth's surface currently provides ten thousand times the energy used by all human activities. Were sufficient suitable human-made capital present to exploit this energy, then it would be capable of supplying human needs (or wants) practically indefinitely.

However, because energy use is irreversible, it places a real physical limit on the growth of economic systems, and in using energy as a numeraire we are explicitly facing this. In money-based economics, there is no such limit applied; money can be created by any government capable of operating a printing press. Thus money-based economics fails us in not recognising important, insurmountable limits to economic growth, and energy-based economics does not.

The other important property of energy is that it is unsubstitutable, meaning that no other physical resource is capable of performing the functions currently effected by energy. In this it is unique. Metals can be substituted by plastics or wood, ceramics by glass, etc. And, provided that sufficient energy is available, no other natural resource is ever depleted, it simply increases in entropy. The factors limiting the accessibility of highentropy resources lie with the ability of the economy to provide the capital and energy supplies needed to access them, not with an insuperable physical limit deriving directly from thermodynamic principles. In other words, the problem lies with distribution of finite capital and energy supply capacity within the economy.

In concluding this section, then, the ECCO methodology is concerned with addressing a particular economic issue, namely how a national or large-scale economy's growth rate is constrained by the physical limitations of its production processes, and how these physical processes underlie much of what we would normally classify as 'economic' factors. The methodology can be usefully applied in a wide variety of contexts, and works best when a narrow sectoral analysis is subsequently broadened out to incorporate linkages with other sectors, as in the case of the renewable energy study presented in this paper. In performing an analysis of these underlying processes, the choice of numeraire is important, as energy-based accounting provides an absolute yardstick that monetary numeraires cannot.

Two numeraires, money and embodied energy, have been examined here, in terms of their ability to express the nature of this problem. The money numeraire is discarded, because of its sensitivity to too many unquantifiable parameters, and its non-conservative nature. Embodied energy, in contrast, is shown to be well suited to this task, given the caveat that energy quality may need to be explicitly introduced in some unusual circumstances.


It might be useful to illustrate the application of energy analysis principles to the extraction of depletable energy resources namely oil, gas and coal. The ECCO model uses the same approach to all three. Firstly, it is assumed that a variety of grades of any particular resource exists and that the distribution of grades is log-normal, tailing off at the lower end towards the background level found in the Earth's crust. (With a log-normal distribution, if the cumulative amount of the resource already extracted is plotted on the x-axis of a graph using a linear scale, and the energy input required to extract one unit of the resource is plotted on the y-axis, using a logarithmic scale, a straight line results. This assumes that extraction takes place with the easiest resource first, progressing to the more difficult. Real life isn't always quite so logical, of course, but on the large scale the pattern has been shown to hold up quite well.)

The important characteristic of a natural resource reserve, in terms of the ECCO methodology, is the amount of energy, direct and indirect, that must be expended in extracting the resource from the ground. This aggregate value covers fuel and electricity demands, non-energy resource demands, and fixed capital consumption. In the case of an energy resource, this is known as the Energy Requirement for Energy, or ERE for short. It is expressed in units of energy input per unit energy extracted.

Obviously, the ERE of a resource reserve will depend upon the grade of the resource, in addition to other geological features, such as depth and hardness of covering rock. Because the grade of the reserve is variable, the ERE will also vary. This holds at any scale, from a single oil well to an entire set of fields, to global reserves of a resource. The exact relationship between resource grade and ERE is discussed more fully in Chapman (1983) but, as a simple assumption, we can assume an inverse relationship of some sort. In other words, as resource grade declines, the ERE will rise.

The final assumption made about the process of resource depletion is that the reserve is depleted in strict order of decreasing grade, i.e. highest grade first. This assumes perfect knowledge of the entire resource reserve before depletion commences, which is obviously fallacious. However, any individual discovery of a new high-grade pocket of resources will simply create a kink in the smooth log-normal decrease in grade observed under a "perfect" model, and will not upset the underlying behaviour of the model. The work of Peckham & Klitz (1978 & 1979) does show that the long-term trends described here operate in reality at a national level.

Because the resource grade declines log-normally, we can expect a log-normal increase in the ERE of the reserve, in the absence of technological change. The ERE of reserves can then be set as functions of cumulative extraction, and so will rise over time at a rate dependent on the rate of extraction from the reserve, which will itself depend on the economic policies being enacted.

Note that the above model does not postulate a cut-off point, at which the reserve runs out. Given suitable energy supplies, the reserve can be depleted down to the grade of the base rock. Of course, the economic consequences of securing such a large energy supply may well provide a cut-off point based on economic, rather than geological, constraints.

The above model structure has been compared to the model for land prices postulated by Ricardo, and, indeed, there is a degree of structural similarity. It is important to note the difference, however: Ricardo's increasing price with scarcity of the commodity arose from an increased valuation being placed upon remaining resources by the market, whereas the driver in the depletable resource model is based on physical variations in the Earth's crust.

Technological change, will, of course, alter the ERE of a given reserve, and, conversely, rising ERE may often provide a spur to developing new technologies. An example of this inter-relationship is the development of sub-sea satellite wells in the UK Continental Shelf, which allow small, high- ERE fields adjacent to large, well-developed fields, to be extracted with a significantly reduced capital input. To state things very broadly, technological change will tend to have a similar effect to the discovery of a new reserve pocket; it will create an anomaly in the smooth rise of the ERE curve, but will not alter the underlying behaviour.

Finally, it is worth mentioning the approach taken in the Irish ECCO model to imports of depletable reserves, such as fossil fuels and metals. The above model cannot be applied to global reserves in a national model, because the overall rate of extraction is not calculated at a global level. In this case, time-series data from a global ECCO model, GlobEcco, has been imported into the Irish ECCO model, using a business- as-usual scenario. Hence, it is assumed that domestic activities have no direct effect upon the world "energy price" of depletable resources.


