Mixture of working fluids in ORC plants with pool boiler evaporator

Applied Thermal Engineering 98 (2016) 1–9

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Applied Thermal Engineering j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / a p t h e r m e n g

Research Paper

Mixture of working fluids in ORC plants with pool boiler evaporator Talieh Rajabloo *, Paolo Iora, Costante Invernizzi Department of Mechanical and Industrial Engineering, University of Brescia, Brescia, Italy

H I G H L I G H T S

• • •

We assess the feasibility of pool boiler in ORCs operating with mixture working fluids. We consider hydrocarbon and siloxane mixtures for low and high temperature ORCs. Plants with pool boiler show comparable performances to once through evaporator.

A R T I C L E

I N F O

Article history: Received 14 August 2015 Accepted 31 October 2015 Available online 12 November 2015 Keywords: Organic Rankine cycles Working fluid Heat exchanger Mixture as working fluid

A B S T R A C T

Power generation using Organic Rankine Cycle was studied in this paper in case of both low and high temperature cycles, exploiting respectively a geothermal heat source available at 167 °C, and heat available at 300 °C from the combustion of biomass. In particular we assess the feasibility of employing mixture of working fluids, in the case of replacing the typical once-through (OT) evaporator with the pool boiler (PB) technology, typically adopted for pure fluids. The analysis evidenced that in general the OT evaporator shows a slightly improved cycle performance in comparison to the PB and it results in some cases advantageous with respect to the pure working fluid. For instance in case of low temperature cycle, the best thermodynamic performances are obtained with mixture of i-C5 and 75% n-C4 in case of OT evaporator, yielding a recovery efficiency higher than the case with pure i-C5 (7.7 vs. 7.4%) given the relatively higher values of both the recovery factor and cycle efficiency. Implementation of PB did not affect the plant performance significantly which shows the feasibility of having PB with potentially easier control. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction The Organic Rankine Cycle (ORC) technology is widely employed for the conversion of heat into electricity in several applications such as geothermal plants [1–3], solar [4], biomass and low grade heat recovery [5–7]. As it is known, from a thermodynamic point of view an ORC cycle is similar to a classical steam plant. However, the former is normally preferred as long as the size of the power plant reduces below values of few MW where the realization of a steam plant poses important technological challenges, particularly in terms of the design of a multistage steam turbine. One main concern in ORC technology is the proper selection of the working fluid. Many aspects need to be taken into account, namely, thermodynamic properties, global warming potential (GWP), thermal stability [8,9], safety and environmental aspects [10–12], toxicity, flammability, auto-ignition temperature, costs [13,14], and availability [15]. Although the use of a pure component is presently considered the common practice in ORCs, mixture of fluids has also been proposed by many authors. The use of mixtures of organic fluids in ORC potentially carries several benefits. First of all, mixtures could

* Corresponding author. Tel.: +39 3203089944; fax: 030/300669. E-mail address: [email protected] (T. Rajabloo). http://dx.doi.org/10.1016/j.applthermaleng.2015.10.159 1359-4311/© 2015 Elsevier Ltd. All rights reserved.

lead to an efficiency increase compared to pure fluids due to a glide match of temperature profiles in the evaporator as long as a variable temperature heat source is available [16–18]. Similarly, the temperature glide in the condenser may lead to a reduction of the mass flow rate of the cooling fluid, which in case of air cooling systems may result in a significant reduction of the electricity consumption of the air fan [18]. Another advantage of the mixture is the possibility of suppressing or reducing undesirable properties of a single fluid, such as the flammability or the global-warming potential [19]. Finally and most importantly, it is virtually possible by mixing appropriate amounts of different components to obtain thermodynamic properties of the working mixture that optimize the cycle conversion efficiency and the design of the plant components, in correspondence with the conditions of the heat and cooling sources. As far as the plant components are concerned, up to now, different studies have introduced various types of evaporator in ORCs, such as plate heat exchangers [20,21], shell and tube heat exchanger [16,18,22–25], and fined tubes heat exchanger [26]. In general, two approaches can be distinguished in the design of the evaporator: (i) the pool boiling system, where the evaporating process occurs in the shell side with a physical separation between the saturated vapor phase (in the upper side of the shell) and saturated liquid phase (on the bottom of the shell); (ii) the oncethrough evaporator, where the evaporation of the working fluid

