In the energy realm there is a need to make decisions about things that matter profoundly, in a world that is complex and characterized by uncertainty, disputed values and increasingly important biophysical limits [1
]. Exergy analysis has been promoted as a thermodynamic tool for assessing energy and resource consumption and waste impact with the aim of providing more informed decision-making for progress towards sustainability [5
]. For example, when discussing green energy technology, Rosen and Dincer [10
] argue that exergy analysis provides information that is more useful and more meaningful than energy analysis. The notable benefits of the exergy concept has led to its application in several different disciplines, including: ecology and complex systems [5
]; resource accounting and lifecycle assessments [7
]; process optimization [10
]; and even social theory [26
Due to its increasing popularity, exergy is being improperly applied in certain situations, and the consequences of such applications are not fully appreciated. The concern is that improper application of exergy may lead to incorrect recommendations and ultimately reduce its appeal for informing decision-making. This paper reviews recent theory and practice of exergy analysis to highlight general challenges, and provide a unique and critical analysis of current major chemical reference environment formulations. The paper complements analyses of the temperature sensitivity of the exergy reference environment [25
]. Three areas of focused that are explored in this thesis are: (1) inconsistent results due to applications of standard and universal exergy reference environments; (2) issues that arise in the attempt to formulate a chemical exergy reference environment similar to the natural environment; (3) the implications of adopting a thermodynamic (in this case exergy) frame of analysis for situations whose relevant characteristics (e.g., scarcity) are non-thermodynamic.
The outline of the paper is as follows: a brief description of inappropriate applications of exergy to characterize waste and resource value is presented to highlight some of the difficulties associated with comprehensive reference environments. Building from difficulties encountered characterizing wastes and resources, the authors provide an in-depth discussion of the predominant comprehensive exergy reference environment formulations to help explain the source of some of the limitations to using exergy. The authors conclude by arguing that exergy practitioners should apply exergy primarily for thermodynamic process optimization, whereby exergy is applied as a context- or environment-dependent decision-making tool and not as an intrinsic characteristic of matter. In this regard, the authors are proposing a return to the original purpose of exergy analysis: as a decision making tool for engineering systems analyses with the general goal of improving process efficiency as measured by work or work potential, or by identifying areas of inefficiency through exergy destruction or entropy production.
As a point of clarification, exergy refers to the total of thermal, mechanical, and chemical exergies as determined from temperature, pressure, and chemical potential gradients, respectively. When the exergy from only one or two of these three thermodynamic gradients is being considered appropriate adjectives will be used, for example, chemical exergy or thermal-mechanical exergy.
4. Discussion: The Limitations of Standard Reference Environment Formulations
While the reference environment formulations discussed above do not represent every possible universal and standardized reference environment, some key insights may still be elaborated. This section will elaborate upon four related issues pertaining to exergy and the reference environment; issues that develop a basic argument when taken as a package. The four issues are: (1) standard and universal chemical exergy reference environments necessarily encounter internal inconsistencies and even contradictions in their very formulations; (2) these inconsistencies are a result of incompatibility between the exergy reference environment and natural environment, and the desire to model the exergy reference environment after the natural environment so as to maintain relevance; (3) the topics for which exergy is most appropriate as an analytical tool are not well served by comprehensive reference environments; and (4) the inconsistencies point to a need for deeper reflection of whether it is appropriate to adopt a thermodynamic frame of analysis for situations whose relevant characteristics are non-thermodynamic.
First, the analysis of Szargut’s and Ahrendts’ reference environment formulations illustrated several inconsistencies and contradictions. For example, Szargut’s formulation is simultaneously described as equilibrium and non-equilibrium, although it is clearly non-equilibrium. Furthermore, Szargut’s model produces impossibly negative exergy values, which should be an early indicator that the underlying theory is not suitable. By contrast, Ahrendts faces his own set of challenges in that the more he tries to model his reference environment as being similar to the Earth in terms of mineral content (i.e.