Suppose that a large reserve of oil is discovered under a house, say 8634 barrels of crude oil. At $20 a barrel, the gross income anticipated is $172,000. Having taken some initial seismic readings, the owners discover that their oil reserve is perfectly cylindrical, with one metre diameter, and is located between 200 and 2200 metres below the ground. There is no gas associated with the oil, so it will be necessary to pump it out of the ground mechanically. This process will require energy. In addition, there will be the cost of buying the pump in the first place, and then the cost of refining the crude output.

Pumping begins, and everything goes well for a few days, then the oil stops coming. As oil is extracted, the level remaining in the well drops, until the remaining oil is too low down for the pump to be able to bring it to the surface. This is remedied by buying a larger, more powerful pump. A side effect of this is that the fuel bill increases; the larger pump requires more energy to bring each barrel of oil to the surface. Say, the small pump required one-fortieth of a barrel of oil per barrel extracted, the larger pump requires one twentieth. It is realised that this larger pump will fail in the future, as the level of oil in the well decreases further. To summarize, there is an energy gain in the form of extracted oil. Energy is spent by the pumps in terms of the fuel required to power them, and the devices for refining the oil. Furthermore, new capital is constantly required, in the form of larger pumps, as the reserves deplete. The manufacture of these pumps required energy; this is the embodied energy content of the machinery. Using the principles of process analysis exact figures can be calculated for the embodied energy, and primary energy (i.e. pump fuel) requirements of the extraction, as a function of the cumulative removal of the oil. By comparing this with the amount of energy extracted, the ERE can be calculated.

As demonstrated above, the ERE of the oil rises as more is extracted. Ultimately the ERE will reach 100%, and the net energy gain from the extraction process will be negative. At this point, the oil well will be physically uneconomic.

In a market economy, of course, the point at which the process becomes uneconomic may arrive earlier. With several wells in operation, all of different shapes, size and levels of extraction, the ones with lower ERE values will be at a competitive advantage, being able to produce their goods at a cheaper energy price. Given sufficient reliable data to calculate the ERE values of different oil-wells or fields it would be possible to predict the economic fates of oil producers without having to discuss (monetary) oil prices, which are subject to considerable fluctuations and uncertainties.


Campbell C (2002) "Limits on Supplies of Conventional Oil" talk given at the Conference Ireland's Transition to Renewable Energy, organised by FEASTA, October 2002

Chapman (1983) Energy Resources, London: Heinemann

Crane DC (1996) "Balancing Pollutant Emissions and Economic Growth in a Physically Conservative World" Ecological Economics 16: 257-68

Crane DC & Foran B (2000) "Modelling the Transition to a Biofuel Economy in Australia" Proceedings of second international workshop, Advances in Energy Studies: Exploring Supplies, Constraints and Strategies, Porto Venere, May 23-27, 2000: pp.23-39

Forrester JW (1971) World Dynamics, Massachusetts: Wright Allen Press.

Forrester JW (1968) Principles of Systems, Massachusetts: Wright Allen Press.

IFIAS (1975) Energy Analysis, Report #6 of the International Federation of Institutes for Advanced Studies

Meadows DL & Meadows DH, eds. (1973) Toward Global Equilibrium: Collected Papers, Massachusetts: Wright Allen Press.

Melman AG, Boot H & Gerritse G (1990) Energiebesparungspotentielen - 2015, TNO Eindrapport 90-258, 2nd. edition April 1991, Institut voor Milieu- en Energietechnologie (IMET)TNO

Peckham, R. & Klitz, K.,(1978) Energy Requirement of Scottish Offshore Oil, Research Paper EUR 6062 EN, EU Joint Research Centre, Ispra.

Prigogine N & Stengers I (1984) Order out of Chaos: Man's New Dialogue with Nature, London: Heinemann

Slesser, M. (1978) Energy in the economy, London: Macmillan.

Slesser M & King J (1993) "Can Solar Energy substitute for Oil? A natural capital accounting approach" Opec Review XVII, 3: 377-98

Slesser M., King J. & Crane D.C. (1997) The Management of Greed: A Bio-Physical Appraisal of Environmental and Economic Potential, Edinburgh: RUI Publishing

Slesser, M, King, J., Revie, C and Crane, D. (1994) Non-monetary indicators for managing sustainability. Contract report to DG XII of the European Community, Centre for Human Ecology, University of Edinburgh, Scotland


In addition to the conventional citations above, some resources used to develop the model, and pertaining to the model, are located on the internet. These are listed separately below. Central Statistics Office, Ireland website, from which a wide range of economic data can be downloaded in spreadsheet-readable format Dept. of Public Enterprise website, from which most of the energy data used to calibrate the model was originated. ECCO model website, containing further essays and resources regarding the ECCO model, and an experimental online simulator for a model of the UK. The simulation software is in active development as part of the 'Uncle Unc' software project at

. (The main purpose of Uncle Unc has relatively little to do with simulation models, and the connection to the ECCO models might not be obvious at first glance. Contact Dave Crane if clarification is required.)

ECCO model available

Those readers who would like to project Ireland's energy future on different assumptions to those used here may purchase the complete software from the Feasta office, 159, Lower Rathmines Road, Dublin 6. The price is 20 euros or £15 sterling. A user-group has been set up and purchasers will be able to download improvements to the software from the internet.

This is one of almost 50 chapters and articles in the 336-page large format book, Before the Wells Run Dry. Copies of the book are available for £9.95 from Green Books.

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