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ORC optimization for medium grade heat recovery
Energy xxx (2014) 1e10
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ORC optimization for medium grade heat recovery Fadhel Ayachi a, b, Elias Boulawz Ksayer c, Assaad Zoughaib c, Pierre Neveu a, b, * a Procédés, Matériaux et Energie Solaire e Centre National de la Recherche Scientifique (PROMES-CNRS), Rambla de la thermodynamique Tecnosud, 66100 Perpignan, France b Université de Perpignan Via Domitia, 52 avenue Paul Alduy, 66860 Perpignan, France c MINES Paris-Tech, CES, 5 rue Leon Blum, 91120 Palaiseau, France
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 March 2013 Received in revised form 2 December 2013 Accepted 19 January 2014 Available online xxx
The ENERCO_LT (ENErgy ReCOvery from Low Temperature heat sources) project is a waste heat recovery project that aims to reduce energy consumption in industrial gas production sites by producing electricity through Organic Rankine Cycles supplied by exothermic process discharges at low and medium temperatures. Two promising thermal sources consisting of (i) almost dry gas flow at 165 C and (ii) moist gas flow at 150 C, were investigated. The optimal recovery solution can be identified via an appropriate system design, an adequate working fluid and suitable operating conditions. Systemic optimization coupling exergy analysis and pinch minimization have been performed to assess the potential of various working fluids within various system designs, i.e. single stage system and double stage system. The results indicate that the global exergy efficiency is strongly linked to the critical temperature of the working fluid. They emphasize the existence of an optimal critical temperature specific to the hot source temperature and the pinch value. An empirical expression of the optimal critical temperature was derived for dry and quasi-isentropic pure fluids and appears to be useful for primary selection of the working fluids. Also, recovery solutions using blends appear very attractive to meet high exergy efficiency and environmental friendly objectives. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Waste heat recovery Moist gas Exergy ORC Pinch Blends
1. Introduction Nowadays, the gradual depletion of fossil fuels associated with constraints on emissions of greenhouse gases leads to increasingly restrictive standards for heavy industries in terms of energy consumption and environmental impact. This fact pushes the large energy consumers to search for innovative solutions to valorize their wasted heat which could be a promising resource for the future. In this context, Organic Rankine Cycles (ORCs) become attractive for potential use in future industrial plants. Several comparative studies in various applications take advantage of the fluid selection to improve the net power output and the system efficiency according to the characteristics of the heat source [1e14]. Hung et al. [1], Liu et al. [2] and Chen et al. [3] have assessed the influence of the fluid properties on the performances of an Organic Rankine Cycle for waste heat recovery systems and showed that the power output depends on the critical * Corresponding author. Tel: þ33 4 68682262; fax: þ33 4 68682213. E-mail addresses: [email protected] (F. Ayachi), elias.boulawz_ [email protected] (E. Boulawz Ksayer), assaad.zoughaib@mines-paristech. fr (A. Zoughaib), [email protected] (P. Neveu).
point, the latent heat and the slope of both saturation lines in a (T, s) diagram. Some analysis in waste heat recovery applications [3,7] have shown that supercritical operating conditions lead to higher performances than subcritical operating conditions. This requires a fluid critical temperature below the hot source temperature. Schuster et al. [7] have indicated that R-245fa, isopentane and R-365mfc are suitable for heat recovery at a hot source temperature of 210 C and have pointed out an improvement of the system efficiency of about 8% given by the transcritical cycle. Tchanche et al. [13] have compared various working fluids for use in solar ORC systems driven by a heat source temperature below 90 C. The authors add safety and environmental indicators to the theoretical performances as comparison criteria. Wang et al. [14] have conducted a comparative experimental study of pure fluids and nonazeotropic blends in low-temperature solar Rankine cycle. The authors have concluded that non-azeotropic blends have the potential for overall efficiency improvement due to the nonisothermal condensation. Other studies perform multi-objective optimization for the fluid selection [15e18]. In this case, the fluid selection is related to both source characteristics and design objectives. Lakew and Bolland [17] have conducted a comparative analysis from low to medium
http://dx.doi.org/10.1016/j.energy.2014.01.066 0360-5442/Ó 2014 Elsevier Ltd. All rights reserved.
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F. Ayachi et al. / Energy xxx (2014) 1e10
d f H L opt p re rec t vg
Nomenclature ex _ Ex h _ m _f m P PC T TC s _ W X DTmin
hex,g x f j
specific exergy (J/kg) exergy flux (W) specific enthalpy (J/kg) mass flow rate of the working fluid (kg/s) mass flow rate of the flue gases (kg/s) pressure (Pa) or (bar) critical pressure (Pa) or (bar) temperature (K) or ( C) critical temperature (K) or ( C) specific entropy (J/kg K) mechanical power output (W) molar fraction (e) pinch (K) global exergy efficiency (-) specific dissipating factor (-) enthalpy flux (W) loss factor (-)
destroyed flue gases high low optimal pump regenerator recovered turbine vapour generator
Acronyms GWP global warming potential HCFC hydrochlorofluorocarbon HFC hydrofluorocarbon ODP ozone depletion potential ORC organic rankine cycle TET turbine exhaust temperature TIT turbine inlet temperature
Subscripts a available cd condenser temperature grade heat sources (80e200 C) based on a subcritical cycle without superheating. They have identified, for each level, the appropriate working fluid and its optimal vaporization pressure for three distinctive objectives: (i) maximum power output, (ii) minimum heat exchanger, area and (iii) minimum turbine size. Recently, Khennich and Galanis [18] have endorsed this theory by developing a numerical model of both subcritical and transcritical power cycles using a fixed-flowrate low-temperature heat source. They have also concluded that, for a given heat source temperature and working fluid, maximizing the thermal efficiency and minimizing the component size lead to different designs. In particular, they have shown that minimizing the turbine size requires a very large heat exchanger thermal conductance. All these studies underline the interest of the multi-objective optimization models to look at the trade-offs of the system between efficiency and cost. In a previous analysis [19], we investigated the valorization of two heat sources involved in CO2 capture unit from oxy-
combustion products. The working fluid critical temperature appeared to be a key parameter when an optimum matching is searched for the temperature profiles of the working fluid and the external flow in the vapour generator. Due to practical considerations, some recovery solutions using pure fluids were presented as compromise between environmental impact and performance. The present study extends the previous work by (i) analysing the system performance trends according to the fluid critical temperature (ii) comparing the performances of various system designs and fluids (iii) assessing the expediency of some binary blends as recovery solutions compared to pure fluid solutions. 2. Problem definition and optimization method Fig. 1 gives the basic overview of the recovery process. The hot source consists of flue gases at the exit of an exothermic process. The overall available resource is defined as bounded by the
Cooler Downstream process
3f
2f Evaporator
3
1f
Upstream process
2
Turbine 4
Pump 1
Condenser
Working cycle Fig. 1. Recovery system layout.
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F. Ayachi et al. / Energy xxx (2014) 1e10
The global exergy efficiency, which measures the converted share compared to the available exergy resource, is written as:
Table 1 Resource characteristics. Resource
T1f ( C)
T3f ( C)
P (bar)
Water molar fraction (%)
Mass flow rate (kg/s)
Dew point ( C)
_ a Ex (kW)
Almost dry Moist
165 150
25 25
25 1
2 20
152.2 130.2
75 60
4950 6148
upstream process outlet 1f and the downstream process inlet 3f. However, due to the unavoidable pinch in the vapour generator (Evaporator) and its related operating conditions, the available resource cannot be completely valorized. The flue gases exit the vapour generator at a temperature T2f higher than T3f, and the heat recovery is then followed by a flue gas cool down to the inlet conditions required by the downstream process. Two heat sources were considered and are summarized in Table 1. The first one, with low moisture content, is cooled at 25 bar from 165 C to 25 C. The second one, with high moisture content, is cooled at 1 bar from 150 C to 25 C and shows a dew point at _ a is determined according to 60 C. The available exergy resource Ex the molar compositions and cooling conditions of the flue gases as presented in the previous work [19]. It is written as:
_ a ¼ m _ f ðex1f ex3f Þ Ex
_ W
hex;g ¼ _ Exa
(5)
_ < 0 is the net mechanical power output (kW). where W The exergy balances of the working cycle and of the whole system are respectively given by Eqs. (6) and (7):
_ _ rec þ W Ex
X
_ Ex d;i ¼ 0
(6)
i
_ Ex _ _ aþW Ex d;total ¼ 0
(7)
P_ Exd;i is the sum of the exergy destroyed by the unitary where _ components of the working cycle and Ex d;total is the exergy destroyed by the whole system. From Eqs. (4), (6) and (7), it follows that:
_ Ex d;total ¼
X
_ _ Ex d;i þ Exloss
(8)
i
Eq. (5) can be rewritten as:
(1)
_ f being the total mass flow rate (kg/s) of the flue gases including m the condensated stream and ex1f (kJ/kg) the specific exergy of the flue gases at point 1f. Fig. 2 illustrates for both cases, the evolution of the recovered _ rec and exergy losses Ex _ exergy flux Ex loss according to the flue gas discharge temperature T2f.
