Net Energy


1. Introduction

One technique for evaluating energy systems is net energy analysis, which seeks to compare the amount of energy delivered to society by a technology to the total energy required to find, extract, process, deliver, and otherwise upgrade that energy to a socially useful form. Energy return on investment (EROI) is the ratio of energy delivered to energy costs (Figure N-1) (Cleveland et al., 1984; Hall et al., 1986; Gever et al., 1986). Biophysical and ecological economists argue that net energy analysis has several advantages over standard economic analysis (Gilliland, 1975; Hall et al., 1986). First, net energy analysis assesses the change in the physical scarcity of energy resources, and therefore is immune to the effects of market imperfections that distort monetary data. Second, because goods and services are produced from the conversion of energy into useful work, net energy is a measure of the potential to do useful work in economic systems. Third, EROI can be used to rank alternative energy supply technologies according to their potential abilities to do useful work in the economy. Most neoclassical economists reject methods of economic analysis that are not based on human preferences, arguing that net energy analysis does not generate useful information beyond that produced in a thorough economic analysis.

Below we discuss some important issues in net energy analysis, including methods for calculating energy costs and energy quality. We then apply the techniques in the assessment of the net energy return from oil and gas extraction in the U.S.

2. Energy and Natural Resource Availability

A natural resource is something that exists in nature which can be used by humans at current economic, technological, social, cultural and institutional conditions. Natural resources are highly concentrated collections of energy and materials relative to other sources that we do not use. If you walked out your back door with a shovel and starting digging a hole, after a few meters you would hit bedrock--the Earth's crust. If you chipped off a chunk of that rock, you would find tiny amounts of economically useful elements such as copper, lead, and phosphorous. In fact, you would find minute amounts of nearly all the 92 naturally occurring elements. But you couldn't set up a viable copper mine in your backyard, or in the vast majority of other locations on the Earth, because the concentrations of copper in those locations are too dilute. The overwhelming majority of copper is produced in a small handful of mines located in the southwestern United States, Canada, Zambia, and a few other locations where copper is highly concentrated.

Biogeochemical cycles produce natural resources by organizing materials and energy into forms that are easily accessible. Nonrenewable resources such as copper are scattered randomly and thinly in the Earth's crust and ocean. The average concentration of an element in the crust is called its crustal abundance. For most elements you would find only a few grams per metric ton of crust. In some areas, however, biogeochemical cycles concentrate metals, minerals and fuels several times greater than their crustal abundance. Rocks that contain high concentrations of metals and minerals metals are called ores. A kilogram of copper ore has 10 to 100 times more copper than the average rock (Table N-1). Mines are located where these unusually high concentrations exist.

Renewable natural resources also are characterized by a high degree of organization. Fish are found everywhere throughout the oceans, but fishing vessels do not randomly trawl the open ocean. The open ocean is a "biotic desert" because low rates of net primary production do not support a rich food chain. Oceanic circulation, wind patterns, and river runoff concentrate nutrients near coasts and in zones of upwelling. The average net primary production of upwelling zones is 225 grams of carbon per square meter per year; the open ocean averages just 57 grams per square meter per year (Table N-2). Coastal regions thus support a rich food chain where the concentration of fish can be 66,000 times greater than that in the open ocean. The vast majority of fish caught each year are taken from a small handful of coastal zone fisheries.

This higher degree of order or organization distinguishes natural resources from all other forms of energy and materials on the planet. Most of the world's agricultural output comes from regions where biogeochemical cycles have produced soil that is far richer in nutrients, water, and other biological important attributes compared to most of soil on the planet. Most of the world's timber is harvested from forest ecosystems that produce large, dense accumulations of stored carbon (wood), and most of the world's drinking water comes from lakes and reservoirs where the planet's morphology stores large quantities of fresh water before it returns to the sea.

2.a Environmental Energy Cost

The high concentration of energy and materials in natural resources is the result of work processes in the environment. Energy is required to produce a gradient, which is nothing more than a difference in the concentration of something compared to its average concentration. This means that energy is used to produced the high concentrations of fish, metals, and other energy and materials that form our natural resource base. Every natural resource thus has an environmental energy cost: the energy required to create a natural resource of a given concentration. There are two sources of environmental energy: solar energy and heat from the Earth's interior. These energies power environmental processes such as wind, rain, tides, primary production, the sedimentary cycle, etc. that create and sustain natural resources. For example, heat energy from the Earth's interior drives the crustal plates, uplifting mountain ranges that play a critical role in regional distribution of precipitation. That energy investment is part of the environmental energy cost of clean water produced by the hydrologic cycle. Solar energy and heat from the core drive the sedimentary cycle that produces the temperature and pressure necessary to transform and concentrate the carbon in dead plant material to a level many times its crustal abundance. This creates oil and coal. Unique combinations of solar energy and ocean currents combine to concentrate energy and nutrients in zones of upwelling that support high concentrations of fish.

More environmental energy must be used to concentrate a resource further away from its average concentration. Higher grade metal ores have much higher concentrations than their crustal abundance, and thus required significant environmental energy to create. For metals this is reflected by the Gibbs free energy of formation for different ores (Figure N-2). For example, three times more energy in the environment is used to produce a gram of iron in a 30% ore compared to a 5% ore.

2.b Economic Energy Costs

Without the work done by energy from the sun and the Earth's interior, there would be no natural resources as we know them. Energy and materials would be randomly distributed in the ocean, crust, and atmosphere at very low concentrations, making them economically and technologically impossible to use. But the work done by energy flows in the environment is only the first step in producing a good or service. Even the richest deposits of copper and the densest stands of timber require further processing before they are useful. Crude oil must be discovered, pumped to the surface and refined into gasoline. Timber must be felled and sawed into useful forms of lumber. Copper must be mined, concentrated and refined into pure copper metal pipes and wire.

An additional investment of energy is needed to concentrate, organize, or upgrade natural resources. This represents the economic energy cost of natural resources: the fossil and nuclear fuels required to locate, extract, refine and otherwise upgrade natural resources to useful raw materials. This work is done by the extractive sector of the economy. This industry includes the mining sector that extracts energy (oil, coal, natural gas), metals (copper, lead, iron) and non-metal minerals (phosphate, salt, sulfur); the forestry and fishery sectors that harvest wood and fish products, respectively; the agricultural sector that harvests crops and livestock as sources of food (grains and meat) and materials (leather and cotton), and utilities that collect water from surface and underground sources.

2.c Natural Resource Quality

Resource quality is defined by the amount of economic energy required to extract a natural resource. Low quality resources require more work (more energy) to extract and refine than high quality resources (Figure N-3). We can produce 99 percent pure copper metal from both 10 percent and 1 percent ore, but the leaner ore requires more energy to upgrade. A lot of energy is needed to crush very lean ores and separate the valuable atoms of metal from the "waste" rock it is part of. The same principle applies to all natural resources. Fish in small, remote populations require more energy to locate and harvest. Growing food in soil with low concentrations of nutrients requires more energy than it does with fertile soil.

There is a tradeoff between environmental energy cost and economic energy cost for many natural resources (Figure N-4). Natural resources with high environmental energy costs have low economic energy cost. The more work done by biogeochemical cycles to create a natural resource, the less work the extractive sector must do to upgrade it to a useful form. For example, the crustal abundance of copper is 50 grams per metric ton. This amounts to about 0.007% by weight of the crust. The concentration of the copper into a piece of metal wire that is 99.9% pure copper requires significantly more economic energy when it starts with a leaner ore.

Resource quality is important because of the pattern in which humans use natural resources. The best first principle states that humans use the highest quality sources of natural resources first. Given a choice, humans will grow crops on fertile (high quality) soil before infertile (low quality) soil. Humans use deposits of copper that are 5 percent pure metal rather than 1 percent pure metal, and deposits of oil that are 1,000 feet deep rather than 10,000 feet deep. Humans harvest timber from forests that are close to a sawmill before forests that are a long distance from the mills. Humans catch fish from large, highly concentrated schools in coastal waters before they harvest smaller, more random collections of fish in the open ocean. As the high quality sources are depleted, lower quality sources must be used. High quality sources require less effort to obtain than low quality resources, so depletion makes it harder and harder to obtain resources.

Differences in resource quality affect the economy via opportunity costs. Opportunity cost is equal to the goods and services that cannot be produced because energy is used elsewhere to produce an alternative good or service. For example, energy used to harvest timber or mine copper cannot be used to heat your home. High quality resources have a lower opportunity cost than lower quality resources. Using ores that are 1 percent copper leaves the economic system with more energy use produce other goods or services compared to using 0.1 percent ores (Figure N-4). Similarly, harvesting fish from productive upwelling zones rather than the open ocean leaves more energy left over to produce other goods and services.

The U.S. Geological Survey characterized all the geologic provinces in the world according to their petroleum volumes (Klett, et al, 1997). Each geologic province is a spatial entity with common geologic attributes. World-wide, 406 geologic provinces were identified that contain some known petroleum volume. The geologic provinces were then ranked by total known petroleum volume in millions of barrels of oil equivalent (MMBOE) within the province. Exclusive of the U. S., the 76 largest geologic provinces in terms of petroleum volume contain 95% of the world's total known petroleum volumes. The 10 largest provinces alone-just 2.5 percent of the total-contain more than half the of planet's petroleum (Figure N-5).

