ARTICLE IN PRESS Energy 32 (2007) 281–296 www.elsevier.com/locate/energy Energy, exergy, and Second Law performance criteria Noam Liora,Ã, Na Zhangb aDepartment of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315, USA bInstitute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100080, PR China Received 14 October 2005 Abstract Performance criteria, such as efficiencies and coefficients of performance, for energy systems, are commonly used but often without sufficient understanding and consistence. The situation becomes particularly incoherent when simultaneous energy interactions of different types, such as work, heating and cooling, take place with a system. Also, the distinction between exergy and Second Law efficiencies is not clearly recognized by many. It is attempted here to clarify the definitions and use of energy and exergy based performance criteria, and of the Second Law efficiency, with an aim at the advancement of international standardization of these important concepts. r 2006 Elsevier Ltd. All rights reserved. Keywords: Thermodynamics; Efficiency; Exergy; Second Law; Performance 1. Introduction easily converted to energy cost efficiencies if the prices of the energy forms of the useful outputs and paid inputs are There are many ways to assess energy system perfor- known. Here we define as ‘‘useful’’ all energy interactions mance, and they must be adapted to the particular use they that have been used by the system ‘‘owner’’, usually in are put to. While the underlying concepts of such terms of monetary value, and ‘‘paid’’ all energy interac- assessments are often well known and documented for a tions that have a direct cost, usually monetary, to the number of systems and cases, there are no clear agreements system owner. Thus, for example, the heat inputs that come or rules about efficiency definitions, and authors often use from the environment for which the owner does not need to different, and sometimes unsuitable, efficiency definitions pay are not included. We hasten to add that analyses that for the same systems. The situation becomes particularly address environmental impact will include exchanges with incoherent when simultaneous energy interactions of the environment too. different types, such as work, heating and cooling, take Since such energy-based criteria do not account for the place with a system. This prevents logical comparison of quality of energy, expressed as exergy, exergy-based criteria results at best, and wrong results at worst. This paper is are also appropriate as they account better for use of intended to provide some clarifications and uniformity in energy resources and give much better guidance for system that area, make a few proposals, and start a discussion that improvement. They also can be converted to exergy cost would hopefully lead to accelerated international standar- efficiencies if the exergy values of the useful outputs and dization of these important concepts. paid inputs can be rationally priced. The most common energy system performance assess- Another set of criteria assess the difference between the ment criteria are energy based (‘‘first law’’) and they are performance of a system relative to an ideal one (reversible) useful for assessing the efficiency of energy use, and can be that operates between the same thermodynamic limits. We shall call these Second Law-based criteria, although many authors use this term for exergy-based criteria. ÃCorresponding author. Tel.: +1 215 573 6000; fax: +1 215 573 6334. Ultimately, decisions on best designs are most often E-mail address: [email protected] (N. Lior). based on economical considerations, in which energy (or 0360-5442/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2006.01.019 ARTICLE IN PRESS 282 N. Lior, N. Zhang / Energy 32 (2007) 281–296 Nomenclature ZIem embodied energy efficiency ZIu utilitarian (task) energy efficiency a specific exergy, J/kg; price of energy unit, $/MJ ZI$ economic energy efficiency A exergy, J ZII Second Law efficiency b price of exergy unit, $/MJ ZQ useful heat production efficiency in a cogenera- cp specific heat at constant pressure, J/kg k tion cycle, Eq. (92) cv specific heat at constant volume, J/kg k Zw work production efficiency in a cogeneration COP coefficient of performance cycle, Eq. (91) ~ COP reversible cycle coefficient of performance, Eq. Z^I energy efficiency when the total energy content (105) of the system is taken into consideration E energy, J Z~hp heat input based reversible cycle