_ rec ¼ m _ f ðex1f ex2f Þ Ex
(2)
_ _ f ðex2f ex3f Þ Ex loss ¼ m
(3)
_ rec quantifies the maximum work power that would be produced Ex _ in a Carnot engine, whereas Ex loss represents the lost part of the overall resource that will be destroyed in the external cooler. The change of the slope comes from the additional latent heat provided by the condensation of water vapour when temperature T2f becomes lower than the dew point temperature. For the moist heat source, this leads to an important increase of the available exergy that could be theoretically valorized. From Eqs. (1)e(3), it follows that:
_ rec þ Ex _ _ a ¼ Ex Ex loss
3
(4)
hex;g ¼ 1
X
xi j
(9)
i
with
_ Ex
xi ¼ _ d;i Exa _ Ex
j ¼ _ loss Exa
(10)
(11)
The specific dissipating factor xi measures the contribution of each unitary component of the working cycle on the efficiency degradation, whereas the loss factor j measures the ratio of available exergy excluded from the recovery process, i.e. destroyed in the ambiance. Systemic optimization [20] coupling exergy analysis and pinch minimization [21,22] has been adopted. All the investigated processes have been optimized by maximizing the mechanical power _ a is given), using the output (i.e. the global exergy efficiency as Ex constant settings reported in Table 2. All the unitary components are considered as open systems in steady state condition and pressure losses are neglected. Once these settings are given, two cycle independent variables, namely high pressure PH and turbine
Fig. 2. Recovered and lost exergy fluxes according to the flue gas discharge temperature T2f. (a) Almost dry heat source; and (b) Moist heat source.
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F. Ayachi et al. / Energy xxx (2014) 1e10 Table 2 System constant settings. Isentropic efficiencies Pump Turbine
0.9 0.85
Condenser settings Water inlet temperature ( C) Water outlet temperature ( C)
15 20
Pinches Vapour generator DTmin,vg (K) Condenser DTmin,cd (K)
10 5
inlet temperature TIT h T3 are sufficient for describing the whole process. For a given couple (PH, TIT), the mass flow rate of the _ (kg/s) leading to the aimed pinch in the vapour working fluid m generator can be determined. Thence, composite curves (and consequently pinch location) can be obtained from a model developed through ProsimÒ Plus 3.1 simulator [23,24]. The working fluid properties are calculated using REFPROPÒ 8.0 developed by the National Institute of Standards and Technology [25]. For a given pressure PH, the optimal turbine inlet temperature TIT is searched by maximizing the power output under the following constraint: the turbine exhaust vapour must be in saturated or superheated state in order to avoid droplet erosion of the turbine blades. Notice that, the whole expansion path may cross the saturation line. In this case, the operation is considered acceptable if the vapour quality along the expansion does not go below 0.95. If not, the turbine inlet temperature TIT is increased to verify this latter constraint. _ correspond, for each Thereby, the optimal conditions (PH, TIT, m) fluid, to the maximal global exergy efficiency. Exergy analysis gives the exergy destruction for each unitary operation occurring in these optimal cycles, and the exergy losses due to the external cooler. Energy and exergy balances, and a detailed examination of the irreversibility trends according to the evaporation pressure PH, are reported in Ayachi et al. [19]. 3. Single stage system Depending on the slope of the vapour saturation line in a (T, s) diagram, working fluids can be classified as dry fluids (i. e. (vT/ vs)sat > 0), isentropic fluids (i. e. (vT/vs)sat w N) and wet fluids (i. e. (vT/vs)sat < 0). In the following section, exergy performance of various dry and quasi-isentropic pure fluids operating in a single stage ORC is first investigated. Afterwards, performance and
Fig. 3. Optimal single stage performances by using dry and quasi-isentropic pure fluids (DTmin,vg ¼ 10 K, PH max ¼ 70 bar).
environmental impact of some binary blends are assessed and compared to pure fluid results. 3.1. Pure fluid assessment Fig. 3 displays the global exergy efficiency given by the optimized cycle for various dry and quasi-isentropic pure fluids, and referring to 10 K-pinch configuration in the vapour generator. The fluids are ranked according to their critical temperatures. This clearly shows a strong link between the global exergy efficiency and the fluid critical temperature, and the existence of an optimum of efficiency for a given thermal source. Thereby, an appropriate range of critical temperature for the selection of the working fluid can be identified. When considering the almost dry heat source at 165 C, the fluid critical temperature appropriate range is located between 90 C and 130 C, and the maximum exergy efficiency reaches 56%. For the case of the moist heat source at 150 C, the critical temperature appropriate range is slightly lower, located between 80 C and 125 C; however, the global exergy efficiency does not exceed 31%. As an example, Figs. 4 and 5 represent the composite curves and the irreversibility repartition by using R-236fa, respectively, for the almost dry heat source and the moist heat source. This fluid is located in the appropriate range in both cases. The composite curves display the temperature of both fluids according to the related enthalpy fluxes:
Fig. 4. Optimal cycle using R-236fa (Almost dry heat source). (a) Composite curves. (b) Irreversibility repartition.
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Fig. 5. Optimal cycle using R-236fa (Moist heat source). (a) Composite curves. (b) Irreversibility repartition.
_ f ðhf ðTf Þ h3f Þ - for the flue gas (hot composite): ff ðTf Þ ¼ m _ - for the working fluid (cold composite): ff ðTÞ ¼ mðhðTÞ h2 Þ þ K _ f ðh2f h3f Þ. The constant K ensures ff ðT1f Þ ¼ fðT3 Þ where K ¼ m at the hot side of the vapour generator. For the first case, the composite curves show adequate temperature matching between the almost dry flue gases and the working fluid over the major part of the available resource (Fig. 4a). In this case, the loss factor is only about 8.6% (Fig. 4b). For the second case, due to the important shape change of the moist flue gas composite curve at low temperature, the optimal cycle leads to a partial recovery from the available resource (Fig. 5a). Consequently, a large amount of exergy is still available at the exit of the process: the loss factor reaches 50% (Fig. 5b). Therefore, it can be considered to implement a second recovery stage before the external cooler. Considering this fact, single stage system is only discussed for the almost dry source case in the following section. On the other hand, Fig. 3 shows for both cases that the optimal cycle corresponds to a transcritical cycle. Such cycle involves a subcritical pressure PL in the condenser and a supercritical pressure PH in the vapour generator. This leads to potentially high pressures and could lead to more expensive devices. It is then interesting to study the impact on the global exergy efficiency when going from an optimal transcritical cycle to a subcritical cycle. Fig. 6 represents the efficiency degradation when constraining the high pressure PH to be slightly lower than the critical pressure (PH z PC e 1 bar). It is
worth noting that the decrease in efficiency is low for fluid critical temperatures close to the optimum. As an example, by using R-236fa, the global exergy efficiency goes from 56% to 54.7% when passing from the optimal transcritical cycle to a subcritical cycle. As the operating high pressure is reduced from 48 bar to 30 bar, subcritical cycles seem more attractive in that case. For lower critical temperatures, the efficiency degradation when passing to a subcritical cycle is more important. A more detailed technical and economic analysis is required to conclude, but interesting trends can be pointed out. Figs. 7 and 8 represent the entropy diagram and the irreversibility repartition when R-1234yf is used respectively in transcritical cycle (optimal: PH ¼ 70 bar) and subcritical cycle (degraded: PH ¼ 32 bar). They illustrate the moving of exergy destruction from the cold part to the hot part of the vapour generator. Going from a transcritical to a subcritical cycle increases the temperature difference between the flue gas inlet and the working fluid outlet in the vapour generator (T1f T3), but decreases the temperature difference between the flue gas outlet and the working fluid inlet in the vapour generator (T2f T2). Therefore, the increase of the thermal irreversibilities occurring at high temperatures is partially compensated by the decrease of those occurring at low temperatures. This results in limited reduction of the global exergy efficiency. When the fluid critical temperature is far lower from the optimum, the subcritical cycle implies large temperature difference at the hot side of the vapour generator. Here, the compensation effect is then less significant.
