Organic rankine cycle systems with mixture of pure fluids On infeasible fluids fractions due to the

Abstract

Keywords: Organic Rankine Cycle; Working Fluids; Mixture; Glide; Pinch; Infeasible Mass Fractions

Introduction

Following the energy shortage and the related environmental pollution problems that have become more serious in recent years, the use of low temperature energy has attracted attention around the world [1, 2]. In fact, renewable energy resources, such as solar or geothermal, often stand as low temperature energy. The industrial heat waste stand also mainly as low temperature energy in the range of 60–250°C. Among the used technologies for heat power conversion for this temperature range, the Organic Rankine Cycle (ORC) systems appear to be the best approved [3–6]. Organic Rankine Cycle has the same system configuration as steam Rankine Cycle but uses organic fluids as the working fluid instead of water [2, 3]. The mean reason is that the performance of this thermodynamic cycle is better with organic fluids when the heat source is a low-grade energy [7]. However, for giving source and sink temperatures, its performances depend on the convenience choose of the working fluid. There are two main working conditions of the heat exchangers (HEXs) of the ORC system’s that directly affect the whole performances of the system. The first is the “pinch” which is the minimum temperature difference between the fluids in each HEX; the second is the entropy generation in the HEX related to the fluids temperature difference. In fact, the lower are the pinchs [8], the higher are the heat exchangers sizes and costs because of the bigger heat exchange surfaces needed in this case. Conversely, the biggest are the pinchs, the lower are the system performances because of the highest entropy generation due to the fluid’s temperature difference. Nevertheless, the pinch had to be maintained above an imposed minimal value in each HEX in order to ensure the heat flow between the fluids with acceptable exchange surfaces sizes. Taking into account this tradeoff between these working conditions in connection with the use of zeotropic mixture as working

fluid, one had to find the working conditions that permits the best thermodynamic and thermo economic performances of the system. In the case of pure fluid assuming a single phase heating/cooling fluid, the HEX’s pinch may stand [9] at the working fluid bubble or dew point depending on the respective fluids mass flows and heat capacity. The pure fluid constant temperature phase change in the HEXs increases its temperature gap with the heating/cooling monophasic fluid along the evaporator/condenser and leads to high entropy generation [10]. Using zeotropic mixtures as working fluids seems to be a viable option to reduce the entropy generation in the HEXs thanks to their non-isothermal phase change process [11–13]. They present a so-called temperature glide when they perform a constant pressure phase change: for a given pressure, the dew point (i.e the mixture vapor condensing start temperature) and the bubble point (i.e the mixture liquid evaporating start temperature) are different, and the glide is the temperature difference between those two points. It depends on the fluid pressure and consequently its values aren’t the same in the evaporator and in the condenser [14, 15]. For the current used working fluid, the glides are in the range 2–20 K [16, 17]. Due to the working fluid phase change temperature glide, the pinch location in both evaporator and condenser can occur at different positions depending on the base fluids (i.e the pure fluids that constitutes the mixture) fractions, and on the system working conditions such as the high and low pressure and the heat and cold fluids inlet temperature in the correspondent HEXs and the fluid’s mass flow rate. However, when the working fluid is a zeotropic mixture, the HEXs need [17–19] wider heat transfer area because of the decrease on the fluids temperature difference. Using zeotropic mixtures as working fluids have gained interest recently by many research in the specialized literature but without special emphasis on the interaction between the working fluid glides and the HEXs pinchs. Kang et al.

[11] studied the effect of 10 zeotropic mixtures on the performance of ORC system. Their results showed that the optimal mass ratio of the base fluids in the mixture that leads to the maximum thermal efficiency corresponds to the maximum temperature glide. Wu et al. [20] investigated first law and second law efficiencies, exergy destruction distributions and the net power output of an ORC system using three zeotropic mixtures as working fluid. They concluded that the better thermal performance is achieved when the cooling water temperature increase in the condenser is nearly equal to the temperature glide of the zeotropic mixture. Shu et al. [21] studied the first and the second law efficiencies of two configurations of ORC systems using mixtures. Their result indicated that the zeotropic mixtures at a certain mixing fraction present better thermodynamic performance than the corresponding pure working fluids. Lecompte et al. [22] analyzed the second law efficiency of an ORC system using seven zeotropic working fluids. They showed that the second law efficiency of mixtures is higher than the one of the corresponding pure working fluids. However, opposite results to the above mentioned ones have been reported by other authors [23–26]. They indicated that mixture fluids don’t always lead to better thermodynamic performances compared to their corresponding pure fluids. Such an opposite result was presented by Van long Le et al. [24] who conducted an optimization study of ORC system using n-pentane, R245fa, and their mixtures and found that pure n-pentane shows better optimal performances regarding the exergy efficiency than its zeotropic mixtures with R245f. Feng et al. [23] showed that mixtures lead to bad thermodynamic and economic performances compared to their corresponding pure fluids. Wu et al. [20] indicated that mixtures had lowest economic performance than the corresponding pure fluids. Liu et al. [27] investigated the effect of the dew point temperature of the mixtures at the condenser pressure on the performance of ORC systems. Their work has

