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Energy Vol. 23, No. 6, pp. 449–463, 1998 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0360-5442/98 $19.00 + 0.00

MULTICOMPONENT WORKING FLUIDS FOR ORGANIC RANKINE CYCLES (ORCs) GIANFRANCO ANGELINO† and PIERO COLONNA DI PALIANO Dipartimento di Energetica, Politecnico di Milano, P.za Leonardo da Vinci 32, 20133, Milano, Italy (Received 7 March 1997)

Abstract—We have evaluated the merits of organic-fluid mixtures as working media for Rankine power cycles. Non-isothermal phase change both at high and low temperature represents the main advantage with respect to pure fluids. StanMix, a computer code using the Wong and Sandler (WS) mixing rules, integrated into a commercial package, is employed for cycle analysis and optimisation. Heat recovery and geothermal applications using mixtures of siloxanes and hydrocarbons, respectively, are illustrated. We demonstrated that optimal selection of working-fluid composition is a powerful tool for an efficient ORC design. 1998 Elsevier Science Ltd. All rights reserved

1. INTRODUCTION

The Carnot efficiency is usually considered to be the limiting performance for power-conversion systems. This idea tacitly implies the assumption that naturally available heat sinks and sources are isothermal. Sea or river waters in evaporatively cooled water loops widely used for waste-heat dumping exhibit a large although not infinite heat capacity and represent a reasonable approximation of an isothermal sink. Atmospheric air used to cool engine radiators or to condense steam in dry cooling towers, owing to its modest volume heat capacity, undergoes large temperature changes and departs significantly from the concept of an isothermal sink. In cogenerative urban heating systems, waste heat is transferred from the thermodynamic cycle to a liquid water loop carrying heat as an enthalpy or temperature change. Hence, there is no reason for considering an isothermal process to be an ideal reference. The assumption that high-temperature heat sources may be considered isothermal is even less justified. Combustion processes make heat available under extremely large temperature differences (from flame to stack). Secondary energy sources such as flue gases exhausted by gas turbines or diesel and gas engines are intrinsically non-isothermal. Gaseous emissions produced in industrial activities must generally be cooled to low temperatures prior to undergoing complex cleaning processes and thus become variable temperature heat sources. Other typical non-isothermal sources are geothermal fluids and liquid-cooled solar collectors. The overall efficiency of a thermodynamic conversion cycle is a consequence of the energy potential of the source-sink combination, of internal inefficiencies (losses in turning machinery, in regenerators, etc.) and of losses from irreversible heat transfer from a source and to a sink. The latter depends mostly on the levels of matching of the apparent heat capacities of the working fluid, source and sink. In principle, a divergence in the thermal behaviour between a working fluid and a source or sink can be counteracted by using complex cycle configurations such as evaporation at multiple pressure levels in modern combined cycles or condensation at 2 or 3 decreasing temperatures in cogenerative district heating systems. Multi-component complex conversion cycles have been developed recently to achieve better matching of working-fluid and source heat capacities [1]. In optimising refrigerating cycles, the potential advantages of using non-azeotropic mixtures to achieve non-isothermal phase changes were recognised [2]. Although some proposals for using specific fluid mixtures are in the literature, for power cycles there

†

Author for correspondence. Fax: 2-2399 3940; e-mail: [email protected] 449

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is no general treatment of how mixtures could represent a powerful tool for energy-conversion optimisation. The purpose of this work is to investigate the merits of simple, closed, condensing power cycles employing multi-component, non-azeotropic working fluids featuring non-isothermal heat addition and heat rejection. Rather than searching for an optimum fluid combination, we show that the selection of the nature and number of the mixture constituents is a useful tool for tailoring conversion cycles to specific applications. For heat addition and rejection, equilibrium temperature-enthalpy curves will be used, which implies that an appropriate heat exchanger must produce the temperature profiles needed in mixed-fluid power cycles. Multi-component and pure substance cycles are compared. The behaviour of organic-fluid conversion systems will not be discussed. Some of their main characteristics may be seen in Fig. 1 which shows two organic-fluid power cycles in the entropy-temperature plane. Both have a pump, regenerator, vaporising heater and condensing cooler. Cycle A is suitable for operation up to ⬇ 400°C and includes a superheater before turbine expansion. Cycle B has saturated vapour expansion and is suitable for use at 150–250°C. Neglecting regeneration, which is not essential, the number of the components is the minimum needed for closed, condensing cycles. 2. THERMODYNAMIC PROPERTIES OF FLUID MIXTURES