The distribution of oil in the United States shows the same distribution pattern where large fields that account for less than one percent of all fields contain more than 40 percent of all the oil illustrates (Nehring, 1981). The pattern of utilization of this oil illustrates the connections among resource quality, the best first principle and opportunity costs. The average field discovered around the turn of the century contained 20 to 40 million barrels of oil, and the largest contained several billion barrels (Figure N-6). But as the use of oil increased, the big, high quality deposits of oil were discovered and depleted. Today, the average field discovered contains less than 1 million barrels. The decline in quality of oil resources greatly increased the work required to find and extract oil. The cost to discover a barrel of oil in the early part of the century was less than $1.00 per barrel--today it is more than $15.00 per barrel (Figure N-7) (Cleveland, 1991).

Many fisheries exhibit a similar pattern of development. High quality accumulations of fish are concentrated in upwelling zones near the coast. These populations are targeted first for development, and often are over-exploited. As the density of fish declines due to over-fishing, fishers must exert more effort to catch the same quantity of fish. A prime example of this is George's Bank, a shallow upwelling region off the coast of Massachusetts that once supported one of the most fertile fishing grounds in the United States. Too many fishing vessels catching too many fish for too many years severely reduced the abundance of important species such as cod and flounder. As a result, fishing vessels have to stay out at sea longer and travel farther distances to catch the same amount of fish. The average trip length per fishing vessel increased from 9 to 13 days over the past several decades; some vessels must travel as far away as the Carolinas to find fish. The decline in quality of the fishery has caused the energy cost of ton of fish to skyrocket (Figure N-8) (Mitchell and Cleveland, 1993).

3. EROI as a Measure of Energy Availability

One measure which has been proposed as a physical representation of natural resource availability is the quantity of energy used to make an additional unit of a resource available to society (Lovering, 1969; Brobst and Pratt, 1974; Page and Creasy, 1975; Cook, 1976; Cleveland et al., 1984; Gever et al., 1986; Hall et al., 1986; Ruth, 1993; Peet, 1993). From this perspective, the availability of an energy resource such as petroleum could be viewed in terms of the quantity of energy used to explore for, develop, extract, refine, and transport a unit of petroleum energy to society. One way to quantify such energy costs is the energy return on investment (EROI) (Figure N-1), which is defined as


Energy here is defined as the physical ability to do useful work, where useful work is done when a body is moved by a force. The physical ability to do work is represented by the enthalpy of the fuel, so the numerator and denominator typically is measured in heat units such as Btus, joules, etc. The convention of measuring and aggregating energy by its heat content is discussed in detail below.

A common related concept is the energy payback period (Figure N-9). Every energy system has initial investments of energy in the construction of facilities. The facility then produced an energy out for a number of years until it reaches the end of its effective lifetime. Along the way. Along the way, additional energy costs are incurred in the operation and maintenance of the facility, including any self use of energy. An example of the latter is the natural gas produced by a gas well that is then used to pump more gas out of the ground, or the electricity from a power plant that is used to run the computers and lights in the plant. The energy payback period is the time it takes a facility "pay back" or produce an amount of energy equivalent to that invested in its start-up.

3.a How "Physical" a Measure is EROI?

The EROI is a physical measure of scarcity in the sense that it is defined in physical units, i.e. BTUs. However, it is not a "pure" physical measure because it is not independent of economic, political, and institutional influences. A "pure" physical index, if such a thing exists, would be a function of only physical phenomenon. For example, the laws of thermodynamics instruct us that there is a minimum, irreducible quantity of energy required to lift a barrel of oil to the surface. Given the distance to the surface and the mass of a barrel of oil, the theoretical minimum energy cost of producing that barrel could be calculated. In reality, of course, the actual energy cost of production is greater than that theoretical minimum due to a variety of physical and non-physical factors. It is impossible to precisely identify and quantify all those factors, or to unequivocally categorize them as either physical or economic factors. Certainly a significant determinant of actual energy costs are physical factors. For example, a critical determinant of the quantity of energy required to lift a barrel is its depth of burial (Funk and Anderson, 1985).

Other physical factors influencing per barrel energy costs are type of formation, porosity, permeability, and water:oil ratios. However, non-physical factors also influence energy costs. For example, the price of oil, both absolute and relative to other fuels, influence the amount of effort devoted to oil development production and would therefore affect the energy required to perform those tasks. Environmental regulations such as those requiring subsurface disposal of harmful chemicals used in oil production affect energy costs. Political decisions such as those governing drilling in the Arctic National Wildlife Range and offshore California affect energy costs.

Thus, it is apparent that the energy costs of petroleum development and production are in part physical manifestations of economic, political, and institutional factors, and in part manifestations of changes in the quality of the resource base itself. To the degree that it is influenced by non-physical factors, the EROI is not a "pure" physical measure. Sorting out the physical factors from the non-physical ones is difficult, if not impossible. At one level, the decision to drill in the Arctic National Wildlife Range is politically driven, but at another level physical factors such as depletion of high quality, low cost deposits in Oklahoma and Texas prompted the need to even consider drilling in the Wildlife Range.

Is the effect on energy costs of that decision to drill physically or non-physically driven? Environmental Protection Agency regulations governing disposal of chemicals used in enhanced recovery operations are political and technological decisions, but declining reservoir pressure and permeability first create the need for enhanced recovery techniques to be employed. Is the energy cost of waste disposal physically or non-physically driven? It should also be noted that the same line of reasoning could be applied to economic measures such as prices which are too often assumed to be driven by purely "market forces." Clearly there is a physical component to many market forces.

3.b The Importance of Energy Surplus

Because the production of goods and services is a work process, economies with access to higher EROI fuel sources have greater potential for economic expansion and/or diversification (Cottrell, 1955; Odum, 1971; Hall, et al., 1986). Cottrell (1955) describes how the history of the expansion of human civilization and its material standard of living is directly linked to, but not caused by, successive access to and development of fuel sources with increasingly greater EROI. The transitions from animate energy sources such as plant biomass, and draft animals, to wind and water power, to fossil fuels and electricity enabled increases in per capita output due to increases in the quantity of fuel available to produce non-energy goods. The transition to higher EROI fuels also enabled social and economic diversification as increasingly less available energy was used in the energy securing process, meaning more fuel was available to support non-extractive activities. Cottrell (1955) and White (1949) also argued that much of inter- and intra- society conflicts can in fact be traced to struggles for control over the disposition of energy surplus.

4. Energy Versus Economic Analysis 1

The energy events of the 1970's raised the issue of whether economic measures such as price or cost accurately captured all the relevant features of an energy supply process. Economists generally argue that, by definition, the price of a fuel automatically captures all such relevant features. Yet, a strong case can be made that the standard economic approach to measuring the economic usefulness of a fuel yields one type of information and only partially informs us about all relevant aspects of resource quality. Net energy analysis, through the calculation of EROI, informs us about some of those other qualities, such as the potential for a fuel source to yield useful energy to the rest of the economy. Such qualities may or may not be reflected in a fuel's price. As Peet et al. (1987, p. 240) stated:

...we believe the conventional economic perception of the 'value' of primary energy resources is incomplete and potentially misleading, in that it does not adequately take account of the factors which constrain a society's ability to obtain useful consumer energy from such sources.

In part because it rejects economic measures of value as necessary and sufficient expressions of resource quality, net energy analysis has been a very controversial analytical tool, generating vigorous and sometimes acrimonious exchanges between net energy analysis practitioners and economists. The debate between net energy analysts and economists became a very heated one for several reasons. One reason is that many economists viewed net energy analysis as another physical model of scarcity which, like the classical economic scarcity model and The Limits to Growth physical models, is obviously inferior to the neoclassical view of scarcity. Many grandiose and unsubstantiated claims were made about the immunity net energy analysis enjoyed from many of the problems facing economic analysis, making it a superior decision-making tool (e.g. Gilliland, 1975). Some energy analysts proposed a theory of economic and social value based on energy (Odum, 1971, 1977; Hannon, 1973; Costanza, 1980, 1981) which economists were quick to criticize.

Economists naturally, and quite justifiably in some cases, reacted very strongly to some of the extreme claims made by some energy analysis. Economists questioned the assumptions and methods of net energy calculations as well as the usefulness of net energy results for energy and economic policy. At the same time, many critics rejected net energy analysis in it's entirety based on the reasonableness of claims made by some energy analysts which were not shared by energy analysts in general. In the process, the nuts and bolts of net energy analysis and it's usefulness in assessing resource quality escaped the objective discussion it deserved. A review of this literature also indicates that some economists engaged in the net energy debate lacked sufficient knowledge of basic ecological and thermodynamic principles to accurately judge the assumptions and methods of net energy analysis, much less its conclusions. Due to this lack of knowledge and to the perceived threat of net energy analysis as a purported replacement for economic analysis, some economists criticized and rejected net energy analysis on the basis of claims never made by its practitioners.