3.2. Pinch impact Pinch setting has important consequences on the system performance and the cost of the heat exchangers. It is then interesting to study the impact of the pinch setting on the above results, especially the working fluid selection. The results are presented in Fig. 9 and refer to 3 different pinches in the vapour generator: 5 K, 10 K and 25 K. The existence of an optimal critical temperature observed previously for a 10 K pinch is also valid for lower and higher pinches. Moreover, the working fluids have been ranked according to (TIT)max TC, where:
ðTITÞmax ¼ T1f DTmin;vg Fig. 6. Performance degradation when passing from an optimal transcritcal cycle to a subcritical cycle (Almost dry heat source at 165 C, Single stage, DTmin,vg ¼ 10 K, PH max ¼ 70 bar).
(12)
(TIT)max represents the highest turbine inlet temperature which can be reachable, for a given inlet source temperature and a given pinch value.
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_ diagram; and (b) Irreversibility repartition. Fig. 7. Optimal transcritical cycle using R-1234yf (Almost dry heat source). (a) (T, ms)
_ diagram; and (b) Irreversibility repartition. Fig. 8. Degraded subcritical cycle using R-1234yf (Almost dry heat source). (a) (T, ms)
From Fig. 9, it appears an empirical expression for the optimal critical temperature, whatever the pinch is:
TC;opt zðTITÞmax 33 K
(13)
The above expression can be used for primary selection of the working fluids. It estimates the optimal critical temperature once
Fig. 9. Impact of the pinch setting on the fluid selection (Almost dry heat source at 165 C, Single stage).
the hot source inlet temperature and the vapour generator pinch value are known. Notice that this expression has also been verified for the moist heat source and it appears to be still valid. However, temperatures T1f are quite close in both cases, and further studies would be required to extend this correlation to other temperature levels.
Fig. 10. System performances by using binary blend {R-1234yfeisobutane} (Almost dry heat source at 165 C, DTmin,vg ¼ 10 K, PH max ¼ 70 bar).
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Table 3 Recovery solutions for the almost dry heat source (DTmin,vg ¼ 10 K): operations and zerformances. Working fluids Mole [%] PC [bar] TC [ C] GWP Oper
_ m[kg/s] PL [bar] PH [bar] TIT [ C] cd.glide [K] T2f [ C] xvg [%] xt [%] xcd [%] xp [%] j [%] hex,g [%] [kW]
R-245fa
e
36.51
154
950
sub-c
66.1
1.48
12
97.7
e
68.6
21.4
R-134a
e
40.59
101.1
1300 sub-c
92.9
6.65
39
108.6
e
53.5
89.1
6.65
69
139.6
e
57.6
sub-c 130.7
6.72
32
95.6
e
tr-c
6.72
70
142.6
e
tr-c R-1234yf
e
32.66
94.8
4
105
7.1
9.9
0.1
20.1
9.3
11.6
0.5
12.5
10.9
10.7
1
44.9
24.2
9.3
12.8
0.6
5.1
48
2376
54.7
12.2
11.1
11.7
1.3
9.6
54.1
2676
i-butane
e
36.29
134.7
20
sub-c
37.8
3.5
34
130.8
e
69.6
13.9
8.8
R-1234yf
48
34.87
115.5
10
sub-c
79.1
4.54
33
113.1
3.1
50.9
17.4
10.3
i-butane
52
tr-c
76.7
4.54
51
138.4
3.1
53.4
13.3
11.2
9.2 10 9.6
18.9
42.6
2107
9
49.5
2451
11.2
53.7
2656
0.4
19.7
48
2374
0.6
7.6
54.1
2679
0.9
8.9
56.1
2776
critical temperature of the blend. It is worth noting that the optimal pseudo-critical temperature is close to the one given by Eq. (13). The above results highlight a main interest of using blends in this recovery problem. They appear very attractive to meet high exergy efficiency and environmental friendly objectives. Finally, by considering the subcritical operation, the optimal blend {R-1234yf (48%mol)eisobutane (52%mol)} reaches the performance obtained with R-236fa, i.e. a global exergy efficiency of about 54% and provides a GWP of 10 kgeqCO2. Besides, the blend reduces the flammability risk of isobutane. Table 3 gathers the operations and performances of some recovery solutions for the almost dry heat source.
3.3. Blend assessment From the above results (Fig. 6), two working fluids appear as best candidates for valorizing the almost dry resource: R-236fa and R-124, and both can operate through a subcritical cycle with high performance and acceptable pressure. However, the final selection must face the environmental constraints. R-236fa is a hydrofluorocarbon (HFC) characterized by a very high Global Warming Potential (GWP) of about 9400 kgeqCO2. R-124 is a hydrochlorofluorocarbon (HCFC) having an Ozone Depletion Potential (ODP) of 0.03. By setting constraints on the environmental impact (ODP ¼ 0 and GWP < 750 kgeqCO2), two candidates come into view: R-1234yf and isobutane. The first is particularly interesting because of its notably low GWP (4 kgeqCO2), the second is less recommended due to its high flammability. Nevertheless, it could be interesting to use a blend mixing two pure fluids located on either sides of the optimal critical temperature. As the blend properties vary with the composition, the idea is that approaching the optimal critical temperature would enhance the performance. To verify this point, a binary blend composed of {R-1234yfeisobutane} was investigated. The results are represented in Fig. 10 for a wide range of molar composition and compared to pure fluid trend. They show specific correlation between the global exergy efficiency and the pseudo-
4. Double stage system Due to its important exergy content, the interest of using the condensing heat available in the moist source has been clearly shown in the previous section. The change in slope of the hot composite curve makes difficult to match the temperature profiles of the hot and cold flows in the vapour generator, as depicted in Fig. 5a: the required pinch then leads to large energy and exergy losses, and only a small part of this additional heat can be valorized
Cooler Downstream process
3f
2f
21f Evaporator1
Evaporator2
2*
3
3
1f
Upstream process
2
Turbine1
Turbine2
4 Pump2
Regenerator
4
2 1
4* Condenser1
Condenser2
Pump1 1
Bottoming cycle
Topping cycle
Fig. 11. Cascading cycle layout.
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Fig. 12. Double stage performances (Moist heat source at 150 C, DTmin,vg ¼ 10 K).
by a single stage system. In the following section cascading cycles are discussed for the case of the moist heat source. The aim is to valorize the exergy losses induced by the first stage by implementing a second stage. Fig. 11 describes the layout of the system. In case of dry working fluid (T4 > T2), an internal transfer of heat (regeneration) into the topping cycle (first stage) allows to valorize the vapour cool down from the turbine outlet (point 4) to the condenser inlet (point 4*). It aims to decrease the thermal flux required by the evaporator of the topping cycle in order to release more energy flux to be transferred into the bottoming cycle (second stage). The pinch in the regenerator was settled to 2 K. Heat regeneration was not expected for the last stage as the discharged flux is totally lost in the external cooler: decreasing the thermal flux required by the evaporator of the bottoming cycle increases the thermal power to be extracted in the external cooler, and appears not to be favourable for the global exergy efficiency. Fig. 12 represents the results obtained when R-1234yf or R-245fa is used as a topping cycle working fluid. It displays the global exergy efficiency given by the optimized cascade according to the critical temperature of the bottoming cycle working fluid.