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occurs in the tubes side of heat exchanger, typically with a counter flow arrangement with respect to the hot stream. In this case, the working fluid experiences a progressive evaporation along the heat exchanger, with a corresponding increase of the vapor fraction of the two phase flow. As it will be better discussed in the following, the pool boiling solution is the typical choice for pure working fluids [27], in particular because it can cope with load variation with a rather simple control strategy, avoiding unstable conditions of the plant. For instance, an unexpected change of the input heat would result in a corresponding variation of the level of liquid in the evaporator, keeping the vapor always in saturated conditions avoiding any undesirable wet vapor fed to the turbine. Thus, a straightforward control strategy may change the mass flow rate of the working fluid (typically varying the rotational speed of the pump) in order to adjust the level of liquid to the set point value. On the contrary, the once through approach is typically recommended in case of mixtures of working fluids because, thanks to the glide in evaporation, a counter flow heat exchange arrangement improves the heat recovery factor in case of a variable temperature heat source. Heat recovery factor is defined as the ratio of intake and available heat while heat recovery efficiency is the ratio of net power to available heat. On the debit side, since there is no net separation between the liquid and vapor phases during the evaporation process, an effective control is needed in off-design conditions, especially in case of an abrupt reduction of the input heat rate, to avoid wet vapor fed to the turbine. Thus, it is normally necessary to design the once through evaporator with a certain amount of superheating even in cases where, from a thermodynamic point of view, a saturated cycle would be a better choice. In this paper, we carry out a thermodynamic study of ORC plants operating with mixtures of working fluids that employ the pool boiler evaporator, in order to assess the feasibility of this solution in comparison with the more established once through evaporation technology. To the best of our knowledge, pool boiling represents a new approach in case of mixtures. We consider two reference plants in order to address low temperature and high temperature ORC applications. The first is an existing geothermal plant operating with iso-pentane (i-C5) as working fluid, which exploits a variable temperature heat source available at 167 °C [28]. The second case study is based on a biomass power plant with octamethyltrisiloxane (MDM) as working fluid, with maximum cycle temperature of 300 °C. In both cases, we study different mixtures of fluids and compare the power plant performances in case of both once through and pool boiler evaporators. All the thermodynamic calculations were carried out by the program Aspen Plus v8.0 [29,30]. At the end, it is noticeable that the suggested ORC plant with pool boiler evaporator shares some similarities with the Kalina cycle in that both utilize a binary mixture of working fluids. However, there are main differences between the two cases. First of all the selected fluids are different. Second, the composition of the mixture is constant at all states of the ORC plant while it changes in the case of Kalina cycle, as explained in [31–34]. Moreover, the straightforward plant configuration of the PB solution remains the same in low and high temperature cycles, while the Kalina cycle becomes more complicated when high temperature sources are exploited [31]. Ultimately, the ORC plant with PB evaporator has a potentially easier control than that Kalina as it has been explained in Section 2.2.1.

Table 1 Calculation assumptions for the geothermal i-C5 ORC plant defined in Fig. 1 [28]. Hot source temperature, T7 in Fig. 1a (°C) Net Power (kW) Cooling water temperature, T5 in Fig. 1a (°C) Evaporation pressure (bar) Condensing pressure (bar) Condensing temperature, Tcond. (°C) Turbine isentropic efficiency, ɳT (%) Pump isentropic efficiency, ɳP (%) Minimum temperature of evaporator, ΔTmin, evap (°C) Minimum temperature of condenser, ΔTmin, cond. (°C)

167 1200 25 20 1.9 47 85 75 5 5

*Note: there are no pressure and heat losses in the heat exchangers.

of a pump, an evaporator, a turbine, and a water cooled condenser as sketched in Fig. 1a, while the corresponding Temperature– Entropy diagram is reported in Fig. 1b considering the enthalpy changes of hot source fluid. Calculation assumptions are reported in Table 1. Thermodynamic properties of i-C5 are evaluated by means of the well-known Peng–Robinson equation of state (EoS). ASME steam tables 1967 is considered for the properties of the geothermal fluid and cooling water – which are assumed as pure water – and ideal gas model for cooling air. The mass flow of the working fluid and of the cooling water is varied in order to match the 5 °C minimum temperature at the evaporator and the condenser respectively. The

2. Low temperature ORC analysis 2.1. Description of the reference plant and model validation The ORC assumed as reference for the low temperature analysis is a geothermal plant operated with pure i-C5 as working fluid, described in the book of DiPippo [28]. The power plant is composed

Fig. 1. (a) Plant layout of the geothermal i-C5 ORC plant [28]. (b) Related T-S diagram.

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Table 2 Results of the model validation for the reference geothermal i-C5 ORC plant defined in Fig. 1 [28].