4.a Energy Analysis and Policymaking

Given 25 years of hindsight, it is useful to review the net energy analysis debate. Much of this debate is a matter of public record (2), some of which is reviewed in Hall et al. (1986).

Net energy analysts promote their discipline using a range of arguments. Gilliland (1975) argued that compared with economic analysis, net energy analysis of alternative energy technologies can provide more information of a less conflicting nature to policy makers. Similarly, the Government Accounting Office (GAO, 1982) argued that the strength of net energy analysis is that it gives policy makers the opportunity to consider the EROI of an energy technology independent of it's profit potential and other financial considerations. Participants at a conference devoted to the critique of net energy analysis concluded that it was a useful tool where market imperfections distorted dollar values (IFIAS, 1978). It was also argued that net energy analysis was useful for technology evaluation, particularly in the identification of potential areas for energy conservation. Bullard (1976) made an analogy between net energy analysis and environmental impact statements, arguing that quantitative assessments of the impact of new technologies may provide information to policy makers in the same way the environmental impact statements address external effects not adequately dealt with in the market. Chapman et al. (1974) cited three reasons why net energy analysis of energy technologies is desirable. First, the energy processing sectors of most industrial nations use significant portions of total national energy use and therefore offer a significant potential for energy conservation. Second, waste heat production from fossil fuel conversion poses a major hazard to local and global climate. Third, it is essential to know the energy costs of energy itself in order to assess the energy costs of other goods and services.

Net energy analysis proponents argue that one advantage it holds over economic analysis is that it is not plagued by many of the problems facing monetary analyses. Energy analysts have argued that inflation, subsidies, regulations, uncertainty about future prices and discount rates, and other market imperfections prevent monetary analyses from making consistently accurate assessments of energy technologies (Gilliland, 1975; Slesser, 1977; Cleveland and Costanza, 1984). Others are concerned that subsidies to some energy technologies can prevent the market from detecting whether a fuel is at or near the energy break-even point (Chambers et al., 1979; Herendeen et al., 1979). Herendeen (1986) argued that net energy analysis is particularly important for highly touted technologies such as gasohol and the solar power satellite which are subsidized with tax dollars and do appear to be near the energy break-even point.

Other energy analysts have argued because it is based on dollar profitability, economic cost-benefit analysis cannot accurately measure the direct and indirect energy inputs to a process, something net energy analysis was designed to do (GAO, 1982). A detailed understanding of the direct and indirect energy costs of energy production is critical to Federal decisions on funding competing energy technologies. Energy analysts argue that this quality gives their models a significant advantage over economic analysis in the effort to evaluate future energy supply and demand. As Slesser (1977, p. 261) stated

Because of a better handle on the future energy requirements for production, as opposed to discounted money costs of production, energy analysis gives a faster signal of impending change. Where energy analysis can be of immense value is in normative forecasting, hence its value to technology assessment and demand forecasting.

Many economists have rejected these claims made by energy analysts. For example, critics have rejected Gilliland's (1975) sweeping claim that the results of net energy analysis do not change when dollar values change due to inflation or changes in the discount rate (Webb and Pearce, 1975; Huettner, 1977; Allesio, 1981). Critics argue that net energy results are sensitive to market circumstances, and therefore subject to change over time just like monetary analyses. Thus, net energy analysis may not be a better allocator of resources where market imperfections exist. Critics point out that EROI calculations are market determined to the degree that they depend on the technology, industry structure, discount rate, and prices that exist at the time. Changes in any of those factors will undoubtedly alter the energy costs of goods, and thereby alter the results of net energy analysis. As Huettner (1976, p. 104) argues

A net energy analysis of a specific technology, such as the present nuclear fuel cycle and its supporting techniques, depends on the prices, discount rates, and other market conditions existing at the time it was made. As prices change through time, the energy content of steel, copper, cement, and all other inputs used in the nuclear fuel cycle are likely to change because of substitution effects, even if there is no change in technology and market structure.
4.b Net Energy Analysis as a Normative Technique

Many critics of net energy analysis have erroneously assumed that all practitioners believe in an energy theory of value (Webb and Pearce, 1975; Hyman, 1980; Alessio,1981). Some energy analysts have proposed an energy theory of value, where the value of goods and services are assumed to related to the direct and indirect energy embodied in them (Odum, 1977; Costanza, 1980, 1981). Costanza (1980) has offered empirical evidence for an embodied energy theory of value. It is safe to say, however, that the vast majority of net energy analysts reject an energy theory of value while embracing the usefulness of net energy calculations, and also argue that the usefulness of net energy analysis does not hinge on whether or not an energy theory of value is "valid". Most energy analysts view net energy analysis as a complement to the results of standard economic analysis, which is always subject to varying degrees of uncertainty and error (Bullard, 1976; Common, 1977; Cleveland et al., 1984; Proops, 1985).

Nevertheless, some critics argue that net energy analysis should be judged by whether or not its conclusions have normative implications (Webb and Pearce, 1975; Hyman, 1980). Having constructed their own straw man, such critics reject net energy analysis because it is a mechanistic tool void of any real value content. Hyman (1980), for example, states that net energy has no connection to social welfare, therefore net energy analysis is not a useful policy tool since it doesn't help satisfy human wants. Similarly, Webb and Pearce (1975) argue that net energy analysis cannot be used, for example, to rank alternative energy technologies because such a procedure requires the specification of an objective function, a normative issue net energy analysis is not equipped to deal with, unless an energy theory of value is assumed. The usefulness of net energy analysis does not depend on its normative value in the sense implied by the aforementioned critics. Resolution of questions such as whether society is maximizing a net energy objective function or whether an energy theory of value is valid is irrelevant to the issue of whether net energy analysis is useful in the overall assessment of resource quality. A more relevant test is whether net energy analysis yields any unique and useful information about the economic usefulness of a fuel which cannot be obtained from other types of analysis. The fact that society is not maximizing a net energy function is not legitimate grounds for dismissing net energy analysis as a useful input to an overall decision-making process.

There are no right or wrong answers to these issues, making it impossible to state just how "physical" a measure the EROI is, or how "economic" prices are. The important point is that any analysis which posits to bridge the two approaches should explicitly recognize and consider their different assumptions and value judgements. EROI emphasizes the physical underpinnings of scarcity, while acknowledging the importance of economic factors. It implicitly assumes that changes in the energy cost of energy have important economic implications that may or may not be reflected in prices.

The economic significance of the EROI does not hinge on the existence or nonexistence of a causal link between changes in the EROI and changes in the structure and direction of change in the economy. Such a relationship or any other form of "energetic determinism" has been neither demonstrated nor argued for here. Social and cultural factors merit equal consideration. For example, both Cottrell (1955) and Cook (1976) described how many societies rejected the opportunity to adopt a higher EROI fuel source because such a transition threatened existing social patterns to the degree that sufficient opposition prevented that transition. Human factors, however, have dominated the development of our perspective of the relationship between nature and society since at least the Industrial Revolution, and in particular have influenced how we describe and measure the economic impacts of changes in resource quality. A balanced view of these issues requires an understanding of the physical framework in which all human ideas, institutions, and aspirations must operate.

5. Methods of Net Energy Analysis 3

Net energy analysis seeks to assess the direct and indirect energy required to produce a unit of energy. Direct energy is the fuel or electricity used directly in the extraction or generation of a unit of energy. An example is the natural gas burned in engines that pump oil to the surface. Indirect energy is the energy used elsewhere in the economy to produce the goods and services used to extract or generate energy. An example is the energy used to manufacture the drilling rig used to find oil. The direct and indirect energy use is called embodied energy. Both the energy product and the embodied energy can be expressed in common physical units of measurement, such as Btus.

What follows is a general, non-technical discussion of how to do net energy analysis. For a more detailed discussion of net energy methodology, see the paper by Bullard et al (1978).

5.a The Energy Cost of the Factors of Production

To calculate the energy cost of energy, or for that matter any good or service, we must be able to quantify in energy terms the fuel, capital, materials, and labor used in the extraction and processing of the energy in question. The energy equivalents of the factors of production can be calculated in one of several rather straightforward methods to be discussed shortly, using readily available data on annual flows of fuels and other materials through the economy.

5.a.i Fuel

The energy costs associated with a fuel have two components: the quantity of energy released on combustion (enthalpy) and the energy required to extract, process, and deliver it to the customer. The first component is called the chemical energy of the fuel and usually is measured by the heat given off by combusting the fuel. For example, a 42-gal barrel of refined crude oil releases approximately 1.5 million kcal of heat when combusted.

The second component of energy consists of processing energy, the energy used by an energy transformation process to secure additional energy supplies. The sum of all such processing energies is the embodied energy cost of a fuel. The embodied energy in a barrel of oil includes the energies required to produce and operate drilling rigs, pipelines, and refineries, as well as the energies used to house and support the geophysicists and other individuals who work in the oil business.

It is important to note that a fuel's embodied energy is not a thermodynamic property of that fuel. Rather, it is an accounting procedure that measures the direct plus indirect energy content of fuel. When a fuel is combusted only the potential energy stored in its chemical bonds is able to do economic work. Nevertheless both the embodied energy of a fuel and its heat o combustion are energy costs of commodities whose production requires the combustion of fuel.