, the thicker he makes the crust), the further his exergy values differ from empirically accepted reality: the very thing he is trying to model. Finally, both Ahrendts and Szargut attempt to reconcile their exergy values with empirical values despite acknowledging that the Earth is not in thermodynamic equilibrium, and therefore there is no reason to expect or desire similarities given that the implication of thermodynamic equilibrium for life on Earth is that there would be no life [53
The second insight builds from the first and relates to how well the exergy reference environment formulations correspond to the natural world outside, and even whether they should. As previously noted, Ao et al.
] claimed that the reference environment is often modeled as the actual environment, and this implies that the properties of exergy and natural environments may be reconciled. There is no a priori reason to assume that the exergy reference environment and the natural world are reconcilable, and in fact there are many reasons to argue just the opposite. To illustrate this, Table 2
provides a basic contrast between the characteristics of the exergy reference environment as defined by Rosen and Dincer [35
] (and elaborated upon by us) compared to a restricted set of characteristics of the natural world [5
A basic contrast between the chemical exergy reference environment and the natural world.
A basic contrast between the chemical exergy reference environment and the natural world.
|The chemical exergy reference environment||The natural world|
|Infinite size: there are no discernable boundaries although a boundary is posited between the reference environment and the system whose exergy is being calculated||Finite size: boundaries are very important (e.g., edge effects)|
|Infinite source and sink: nothing can harm the reference environment||Finite source and sink: displays catastrophic behavior when it crosses a threshold|
|In stable thermodynamic equilibrium||Inherently non-equilibrium: one measure of complexity is how far the environment is from thermodynamic equilibrium|
|Homogenous throughout||Heterogeneous throughout: structures and scale are important. Hierarchy results from self-organization|
|Intensive state properties remain unaltered in time||State properties change in time as a result of evolution and development (among other things)|
It should be immediately clear that the characteristics of the reference environment and the natural environment are diametrically opposed. For example, with regards to the use of exergy as a measure of waste impact, one must seriously question how anything can harm an environment that is infinite in size, is an infinite source and sink, and by its very definition never changes. This is not to say that waste items with higher exergy contents never have a higher capacity for impact. There are no doubts many instances in which the higher work producing potential of a waste increases its harm on the environment. However, to argue that exergy as defined through a universal reference environment is a valid measure of harm is simply erroneous [33
The end result of mapping the exergy reference environment to the natural environment is the generation of a paradoxical situation: (1) exergy has little applicable value or meaning for waste impact and resource consumption if it is defined by a purely theoretical reference environment that has no similarity to the real world; and (2) the attempts to reconcile a standard or universal reference environment with the natural environment are bound to fail because the very characteristics of the natural environment are antithetical to those of the exergy reference environment.
The third argument is that the topics for which exergy is most appropriate as an analytical tool are not well served by comprehensive reference environments. For example, for energy systems not predicated upon chemical exergy (e.g., solar, wind, nuclear, tidal, geothermal, hydro), a standard chemical reference environment is irrelevant, and any addition of these energy types to the comprehensive reference environment will be ad hoc. Furthermore, for the case of chemical exergy, such as the combustion of fossil fuels or biomass, neither Ahrendts’ nor Szargut’s reference environments are applicable. In Ahrents’ case, the situation was deemed a paradox, because the reference environment indicated a low value for fossil fuels and a high value for oxygen; the very opposite situation of what is generally considered to be the case. By contrast, Szargut does not use his reference environment to calculate the exergy of liquid fuels, but rather correlations based on the lower heating value of the fuel [36
]. Effectively, neither reference environment is able to account for non-chemical work production, and nor are they internally able to account for essentially chemical combustion. Ultimately, we need to ask what useful work metrics do these reference environments actually account for within their own formulation.
To be clear, we are not implying that correlations to lower heating value are an inappropriate means of measuring how much useful work can be obtained from fossil fuels. What we are saying is that these correlations have nothing to do with comprehensive chemical exergy reference environments, nor with some idealized concentration exergy that is achieved through the movement of purely theoretical semi-permeable membranes. Ultimately we have a thermodynamic concept predicated on the determination of useful work production, but which is completely unable to provide sound framework to do so.
