Energy 36 (2011) 1442e1459
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Energy
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An exergy-based framework for evaluating environmental impact
Adam P. Simpson*, Chris F. Edwards
Stanford University, Department of Mechanical Engineering, Stanford, CA 94305, USA article info abstract
Article history: The analysis framework introduced in this paper utilizes the recognition that exergy is a form of envi- Received 25 July 2010 ronmental free energy to provide a fundamental basis for valuing environmental interactions inde- Received in revised form pendent from their secondary impacts (e.g., global warming, photochemical smog). In order to extend 7 December 2010 exergy to analyze environmental interactions, modifications are required to the traditional representa- Accepted 17 January 2011 tion of the environment and definition of the dead state used in technical exergy analysis. These are Available online 27 January 2011 accomplished through a combination of logical extensions and use of non-equilibrium thermodynamic principles. The framework is comprised of two separate components: (1) environmental exergy analysis Keywords: Exergy and (2) anthropocentric sensitivity analysis. Environmental exergy analysis is based on fundamental Exergy analysis thermodynamic principles and analysis techniques. It extends the principles of technical exergy analysis Reference state to the environment in order to quantify the locations, magnitudes, and types of environmental Dead state free energy impactdstate change, alteration of natural transfers, and destruction change. Anthropocentric sensitivity Environmental change analysis is based on the concepts of anthropocentric value and anthropocentric sensitivity. It enables the Environmental impact results of environmental exergy analysis to be interpreted for decision making, but at the expense of introducing some subjectivity into the framework. A key attribute of the framework is its ability to evaluate and compare the environmental performance of energy systems on a level playing field, regardless of the specifics of the systemsdresources, by-products, sizes, time scales. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction sulfur dioxide, carbon dioxide, and chlorofluorocarbons (CFCs). The emission of these particular species are monitored because of With the supply of conventional energy resources being identified adverse environmental consequencesdphotochemical depleted at their fastest rates, and the environmental impacts of smog, acid rain, global warming, and ozone depletion. Species- their use better understood, there is an increasing desire to develop based techniques typically communicate an energy system’s envi- and employ alternative energy technologies that lessen depen- ronmental performance by the mass of a species emitted per unit of dence on these resources and reduce environmental impact. This desired output (e.g., kg-CO2/MWhelec). leads to the question: Which alternative energy technologies Extensions have been made to species-based techniques for should we pursue? In order to answer this question, the potential comparing a range of species on the basis of their potential to cause technologies need to be compared on a level playing field based on a common environmental consequence. The most prominent of their environmental performance. these extensions is the use of Global Warming Potentials (GWPs) by There currently exist several analysis techniques for evaluating the government agencies such as the U.S. Environmental Protection environmental performance of energy systems. These can be cate- Agency (EPA) and the Intergovernmental Panel on Climate Change gorized as being based on species, economics, or thermodynamics. (IPCC). GWPs provide a measure of a species’ potential to cause Species-based techniques measure the environmental perfor- global warming relative to that of carbon dioxide. The details of and mance of energy systems based on the amount of a particular standard methods used to measure GWPs are defined by the IPCC species emitted by a system. The species of interest are typically [1]. When GWPs are employed to measure an energy system’s those that have been identified as causing adverse environmental environmental performance, the results are communicated consequences. Example species include oxides of nitrogen (NOx), through a mass of carbon-dioxide-equivalent emission per unit of desired output (e.g., kg-CO2-eq./MWhelec). Economics-based techniques measure environmental perfor- mance by assigning a monetary value to the undesirable outputs * Corresponding author. Tel.: þ1 650 725 2012; fax: þ1 650 723 1748. E-mail addresses: [email protected], [email protected] from energy systems that are known to cause adverse environ- (A.P. Simpson). mental consequences. In economics, the adverse environmental
0360-5442/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.01.025 A.P. Simpson, C.F. Edwards / Energy 36 (2011) 1442e1459 1443 consequences are referred to as environmental damages, and the Cumulative Exergy Extraction from the Natural Environment cost assigned to these damages are referred to as an environmental extends the embodied exergy concept used in CEC to include the external cost. There are several methods employed to define what exergy of renewable resource inputs, such as solar radiation, wind, is considered environmental damage and to prescribe an environ- and geothermal exergy. CEENE measures the environmental mental external cost. A detailed review of these methods is performance of energy systems through the total amount of provided by Riva and Trebeschi [2]. Economists and policy makers embodied exergy (measured through the CEC approach) and typically use the environmental external cost of an energy system renewable exergy required to produce a desired output (i.e., as a measure of its environmental performance. The environmental through the total amount of exergy removed from the natural external cost of an energy system can be combined with its internal environment). Dewulf et al. [7] describe the details and applica- cost (i.e., internalized) to provide a measure of the system’s real tions of CEENE. cost. It is often argued that the real cost of an energy system Extended Exergy Accounting tracks the extended exergy provides a more appropriate measure of economic performance content of all inputs and outputs of an energy system over its entire than internal cost when comparing energy system options [2,3]. life, including capital and labor. The extended exergy content of A significant shortcoming of species- and economic-based non-capital and non-labor inputs is calculated through the analysis techniques is that the environmental transfers of concern embodied exergy methods used in CEC. The extended exergy must be identified as being undesirable a priori of the analysis. content of capital is calculated by assigning an exergy value to Environmental transfers from an energy system are typically only a unit of a country’s currency based on the country’s gross domestic identified as being undesirable after they have caused some type of product (GDP) and the total amount of natural resource exergy adverse consequence. Neither technique is capable of evaluating consumed by the country in a given year (e.g., MJ/$GDP). The the environmental performance of an energy system without prior extended exergy content of labor is calculated by assigning an knowledge of the system’s environmental transfers causing exergy value to a hour of work (a “man-hour”) based on the total adverse consequences. Furthermore, both techniques only provide amount of natural resource exergy consumed by a person to proxy measures of environmental performance. They do not support 1 h of work (e.g., MJ/man-hour). EEA assigns an extended provide the ability to evaluate the environmental change driven by exergy content to an energy system’s undesired outputs (e.g., an energy system’s environmental interactions (upstream and emissions, waste) based on the extended exergy content of all downstream environmental transfers). inputs that would be required to reduce their exergy (thermo- Thermodynamics-based techniques employ thermodynamic mechanical and chemical) to zero. EEA measures the environ- concepts to evaluate and measure the environmental performance mental performance of energy systems through the total amount of of energy systems. The noteworthy thermodynamics-based anal- extended exergy input to a system in order to produce a desired ysis techniques are: Life Cycle Assessment (LCA), Cumulative output and reduce the exergy of undesired outputs to zero. The Exergy Consumption (CEC), Cumulative Exergy Extraction from the details and applications of EEA are described by [8e14]. Natural Environment (CEENE), Extended Exergy Accounting (EEA), Emergy Analysis tracks the solar emergy of all inputs to an energy and Emergy Analysis. All of these analysis techniques extend the system over its entire life, including capital and labor. Solar emergy is control boundary of an energy system and the time scale of the defined as the total amount of solar exergy directly or indirectly analysis to include all components and processes required to required to produce a given flow, and is measured in solar equivalent support the system over its entire life (often referred to as “cradle- joules (seJ). The solar emergy of capital is calculated by assigning to-grave” analysis). The key differences between the five tech- a solar emergy value to a unit of a country’s currency based on the niques are in how they value the inputs and outputs of a system, country’s GDP and the total amount of solar exergy incident on and and how they measure environmental performance. solar emergy consumed by the country over a given year (e.g., seJ/ Life Cycle Assessment is essentially an extension of first law- $GDP). The solar emergy of labor is calculated by assigning a solar analysis. It tracks the mass and energy of inputs and outputs of an emergy value to a man-hour based on the total amount of solar energy system over its entire life (not including capital and labor). emergy consumed by a person to support 1 h of work (e.g., seJ/man- The energy of physical inputs and outputs are typically measured hour). Emergy Analysis measures the environmental performance of based on their heating value (lower or higher). LCA measures the an energy system through various metrics based on the total amount environmental performance of an energy system through the total of solar emergy required to support the production of a desired amount of natural resource energy required to produce a desired output. The development, details, and applications of Emergy product, and through the total amount of emissions produced by Analysis are described by [12,15e17]. the system. The former is typically communicated via a net energy Emergy and EEA analysis can be viewed as overall performance value (e.g., LHVnet ¼ LHVdesired products LHVresource inputs)oran analysis techniques because of their inclusion of capital and labor. overall first-law efficiency (e.g., LHVdesired products/LHVinputs), and They essentially roll environmental and economic performance the later is typically communicated via the mass of emissions per components into one unit of measuredsolar emergy and extended unit of desired product (e.g., kg-CO2,total/MWhelec). The methods exergy content, respectivelydin order to internalize all transfers to and applications used in LCA are described by the U.S. EPA [4]. and from an energy system. This is similar to the economic Cumulative Exergy Consumption tracks the embodied exergy of approach of measuring environmental damages through an envi- inputs to an energy system over its entire life (again, not including ronmental external cost and internalizing this cost to form the real capital and labor). The embodied exergy of an input is measured by the cost of an energy system or energy product. sum of the fossil and nuclear resource exergy that went into its pro- While all of the existing environmental analysis techniques have duction (e.g., the embodied exergy of a kg of steel is the amount of individual merit, they do not provide a fundamental basis for eval- resource exergy consumed during its production). CEC measures the uating environmental impact, or environmental change. Even those environmental performance of energy systems through the total am- techniques that use exergy analysis as a tool for tracking energy ount of embodied exergy required to produce a desired output (i.e., flows into, within, and from an energy system miss the essential fact through the desired output’s cumulative, or embodied, exergy content). that it is the free energy of those flows to and from the system that CEC communicates environmental performance via an overall exergy causes environmental change. And with the additional realization efficiency, which is referred to as the cumulative degree of perfection. that exergy is environmental free energy comes recognition that the The details and applications of CEC are described by Szargut et al. [5,6]. study of exergy balances as applied to the environment as well as the 1444 A.P. Simpson, C.F. Edwards / Energy 36 (2011) 1442e1459 traditional engineering system is required to provide a fundamental This section presents an alternative derivation of exergy similar assessment of environmental impact. to a derivation of Gibbs free energy in order to introduce the idea This paper presents an analysis framework based on thermo- that exergy is a form of free energydspecifically, environmental dynamic principles and analysis techniquesdnamely exergy and free energy. All forms of free energy measure the maximum exergy analysisdfor evaluating the environmental impact of amount of work that can be extracted from a non-equilibrium energy systems. The framework utilizes the recent recognition that system