5.a.ii Capital

Capital can be viewed as economic energy invested in machines and tools that replace or empower human labor, thereby making workers more productive and, ultimately, allowing for higher wages. Capital can be used to do economic work that is difficult and/or dangerous for human labor to do alone. Capital also can be used to reduce the quantity of time, fuel, or labor used to produce a good or to provide a service. The energy equivalent of a unit of capital equipment normally is calculated as the quantity of fuel energy used to produce and maintain it. Alternatively, the energy cost of capital can be thought of as the fuel energy or labor energy saved by capital equipment at the margin (Baumol and Wolf, 1981).

The energy required to produce a dollar's worth of capital equipment for a given industry is calculated by summing all the fuel used to produce each year's new capital according to the appropriate standard industrial classifications. For example, in 1979 SIC sector 3553 used 3.1 trillion kcal of fuel (at both the site of manufacture and embodied in the materials it purchased from other sectors) to produce $727 million worth of woodworking machinery. There were therefore 426,4 kcal of fuel embodied in each dollar's worth of woodworking machinery produced in 1979. If a particular industry purchased $1 million of this type of machinery, the embodied energy of that equipment would be about 4.3 billion kcal.

The economic usefulness of capital tends to diminish as it wears out, requiring increasing amounts of energy to maintain and repair it. Eventually, capital equipment becomes so worn out that it must be discarded altogether. The rate at which capital depreciates or becomes less useful is not constant but depends in part on the rate at which the capital is used to do economic work, the type of work it performs, and the rate at which it is economically efficient to replace. Although a piece of capital continues to degrade even when idle, the rate at which it wears out increases as its rate of doing economic work increases.

Energy analysts often assume that capital degrades at a constant rate and that this rate is caused by, and spread evenly over, each unit produced by a machine. Based on this assumption, one method for estimating the embodied energy in capital used to produce a good or service is to divide the total energy cost of capital used in production by the number or value of goods and services that the capital produces over its lifetime. This ratio is the quantity of embodied energy used to produce one unit of a good or service. Unfortunately this procedure would be difficult or tedious for every piece of capital.

A second method used in most energy analyses assumes that capital is replaced at a more or less constant rate. The monetary value of the capital "used up" or depreciated each year, converted to its energy equivalent, is an estimate of the energy cost of capital.

5.a.iii Human Labor

Some analysts view labor as just another input that has direct and indirect energy costs of production. Households produce and support human labor just as firms produce capital. In doing so households invest energy and other resources to produce and maintain labor in its economic role Therefore, labor also has an energy cost associated with its use. These energy costs can be separated into three components: (1) the caloric value of the food the worker consumes, (2) the embodied energy of that food (i.e., the direct plus indirect fuel used to produce food), and (3) the fuel purchased with the wages and salaries of labor. Obviously, there are important differences between human labor and other factors, but this does not alter the fact that labor requires a continuous input of energy to sustain itself.

The biological energy equivalent of labor is the fuel burned when human labor does mechanical work. This quantity of fuel can be measured directly by a respirometer, a device that measures the rate at which oxygen is combined with food to produce carbon dioxide and work. The amount of fuel used depends in part on the type of work being done. For example, a person doing desk work uses about 71 kcal/hr whereas a manual laborer uses about twice that quantity.

A comprehensive analysis of the energy equivalent of labor would include the economic energy required to grow the food metabolized by the worker. The U.S food system uses large amounts of fossil fuels and electricity to grow, harvest, transport, market and prepare food (Steinhart and Steinhart, 1974; Pimentel and Pimentel, 1996; Cleveland, 19xx). Based on this use of fuel, the embodied energy cost of food used by human labor could be estimated as the quantity of fuel used to grow and distribute the amount of food consumed by each person: 1354 kcal/hr based on the average American's diet of 3400 kcal/day in 1980. Some methods for energy cost accounting have used this biological measure as the energy equivalent of human labor (see Odum, 1971).

A still more comprehensive assessment of the energy cost of labor would account for all the direct and indirect uses of fuel that are used to produce the goods and services a worker buys with his or her paycheck. This is a measure of the energy cost of producing and maintaining labor in the household sector. This method overestimates the energy cost of labor because it assumes that all the energy used to support a laborer's paycheck is necessary to produce and maintain the laborer in his or her economic role. Certainly there is a portion of almost everyone's income that, if taken away, would not reduce his or her ability to perform on the job (although it would certainly make the laborer less well off). Equally as certain, however, a portion of wages and salaries exists beyond that required for basic needs (food, shelter, clothing) that, if removed, would diminish a laborer's economic performance. For example, a business woman must receive a salary sufficient to cover the costs of food, shelter, and clothing for her and her family to survive. She also needs enough income to purchase transportation to and from her job. She may also subscribe to several journals in order to stay abreast of advances in her particular field. The reader can see that the list could be expanded substantially.

Suffice it to say that a portion, and probably a substantial portion, of the energy represented by a laborer's paycheck is a necessary and unavoidable energy cost of producing labor. And, as most businesses recognize, if skilled labor is to be secured for one's own business, competitive wages must be paid, requiring a substantial portion of the nation's total energy resource toward giving meaning to those paychecks.

When calculating the energy costs of goods and services, the energy cost of labor should not include all the fuel and nonfuel goods and services bought by a worker's paycheck because hiring a new worker does not always create new demands for goods and services. It may instead only increase existing demand—that is. people buy fuel and nonfuel goods and services whether they are employed or not. The impact of a new worker on the demand for fuel, which is implicit in the demand for goods, can be estimated by examining the energy used to support an employed laborer versus an unemployed laborer. For example, in 1979 the medium income of families in the United States with one employed wage earner was $15,607, whereas the medium income of $7648 for households with no wage earner was 49% less. Although the percentage of income spent on direct versus indirect purchases of fuel varies with income, a rough approximation is that the employed earner used about 51% more fuel and bought 51% more goods and services than did an unemployed laborer. Based on this assumption the energy cost to society of having an average new laborer can be estimated as 51% of the fuel represented by all dollar purchases of that employed laborer. Since some new jobs are filled not by unemployed workers but by individuals who change jobs, the estimate for the energy equivalent of labor must be corrected for employment levels.

Some analysts have argued that labor should not be assigned an energy cost (Slesser, 1985), while others argue that like all factors of production, labor has energy costs associated with its production and maintenance which need to be included in net energy analysis (Costanza, 1980). The difficulty centers in part on what portion of the total energy used by labor should be included as an energy cost. Should the energy equivalent of a laborer's entire paycheck be included, or just that portion necessary to support labor in its economic role? If one chooses the latter option, then what energy use by labor is "necessary" to maintain labor as factor of production? Such decisions are arbitrary and can produce very large differences in estimates of the energy costs of goods or services.

By modifying the models used by Bullard and Herendeen (1975), Costanza (1980) calculated the energy costs of goods and services in the U.S. with an estimate of the energy cost of labor and government services. The energy costs of goods increase substantially because Costanza's model allocates the energy equivalent of labor's entire income to goods produced by labor. To calculate the energy costs of labor, Costanza modified the boundaries of the input-output model used by Bullard and Herendeen (1975) to include labor and government energy costs. Consumption of GNP by households was assumed to be a necessary cost of producing and maintaining labor as a factor of production. In GNP accounting terms, the energy equivalent of personal consumption expenditures represent the energy cost of labor. With labor and government made endogenous to the input-output model, the only major output of Costanza's revised "economy" was gross capital formation. Although it was not explicitly stated, an underlying assumption made by Costanza was that the primary "purpose" of economic activity was to increase capital stocks. This is quite a different assumption from the conventional definition of GNP which has consumption expenditures, government services and net exports as outputs as well as investment. Because of the different value judgements used to define system boundaries, Costanza's estimates of the energy costs of goods and services are not directly comparable to energy intensities calculated using conventional GNP definitions (e.g. Bullard and Herendeen, 1975). Although labor does have energy costs associated with it, Costanza's method overestimates those costs by counting all of labors' income as an energy cost. More importantly, his calculations are derived from a model of the economy that is radically different than the one which generates most economic data.

5.a.iv Environmental Services

Most energy analysts ignore the energy costs of environmental services used in the energy supply process. In this regard energy analysis fares no better than economic analysis. Herendeen (1986) argued that the theory and techniques to estimate the energy costs of environmental services are not sufficiently developed to stand the test of self- consistency, completeness, and coherence. Net energy analyses which have attempted to incorporate estimates of the energy costs of degraded environmental services have used very aggregated estimates that have errors of unknown type and magnitude (Lavine et al., 1982; Cleveland and Costanza, 1984).

A notable exception to this is Odum's (1996) eMergy analysis. This method calculates the amount of one type of energy required to produce a heat equivalent of another type of energy. To account for the difference in quality of thermal equivalents among different energies, all energy costs are measured in solar emjoules (SEJ), the quantity of solar energy used to produce another type of energy. Odum's method is extremely comprehensive in that it attempts to account for every physical flow of energy and material that supports a given economic activity. As such, it attempts to aggregate disparate energy and material flows into single numeraire that indicates the quantity of environmental support associated with economic activity. As we develop below, however, there are serious conceptual and methodological problems that plague eMergy analysis and thereby limit its usefulness as a tool to analyze economy-environment interactions.