Reference Model Error

M ˙ Working (kg/s)

M ˙ Cooling water (kg/s)

Qin (kW)

WNet (kW)

ηC%

fluid

16.3 16.7 2.45%

NA 308.3 –

7946.3 8127.4 2.28%

1200.0 1200.6 0.05%

15.1 14.8 1.99%

TOut, evap.

(K)

420.2 416.3 0.93%

results of simulation are reported in Table 2 which shows a good agreement with reference data. 2.2. Analysis in case of mixture of working fluids 2.2.1. Choice of the mixtures As anticipated in the introduction, we aim to investigate possible advantages that may result from the adoption of mixture of fluids in ORC plants, particularly focusing on two different evaporator arrangements, namely the Once Through (OT) versus the Pool Boiler (PB) technologies (see Section 2.2.2). To this purpose, we considered different binary mixtures of hydrocarbons with variable compositions of the following pure fluids: i-C5, n-C4, n-C6, n-C7, and n-C8. The criterion adopted for the selection of the components and the composition of the resulting mixture is based on the compatibility of the thermodynamic properties of the mixture with the hot and cold sources and to obtain reasonable pressure values in the power plant. As a case in point, the working fluid should not become superheated in the hot source temperature ranges as it was discussed in the introduction. To better focus on this analysis, pressure–temperature (P–T) curves of binary mixtures were estimated with the considered hydrocarbons. An example of such diagrams is reported in Fig. 2 in case of binary mixtures of n-C4 and i-C5 where the vertical dotted lines indicate the hot and cold source temperatures. It can be observed that at the working conditions of the power plant, the operating pressure is in the range 1–30 bar, adequate for the reasonable design of typical ORC plant components. In particular, it is possible to increase the pressure of evaporation up to 30 bar in the case of i-C5 and n-C4, at compositions of 25%, 50%, and 75% (Fig. 2a), while, different binary mixtures of i-C5 and n-C8 can reach limited evaporation pressures of 20, 12, and 7 bar respectively for 25%, 50%, and 75% of n-C8 (Fig. 2b). Since the other percentages of concentration of binary mixture do not affect the cycle efficiency significantly, these three amounts (25, 50 and 75%) represent this effect very well. Mixture compositions are based on mass fractions. Also, it can be noted that the glide in evaporation and condensation is rather low for i-C5 and n-C4 (for instance, 4.2 °C in the case of 50% n-C4 at 17 bar) while it is higher for i-C5 and n-C8 (36.0 °C in the case of 50% n-C8 at 17 bar). 2.2.2. Once-Through (OT) versus Pool Boiler (PB) evaporator in case of mixture of working fluids A basic representation of an OT evaporator is shown in Fig. 3. Conceptually it is a counter flow heat exchanger where the working mixture experiences progressive evaporation along the cold stream, reaching condition of saturated vapor at the exit. It can be observed that with respect to the pure fluid, the glide in evaporation allows a better recovery of the variable temperature hot source in a slope closer to the related enthalpy drop of hot source (Fig. 3b). On the other hand there is no net separation between the liquid and vapor phases during the evaporation, with the potential risk of unwanted liquid in the turbine, in case the working mixture does not reach a complete evaporation, as it might happen in case of an abrupt reduction of the input heat available from the hot source. To limit the consequences of such events, it can be either necessary to run the cycle with a certain amount of superheating

Fig. 2. Pressure–temperature curves of binary mixtures of (a) i-C5 and n-C4, and (b) i-C5 and n-C8, at different compositions.

or to resort to a vapor–liquid separator to be implemented at the evaporator outlet. Conversely, in a pool boiling system, the evaporation occurs in the shell side of PB with a physical separation between the saturated vapor phase (in the upper side of the shell) and saturated liquid phase (on the bottom of the shell), so that the vapor fed to the turbine is always in saturated conditions. This is well-established technology adopted in ORC plants and typically proposed for pure fluids [27]. This solution guarantees stable operation of the power plant in a rather wide range of transient and off-design conditions, in that any change of the input heat or the load results in a change in the liquid level of the evaporator with virtually no possibility of liquid in turbine as long as the level of liquid reaches the top of the shell. Also, the control strategy of such system is rather straightforward as it is based on the control of level of liquid in the evaporator and it can be easily achieved by properly varying the mass flow rate of the working fluid. Although the pool boiler is presently employed in ORC plant with pure working fluids, the same advantages can be envisaged in the case of mixtures. The behavior of the pool boiler in case of binary mixture is shown in Fig. 4. Let us consider a mixture of two components C1 and C2, C1 being the more volatile species and X the fraction of component C1 (see Fig. 4c). If we set the nominal operating conditions of the PB evaporator with a vapor fraction of, let’s say 50%, the conditions of the binary two-phase mixture are those defined by point a where the fraction of component C1 in the vapor (V) and liquid (L) phases is Y1,a and X1,a respectively (see Fig. 4a). Let us now assume that the power of the input hot source has increased somewhat, thus enhancing the evaporation rate of the mixture. The obvious result is

