EtOLOGItlIL mODELLIHG ELSEVIER Ecological Modelling 84 (1996) 291-303

Ecological analysis: a new method for ecological energetics research

Jizhong Zhou a,., Shijun Ma a,1, George W. Hinman b a Research Center of Eco-Environmental , Academia Sinica, Beijing, People's Republic of China b Environmental and Regional Planning, Washington State University, Pullman, WA 99164, USA Accepted 24 August 1994

Abstract

A new method for ecological energetics research, ecological exergy analysis, is developed based on the exergy analysis in and the characteristics of living systems. This method takes account of both quantity and . Exergy balance equations for both an animal and a plant are constructed, and methods for estimating different types of exergy in living systems are proposed that consider the complex physical-chemical and physiological-ecological processes. Four ecological indices for evaluating different ecological processes are proposed based on the exergy balance equations.

Keywords: Exergy; Thermodynamics

I. Introduction plants from is equal to the de- crease in in the . Al- All living systems (organisms, populations, and though the total energy remains constant during communities) can be considered as open thermo- this conversion process, solar energy is converted dynamic systems that are not in thermodynamic into and fixed within the plants equilibrium and that continuously utilize and of the . A part of this fixed solar energy convert energy. Energy transfers and conversions is used by the plants to maintain metabolic activi- in these systems strictly obey the first and second ties such as osmosis, absorption, transportation, . Energy change in the and evaporation. The rest is utilized to construct organisms in an ecosystem must be accompanied new tissues and is thereby stored in the plants in by a corresponding energy change in the environ- the form of internal . The stored ment. For instance, the increase of energy in energy can then be transferred along food chains among various kinds of consumers, each transfer being accompanied by an energy loss in the form * Corresponding author. Present address: Center for Micro- of heat (i.e., increased ). According to the bial , Plant and Soil Sciences Building, Michigan State University, East Lansing, MI 48824-1325, USA. second law, it is impossible for organisms to con- 1 Deceased. vert this heat completely into other types of en-

0304-3800/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0304-3800(94)00135-9 292 J. Zhou et al. / Ecological Modelling 84 (1996) 291-303 ergy, such as chemical energy. Thus, an ecosys- tropy concept to the network theory of ecological tem continually uses high quality energy and systems at steady state and presented entropy gradually degrades it to heat at ambient tempera- laws in network systems (Aoki, 1988). Also re- ture, at which point it is no longer available to lated to irreversibility, another quantity, exergy, carry out the processes necessary to maintain life which is the potential- measure of the depar- in the ecosystem in its highly organized state. ture from equilibrium, was introduced into ecol- From the viewpoint of the ultimate results of ogy (J#rgensen and Mejer, 1977) and its ecologi- energy transfers and conversions, living systems cal applications and implications were discussed are merely complex physical and chemical sys- (Mejer and Jcrgensen, 1979; Jcrgensen and tems. Therefore, the principles and methods de- Mejer, 1981; Jcrgensen, 1986, 1988, 1990, 1992a, rived in the physical and chemical sciences should 1992b, 1992c, 1992d; Herendeen, 1989; Aoki, be directly applicable to living systems. The wide 1992, 1993; Salomonsen, 1992). application of thermodynamics in ecology leads In an attempt to consider energy quality and to the formation of ecological energetics, which is find a common denominator in , H.T. a branch of ecology that studies energy transfers, Odum (1983) proposed the concepts of trans- conversions and dynamic equilibria in ecosystems fortuity, the of one type of energy required and the relationships between energy flows and to generate a of another type, and , organism adaptation. Although ecological ener- the energy of one type required to generate that getics only recently became an independent sub- of another. The emergy flow of a system is ob- ject, the work leading up to it was carried out in tained by multiplying by different the early development of ecology (Forbes, 1887; weighting factors, i.e., transformities. As a result, Lindman, 1942; Macfadyen, 1948). After 1950, emergy does not really concern energy loss caused ecological energetics was developed rapidly along by irreversible processes and, therefore, does not two lines: one represented by E.P. Odum and deal with energy quality in the sense of thermody- H.T. Odum who emphasized the energy flows namics. through trophic levels of ecosystems (Odum and From the methodological viewpoint, most stud- Odum, 1955; Teal, 1957; Odum, 1960); another ies only consider energy quantity, not energy represented by Slobodkin who focused on the quality. In fact, all energy transfer and conversion energy dynamics of a single population or food processes are accompanied by changes in both chain (Trama, 1957; Richman, 1958; Slobodkin, energy quantity and quality. To some extent, the 1959, 1960, 1961, 1962). In the 1960s, the pattern change in energy quality is more important in of energetics studies as a quantitative description living systems than the change in energy quantity. of energy flow had been established (Engelmann, Therefore, it is important for ecologists to de- 1961; Wiegert, 1961, 1964, 1968; Scott, 1965; velop new methods to deal with energy quality as Johnson and Maxell, 1966; Phillipson, 1966). well as quantity. In this paper, a new method is Gates (1962, 1966, 1967, 1968) used an analytical presented - ecological exergy analysis, which is a approach involving the laws of and chem- modification and improvement, in light of living istry to study interactions between organisms and system characteristics, of the exergy analysis their environment. Since 1970, the emphasis of method of thermodynamics. ecological energetics has shifted to the construc- tion of predictive models of energy flow (Wiegert, 1973, 1975; Zucchetto, 1975; Patten, 1976, 1983, 1984, 1985; Odum, 1983, 1984a, 1984b, 1988; 2. Exergy flows in living systems White, 1984a,b; Limburg, 1985; Parikh, 1985). Instead of considering energy flow, Aoki studied Energy exchanges between an organism and its entropy flow and in animals environment occur in the following way: (1) heat (Aoki, 1987a), plants (Aoki, 1987b,c) and lake exchange, (2) work exchange, and (3) matter ex- ecosystems (Aoki, 1987d, 1989), applied the en- change (Fig. 1). J. Zhou et al. / Ecological Modelling 84 (1996) 291-303 293