Operating conditions and irreversibility repartition of some investigated cascades are reported in Table 4. The results indicate that global exergy efficiency of about 40% is achievable when using a transcritical cycle in the first stage. A twotranscritical cycle cascade using R-1234yf in the topping cycle and carbon dioxide in the bottoming cycle provides adequate temperature matching in both upper and lower zone of the hot composite and leads to global exergy efficiency of about 42%. However, the topping cycle involves a supercritical pressure of 60 bar and the bottoming cycle involves a supercritical pressure of 90 bar. Also, It appears that the global efficiency is little sensitive to the bottoming cycle fluid selection which could be orientated to environmental and economic criteria. On the other hand, when passing from the optimal two-transcritical cycle cascade to a two-subcritical cycle cascade, the global exergy efficiency drops to around 37%. A twosubcritical cycle cascade seems more attractive as it provides lower operating pressures. Fig. 13 displays the repartition of irreversibilities when going from a subcritical single stage using R-1234yf to a two-subcritical cycle cascade using R-1234yf and R-41, respectively, in the topping cycle and bottoming cycle. The exergy losses of the topping cycle are then used in the bottoming cycle, but a large part of this potential is destroyed in the added components. Nevertheless, the global exergy efficiency increases by approximately 1/3 compared to the single stage. Fig. 14 illustrates the composite curves of this cascade. Heat regeneration is not realizable for a topping cycle using R-1234yf since for this isentropic fluid the turbine exhaust temperature TET h T4 is close to the vapour saturation temperature at low pressure PL. In case R-245fa is used as a topping cycle fluid, the results show a weak regeneration contribution, less than 1.5%. When considering the recovery process from the condensing heat at low temperature, Table 4 indicates that using fluid with low critical temperature and high critical pressure, such as R-41, leads to high optimal pressure PH even subcritical (w52 bar). On the other hand, using fluid with critical temperature much higher than the dew temperature, such as R-245fa, leads to weak subcritical pressure level PH (less than 3 bar) which would require high turbine size. Here, adapting the critical point by using blend could be useful to provide a more practical solution. Also, the presence of
Table 4 Recovery solutions for the moist heat source (DTmin,vg ¼ 10 K): operations and performances. Working fluids PC [bar] TC [ C] GWP Oper R-1234yf
2R-245fa
32.66
36.51
94.8
154
4
950
top: R-1234yf
32.66
94.8
4
bott: R-245fa
36.51
154
950
top: R-1234yf
32.66
94.8
4
bott: R-41
58.97
44.1
97
top: R-1234yf
32.66
94.8
4
bott: CO2
73.77
31
1
_ _ m[kg/s] PL [bar] PH [bar] TIT [ C] TET [ C] T2f [ C] xvg [%] xt [%] xcd+re [%] xp [%] j [%] hex,g [%] W[kW]
sub-c
88.3
6.72
32
tr-c
88.4
6.72
60
sub-c sub-c
45.6 93.1
1.48 1.48
11 2.48
sub-c/regen sub-c
45.6 95.2
1.48 1.48
sub-c sub-c
88.3 78.5
tr-c sub-c
98.5
31.9
58.4
11.9
5.3
7.4
0.3
47
28.1
1725
25.2
58.6
7.4
6.5
6.9
0.7
48
30.5
1876
93.8 39.7
42.3 28.2
71.2 48.1
11.5 14
3.8 1.9
5.5 9.8
0.1 0.01
19.2
34.2
1391 709
11 2.5
93.8 39.9
42.3 28.2
76 48.3
10.3 14.7
3.8 2
4.9 10.1
0.1 0.01
19.5
34.6
1391 737
6.72 1.48
32 2.36
98.5 38.2
31.9 27.8
58.4 46.9
11.9 11.3
5.3 1.5
7.4 8.3
0.3 0.01
17.2
36.8
1725 540
88.4 79.5
6.72 1.48
60 2.38
129 38.5
25.2 27.9
58.6 47.1
7.4 11.4
6.5 1.6
6.9 8.4
0.7 0.01
17.5
39.6
1876 557
sub-c sub-c
88.3 70
6.72 38.3
32 52
98.5 48.3
31.9 27
58.4 44.9
11.9 11.4
5.3 2.2
7.4 9.3
0.3 0.3
14.1
37.8
1725 596
tr-c sub-c
88.4 70.3
6.72 38.3
60 53
129 48.6
25.2 26
58.6 45.5
7.4 11.1
6.5 2.3
6.9 9.2
0.7 0.3
15
40.6
1876 618
sub-c tr-c
88.3 162.3
6.72 64.3
32 90
98.5 48.3
31.9 25.6
58.4 41.2
11.9 10.7
5.3 3.7
7.4 11
0.3 1
9.5
39.2
1725 683
tr-c tr-c
88.4 164.6
6.72 64.3
60 90
129 48.6
25.2 25.8
58.6 41.1
7.4 11.1
6.5 3.7
6.9 11.3
0.7 1
9.4
42
1876 706
129
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9
Fig. 13. Irreversibility repartition (Moist heat source). (a) Subcritical single stage (R-1234yf). (b) Subcritical double stages (R-1234yf þ R-41).
Fig. 14. Composite curves of a two-subcritical cycle cascade using R-1234yf and R-41 (Moist heat source).
contaminants and the possible condensation involved for the moist source will require high quality materials for the vapour generator of the second stage. All these concerns emphasize the difficulties to valorize the low temperature part of the resource. The global exergy efficiency increasing of 1/3 offered by the second stage would require approximately doubling the investment cost. A more detailed technical and economic analysis is required to conclude. 5. Conclusion The present paper has conducted large comparative analysis on ORC recovery solutions from one almost dry heat source and one highly moist heat source at medium temperature (respectively 165 C and 150 C). Systemic optimization coupling exergy analysis and pinch minimization has been adopted and various working fluids integrated in different designs have been investigated. The main results of the study can be extracted as follow: - Strong mean correlation was found between the global exergy efficiency and the fluid critical temperature. It shows the existence of an optimal critical temperature specific to the hot source temperature and the pinch value. - An empirical expression of the optimal critical temperature was derived for dry and quasi-isentropic pure fluids. It can be used for primary selection of the working fluids, once the hot source inlet temperature and the vapour generator pinch setting are defined.
- The highest performances are given by the supercritical operating conditions. However, for fluid critical temperatures close to the optimum, subcritical cycles seem more attractive as they approach the highest efficiencies and involve acceptable operating pressures. - Environmental constraints of pure fluid solutions prevent from reaching the highest power output as an objective function. Using blends allows to sidestep these constraints to meet high exergy efficiency and environmental friendly objectives. - A two-cycle cascade appears as an appropriate recovery design for the moist heat source; the topping cycle working on the upper zone of the dew point and the bottoming cycle taking advantage of the condensing process. The involvement of a second stage offers a global exergy efficiency increasing of about 1/3. However, the added components and the need of high quality materials due to the condensing process would require a high investment cost. Acknowledgements This work has been supported by the French Research National Agency (ANR) through the ENERCO_LT-EESI-09 research project. References [1] Hung TC, Shai TY, Wang SK. A review of organic Rankine cycles (ORCs) for the recovery of low-grade waste heat. Energy 1997;22:661e7. [2] Liu BT, Chien KH, Wang CC. Effect of working fluids on organic Rankine cycle for waste heat recovery. Energy 2004;29:1207e17. [3] Chen H, Yogi Goswami D, Stefanakos EK. A review of thermodynamic cycles and working fluids for the conversion of low-grade heat. Renew Sustain Energy Rev 2010;14:3059e67. [4] Maizza V, Maizza A. Working fluids in non-steady flows for waste energy recovery systems. Appl Therm Eng 1996;16:579e90. [5] Maizza V, Maizza A. Unconventional working fluids in organic Rankine-cycles for waste energy recovery systems. Appl Therm Eng 2001;21:381e90. [6] Hung TC. Waste heat recovery of organic Rankine cycle using dry fluids. Energy Convers Manage 2001;42:539e53. [7] Schuster A, Karellas S, Aumann R. Efficiency optimization potential in supercritical organic Rankine cycles. Energy 2010;35:1033e9. [8] He C, Liu C, Gao H, Xie H, Li Y, Wu S, Xu J. The optimal evaporation temperature and working fluids for subcritical organic Rankine cycle. Energy 2012;38:136e43. [9] Wang EH, Zhang HG, Fan BY, Ouyang MG, Zhao Y, Mu QH. Study of working fluid selection of organic Rankine cycle (ORC) for engine waste heat recovery. Energy 2011;36:3406e18. [10] Saleh B, Koglbauer G, Wendland M, Fischer J. Working fluids for lowtemperature organic Rankine cycles. Energy 2007;32:1210e21. [11] Desai NB, Bandyopadhyay S. Process integration of organic Rankine cycle. Energy 2009;34:1674e86.
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[12] Hung TC, Wang SK, Kuo CH, Pei BS, Tsai KF. A study of organic working fluids on system efficiency of an ORC using low-grade energy sources. Energy 2010;35:1403e11. [13] Tchanche BF, Papadakis G, Lambrinos G, Frangoudakis A. Fluid selection for a low-temperature solar organic Rankine cycle. Appl Therm Eng 2009;29: 2468e76. [14] Wang JL, Zhao L, Wang XD. A comparative study of pure and zeotropic mixtures in low-temperature solar Rankine cycle. Appl Energy 2010;87: 3366e73. [15] Madhawa HD, Golubovic M, Worek WM, Ikegami Y. Optimum design criteria for an Organic Rankine cycle using low-temperature geothermal heat sources. Energy 2007;32:1698e706. [16] Guo T, Wang HX, Zhang SJ. Fluids and parameters optimization for a novel cogeneration system driven by low-temperature geothermal sources. Energy 2011;36:2639e49. [17] Lakew AA, Bolland O. Working fluids for low-temperature heat source. Appl Therm Eng 2010;30:1262e8. [18] Khennich M, Galanis N. Optimal design of ORC systems with a lowtemperature heat source. Entropy 2012;14:370e89.