5.b Joint Products

The problem of allocating joint costs is as difficult in net energy analysis as it is in economic analysis. The problem is difficult for two jointly produced fuels such as oil and gas, but is even more intractable when a fuel is jointly produced with a non-fuel. For example, uranium is a byproduct of phosphate mining in Florida, and the conversion of shale oil to a liquid fuel also produces sulfur and ammonia. The net energy analyst is thus confronted with choosing a system to allocate jointly incurred costs amongst various joint products. Any joint cost allocation scheme, even those based on "reasonable" assumptions about the system in question, is ultimately arbitrary, and the choice of allocation methods can have significant impacts on EROI calculations. For example, ethanol production from grain produces crop residues as a byproduct of the harvesting process, and a feed byproduct in the distillation stage. The crop residues are potential fuel source, and the feed byproduct can be used as a fuel or as a foodstuff for cattle. Chambers et al. (1979) showed that the EROI for ethanol production was sensitive to the method used to allocate joint costs.

A variety of joint cost allocation schemes have been proposed by energy analysts (Chapman et al., 1974; Leach, 1975):

1)Assign all energy costs to the principal output.

2)Assign energy costs so that each product has the same energy cost per dollar value.

3)Assign energy costs on a weight basis so each product has the same energy cost per ton.

4)Assign energy costs on a calorific basis so each product has the same energy cost per BTU.

The first method is the easiest and embodies a strong value judgement about the purpose of the process, for example that crude oil is much more valuable to the firm or to the society than natural gas and therefore should be assigned all production costs. The second method is dangerous because prices change frequently over time and may be different to different users of energy. Allocation by weights is attractive because it is physically based, but could lead to the illogical result of an energy cost of a product being less than it's true calorific value.

Chapman et al. (1974) argued that allocation according to the enthalpies of the byproducts is the only "physically sensible" approach. Leach (1975), however, noted that this method is not suitable in the case of fuel and nonfuel byproducts such as uranium and phosphate. When applied to the joint production of oil and gas, this approach assumes that a BTU of crude oil requires the same amount of energy to lift as natural gas. By its nature, however, natural gas is much less energy-intensive to lift than a liquid such as crude oil, and in certain circumstances provides energy to help lift oil out of a reservoir. In the EROI model developed in the next chapter, an alternative method of allocating joint oil and gas production costs will be developed based on such physical differences.

5.c Energy Discounting

Is a BTU of crude oil extracted today worth the same to society as a BTU produced 10 years from today? The heating value of oil would be the same, but it is possible that its economic usefulness will change as a function of a variety of economic, social, institutional, and technological factors. Critics of net energy analysis have charged that net energy analysis is not a useful policy tool because it assumes that all BTU's produced or conserved over time have the same utility to society (Webb and Pearce, 1975; Hyman, 1980). Such critics have argued that people prefer present use of energy over future use in a manner similar to the way they are assumed to discount dollar values. A frequently cited example of this problem is the use of the energy payback period in which the quantity calculated is the length of time an energy system (e.g. a power plant) takes to produce as much energy as was required for that system's construction. By not discounting energy costs and benefits, some net energy analysts have assumed that society is indifferent between two facilities that have equivalent EROI's, but one facility pays back its energy costs in the first few years while the other takes ten years (Webb and Pearce, 1975).

Since there is no a priori reason to believe that users of energy don't discount energy like they discount dollars, certain types of net energy analyses may be justifiably criticized for not addressing the issue of discounting. On the other hand, if future alternative fuels are of lower quality than petroleum, the last barrels of petroleum produced may be more valuable than those currently being used. It should be noted, however, that despite its widespread use, there is not a consensus amongst economists about what the appropriate discount is, or if discounting nonrenewable resources maximizes the rate of resource use in the present at the expense of the welfare of future generations (Page, 1977).

Hannon (1981) employed a standard continuous discounting function in EROI calculations for various energy systems. Hannon defined that discount rate as the mechanism by which society implicitly expresses its desire to convert a present surplus of energy into an energy supply process to insure future supplies of that energy, rather than consuming that energy now for purposes such as home heating and leisure living. Hannon found that different energy systems had different discount factors associated with them. Not surprisingly, using an energy discount rate in EROI calculations had the largest impact on energy systems such as nuclear power and the solar- powered satellite which require large capital (and hence indirect energy) outlay before energy delivery begins.

5.d Methods of Energy Cost Accounting

There are two general methods of calculating the embodied energy cost of goods and services: process analysis and input-output analysis. Both process and input-output analyses condense the use of energy in production into two general types: fuel burned at the site of energy extraction (direct fuel use), and fuel burned in other sectors to produce the materials purchased and used as inputs at the site of extraction (indirect fuel use). Process analysis and energy input-output analysis, and variants of each, differ in the way the flow of material is traced through the extraction process, the types of energy costs included in the analysis (e.g., just fuel, or fuel, capital, and labor), and the energy equivalents assigned to the three factors of production. As a result, the methods give somewhat different values for embodied energy even when applied to the same set of data.

5.d.i Process Analysis

In theory, process analysis provides the most detailed information on the energy cost of goods and services. There are several practical problems, however, such as data limitations, that effectively limit its applicability. Process analysis assesses the energy used directly in each successive step of the production of a good or service. Depending on the data available, energy requirements may be calculated per unit mass or per dollar value of the input. Consider Figure N-10, which depicts schematically how the energy cost of producing a power plant might be calculated by the process analysis approach. The same general format would apply to any energy system.

Direct energy costs of a power plant refer to the fuel burned at the site of production— diesel fuel burned by cement trucks, electricity and gas used by welders, and so on. Indirect energy costs are those incurred in the production of the steel, cement, and other raw materials. Going one step further, indirect energy costs also include the energy used to make the structural steel and mine the iron ore used to build the power plant. This leads to one of the problems with process energy analysis, namely, where does one draw the system boundary? This is referred to as the truncation problem because there is no standard procedure for determining when energy costs become small enough to neglect.

5.d.ii Energy Input-Output Analysis

The energy input-output approach is more comprehensive than process analysis and is analogous to and derived from the input-output matrix used in standard economic analyses. Herendeen and Bullard (1975), Hannon et al. (1981), and others at the Energy Research Group the University of Illinois modified the economic input-output tables that are based on dollar flows to energy input-output tables based on embodied energy flows between industries. The input-output table breaks the economy into about 400 different sectors. The numbers in the table represent the quantity of direct plus indirect energy that each industry purchases from all other sectors in order to manufacture its product. Combined with the dollar flows between industries, the energy intensity factor (Btu/$) of each good service can be calculated (Figure N-11). These results give a comprehensive and reasonably accurate representation of both the direct and indirect energies used to manufacture a product. The input-output approach does not suffer from the truncation problem of process analysis.

Hall et al. (1979a, b) modified the energy input output analysis so that they did not need to specify the specific upstream sector(s) from which a sect producing final goods purchased materials. Instead, their method is based on a very aggregated estimate of the energy embodied in the intermediate goods at the site of final manufacture.

Costanza (1980) modified the boundaries of the traditional input-output tables so that fuel energy (including solar energy) would be the only net input to the economy, with labor and government classified as internal transactions within the economic system and gross capital formation as the principal output. Costanza estimated the quantity of fuel energy used to support labor and government services-as well as that used directly for production-and divided this amount of fuel use by employee compensation and indirect business taxes to estimate the energy used to support a dollar's worth of labor and government service, respectively. Double counting was avoided by constraining the analysis to use only actual total energy use. In other words the energy used directly by labor was included, but not the energy embodied in goods and services purchased by labor.

For an excellent discussion and technical explanation of these methods, see Bullard et al. (1978) and Spreng (199_).

6. Energy Aggregation and Energy Quality

The calculation of the EROI and its variants reflects the desire to arrive at a single number for a system's performance. But to do so the analyst must add up and compare many different forms of energy. For example an energy system such as petroleum extraction yields three different forms of energy: crude oil, natural gas, and natural gas liquids. Figure N-12 demonstrates this for petroleum extraction in the U.S. in 1997. In turn, the extraction process is powered by a range of fuels: gasoline, distillate and residual fuels, natural gas, electricity and small amounts of other fuels (Figure N-13). When measured in thermal units, crude oil accounts for 38 percent of energy extraction, yet oil products account for just 15 percent of energy used in the extraction industry Furthermore, the oil products used in the extraction process (gasoline, distillate and residual fuels) have been refined, making them qualitatively very different from crude oil. Another important difference is that electricity and coal are used in extraction, but are absent from the outputs of extraction.

This raises a critical question in energy analysis: how does one aggregate forms of energy with disparate attributes? The simplest and most common form of aggregation, is addition by thermal equivalents (BTUs, joules etc):


where E represents the thermal equivalent of fuel i (N types) at time t. The advantage of the thermal equivalent approach is that it uses a simple and well-defined accounting system based on the conservation of energy, and the fact that thermal equivalents are easily and uncontroversially measured. This approach underlies most methods of energy aggregation in economics and ecology, such as trophic dynamics (Odum, 1957), national energy accounting (EIA, 2000), energy input-output modeling in economies (Bullard et al., 1978) and ecosystems (Hannon, 1973), most analyses of the energy/GDP relationship (e.g. Kraft and Kraft, 1978) and energy efficiency, and most net energy analyses (Chambers et al., 1979).