2.1. Introductory remarks Theories and methods for predicting mixture thermodynamic properties for engineering purposes abound in chemical engineering [3]. The field is still evolving and some key advances have been made as recently as the early 1990s. For thermodynamic cycle analysis and design, the precise composition in the vapour-liquid region is not a primary concern, while values of the thermodynamic properties v, h, u, s are often required over wide ranges of pressures and temperatures. Computer calculations should not require excessive CPU time because thermodynamic properties must be calculated many times in a typical optimisation analysis. For these reasons, the use of an equation of state (EOS) is, at present, the most practical choice because more sophisticated techniques such as statistical mechanics modelling can be used for EOS improvement or development of new EOS. For pure fluids, it is only necessary to have experimental PvT data for EOS optimisation, as well as ideal-gas heat capacities (C0v ) as functions of temperature [4]. Other properties may be derived from these basic equations by using thermodynamic relations. If PvT data are not available, the principle of corresponding states or other relations may be employed. Extension of these methods to mixtures presents additional problems. Experimental PvT data are limited to specific compositions and pressure-temperature ranges, whereas arbitrary compositions and widely varying T and P must be considered for optimisation. Current computational models permit

Fig. 1. Plant layout for an ORC (a) and its representations in the T-s plane for (b) high-temperature and (c) low-temperature applications.

Multicomponent working fluids for organic rankine cycles (ORCs)

451

Fig. 2. Qualitative representation of an isobaric phase change for a two-components mixture in the T-s and T-x (x = mole fraction) planes.

estimations of mixtures thermodynamic properties starting from EOS for pure fluids and complemented by limited data on fluid-interaction parameters. At present, no rigorous generalised theory exists for mixing rules because a universal theory on molecular interaction is not available. Therefore, all mixing rules must rely on experimental evidence. However, mixing rules should meet a number of thermodynamic constraints and the best available models comply with this requirement. An important feature of multi-component mixtures is that the P-T relation during a vapour-liquid transition is more complex than that for a pure substance, for which the temperature is constant during a constant-pressure phase change. The T-s and T-x charts in Fig. 2 (with composition given on a mole basis) represent a two-component mixture qualitatively and are useful in highlighting the nature of the phase change. The compositions of vapour and liquid vary continuously along the isobar, and the compositions in the two phases are not the same. Another marked difference between mixtures and pure fluids occurs in the critical region, as is shown in Fig. 3 for a two-component mixture. The critical

Fig. 3. P-T saturation envelopes for a binary mixture.

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point is located where the bubble and dew curves are tangent to the critical locus curve. It is not characterised by the maximum T and P at which vapour and liquid can coexist. The mixture critical point is calculated from the Gibbs definition [5] and is not related to an observed phenomenon. In the critical region, the peculiar thermal behaviour named retrograde condensation occurs, i.e. is the vapour is condensed by a pressure reduction at constant temperature [6]. 2.2. StanMix: a computer code for thermodynamic property estimations of mixtures After an extensive survey [7] of available methods for estimations of mixture thermodynamic properties, the mixing model proposed by Wong and Sandler [8], which is applicable to cubic equations of state (CEOS), was selected for implementation into a computer code. This choice reflects its sound theoretical basis, suitability for predicting properties over wide ranges of pressures and temperatures starting from limited information and the direct and consistent use that is made of available binary interactions or group-contribution models. Higher order EOS were discarded because mixing-rule parameters are available for few mixtures and are based on empirical data. The importance of adoption of a flexible and theoretically based thermodynamic model can hardly be overemphasised. Use of the working-fluid compositions as a tool for the development of new energy processes demands the ability of modelling a wide variety of fluid mixtures composed of hydrocarbons, fluorocarbons, hydrofluorocarbons, siloxanes and inorganic substances such as water or ammonia. StanMix for Windows [7], an Excel add-in software module for multicomponent-mixture-property predictions and process simulation, was used for thermodynamic cycle calculations. In this model, the WS mixing rules are applied to the Stryjeck Vera modification of the Peng-Robinson EOS (PRSV) [9], i.e. P=