constrained to equilibrate under specified interaction con- exergy is a form of free energy to extend the models and techniques straintsde.g., constant temperature and pressure for Gibbs free used in technical exergy analysis to the environment. This exten- energy, and constant temperature and volume for Helmholtz free sion enables the locations, magnitudes, and types of environmental energy. Exergy is, by definition, the maximum amount of work that impact caused by energy systemsdboth upstream and down- can be extracted from a system comprised of a resource and its streamdto be evaluated on a level playing field across the range of environment constrained to equilibrate at the conditions of the possible resources used (renewable and non-renewable) and environment. Therefore, exergy is the free energy of a resource outputs produced (desired and undesired) over the time scales in relative to its environment. which energy systems operate. To show this, a derivation of Gibbs free energy is presented first. The following section provides a discussion of the connection Consider a closed system of fixed temperature and pressure that is between exergy and free energy, and a proof that exergy is a form of initially separated into two regions by a partition, with regions A free energy and therefore a measure of the ability to drive change. and B on either side of the partition. The individual regions are Next, exergy analysis is applied to a well-defined model system to initially in internal equilibrium and at the same temperature and demonstrate its application outside of an energy system for the pressure, but they are not in chemical equilibrium. The temperature purpose of evaluating environmental change. The following two and pressure of the system are held constant through heat and sections discuss key concepts that are needed in order to effectively boundary-work transfers with an external thermo-mechanical extend exergy analysis to the natural environmentdnamely, revi- reservoir controlled by a thermostat and barostat, respectively. sions to the traditional understanding of a reference state, and the Since the system is initially out of equilibrium, there exists a driving model representation of the environment used in technical exergy potential that can theoretically be extracted as work. A diagram of analysis. Next, the ways in which energy systems interact with and this closed system in communication with a thermo-mechanical impact the environment are discussed. The following section reservoir with work extraction is shown in Fig. 1. outlines the application of environmental exergy analysis for The maximum amount of work that can be extracted from the evaluating the environmental impact of energy systemsdor more system is derived by applying the First and Second Laws of ther- general anthropogenic activity. The paper then introduces the modynamics to the control boundary around the system. The diff- concept of anthropocentric sensitivity and discussing its role in erential expressions of the First and Second Laws for the system are: environmental impact analysis and decision making. The paper d d d concludes by applying that analysis framework to a real world dU ¼ Q Wb W (1) environmental problem to illustrate the analysis technique’s ability to both evaluate environmental impact and provide guidance for dQ dS ¼ þ dS (2) decision making. T gen Combining Eqs. (1) and (2) and employing the definition of 2. Environmental free energy d boundary work, Wb ¼ PdV, yields a expression for the differential amount of work extracted from the system. Exergy is defined as the maximum amount of work that can be extracted from a resource relative to its environment. The terms dW ¼ dU PdV þ TdS TdSgen (3) resource and environment are italicized to emphasis both their importance and interdependence. A resource refers to any energy The maximum amount of work is realized when interactions accumulation or energy flow that has the potential to do work between the regions occur reversibly (i.e., no entropy generation). relative to its environment. The environment refers to the portions Therefore, the expression for the maximum work that can be of the natural environment that enable work to be extracted from extracted from the system is: a resource because it acts as a thermal, mechanical, and/or chemical d reservoir to the resource. A resource has the ability to do work Wmax ¼ dU PdV þ TdS because it is out of equilibrium with its environment. Work can h ¼ dðU þ PV TSÞT ¼ const: dG (4) theoretically be extracted from any system that is out of equilibrium, P ¼ const: and the maximum amount of work is realized when the system equilibrates reversibly. Exergy is an extension of this principle in which the system is comprised of a resource and the environment. Exergy is derived by applying the First and Second Laws of thermodynamics to a resource in communication with its envi- ronment and calculating the reversible (i.e., maximum) amount of work that can be extracted as equilibrium is reached. Reversibility requires that the resource transfer heat at the environmental temperature, boundary work at the environmental pressure, and exchange environmental species at their environmental chemical potentials. In traditional derivations of exergy, reversible interac- tions are realized by modeling the environmental surroundings as a large reservoir with fast internal transport such that its intensive state does not change (i.e., as a thermodynamic reservoir). A deri- Fig. 1. Closed system in communication with a thermo-mechanical reservoir with vation of exergy that models the environmental surroundings in work extraction. The thermostat and barostat control heat and boundary-work this manner is provided in Appendix A. transfers to maintain temperature T and pressure P inside the system. A.P. Simpson, C.F. Edwards / Energy 36 (2011) 1442e1459 1445
As shown in the above equation, the maximum work that can be extracted from a closed, isothermal, isobaric system is equal to the Thermodynamic differential change in the Gibbs function of the system. The Reservoir maximum amount of work that can be extracted from the system is Thermostat, T calculated by integrating Eq. (4) from the initial state to the final o Barostat , P equilibrium state of the system. This yields: o Chemostat , μ i,o D δ Q δ δ Wmax ¼ G ¼ Ginitial GEQ (5) Wb Ni δW The above equation shows that the maximum amount of work that Environment Resource can be extracted from a closed, isothermal, isobaric system is equal () to the change in the Gibbs function from the initial state to the final ()TPNoo,, io, TPN,, k state of the system. In other words, the change in Gibbs function for a closed, isothermal, isobaric system between its initial state and Fig. 2. Open system in communication with a thermodynamic reservoir. The ther- fi nal equilibrium state is free to be extracted as work. Hence the mostat, barostat, and chemostat control heat, boundary work, and matter transfers, m term Gibbs free energy. respectively, to maintain the state of the environment region (To, Po, and i;o). Subscript The same approach used to derive Gibbs free energy can be i designates environmental species and subscript k designates species initially present applied to other closed systems with different interaction in the resource region, which can include both environmental species (i) and non- environmental species (j). constraints. It can be shown that the maximum amount of work that can be extracted from a closed system constrained to equili- brate at constant temperature and volume is its change in Helm- P d d holtz function ( DA, or Helmholtz free energy), at constant entropy W ¼ dU PodV þ TodS þ hi;o Tosi;o Ni and volume it is the change in internal energy ð DUÞ, and at i (8) T dS constant entropy and pressure it is the change in enthalpy ð DHÞ. o gen Therefore, for closed, isentropic, isochoric systems, the internal The maximum work is realized when the interactions between the energy is a form of free energy, and for closed, isentropic, isobaric reservoirs occur reversibly (i.e., no entropy generation). Therefore, systems, the enthalpy is a form of free energy. the expression for the maximum differential amount of work that To show that exergy is a form of free energy, consider an open can be extracted from the system is: system in communication with an external thermodynamic reser- X d m d voir. The system is comprised of two regions, with one called an Wmax ¼ dU PodV þ TodS þ i;o Ni (9) “environment” and the other a “resource”, initially separated by i a partition. Each region is initially in internal equilibrium, but not in The maximum amount of work is calculated by integrating Eq. (9) mutual equilibrium. The environment region is in communication from the initial state of the system to the mutual equilibrium with the thermodynamic reservoir controlled by a thermostat, state of the two regions, which is equal to the state of the envi- barostat, and a series of selective chemostatsdone for each envi- ronment region. In order to perform this integration, the inexact ronmental species (i). The thermostat, barostat, and chemostats differential for the transfer of moles must be converted to an exact control heat, boundary work, and matter transfers, respectively, to differential. This can be accomplished by considering the reversible maintain the environment region at its initial thermodynamic transformation of all non-environmental species (j) present in the statedT , P , and m ; . Since the regions are initially out of equilib- o o i o resource region (non-environmental resource species) to species rium, there exists a driving potential that can theoretically be present in the environment region (i) through the following extracted as work. The maximum amount of work that can be reaction: extracted from the system is realized as it equilibrates reversibly. The final equilibrium state of the system is equal to the state of the : / ; Rj aA þ bB cC þ dD environment region since it is maintained constant. A diagram of ; x ; this open system in communication with a thermodynamic reser- with extensive extent of reaction j voir with work extraction is shown in Fig. 2.1 / (10) The maximum amount of work that can be extracted from the aA bB þ cC þ dD P system is derived by applying the First and Second Laws to the n / n jAj i;jAi control boundary around the system. The differential expressions of i the First and Second Laws for the system are: where n is the stoichiometric coefficient for the non-environmental X j n fi d d d d resource species (j), and i;j is the stoichiometric coef cient for the dU ¼ Q Wb þ hi;o Ni W (6) i environmental species (i) used or created by the transformation of non-environment resource species.2 The species balances for environmental species and non-environmental resource species dQ X dS ¼ þ s ; dN þ dS (7) are: T i o i gen o i X d n x dNi ¼ Ni þ i;jd j (11) where hi;o and si;o are the molar enthalpy and entropy of the species j i in the environment region. Combining Eqs. (6) and (7) and employing the definition of boundary work, dW ¼ P dV, yields an b o n x expression for the differential work extracted from the system. dNj ¼ jd j (12)
1 2 n The environment and resource regions of this example shown in Fig. 2 are As indicated by Eq. (10), the sign correction used for i;j is such that product analogous to regions A and B of the pervious example shown in Fig. 1. species are taken as positive and reactant species are negative. 1446 A.P. Simpson, C.F. Edwards / Energy 36 (2011) 1442e1459
Combining Eqs. (11) and (12) through the differential extent of reaction yields an exact differential expression for the transfer of moles of environmental species between the environment region and the thermodynamic reservoir: X d n =n Ni ¼ dNi þ i;j j dNj (13) j
Combining the above expression and Eq. (9) yields an exact differential equation for the maximum amount of work: P d m Wmax ¼ dU PodV þ TodS þ i;odNi P P i m n =n (14) þ i;o i;j j dNj i j Fig. 3. Model system comprised of a heat engine located within a local environment. Integration of the above equation from the initial state of the system to the state of environment region yields an expression for first. The purpose of applying exergy analysis to a well-defined the maximum amount of work that can be extracted from the environment is to introduce and gain comfort with the techniques 3 system. and models used to quantify environmental change before applying P m environmental exergy analysis to the natural environmentda Wmax ¼ðU þ PoV ToSÞ i;oNi " #i complex system. The techniques and models used to quantify the P P (15) change this small-scale energy system drives in its local environ- m n =n i;o i;j j Nj ment can be extended to large-scale energy systems operating j i within the natural environment, as is shown in the following Equation (15) was derived by applying the same approach used to sections. derive Gibbs free energy, and represents the free energy of an open A diagram of the model system considered here is shown in system comprised of two regions in communication with a ther- Fig. 3. The energy system is an insulated heat engine, and the local modynamic reservoir that maintains the state of one of the regions environment is comprised of a hot copper block, an open water constant. The equation is equivalent to the equation of internal tank, a rigid, closed laboratory, and a large reservoir called the exergy derived in Appendix A. Therefore, the free energy of “surroundings”. The heat engine cross-connects the copper block a system comprised of a resource and an environmental reservoir and water tank, which are both located within the laboratory. The constrained to equilibrate at the state of the environment is equal initial states of the environmental reservoirs are specified in the to the exergy of the resource. In other words, exergy is the envi- figure. The composition of the laboratory