been conducted under different restrictive conditions in reference to the work of J. Lu et al. [28]. Their results indicated that when the mixture dew point at the condenser pressure is fixed, there is only one optimal working fluid mass fraction that maximizes the thermal efficiency and, simultaneously maximizes the net power output and the exergy efficiency. The work of Li et al. [29] concluded that each mixture presents a range of operating conditions where the corresponding pure fluids perform better. Venkatarathnam et al. [30] investigated the issue of pinch points temperature and glide matching in condensers and evaporators for zeotropic refrigerant mixtures and they developed a simple procedure to find the location of the pinchs in the HEXs. Regarding the above mentioned recent studies, the use of pure or mixture fluid is still a controversial question in the literature and it seems that there are no systematic studies on the interaction between the zeotropic fluid glide and the pinch location and value, and consequently on the incidence of this interaction on the whole performance of the ORC. Furthermore, one can notice that the comparisons between the performances of the zeotropic mixture and their corresponding pure fluids have been made under different conditions regarding the working fluid’s pressure [24]. Besides, among the above-mentioned studies there are some [19, 31] where the authors didn’t pay attention to the fact that the glides of their used fluid mixture induce a non-realistic value of the pinch value in their ORC HEXs, and to the fact that despite what they expect their actual pinchs located in the HEXs are too little and sometimes null. Hence, the issue is that, given a fluid’s fractions in the mixture, under a given set of working conditions, i.e. the imposed/ desired HEXs pinch, the working fluid flow rate, the pressure and the temperature, and the heating fluid mass flow rate and temperature, the temperature glide of mixture fluid leads to decreasing the two fluids temperature difference in the condenser and in the evaporator under the pinch

desired value. Since the HEXs are designed under the expected pinch value, this actual pinch issue hugely affects the HEXs performances and hence, the overall ORC system performances. Although there were many investigations associated with the optimization of the ORC system using zeotropic mixture as working fluids, detailed influence of the pinch temperature difference on the ORC performance was rarely found. Hence, the main objective of this study is to analyze the influences of the pinch temperature difference on the performance of an ORC system for low-grade heat source with different pure working fluids with different critical temperature and their zeotropic mixtures. A comprehensive comparison of their thermodynamic performances is performed using the Refprop® database from NIST for the physical properties of organic used fluids. In fact, under the same working conditions, due to entropy generation, one had to expect that performances of the zeotropic mixture working fluid shall remain better than those of the correspondent pure fluids if the value and location of the pinch is carefully sought considering the fluid’s glide. Using case studies of a standard ORC system with seven pure working fluids and their mixtures at different fractions, the main purpose of the present study is to show that when keeping unchanged the working conditions (i.e the imposed HEXs pinch, the working fluid flow rate, pressure and temperature, and the heating fluid mass flow rate and temperature), and systematically checking that the fluid’s temperature difference don’t falls under the desired pinchs thorough the HEXs, the thermal performances of ORC system using mixture are always better than the thermal performances of the same systems using the corresponding pure fluids. However, under each working conditions, there may exist “infeasible fractions” of the mixture that leads to pinch value that stands under the imposed values in one or two HEXs.