RT aT − . (v − b) v(v − b) + b(v − b)

(2.1)

To achieve high accuracy for saturation-pressure estimates of pure fluids, the temperature-dependent parameter a in Eq. (2.1) is expressed as a(T) = ac × ␣(T),

(2.2)

ac = 0.457235(R2Tc )/Tc,

(2.3)

2 ␣(T) = [1 + k(1 − T 0.5 r )] ,

(2.4)

k = k0 + k1(1 + T 0.5 r )(0.7 − Tr ) for Tr ⬍ 1; k1 = 0 for Tr ⱖ 1

(2.5)

k0 = 0.378893 + 1.4897153 − 0.171318482 + 0.01965543;

(2.6)

k1 is obtained from saturation-pressure fitting of experimental data or from fitting values to an accurate P(T) equation. Details of the theory used to derive the WS mixing model are given in Ref. [10]. The final forms of the two EOS parameters are bmixture =

再冘 冘

冎

E xixj [bij − aij /(RT)] /[1 + glowP /(RT) −

i

j

冘(a x )/(b RT)] i i

i

(2.7)

i

and

冋冘

amixture = bmixture

(xiai )/bi − gElowP

i

册

(2.8)

The excess Gibbs energy at low pressure gElowP must be determined from a low-pressure-liquid activitycoefficient model. The binary interaction parameter kij contained in the combining rule

Multicomponent working fluids for organic rankine cycles (ORCs)

[bij − aij /(RT)] = 兵[bi − ai /(RT)] + [bj − aj /(RT)]其(1 − kij )/2

453

(2.9)

must be computed from the same liquid model. A number of liquid activity models, like those of Van Laar, NRTL (non-random two-liquid), Wilson, UNIQUAC (UNIversal QUAsi Chemical) are well known [11]. Collections of carefully evaluated binary interaction parameters for these models are available [12]. If experimental PTx data are not E available, then glowP can be estimated from UNIFAC (UNIversal FActor Contribution) [13], a widely used atomic-group contribution method. StanMix allows estimations of P (pressure), T (temperature), v (specific volume), Vfrac (vapour fraction), h (enthalpy), s (entropy), u (internal energy), with input BubbleP, BubbleT, DewP, DewT, FlashTP, T-P, P-Vfrac, P-h, P-s, T-s. The necessary inputs are obtained by using critical temperatures and pressures, acentric factors, k1 constants for the PRSV EOS, constants for the third-degree polynomial expression of the specific heat in the ideal gas state (C0p ) and binary interaction parameters (VanLaar, NRTL or UNIQUAC). Data relating to many pure compounds and binary systems have been evaluated, regressed if necessary and stored in an interactive database. A new method that uses the HiedemannKhalil approach for direct calculation of the critical points of mixtures by solving the Gibbs conditions [14] has been included in the program [15]. StanMix has been extensively validated [16], first by comparing pure fluid calculations with reliable literature data to assess the CEOS accuracy, then by performing PTx calculations for different binary systems (polar-aqueous, polar-polar, polar-hydrocarbon, refrigerant-refrigerant, refrigerant-polar systems) and, finally, by considering some ternary hydrocarbon systems. Fig. 4 shows a comparison between saturation calculations and experimental data [17] for a highly non-ideal system. StanMix calculations were also checked against a unique set of benzene-cyclohexane calorimetric data [18]. It should be noted that if PvT estimates are accurate, the correct prediction of quantities related to the latent heat is assured by basic thermodynamic relations. In the comparisons between experimental and calculated data, deviations were always consistent with the level of accuracy required for the engineering purpose of this work. StanMix critical point-estimations have been validated with some of the few available experimental values [19]. The prediction is particularly accurate for siloxanes systems, a fluid class of special interest for engineering applications (Fig. 5). No other experimental data for siloxane mixtures were found, but the suitability of the method for estimating the critical point is believed to assure good accuracy also in the prediction of other properties. Fig. 6 shows the T-s diagram for the mixture MM(0.5)/MD2M(0.5) as an example of the kind of information useful for conversion cycle analysis produced by StanMix. The CEOS are inherently limited in describing the region very close to the critical point [20] and the PRSV CEOS is not optimised for liquid volume. The Peng-Robinson estimates of non-polar hydrocarbon liquid volumes are reasonably accurate even without any specific optimisation. Siloxane liquidvolume predictions by the same method are assumed to be sufficiently accurate since siloxane polarities behave like hydrocarbons.