6.a Defining Energy Quality

Despite its widespread use, aggregating different energy types by their heat units embodies a serious flaw: it ignores qualitative differences among energy vectors. Here we must be explicit about what we mean by energy quality. We define energy quality as the relative economic usefulness per heat equivalent unit of different fuels and electricity (Kaufmann, 1994; Cleveland et al., 2000). Thus, the essence of energy quality is not derived entirely from a fuel's physical, thermodynamic or engineering attributes, nor entirely by people's preferences as expressed in the market. Rather, the quality of energy us defined by at the nexus of how a fuel's physical, thermodynamic or engineering attributes affect its usefulness to people, and, in turn, how people value the services derived from the use of energy.

Schurr and Netschert (1960) were among the first to recognize the economic importance of energy quality. Noting that the composition of energy use changes significantly over time Schurr and Netschert argue that the general shift to higher quality fuels affects how much energy is required to produce GNP. The quality of electricity has received considerable attention in terms of its effect on the productivity of labor and capital and on the quantity of energy required to produce a unit of GDP (Schurr and Netschert, 1960; Jorgenson, 1986; Devine, 1986; Rosenberg, 1998). Less attention has been paid to the quality of other fuels, and few studies use a quality-weighting scheme in empirical analysis of energy use.

Taking energy quality into account in energy aggregation requires more advanced forms of aggregation. Some of these forms are based on concepts developed in the energy analysis literature such as exergy or emergy analysis. These methods take the following form:


where the l's are quality factors that may vary among fuels and over time for individual fuels. In the most general case that, an aggregate index can be represented as:


where f( ) and g( ) are functions, lit are weights, the Eit are the N different energy vectors and Et is the aggregate energy index in period t. An example of this type of indexing is the discrete Divisia Index or Tornquist-Theil Index described below.

6.b Economic Approaches to Energy Quality

From an economic perspective, the value of a heat equivalent of fuel is determined by its price. Price-taking consumers and producers set marginal utilities and products of the different energy vectors equal to their market prices. These prices and their marginal productivities and utilities are set simultaneously in general equilibrium. The value marginal product of a fuel in production is the marginal increase in the quantity of a good or service produced by the use of one additional heat unit of fuel multiplied by the price of that good or service. We can also think of the value of the marginal product of a fuel in household production.

The marginal product of a fuel is determined in part by a complex set of attributes unique to each fuel such as physical scarcity, capacity to do useful work, energy density, cleanliness, amenability to storage, safety, flexibility of use, cost of conversion, and so on. But the marginal product is not uniquely fixed by these attributes. Rather, the energy vector's marginal product varies according to the activities in which it is used, how much and what form of capital, labor, and materials it is used in conjunction with, and how much energy is used in each application. As the price rises due to changes on the supply- side, users can reduce their use of that form of energy in each activity, increase the amount and sophistication of capital or labor used in conjunction with the fuel, or stop using that form of energy for lower value activities. All these actions raise the marginal productivity of the fuel. When capital stocks have to be adjusted, this response may be somewhat sluggish and lead to lags between price changes and changes in the value marginal product.

The heat equivalent of a fuel is just one of the attributes of the fuel and ignores the context in which the fuel is used, and thus cannot explain, for example, why a thermal equivalent of oil is more useful in many tasks than is a heat equivalent of coal (Adams and Miovic, 1968; Mitchell, 1974; Webb and Pearce, 1975). In addition to attributes of the fuel, marginal product also depends on the state of technology, the level of other inputs, and other factors. According to neoclassical theory, the price per heat equivalent of fuel should equal its value marginal product, and, therefore, represent its economic usefulness. In theory, the market price of a fuel reflects the myriad factors that determine the economic usefulness of a fuel from the perspective of the end-user.

Consistent with this perspective, the price per heat equivalent of fuel varies substantially among fuel types (Table N-3). The different prices demonstrate that end-users are concerned with attributes other than heat content. As Berndt (1978) states:

Because of [the] variation in attributes among energy types, the various fuels and electricity are less than perfectly substitutable - either in production or consumption. For example, from the point of view of the end-user, a Btu of coal is not perfectly substitutable with a Btu of electricity; since the electricity is cleaner, lighter, and of higher quality, most end-users are willing to pay a premium price per Btu of electricity. However, coal and electricity are substitutable to a limited extent, since if the premium price for electricity were too high, a substantial number of industrial users might switch to coal. Alternatively, if only heat content mattered and if all energy types were then perfectly substitutable, the market would tend to price all energy types at the same price per Btu (p. 242).

Do market signals (i.e. prices) accurately reflect the marginal product of inputs? Kaufmann (1994) investigates this question in an empirical analysis of the relation between relative marginal product and price in US energy markets. To do so, he estimates a reduced form of a production function that represents how the fraction of total energy use from coal, oil, natural gas, and primary electricity (electricity from hydro and nuclear sources) affects the quantity of energy required to produce a given level of output. The partial derivatives of the production function with respect to each of the fuels gives the marginal product of individual fuels, in which marginal product is defined as the change in economic output given a change in the use of a heat unit of an individual fuel. The equations are used to calculate the marginal product for each fuel type for each year between 1955 and 1992. The time series for marginal products are compared among fuels, and these ratios are related to relative prices using a partial adjustment model. The results indicate that there is a long run relation between relative marginal product and relative price, and that several years of adjustment are needed to bring this relation into equilibrium. The results are summarized in Table N-4, and suggest that over time prices do reflect the marginal product - and hence the economic usefulness - of fuels.

Other analysts calculate the average product of fuels, which is a close proxy for marginal products. Adams and Miovic (1968) estimate a pooled annual cross-sectional regression model of industrial output as a function of fuel use in seven European economies from 1950 to 1962. Their results indicate that petroleum is 1.6 to 2.7 times more productive than coal in producing industrial output. Electricity is 2.7 to 14.3 times more productive than coal. Using a regression model of the energy/GDP ratio in the U.S., Cleveland et al. (1984) find that the quality factors of petroleum and electricity relative to coal were 1.9 and 18.3, respectively.

6.b.i Price-Based Aggregation

If marginal product is related to its price, energy quality can be measured by using the price of fuels to weight their heat equivalents. The simplest approach defines the weighting factor (l's) as:


where Pit is the price per Btu of fuel. In this case, the price of each fuel is measured relative to the price of fuel type 1. Turvey and Nobay (1965) use equation N-4 to aggregate fuel use in the UK.

The quality index in equation N-4 embodies a restrictive assumption - that fuels are perfect substitutes - and the index is sensitive to the choice of numeraire (Berndt, 1978; Stern, 1993). Because fuels are not perfect substitutes, a rise in the price of one fuel relative to the price of output will not be matched by equal changes in the prices of the other fuels relative to the price of output. For example, the rise in oil prices in 1979- 80 would cause an aggregate energy index which uses oil as the numeraire to fall dramatically. An index that uses coal as the numeraire would show a large fall in 1968- 74, one not indicated by the oil-based index.

To avoid dependence on a numeraire, Berndt (1978, 1990) proposed a discrete approximation to the Divisia index to aggregate energy. The formula for constructing the discrete Divisia index E* is :


where P are the prices of the n fuels, and E are the quantities of BTU for each fuel in final energy use. Note that prices enter the Divisia index via cost or expenditure shares. The Divisia index permits variable substitution among material types without imposing a priori restrictions on the degree of substitution (Diewert, 1976). Diewert (1976) shows that this index is an exact index number representation of the linear homogeneous translog production function where fuels are homothetically weakly separable as a group from the other factors of production. With reference to equation N-3

f( ) = g( ) = Dln( ),

while lit is given by the average cost share over the two periods of the differencing operation.

Aggregation using price has its shortcomings. Lau (1982) suggests that prices provide a reasonable method of aggregation if the aggregate cost function is homothetically separable in the raw material input prices. This means that the elasticity of substitution between different fuels is not a function of the quantities of non-fuel inputs used. This may be an unrealistic assumption in some cases. Also, the Divisia index assumes that the substitution possibilities among all fuel types and output are equal. It is well-known that energy prices do not reflect their full social cost due to a number of market imperfections. This is particularly true for the environmental impact caused by their extraction and use. These problems lead some to doubt the usefulness of price as the basis for any indicator of sustainability (Hall, 1990; Odum, 1996). But with or without externalities, prices should reflect productivities. Internalizing externalities will shift energy use, which, in turn, will then change marginal products.

Moreover, prices produce a ranking of fuels (Table N-3) that is consistent with our intuition and with previous empirical research (Schurr and Netschert, 1960; Adams and Miovic, 1968; Cleveland et al., 1984; Kaufmann, 1991). One can conclude that government policy, regulations, cartels and externalities explain some of the price differentials among fuels, but certainly not the substantial ranges that exist. More fundamentally, price differentials are explained by differences in attributes such as physical scarcity, capacity to do useful work, energy density, cleanliness, amenability to storage, safety, flexibility of use, cost of conversion, and so on. Wipe away the market imperfections and the price per BTU of different energies would vary due to the different combinations of attributes that determine their economic usefulness. The different prices per BTU indicate that users are interested in attributes other than heat content.