System Configuration Figure 1a shows the configuration of the ORC system considered in the present study. It consists of a basic ORC with its four components: evaporator, pump, turbine, and condenser. The heating/cooling fluids are assumed to be single phase fluids. The working fluid (Fig. 1b) in saturated liquid state (1) is pumped to the evaporator (2) and receives energy from heating source fluid to turn into high-temperature and high-pressure saturated steam (3). The fluid is then expanded in the turbine and rotates its shaft. At the outlet of the last (4), the pressure falls to the condensing pressure. Then the steam of the working fluid enters the condenser where it condenses into a saturated liquid state to start a new cycle. The thermodynamic process for the basic ORC system using pure working fluids is illustrated on a temperature-entropy (T- s) diagram shown in Figure 1b. The corresponding temperature-entropy diagram for basic ORC system using zeotropic mixture working fluids is shown in Figure 1c. It appears that due to the zeotropic fluid phase change temperature glide (Fig. 2a); the temperatures differences between the heating/ cooling fluid in the evaporator/ condenser and the working fluid are less than in the case of pure fluid. This fact leads to smaller entropy generation. However, larger heat exchange surfaces are needed because of the smallest temperature difference between the fluids in such a way that affects the whole thermo economic performances of the ORC. Notice that for the zeotropic working fluids, one had also to pay special attention to the pinch value to avoid it to go under a chosen limit. According to the first law, the following equations describe the net power output and the thermal efficiency of an ORC basic system [23];

The Thermodynamic Process

Evaporator The thermodynamic process in the evaporator can be expressed with the following equations:

Where is the heat flow rate that the working fluid exchanges in the evaporator, is the heating fluid temperature drop in the evaporator, and is the heating water constant pressure specific heat. In the case of a pure fluid, Figure 1b and Figure 2b shows that the evaporator pinch location (i.e the actual location in the HEX where the minimum temperature difference between the fluids happens) stands at the bubble

temperature of the working fluid. Notice that in the case of a very low heating fluid mass flow rate, the pinch point occurs at the heating fluid outlet. But in this case it’s inlet temperature had to be very high leading to high entropy generation on the evaporator, and hence this configuration is excluded here after. In the case of a mixture (Fig. 1c and Fig. 2c), due to its evaporation glide, the evaporator pinch location may occur at any point between the mixture bubble and dew points at the evaporator pressure (Fig. 2c). Moreover, fixing the base fluids fractions in the mixture, the pinch location and value in the evaporator depends on the ORC system working conditions that are the heating fluid mass flow and inlet temperature, the ORC system high pressure, the working fluid mass flow, the bubble temperature, and the glide at the evaporator pressure.

Condenser The thermodynamic process in the condenser can be expressed with equations (5–6).

Where is the heat flow that the fluids exchange in the condenser. is the cooling fluid temperature rise in the condenser and is the cooling fluid constant pressure specific heat. In the case of a pure working fluid, the pinch location of the condenser happens (Fig. 1b) at the working fluid dew point. In the case of zeotropic mixture, the fluid behaves in the condenser in the same way than in the evaporator: the pinch location may occur in any point between the fluid’s dew and bubble points at the condenser pressure. Hence, fixing the base fluids fractions in the mixture, the pinch location and value in the condenser depend on the ORC system working conditions: the cooling fluid mass flow and inlet temperature, the ORC system low pressure, the working fluid mass flow, the dew temperature, and the glide at the condenser pressure.

in the connecting tubes, the generated power by the turbine is:

Where is the turbine isentropic efficiency, is the working fluid enthalpy at the evaporator outlet, is the turbine outlet enthalpy for is the an isentropic expansion process and actual specific working fluid enthalpy at the turbine outlet. The power consumed by the working fluid feed pump is:

Where is the pump isentropic efficiency, is the working fluid enthalpy at the conTurbine and Pump denser outlet, is the pump outlet enthalpy Assuming that all the ORC system compo- for an isentropic compression process and is nents heat losses to the surrounding environ- the actual working fluid specific enthalpy at the ment are negligible, as well as the pressure drops pump outlet.

Computing Model

To ensure a realistic dimension for each HEX of the ORC system, one had to put a constraint on the pinch values in the HEXs. This constraint on the pinch value is taken usually in the range 5–20 K. Van long Le et al. [24] take a pinch constraint of 10 K and 5 K in the evaporator and condenser respectively. It’s important to find the actual minimum temperature difference between the fluids that flow in each HEX and to compare it to the minimal authorized value with respect to the imposed constraint. In an automatized computational procedure aiming to test the performances of an ORC system with a given working fluid, one had to reject each pure or mixture fluids if there is a violation of the constraint on the pinch values in the HEXs. In the case of a zeotropic mixture, the classical method used to determine in the evaporator and the condenser is firstly exposed.