Fig. 4. Psat-x diagrams for R14/R23. ( – ) StanMix calculations with PRSV EOS and WS mixing rules (NRTL) liquid model). Binary interaction parameters from low-pressure vapour-liquid equilibrium data. (䊊쐌) [15].

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Fig. 5. Critical locus and saturation curves in the T-x plane for the MM/MD2M mixture. ( – ) StanMix calculation using the Heidemann-Khalil method and the PRSV EOS with WS mixing rules. Binary interaction parameters derived from the use of the low-pressure UNIFAC group contribution method. (䊊) [17].

Fig. 6. T-s diagram for MM (50%)/MD2M (50%) calculated with StanMix.

Multicomponent working fluids for organic rankine cycles (ORCs)

455

3. POWER-CYCLE CONFIGURATIONS

The fundamental configurations of power cycles based on multi-component working media can be derived from those of pure fluids, taking into account the peculiar thermodynamic behaviour of mixtures. It is known that the general character of a conversion cycle is basically determined by the fluid molecular complexity and by the relative location of the critical point with respect to the power-cycle placement in the entropy-temperature plane. Organic fluids composed of comparatively simple molecules are the following: ammonia, methane, halo-substituted ethanes and light hydrocarbons. Typical fluids of complex molecules are the propane series or higher-order halo-substituted hydrocarbons and ethers, most linear, cyclic and aromatic hydrocarbons and siloxanes. Mixtures share the level of molecular complexity with the pure parent substances. Each cycle configuration will be illustrated in the following discussion with reference to a typical fluid composed of simple and complex molecules. 3.1. Saturated cycles The component layout of Fig. 1a and the conversion cycle of Fig. 7a are related to a mixture of fluids made up of simple molecules (R22 and R114). The turbine expansion ending at point 5 in the wet vapour region is considered in the first example. If the temperature difference T5 − T1 is reasonably large, then it is possible to preheat the compressed liquid from state 2 to state 7 by recovering a fraction of the heat of condensation of the vapour in a condensing regenerator. When the fluid is made up of complex molecules with large molar specific heats (as in the case of a mixture of linear siloxanes),

Fig. 7. Saturated cycle configuration in the T-s plane for mixtures of simple molecules (R22/R114) (a) and for mixtures of complex molecules (siloxanes) (b), together with the corresponding regenerator temperature profiles (c).

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Fig. 8. Superheated cycle configuration in the T-s plane for a mixture of simple molecules (propane/n-pentane) (a) and for mixture of complex molecules (siloxanes) (b).

the turbine exhausts a superheated vapour (Fig. 7b) and regeneration can be performed either by utilising only the heat of superheating (from 5 to 6) or by extending the heat recovery to the two-phase region (from 6 to 6*). Regenerator temperature profiles for the examples given here are shown in Fig. 7c. 3.2. Superheated cycles For heat exploitation at comparatively high temperature, a saturated cycle requires a working fluid with a very high critical temperature which implies an unrealistically low condensation pressure. Hence, a superheated cycle should be adopted (see Fig. 8a and b, both of which refer to the layout of Fig. 1a). While in Fig. 8a (simple molecule) the regeneration process involves the transfer of a moderate amount of heat, in Fig. 8b (complex molecules) superheating overloads an already demanding regenerator. Temperature profiles within the primary heaters in all of the cycles considered involve a nonisothermal heat addition since all of the heat-transfer modes (liquid pre-heating, mixture vaporisation and vapour super-heating) require temperature differences. Hence, sensible heat sources match the working fluid thermal requirements fairly well (Fig. 9a and b). 3.3. Supercritical cycles The limited critical pressure of organic mixtures (often of the order of one tenth of that of water) makes super-critical cycles practically feasible without running into prohibitive material stresses. Cycle

Fig. 9. Temperature-profile examples in primary heat exchangers.