6.b.ii The eMergy Approach to Aggregation

Odum (1996) and his colleagues (Odum and Odum, 1983; Odum et al., 1987; Odum, 1988; Huang and Odum, 1991) analyze energy and materials with a system that traces their flows within and between society and the environment. It is important to differentiate between two aspects of Odum's contribution. The first is his development of a biophysically-based, systems-oriented model of the relationship between society and the environment. Here Odum's (1971; Odum and Odum, 1976) early contributions helped lay the foundation for the biophysical analysis of energy and material flows, an area of research that forms part of the intellectual backbone of ecological economics (Martinez-Alier, 1987; Krishnan, et al., 1995; Costanza et al, 1997). The insight from this part of Odum's work is illustrated by the fact that ideas he emphasized- energy and material flows, feedbacks, hierarchies, thresholds, time lags-are key concepts of the analysis of sustainability in a variety of disciplines.

The second aspect of Odum's work, which we are concerned with here, is a specific empirical issue: the identification, measurement, and aggregation of energy inputs to the economy. Emergy (with an "m") analysis is a pure cost-of-production approach that measures the quality of a particular type of energy by its transformity. Transformity is the amount of one type of energy required to produce a heat equivalent of another type of energy. To account for the difference in quality of thermal equivalents among different energies, all energy costs are measured in solar emjoules (SEJ), the quantity of solar energy used to produce another type of energy. Fuels with higher transformities require larger amounts of sunlight for their production and therefore are more economically useful (Odum, 1988).

Odum's method of calculating transformities assesses the efficiency of the sequence of energy conversions that produce a thermal equivalent of fuel. That sequence has two components: environmental energy conversions and industrial energy conversions. The basis for these calculations is the production of electricity in a wood-fired power plant (Odum and Odum, 1983). The principal environmental energy conversion is the solar energy required to produce a heat equivalent of wood in the standing stock of the forest: 3.23*104 SEJ of sunlight are required to produce one joule of standing wood. The sunlight embodied in the wood undergoes a series of energy conversions in the economy (harvest, transport, combustion, etc.) that generate a joule of electricity. The generation of each heat unit of electricity requires 1.59*105 SEJ. The transformities for coal, oil, and natural gas are based on a series of calculations that assess the efficiency of converting coal to electricity, crude oil to refined fuel, and the efficiency of coal relative to natural gas as a boiler fuel.

This approach raises a fundamental question about the appropriateness of transformities to reflect energy quality: Is the usefulness of a fuel as an input to production related to its transformity? Probably not. Users value coal based on it heat content, sulfur content, cost of transportation and other factors that form the complex set of attributes that determine its usefulness relative to other fuels. It is hard to imagine how this set of attributes is in general related to-much less determined by-the amount of embodied emergy. Similarly, any differences in the economically useful attributes of coals laid down 500 or 100 million years ago are not determined by the enormous differences in their embodied emergies. Thus, while Odum's method provides a useful framework for highlighting he important role the environment plays in generating energy and material resources, it is of dubious value in comparing and aggregating energy flows in economic applications.

In addition to this conceptual issue, there are computational problems with emergy analysis that make transformities incomplete indicators of energy quality. The calculation and application of transformities are time, location, and technology specific, yet Odum and his colleagues mix the temporal, spatial, and technical scales of their analysis in ways that are poorly defined. First, Odum presents the transformities as constants, but based on the method used to calculate them (Odum and Odum, 1983), the transformities are clearly dynamic because they are based on the first law efficiency of technologies such as power plants, coal liquefaction, and oil refineries. The efficiency of those technologies have changed dramatically over time. Second, the emergy calculations also contain an ad hoc mixture of spatial scales. The basis for the calculation of the transformities is the thermal efficiency of a wood-fired power plant in Brazil, but the efficiency of power plants vary throughout the world (Smil,1991) as do all the other energy conversion technologies used in the emergy calculations. Similarly, energy/output data from the New Zealand economy are mixed with the Brazil power plant data to calculate the transformities, which are then applied to many other economies throughout the world (Odum and Odum, 1983; Odum et al., 1987; Odum and Arding, 1990; Huang and Odum, 1991). Third, the values of the transformities are highly sensitive to technological assumptions made by Odum and Odum (1983). They calculate the relative quality of oil, gas, and coal based in part on the fact that the first law thermal efficiency of converting natural gas in boilers is 20 percent more efficient than the conversion of coal. However, the relative thermal efficiency of fuels varies with the task they perform (Adams and Miovic, 1968). The transformities would change, and hence the estimate of relative fuel qualities, if a different task were used for comparing the thermal efficiency of fuel conversion.

6.b.iii The Exergy Approach to Aggregation

Exergy analysis is based on the second law of thermodynamics that describes the change in the quality of energy that accompanies its conversion from one form to another. Exergy therefore accounts for physical quality differences among different forms of energy. Exergy is the maximum amount of physical work that can be extracted from a given flow of energy. Exergy is calculated by multiplying the heat equivalent of a fuel or heat source by the appropriate Carnot factor [1-(Ta/To)], where Ta and To are the ambient temperature and output temperature of the process, respectively, measured on the Kelvin scale. Note that energy quality in exergy analysis is defined in concise thermodynamic terms: the potential to do mechanical work. Mechanical drive and electricity are rated the highest in the exergy hierarchy of energy quality because of the theoretical capacity of those sources to be transformed into useful work with 100 percent efficiency. The exergy approach accounts for the important reduction in quality (ability to do work) that accompanies the conversion of energy from one form to another, and is typically applied to individual processes or technologies (Cleveland and Herendeen, 1989; Schilizzi, 1987).

Ayres et al. (1996) and Ayres and Martiñas (1995) propose a system of aggregating energy and materials based on exergy. Exergy measures the useful work obtainable from an energy source or material, and is based on the chemical energy embodied in the material or energy based on its physical organization relative to a reference state. Thus, exergy measures the degree to which a material is organized relative a random assemblage of material found at an average concentration in the crust, ocean or atmosphere. The higher the degree of concentration, the higher the exergy content. The physical units for exergy are the same as for energy or heat, namely kilocalories, joules, BTUs, etc. For fossil fuels, exergy is nearly equivalent to the standard heat of combustion; for other materials specific calculations are needed that depend on the details of the assumed conversion process.

Ayres argues that exergy has a number of useful attributes for aggregating heterogeneous energy and materials. Exergy is a property of all energy and materials and in principle can be calculated from information in handbooks of chemistry and physics (e.g. Linde 1991-1992) and secondary studies (e.g. Szargut et al. 1988). Thus, exergy can be used to measure and aggregate natural resource inputs as well as wastes. For these reasons, Ayres argues that exergy forms the basis for a comprehensive resource accounting framework that could "provide policy-makers with a valuable set of indicators." One such indicator is a general measure of "technical efficiency," the efficiency with which "raw" exergy from animals or inanimate source is converted into final services. A low exergy efficiency implies potential for efficiency gains for converting energy and materials into goods and services. Similarly, the ratio of exergy embodied in material wastes to exergy embodied in resource inputs is the "most general measure of pollution" (Ayres, et al. 1996). Ayres and Martiñas (1995) also argue that the exergy of waste streams is a proxy for their potential ecotoxicity or harm to the environment, at least in general terms.

Cleveland and Herendeen (1988) used exergy in their EROI calculations for solar parabolic trough energy systems, which produce heat at temperatures ranging from 50° to 350° C. A standard EROI calculation treats heat produced at the lower temperature as qualitatively the same as heat at higher temperatures, despite the fact that higher temperature heat has greater potential to do work. Cleveland and Herendeen corrected for this quality difference by multiplying the EROI by a Carnot factor which incorporates thermodynamic quality. While the correction procedure was crude, it did demonstrate how fuel quality differences can be incorporated into an EROI analysis.

From an accounting perspective, exergy is appealing because it is based on the science and laws of thermodynamics and thus has a well-established system of concepts, rules, and information that are available widely. But like enthalpy, exergy should not be used to aggregate energy and material inputs aggregation because it is one-dimensional. Like enthalpy, exergy does not vary with, and hence does not necessarily reflect attributes of fuels that determine their economic usefulness, such as energy density, cleanliness, cost of conversion, and so on. The same is true for materials. Exergy cannot explain, for example, impact resistance, heat resistance, corrosion resistance, stiffness, space maintenance, conductivity, strength, ductility, or other properties of metals that determine their usefulness. Like prices, exergy does not reflect all the environmental costs of fuel use. The exergy of coal, for example, does not reflect coal's contribution to global warming or its impact on human health relative to say natural gas. As Ayres (1997) himself notes, the exergy of wastes is at best a rough first-order approximation of environmental impact because it does not vary with the specific attributes of a waste material and its receiving environment that cause harm to organisms or that disrupt biogeochemical cycles. In theory exergy can be calculated for any energy or material, but in practice, the task of assessing the hundreds (thousands?) of primary and intermediate energy and material flows in an economy is daunting.