The local temperature of the working fluid in the segment k is then deduced from thanks to the known properties of the working fluid. The local temperature difference between the fluids in the evaporator is computed for k=1 to 20. The pinch, which is the minimum value of is this way found.

Condenser Pinch Computing The condenser includes two sections: the desuperheating and the condensing process. For an ORC system with a pure working fluid, the condenser pinch location stands at the dew point. In the case of an ORC with a zeotropic mixture working fluid, the pinch location may stand at any position of the condensing process. A similar model to the above exposed one for the evaporator is currently used [16] to determine the pinch location in the condenser: the Evaporator Pinch Computing condenser is divided into 20 segments k where The evaporator includes three sections: the find working fluid and the cooling fluids tempreheating, the evaporation, and when needed, peratures are assumed constant. The exchanged the superheating process of the working fluid. enthalpy rate between the HEX’s fluid since the The current method used for finding the evap- working fluid inlet is given by: orator pinch value had been developed particularly by Qiang Liu and al. [32]. It consists on a discretization of the evaporator process into 20 segments where both the heating and the is the local specific enthalpy of the workworking fluid temperatures are assumed to be ing fluid. From equations (5) and (11), can constant. This method is conducted as follows: For each position k(1≤ k ≤20) during the be expressed as following: evaporation process where the heating fluid is at a temperature the exchanged enthalpy rate between the HEX’s fluid since the working fluid inlet is given by: The local temperature difference of the working fluid in the segment k is then deduced form thanks to the known properties of the is the local specific enthalpy of the working fluid. The local temperature difference between the fluids in the condenser working fluid. From equations (3) and (9), the expression of is computed for k=1 to 20. The pinch, which is is:

Table 1. Simulation parameters and boundary conditions used in this study Item

Table 2. Properties of the studied working fluids [36] Working fluid

the minimum value of is this way found. At this level, it’s noticed that the limitation at 20 of the total number of segments k is induced [32] by the fact that a higher number needs higher computing time that may be troublesome when an optimization procedure is conducted for the whole working conditions of a considered ORC system.

the HEXs, are analyzed below with particular simulation conditions. The condenser and the evaporator are assumed to be in counter flow and for both a constraint on the pinch are used in order to avoid unreal HEX size. The pinch constraint value is chosen to be 10 K and 5 K for the evaporator and the condenser respectively. The used ORC conditions are the same as the one’s used by former authors [20, 29] and are given in Table 1. The high pressure bubble point temperature is fixed at 90°C and the low

Simulation Conditions

pressure dew point temperature is fixed at 35°C. The influence of the fractions of the mix- Furthermore, in order to simplify the analysis ture’s base fluids and the temperature glides of the system, the following assumptions have of different fluid mixtures on the performance been made: of the ORC system, as well as the interaction • All components in each configuration of ORC operate in steady state conditions between the glide and the pinch temperature in

Table 3. Comparison between the results of the present study and Ref. [37] Fluid

• The heat losses to the surrounding environment, and the pressure drops in the connecting tubes are neglected • The ambient temperature and pressure are 298.15 K and 1 atm, respectively.

or mixture working fluid, were calculated by the Refprop® database from NIST connected with Matlab®.

Validation The work starts by comparing the present Working Fluids model with the results of Wang et al. [37]. Table Working fluid selection has wide effects on 3 shows excellent agreement between the results ORC system. For the chosen ORC configuration from [37] and the present study. The relatively without superheating, to avoid two-phase flow small differences are due to the various versions in the expander, the used working fluid consists of Refprop® used in the two works. of dry and isentropic mixture [33, 34]. It’s established [35] that a dry zeotropic mixture comes

Results And Discussion

from mixing of two pure dry fluids, while a wet zeotropic mixture comes from mixing of two The Mixture Glide Temperature In Figures 3, the temperature glides of some pure wet fluids, and mixing two isentropic pure fluids leads to an isentropic zeotropic mixture. used mixture in the present study are illustrated. However, mixing two different types of pure flu- For a dew temperature of 35°C, the glides of ids could lead to any of the three types, depend- mixtures of Isobutane with R245fa, R141b and with R123 are illustrated with mass fractions of ing on the molar concentration of each fluid. The seven pure fluids investigated in the pres- Isobutane varied from 0 to 1. It’s noticed that ent study are listed in Table 2. The related main the temperature glide depends significantly on thermodynamic properties of each tested fluid the mass fraction of the base fluids. Figure 3b shows the temperature glides of such as its critical temperature and pressure, the type of its expansion behavior and its environ- the mixtures of butane with R245fa, R141b and mental, health and safety indices are also shown with R123. For a dew temperature of 35°C, it’s seen that the mixture of butane with R245fa on the same table. For the computation conducted in this work, presents an azeotropic behaviour (i.e. a conthe thermodynamic properties of the used pure stant temperature, constant pressure phase

