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A General Mathematical Framework for Calculating Systems Energies 2011, 4, 1211-1245; doi:10.3390/en4081211 OPEN ACCESS energies ISSN 1996-1073 www.mdpi.com/journal/energies Article A General Mathematical Framework for Calculating Systems-Scale Efficiency of Energy Extraction and Conversion: Energy Return on Investment (EROI) and Other Energy Return Ratios Adam R. Brandt 1;? and Michael Dale 2 1 Department of Energy Resources Engineering, Stanford University, Stanford, CA 94305, USA 2 Global Climate and Energy Project (GCEP), Stanford University, Stanford, CA 94305, USA; E-Mail: [email protected] ? Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +1-650-724-8251; Fax: +1-650-723-9091. Received: 14 April 2011; in revised form: 29 July 2011 / Accepted: 17 August 2011 / Published: 19 August 2011 Abstract: The efficiencies of energy extraction and conversion systems are typically expressed using energy return ratios (ERRs) such as the net energy ratio (NER) or energy return on investment (EROI). A lack of a general mathematical framework prevents inter-comparison of NER/EROI estimates between authors: methods used are not standardized, nor is there a framework for succinctly reporting results in a consistent fashion. In this paper we derive normalized mathematical forms of four ERRs for energy extraction and conversion pathways. A bottom-up (process model) formulation is developed for an n-stage energy harvesting and conversion pathway with various system boundaries. Formations with the broadest system boundaries use insights from life cycle analysis to suggest a hybrid process model/economic input output based framework. These models include indirect energy consumption due to external energy inputs and embodied energy in materials. Illustrative example results are given for simple energy extraction and conversion pathways. Lastly, we discuss the limitations of this approach and the intersection of this methodology with “top-down” economic approaches. Keywords: energy return on investment; energy efficiency; energy quality Energies 2011, 4 1212 1. Introduction The overall efficiency of our energy extraction and conversion systems strongly influences the economics of energy supply and the environmental impacts of the energy consumed by end users. This “systems scale” efficiency of energy production and processing is difficult to conceptualize and difficult to measure rigorously. Net energy analysis (NEA) is a broad class of methods used to determine the effectiveness of energy capture and conversion systems [1]. In this sense, NEA is the systems-scale analog to efficiency analysis of technologies. The end result from NEA is often an energy return ratio (hereafter ERR), which compares the amount of energy consumed in extracting an energy resource to the amount of valuable energy provided to society (or to the next stage in the energy processing chain if a tighter system boundary is used). For example, a gas turbine might be characterized by a well-defined conversion efficiency (e.g., MJ electricity/MJ natural gas input, LHV basis), while the efficiency of a natural gas extraction, processing, and distribution pathway can be measured using an ERR. Numerous ERRs exist, and the usefulness of a given ratio depends on its formulation and the question of concern. Net energy analysis rose and then fell from favor in the energy analysis community, with high interest occurring from ≈1975–1985 and again in recent years [1]. One factor in the declining interest in NEA in the 1980s were concerns that an ERR provides no additional information beyond economic analyses [2]. Also, NEA faced methodological difficulties without clear solutions. Recent interest has been spurred by concerns over oil depletion [3,4] and interest in the fundamental energetics of the transition to renewable resources [5,6]. This recent resurgence in interest in NEA sees current attention focused on a specific ERR known as the energy return on investment, or EROI [7]. In this paper we develop a general mathematical framework for calculating ERRs in a bottom-up fashion. We generate formulas for four ERRs for a general n-stage energy extraction and conversion pathway with varying system boundaries. These ERRs are calculated using both magnitudes of flows (a “flow-based” formulation) and processing efficiencies (an “efficiency-based” formulation). We then compute ERRs for simple illustrative conversion pathways, showing that the results conform to those expected from intuition. Lastly, we discuss the limitations of this approach and discuss extensions such as multi-fuel pathways and integration with top-down economic modeling. 2. Energy Ratios and Their Uses 2.1. Development of Energy Return Ratios The net energy output from an energy extraction and conversion pathway is the energy made available from a natural resource in useful form less that energy consumed in extracting, upgrading, and distributing the energy [1]. Net energy analysis (NEA) seeks to compare this net output to the energy consumed in producing the output. Historically, Hall developed the concept of energy return on investment (EROI) and applied it to migrating fish populations [8]. Other roots of NEA include the work of Odum on power flows in social and environmental systems [9]. An early formal framework was developed by the Colorado Energy Research Institute (CERI) [10], which outlined pathways (“trajectories” in their terminology) of energy Energies 2011, 4 1213 conversion processes (“modules”) with a variety of primary energy input types. In the CERI framework, there are two types of inputs to each module: principal energy, or the energy resource undergoing extraction and refining, and external energy, or other energy types consumed in the pathway. Also, there are two types of energy that emerge from a given process: energy products, which represent the useful modified principal energy stream, and energy losses, which are outputs of energy in non-useful forms (waste heat or physical loss of product). Later, Spreng illustrated a simple case of gross vs. net energy requirements in a one-energy-resource economy [11] (p. 132). Similar diagrams were developed by Hannon [12] and others. In these simple NEA models, there is only one energy type, and the extraction and refining of energy consumes energy of that type. This formulation can be used to construct “self net-energy ratios”, which assume that the process provides its own direct and indirect energy inputs. A variety of complexities and additions to NEA models have been made over time, including differentiating the fractions of fossil and renewable energy used in a process [13], and including temporal aspects of energy return over time [12]. Recently, Spitzley and Keoleian [13] listed numerous published definitions of energy return ratios, starting with the work of Odum in the early 1970s, in a review focused on ratios that differentiate between fossil and renewable energy inputs. Modern efforts to standardize NEA methodologies have focused on standardization of EROI [14,15]. 2.2. The Usefulness of Energy Return Ratios Energy return ratios give different information depending on their formulation. For example the net energy ratio (NER) has as its numerator net output of refined energy to society, while the denominator contains all energy consumed in the energy production and refining process. In contrast, the denominator of the net external energy ratio (NEER) includes only those inputs that are consumed from the existing industrial energy system, excluding any “self use” (e.g., produced oil burned on site to power oil producing operations). Therefore, the NER is a more comprehensive measure of the total energy return from a production pathway, and will be closely correlated with environmental impacts of a pathway (such as greenhouse gas emissions). In contrast, the NEER is a more useful measure of the potential growth in energy supply to society because it only counts those inputs that must be produced and delivered externally through the existing energy supply system. Useful information can be obtained by comparing the values of NER and NEER for a given process. This comparison indicates to what extent a conversion and extraction process is self-fueled. For example, recent studies of oil shale development in the Green River formation of Colorado found that NEER was significantly higher than the NER for in situ and mine-and-retort oil shale extraction schemes [16,17]. This is because the oil shale retorting processes studied were fueled primarily by the energy content of the shale itself (either through combusting the spent shale “char” or by using co-produced HC gases to fuel shale retorting), not by external energy inputs. Thus, while the total amount of energy used in extracting oil from oil shale is large, comparatively little of that is commercial energy that must be provided by the rest of the energy system (thus NEER NER and the process is largely self fueling). Energy return ratios can also help illuminate two important aspects of an energy system: the quality of the energy resource being extracted, and the ingenuity with which humans extract that energy. A shift from high-quality resources (e.g., light, sweet conventional oil) to low-quality resources (e.g., Canadian Energies 2011, 4 1214 oil sands) affects the efficiency of extraction, the cost of energy, and the overall environmental impacts from our energy system. Similarly, the sophistication with which we extract and convert energy affects the end cost to users and the environmental profile of energy use. In practice, it is
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