Multicomponent working fluids for organic rankine cycles (ORCs)

457

configurations similar to those given in Fig. 10a and b are thus admissable. Primary heater-temperature profiles feature almost uniform heat absorption, which implies very good matching with sensible heat sources (see Fig. 10c). Besides the peculiar characters of regeneration and vaporisation, a third main difference between pure and mixed fluids lies in non-isothermal condensation. The overall temperature drop and the shape of the temperature-enthalpy curve (i.e. the apparent heat capacity) are the main features which determine the practical use of multi-component cycles. Both the temperature drop and profile depend on the nature, number and difference in critical temperatures of mixture constituents and on the mixture composition. Although no general rule can be given to predict these characteristics, it was found empirically that mixtures of 3 or more components in similar proportions exhibit almost constant apparent heat capacity during condensation, which allows good matching to the requirements of sensible heat uses (district

Fig. 10. Supercritical cycle configuration in the T-s plane for a mixture of simple molecules (propane/npentane) (a) and for a mixture of complex molecules (siloxanes) (b), together with an example temperature profile in a primary heat exchanger (c).

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heating, sanitary water production, etc., see Fig. 11a). On the other hand, two-component mixtures with a marked composition imbalance produce large variations in apparent heat capacities with unfavourable temperature profiles (Fig. 11b). 4. POWER-CYCLE PERFORMANCE

The most obvious merit parameter for a power cycle is the first-law efficiency

I = Wnet /Qin,

(4.1)

which does not reflect the thermodynamic quality of the conversion process since the same I can be obtained for widely different thermal potentials. A more satisfactory index involves a comparison of the actual work generated with that obtained for a given heat input from an ideal cycle at the same maximum and minimum temperatures (second-law efficiency), i.e.

II = Wnet /Wideal = I /[1 − (Tmin /Tmax )] = I / ideal.

(4.2)

The assumption implicit in this definition is that the heat source and sink interacting with the working fluid are isothermal. In this case, II is a good measure of the conversion-cycle quality. For multicomponent working fluids, which absorb the primary heat at temperatures that are always lower than Tmax and reject waste heat at temperatures always higher than Tmin, II turns out to be unduly low since it is subject to the thermodynamic penalty connected with this peculiar thermal behaviour without compensating the conversion process by an operational advantage. In order to overcome this unsatisfactory situation, the energy-equivalent temperatures Teq.,max = (h4 − h7 )/(s4 − s7 )

(4.3)

Teq.,min = (h6 − h1 )/(s6 − s1 )

(4.4)

and

are usually defined for heat addition and heat rejection (see Fig. 10a or 10b). The overall thermodynamic values (exergy) of the input and rejected heats are equal to the heat absorbed or rejected isothermally at Teq.,max and Teq.,min. An ideal efficiency may be defined as

Fig. 11. Temperature profiles at different condensation pressures for a multi-component mixture. The quasilinear behaviour (a) provides good matching to the requirements of heat users and air coolers, while the sshape in two-component mixtures (b) are unfavourable.

Multicomponent working fluids for organic rankine cycles (ORCs)

*ideal = 1 − Teq.,min /Teq.,max

459

(4.5)

which represents a more appropriate value than ideal for a conversion cycle with variable heat addition and rejection using a non-isothermal source and heat rejection to a non-isothermal sink. A new secondlaw efficiency is then defined as