efficiency h specific enthalpy, kJ/kg definition, Eq. (104) I irreversibility, J Z~hu heat output based reversible cycle efficiency j the number of useful work or inputs and definition, Eq. (106) outputs tpayback energy payback time, years ke specific kinetic energy, J/kg m_ mass flow rate of a stream Subscripts n the number of paid-for heat inputs q heat per unit mass, J/kg 0 dead state pe specific potential energy, J/kg a absorber P pressure, Pa c cooling, or cold temperature reservoir Q heat, J con condenser _ Q heat invested in plant construction, J cu for refrigeration use rc the useful cooling to work output ratio, Eq. cp paid-for refrigeration (89) d direct rh the useful heat to work output ratio, Eq. (90) e environment of a system R universal gas constant em embodied, Eq. (12) RI,e First Law environmental impact ratio, Eq. (13) E direct energy invested in plant construction s specific entropy, J/kg k f heating or cooling fluid S entropy, J/K h heating, or high temperature reservoir Sgen entropy generation, J/K hp paid-for heat t time, s hu for heating use T temperature, K i incoming T^ entropic temperature, Eq. (54), K I First Law v specific volume, m3 II Second Law w specific work, J/kg j index, the jth heat or work exchange W work, J k number of material products of a plant W^ work invested in plant construction, J l labor x price per unit exergy of heat, $/MJ L index of energy needed for restoration of the environment to its original state Greek letters m materials o outgoing e exergy efficiency p paid for ^t The ‘‘total’’ (or ‘‘overall’’) unsteady state rev reversible exergy efficiency s system ~t The ‘‘total’’ (or ‘‘overall’’) steady state exergy t total efficiency, including the system exergy u useful ZI energy (First Law) efficiency exergy) are only one part, and sometimes not the most energy conversion device, they can be applied at any level, significant one, where the other parts include capital such as to different components, inside spatial and investment, labor, insurance, taxes, etc. temporal processes, and down to the smallest particle It is also worth noting that while performance criteria interactions, when there is an interest in that kind of are most often applied to the entire system, such as plant or exploration. ARTICLE IN PRESS N. Lior, N. Zhang / Energy 32 (2007) 281–296 283 2. Energy-based criteria As usual, both the work and heat terms may be composed of flow and direct components, or in general 2.1. Introduction W ¼ mke_ ðÞþþ pe W d ; Q ¼ mh_ þ Qd , (3) There are many definitions of energy efficiency, based on where m_ is the mass flow rate of the stream carrying the need (or greedy), and some of the more common ones are specific kinetic and potential energy work, or h in or out of reviewed below. the system, and Wd and Qd are the direct energy input to- and output from- the system. For work terms the latter may be a direct mechanical interaction with the system, 2.2. Total energy efficiency such as a stirrer inserted into it, and for heat ones it may be irradiation or any exothermic reaction. We start with the energy conservation equation for a A total energy efficiency Z^It can be defined in its broadest system (Fig. 1) undergoing a process from state 1 to state 2, manner as P P where the values of the system energy at these states are E1 E2 þ jW o;j þ jQo;j and E , respectively, and which undergoes j work and heat Z^ ¼ P P 2 It E þ Q þ W interactions 1 j i;jÀÁj i;j !E2 þ W o þ Q À Q þ Q X X X X ¼ ÀÁo;h o;c o;e ¼ 1. ð4Þ E1 þ W i þ Qi;h À Qi;c þ Qi;e E1 À E2 ¼ W o;j þ Qo;j À Qi;j þ W i;j j ÀÁj j j Obviously, the ratio of all energy outputs to inputs, Eq. ¼ W þ Q À Q þ Q (4), is always equal to 1 and is thus useless for system oÂÃoÀÁ;h o;c o;e performance assessment, although it should always be used À W i þ Q À Q þ Q , ð1Þ i;h i;c i;e in computations as a part of results validation. where in the second line we use the notation Most often, the steady-state total energy efficiency is X X defined without consideration of the energy value of the W o W o;j W i W i;j, system, E, to more clearly focus on the energy inputs and j X j outputs only, and thus the best known form of the steady- Qo;h À Qo;c þ Qo;e Qo;j, state total energy efficiency takes the form j P P ÀÁ X W o;j þ Q W o þ Q À Q þ Q Z Pj P j o;j ¼ ÀÁo;h o;c o;e ¼ 1. Qi;h À Qi;c þ Qi;e Qi;j ð2Þ It Q þ W i;j W i þ Q À Q þ Q j j i;j j i;h i;c i;e (5) for compactness; the terms Q express the thermal energy interactions of heating, cooling, and heat interactions with 2.3.