[19] Ayachi F, Boulawz Ksayer E, Neveu P. Exergy assessment of recovery solutions from dry and moist gas available at medium temperature. Energies 2012;5: 718e30. [20] Leide B, Gicquel R. Systemic approach applied to dual pressure HRSG. Int J Power Plant Technol 1998;78:37e43. [21] Linnhoff B. Pinch analysis e a state-of-the-art overview. Chem Eng Res De 1993;71:503e22. [22] Staine F, Favrat D. Energy integration of industrial processes based on the pinch analysis method extended to include exergy factors. Appl Therm Eng 1996;16:497e507. [23] Spedding TA, Chandrashekar M. A component-based simulation environment for statistical process control systems analysis. Robot Comput Integr Manuf 2005;21:99e107. [24] Baudouin O, Dechelotte S, Guittard P, Vacher A. SimulisÒ thermodynamics: an open framework for users and developers. Comput Aid Chem Eng 2008;25: 635e40. [25] Lemmon EW, Huber ML, McLinden MO. Reference fluid thermodynamic and transport properties e REFPROP, version 8.0, standard reference database 23. Gaithersburg, MD, USA: National Institute of Standards and Technology; 2007.
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Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
ORC optimization for medium grade heat recovery Fadhel Ayachi a, b, Elias Boulawz Ksayer c, Assaad Zoughaib c, Pierre Neveu a, b, * a Procédés, Matériaux et Energie Solaire e Centre National de la Recherche Scientifique (PROMES-CNRS), Rambla de la thermodynamique Tecnosud, 66100 Perpignan, France b Université de Perpignan Via Domitia, 52 avenue Paul Alduy, 66860 Perpignan, France c MINES Paris-Tech, CES, 5 rue Leon Blum, 91120 Palaiseau, France
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 March 2013 Received in revised form 2 December 2013 Accepted 19 January 2014 Available online xxx
The ENERCO_LT (ENErgy ReCOvery from Low Temperature heat sources) project is a waste heat recovery project that aims to reduce energy consumption in industrial gas production sites by producing electricity through Organic Rankine Cycles supplied by exothermic process discharges at low and medium temperatures. Two promising thermal sources consisting of (i) almost dry gas flow at 165 C and (ii) moist gas flow at 150 C, were investigated. The optimal recovery solution can be identified via an appropriate system design, an adequate working fluid and suitable operating conditions. Systemic optimization coupling exergy analysis and pinch minimization have been performed to assess the potential of various working fluids within various system designs, i.e. single stage system and double stage system. The results indicate that the global exergy efficiency is strongly linked to the critical temperature of the working fluid. They emphasize the existence of an optimal critical temperature specific to the hot source temperature and the pinch value. An empirical expression of the optimal critical temperature was derived for dry and quasi-isentropic pure fluids and appears to be useful for primary selection of the working fluids. Also, recovery solutions using blends appear very attractive to meet high exergy efficiency and environmental friendly objectives. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Waste heat recovery Moist gas Exergy ORC Pinch Blends
1. Introduction Nowadays, the gradual depletion of fossil fuels associated with constraints on emissions of greenhouse gases leads to increasingly restrictive standards for heavy industries in terms of energy consumption and environmental impact. This fact pushes the large energy consumers to search for innovative solutions to valorize their wasted heat which could be a promising resource for the future. In this context, Organic Rankine Cycles (ORCs) become attractive for potential use in future industrial plants. Several comparative studies in various applications take advantage of the fluid selection to improve the net power output and the system efficiency according to the characteristics of the heat source [1e14]. Hung et al. [1], Liu et al. [2] and Chen et al. [3] have assessed the influence of the fluid properties on the performances of an Organic Rankine Cycle for waste heat recovery systems and showed that the power output depends on the critical * Corresponding author. Tel: þ33 4 68682262; fax: þ33 4 68682213. E-mail addresses: [email protected] (F. Ayachi), elias.boulawz_ [email protected] (E. Boulawz Ksayer), assaad.zoughaib@mines-paristech. fr (A. Zoughaib), [email protected] (P. Neveu).
point, the latent heat and the slope of both saturation lines in a (T, s) diagram. Some analysis in waste heat recovery applications [3,7] have shown that supercritical operating conditions lead to higher performances than subcritical operating conditions. This requires a fluid critical temperature below the hot source temperature. Schuster et al. [7] have indicated that R-245fa, isopentane and R-365mfc are suitable for heat recovery at a hot source temperature of 210 C and have pointed out an improvement of the system efficiency of about 8% given by the transcritical cycle. Tchanche et al. [13] have compared various working fluids for use in solar ORC systems driven by a heat source temperature below 90 C. The authors add safety and environmental indicators to the theoretical performances as comparison criteria. Wang et al. [14] have conducted a comparative experimental study of pure fluids and nonazeotropic blends in low-temperature solar Rankine cycle. The authors have concluded that non-azeotropic blends have the potential for overall efficiency improvement due to the nonisothermal condensation. Other studies perform multi-objective optimization for the fluid selection [15e18]. In this case, the fluid selection is related to both source characteristics and design objectives. Lakew and Bolland [17] have conducted a comparative analysis from low to medium
http://dx.doi.org/10.1016/j.energy.2014.01.066 0360-5442/Ó 2014 Elsevier Ltd. All rights reserved.
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F. Ayachi et al. / Energy xxx (2014) 1e10
d f H L opt p re rec t vg
Nomenclature ex _ Ex h _ m _f m P PC T TC s _ W X DTmin
hex,g x f j
specific exergy (J/kg) exergy flux (W) specific enthalpy (J/kg) mass flow rate of the working fluid (kg/s) mass flow rate of the flue gases (kg/s) pressure (Pa) or (bar) critical pressure (Pa) or (bar) temperature (K) or ( C) critical temperature (K) or ( C) specific entropy (J/kg K) mechanical power output (W) molar fraction (e) pinch (K) global exergy efficiency (-) specific dissipating factor (-) enthalpy flux (W) loss factor (-)
destroyed flue gases high low optimal pump regenerator recovered turbine vapour generator
Acronyms GWP global warming potential HCFC hydrochlorofluorocarbon HFC hydrofluorocarbon ODP ozone depletion potential ORC organic rankine cycle TET turbine exhaust temperature TIT turbine inlet temperature
Subscripts a available cd condenser temperature grade heat sources (80e200 C) based on a subcritical cycle without superheating. They have identified, for each level, the appropriate working fluid and its optimal vaporization pressure for three distinctive objectives: (i) maximum power output, (ii) minimum heat exchanger, area and (iii) minimum turbine size. Recently, Khennich and Galanis [18] have endorsed this theory by developing a numerical model of both subcritical and transcritical power cycles using a fixed-flowrate low-temperature heat source. They have also concluded that, for a given heat source temperature and working fluid, maximizing the thermal efficiency and minimizing the component size lead to different designs. In particular, they have shown that minimizing the turbine size requires a very large heat exchanger thermal conductance. All these studies underline the interest of the multi-objective optimization models to look at the trade-offs of the system between efficiency and cost. In a previous analysis [19], we investigated the valorization of two heat sources involved in CO2 capture unit from oxy-
combustion products. The working fluid critical temperature appeared to be a key parameter when an optimum matching is searched for the temperature profiles of the working fluid and the external flow in the vapour generator. Due to practical considerations, some recovery solutions using pure fluids were presented as compromise between environmental impact and performance. The present study extends the previous work by (i) analysing the system performance trends according to the fluid critical temperature (ii) comparing the performances of various system designs and fluids (iii) assessing the expediency of some binary blends as recovery solutions compared to pure fluid solutions. 2. Problem definition and optimization method Fig. 1 gives the basic overview of the recovery process. The hot source consists of flue gases at the exit of an exothermic process. The overall available resource is defined as bounded by the
Cooler Downstream process
3f
2f Evaporator
3
1f
Upstream process
2
Turbine 4
Pump 1
Condenser
Working cycle Fig. 1. Recovery system layout.