and surroundings is ronmental free energy of a resource. engineering air with an initial relative humidity of 50%, and the The connection between exergy and free energy is significant water in the tank is pure (i.e., no dissolved air). The surroundings because of the connection between free energy and the potential to are considered as being a thermodynamic reservoir, and each drive change. In order for a system to have free energy, the system environmental reservoir is in local thermodynamic equilibrium. must be out of equilibrium, and all systems that are out of equi- The natural and anthropogenic energy transfers within the librium have the potential to drive change [18]. Therefore, all forms model system during heat engine operation are shown in Fig. 4. of free energy inherently measure the ability to drive changed Natural transfers are the result of the environmental reservoirs albeit with differing interaction constraints. The free energy of being out of equilibrium, and anthropogenic transfers are caused by a system can be extracted from the system as work, or if no work is the operation of the heat engine. The natural transfers considered extracted, change will occur within the system. When a system is in this analysis include the transfers of heat from the copper block comprised of a resource and the environment, the exergy of the (C) to the laboratory, heat and matter from the water tank (W)to resource provides a measure of its potential to drive change in the the laboratory, and heat from the laboratory (L) to the surroundings environment. Recognizing this fact enables the exergy of transfers (S). The anthropogenic transfers considered in this analysis include to and from the environment to be used as a measure of the the upstream transfer of heat to the heat engine (H) and the potential to drive change in the environment. In technical (or downstream transfers of water between the water tank and heat 4 traditional) exergy analysis, exergy is tracked within an energy engine. Implied by the limited number of transfers shown in the system to quantify the locations, magnitudes, and types of lost figure, are the assumptions that the heat engine is perfectly insu- work within an energy systemdexergy destruction within the lated, the laboratory is perfectly rigid and closed, the water in the system or transfers of unused exergy from the system. The same water tank remains pure, and there is negligible heat conduction analysis techniques can be extended outside of the energy system along the pipes connecting the heat engine and water tank. to within the environment to quantify the locations, magnitudes, To measure the exergy of the transfers and individual reservoirs, and types of environmental change caused by an energy system. an appropriate reference state must be chosen. A reference state, or “dead state”, can be defined by a reference temperature (Tref), pres- sure (Pref), and chemical potentials for all relevant species in the 3. Extending exergy analysis to the environment m system ð i;ref Þ. For this isolated model system, the state of the surroundings provides a reference state from which the exergy (i.e., To demonstrate the application of exergy analysis for quanti- driving potential) of the transfers and reservoirs can be measured fying the locations, magnitudes, and types of environmental change caused by an energy system, a small-scale energy system operating within a well-defined, local environment is analyzed
4 Strictly speaking, the engine is a “heat-matter” engine because the resource is heat but entropy is rejected to the environment in the form of matter. A true heat 3 The details of this integration are provided in Appendix A. engine uses heat as both the resource and means of entropy rejection. A.P. Simpson, C.F. Edwards / Energy 36 (2011) 1442e1459 1447
transfers, state changes, and destructions is again shown through the exergy balances for the individual reservoirs:
: d d d ½C XC/H þ XC/L ¼ dXC Xdest;C (20)
: d d d d ½W XW/H XH/W þ XW/L ¼ dXW Xdest;W (21)
: d d d ½L XC/L þ XW/L ¼ dXL þ Xdest;L (22)
: d d ½S XL/S ¼ dXS þ Xdest;S (23)
Fig. 4. Natural and anthropogenic transfers in the model system during heat engine As in Eqs. (16)e(19), the above equations show that, at any instant, operation. Red arrows: upstream transfers; black arrows: downstream transfers; blue the net exergy transferred to a reservoir is equivalent to the sum of arrows: natural transfers; black dashed lines: control boundaries. (For interpretation of the exergy change and exergy destruction within the reservoir. the references to colour in this figure legend, the reader is referred to the web version of this article.) However, due to the anthropogenic transfers, the natural transfer, exergy change, and exergy destruction terms in the above equa- 5 since it is modeled as a thermodynamic (“infinite”) reservoir. Since tions are different from those in Eqs. (16)e(19). copper is not present in the surroundings, a reference state for copper The change due to the heat engine can be shown by taking the is required to quantify its chemical exergy. An appropriate chemical difference between the exergy balances for the individual reser- reference state for copper would be that of solid copper, which means voirs during heat engine operation and in the absence of the heat that the copper block only has thermo-mechanical exergy. engine. Doing this and rearranging the equations yields: The change that the heat engine drives in its environment can be h i quantified by tracking the exergy of transfersdnatural and : d o d d o ½C XC/H ¼ dXC dX Xdest;C X ; d C dest C anthropogenic within the environment. In the absence of heat engine operation (the anthropogenic activity), exergy would be d d o ð24Þ XC/L XC/L naturally transferred between the environmental reservoirsd driving natural state change and natural exergy destruction within h i : d o d d o ½W XH#W ¼ dXW dXW þ Xdest;W X ; the environment. The relationship between the natural exergy dest W transfers, state changes, and destructions is shown through the d d o þ XW/L XW/L ð25Þ exergy balances for the individual reservoirs: d d o d d o o : d o o d o ½L : XC/L X / þ XW/L X / ¼ dXL dX ½C XC/L ¼ dXC Xdest;C (16) C L W L L h i o o þ dX ; dX þ dX / dX ð26Þ : d o o d o dest L dest;L L S L/S ½W XW/L ¼ dXW Xdest;W (17) h i : d d o o d d o : d o d o o d o ½S XL/S XL/S ¼ dXS dXS þ Xdest;S Xdest;S (27) ½L XC/L þ XW/L ¼ dXL þ Xdest;L (18)
# d hd : d o o d o where represents a net transfer (e.g., XH#W XH/W ½S XL/S ¼ dXS þ Xdest;S (19) dXW/H). where the superscript o designates values in the absence of Equations (24) and (25) show that, at any instant during heat anthropogenic activity.6 engine operation, the net exergy directly transferred to the copper Equations (16)e(19) show that, at any instant, the net exergy block and water tank (upstream or downstream of the work transferred to a reservoir is equivalent to the sum of the exergy extraction process) is equivalent to the sum of the differences change and exergy destruction within the reservoir. The equations between the exergy change, exergy destruction, and net exergy can be interpreted as showing that the natural exergy transfers transferred from the reservoirs during the activity and in the between the reservoirs are the drivers of natural state change and absence of the activity. The equations can be interpreted as showing natural exergy destruction. that direct transfers of exergy caused by the heat engine are the During heat engine operation, state change and exergy drivers of environmental change in the copper block and water tank, destruction is caused by both anthropogenic and natural transfers. and the types of change are state change, destruction change, and The relationship between the natural and anthropogenic exergy alterations of natural transfers. In order for no change to occur, the anthropogenic transfers must have zero exergydwhich means that no work would be produced from the heat engine. Equations (26) and (27) show that, at any instant during heat 5 Only the reservoirs shown in the Fig. 3 are considered in this analysis. If the engine operation, the difference between the net exergy naturally model system was considered to be within the terrestrial environment, a more transferred to the laboratory and surroundings during the activity appropriate reference state would be the mutual stationary state of the terrestrial and in the absence of the activity is equivalent to the sum of the environment. The concept of a mutual stationary state is discussed in Section 4. 6 Implicit in the differential impact equations are the surface and volume inte- differences between the exergy change, exergy destruction, and net grals that correspond to the control boundaries shown in Fig. 4. All exergy transfers exergy naturally transferred from the reservoirs during the activity are integratedR over the surface of the control boundary they cross (e.g., and in the absence of the activity. d _ 00 _ 00 XC/H ¼ dt XC/H dSC , where X is exergy transfer rate per surface area, and SC is To illustrate the correspondence between this model problem the surface area of the copper block), and all exergy changes and destructions are and an actual energy system operating within the natural envi- integratedR over the volumeR enclosed by the control boundary (e.g., _ 000 d _ 000 _ 000 ronment, consider the geothermal power plant illustrated in Fig. 5. dXC ¼ dtð XC dVC Þ, Xdest;C ¼ dt Xdest;C dVC , where X is exergy change or destruction rate per volume, and VC is the volume of the copper block). The geothermal power plant and its environmental reservoirs 1448 A.P. Simpson, C.F. Edwards / Energy 36 (2011) 1442e1459
Initial Equilibrium States Final Equilibrium State Space
Atmosphere AT( AAiA,, P µ , ) AB( T,, P ) Geothermal AAiAµ ,
Power Plant BU( BB,, V N kB, ( Surface Water Reservoir Fig. 6. Isolated, two-reservoir system of differing thermodynamic states with reservoir Upper Lithosphere A being large relative to reservoir B such that it is modeled as a thermodynamic Geothermal Reservoir (Hot Rock) reservoir (left). Final state of the system after equilibrium is reached, which is equal to the initial intensive state of reservoir A (right). Subscript i designates species initially present in reservoir A and subscript k designates species initially present in reservoir B, Fig. 5. Illustration of a geothermal power plant. which can include both reservoir A species (i) and non-reservoir A species (j). shown in the figure are analogous to the heat engine and its local environmentdthe power plant is analogous to the heat engine, the reservoir A (which is constant), subscripts i and j refer to species geothermal reservoir to the copper block, the surface water reser- present and not present in reservoir A, respectively, and nj and nij voir to the water tank, the atmosphere to the laboratory, and space are the stoichiometric coefficients for the reaction of species. A to the surroundings. The same analysis techniques used to quantify detailed derivation of Eq. (28) is presented in Appendix A. the local environmental change driven by the heat engine can be Equation (28) is equivalent to the traditional equation for applied to the geothermal power plant to quantify the change it internal exergy derived in Appendix A if the state of reservoir A is fi drives in the natural environment. However, in order to make this de ned as the state of the reference environment (i.e., if TA ¼ To, extension, an appropriate reference state must be defined to m m PA ¼ Po, and i;A ¼ i;o for all i). Considering reservoir A to be an measure the exergy (i.e., driving potential) of the power plant’s environmental reservoir, then the free energy of the system is equal environmental interactions, the environmental reservoirs, and the to the exergy of reservoir B relative to its its environment natural environmental transfers. This requires revisions to the (Wmax;System ¼ Wmax;B ¼ XB). traditional understanding and definition of a reference state (or The two-reservoir system just considered involved a thermo- dead state) and a model representation of the natural environ- dynamic reservoir that, when considered to be an environmental mentdthese are the topics of the next two sections, respectively. reservoir, provides a reference state from which the exergy of the other reservoir could be defined. The inherent principle of exer- 4. Defining reference states gyda measure of the ability to produce work or to drive changedis not limited to systems involving a large environmental reservoir. To As discussed in Section 2, the maximum amount of work that illustrate this, consider a two-reservoir system with both reservoirs can be extracted from a non-equilibrium system under specific considered to be of similar size, as shown in Fig. 7. Since the interaction constraints is the system’s free energy. If the system is reservoirs are initially out of equilibrium, each reservoir has comprised of a resource and its environment, then the system’s free the potential to drive change relative to the other reservoir. The energy is equal to the exergy of the resource. In order to define the potential to drive change vanishes when the two reservoirs reach exergy, or free energy, of a system, a reference state is required. A equilibrium. The mutual equilibrium state of the system defines reference state of a system provides a datum from which the work a reference state from which the exergy of the individual reservoirs potential, or change potential, of the system is measured. When the and therefore the joint system can be measured. In other words, the system reaches the reference state, no work can be produced from, mutual equilibrium state is a kind of “dead state” from which no or no change can occur within, the system. An appropriate refer- change can occur. The exergy of the composite system and indi- ence state for a system depends on the specifics of the system. To vidual reservoirs relative to the mutual equilibrium statedreferred illustrate this, several example systems are considered. to here as the reference statedis given by: First, consider a two-reservoir system of differing thermody- namic states and initially restrained from interaction, as shown in XSystem ¼ XA þ XB (29) Fig. 6. Reservoir A is sufficiently large with respect to reservoir B P m such that it can be modeled as a thermodynamic reservoir (i.e., as XA ¼ UA þ Pref VA Tref SA i;ref Ni;A fi " # i having a xed intensive state). Each reservoir is initially in internal P P n (30) equilibrium, but not in mutual equilibrium. The free energy of the ij m ; N ; i ref nj j A joint system is measured by the maximum amount of work that can j i be extracted as the system equilibrates reversibly. Since reservoir A is large with respect to reservoir B, the final (i.e., equilibrium) intensive state of the system is the same as the original state of reservoir A, as shown in the figure. Therefore, the free energy of the Initial Equilibrium States Final Equilibrium State system is measured as the work potential of reservoir B relative to AU( ,, V N ) reservoir A, which serves as the reference state. The free energy of AA kA, this two-reservoir system is given by: AB( Tref,, P ref µ i, ref )