2.1. Animal exergy balance Q'I I Q'2 I All living systems consume energy as well as ~[ Organism I' ' exergy because exergy is the part of the energy HI H2 which can be utilized to do work. The exchange ! i of energy and exergy in an animal is represented in Fig. 2. It should be noted that Q1 and Q2 Fig. 1. Energy exchange between an organism and its environ- include only the direct heat exchange and do not ment. The explanation for the symbols is in the text. include respiration. As is shown in Fig. 2, an animal ingests food From Fig. 1, the energy balance equation at from its environment. Under the action of a se- constant is ries of enzymes, some of the ingested energy is assimilated and some is egested. Of the assimi- AHs = (H1 -H2) + (Q'1 - Q~) + (W, - 14'2) lated energy, a part is transformed into animal =AH+AQ'+AW (1) tissue and storage materials (i.e., production), most is used to maintain respiration, and a small where H 1 and H 2 are the content of portion is excreted in feces and urine. Energy ingested matter and egested-exereted matter. Q] flows are accompanied by exergy flows, which are is the directly absorbed heat, Q~ is the dissipated necessary to keep the system functioning. For heat, W1 is the work (excluding PdV work) of the convenience, the exergy contained in the ingested environment on the organisms (e.g., wind on food is referred to as ingestion exergy (E~) and plants, tides on fishes, airstreams on insects and that in feces and urine as egestion-excretion ex- birds), which ultimately tends to zero, W2 is the ergy (EF). The exergy embodied in production is work (also excluding PdV work) of organisms called production exergy (Ep) and that embodied acting on their environments (e.g., animals feed- in respiration is named respiration exergy (ER). ing), which is very small compared to the total An animal may absorb the heat exergy (EQI) as amount of energy exchange so that it may be well as heat from its environment through radia- neglected (Wiegert, 1968). As a result, the net tion, and it may release heat exergy (EQ2) as well work exchange between an organism and its envi- as heat to its environment through radiation, ronment, AW = W 1 - W2, may be omitted. AH s is conduction, convection, and latent heat transfer. the overall enthalpy change of the organism. Assume the net direct heat exergy exchange to be In comparison with the classical equation for EQ = EQ2 -- Eo . When EQ > O, an animal re- the energy budget leases heat exergy to its environment, otherwise it P=I-R-F. (2) absorbs heat exergy from its environment. Fur- Wiegert (1968) found that AHs, H 1 and H2 are thermore, an animal may exchange mechanical equivalent to the energy of production (P), inges- work with its environment but, as mentioned tion (I) and egestion-excretion (F). The net heat above, the net work exchange usually is very small exchange, AQ = (Q]- Q~) = (Q, - Q2-R), QIIEQ1 Q2[EQ2 is approximately equal to the negative of the energy of respiration (R) because, within a longer I, El, EPI (P,animal Ep) , F,CO 2EF, , ECO EPF2 period, the net direct heat exchange, (Q1- Qz), O2"Eo2 "I ~ EL (i.e., radiation, conduction, convection and latent i i heat transfer excluding respiration) between an WIIEwI W2~Ew2 organism and its environment tends to zero. Oth- Fig. 2. The energy and exergy exchanges between an animal erwise, the organism will die from over- or and its environment. The explanation for the symbols is in the under-heating (Wiegert, 1968). text. 294 J. Zhou et al. / Ecological Modelling 84 (1996) 291-303