The inconsistencies noted above point to a need for deeper reflection about the exergy concept as it is being applied for resource accounting and waste impact. It is clear that chemical exergy, as determined by comprehensive reference environments, is not about useful work production; the items that may be characterized, however improperly, by a universal exergy reference environment (e.g., minerals) are not work producing, and therefore their chemical exergy content does not measure anything particularly useful nor relevant about them [29
]. Instead, chemical exergy is really being applied as a means to quantify scarcity. Effectively, both Ahrendts’ and Szargut’s reference environments attempt to provide a thermodynamic (i.e.
, biophysical) value to scarce minerals and compounds, and this is even explicitly stated as the third principle of Ahrendts’ approach [49
]. Unfortunately, neither reference environment formulation is able to achieve this goal, as is illustrated by the k
-values in Table 1
and Ahrendts’ “paradox”. But whether the goal is achieved or not, there is no good justification for developing a thermodynamics of scarcity in the manner that has been done. Things have value for many reasons, of which scarcity is only one measure [48
]. Some very scarce products may still appear to have no value if they have no utility. Furthermore, to imply that scarcity is commensurable with work production is simply incorrect, but that is exactly what occurs when scarce substances are characterized in terms of their chemical exergy content.
While we recognize the desire to provide an alternative means of valuing natural resources than purely monetary value [62
], the use of exergy as the common denominator is equally inappropriate. Both economic and exergy approaches to value are simply different forms of reductionism [38
]. Furthermore, it is completely inappropriate to imply that an item has a higher work producing potential simply because it is scarcer in the environment, but that is exactly what is implied by quantifying scarce items through exergy.
An ecological example of thermodynamic reductionism is Jorgensen’s [5
] eco-exergy concept which converts DNA length into an organism’s exergy by multiplying all organisms by the exergy content of detritus. However, if everything has the same base multiplier of the detritus exergy content, then organisms are not being compared on thermodynamic basis (at least not directly), but rather based on their DNA length [28
]. In such situations, switching into a thermodynamic frame provides no obvious benefits, an opens up the analysis to further critique.
It is important to be clear that the discussion provided above does not critique all applications of exergy, but rather specifically to the use of exergy as an intrinsic and universal characteristic of all items, and as a means of valuing scarce items. In fact, despite the difficulties with standard reference environment formulations, exergy still has much value and insight to offer. The challenge is to work within the constraints of the exergy concept and its formulation [17
5. Exergy to Inform Decision-Making
Building from the analysis in this paper, it appears necessary to move beyond attempts for a comprehensive standard reference environment that yields standard (universal) exergy values, as these produce exergy values with no obvious relevance or usefulness. Exergy is not an intrinsic characteristic of an item, and the exergy value of an item is a measure of thermodynamic distance between the item and a reference environment, and should not be attributed to the item, but rather it must be seen as being assigned to the combined ‘system’ of the item and its reference environment.
By stepping away from a universal reference environment, we may return to process dependent reference states—that is reference states developed to model specific
processes and situations, and informed by the second law of thermodynamics [50
]. Using process dependent reference environments allow exergy to be useful for many applications, including: (a) efficiency comparisons between disparate systems [e.g., comparing an internal combustion engine (Carnot limited heat engine) to a fuel cell (non-heat engine) via a second law efficiency]; (b) inefficiency magnitude identification within a given system (e.g., quantifying the work potential lost during heat transfer in a furnace); (c) inefficiency location identification within a given system (e.g., identifying the heat transfer to the boiler of a Rankine cycle system as a major location for work potential loss); and (d) enabling optimization of a given system (e.g., determining an optimum radiator temperature by minimizing exergy destruction).
In many situations the useful work that may be obtained from an item (e.g., coal) will be more or less identical simply because the process (combustion) and the relevant chemical species of the atmospheric are the same, and the temperature is within an acceptable range. While for the sake of simplicity and ease of communication, there is merit in attributing this useful work potential to the coal itself, this useful work is in fact equally dependent upon the process (combustion) and the reference environment. Furthermore, it is important to be clear that in process dependent models, exergy is seen as measuring the thermodynamic efficiency of a process (e.g., a conversion process) as opposed to characterizing a specific object (e.g., the exergy content of tin). While this difference appears subtle at times, these two perspectives of exergy represent fundamentally different conceptions of the exergy concept.