BU( BB,, V N kB, ) W ; ¼ W ; ¼ U þ P V T S max System max B B A "B A B !# X X X n m m ij i;ANi;B i;A n Nj;B ð28Þ Fig. 7. Isolated, two-reservoir system of differing thermodynamic states with both j i j i reservoirs of similar size (left). Final state of the system after equilibrium is reached
(right). Subscript i designates species present at equilibrium and subscript k designates where all extensive properties are evaluated at the initial state of species initially present in reservoirs A and B, which can include both equilibrium reservoir B, all intensive properties are evaluated at the state of species (i) and non-equilibrium species (j). A.P. Simpson, C.F. Edwards / Energy 36 (2011) 1442e1459 1449 P m XB ¼ UB þ Pref VB Tref SB i;ref Ni;B " # i P P (31) nij m ; N ; i ref nj j B j i where the properties of the reference state are considered to be known (or knowable) constants.7 This same approach to defining the dead stateda mutual equilibration of isolated systemsdcan be used to define the dead state for any number of interacting reservoirs of any size. A similar approach may be taken for defining the dead state of open/driven systems. To illustrate this, consider a two-reservoir system driven by heat transfer between two large thermal reservoirs, as shown in Fig. 8. Driven, two-reservoir system in thermal stationary states at the same pressure, but with differing compositions (left). Final non-equilibrium stationary state of the Fig. 8. Energy is transferred to the system (reservoirs A and B) from system after chemical equilibrium is reached (center). Temperature profiles of the a high-temperature thermal reservoir, and energy is transferred initial and final stationary systems (right). Subscript i designates species present at from the system to a low-temperature thermal reservoir. The equilibrium and subscript k designates species initially present in reservoirs A and B, individual reservoirs are initially in thermal stationary states at the which can include both equilibrium species (i) and non-equilibrium species (j). same pressure, but with differing compositions (and therefore thermal conductivities). The initial stationary temperature distri- maintaineddis the altitude at which the anthropogenic energy bution of the system might then be shown in the figure.8 Since the conversion system will be situated. Note that if the conversion reservoirs initially have different compositions, each reservoir has system interacts at two (or more) altitudes so as to take advantage the potential to drive change relative to the other. The potential to of the inhomogeneity, then the appropriate view would be to break drive change vanishes when the reservoirs reach chemical equi- the reservoirs apart into separate regions, each with an appropri- librium, and a final (non-equilibrium) thermal stationary state is ately defined state, such that mutual equilibration of reservoirs was formed. The final state defines a reference “state” from which the again the basis for defining the reference state. In the present case, free energy, or exergy, of the individual reservoirs and system can this would result in use of an energy-mean temperature (and cor- be measureddsimilar to the mutual equilibrium state for isolated, responding altitude) as being the appropriate reference. Similar multi-reservoir systems. arguments can be made with respect to the temporal variations in The final, or mutual, stationary state is reached when the reservoir state, whether they be daily, seasonal, or of some longer entropy generation rate within the system is minimized [19]. This is epoch. In each case, the appropriate definition of reference state known as the theorem of Minimum Entropy Production, and follows from the state at which further work extraction is not applies to all driven systems that are in the linear regime (i.e., it is possible by virtue of some form of mutual equilibration. not limited to systems driven by thermal flows).9 For this system, if both reservoirs are gaseous, and gravitational and buoyancy forces 5. An Expanded model of the environment are negligible, the final stationary state will have uniform compo- sition and pressure with a linear temperature distribution, as In technical exergy analysis, the environment is typically shown in the figure. The final stationary state for the systemd modeled based on the properties of the atmospheredwith modi- referred to here as the reference statedis defined by its pressure fications for solid mineral and liquid substancesdas a large reser- m (Pref), chemical potentials ( i;ref ), and temperature as a function of voir with fast internal relaxation such that its intensive state does position ðTðyÞref Þ. In general, the reference state for a driven, multi- not change (i.e., a thermodynamic reservoir)[5]. This type of reservoir system can be defined by its intensive properties as reference environment simplifies exergy calculations because the functions of position (e.g., Tref ¼ TðxÞ, Pref ¼ PðxÞ, and final (equilibrium) intensive state of a resource and its environment m m i;ref ¼ iðxÞ for all i, where x is a general position vector). is equal to the state of the reference environment. It also implies The problem that remains is possible ambiguity due to inho- that any exergy transferred from an energy system to the envi- mogeneity of the reservoirs in space and/or time. In fact, the ronment only causes exergy destruction within the environment example just considered immediately begs the question: At which (i.e., no environmental state change). This traditional representa- altitude y should the value of Tref be chosen? There are two tion of the environment is sufficient for calculating exergy as potential answers to this question. The firstdapplicable in the case a measure of maximum work when performing technical exergy where the open/driven system has the potential to be decoupled analysis. However, in order to effectively extend the principles of from its driving reservoirsdis that altitude which corresponds to exergy and exergy analysis to analyze environmental change, the subsequent, isolated equilibration of the non-equilibrium a more detailed representation is required. This can be accom- system. The seconddapplicable when the driving forces are plished by taking a macroscopic view of the natural environment. The terrestrial environment can be broken down into three major environmental reservoirs: atmosphere, hydrosphere, and litho- 7 Equations (29)e(31) can also be derived by considering a three-reservoir sphere. The atmosphere is a reference environment of the air (similar system composed of the two environmental reservoirs of similar size, and a “large” to the traditional atmosphere-based reference environment), the environmental reservoir that has the same state as the mutual equilibrium state of hydrosphere is a reference environment of the oceans, and the the other two reservoirs. The state of the “large” reservoir acts as a reference state lithosphere is an aggregated reference environment of the earth’s from which the exergy of the composite system and other two reservoirs can be defined. Therefore, by analogy, the mutual equilibrium state of the two-reservoir crust and surface water (e.g., lakes, rivers, snow pack). Depending on system shown in Fig. 7 serves as a fiducial state for defining exergy. the specifics of the energy system and type of analysis, the major 8 A stationary temperature TðyÞ implies that mean heat flow is uniform; other- reservoirs may need to be further broken down into sub-reservoirs, wise there will be an accumulation or depletion of energy within the system, which or minor reservoirs, in order to provide a suitable representation of would require a time-dependent temperature profile [19]. the environment. For example, when analyzing a power plant that 9 Linear regime refers to thermodynamic flows (e.g., heat transfer, diffusion, chemical reactions, electrical conduction) that are linear functions of their driving uses a lake for cooling water, the lake should be broken apart from forces (e.g., temperature, concentration, chemical affinity, electric field). the lithosphere and modeled as a separate, finite reservoir. 1450 A.P. Simpson, C.F. Edwards / Energy 36 (2011) 1442e1459
The terrestrial environmental reservoirs serve as large reservoirs for resources to be converted into exergetic products (e.g., work, Sun electricity, commercial fuels, heat).10 A review of the global exergy resources available for work production on Earth is presented by Space Hermann [20]. Global exergy resources can be categorized as either fl exergy accumulations or exergy ows. The majority of the work on High Atmosphere Earth is produced from accumulated fossil and nuclear resources. K.E. Fossil resources are the by-products of plant and animal matter that have been converted by the Earth’s natural exergy flows and Surface Biosphere Water processes into higher quality resources (e.g., crude oil, natural gas, Lithosphere Fossil coal). They are typically located within the lithosphere and naturally Resources Nuclear Hydrosphere segregated from communication with the other major reservoirs. Geothermal Resources Nuclear resources are from the origin of the universe and are located within the lithosphere and hydrosphere. Both resources are typi- Fig. 9. Model representation of the natural environment. cally considered non-renewablednuclear resources because they are finite, and fossil resources because the time scales over which they are replenished are significantly longer than the anthropogenic The environmental and resource reservoirs can be represented 11 time scales in which they are extracted and consumed. For modeling graphically, as shown in Fig. 9. The environmental reservoirs are purposes, fossil and nuclear resources are represented as individual naturally out of equilibrium with one another, and therefore have resource reservoirs located within their respective terrestrial envi- the potential to drive change. As a result, exergy is naturally ronmental reservoirs. transferred between the reservoirs, driving natural state change The Earth’s second largest accumulated resource after nuclear and natural exergy destruction. These natural interactions, and the matter is the thermal energy in its mantle and core, which is resulting natural changes and destructions, occur on a wide-range called crustal thermal energy. Crustal thermal energy is derived of time scales and magnitudes. Natural interactions enable and from the decay of nuclides in the Earth’s interior, the original support life on Earth. Living organisms (e.g., animals, plants, internal energy from the gravitational collapse of the Earth, and to fungus, micro-organisms) exist in all three terrestrial environ- a lesser extent, the dissipation of tidal forces [20]. The Earth’s mental reservoirs. For modeling purposes, living organisms are crustal thermal energy provides a relatively constant flow of represented in their own region, referred to here as the biosphere. fi exergy through the lithosphere in the form of heat. The quality of The pathways for natural interactions are depicted in the gure by the heat that reaches the surface of the lithosphere is, in most the locations of the reservoirs. For example, the atmosphere cases, too low for it to be economically converted to work. interacts with the lithosphere, hydrosphere, biosphere, and space. Therefore, work is typically produced by intervening in the natural In order to measure the exergy (i.e., driving potential) of natural exergy flow deep within the lithosphere. The locations of heat interactions and environmental reservoirs, an environmental extraction are commonly referred to as geothermal reservoirs. reference state is required. As shown in Section 4, the exergy (i.e., Exergy extracted from geothermal reservoirs is typically consid- environmental free energy) of multi-reservoir systems can be ’ ered a renewable resource; however, this is only true when the measured relative to either the system s mutual equilibrium state if ’ exergy is extracted in a manner such that there is sufficient time it is isolated, or the system s mutual stationary state if it is driven. for natural replenishment to take place. For modeling purposes, Since the Earth is a driven, multi-reservoir system, in theory its fi geothermal reservoirs are represented as resource reservoirs mutual stationary state de nes an environmental reference state located within the lithosphere. from which the exergy of reservoirs and interactions can be fi The Earth’s largest resource flow is solar radiation generated measured. Any stationary state can be de ned by