QIIEQ I Q2 IEQ2 3. Estimation of the different types of exergy i~" , R, E R I, E I l animal I , F, E F 3.1. Chemical exergy (P, Ep) ~ E L

Fig. 3. Simplified energy and exergy exchange between an Generally speaking, exergy can be classified animal and its environment. The explanation for the symbols into two main types: physical and chemical exergy is in the text. (Appendix). Ingestion, production and egestion- excretion exergy are chemical exergy and they can be estimated by the following methods. and may be neglected so that the net exergy Shieh and Fan (1982) suggested the estima- exchange of mechanical work, (E w = Ew2 - Ew), tions of exergy contents in structurally compli- may also be omitted. In addition, during the cated materials as: process of ingestion, egestion and excretion, the ingested food and egested-excreted waste materi- Ec~ = 340.124[C] + 5.25[N] + 5996.25[H] als may possess physical exergy (Ept and EpF) + 1062.4510] + 2147.45[S] + 2733.411[F] due to the difference of and pres- sure between the animal and its environment. For + 2085.698[C1] + 1022.642[Br] most animals, however, this difference may be + 684.46611] - 298.15S~hW~s h small so that physical exergy may also be omitted. Finally, animals exchange gases (0 2 and CO 2) - AH" (kcal/kg) (7) with their environments through respiration and where Ecnh is the chemical exergy content of com- the body surface so that they may exchange diffu- plex materials (kcal/kg) under standard condi- sion exergy (Eo~ and Eco:). However, we assume tions (pn = 1 atm, T n = 298.15 K). [C], [H], [O], that the diffusion exergy is very small, or the net [N], [S], [F], [Cl], [Br] and [I] are respectively the exchange of diffusion exergy is zero. From the contents of carbon, hydrogen, oxygen, nitrogen, above, we obtain the animal exergy balance equa- sulfur, fluorine, chlorine, bromine and iodine per tion (Fig. 3): kg of complex materials. Wash is the weight of ash EI=Ee+ ER +EF+ EQ +E L (3) per kg of material and Sanh is the specific entropy of ash. sanh is assumed to have a value of 0.17152 where E L is exergy loss (Appendix). kcal/(kg of ash, K), which is an average of the As mentioned previously, the net direct heat values of Sa~sh for 12 types of . AH n is the exchange between an animal and its environment negative of the heat of of a com- may be ignored, and thus the net direct heat bustible structurally complicated material. exergy exchange can be omitted. Therefore When AH n is not available, the specific ex- El = Ep + E R + E v + E L. (4) ergy can be estimated by the following equation (Shieh and Fan, 1982):

2.2. Plant exergy balance E~h = 8177.79[C] + 5.25[N] + 27892.63[H] + 4364.33[S] - 3173.6610] + 5763.41[F] The plant exergy equation is constructed in a similar way, i.e., + 2810.57[C1] + 1204.3[Br] + 692.511] Es=E +ER+eo+EL (5) - 298.15SnshWash + 0.1510]{7837.667[C] or + 33888.889[H] - 4236.110] + 3828.75[S] + 4447.37[F] + 1790.9[C1] + 681.97[Br] E s = E 1. + E R + E L (6) where E s is the photosynthetically active radia- + 334.8611]} (kcal/kg). (8) tion exergy. The other terms have the same From Eqs. 7 and 8, we can obtain the specific meaning as in Eq. 3. chemical exergy under the standard conditions. J. Zhou et al. ~Ecological Modelling 84 (1996) 291-303 295