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Fig. 3. Scheme of once through evaporator (a) and related temperature–entropy profile (b).

the reduction of the level of the liquid in the PB, shifting the operating conditions of the PB to point b with a higher vapor fraction (75% in the example shown in Fig. 4b). In fact, more vapors are available at higher temperatures due to the leveler rule. Thus, in principle the PB evaporator seems a suitable solution for both mixtures and pure fluids, carrying the advantage of avoiding wet vapor in the turbine and sharing the same regulation criteria based on the control of the level of liquid.

Fig. 4. Operating principle of the PB evaporator in case of a binary mixture of working fluids. Schematic representation of the boiler subjected to an increase of the power of the hot source (a and b); T-xy diagram of the mixture in the related states (c).

2.2.3. Plant modeling The thermodynamic performances of the power plant shown in Fig. 1 were evaluated considering different working fluids, namely pure i-C5 and various binary mixture of hydrocarbons in case of both OT and PB evaporators. The calculation assumptions are the same of reference plant defined in Table 1, with the following further hypothesis:

• •

the evaporating pressure was optimized in order to maximize the power of the plant we considered an air cooled instead of the water cooled condenser in order to better evidence the possible advantages of the glide in condensation in case of the mixture of working fluids. In particular, the fan power of the air-cooled condenser was calculated according to Eq. (1), assuming a design pressure drop of 170 Pa [35], and an electric efficiency of the fan equal to 75%.

W Fan

 air × ΔPFan M ρair = ηFan

(1)

Notably, no standard component in Aspen Plus is available to simulate the pool boiler. To overcome this problem, we introduced two flash drums combined with heaters as shown in the dashed area of Fig. 5. The working fluid reaches the conditions of saturated liquid

Fig. 5. Layout of ORC plant with pool boiler evaporator realized in Aspen Plus environment.

T. Rajabloo et al./Applied Thermal Engineering 98 (2016) 1–9

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Table 3 Model validation with pure i-C5 by comprising pool boiler and once through evaporator. Pure i-C5

POpt (bar)

Qin (MW)

Wnet (kW)

ηC%

PCond. (bar)

M ˙ Working fluid (kg/s)

M ˙ cooling air (kg/S)

WFan (MW)

TOut, Evap (K)

HRF

ηRecovery% (Wnet/Qav)

OT PB (VF = 0.5) Error%

9.5 9.5 0

27.84 27.71 0.47

2.94 2.92 0.68

10.54 10.55 0.09

1.914 1.914 0

62.1 64.36 3.64

1222 1218 0.33

0.234 0.233 0.43

357.25 357.55 0.084

0.71 0.70 1.41

7.47 7.44 0.41

Table 4 Results comparison of once through (OC) and pool boiler (PB) evaporators in the case of various mixtures of hydrocarbons. Working fluid composition

POpt (bar)

Cond. P. (bar)

M ˙ of cooling air (kg/s)

WFan (kW)

WNet (kW)

Qin (kW)

ηC (%)

Tout, evap. (°C)

HRF

ηRecovery (%)

Pure i-C5 i-C5&50%n-C4-OT i-C5&50%n-C4-PB i-C5&75%n-C4-OT i-C5&75%n-C4-PB i-C5&50%n-C6-OT i-C5&50%n-C6- PB i-C5&50%n-C7-OT i-C5&50%n-C7-PB i-C5&50%n-C8-OT i-C5&50%n-C8-PB