its intensive from fusion reactions occurring within the sun. The sun is a finite properties as functions of position. For the purposes of environ- fi resource, however, the solar radiation produced is typically mental exergy analysis, we choose to de ne the environmental considered a renewable resource because of the relatively rapid reference state (a stationary state) using a mean temperature (Tref), m rate of replenishment on Earth. Solar radiation travels through pressure (Pref), and chemical potential for all relevant species ð i;ref Þ. space, which acts as a medium for transmitting radiation to the Now that a more detailed representation of the natural envi- Earth, as well as a sink for the Earth’s re-radiation. For modeling ronment and a reference state for measuring the exergy of envi- purposes, the sun is represented as a resource reservoir and space is ronmental reservoirs and natural transfers have been established, included as an environmental reservoir. the ways in which humans interact with and impact the environ- Other major resource flows include wind, tides, waves, and ment can now be discussed. rivers. All of these occur within the terrestrial environmental reservoirs and are typically considered renewable resources due to 6. Anthropogenic interactions and environmental impact the relatively short time scales over which they are regenerated. In order to model work extraction from these resources, the terrestrial Human activity occurs within the natural environment in environmental reservoir in which the flow is located must be a region referred to as the anthrosphere. The anthrosphere is broken apart into a resource reservoir and an environmental defined as the part of the natural environment physically modified reservoir. For example, when analyzing work extraction from wind, by humans and used for their activities [21]. The size of the the atmosphere must be broken apart into high and low kinetic anthrosphere depends on the specifics of the activity. For example, energy reservoirsdwith the high kinetic energy reservoir modeled as the resource and the low kinetic energy reservoir modeled as the environment. 11 The distinction between environmental and resource reservoirs depends on the relative sizes of the reservoirs. For example, if a small amount of air is introduced into a large fossil resource reservoir (e.g., a natural gas reservoir), the air is the resource because it has the potential to produce work relative to its fossil resource surround- 10 For the sake of brevity, the term work is used to represent all exergetic ings. For the sake of brevity, environmental and resource reservoirs will be referred to products. as environmental reservoirs. When necessary, the distinction is made explicit. A.P. Simpson, C.F. Edwards / Energy 36 (2011) 1442e1459 1451
Sun Sun Space Space
Surface-Incident Heat Noise Heat Solar Radiation Air Exhaust Gas Radiation Anthrosphere Anthrosphere Cooling Water Biosphere Natural Lithosphere Lithosphere Hydrosphere Hydrosphere Gas
Fig. 10. Example of the first conversion pathway. Red arrows: upstream interactions; Fig. 11. Example of the second conversion pathway. Red arrows: upstream interac- black arrows: downstream interactions. (For interpretation of the references to colour tions; black arrows: downstream interactions. (For interpretation of the references to in this figure legend, the reader is referred to the web version of this article.) colour in this figure legend, the reader is referred to the web version of this article.)
transferred between environmental reservoirs driving natural state when analyzing the extraction of natural gas from an underground change and natural exergy destruction within the reservoirs. The reservoir, the anthrosphere extends into the lithosphere to the natural exergy transfers, state change, and destruction set a baseline location of extraction within the reservoir. from which any changes caused by anthropogenic activity can be There are two main pathways by which energy systems within measured. Any changes to the states of, natural exergy transfers the anthrosphere convert resources to work: (1) by cross-con- between, or exergy destruction within the environmental reservoirs necting environmental reservoirs, and (2) by intervening in natural caused by anthropogenic activity is defined as environmental exergy flows. Both conversion pathways interact with the envi- impact. This definition of environmental impact is agnostic to the ronment. Each pathway’s environmental interactions can be consequences of the impact, and it is not limited to a specific type of broken down into upstream and downstream interactions. impact (e.g., atmospheric state change) or consequence (e.g., global Upstream interactions are defined as exergy transfers to or from the warming). anthrosphere, or alterations of natural exergy transfers within the A diagram illustrating the drivers of environmental impact and anthrosphere, in order to extract and convert a resource to work. the terminology used to describe environmental interactions and Downstream interactions are defined as energy transfers from the impacts is shown in Fig. 12. Environmental impact begins with anthrosphere as a consequence of the conversion process. anthropogenic activity. The environmental interactions of anthro- An example of the first conversion pathway is the extraction and pogenic activity may involve upstream or downstream transfers conversion of natural gas into electricity using air from the atmo- (e.g., transfers of natural gas to the anthrosphere or emissions from sphere and cooling water from a surface water reservoir. A diagram the anthrosphere), which are called direct transfers, or upstream illustrating the environmental interactions of this example energy alterations of natural transfers (e.g., alteration of surface incident system is shown in Fig. 10. The upstream interactions include the solar radiation within the anthrosphere), which are called direct transfers of natural gas from the gas reservoir, air from the atmo- alterations of natural transfers. Direct transfers and direct alter- 12 sphere, and water from the surface water reservoir. The down- ations of natural transfers have exergy, and therefore the potential stream interactions include the transfers of cooling water to the to cause environmental impact (i.e., drive environmental change). surface water reservoir, and exhaust gases, heat, and noise to the Direct transfers impact the environmental reservoirs to or from atmosphere. Both upstream and downstream interactions transfer which the transfers occur (e.g., gaseous emissions to the atmo- energy between the anthrosphere and connected environmental sphere impact the atmosphere; natural gas removal from an reservoirs. The electricity produced by the conversion process underground reservoir impacts the reservoir), and direct alter- remains in the anthrosphere until final consumption by an elec- ations of natural transfers impact the environmental reservoirs trical device. from which the alterations occurs (e.g., intercepting solar radiation An example of the second conversion pathway is the conversion normally incident on the lithosphere impacts the lithosphere). of surface-incident solar radiation into electricity via photovoltaic Environmental impact caused by direct transfers and direct alter- (PV) cells. A diagram illustrating the environmental interactions of ations of natural transfers is referred to as direct impact. this example energy system is shown in Fig. 11. The anthrosphere is Direct impact may cause alterations of natural transfers located at the intersection of the lithosphere, biosphere, and between environmental reservoirs (e.g., direct changes to the fl atmosphere. The activity intervenes in the natural exergy ow of amount of CO2 in the atmosphere may cause alterations of natural solar radiation above the lithosphere and biosphere, and as a result transfers of CO2 between the atmosphere and hydrosphere), or of the conversion process, transfers heat and radiation to the transfers between environmental reservoirs that did not occur atmosphere. The surface-incident solar radiation altered within prior to the anthropogenic activity (e.g., direct changes to the the anthrosphere is considered the upstream interaction, and the amount of fertilizer on the surface of the lithosphere may cause transfers of heat and radiation from the anthrosphere are the fertilizer run-off into the hydrosphere). Transfers and alterations of downstream interactions. natural transfers caused by direct impact are called indirect In the absence of anthropogenic activity, natural interactions transfers and indirect alterations of natural transfers, respectively. would occur without disturbancedexergy would be naturally Indirect transfers and indirect alterations of natural transfers have exergy, and therefore the potential to cause environmental impact. Environmental impact caused by indirect transfers and indirect alterations of natural transfers is referred to as indirect impact. 12 An example of an upstream interaction involving a transfer from the anthro- sphere to an environmental reservoir is the injection of CO2 into an oil reservoir for As illustrated in Fig. 12, the drivers of environmental the purpose of enhancing oil recovery. impactddefined as changes to the states of, exergy transfers 1452 A.P. Simpson, C.F. Edwards / Energy 36 (2011) 1442e1459
Anthropogenic Activity
Direct Alterations Direct of Natural Transfers Transfers Direct Impact
Indirect Alterations Indirect Transfers of Natural Transfers Fig. 13. Model representation of the conversion of a geothermal resource to electricity. Indirect Black arrows: downstream transfers; red arrows: upstream transfers; blue arrows: natural exergy transfers; black dashed lines: reservoir control boundaries. (For inter- Impact pretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Fig. 12. Environmental impact drivers and terminology. X X o o o o ½b : dXb #b þ dXa #b ¼ dXb þ dX ;b (33) k l k m k k dest k between, or exergy destruction within environmental reser- l m d voirs are the transfers and alterations of natural transfers caused where the superscript o again designates values in the absence of by an anthropogenic activity. The potential for transfers and alter- anthropogenic activity, the indices j and k refer to a and b reservoirs ations of natural transfers to drive environmental impact is in communication with reservoir ai, and indices l and m refer to measured by their exergy (i.e., environmental free energy). As 13 b and a reservoirs in communication with reservoir bk. All exergy shown in the next section, the locations, magnitudes, and types of values are measured relative to the environmental reference state environmental impact caused by an anthropogenic activity can be discussed in Section 5. The above exergy balances show that, at any fi quanti ed by applying exergy analysis to the environment using instant, the net exergy transferred to a reservoir is equivalent to the the same approach demonstrated in Section 3 to quantify the sum of the exergy change and exergy destruction within impact of the heat engine on its local environment. the reservoir. The equations can be interpreted as showing that the natural exergy transfers between the reservoirs are the drivers of 7. Environmental exergy analysis natural state change and natural exergy destruction. During anthropogenic activity, state change and exergy To demonstrate the application and utility of exergy analysis for destruction is caused by both anthropogenic and natural transfers. quantifying environmental impact, the geothermal power plant The relationship between the natural and anthropogenic exergy introduced in Section 3 is considered. A diagram illustrating the transfers, state changes, and destructions is again shown through the exergy balances for the a and b reservoirs: environmental interactions of such a plant is shown in Fig. 13.As P P fi shown in the gure, activities in the anthrosphere cross-connect dX #a þ dXa #a þ dXb #a Anth i j i k i a geothermal reservoir located within the lithosphere to a surface j k (34) water reservoir. The upstream interactions include exergy transfers dXa dX ¼ i þ dest;ai from the geothermal reservoir (heat) and surface water reservoir X X (cooling water), and the downstream interactions include exergy ½b : dXb #b þ dXa #b ¼ dXb þ dX ;b (35) k l k m k k dest k transfers to the surface water reservoir (coolant return) and l m atmosphere (heat and noise). Both the upstream and downstream As in Eqs. (32) and (33), the above equations show that, at any interactions are direct transfers between the anthrosphere and instant, the net exergy transferred to a reservoir is equivalent to the environmental reservoirs. Also shown in the figure are the natural sum of the exergy change and exergy destruction within the exergy transfers between the environmental reservoirs. reservoir. However, due to the anthropogenic transfers, the natural The environmental reservoirs can be categorized based on their transfer, exergy change, and exergy destruction terms in the above communication with the anthrosphere. Reservoirs in direct equations are different from those in Eqs. (32) and (33). communication with the anthrosphere are referred to as a reser- The environmental impact that anthropogenic activity has on voirs, and reservoirs not in direct communication with the a given a reservoir can be shown by taking the difference between anthrosphere are referred to as b reservoirs. The a reservoirs in this the exergy balances for the reservoir with anthropogenic activity example include the geothermal and surface water reservoirs, and and in the absence of the activity. Doing this and rearranging the the b reservoirs include the atmosphere, lithosphere, biosphere, equation yields: hydrosphere, and space. The control boundaries for the individual h i h i reservoirs are shown by the dashed lines in Fig. 13. o o dX #a ¼ dXa dXa þ dX ;a dX Anth i i i dest i dest;a In the absence of anthropogenic activity, exergy would be i Ph i Ph i (36) naturally transferred between the environmental reservoirs. The d d o d d o þ Xai#aj Xa #a þ Xa #b X i j i k ai#b relationship between the natural exergy transfers, state change, j k k and destruction is shown through the exergy balances for the a and b reservoirs:
X X 13 o o o o As in the laboratory-scale example, implicit in the differential impact equations ½a : dXa #a þ dXb #a ¼ dXa þ dX ;a (32) i j i k i i dest i are surface and volume integrals that correspond to the control boundaries shown j k in Fig. 13. A.P. Simpson, C.F. Edwards / Energy 36 (2011) 1442e1459 1453
The equation shows that, at any instant during anthropogenic h i h i o o o a dXa /a dXa /a ¼ dXa dXa þ dX ;a dX activity, the net exergy directly transferred to an reservoir j i j i i i dest i dest;ai (upstream or downstream of the conversion process) is equivalent h i Ph i to the sum of the differences between the exergy change, exergy þ dXa /a dXao a þ dXa #a dXao a i j i/ j i k i# k (39) destruction, and net exergy transferred from the a reservoir during k Ph i the activity and in the absence of the activity. The equation can be o þ dXa #b dX i l ai#b interpreted as showing that direct transfers are the drivers of l l environmental impact on a reservoirs, and the types of direct The difference on the left hand side of this equation represents the impact on a reservoirs are state change, destruction change, and amount of exergy altered within the anthrosphere from naturally alterations of natural transfers.14 being transferred from reservoir a to reservoir a (e.g., the amount The environmental impact that anthropogenic activity has on j i of surface-incident solar radiation altered by PV cells from being a given b reservoir can be shown by taking the difference between transferred from the atmosphere, a , to the lithosphere, a ). The the exergy balances for the reservoir with anthropogenic activity j i difference can be thought of, or viewed, as a direct transfer of and in the absence of the activity, and rearranging the equation. exergy from a The equation shows that, at any instant during an Doing this for a b reservoir in communication with an a reservoir j. anthropogenic activity, the exergy altered from reaching an yields: a reservoir is equivalent to the sum of the differences between the h i h i exergy change, exergy destruction, and net exergy naturally o o o dXa #b dX ¼ dXb dX þ dX ;b dX transferred from the reservoir during the activity and in the i k a #b k b dest k dest;b i k k k absence of the activity. The equation can be interpreted as showing (37) Ph i Ph i that direct alterations of natural transfers are the drivers of envi- o o a þ dXb #b dX þ dXb #a dX ronmental impact on reservoirs from which exergy is altered, and k l b #b k m b #am l k l m k the types of direct impact on the reservoir are state change, destruction change, and alterations of natural transfers. and doing this for a b reservoir not in communication with an As in the laboratory-scale example, the differential impact a reservoir yields: equations provide insight into the possible locations and types of h i h i environmental impact caused by an anthropogenic activity. In d d o o d d o order to solve for the actual locations, magnitudes, and types of Xb #b Xb #b ¼ dXb dXb þ Xdest;b X ;b k m k m m m m dest m environmental impact, the differential impact equations must be integrated over the interval of interestdfrom the start of the Xh i o activity to the integration time, tint. Information about the prop- þ dXb #b dXb #b (38) m n m n n erties of transfers and reservoirs is required in order to solve the differential impact equations. Although the natural environment The above equations show that, at any instant during an anthro- is a more complex system than the local environment in the pogenic activity, the difference between the net exergy naturally laboratory-scale example, the same engineering models and transferred to a b reservoir during the activity and in the absence of assumptions used to model the the laboratory’s environment and the activity is equivalent to the sum of the differences between the solve its differential impact equations can be applied to the exergy change, exergy destruction, and net exergy naturally natural environmentdchoosing appropriate control boundaries, transferred from the b reservoir during the activity and in the reservoir classifications, time scales, etc. The appropriate envi- absence of the activity. The equations can be interpreted as ronmental models and the amount of information required to showing that alterations of natural transfers are the drivers of solve the differential impact depends on the specifics of the indirect impact on b reservoirs, and the types of impact on anthropogenic activity (e.g., power plant size, number of power b reservoirs are state change, destruction change, and other alter- plants, time of operation) and the questions being asked of the ations of natural transfers. analysis (e.g., local impact on a water reservoir, global impact on Equations (36)e(38) can be referred to as the differential impact atmosphere). equations. They apply to any energy system categorized by the first When sufficient information is known to solve the differential conversion pathwaydi.e., they are not limited to geothermal impact equations, Eqs. (36)e(39):, integration from the start of an conversion processes. For energy systems categorized by the activity to a specified integration time (tint) yields the (integrated) second conversion pathway, the above impact equations apply for impact equations. all reservoirs except for a reservoirs that would have received the h i h i o o natural exergy flow altered within the anthrosphere. As discussed X #a ¼ Xa ;t Xa ; þ X ;a X Anth i i int i tint dest i dest;ai in the previous section, direct alterations of natural transfers Ph i Ph i (40) impact the environmental reservoirs from which the alterations o o þ Xa #a Xa #a þ Xa #b X i j i j i k ai#b occur (e.g., alteration of surface-incident solar radiation impacts the J k k lithosphere). Therefore, a reservoirs from which exergy is altered h i h i within the anthrosphere are directly impacted by the exergy o o o Xa #b Xa #b ¼ Xb ; Xb ; þ X ;b X ;b altered from naturally reaching the reservoirs. The differential i k i k k tint k tint dest k dest k impact equation for an a reservoir from which exergy is altered is Ph i Ph i (41) o o given by: þ Xb #b Xb #b þ Xb #a Xb #a k l k l k m k m l m h i h i o o o Xb #b X ¼ Xb ; X þ X ;b X k m b #b m tint b ;t dest m dest;b 14 When using Eqs. (37) and (38) to quantify the impact on b reservoirs caused by k m m int m indirect transfers (i.e., transfers between environmental reservoirs that did not Ph i (42) o occur prior to the anthropogenic activity), the net exergy transferred to the reser- þ Xb #b X #b m n b n d o d o n m voir in the absence of the activity is zero (i.e., Xa #b ¼ 0, Xb #b ¼ 0). i k k m 1454 A.P. Simpson, C.F. Edwards / Energy 36 (2011) 1442e1459 h i h i o o o Xa /a Xa /a ¼ Xa ;t Xa ; þ X ;a X j i j i i int i tint dest i dest;ai h i Ph i þ Xa /a Xo þ Xa #a Xo i j ai/aj i k ai#ak (43) Ph i k o þ Xa #b X i l ai#b l l In each of the impact equation, the exergetic magnitude of the drivers of impact (transfers or alterations of natural transfers) on a reservoir is equal to the sum of the types of impact within the reservoirdstate change, destruction change, and alterations of natural transfers. As shown in the equations, state change is measured as the difference between the exergy of a reservoir Fig. 14. Three reservoir system in communication with an anthropogenic activity. evaluated at the end of integration with anthropogenic activity and Black arrows: downstream transfers; blue arrows: natural transfers; black dashed fi in the absence of the activity. The initial exergy of the reservoirs lines: control boundaries. (For interpretation of the references to colour in this gure legend, the reader is referred to the web version of this article.) with and without activity cancel because they are equal at time zero (i.e., the beginning of the integration). h i The actual locations, magnitudes, and types of environmental d o d d o XAnth/a ¼ dXa dXa þ Xdest;a Xdest;a impact caused by an anthropogenic activity depend on the form h i h i o o (e.g., thermal, mechanical, chemical, gravitational potential, etc.), þ dXa#b dXa#b þ dXa#x dXa#x ð44Þ rate, and magnitude of the direct exergy transfers and alterations, and the properties and size of the environmental reservoirs. For h i h i d d o o d d o example, a direct transfer of thermal exergy to an environmental Xa#x Xa#x ¼ dXx dXx þ Xdest;x Xdest;x (45) reservoir can cause different impacts than a direct transfer of h i h i chemical exergy to the same reservoir at the same rate and o o o dXa b dX ¼ dXb dX þ dX b dX (46) magnitude. Or, a direct transfer of chemical exergy to a small # a#b b dest; dest;b reservoir can cause different impacts than the same direct transfer The differential impact equations provide insight into the possible to a larger reservoir with the same properties (less state change and locations and types of environmental impact. To interpret the more destruction change). equations for decision making, a value for each type of impact must The framework of environmental exergy analysis presented in be assigned. this section is based on fundamental thermodynamic principles. Consider the case where region x has been identified as being The differential impact equations derived through environmental sensitive to state change, such that any state change within the exergy analysis provide insight into the possible locations and types region is valued as being undesirable. As shown by Eq. (45), the of environmental impact, and evaluation of the impact equations driver of impact on region x is the alteration of natural transfers quantifies the actual locations, types, and magnitudes of environ- between the region and the a reservoir, and the types of impact are mental impact. As shown in the next section, the impact equations state change and destruction change. With knowledge of the provide a basis for decision making. sensitivity to, and value of, state change within region x, the prac- tical objective is to design or choose an energy system that directly 8. Interpreting the impact equations for decision making transfers exergy to the a reservoir in a form that does not cause state change within region x. The direct exergy transfer term in Eq. The impact equations can be interpreted as showing that in (44) can therefore be viewed as the control variable, and since the order to avoid environmental impact, all direct transfers must have driver of state change is the alteration of natural transfers, it can be zero exergy. However, it is impossible to produce work in the viewed as the sensitivity constraint. anthrosphere without directly transferring exergy upstream or The differential impact equations provide insight for designing 15 downstream of a conversion process. Therefore, a practical or choosing an energy system that avoids causing state change objective inferred from the impact equations might be to minimize within region x. There are two options for avoiding state change the exergy of direct transfers, regardless of the form in which the within the region: (1) directly transfer exergy in a form such that exergy is transferred, in order to minimize the overall environ- there is no alteration of natural transfers between the region and mental impact. This approach is valid if the consequences of the the a reservoir, or (2) directly transfer exergy in a form such that types of impacts caused by an activity are all valued equally. On an any alteration of natural transfers only cause destruction change exergetic basis, the types of impact are all valued equally. However, within the region. Information is needed in order to know which from an anthropocentric viewpoint, the types of impact are not forms of exergy cause alterations of natural transfers between the likely to be of equal value. The anthropocentric value a type of region and the a reservoir, and which forms only cause destruction impact has depends on the consequences of the impact and change. If this information is known, an energy system can be anthropocentric sensitivity to the impact. designed or chosen to avoid directly transferring exergy in these To introduce the concepts of anthropocentric value and sensi- forms. tivity, consider the activity shown in Fig. 14. The activity directly In order to identify the sensitivities to a type of impact, the a transfers exergy to an reservoir that is in communication with consequences of the impact must inherently have some value to b x a reservoir and another reservoir called region . The differential humansdeither directly or indirectly. A consequence can be valued impact equation for the reservoirs are: as being negative (e.g., global warming, loss of biodiversity, adverse health affects) or positive (e.g., global warming remediation, enhanced biodiversity, beneficial health affects). Often, the sensi- 15 As discussed in Section 2, the potential for work extraction only exists when tivities to a type of impact are not identified until after the conse- a system is out of equilibrium. Therefore, exergy, or free energy, must be transferred upstream or downstream of a given conversion process in order for work extraction quences of the impact have negatively affected humans (e.g., ocean to take place. acidification, acid rain, photochemical smog, global warming). In A.P. Simpson, C.F. Edwards / Energy 36 (2011) 1442e1459 1455
Sun Space
Upper Atmosphere Lower Inversion Region Atmosphere Local Hydrosphere
Fig. 15. Diagram of L.A. Basin for illustrating the environmental conditions that promote photochemical smog formation.