The specific chemical exergy under any other erties of fluid media, and air pressure. In addi- condition can be calculated as (Shieh and Fan, tion, the four heat transfer processes are accom- 1982) panied by the processes of active absorption or release by respiration, drinking, egesting, excret- Ech(T,P) = Enn + f;c,,(1 - To/T)dT ing and sweating, so that heat exchange is not only a complicated physical and chemical process but also a complex living process. It is technically + f;[v-. (T- To)(Ov/or)p]de difficult and tedious to precisely estimate the (9) heat of different transfers. But, for an organism, the ultimate result of various transfers is the where Cp is the specific heat capacity at constant absorption or rejection of heat, however compli- pressure in kcal/kg. K, and T O is the tempera- cated these processes are. The absorption or re- ture of the environment. When the pressure ef- jection of heat ultimately leads to the increase or fect is negligibly small, Eq. 9 becomes decrease of the body temperature so that the heat exchange may be approximately estimated Ech(T,P ) =Ec"h + frCe(1 - To/T)dT. (10) based on the temperature of the organism and its ,,T n environment. Assume the body temperature of an organism 3.2. Heat exergy at times t I and t 2 to be T 1 and T 2 and the temperature of its environment to be T 0. If T 1 < While a system is reaching thermal equilibrium T2, then the net heat absorbed by the organism with its environment, heat exergy exchange as from its environment is well as heat exchange occurs. The heat exergy of a system is defined as the maximum work that O = Cp(T2 - T1). (13) can be done under given conditions by heat trans- The increase in entropy of the organism during ferred out of the system in a reversible way (Zhao the process of heat absorption is and Qian, 1984; Yang, 1986). From thermodynamics, the gain in heat exergy As= f2(1/r)de= (E o) by a system receiving heat Q from the environment can be estimated by = C~ln( Tz/T 1). (14)

EQ = a - T0(S 2 - S1) = Q - ToAS (11) From Eq. 11, the heat exergy absorbed by the and the gain in anexergy by organism from its environment during the inter- val of t I and t2 is A O = T0(S 2 - SI) (12) E o = Q - ToAS where T o is the temperature of environment, S 1 and S 2 are the of the system in states 1 ~- Cp(T 2 -- T1) -- ToCeln(T2/T,). (15) and 2, and AS is the production of entropy in the system. If T z < T 1, Q and EQ are negative, the organ- Eq. 11 is the general form of heat exergy. ism releases heat exergy as well as heat to its The processes of heat exchange between an environment. In addition, if we consider different organism and its environment are very compli- processes of heat transfers in detail, the net heat cated. Heat transfer in various forms (radiation, absorbed or released by an organism can be com- conduction, convection and latent heat transfer) puted as (Gates and Schmerl, 1975) relates not only to the temperature of the organ- Q = fQabsdt ism and its environment but also to many other factors such as radiation intensity and surface = f(Orad + aconv + Ocond + Ovapor)dt. (16) reflectivity, surface textures, wind velocity, prop- 296 J. Zhou et al. / Ecological Modelling 84 (1996) 291-303