9.5 15 12 18.5 12 6 7 5 5 5 6

1.914 3.37 3.06 3.99 3.56 1.25 1.62 1.16 1.38 1.17 1.79

1222 975 1008 1072 1120 718 695 439 415 291 532

234 187 193 205 214 137 133 84 80 56 102

2935 2922 2732 3036 2684 2659 2497 2321 1883 2035 1990

27,826 28,267 28,781 28,397 30,686 27,188 25,082 27,075 23,543 25,738 24,502

10.5 10.3 9.5 10.7 8.8 9.8 10 8.6 8.0 8.1 8.1

84 83 81 82 75 86 86 86 97 90 92

0.71 0.72 0.73 0.72 0.78 0.70 0.70 0.70 0.61 0.67 0.66

7.4 7.4 7.0 7.7 6.8 6.9 6.7 6.0 5.1 5.3 5.4

in the first set of flash drum and heater while the second set produces saturated vapor at constant temperature. The liquid phase is recycled within a mixer and fed to the evaporator. It is worth noting that a rigorous modeling of the phenomena occurring in the PB represented in Fig. 5 would require a specific study of this component with a preliminary design of his geometry in order to correctly take into account local effects of both mixing and heat exchange. However, given the preliminary character of this study we set, for the sake of comparison with the other cases, the minimum ΔT in correspondence with the saturated liquid, i.e. at the outlet of the first flash drum. In accordance with the other cases, mass flow rate of working fluid is then determined in order to comply with the defined minimum ΔT. Clearly, in case of pure fluid with PB, results are the same as the case of OT evaporator (Table 3). These results validate our suggested model for PB in Aspen plus environment. 2.2.4. Results and discussion The results of the simulations are reported in Table 4, showing the comparison of the relevant cycle parameters between the case with pure i-C5 (second line) and the selected hydrocarbon binary mixtures, in case of both PB and OT evaporators. As already mentioned, the evaporating pressure (second column) is chosen to optimize the recovery efficiency (ηRecovery), which maximizes the electric power produced. In fact, in a heat recovery cycle, the overall recovery efficiency ηRecovery is given by the product of the cycle thermodynamic efficiency ηCycle and the heat recovery factor HRF, as pointed out by the following equations:

ηRecovery = ηCycle × HR F

(2)

HR F = Q in Q av

(3)

ηCycle = Wnet Q in

(4)

shown in Fig. 2. Compositions reported in Table 4 are indeed those with the resulting highest ηRecovery. Furthermore, in case of the PB, the vapor fraction is in principle an additional degree of freedom. Vapor fraction is considered volume based in this study. Generally, if the vapor fraction changes, the vapor composition changes. The compositions of mixtures are considered mass based. The vapor from PB is richer in the more volatile component (the lighter one). When the molar mass of the vapor varies, the isentropic enthalpy drop in expansion and the turbine characteristics change in consequence. However, we observed that in all considered cases the amount of vapor fraction has a minor impact on the plant performances in comparison to the effect of mixture composition. For example, the results of these two variables on cycle performance are available for a selected mixture of i-C5 and n-C6 in Tables 5 and 6. Therefore, we fixed the vapor fraction value to 0.5, in order to set the design level of liquid at about half of the height of the evaporator, following the general rules in the operation of a PB [36]. The analysis of the results (Table 4) shows that the best thermodynamic performances are obtained with mixture of i-C5 and 75%

Table 5 Effect of different mixture compositions on performance of ORC in the case of mixture working fluids i-C5 and n-C6. VF at constant composition of 50% n-C6

Qin (MW)

0.25 0.50 0.75

26.94 25.08 24.62

WNet (MW)

ηC%

M ˙ air (kg/s)

M ˙ Working (kg/s)

fluid

2.55 2.50 2.54

9.47 9.97 10.32

857 695 645

61.72 55.14 52.79

*VF stands for vapor fraction.

where Qin is the input thermal power of the cycle and Qav is the available thermal power calculated assuming a theoretical cooling of the hot source to 50 °C. It is worth noting that, since in case of mixtures different compositions are possible, a preliminary selection was carried out based on thermodynamic reasoning according to diagrams similar to those

Table 6 Effect of different vapor fractions on performance of ORC in the case of mixture working fluids i-C5 and n-C6. n-C6% at constant VF of 0.5

Qin (MW)

25 50 100

39.15 25.08 19.32

WNet (MW)

ηC%

M ˙ air (kg/s)

M ˙ Working (kg/s)