Fig. 16. Environmental reservoirs and interactions for analyzing the environmental order to avoid unintended consequences, even when the objective impact of photochemical smog. Red arrows: upstream transfers; black arrows: is to maximize positive consequences, all other types of impact downstream transfers; blue arrows: natural transfers; black dashed lines: reservoir should be minimized. Therefore, the practical objective for decision control boundaries. making is three-fold: (1) avoid direct transfers of exergy that cause 9. Example application: photochemical smog mitigation environmental impact with negative consequences, (2) maximize direct transfers of exergy that cause environmental impact with Photochemical smog is formed by the chemical and photo- positive consequences, and (3) minimize the exergy of direct chemical reactions of NO, NO2, oxygen, ozone, and reactive organic transfers with no known sensitivities in order to avoid changes gases (ROGs, total organic gases exclusive of methane) in the with unintended consequences (since exergy measures the atmosphere [22]. Photochemical smog is a concern because the potential to drive change). ozone produced by the smog-forming reactions can be detrimental Meeting the practical objective for decision making can be to human health. Exposure to ozone concentrations above 60 ppb accomplished by: (1) controlling the magnitude, rate, and form in causes human respiratory and eye irritation [23], and long-term which exergy is directly transferred from the anthrosphere, (2) exposure has been shown to increase risk of death from respiratory controlling the reservoir to which the direct transfers occur, or (3) illness [24]. The amount of ozone formed in a given region depends fi a combination of both. An example of the rst approach is on the initial composition of NO and ROGs present in the region, as fi x increasing the conversion ef ciency of fossil-based power plants to well as the region’s meteorology. reduce the amount of emissions transferred to the atmosphere. Photochemical smog is especially prevalent in urban areas and is Another example of the first approach is given in the next section. primarily caused by the emissions of NOx and ROGs from vehicles An example of the second approach is carbon capture and and power plants. The meteorology and dense concentration of sequestration (CCS) from stationary, fossil-resource-based power vehicles in the Los Angeles Basin promote the formation of plants in order to mitigate global increases in atmospheric CO2 photochemical smog. The Basin’s meteorology that promotes concentrations. An example that combines both approaches is the photochemical smog formation is the frequent formation of an mitigation of thermal pollution (i.e., temperature change) in inversion layer, which acts as a cap that essentially prohibits matter existing water reservoirs caused by cooling water from power transfer with the upper atmosphere. Photochemical smog is most fi plants. This is accomplished by using a suf ciently large water prevalent on days in which an inversion layer exists and there is fl reservoir (to avoid global temperature increase) and water ow little or no wind activity (onshore or offshore). When this occurs, an rate (to minimize return temperature and avoid local temperature inversion region is created around the Basin that essentially increase). In each of these examples, a larger amount of exergy is prohibits matter transfer with the surrounding atmosphere. Fig. 15 destroyed within the anthrosphere in order to avoid transferring shows a diagram of the L.A. Basin when an inversion region exists. exergy in a form (or to a reservoir) that causes environmental Emissions of NO and ROGs from anthropogenic activitydnamely fi x impact with identi ed negative consequences. I.C. engine-based transportationdare trapped within the region Applying the concepts of anthropocentric value and sensitivity where they react chemically and photochemically causing elevated to interpret the results of environmental exergy analysis for deci- ozone concentrations. Inversion regions typically exist only for d sion making referred to here as anthropocentric sensitivity ana- a day, but can last up to several days. d lysis introduces subjectivity into the environmental analysis The environmental analysis framework can be applied to framework. The anthropocentric value a type of impact has, and the analyze the anthropogenic activities that lead to the formation of threshold for which the magnitude of an impact is considered photochemical smog, and explain the techniques used in practice to sensitive, can vary across decision makers (e.g., individuals, groups, avoid its negative consequences. A diagram illustrating the envi- agencies, countries). However, in the absence of anthropocentric ronmental reservoirs and interactions that promote the formation value and sensitivity, the exergetic magnitudes of the terms in the of photochemical smog is shown in Fig. 16. In this example, the impact equations provide limited information for decision making. anthropogenic activity is I.C. engine-based transportation, and the Exergy is only a measure of the potential to environmental drive biosphere’s interactions is human breathing. change; it does not provide insight into the types of change that Using Eqs. (36) and (37), the differential impact on the inversion fi have identi ed (human) sensitivities (direct or indirect). If an region and biosphere is given by: anthropogenic activity transfers exergy to or from the environ- h i ment, change will occur. It is through anthropocentric sensitivity o o dX / dX / ¼ dX dX þ dX ; dX analysis that this change is assigned a value. The combination of Anth I I Anth I I dest I dest;I environmental exergy analysis and anthropocentric sensitivity o o þ dX # dX þ dX # dX ð47Þ analysis provides an environmental analysis framework capable of I A I#A I L I#L both quantifying environmental impact and providing insight for o þ dX # dX decision making. I B I#B 1456 A.P. Simpson, C.F. Edwards / Energy 36 (2011) 1442e1459 h i d d o o d d o quantifying environmental impact and providing insight for deci- XI#B X # ¼ dXB dX þ Xdest;B X ; (48) I B B dest B sion making. Keeping the two analysis components separate enables environmental impact to be quantified independent from The direct impact equation for the inversion region shows that the the anthropogenic sensitivity to and value of the impact. net exergy directly transferred to the inversion region drives state The analysis framework can be applied to individual energy change, destruction change, and alterations of natural transfers systems to aid in system design, or to a set of energy systems to aid with the atmosphere, lithosphere, and biosphere. The indirect in system selection. In both cases, the objective is to minimize or impact equation for the biosphere shows that the alteration of avoid causing the types of impacts with negative consequences, natural transfers between the biosphere and inversion region drive and/or maximize causing those with positive consequences. One of state change and destruction change within the biosphere. the key attributes of the analysis framework is its ability to quantify The direct transfers between the anthrosphere and inversion and compare the environmental performance of energy systems on region indirectly impact the biosphere by altering its transfers with a level playing field, regardless of the specifics of the system- the inversion region. Since the biosphere has been identified as sdresources, products, by-products, sizes, or time scales. This being sensitive to transfers of ozone, it is desirable to avoid direct capability is not provided by the existing environmental analysis transfers that cause an increase in the ozone concentration in the techniques discussed in Section 4. With the increasing desire to inversion regiondnamely transfers of NOx and ROGs. For this transition from traditional, fossil-resource-based energy systems to example, the inversion region’s state change term in Eq. (47) can be alternative, renewable-resource-based systems (e.g., from crude o treated as the sensitivity constraint ðdXI dXI Þ, and the down- oil-derived transportation fuels to biofuels, or from coal-derived stream direct transfer term in the equation is the design variable electricity to solar), having this capability is essential to making d d fi ð XAnth/I XI/AnthÞ. The sensitivity constraint can be speci ed by sound policy and investment decisions. a maximum allowable concentration of ozone within the inversion region over a specified amount of time. An example sensitivity constraint could be the Air Quality Index developed by the U.S. Acknowledgements Environmental Protection Agency, which classifies eight-hour- fi average ozone concentrations between 85 and 104 ppb as This work was supported by the Precourt Energy Ef ciency “unhealthy for sensitive group”, between 105 and 124 ppb as Center (PEEC) at Stanford University. “unhealthy”, and between 125 and 400 ppb as “very unhealthy” [25]. The design objective is to avoid directly transferring NOx and ROGs in Nomenclature an amount and at a rate that would violate the sensitivity constraint. In practice, this is accomplished by reducing the amount of NOx ’ and ROGs in a vehicle s exhaust through the use of a three-way G Gibbs Free Energy catalyst, which converts NOx, ROGs, and CO to stable N2,CO2, and h molar-specific enthalpy H2O. The reactions that take place within a three-way catalytic N mole converter are (net) exothermic. This design approach reduces the P pressure chemical exergy of exhaust, but at the expense of increasing its Q heat thermal exergy and increasing the amount of exergy destroyed S entropy within the vehicle (anthrosphere). By shifting the form in which s molar-specific entropy d exergy is directly transferred to the inversion region from T temperature d chemical to thermal the type of impact is shifted from chemical t time state change with a high anthropocentric sensitivity to destruction U internal energy change (due to thermal dissipation) with a low anthropocentric W work sensitivity. Note that the optimal action to be taken from an envi- X exergy _ ronmental perspective involves increasing the exergy destruction X exergy transfer rate in the engineered system (via the catalyst), an action that is contrary to conventional wisdom in technical exergy analysis. Greek Symbols 10. Conclusion m chemical potential n stoichiometric coefficient The environmental analysis framework can be broken down x extensive extent of reaction into two parts: first, the application of environmental exergy analysis to quantify environmental impact, and second, the appli- Subscripts cation of anthropocentric sensitivity analysis to interpret the dest destruction results of environmental exergy analysis for decision making. EQ equilibrium Environmental exergy analysis is based on fundamental thermo- gen generation dynamic principles and analysis techniques. It extends the princi- i species i ples of technical exergy analysis to the environment in order to j species j quantify the locations, magnitudes, and