If we substitute Eq. 16 into 15, we may also ism. The direction of amino acid metabolism in obtain the value of heat exergy, but this approach higher plants and most of bacteria is composition leads to the complications described above. not (Lehninger, 1975). Generally For homoiothermal animals, although heat ex- speaking, animals rarely take amino acids as their change occurs, the body temperature remains respiratory substrate under the conditions of suf- constant. The net heat exchange and net entropy ficient sugar and fat, little supply of exogenous exchange are equal to zero so that the net exergy amino acids, and great requirement for amino exchange also equals zero. acids. In this case, for animals to take amino acids as their respiratory substrate is not econom- 3.3. Respiration exergy ical and favorable. Even if there is only a small amount of amino acids as respiratory substrate, Respiration is a fundamental and important we may consider the energy efficiency of amino life process which provides not only energy for all acids for complete oxidation as the same as that life activities but also the necessary raw materials of carbohydrates and lipids (Bell, 1985). Thus, for all biosyntheses. It is the metabolic center of respiration exergy can be estimated as matter such as carbohydrates, lipids and proteins. E R = 0.4R. (17) During the process of respiration, all respiratory substrates can be degraded into CO z and H20 through the Krebs cycle by the action of a series 3.4. Photosynthetically active radiation exergy of enzymes. A part of energy stored in respiratory substrates dissipates into heat. The rest is fixed to The light incident on a green plant may (1) be ATP, which is used, on the one hand, to do reflected at the interface between the plant and internal work such as osmosis, absorption, secre- the air (catoptric light), (2) pass through the green tion, transportation and muscle constriction, and, plant without being absorbed by it (transmission on the other hand, to construct cellular structural light), or (3) enter the green plant and be ab- materials. The energy which is used to do internal sorbed by it. The ratio of reflection, transmission, work ultimately dissipates into heat. Therefore, and absorption of light to the incident radiation some of the chemical energy in ATP is trans- depends on the incident angle, plant shape, formed into heat, and the rest into the chemical growth period, , and etc. energy contained in the tissues and the stored (Bell, 1985). Not all solar radiation can be ab- materials. sorbed by green plants to elicit photosynthesis. According to the definition of exergy, respira- Solar radiation in the wave length range 380-710 tion exergy (E R) is defined as the part of energy nm is defined as photosynthetically active radia- stored in respiratory substrates that is trans- tion, which can lead to photosynthesis of green formed into the chemical energy contained in plants. ATP, which drives all life processes. Photosyntheses are very complicated pro- From biochemistry, we know that 40% of en- cesses. Photosynthetic in chloroplasts ergy stored in carbohydrates and lipids can be are excited by absorbing the energy of photons. A transformed into the chemical energy in ATP. few of the excited pigment molecules return to However, it is difficult to find out how much the ground state after releasing heat or light energy stored in proteins can be fixed in ATP energy in the process called fluorescence or phos- after complete oxidation because the ways by phorescence. The energy in most of the excited which amino acids join in the Krebs cycle are pigment molecules is transferred along the se- different. Based on the properties of metabolism quence of pigment molecules to the reaction cen- and various kinds of substrates, we may assume ter of the pigment system. From there, the ex- that, generally, proteins are not taken as the cited electrons of the energy-trapping molecules substrates of respiration when there are sufficient in the reaction center are transferred along the carbohydrates and lipids in the body of the organ- carrier chain to NADP +. Meanwhile, non-cyclic J. Zhou et al. / Ecological Modelling 84 (1996) 291-303 297 photophosphorylation is initiated, and assimila- efficiency of the ith sequential process. Thus, tory power (ATP and NADPH) is formed with = ]-I j[~i" the release of 0 2. At the expense of ATP and An absorbed quantum may be inefficient for NADPH, CO 2 and H20 are reduced to carbohy- several reasons. In the first place, the excitation drates through the Calvin cycle. energy may not reach the reaction center. In From the definition of exergy and the pro- particular, some quanta may be re-emitted as cesses of photosynthesis, photosynthetically active fluorescent light. Even if the energy reaches the radiation exergy is defined as the amount of reaction center, it may not be trapped by the incident energy which theoretically leads to an latter, and this will further reduce the efficiency. increase of the free energy of plants. Some of the energy may be lost in the charge Let A be the wavelength of light, f(A) be the separation processes. In addition, since the two spectral distribution function of the incident radi- photosystems must operate in a concerted man- ation, and A(A) be the absorptance of the body ner, some of the excitation energy may be lost in storing the light energy of wavelength A. In a the electron transport along the carrier chain to narrow spectral interval (A,A + dA), the flux of NADP ÷, which involves at least 10 partial pro- the incident energy is f(A)dA and the flux of cesses. The formation of the assimilatory powers absorbed energy is A(A)f(A)dA. (ATP and NADPH) at the expense of the energy Photosynthesis includes a series of photophysi- trapped in the reaction center is probably less cal, photochemical and biochemical processes. efficient than 100%. Finally, the numerous stages Not all of this primary stored energy (i.e., ab- in the biochemical pathway of the Calvin cycle sorbed energy) is utilized by green plants for the may also lead to inefficient utilization of the formation of carbohydrates because various types assimilatory power for the reduction of CO 2. The of energy losses may occur on further transforma- quantum efficiency of various stages of photosyn- tion of the energy. Let • be the fraction of the thesis under optimal conditions is summarized in primarily stored energy that ultimately remains in Table 1 (Bell, 1985). green plants, i.e., the ratio of free energy increase From Table 1, the maximum overall quantum of the green plant to the amount of absorbed efficiency is light energy. It is called energy yield (Bell, 1985). a = IIa i = 0.629 to 0.696. (20) Thus, for light of wavelength (A,A + dA), the amount of stored energy is Bell (1985) concluded that the total energy loss per quantum in the various processes of photo- • A(A)f(A)dA. (18) synthesis is (11 + 1 + 24/n + 28/n), where n is From the definition of photosynthetically ac- the quantum requirement for the reduction of tive radiation exergy, we have one CO 2 . Theoretically, the minimum