*II = I / *ideal,

(4.6)

which represents a consistent merit parameter for conversion cycles. Meanings and uses of the three defined efficiencies will be made clearer by the following example. We consider an air-cooled power cycle for heat recovery from a liquid or gas stream at moderate temperatures. A conventional, pure fluid is shown in the T-S diagram of Fig. 12a (n-pentane, regenerated cycle at Tmax = 172°C, Tmin = 34°C). An alternate multi-fluid option with similar critical temperature and pressure levels is shown in Fig. 12b (the 50% n-butane + 50% n-hexane cycle at Tmax = 170°C, Tmin = 20°C). Fluid parameters are selected so that Teq.,min and Teq.,max are the same for both cycles (307 and 413 K, respectively). Assuming a turbine efficiency of 75% and a ⌬TPinch Point, Regenerator of 10°C, I is 0.184 for the n-pentane cycle and 0.179 for the mixed-fluid cycle, while the II are 0.59 and 0.53, respectively. These last numbers appear to be excessively pessimistic since they do not take into account the cycle capabilities of using heat at temperatures much lower than Tmax and, in the case of the multicomponent working medium, the fact that waste heat is rejected at temperatures higher than Tmin (between 20 and 52°C). A realistic figure of merit is *II, which is 0.72 for the first and 0.70 for the second cycle (the entropy analysis shows that the slightly better behaviour of the n-pentane cycle is due to less irreversible heat transfer within the regenerator). The basically equivalent energy performance of pure and mixed-component cycles at the same Tcritical and Teq. was found empirically in our analysis to be a general rule (see the diagrams of Fig. 13). In conclusion, we note that the usual preference for isothermal processes (and, consequently, for the Carnot-cycle efficiency) should be complemented by the observation that each source-sink system requires, for best efficiency, well defined temperature profiles in the primary heater and cooler. Mixtures may be found, in many cases, to achieve these profiles without a notable thermodynamic penalty. 5. APPLICATIONS

The potential performance of multi-component cycles will be illustrated by the following examples.

Fig. 12. Comparison between an n-pentane regenerative cycle (a) and an equimolar n-butane/n-hexane cycle (b) in the T-s plane. Fluid parameters are selected so that Teq.,min and Teq.,max are the same for both cycles.

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Fig. 13. Performance of cycles using n-pentane and an equimolar mixture of n-butane and n-hexane for a varying equivalent condensation temperature. Tmax is fixed at 170°C for the n-butane/n-hexane cycles. For the corresponding n-pentane cycle, the same Teq.,max is adopted.

5.1. High-temperature siloxane conversion cycles In the low power range (10 to 1000 kW), internal combustion engines are the most widely adopted prime movers. However, if the energy source is a solid fuel (coal, peat, biomass, etc.) or heat (flue gases, solar thermal energy, etc.), externally heated engines represent the only feasible solution. In this case, organic power cycles are known to yield excellent performance at temperatures up to about 400°C. Among organics, siloxanes are particularly attractive [21] in that they are exceptionally stable with rising temperatures, physiologically benign and, although flammable, much safer than hydrocarbons. Furthermore, commercially available siloxane fluids as heat carriers are usually a mixture of a number of compounds of different molecular weight: it seems natural, then, to apply our computational method to predict the performance that is obtained for these working media. In view of the use of comparatively high temperatures, mixtures of fluids with the highest possible critical temperature should be selected, with the limitation that the condensation pressure may not drop below a practical limiting range of 0.03 to 0.05 bar. With the goal of finding a class of power cycles suitable for both cogeneration and direct air cooling, the performance of a working fluid made up of by 0.4 MM, 0.3 MDM and 0.3 MD2M was thoroughly investigated. For example, at Tmax = 350°C, Pmax = 22.7 bar (Pr,max = 1.2), Tmin = 50°C, Pcond = 0.06 bar, an efficiency of 27.6% is obtained ( turbine = 0.75, ⌬ TPinch Point,Regenerator = 10°C). Since condensation occurs at a Teq. = 65°C (from 83 to 50°C), a compact air-cooled radiator could be designed. If cooling water is available, the condensation temperatures may be lowered to 30– 64°C (Pcond = 0.027 bar) with an efficiency rise to 30.4%. For cogeneration applications at condensation temperatures of 60–92°C (Pcond = 0.10 bar), the efficiency drops to 26.3%. Cycle configurations for the quoted examples are given in Fig. 14. 5.2. Low-temperature hydrocarbon cycles Whenever heat is recovered from a gas or liquid stream and used to generate electric power, the amount of energy eventually produced depends on both the efficiency of the conversion cycle and the capacity of the working fluid to cool the source as thoroughly as possible. A situation of this kind is typical for electricity generation using a liquid geothermal resource. To show the potential benefits of using a multi-component working fluid it is assumed that a geothermal liquid stream is available at a temperature of 140°C at a site where heat rejection is to be performed by means of dry cooling towers. Condensation is achieved so that Teq.,min = 34°C, with ambient air at 12°C; n-pentane or a 50% mixture of n-butane and n-hexane with similar critical temperatures and pressures are considered as working fluids. Stipulating a minimum temperature difference of 10°C in both the regenerator and the primary