types of environmental o dead state impactdstate change, alteration of natural transfers, and destruc- ref reference state tion change. Anthropocentric sensitivity analysis is based on the # net transfer concepts of anthropocentric value and anthropocentric sensitivity. It enables the results of environmental exergy analysis to be interpreted for decision making, but at the expense of introducing Superscripts some subjectivity into the framework. Together, environmental o in the absence of anthropogenic activity exergy analysis and anthropocentric sensitivity analysis form an 00 per area environmental analysis framework that is capable of both 000 per volume A.P. Simpson, C.F. Edwards / Energy 36 (2011) 1442e1459 1457 X Appendix A. Derivation of exergy as a measure of maximum d d d d dU ¼ Q Wb þ hi;o Ni W (49) work i dQ X Exergy is defined as the maximum amount of work that can be dS ¼ þ s ; dN þ dSgen (50) T i o i extracted from a resource relative to the environmental o i fi surroundings with which it interacts. A resource is de ned as any Combining Eqs. (6) and (7) and employing the definition of energy accumulation or energy flow that has the potential to d boundary work, Wb ¼ PodV, yields an expression for the differ- produce work relative to its environmental surroundings. The ential work extracted from the resource. environmental surroundings are defined as the portions of the X natural environment that enable work to be extracted from d d d a resource because they act as a thermal, mechanical, and chemical W ¼ dU PodV þ TodS þ hi;o Tosi;o Ni To Sgen (51) i reservoir to the resource. The maximum amount of work is realized when the resource is reversibly brought into equilibrium with its The maximum amount of work is realized when the interactions environmental surroundings. The exergy of a resource can be occur reversibly (i.e., no entropy generation). Therefore, the broken down into various forms. The relevant forms of exergy for expression for the maximum differential amount of work that can energy systems analysis include: thermal, mechanical, chemical, be extracted from the resource is: kinetic, potential, radiation, and nuclear. The thermal, mechanical, X d m d and chemical exergy of a resource are commonly referred to as its Wmax ¼ dU PodV þ TodS þ i;o Ni (52) internal exergy, and the kinetic and gravitational potential exergy i of a resource are commonly referred to as its external exergy. m where i;o ¼ hi;o Tosi;o is the chemical potential of species i at the Presented in this section is a derivation of internal and external environmental temperature and pressure. 16 exergy. Internal exergy is defined as the integral of Eq. (52) from the resource state to the state of the environment, called the dead state.17 Appendix A.1. Internal exergy In order to perform this integration, the inexact differential for the transfer of species must be converted to an exact differential. This can The internal exergy of a resource is the maximum amount of be accomplished by considering the reversible transformation of all work that can be extracted from a resource as it reversibly reaches non-environmental species (j) present in the resource to environ- thermal, mechanical, and chemical equilibrium with the environ- mental species (i) through the following reaction: ment with which it interacts. Reversibility requires that the R : aA þ bB/cC þ dD; resource must transfer heat at the environmental temperature, j boundary work at the environmental pressure, and environmental ; x ; with extensive extent of reaction j species at their environmental chemical potentials. In technical (53) exergy analysis, reversible interactions can be realized by modeling aA/ bB þ cC þ dD fi the environment as a single reservoir that is suf ciently large and P fi n / n has suf ciently fast transport that its intensive state does not jAj i;jAi change during equilibration (i.e., the environmental temperature, i pressure, and composition are fixed). An illustration of a resource in where nj is the stoichiometric coefficient for the non-environ- communication with the environment is shown in Fig. 17. n mental species (j) in the resource, and i;j is the stoichiometric coefficient for the environmental species used or created by the Environment transformation of non-environmental species (j) to environmental δ species (i). The species balances for environmental species (i) and δ Wb δ Q Ni non-environmental species (j)are: P X To o δ io, d n x dNi ¼ Ni þ i;jd j (54) Resource δW j n x dNj ¼ jd j (55) Fig. 17. Resource in communication with the environment. Combining Eqs. (54) and (55) through the differential extent of reaction yields an exact differential expression for the moles of fi environmental species transferred (i): As shown in the gure, there are three types of transfers between X d d the resource and the environment: boundary work ð WbÞ, heat ð QÞ, dN ¼ dN þ n ; =n dN (56) d i i i j j j and environmental species ð NiÞ. Boundary work is transferred at j the environmental pressure (Po), heat at the environmental Combining the above expression and Eq. (52) yields an exact temperature (To), and environmental species at their environmental differential equation for the maximum amount of work: m chemical potentials ð i;oÞ. The maximum amount of work that can be P extracted from the resource relative to the environment is derived d m Wmax ¼ dU PodV þ TodS þ i;odNi by applying the First and Second Laws of thermodynamics to the P P i m n =n (57) control boundary around the resource. The differential expressions þ i;o i;j j dNj of the First and Second Laws for the resource are: i j
16 The derivation of internal exergy is based on lecture notes from ME370B: Energy Systems II, at Stanford University, by Professor Chris Edwards. 17 The dead state is discussed in Section 4. 1458 A.P. Simpson, C.F. Edwards / Energy 36 (2011) 1442e1459
The state of the environment enters the maximum work calculation environmental species (j) present in the environment (fNj;og)are through the fixed, intensive environmental parameters To, Po, and zero. The chemical exergy therefore simplifies to: m ; . Since the right-hand side of Eq. (57) is an exact function, the i o X X X integral is independent of the path chosen. The internal exergy can m m n =n XC ¼ GTM i;oNi i;o i;j j Nj (63) be calculated by integrating Eq. (57) along two paths: (1) from the i j i resource state (RS) to the environmental temperature and pressure, called the thermo-mechanical dead state (TM DS), while at fixed The first summation is the diffusive work potential of environmental resource composition (i.e., no diffusion or reaction permitted), and species (i) present in the resource, and the second summation is the (2) from the thermo-mechanical dead state to the dead state (DS), reactive and diffusive work potential of non-environmental species while at the fixed environmental temperature and pressure. present in the resource. Defining the two summations as:
0 1 TMZ DS ZDS X X X @ A X h ð dU PodV þ TodSÞj þ dU PodV þ TodS þ m ; dN þ m ; n ;=n dN int Fixed Comp: i o i i o i j j i i j T ¼ To RS No Reaction TM DS P ¼ Po (58)
" # The first integral in the above equation is defined as the thermo- X X X m m n =n mechanical exergy, XTM, and the second integral is defined as the Go ¼ i;oNi þ i;o i;j j Nj (64) i j i chemical exergy, XC. The internal exergy of a resource is then: then the chemical exergy simplifies to: Xint ¼ XTM þ XC (59)
Integration of the first integral yields the thermo-mechanical XC ¼ GTM Go (65) exergy: The chemical exergy is therefore the difference between the chemical potential (i.e., Gibbs Function) of the resource at the XTM ¼ðU þ PoV ToSÞ ðUTM þ PoVTM ToSTMÞ (60) thermo-mechanical dead state before and after it has reacted and diffused to become part of the environment (all at To and Po). All properties are evaluated at the extensive composition of the The internal exergy of a resource is the sum of the thermo- resource ðfNkgÞ, where subscript k represents both environmental mechanical and chemical exergy of the resource: (i) and non-environmental (j) species present in the resource. The terms in the first set of brackets are evaluated at the resource X ¼ X þ X ¼ðA G ÞþðG GoÞ¼A Go int TM C PTM TM intensive state (T, P), and are defined as the Availability Function of m ¼ðU þ PoV ToSÞ i;oNi the resource, A. The terms in the second set of brackets are evalu- " #i (66) ated at the environmental temperature and pressure (T , P ), and P P o o m n =n are the Gibbs Function of the resource at the thermo-mechanical i;o i;j j Nj j i dead state, GTM. The thermo-mechanical exergy simplifies to: The internal exergy is therefore the difference between the Avail- XTM ¼ A GTM (61) ability of the resource at the extensive resource state (T, P, fNkg) and the chemical potential of the resource after it has reacted and The thermo-mechanical exergy is therefore the difference between diffused at the thermo-mechanical dead state (To, Po) to become the Availability of the resource at the resource state and the Gibbs part of the environment. energy of the resource at the temperature and pressure of the environment. Integration of the second integral in Eq. (66) yields the chemical Appendix A.2. External exergy exergy: A resource has external exergy as a result of its velocity relative XC ¼ðUTM þ PoVTM ToSTMÞ ðUo þ PoVo ToSoÞ to the reference environment and height within the reference P P P environment. The maximum amount of work that can be extracted m m n =n (62) i;o Ni Ni;o i;o i;j j Nj Nj;o from a resource’s velocity is the difference between the kinetic i i j energy of the resource evaluated at the velocity of the resource and The terms in the first set of brackets are again the Gibbs Function of the velocity of the reference environment, and is called the kinetic exergy. The maximum amount of work that can be extracted from the resource at the thermo-mechanical dead state, GTM. The terms in the second set of brackets are evaluated at the environmental a resource’s height is the difference between the potential energy of the resource evaluated at the height of the resource and the height temperature (To) and pressure (Po) and extensive state (fNi;og). In the first summation, the chemical potential of each environmental of the environment, and is called gravitational potential exergy. The species (i) present in the resource, evaluated at the environmental external exergy of a resource is the sum of kinetic and gravitational potential exergy: intensive state (To, Po), is multiplied by the difference between the moles of environmental species (i) in the resource (Ni) and in the m 2 environment (N ; ). The extensive state of the environment (fN ; g) X ¼ X þ X ¼ ðv v Þ þmgðz z Þ (67) i o i o ext KE PE 2 o o is unknown; however, the extensive properties in the second set of brackets cancel with the extensive properties of the environment in where m is the mass of the resource, g is the gravitational constant, fi the rst summation. In the second summation, the moles of non- v and vo are the velocities of the resource and environment, and z A.P. Simpson, C.F. 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