Es = f3~°•A( h ) f( h )dh. (19) Table 1 Quantum efficiencyof various stages of photosynthesis Energy yield is the product of the overall Processes Upper limit quantum efficiency (a) and the overall energy of quantum efficiency (B) (Bell, 1985). The overall quantum efficiency (o/i) efficiency of the photosynthetic processes as a Retainment of absorbed quantum 0.95 whole is the proportion of the quanta eliciting the Migration of excitation energy 0.95 to reaction center reduction of CO2 into carbohydrates to the pri- Trapping of excitation energy 0.95 marily absorbed quanta. I~t a i be the quantum Charge separation 0.95 efficiency of the ith sequential process, then a = Transport of electron along 0.8-0.9 Ha i. The overall energy efficiency is the fraction carrier chain to NADP of the energy of one quantum that can be fixed PGA reduction and RDP 0.95 regeneration into carbohydrates. Assume fli to be the energy 298 3". Zhou et al. /Ecological Modelling 84 (1996) 291-303 quantum requirement is eight. Based on the red Assimilation exergy efficiency is estimated as quantum, the input energy is 8 × 42 = 336 kcal. The energy loss for reduction of one CO2 2 EI- E1 Ee+E R (24) molecule is 12 × 8 + 24 + 28 = 148 kcal. The in- E----S-=---U/, crease of free energy is 336- 148 = 188 kcal. If ~72 measures the ability for organisms to assimi- all quanta are used with 100% efficiency, the late exergy. overall energy efficiency/3 = 188/336 = 0.56. From above, we know that the maximum en- 4.3. Production exergy efficiency ergy yield is 0.35 to 0.39 (i.e., 0.619 × 0.56 = 0.35, 0.696 × 0.56 = 0.39). This is consistent with the Modifying exergy balance Eq. 3 as experimentally observed value of maximum en- ergy efficiency (0.35 to 0.40) (Bell, 1985). We take E I - E F - EQ = E e + E R + E L . (25) the mean value of 0.37 as the estimation of en- If respiration exergy is considered as an external ergy yield in Eq. 19, i.e. E = 0.37. exergy loss, then the total exergy loss is E 2 = E R + E L. (26) 4. Ecological exergy efficiency Production exergy efficiency