fluid

2.68 2.50 2.18

6.85 10.32 11.28

1013 695 495

67.82 55.14 39.45

6

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n-C4. In case of OT evaporator, the ηRecovery and more significantly the net power are higher than that of the pure i-C5, (7.7 vs. 7.4% and 3036 kW vs. 2935 kW, respectively) given the relatively higher values of both HRF and ηCycle. These are a consequence of the glide in evaporation and condensation: the former improves the recovery of the heat source, while the latter results in a lower mass flow of cooling air and a lower fan consumption WFan. However, this result is limited to the thermodynamic context and should not be considered as conclusive in terms of the choice between pure fluid or mixture. More investigation is of course necessary in view design and costs of system. For instance one aspect to be taken into account is that in general, heat transfer coefficient of mixtures is less than pure fluids [37,38] resulting in a comparatively higher area of the heat exchangers which in turn increases the overall cost of the system. As far as the comparison between the two evaporator solutions is concerned, it comes out that the mixtures with PB show thermodynamic performance a little lower than the corresponding OT cases. Although both OT and PB cases, with respect to the pure fluid, share the advantage of a lower air fan consumption, this effect in case of PB evaporator is overwhelmed by the comparatively low turbine power. In fact, for any considered mixture, the composition at the evaporator outlet changes between the PB and OT cases and so does the glide in condensation, the turbine outlet temperature, and isentropic enthalpy change through the expansion and the overall cycle pressure ratio. For the most significant mixtures considered here, the result in general is a reduction of ηCycle. In fact, in the case of PB evaporator, the expanding mixture results always richer in the more volatile component. In addition, for a better understanding of the investigated process, the state points of the process are listed in Tables 7 and 8 regarding Fig. 5, in both cases of pure working fluid (i-C5) and a binary mixture (i-C5 and 50% n-C4). As it is clear in Table… the composition of working fluid changes inside the pool boiler but it remains constant outside the pool boiler. In other words, if we consider pool boiler as an independent component, the composition of working fluid is constant at all states of ORC.

Table 7 State points of the process in the case of pure i-C5 and vapor fraction of 0.5. Stream number

Temperature (°C)

Pressure (bar)

Enthalpy (kW)

Composition% i-C5

1 2 S1 S2 S3 3 4

47.54 112.42 81.79 112.42 112.42 76.04 47

9.5 9.5 9.5 9.5 9.5 1.91 1.91

156.106 128.399 301.243 290.274 145.137 131.665 156.216

100 100 100 100 100 100 100

Table 8 State points of the process in the case of i-C5 and 50% n-C4, and vapor fraction of 0.5. Stream number

Temperature (°C)

Pressure (bar)

Enthalpy (MW)

1 2 S1 S2 S3 3 4

48.19 125.24 90.23 123.39 125.24 71.94 47.00

18.50 18.50 18.5 18.50 18.50 3.62 3.62

138.35 113.39 266.73 254.84 128.38 116.53 138.55

Composition (mass based) % i-C5

n-C4

50 50 55 55 60 50 50

50 50 45 45 40 50 50

Table 9 Calculation assumptions for high temperature cycle defined in Fig. 6 [39]. Hot source temperature, T7 in Fig. 6a (°C) Input heat (MW) Power of the fan power consumption (kW) Evaporation pressure (bar) Condensing temperature, Tcond.(°C) Turbine isentropic efficiency, ɳT (%) Pump isentropic efficiency, ɳP (%) Minimum temperature of evaporator, ΔTmin, evap (°C) Minimum temperature of regenerator, ΔTmin, reg (°C) Minimum temperature of condenser, ΔTmin, cond. (°C)

300 8.7 180 9 90 80 75 25 25 5

3. High temperature ORC analysis 3.1. Reference plant The case study considered in this section is based on a biomass fired ORC plant discussed by two of the authors in a previous publication [39] operated with MDM. Calculation assumptions are reported in Table 9. As can be seen from the Temperature–Entropy diagram shown in Fig. 6b, the working fluid undergoes high superheating after expansion in turbine, thus requiring the presence of regenerator to achieve acceptable value of conversion efficiency [40]. The resulting plant layout is depicted in Fig. 6a. Thermodynamic properties of MDM are calculated by means of Peng–Robinson EoS, in accordance with [39]. Table 10 shows the results for validation of the model, showing a good agreement between the reference and calculated data. It can be observed that a significant difference exists between the power consumed by the fan in the air condenser due to the different assumptions adopted in reference article where a fan compression ratio of 1.1 was considered. However this has only a marginal effect on the resulting cycle efficiency. 3.2. Mixture of siloxanes Following the same approach adopted for the mixture of hydrocarbons discussed in Section 2.2, to investigate the behavior of mixtures as working fluid in the case of high temperature ORCs, binary mixtures of MDM, hexamethyldisiloxane (MM), and decamethyltetrasiloxane (MD2M) were studied. The power plant is the recuperative ORC depicted in Fig. 6a. With respect to the assumption of the reference case reported (Table 10), in the following analysis we fixed the temperature difference of the hot source (thermal oil) within the evaporator (T7–T8) equal to 50 °C, so that the evaporating pressure is calculated in each case to comply with this condition. 3.2.1. Equation of state for mixture of siloxanes Although the Peng–Robinson EoS is a reasonable choice to model the thermodynamic properties of several families of pure fluids, its extension to the analysis of mixture of siloxanes would require the knowledge of the relevant binary interaction parameters (that are typically obtained through experimental analysis). Since presently no published data are available on such parameters for mixtures

Table 10 Results of the model validation for the reference high temperature ORC plant defined in Fig. 6 [39].