Multicomponent working fluids for organic rankine cycles (ORCs)

461

Fig. 14. Supercritical siloxane-cycle (0.4 MM, 0.3 MDM and 0.3 MD2M) configurations at three different condensation pressures for high-temperature heat-recovery applications.

heat exchanger, a turbine efficiency of 75% and a pump efficiency of 50%, the thermodynamic cycles are optimised by using an appropriate computer program to produce the maximum amount of electric energy. The optimal n-pentane cycle has the following operating parameters: Tmax = 83.3°C, Pmax = 4.02 bar, Pmin = 0.94 bar, I = 9.3%. The liquid stream is cooled to 78.5°C (Fig. 15a). Similarly, the optimum two-component cycle has Tmax = 104.4°C, Pmax = 4.85 bar, Pmin = 1.06 bar, I = 10.2% and cools the source to 80.1°C (Fig. 15b). Since the electric power generated is proportional to I × ⌬Tsource, the second solution yields 6.8% more electricity than the first. The improved performance obtained with the two-component cycle is a direct consequence of the raised mean heat-addition temperature. In the air-cooled condenser, assuming a log-mean temperature difference of about 10°C, air is heated from 12 to 30.5°C in the n-pentane cycle and to 37°C in the two component cycle. Therefore, in the latter case and for the same heat removal, about 25% less air is used with potential benefits in both cooler frontal area and fan power consumption.

Fig. 15. Diagrams showing n-pentane (a) and 50% n-butane plus 50% n-hexane (b) cycle configurations for geothermal ORC applications in the T-s plane.

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G. Angelino and P. Colonna di Paliano 6. CONCLUSIONS

The thermodynamic analyses described in the previous sections lead to the following conclusions: (a) ORCs represent effective heat-conversion devices in many energy fields (e.g., uses of biomass, solar or geothermal energy, heat recovery, etc.). The performance may be improved by adopting multicomponent, zeotropic working media. Advantages are predictable whenever the heat sources and sinks exhibit marked temperature differences. In particular, the cogenerative production of water for heating and waste heat rejection through air-cooled radiators benefit from tailored condensation temperature drops. (b) Complex analytical tools are required to predict the thermodynamic behaviour of mixtures. A fully satisfactory theoretical model of universal use is not yet available. A computational approach based on experimental data about molecular or atomic group interactions should be employed, depending on the available information. A comprehensive computer module (StanMix) for thermodynamic property estimations yields results of sufficient accuracy for preliminary evaluations. (c) Extensive thermodynamic computations show that the internal efficiencies of multi-component conversion cycles are similar to those obtained with pure fluids, i.e. no thermodynamic penalty is connected with replacement of the usual isothermal phase changes by variable temperature processes. Since the apparent heat capacity in the vaporisation and condensation processes is a complex function of the mixture chemical characteristics, an analytical effort is required to find compositions exhibiting nearly linear temperature profiles which are best for practical use. (d) For applications, a number of technical problems must be considered. In particular, heat exchangers should be designed to prevent fluid fractionation during phase changes. Furthermore, information about heat-transfer coefficients (which are known to be strongly affected by mixture properties) should be obtained.