Similar to an index, which 3 (E 1 - EF -- EQ) - E~ is calculated on the basis of an energy balance ~e ~ EI-EF-Eo E l - E F - Eo' equation, an ecological exergy efficiency, which is the index to evaluate the thermodynamic perfect- (27) ness of different ecological processes, can be esti- r/e3 measures the ability of organisms to produce mated based on the ecological exergy balance exergy. equation. 4.4. Respiration exergy efficiency 4.1. Ecological process exergy efficiency Relative to the metabolic processes them- The exergy efficiency of any can be estimated based on the exergy selves, production exergy can be considered as an external exergy loss, then the total exergy loss is input and output of the system (Appendix). From Eq. 3, the ecological process exergy efficiency of E 3 = Ee + E L. (28) an animal system can be obtained From the definition of exergy efficiency and Eq. ~7~ El - EL Ee + ER + EF + Ea (21) 25, we have El Et 4_ (E,- - EQ) - El r/e1 measures the thermodynamic perfectness of T/e- E l - E F - EQ E l - E F - EQ ecological processes. (29) 4.2. Assimilation exergy efficiency 714 expresses the fraction of the assimilated ex- ergy which organisms use to maintain their life If the heat exergy and egestion-excretion ex- activities. ergy are taken as external exergy loss (Appendix), the total exergy loss is E 1 = E F + EQ + E L. (22) 5. Discussion Thus, the exergy balance Eq. 3 becomes An ecological exergy analysis method is devel- EI= Ee + EIc + E~. (23) oped on the basis of the exergy analysis method J. Zhou et al. / Ecological Modelling 84 (1996) 291-303 299 in thermodynamics in light of the features of ergy in the sense of thermodynamics. The method living systems. This method takes account of both developed here provides a way to investigate ex- energy quantity and energy quality in the sense of ergy flow and exergy production in biological thermodynamics. It should have significant appli- systems in the sense of thermodynamics. cations in theory and practice when experiments Eqs. 7 and 8 to estimate chemical exergy may are carried out that can be used to evaluate the have some limitations in estimating exergy of exergy coefficients developed. So far applicable biological materials because some biologically im- experimental data do not appear to be available. portant and abundant elements such as phospho- An ecosystem is a large energy convector con- rus are not considered. Further modifications of sisting of many components. With the help of the this formula to include other biologically impor- ecological exergy analysis method, the weak en- tant and abundant elements are needed. In addi- ergy transfer and conversion links in the ecologi- tion, the content of halogens except chlorine in cal network can be identified, and this method, biological materials appears to be very small therefore, appears to supply a theoretical basis (Morowitz, 1968) so that the contribution of ex- for the management of ecosystems. Ecological ergy from these halogens to the total exergy in exergy efficiency is a unified measure of the ulti- biological materials may be very small and can be mate thermodynamic limitations on various eco- ignored. logical processes so that it can be taken as the An ecosystem consists of many components objective function in the optimization of an which interact with each other through the net- ecosystem. In particular, thermo-economic analy- works of flows of energy as well as exergy, matter sis, which is derived from a combination of exergy and information. Aoki (1992) applied network analysis and economic analysis (Yang, 1986), is a analysis to ecological systems based on the con- powerful method to deal with problems in multi- cepts of exergy content, exergy input-output and ple complex systems. Based on thermal eco- exergy loss but did not present how to estimate nomics, it appears to be possible to realize the them in complicated ecosystems. With the help of unity of ecological benefits and economic benefits the method developed here, it is possible to apply in a single research method. However, the appli- the exergy network analysis theory to complex cation of thermal to multiple complex ecosystems and develop mathematical models to ecosystems depends on the estimation of exergy simulate the dynamic changes of ecosystems based flows. From the exergy flows at the level of organ- on the quantity of exergy. isms, it is easy to obtain exergy flows at the level Exergy depends on the states of both system of ecosystems. This paper lays a foundation for and environment so that exergy is not a state the application of thermal economics to ecosys- variable (Yang, 1986). However, under a given tems. environmental condition, exergy is only depen- Mejer and Jcrgensen (1979) proposed a for- dent on the state of the system (Yang, 1986) so mula to calculate exergy for a system with an that it can be treated as a state variable to de- inorganic net flow and passive outflow based on scribe the changes of the system. Many different and thermodynamics. Strictly environmental state models have been proposed speaking, this formula is appropriate for the ex- to be used as reference (or datum) states in the ergy calculation of a pure substance such as phos- estimation of exergy (Yang, 1986). The environ- phorus but may be not proper for the exergy mental state model used to obtain Eqs. 7 and 8 calculation of complex biological materials be- appears to be superior to other environmental cause their free of formation (AG~) are models (Shieh and Fan, 1982; Yang, 1986). This unknown. In addition, the equilibrium values used environmental state model, however, may also be in this formula are not from the equilibrium not proper for living systems because the equilib- defined in thermodynamics (Yang, 1986) so that rium state in ecosystems appears to be different the calculated exergy for a system with an inor- from that in physical and chemical systems. Alter- ganic netflow and passive outflow is not the ex- natively we could stipulate a datum state for 300 J. Zhou et al. / Ecological Modelling 84 (1996) 291-303 calculating chemical exergy based on chemical of energy quality at the level of the biological- and physical conditions of ecological equilibrium ecological process, but transformity should be and thus develop a more universal method to estimated according to exergy rather than energy. deal with ecological problems. However, there are some difficulties to estimate Based on the concept of exergy and - the exergy of different energy forms in compound ary theory, Jcrgensen (1992a) proposed a tenta- ecosystems that include industrial products, hu- tive ecological law of thermodynamics, which man labor, and animal power. How to estimate states that "a system with a through-flow of ex- the exergy of these different energy forms and ergy will attempt to