To summarize, emergy and exergy are not appropriate to aggregate energy in an economic analysis because they are one-dimensional. Like enthalpy, exergy and emergy do not vary with, and hence do not necessarily reflect attributes of fuels that determine their economic usefulness, such as energy density, cleanliness, cost of conversion, and so on.

7. Application to Petroleum Extraction in the U.S.

The EROI for petroleum and coal is calculated at the extraction stage of the resource transformation process. Only industrial energies are evaluated: the fossil fuel and electricity used directly and indirectly to extract petroleum. The costs include only those energies used to locate and extract petroleum and prepare it for shipment from the lease. Transportation and refining costs are excluded from this analysis.

Crude oil, natural gas, and natural gas liquids are extracted by Standard Industrial Code sector 13, "Oil and gas extraction," which includes several subsectors. The oil and gas extraction industry includes firms that explore for oil and gas, drill oil and gas wells, operate and maintain oil field properties that produce oil and gas, and all other activities in the preparation of oil and gas up to the point of shipment from the producing property. Sector 13 also includes firms engaged in producing liquid hydrocarbons (natural gas liquids) from oil and gas field gases. Output in the petroleum industry is the sum of the marketed production of crude oil and natural gas.

7.a Direct Energy Costs

The direct energy cost of extracting petroleum is the fuel and electricity used in oil and gas fields. These data are from the Census of Mineral Industries which reports the quantities of fuel and electricity used in the petroleum sector at five year intervals from 1954 to 1997. The fuels used are coal, crude oil, natural gas, and refined liquid fuels such as gasoline, residual, and distillate fuel. The electricity data reported by the Census include purchased electricity and electricity generated by captive fuel use. I exclude self- generated electricity because including it would double count the fuels used to generate it. I have modified the Census data to correct for reporting errors and omissions based on fuel use data from other sources and from conversations with the Census staff (Cleveland, 1988).

Fuel use in years not covered by a Census is estimated with a technique used to construct the National Energy Accounts. For Census years, energy intensities for each fuel are defined as the quantity of fuel used per constant dollar of GNP originating in sector 12 or 13. The data on GDP are published annually in the National Income and Product Accounts of the United States. Linear interpolation between Census years is used to estimate the energy intensities non-Census years. Fuel use in non-Census years is estimated by multiplying the estimated energy intensity times real GDP.

7.b Indirect Energy Costs

Indirect energy is the energy used in the economy to produce material inputs and to produce and maintain the capital used to extract petroleum and coal. The indirect energy cost of materials and capital is calculated with data on the dollar cost of those inputs to the petroleum and coal extraction processes. The dollar value of material inputs is from the Census of Mineral Industries. Materials include the purchase of chemicals, wood products, steel mill shapes and forms, and other supplies "used up" each year in the coal and petroleum industries. The dollar value of capital inputs is from the National Income and Product Accounts of the United States. Capital use is approximated by the dollar value of capital depreciation in SIC sector 13. Capital depreciation is not an ideal measure of capital input because it reflects financial variables in addition to actual physical depreciation. However, capital depreciation is the only aggregate measure of capital input for the petroleum industry, and despite its shortcomings it serves as an approximate indicator of the trend in capital use over time.

The indirect energy cost of capital and materials is defined as the dollar cost of capital and materials times the energy intensity of capital and materials (BTU/$). The energy intensity of capital and materials is measured by the quantity of energy used to produce a dollar's worth of output in the industrial sector of the U.S. economy. (4) That quantity is the ratio of fossil fuel and electricity use to real GNP produced by industry (Department of Energy, 2000; Bureau of Economic Analysis, various years). The energy/GNP ratio is an aggregate measure of the energy cost of producing a dollar's worth of industrial output.

7.c Construction of the EROI

Two indexes are constructed for the EROI from petroleum extraction. The first is the thermal equivalent EROI, which defined as:


where Eo and Ec are the energy output and input, respectively, of energy type n at time t, measured in thermal equivalents. The quantity Ec is the sum of direct and indirect energy inputs to the energy system. equation N-6 is the technique used in the vast majority of net energy analyses.

Following the definitions in equation N-2, a quality-corrected EROI* is defined by:


whereli,t is the quality factor for fuel type i at time t and Eo and Ec are the thermal equivalents of energy outputs and energy inputs, respectively. Divisia indices are constructed for energy inputs and outputs to account for energy quality in the numerator and denominator. The prices for energy outputs (oil, natural gas, natural gas liquids) and energy inputs (natural gas, gasoline, distillate fuels, coal, electricity) are the prices paid by industrial end-users for each energy type (Department of Energy, 2000).

7.d Results

The thermal equivalent and Divisia EROI for petroleum extraction show the same general pattern: a rise to a maximum in the early 1970s, a sharp decline throughout the 1970s, a recovery in the 1980s, and then another modest decline in the 1990s (Figure N-14).

Beyond this, there are important differences between the two indexes. The Divisia EROI is consistently much lower than the thermal equivalent EROI. The principal reason for this is the difference in the fuel mix, and hence fuel quality, between the numerator and denominator of the EROI. The outputs are the crude, unprocessed forms of oil and natural gas. The inputs are electricity and refined fuels such as gasoline and other distillate fuels. The latter are higher quality than the former, and have higher prices. Refined fuels and electricity are, therefore, weighted more heavily in the Divisia formulation.

The Divisia EROI declines faster and to a greater extent than the thermal-equivalent EROI. In 1997 the Divisia ERIO is 42 percent lower than its maximum in 1972; the thermal equivalent EROI is 28 percent lower than its maximum. In 1997 the thermal- equivalent EROI is 1.6 times the Divisia EROI than it was in 1954. Again this is due to largely by changes in the mix of fuels qualities in energy inputs and energy outputs. Electricity, the highest quality fuel, is an energy inputs but not an energy output. Its share of total energy use rises from 2 to 12 percent over the period; its cost share increases from 20 to 30 percent. Thus, in absolute terms the denominator in the Divisia EROI is weighted more heavily than in the thermal equivalent EROI. On the output side, crude oil is a higher quality fuel than natural gas, as reflected in its higher price per Btu. However, on a thermal equivalent basis, the share of oil in the output of the industry steadily falls from about 56 percent in 1954 to about 38 percent in 1997.

7.e Discussion

Energy return on investment is derived from the biophysical model of resource scarcity (Hall et al., 1986; Gever et al., 1986; Cleveland, 1991). The biophysical manifestation of scarcity is the use of increasing amounts of natural capital to deliver a unit of resource to society. Energy frequently is used to reflect and measure such costs (e.g., Folke, 1988, Chapman and Roberts, 1983). In general, there is inverse relation between resource quality and energy costs. A decline in the quality of the natural resource base due to cumulative depletion, an increase in the instantaneous rate of exploitation, or an increase in the scale of extraction, increases the amount of energy used to extract a unit of natural resource.

The decline in the EROI for petroleum extraction in the U.S. suggests that depletion has raised the energy costs of extraction. There is no single measure of the quality of the oil and gas resource, but a number of such indicators describe its physical deterioration. On the discovery side, one indicator is the average size of new discoveries. Here we find that the average oil field has declined in size from 20-40 million barrels in the 1930s to less than 1 million barrels today (Figure N-6). The new discoveries, are ,on average, found at greater depth that in the past. The average depth of new exploratory wells has increased from about 3,000 feet in the 1930s to more than 6,000 today.

Petroleum reservoirs have natural mechanisms that drive oil from the reservoir rock into the well bore. As cumulative extraction proceeds, the natural drive mechanism is depleted and must be replaced by human-directed energies in "secondary recovery" operations. Waterflooding is a common form of secondary recovery in which water is injected into an oil reservoir to force additional oil out of the reservoir rock. Enhanced oil recovery (EOR) is used when depletion makes secondary recovery unfeasible, and EOR is extremely energy-intensive. EOR methods such as chemical flooding uses a mixture of water and polymers, surfactants, or inorganic alkaline chemicals that reduce the forces that trap oil in the reservoir. Thermal methods such as steamflooding add heat to the reservoir and reduce the viscosity of oil. Production from EOR projects now accounts for about 12 percent of total U.S. oil production (Figure N-15). Upward pressure on overall costs also has been applied by actions required to prevent or mitigate environmental degradation (Bohi, 1999).

Opposing these effects are technological, organizational and institutional changes that have worked to reduce costs in the industry. There is no research that identifies the effects of these changes on energy use per se, but we do know something about their effect on overall costs of exploration, development and production (Bohi, 1999). On the technology front, 3D seismology, horizontal drilling and deepwater production systems have put strong downward pressure on costs in the past 15 years. Cost savings also have been realized through the adoption of new management techniques, a shift in the mix of independent and major firms, and an increased reliance on outsourcing for services. On balance, however, the effects of these changes on the energy cost of extraction have been outweighed by the depletion effects, producing a decline in the EROI.

As defined by the Department of Energy (2000), the industrial sector includes agriculture, forestry, fisheries, mining, construction, and all manufacturing industries.