REFERENCES

1. Verschoor, M. J. E. and Brouwer, E. P., Energy – The International Journal, 1995, 20, 295; Kalina, A. L. and Leibowitz, H. M., ASME, 1987, 87-GT-35. 2. Radermacher, R., Int. J. Heat and Fluid Flow, 1989, 10, 90; Didion, D. A. and Bivens, D. B., Int. J. Refrigeration, 1990, 13, 163; Jung, D. S., McLinden, M., Radermacher, M. R. and Didion, D. A. Int. J. of Heat and Mass Transfer, 32, 1989, 1751. 3. Models For Thermodynamic And Phase Equilibria Calculations, ed. S. I. Sandler. Marcel Dekker Inc., New York, NY, 1994. 4. Reynolds, W. C., Thermodynamic properties in S.I., Department of Mechanical Engineering – Stanford University, Stanford, CA, 1979, p. 157. 5. Modell, W. C. and Reid, R. C., Thermodynamics And Its Applications, Prentice Hall International Series in the Physical and Chemical Engineering Sciences, Prentice-Hall Inc., second edition, Englewood Cliffs, NJ, 1983, p. 228. 6. Smith, J. M. and Van Ness, H. C., Introduction To Chemical Engineering Thermodynamics, McGraw-Hill Inc., fourth edition, New York, NY, 1987, p. 368. 7. Colonna, P., Properties of Fluid Mixtures for Thermodynamic Cycles Applications, Report, June 1995, Mech. Eng. Dept. Stanford University, Stanford, CA. 8. Wong, D. S. H. and Sandler, S. I., AIChE J., 1992, 38, 671. 9. Stryjeck, R. and Vera, J. H., Can. J. Chem. Eng., 1986, 64, 323. 10. Wong, D. S. H., Sandler, S. I. and Orbey, H., Ind. Eng. Chem. Res., 1992, 31, 2033. 11. Prausnitz, J. M., Lichtenthaler, R. N., and Gomes de Azevedo, E., Molecular Thermodynamics Of Fluid-Phase Equilibria, Prentice-Hall Inc. International Series in the Physical and Chemical Engineering Sciences, second edition, Englewood Cliffs, NJ, 1986. 12. DECHEMA Chemistry Data Series, Vol. I, IV, VI, IX, XIII, Frankfurt am Main, Germany, 1977. 13. Fredenslund, Aa., Fluid Phase Equil., 1989, 52, 135. 14. Heidemann, R. A. and Khalil, A. M., AIChE J., 1980, 26, 769. 15. Fromm, M., Calculation of Mixture Critical Point as a Tool to Optimize Thermodynamic Power Cycles, Report, June 1996, Dip. Energetica, Politecnico di Milano, Milano. 16. Colonna, P., Fluidi di Lavoro Multi Componenti Per Cicli Termodinamici di Potenza, Ph.D. Thesis, 1996, Milano. 17. Piacentini, A. and Stein, F., AIChE Symp. Ser., 1980, 63, 28. 18. Lenoir, J. M. and Hayworth, K. E., J. Chem. Eng. Data, 1971, 16, 285. 19. Young, C. L., J. Chem. Soc. Faraday Trans., 1972, 2, 580. 20. Abbot, M. M., AIChE J., 1973, 19, 596. 21. Angelino, G. and Invernizzi, C., Transactions of the ASME, 1993, 115, 130.

Multicomponent working fluids for organic rankine cycles (ORCs) NOMENCLATURE

⌬TPinch Point

a = Temperature-dependent parameter in the PRSV equation b = Parameter in the PRSV equation

= Minimum temperature difference in the regenerator h = Enthalpy I = First-law efficiency II = Second-law efficiency *Ideal = First-law efficiency (nonisothermal case), Eq. (4.5) *II = Second-law efficiency (nonisothermal case), Eq. (4.6) kij = Binary interaction parameter MD2M = Decamethyltetrasiloxane MM = Hexamethyldisiloxane P = Pressure Pcond. = Condensation pressure

regenerator

Pr = Reduced pressure (P/Pcritical ) Psat = Saturation pressure Q = Heat R = Universal gas constant s = Entropy T = Temperature Tcritical = Critical temperature Teq. = Equivalent thermodynamic temperature ( ⌬h/ ⌬s) Tmax = Maximum cycle temperature Tmin = Minimum cycle temperature Tr = Reduced temperature (T/Tcritical ) u = Internal energy v = Specific volume Vfrac = Vapour fraction W = Work x = Mole fraction

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