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F. Ayachi et al. / Energy xxx (2014) 1e10
The global exergy efficiency, which measures the converted share compared to the available exergy resource, is written as:
Table 1 Resource characteristics. Resource
T1f ( C)
T3f ( C)
P (bar)
Water molar fraction (%)
Mass flow rate (kg/s)
Dew point ( C)
_ a Ex (kW)
Almost dry Moist
165 150
25 25
25 1
2 20
152.2 130.2
75 60
4950 6148
upstream process outlet 1f and the downstream process inlet 3f. However, due to the unavoidable pinch in the vapour generator (Evaporator) and its related operating conditions, the available resource cannot be completely valorized. The flue gases exit the vapour generator at a temperature T2f higher than T3f, and the heat recovery is then followed by a flue gas cool down to the inlet conditions required by the downstream process. Two heat sources were considered and are summarized in Table 1. The first one, with low moisture content, is cooled at 25 bar from 165 C to 25 C. The second one, with high moisture content, is cooled at 1 bar from 150 C to 25 C and shows a dew point at _ a is determined according to 60 C. The available exergy resource Ex the molar compositions and cooling conditions of the flue gases as presented in the previous work [19]. It is written as:
_ a ¼ m _ f ðex1f ex3f Þ Ex
_ W
hex;g ¼ _ Exa
(5)
_ < 0 is the net mechanical power output (kW). where W The exergy balances of the working cycle and of the whole system are respectively given by Eqs. (6) and (7):
_ _ rec þ W Ex
X
_ Ex d;i ¼ 0
(6)
i
_ Ex _ _ aþW Ex d;total ¼ 0
(7)
P_ Exd;i is the sum of the exergy destroyed by the unitary where _ components of the working cycle and Ex d;total is the exergy destroyed by the whole system. From Eqs. (4), (6) and (7), it follows that:
_ Ex d;total ¼
X
_ _ Ex d;i þ Exloss
(8)
i
Eq. (5) can be rewritten as:
(1)
_ f being the total mass flow rate (kg/s) of the flue gases including m the condensated stream and ex1f (kJ/kg) the specific exergy of the flue gases at point 1f. Fig. 2 illustrates for both cases, the evolution of the recovered _ rec and exergy losses Ex _ exergy flux Ex loss according to the flue gas discharge temperature T2f.
_ rec ¼ m _ f ðex1f ex2f Þ Ex
(2)
_ _ f ðex2f ex3f Þ Ex loss ¼ m
(3)
_ rec quantifies the maximum work power that would be produced Ex _ in a Carnot engine, whereas Ex loss represents the lost part of the overall resource that will be destroyed in the external cooler. The change of the slope comes from the additional latent heat provided by the condensation of water vapour when temperature T2f becomes lower than the dew point temperature. For the moist heat source, this leads to an important increase of the available exergy that could be theoretically valorized. From Eqs. (1)e(3), it follows that:
_ rec þ Ex _ _ a ¼ Ex Ex loss
3
(4)
hex;g ¼ 1
X
xi j
(9)
i
with
_ Ex
xi ¼ _ d;i Exa _ Ex
j ¼ _ loss Exa
(10)
(11)
The specific dissipating factor xi measures the contribution of each unitary component of the working cycle on the efficiency degradation, whereas the loss factor j measures the ratio of available exergy excluded from the recovery process, i.e. destroyed in the ambiance. Systemic optimization [20] coupling exergy analysis and pinch minimization [21,22] has been adopted. All the investigated processes have been optimized by maximizing the mechanical power _ a is given), using the output (i.e. the global exergy efficiency as Ex constant settings reported in Table 2. All the unitary components are considered as open systems in steady state condition and pressure losses are neglected. Once these settings are given, two cycle independent variables, namely high pressure PH and turbine
Fig. 2. Recovered and lost exergy fluxes according to the flue gas discharge temperature T2f. (a) Almost dry heat source; and (b) Moist heat source.
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F. Ayachi et al. / Energy xxx (2014) 1e10 Table 2 System constant settings. Isentropic efficiencies Pump Turbine
0.9 0.85
Condenser settings Water inlet temperature ( C) Water outlet temperature ( C)
15 20
Pinches Vapour generator DTmin,vg (K) Condenser DTmin,cd (K)
10 5
inlet temperature TIT h T3 are sufficient for describing the whole process. For a given couple (PH, TIT), the mass flow rate of the _ (kg/s) leading to the aimed pinch in the vapour working fluid m generator can be determined. Thence, composite curves (and consequently pinch location) can be obtained from a model developed through ProsimÒ Plus 3.1 simulator [23,24]. The working fluid properties are calculated using REFPROPÒ 8.0 developed by the National Institute of Standards and Technology [25]. For a given pressure PH, the optimal turbine inlet temperature TIT is searched by maximizing the power output under the following constraint: the turbine exhaust vapour must be in saturated or superheated state in order to avoid droplet erosion of the turbine blades. Notice that, the whole expansion path may cross the saturation line. In this case, the operation is considered acceptable if the vapour quality along the expansion does not go below 0.95. If not, the turbine inlet temperature TIT is increased to verify this latter constraint. _ correspond, for each Thereby, the optimal conditions (PH, TIT, m) fluid, to the maximal global exergy efficiency. Exergy analysis gives the exergy destruction for each unitary operation occurring in these optimal cycles, and the exergy losses due to the external cooler. Energy and exergy balances, and a detailed examination of the irreversibility trends according to the evaporation pressure PH, are reported in Ayachi et al. [19]. 3. Single stage system Depending on the slope of the vapour saturation line in a (T, s) diagram, working fluids can be classified as dry fluids (i. e. (vT/ vs)sat > 0), isentropic fluids (i. e. (vT/vs)sat w N) and wet fluids (i. e. (vT/vs)sat < 0). In the following section, exergy performance of various dry and quasi-isentropic pure fluids operating in a single stage ORC is first investigated. Afterwards, performance and
Fig. 3. Optimal single stage performances by using dry and quasi-isentropic pure fluids (DTmin,vg ¼ 10 K, PH max ¼ 70 bar).
environmental impact of some binary blends are assessed and compared to pure fluid results. 3.1. Pure fluid assessment Fig. 3 displays the global exergy efficiency given by the optimized cycle for various dry and quasi-isentropic pure fluids, and referring to 10 K-pinch configuration in the vapour generator. The fluids are ranked according to their critical temperatures. This clearly shows a strong link between the global exergy efficiency and the fluid critical temperature, and the existence of an optimum of efficiency for a given thermal source. Thereby, an appropriate range of critical temperature for the selection of the working fluid can be identified. When considering the almost dry heat source at 165 C, the fluid critical temperature appropriate range is located between 90 C and 130 C, and the maximum exergy efficiency reaches 56%. For the case of the moist heat source at 150 C, the critical temperature appropriate range is slightly lower, located between 80 C and 125 C; however, the global exergy efficiency does not exceed 31%. As an example, Figs. 4 and 5 represent the composite curves and the irreversibility repartition by using R-236fa, respectively, for the almost dry heat source and the moist heat source. This fluid is located in the appropriate range in both cases. The composite curves display the temperature of both fluids according to the related enthalpy fluxes:
Fig. 4. Optimal cycle using R-236fa (Almost dry heat source). (a) Composite curves. (b) Irreversibility repartition.
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F. Ayachi et al. / Energy xxx (2014) 1e10
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Fig. 5. Optimal cycle using R-236fa (Moist heat source). (a) Composite curves. (b) Irreversibility repartition.
_ f ðhf ðTf Þ h3f Þ - for the flue gas (hot composite): ff ðTf Þ ¼ m _ - for the working fluid (cold composite): ff ðTÞ ¼ mðhðTÞ h2 Þ þ K _ f ðh2f h3f Þ. The constant K ensures ff ðT1f Þ ¼ fðT3 Þ where K ¼ m at the hot side of the vapour generator. For the first case, the composite curves show adequate temperature matching between the almost dry flue gases and the working fluid over the major part of the available resource (Fig. 4a). In this case, the loss factor is only about 8.6% (Fig. 4b). For the second case, due to the important shape change of the moist flue gas composite curve at low temperature, the optimal cycle leads to a partial recovery from the available resource (Fig. 5a). Consequently, a large amount of exergy is still available at the exit of the process: the loss factor reaches 50% (Fig. 5b). Therefore, it can be considered to implement a second recovery stage before the external cooler. Considering this fact, single stage system is only discussed for the almost dry source case in the following section. On the other hand, Fig. 3 shows for both cases that the optimal cycle corresponds to a transcritical cycle. Such cycle involves a subcritical pressure PL in the condenser and a supercritical pressure PH in the vapour generator. This leads to potentially high pressures and could lead to more expensive devices. It is then interesting to study the impact on the global exergy efficiency when going from an optimal transcritical cycle to a subcritical cycle. Fig. 6 represents the efficiency degradation when constraining the high pressure PH to be slightly lower than the critical pressure (PH z PC e 1 bar). It is
worth noting that the decrease in efficiency is low for fluid critical temperatures close to the optimum. As an example, by using R-236fa, the global exergy efficiency goes from 56% to 54.7% when passing from the optimal transcritical cycle to a subcritical cycle. As the operating high pressure is reduced from 48 bar to 30 bar, subcritical cycles seem more attractive in that case. For lower critical temperatures, the efficiency degradation when passing to a subcritical cycle is more important. A more detailed technical and economic analysis is required to conclude, but interesting trends can be pointed out. Figs. 7 and 8 represent the entropy diagram and the irreversibility repartition when R-1234yf is used respectively in transcritical cycle (optimal: PH ¼ 70 bar) and subcritical cycle (degraded: PH ¼ 32 bar). They illustrate the moving of exergy destruction from the cold part to the hot part of the vapour generator. Going from a transcritical to a subcritical cycle increases the temperature difference between the flue gas inlet and the working fluid outlet in the vapour generator (T1f T3), but decreases the temperature difference between the flue gas outlet and the working fluid inlet in the vapour generator (T2f T2). Therefore, the increase of the thermal irreversibilities occurring at high temperatures is partially compensated by the decrease of those occurring at low temperatures. This results in limited reduction of the global exergy efficiency. When the fluid critical temperature is far lower from the optimum, the subcritical cycle implies large temperature difference at the hot side of the vapour generator. Here, the compensation effect is then less significant.