Conclusion

with the maximum glide. It’s pointed out in this study that some • When the mixture has an azeotropic pure fluid mixture, shows “unfeasible flupoint, the lowest thermal efficiency corid’s fraction zone” that leads to temperature responds to a working mixture fluid with difference of the fluids in the HEXs that are the azeotropic fractions. below than the desired pinch values. • For each mixture, which hasn’t an azeoFurthermore, seven refrigerants and tropic point, the thermal efficiency of the their binary mixtures were evaluated as ORC systems is better than the correworking fluid for Organic Rankine Cycle sponding pure fluids. (ORC) system with emphasis placed on the interaction between temperatures glides and heat exchangers pinchs in both evap- NOMECLATURE orator and condenser. The parameters of Symbols Constant pressure specific heat [kJ kg-1 the ORC systems are performed with con- cp straint on the pinchs values for both evapK-1] orator and condenser, and performance of P Pressure [kPa] the ORC system using these different mix- T Temperature [K] ture working fluids are compared and anaHeat absorption capacity [kW] lyzed using the same parameters. The main Power output [kW] Mass flow rate [kg s-1] conclusions based on the studded pure Specific enthalpy [kJ kg-1] fluids and mixtures can be summarized as h x Mole fraction [-] follows: • The constraint on the pinchs (i.e the fluTemperature difference id’s temperature difference in the HEXs) Acronyms avoids the rise of situation with unreal HEX Heat exchanger HEXs dimension and have to be consid- ORC Organic rankine cycle ered and checked thorough the HEXs in Yrs Year all simulation/optimization ORC systems Greek symbols that involves mixtures with temperature η Cycle efficiency [%] glides. Subscripts and superscripts • For all the seven studded fluid mixture, B Boiling point there exist mass fraction range(s) that is Cr Critical point (are) not consistent with the pinch values C Condenser in the HEXs: so called “infeasible zone” cl Heat sink appears because of to the interaction e Evaporator

GWP Global warming potential G Glide in Inlet h Heat source T Turbine ODP Ozone depletion potential out Outlet P Pump wf Working fluid pinch* Pinch limit max Maximum min Minimum net Net power output

rankine cycle applications. J Therm Eng 2021;7:1110–1120. [CrossRef] [2] Ghasemi A, Shayesteh AA, Doustgani A, Pazoki M. Thermodynamic assessment and optimization of a novel trigeneration energy system based on solar energy and MSW gasification using energy and exergy concept. J Therm Eng 2021;7:349–366. [CrossRef] [3] Hamdi B, Tahar Mabrouk M, Kairouani L, Kheiri A. Analysis and optimization of three main organic Rankine cycle configurations using a set of working fluids with different thermodynamic

Authorship Contributions

behaviours. Eur Phys J Appl Phys Authors equally contributed to this work. 2017;78:34808. [CrossRef] [4] Wang D, Dai X, Wu Z, Zhao Z, Wang

Data Availability Statement

P, Hu P, Shi L. Design and testing of a The authors confirm that the data that 340 kW Organic Rankine Cycle syssupports the findings of this study are availtem for Low Pressure Saturated Steam able within the article. Raw data that supheat source. Energy 2020;210:118380. port the finding of this study are available [CrossRef] from the corresponding author, upon rea[5] Wang C, Yang F, Zhang H, Zhao R, sonable request. Xu Y. Energy recovery efficiency analysis of organic Rankine cycle system

Conflict Of Interest

in vehicle engine under different road The author declared no potential conconditions. Energy Convers Manag flicts of interest with respect to the research, 2020;223:113317. [CrossRef] authorship, and/or publication of this article. [6] Xu B, Rathod D, Yebi A, Filipi Z, Onori S, Hoffman M. A comprehenETHICS sive review of organic Rankine cycle There are no ethical issues with the publiwaste heat recovery systems in heavycation of this manuscript. duty diesel engine applications. Renew Sustain Energy Rev 2019;107:145–170.

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