Reference Calculated Error

Qin (MW)

Qcond. (MW)

WFan (kW)

WNet (MW)

ηC%

8.46 8.25 2.5%

6.8 6.6 3%

183 30 83.6%

1.50 1.50 0

17.73 18.18 2.5%

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Fig. 7. Comparison of the results obtained with PSRK EoS with experimental data available in [44] in the case of a mixture of 50% MDM and 50% MM at 363 K.

of siloxanes [41], we resort to Predictive Soave–Redlich–Kwong (PSRK). This EoS indeed covers prediction of thermodynamic properties for both polar and non-polar fluids and may be exploited to predict the binary interaction coefficients of mixtures [42,43] To assess the validity of this choice we first compared PSRK with PR in case of the ORC plant operated with pure MDM. Results of such comparison are listed in Table 11, showing, for our purposes, acceptable agreements between the two EoS. Moreover, in a second step we compared the results given by PSRK EoS with some experimental data available from [44] in the form of pressure–composition diagram at saturated vapor state for the mixture of 50% MDM and 50% MM at 363 K (Fig. 7). On the basis of this preliminary validation, we proceed with the analysis of the ORC in the case of mixture of siloxanes by means of PSRK EoS.

Fig. 6. (a) Layout of the reference regenerative cycle for the high temperature ORC analysis, (b) T-S diagram of the related cycle [39].

3.2.2. Results and discussion Table 12 reports the main results of the simulations in case of various binary mixtures of MM, MDM and MD2M. Mixture composition is selected following the same criterion adopted for hydrocarbons in Section 2.2.1, based on the study of their P–T curves. Results of pure fluids are also included in the table. The analysis evidenced that in general the OT evaporator shows a slightly improved cycle performance in comparison to the PB. Thus it can be argued that the marginal advantage of the OT solution might be overwhelmed by the discussed benefits associated to the use of

Table 11 Results of high temperature cycle with Peng–Robinson and PSRK EOS in the case of pure MDM as working fluid.

Pure MDM with PR EoS Pure MDM with PSRK EoS Error

Qin (MW)

Qcond. (MW)

M ˙ cooling air (kg/s)

WFan (kW)

WNet (MW)

ηC%

8.25 8.64 4.7%

6.61 6.94 5%

142.8 142.8 0

30 30 0

1.50 1.57 4.7%

18.19 18.17 0.1%

Table 12 Results for the high temperature ORC plant adopting siloxanes as a working fluid. PSRK_AC

M ˙ Working Fluid (kg/s)

WNet (MW)

ηC%

Qcond. (MW)

M ˙ Cooling air (kg/s)

WFan (kW)

Pevap (bar)

MDM MDM&25%MM-OT MDM&25%MM-PB MDM&50%MD2M-OT MDM&50%MD2M-PB MM&50%MD2M-OT MM&50%MD2M-PB MD2M

32.64 32.09 32.01 34.4 34.22 33.45 32.65 35.64

1.57 1.45 1.43 1.53 1.5 1.37 1.34 1.6

17.90 16.51 16.29 17.42 17.10 15.59 15.26 18.22

7.04 7.18 7.21 7.11 7.12 7.28 7.31 7.03

96.6 88.3 88.1 88.9 89.3 72.3 75.3 95

18 17 17 17 17 14 14 18

9.21 12.83 13.08 5.99 6.06 12.15 12.31 3.63

8

T. Rajabloo et al./Applied Thermal Engineering 98 (2016) 1–9

curves for hot and cold fluids match better in this case. Therefore, the mass flow rate of cooling air and consequently the fan consumption power have been decreased for this binary mixture, in comparison to other cases (Table 10). However, at a fixed condensing temperature (for example, 90 °C in our cycles), condensation starts at the higher temperatures in the case of more different mixture components, which means higher pressure out of turbine. Hence the enthalpy drop decreases across turbine which results in less generated power. 4. Conclusion

Fig. 8. T-S diagrams of different mixtures in the case of high temperature ORC.