3.2. Pinch impact Pinch setting has important consequences on the system performance and the cost of the heat exchangers. It is then interesting to study the impact of the pinch setting on the above results, especially the working fluid selection. The results are presented in Fig. 9 and refer to 3 different pinches in the vapour generator: 5 K, 10 K and 25 K. The existence of an optimal critical temperature observed previously for a 10 K pinch is also valid for lower and higher pinches. Moreover, the working fluids have been ranked according to (TIT)max TC, where:
ðTITÞmax ¼ T1f DTmin;vg Fig. 6. Performance degradation when passing from an optimal transcritcal cycle to a subcritical cycle (Almost dry heat source at 165 C, Single stage, DTmin,vg ¼ 10 K, PH max ¼ 70 bar).
(12)
(TIT)max represents the highest turbine inlet temperature which can be reachable, for a given inlet source temperature and a given pinch value.
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F. Ayachi et al. / Energy xxx (2014) 1e10
_ diagram; and (b) Irreversibility repartition. Fig. 7. Optimal transcritical cycle using R-1234yf (Almost dry heat source). (a) (T, ms)
_ diagram; and (b) Irreversibility repartition. Fig. 8. Degraded subcritical cycle using R-1234yf (Almost dry heat source). (a) (T, ms)
From Fig. 9, it appears an empirical expression for the optimal critical temperature, whatever the pinch is:
TC;opt zðTITÞmax 33 K
(13)
The above expression can be used for primary selection of the working fluids. It estimates the optimal critical temperature once
Fig. 9. Impact of the pinch setting on the fluid selection (Almost dry heat source at 165 C, Single stage).
the hot source inlet temperature and the vapour generator pinch value are known. Notice that this expression has also been verified for the moist heat source and it appears to be still valid. However, temperatures T1f are quite close in both cases, and further studies would be required to extend this correlation to other temperature levels.
Fig. 10. System performances by using binary blend {R-1234yfeisobutane} (Almost dry heat source at 165 C, DTmin,vg ¼ 10 K, PH max ¼ 70 bar).
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7
Table 3 Recovery solutions for the almost dry heat source (DTmin,vg ¼ 10 K): operations and zerformances. Working fluids Mole [%] PC [bar] TC [ C] GWP Oper
_ m[kg/s] PL [bar] PH [bar] TIT [ C] cd.glide [K] T2f [ C] xvg [%] xt [%] xcd [%] xp [%] j [%] hex,g [%] [kW]
R-245fa
e
36.51
154
950
sub-c
66.1
1.48
12
97.7
e
68.6
21.4
R-134a
e
40.59
101.1
1300 sub-c
92.9
6.65
39
108.6
e
53.5
89.1
6.65
69
139.6
e
57.6
sub-c 130.7
6.72
32
95.6
e
tr-c
6.72
70
142.6
e
tr-c R-1234yf
e
32.66
94.8
4
105
7.1
9.9
0.1
20.1
9.3
11.6
0.5
12.5
10.9
10.7
1
44.9
24.2
9.3
12.8
0.6
5.1
48
2376
54.7
12.2
11.1
11.7
1.3
9.6
54.1
2676
i-butane
e
36.29
134.7
20
sub-c
37.8
3.5
34
130.8
e
69.6
13.9
8.8
R-1234yf
48
34.87
115.5
10
sub-c
79.1
4.54
33
113.1
3.1
50.9
17.4
10.3
i-butane
52
tr-c
76.7
4.54
51
138.4
3.1
53.4
13.3
11.2
9.2 10 9.6
18.9
42.6
2107
9
49.5
2451
11.2
53.7
2656
0.4
19.7
48
2374
0.6
7.6
54.1
2679
0.9
8.9
56.1
2776
critical temperature of the blend. It is worth noting that the optimal pseudo-critical temperature is close to the one given by Eq. (13). The above results highlight a main interest of using blends in this recovery problem. They appear very attractive to meet high exergy efficiency and environmental friendly objectives. Finally, by considering the subcritical operation, the optimal blend {R-1234yf (48%mol)eisobutane (52%mol)} reaches the performance obtained with R-236fa, i.e. a global exergy efficiency of about 54% and provides a GWP of 10 kgeqCO2. Besides, the blend reduces the flammability risk of isobutane. Table 3 gathers the operations and performances of some recovery solutions for the almost dry heat source.
3.3. Blend assessment From the above results (Fig. 6), two working fluids appear as best candidates for valorizing the almost dry resource: R-236fa and R-124, and both can operate through a subcritical cycle with high performance and acceptable pressure. However, the final selection must face the environmental constraints. R-236fa is a hydrofluorocarbon (HFC) characterized by a very high Global Warming Potential (GWP) of about 9400 kgeqCO2. R-124 is a hydrochlorofluorocarbon (HCFC) having an Ozone Depletion Potential (ODP) of 0.03. By setting constraints on the environmental impact (ODP ¼ 0 and GWP < 750 kgeqCO2), two candidates come into view: R-1234yf and isobutane. The first is particularly interesting because of its notably low GWP (4 kgeqCO2), the second is less recommended due to its high flammability. Nevertheless, it could be interesting to use a blend mixing two pure fluids located on either sides of the optimal critical temperature. As the blend properties vary with the composition, the idea is that approaching the optimal critical temperature would enhance the performance. To verify this point, a binary blend composed of {R-1234yfeisobutane} was investigated. The results are represented in Fig. 10 for a wide range of molar composition and compared to pure fluid trend. They show specific correlation between the global exergy efficiency and the pseudo-
4. Double stage system Due to its important exergy content, the interest of using the condensing heat available in the moist source has been clearly shown in the previous section. The change in slope of the hot composite curve makes difficult to match the temperature profiles of the hot and cold flows in the vapour generator, as depicted in Fig. 5a: the required pinch then leads to large energy and exergy losses, and only a small part of this additional heat can be valorized
Cooler Downstream process
3f
2f
21f Evaporator1
Evaporator2
2*
3
3
1f
Upstream process
2
Turbine1
Turbine2
4 Pump2
Regenerator
4
2 1
4* Condenser1
Condenser2
Pump1 1
Bottoming cycle
Topping cycle
Fig. 11. Cascading cycle layout.
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Fig. 12. Double stage performances (Moist heat source at 150 C, DTmin,vg ¼ 10 K).
by a single stage system. In the following section cascading cycles are discussed for the case of the moist heat source. The aim is to valorize the exergy losses induced by the first stage by implementing a second stage. Fig. 11 describes the layout of the system. In case of dry working fluid (T4 > T2), an internal transfer of heat (regeneration) into the topping cycle (first stage) allows to valorize the vapour cool down from the turbine outlet (point 4) to the condenser inlet (point 4*). It aims to decrease the thermal flux required by the evaporator of the topping cycle in order to release more energy flux to be transferred into the bottoming cycle (second stage). The pinch in the regenerator was settled to 2 K. Heat regeneration was not expected for the last stage as the discharged flux is totally lost in the external cooler: decreasing the thermal flux required by the evaporator of the bottoming cycle increases the thermal power to be extracted in the external cooler, and appears not to be favourable for the global exergy efficiency. Fig. 12 represents the results obtained when R-1234yf or R-245fa is used as a topping cycle working fluid. It displays the global exergy efficiency given by the optimized cascade according to the critical temperature of the bottoming cycle working fluid.