As a final point of note, we return to the issue of when there is merit in framing the analysis in terms of exergy. It is worth noting that exergy destruction minimization is effectively the same as entropy generation minimization through the Guoy-Stodola theorem. However, exergy is useful because it is based in units of work (e.g., kJ), which in general is easier for decision makers to comprehend than entropy units (e.g., kJ/K). In other instances, the benefit of an exergy framing is less certain. For example, while exergy is promoted as a means of improving lifecycle assessments [7
] (and some exergy-based LCAs even predate generalized approaches to LCA), many lifecycle assessments already contain quality factors that relate to the question of useful work. Since the quality factors are already present, it is debatable whether significant further insight may be gained by explicitly adopting exergy. Ultimately, it is up to the analyst to adopt the most appropriate method of analysis for the case at hand, as opposed to pre-analytically framing the analysis through a particular lens [64
], such as the exergy lens.
This paper provides a critical analysis of universal and comprehensive formulations of the chemical exergy reference environment, for the purpose of better understand how exergy can inform decision-making. By analyzing the theory and practice of Ahrendts’ [49
] and Szargut’s [36
] reference environment formulations, three related insights emerged, notably: (1) standard and universal chemical exergy reference environments necessarily encounter internal inconsistencies and even contradictions in their very formulations; (2) these inconsistencies are a result of incompatibility between the exergy reference environment and natural environment, and the desire to model the exergy reference environment after the natural environment so as to maintain relevance; (3) the topics for which exergy is most appropriate as an analytical tool are not well served by comprehensive reference environments, and (4) the inconsistencies point to a need for deeper reflection of whether it is appropriate to adopt a thermodynamic frame of analysis for situations whose relevant characteristics (e.g., scarcity) are non-thermodynamic.
Building from the analysis in this paper, we argue it is necessary to move beyond attempts for a comprehensive standard reference environment that yields standard (universal) exergy values and instead return to process dependent reference states; that is reference states developed to model specific processes and situations. Using process dependent reference environments allow exergy to be useful for many applications, including: (a) efficiency comparisons between disparate systems; (b) inefficiency magnitude identification within a given system; (c) inefficiency location identification within a given system; and (d) enabling optimization of a given system.
The analysis of Szargut’s and Ahrendts’ reference environment formulations reveal an underlying attempt to provide a biophysical means of value all objects, in this case based on their scarcity. While a thermodynamics of scarcity may be intuitively pleasing, and may provide a common metric by which all things (both work producing and not) can be characterized, we are concerned that such an interpretation of exergy ignores the intent of exergy analysis, which is to characterize and optimize work producing systems. On a more philosophical level, this attempt to reduce all means of value to exergy is no different than when economists attempt to value everything in monetary terms. If it is clearly wrong to value everything in terms of money, the same can be said of exergy. Many things that matter have no value with regards to their exergy content, and attempting to characterize them in terms of exergy does an injustice to all concerned.
The initial exploration of comprehensive and universal exergy reference environments was beneficial because it provides an opportunity for deeper critical analysis of the opportunities and limitations of the exergy concept. At this point, however, the continued application of comprehensive reference environments for the purpose of characterizing resources and wastes, and even process optimization, risks reducing both the usefulness and credibility of exergy for informing decision-making. Now is the time to close the door on such applications, unless a complete reformulation of the concept is undertaken so as to avoid the limitations discussed above, while recognizing that such a reformulation may not even be possible. While many of the insights developed above are probably inherently recognized by many exergy practitioners (e.g., [65
]), these problems have not been sufficiently nor formally recognized in the exergy literature.
By recognizing and working within the constraints of exergy, the authors believe that exergy may still inform decision-making for progress towards sustainability. To do so, however, requires a deeper discussion of what insights can be obtained from thermodynamic analyses and what tradeoffs occur when the frame of reference becomes thermodynamic.