a PB evaporator. Nonetheless, a definite conclusion on this question would require a detailed techno economic comparison of the two solutions, which is however beyond the scope of this study. Finally, it can be noted that the use of pure fluids, from a thermodynamic point of view, seems a better choice in this application. This can be explained considering that here, different from the low temperature case – which was based on the recovery of a geothermal source – no variable temperature heat source is exploited, thus limiting the potential advantage given by glide in evaporation of the mixture to obtain a better cooling of the hot source. Although the presence of the glide in condensation still allows a lower consumption at the air cooled condenser with respect to the case with pure fluids, it turns out that this effect does not compensate the intrinsically lower thermodynamic conversion efficiency of the cycle resulting from the mixture. As it is clear in Fig. 8, there are temperature glides at evaporation and condensation states. The temperature glide becomes higher when molecular weight and complexity of components are more different. Moreover, in the case mixture of MM and 50% MD2M, the condensation pressure is higher which leads to less enthalpy drop, generated power and net power in the turbine. In addition, some examples of temperature–duty (T-Q) diagrams for condenser are available in Fig. 9. Higher glide temperature leads to lower mass flow rate of cooling air and fan power. Overall, by applying mixture to the cycle the location of minimum temperature changes in heat exchanger (Fig. 9). In this case it shifted toward the entrance of hot working fluid. More interesting results are apparent in the case of mixture with more different components in which minimum temperature occurs at the entrance of hot working fluid to the condenser, such as mixture of MM and 50% MD2M in Fig. 9. Due to resulted temperature glide, slopes of heat

Fig. 9. T-Q diagrams of condenser for different working fluids in the case of air cooled high temperature ORC.

In this paper we explore the possibility of employing mixture of working fluids in ORC plants, particularly in the case of replacing the well-established once-through (OT) evaporator with the pool boiler (PB) technology. The PB component is in fact already a typical choice for pure working fluids in particular because it can cope with load variation with a rather simple control strategy, based on the control of the level of liquid. In this study we aim at evaluating the feasibility of this solution in case of mixtures, in order to extend its use and its advantages whenever the adoption of a mixture of working fluids may result appropriate. We carry out our analysis considering two reference case studies. The first, which is representative of low temperature ORC applications, is based on existing geothermal plant operating with isopentane (i-C5) as a working fluid, which exploits a geothermal water at 167 °C. The second is based on a biomass power plant operated with octamethyltrisiloxane (MDM) as a working fluid, with maximum cycle temperature of 300 °C, to be considered representative of high temperature ORC applications. In both cases, we study different binary mixtures of fluids based on hydrocarbons and siloxanes respectively and compare the power plant performances in case of both OT and PB evaporators. The analysis evidenced that in general the OT evaporator shows a slightly improved cycle performance in comparison to the PB. Thus, it can be argued that the marginal advantage of the OT solution might be overwhelmed by the discussed benefits associated to the use of a PB evaporator. Clearly, a definite conclusion on this subject would require a detailed techno economic comparison of the two solutions, which is however beyond the scope of this study. Regarding the comparison with the pure fluids, the siloxane mixture (adopted in case of high temperature ORC) does not prove to be advantageous in terms of thermodynamic performances of the power cycle. This can be explained considering that in case of combustion of biomass – different from the geothermal case – no variable temperature heat source is exploited, thus limiting the potential advantage given by glide in evaporation of the mixture to obtain a better cooling of the hot source. Although the presence of the glide in condensation still allows a lower consumption at the air cooled condenser with respect to the case with pure fluids, it turns out that this effect does not compensate the intrinsically lower thermodynamic conversion efficiency of the cycle resulting from the mixture. On the contrary, for the low temperature ORC, with mixture of i-C5 and 75% n-C4, in case of OT evaporator, the recovery efficiency (ηRecovery) is higher than that in the pure i-C5 (7.7 vs. 7.4%), given the relatively higher values of both the recovery factor (HRF) and cycle efficiency (ηCycle). These are a consequence of the glide in evaporation and condensation: the former improves the recovery of the heat source, while the latter results in a lower mass flow of cooling air and a lower fan consumption. However this result is limited to the thermodynamic context and should not be considered as conclusive in terms of the choice between pure fluid and mixture. A more comprehensive analysis will be carried out in future works considering the design of main components – particularly the PB and OT evaporators and the turbine – together with the relevant techno economic implications.

T. Rajabloo et al./Applied Thermal Engineering 98 (2016) 1–9

Nomenclature AC Cond. Evap. ɳT ɳG ɳC ɳFan ɳP ɳPD ɳRecovery HRF ρair P T ΔTmin ΔTLMTD OT PB Q M ˙ WNet WF

Air cooling Condensation Evaporation Efficiency of turbine (–) Efficiency of generator (–) Thermal efficiency of cycle (–) Efficiency of fan (–) Efficiency of pump (–) Efficiency of pump driver (–) Recovery efficiency (–) Heat recovery factor (–) Density of air (kg·m−3) Pressure (bar) Temperature (°C) Minimum temperature approach (°C) Logarithmic mean temperature difference (°C) Once through Pool boiler Heat rate (W) Mass flow rate (kg s−1) Net power (W) Fan power consumption (W)

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