Operating conditions and irreversibility repartition of some investigated cascades are reported in Table 4. The results indicate that global exergy efficiency of about 40% is achievable when using a transcritical cycle in the first stage. A twotranscritical cycle cascade using R-1234yf in the topping cycle and carbon dioxide in the bottoming cycle provides adequate temperature matching in both upper and lower zone of the hot composite and leads to global exergy efficiency of about 42%. However, the topping cycle involves a supercritical pressure of 60 bar and the bottoming cycle involves a supercritical pressure of 90 bar. Also, It appears that the global efficiency is little sensitive to the bottoming cycle fluid selection which could be orientated to environmental and economic criteria. On the other hand, when passing from the optimal two-transcritical cycle cascade to a two-subcritical cycle cascade, the global exergy efficiency drops to around 37%. A twosubcritical cycle cascade seems more attractive as it provides lower operating pressures. Fig. 13 displays the repartition of irreversibilities when going from a subcritical single stage using R-1234yf to a two-subcritical cycle cascade using R-1234yf and R-41, respectively, in the topping cycle and bottoming cycle. The exergy losses of the topping cycle are then used in the bottoming cycle, but a large part of this potential is destroyed in the added components. Nevertheless, the global exergy efficiency increases by approximately 1/3 compared to the single stage. Fig. 14 illustrates the composite curves of this cascade. Heat regeneration is not realizable for a topping cycle using R-1234yf since for this isentropic fluid the turbine exhaust temperature TET h T4 is close to the vapour saturation temperature at low pressure PL. In case R-245fa is used as a topping cycle fluid, the results show a weak regeneration contribution, less than 1.5%. When considering the recovery process from the condensing heat at low temperature, Table 4 indicates that using fluid with low critical temperature and high critical pressure, such as R-41, leads to high optimal pressure PH even subcritical (w52 bar). On the other hand, using fluid with critical temperature much higher than the dew temperature, such as R-245fa, leads to weak subcritical pressure level PH (less than 3 bar) which would require high turbine size. Here, adapting the critical point by using blend could be useful to provide a more practical solution. Also, the presence of
Table 4 Recovery solutions for the moist heat source (DTmin,vg ¼ 10 K): operations and performances. Working fluids PC [bar] TC [ C] GWP Oper R-1234yf
2R-245fa
32.66
36.51
94.8
154
4
950
top: R-1234yf
32.66
94.8
4
bott: R-245fa
36.51
154
950
top: R-1234yf
32.66
94.8
4
bott: R-41
58.97
44.1
97
top: R-1234yf
32.66
94.8
4
bott: CO2
73.77
31
1
_ _ m[kg/s] PL [bar] PH [bar] TIT [ C] TET [ C] T2f [ C] xvg [%] xt [%] xcd+re [%] xp [%] j [%] hex,g [%] W[kW]
sub-c
88.3
6.72
32
tr-c
88.4
6.72
60
sub-c sub-c
45.6 93.1
1.48 1.48
11 2.48
sub-c/regen sub-c
45.6 95.2
1.48 1.48
sub-c sub-c
88.3 78.5
tr-c sub-c
98.5
31.9
58.4
11.9
5.3
7.4
0.3
47
28.1
1725
25.2
58.6
7.4
6.5
6.9
0.7
48
30.5
1876
93.8 39.7
42.3 28.2
71.2 48.1
11.5 14
3.8 1.9
5.5 9.8
0.1 0.01
19.2
34.2
1391 709
11 2.5
93.8 39.9
42.3 28.2
76 48.3
10.3 14.7
3.8 2
4.9 10.1
0.1 0.01
19.5
34.6
1391 737
6.72 1.48
32 2.36
98.5 38.2
31.9 27.8
58.4 46.9
11.9 11.3
5.3 1.5
7.4 8.3
0.3 0.01
17.2
36.8
1725 540
88.4 79.5
6.72 1.48
60 2.38
129 38.5
25.2 27.9
58.6 47.1
7.4 11.4
6.5 1.6
6.9 8.4
0.7 0.01
17.5
39.6
1876 557
sub-c sub-c
88.3 70
6.72 38.3
32 52
98.5 48.3
31.9 27
58.4 44.9
11.9 11.4
5.3 2.2
7.4 9.3
0.3 0.3
14.1
37.8
1725 596
tr-c sub-c
88.4 70.3
6.72 38.3
60 53
129 48.6
25.2 26
58.6 45.5
7.4 11.1
6.5 2.3
6.9 9.2
0.7 0.3
15
40.6
1876 618
sub-c tr-c
88.3 162.3
6.72 64.3
32 90
98.5 48.3
31.9 25.6
58.4 41.2
11.9 10.7
5.3 3.7
7.4 11
0.3 1
9.5
39.2
1725 683
tr-c tr-c
88.4 164.6
6.72 64.3
60 90
129 48.6
25.2 25.8
58.6 41.1
7.4 11.1
6.5 3.7
6.9 11.3
0.7 1
9.4
42
1876 706
129
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9
Fig. 13. Irreversibility repartition (Moist heat source). (a) Subcritical single stage (R-1234yf). (b) Subcritical double stages (R-1234yf þ R-41).
Fig. 14. Composite curves of a two-subcritical cycle cascade using R-1234yf and R-41 (Moist heat source).
contaminants and the possible condensation involved for the moist source will require high quality materials for the vapour generator of the second stage. All these concerns emphasize the difficulties to valorize the low temperature part of the resource. The global exergy efficiency increasing of 1/3 offered by the second stage would require approximately doubling the investment cost. A more detailed technical and economic analysis is required to conclude. 5. Conclusion The present paper has conducted large comparative analysis on ORC recovery solutions from one almost dry heat source and one highly moist heat source at medium temperature (respectively 165 C and 150 C). Systemic optimization coupling exergy analysis and pinch minimization has been adopted and various working fluids integrated in different designs have been investigated. The main results of the study can be extracted as follow: - Strong mean correlation was found between the global exergy efficiency and the fluid critical temperature. It shows the existence of an optimal critical temperature specific to the hot source temperature and the pinch value. - An empirical expression of the optimal critical temperature was derived for dry and quasi-isentropic pure fluids. It can be used for primary selection of the working fluids, once the hot source inlet temperature and the vapour generator pinch setting are defined.
- The highest performances are given by the supercritical operating conditions. However, for fluid critical temperatures close to the optimum, subcritical cycles seem more attractive as they approach the highest efficiencies and involve acceptable operating pressures. - Environmental constraints of pure fluid solutions prevent from reaching the highest power output as an objective function. Using blends allows to sidestep these constraints to meet high exergy efficiency and environmental friendly objectives. - A two-cycle cascade appears as an appropriate recovery design for the moist heat source; the topping cycle working on the upper zone of the dew point and the bottoming cycle taking advantage of the condensing process. The involvement of a second stage offers a global exergy efficiency increasing of about 1/3. However, the added components and the need of high quality materials due to the condensing process would require a high investment cost. Acknowledgements This work has been supported by the French Research National Agency (ANR) through the ENERCO_LT-EESI-09 research project. References [1] Hung TC, Shai TY, Wang SK. A review of organic Rankine cycles (ORCs) for the recovery of low-grade waste heat. Energy 1997;22:661e7. [2] Liu BT, Chien KH, Wang CC. Effect of working fluids on organic Rankine cycle for waste heat recovery. Energy 2004;29:1207e17. [3] Chen H, Yogi Goswami D, Stefanakos EK. A review of thermodynamic cycles and working fluids for the conversion of low-grade heat. Renew Sustain Energy Rev 2010;14:3059e67. [4] Maizza V, Maizza A. Working fluids in non-steady flows for waste energy recovery systems. Appl Therm Eng 1996;16:579e90. [5] Maizza V, Maizza A. Unconventional working fluids in organic Rankine-cycles for waste energy recovery systems. Appl Therm Eng 2001;21:381e90. [6] Hung TC. Waste heat recovery of organic Rankine cycle using dry fluids. Energy Convers Manage 2001;42:539e53. [7] Schuster A, Karellas S, Aumann R. Efficiency optimization potential in supercritical organic Rankine cycles. Energy 2010;35:1033e9. [8] He C, Liu C, Gao H, Xie H, Li Y, Wu S, Xu J. The optimal evaporation temperature and working fluids for subcritical organic Rankine cycle. Energy 2012;38:136e43. [9] Wang EH, Zhang HG, Fan BY, Ouyang MG, Zhao Y, Mu QH. Study of working fluid selection of organic Rankine cycle (ORC) for engine waste heat recovery. Energy 2011;36:3406e18. [10] Saleh B, Koglbauer G, Wendland M, Fischer J. Working fluids for lowtemperature organic Rankine cycles. Energy 2007;32:1210e21. [11] Desai NB, Bandyopadhyay S. Process integration of organic Rankine cycle. Energy 2009;34:1674e86.
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Please cite this article in press as: Ayachi F, et al., ORC optimization for medium grade heat recovery, Energy (2014), http://dx.doi.org/10.1016/ j.energy.2014.01.066