utilize the flow to increase how to consider, for the purpose of finding a the exergy of system, and the organization of the common denominator in ecosystems, energy qual- system that is able to give the system the highest ity at the three levels need further study. exergy will be selected". The method developed here provides a way to measure the exergy flow in living systems. By comparing the exergy flows and Acknowledgements fitness of different living systems, this tentative law can be directly tested by experimentation. We wish to thank Professors James M. Tiedje, Respiration exergy is a particular form of ex- David Pimentel, Alan A. Berryman, Robert ergy. It differs from ingestion, production and Herendeen, Lan Zhongxiong, Ding Yanqin, Niu egestion-excretion exergy. Although most of the Wenyun, Chen Changming, and Wu Kunjun for respiration exergy ultimately is dissipated into their valuable suggestions about the text. Jizhong heat after doing internal work, the description of Zhou wishes to acknowledge the contributions the process differs from the corresponding de- and encouragement of Professor Ma to his educa- scription of the flow of the part of respiration tion in Beijing and to express his regret and energy that is not embodied in ATP. Respiration sorrow at Professor Ma's untimely death in an exergy indicates not only the intensity of automobile accident in Beijing in 1991. metabolism but also the ways and strategies by which organisms utilize and distribute available energy. Appendix 1 In this paper, thermodynamic exergy has been used as the measure of energy quality to describe the physical-chemical processes in organisms. Exergy and exergy efficiency However, in the analysis of ecosystems, especially compound ecosystems (e.g. rural and urban sys- The second law of thermodynamics places lim- tems), there are three levels of energy quality to its on energy conversion processes, especially be considered relative to the three major pro- those involving conversions of heat into other cesses: physical-chemical process, biological-eco- energy forms. Under given environmental condi- logical process and economic process. In order to tions, the exergy of a system is defined as that deal with problems in compound ecosystems, en- part of the energy that can be utilized to do work, ergy quality must be considered at all three lev- and anexergy signifies that part which cannot do els, and the energy quality in the levels of biologi- work (Zhao and Qian, 1984; Yang, 1986). Thus, cal-ecological and economic processes must be based on the level of the physical-chemical pro- Energy = Exergy + Anexergy. (A1) cess. As noted above, the ecological exergy analy- Exergy is dependent on the states of both sis method presented in this paper concerns the system and environment. The state in which a energy quality at the level of the physical-chem- stands in complete ther- ical process, i.e., in the sense of thermodynamics. modynamic equilibrium with its environment is Perhaps, the concept of transformity suggested by defined as the datum state of exergy (Zhao and Odum (1983) could be used to tackle the concept Qian, 1984; Yang, 1986). Complete thermody- Z Zhou et al. / Ecological Modelling 84 (1996) 291-303 301 namic equilibrium for a system requires that there entropy parameter (Zhao and Qian, 1984): are no unbalanced forces, variations in tempera- (EL)in = ToASi, s (A4) ture, potential chemical reactions, and possible diffusion processes within the system, and be- where T o is the environmental temperature and tween it and the environment. The exergy of any ASi. S is the entropy increase of a system caused system in the datum state is zero. Any system by irreversible processes, which is not in the datum state has exergy. Exergy loss may also be estimated from the Exergy (E) can be divided into physical exergy exergy balance Eq. A3: (Eoh) and chemical exergy (Ech), i.e., Exergy loss = Input of exergy - Output of exergy E = Eph + Ech. (m2) - Exergy change of the system. Physical exergy of a system is the maximum work (as) which can be done by the system when it is It should be noted that the estimation of ex- brought into mechanical and thermal equilibrium, ergy loss from the exergy balance equation in- but not , through reversible cludes the external exergy loss if it occurs. physical processes, whereas chemical exergy of a The ability of a system to utilize exergy can be system is the maximum work that can be provided measured by exergy efficiency (Lie); i.e., by the system when it is changed from incomplete to complete thermodynamic equilibrium through "r]e -~ Egain/Epay • (A6) one or more reversible chemical processes. Egain is the exergy increase of the system, and In reversible processes, no anexergy is created Epay is the difference between the input and and the total amount of exergy in a system plus output of exergy. From Eq. 5 its surroundings remains constant. In irreversible processes, some of the exergy is inevitably trans- E L = Epay - Egain. (A7) formed into anexergy. This decrease is the exergy loss caused by the and is Therefore denoted as E L. The exergy loss caused by irre- gpay - E L EL versible processes within a system is called inter- ~Te = Epay = 1 - --Epay = 1 - ~" (A8) nal exergy loss, denoted by (EL)i, and that which is associated with flows into and out of the envi- where ~" is the coefficient of exergy loss. ronment from and to the system is called external In the light of the second law, it is impossible exergy loss, denoted by (EL)out. From a thermo- for the exergy efficiency of a system or process to dynamic viewpoint, all real processes in the natu- be larger than 1. A reversible process is occurring ral world are irreversible. Any irreversible pro- when ~e = 1 and an irreversible process when cess inevitably causes a decrease of exergy and an ~Te < 1. Exergy efficiency reflects the difference increase of anexergy. Therefore, there is no con- between a realistic process and a reversible (ideal) servation of exergy in any realistic process. In process, i.e., the degree of thermodynamic per- order to establish an exergy balance equation, fection of the realistic process. Therefore, exergy exergy loss must be added to the right hand side efficiency indicates the possibility of improving of the equation giving a general exergy balance systems or processes and can be used as a unified equation for any thermodynamic system: measure of the thermodynamic perfection of a Input of exergy system or process. = Output of exergy + Exergy change of the system References + Exergy loss. (A3) Aoki, I., 1987a. Entropy balance of a white-tailed deer during Internal exergy loss can be estimated from the a winter night. Bull. Math. Biol., 49: 321-327. 302 J. Zhou et al. /Ecological Modelling 84 (1996) 291-303

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