Parametric Optimization and Thermodynamic
Article Parametric Optimization and Thermodynamic Performance Comparison of Organic Trans-Critical Cycle, Steam Flash Cycle, and Steam Dual-Pressure Cycle for Waste Heat Recovery
Liya Ren and Huaixin Wang * MOE Key Laboratory of Efficient Utilization of Low and Medium Grade Energy, School of Mechanical Engineering, Tianjin University, Tianjin 300072, China; [email protected] * Correspondence: [email protected]
Received: 7 November 2019; Accepted: 4 December 2019; Published: 5 December 2019
Abstract: Compared with the basic organic and steam Rankine cycles, the organic trans-critical cycle (OTC), steam flash cycle (SFC) and steam dual-pressure cycle (SDC) can be regarded as the improved cycle configurations for the waste heat power recovery since they can achieve better temperature matching between the heat source and working fluid in the heat addition process. This study investigates and compares the thermodynamic performance of the OTC, SFC, and SDC based on the waste heat source from the cement kiln with an initial temperature of 320 ◦C and mass flow rate of 86.2 kg/s. The effects of the main parameters on the cycle performance are analyzed and the parameter optimization is performed with net power output as the objective function. Results indicate that the maximum net power output of SDC is slightly higher than that of SFC and the OTC using n-pentane provides a 19.74% increase in net power output over the SDC since it can achieve the higher use of waste heat and higher turbine efficiency. However, the turbine inlet temperature of the OTC is limited by the thermal stability of the organic working fluid, hence the SDC outputs more power than that of the OTC when the initial temperature of the exhaust gas exceeds 415 ◦C.
Keywords: waste heat recovery; thermodynamic optimization; performance comparison; organic trans-critical cycle; steam flash cycle; steam dual-pressure cycle
1. Introduction A great deal of waste heat energy with exhaust gas as the carrying medium is available in the industrial processes. To generate electricity based on waste heat can reduce the consumption of fossil energy and alleviate the strain on the environment caused by the burning of fossil fuels. The power cycle system is the most common technology to realize the conversion of the heat into electricity. Selecting the proper cycle configuration, working fluid, and operating parameters based on the heat source condition is crucial for the economic profitability of the power system [1]. Rankine cycle (RC) is a classic option for the power system [2]. However, RC cannot match with the waste heat source well from the perspective of thermodynamics. The temperature of exhaust gas decreases along with its exothermic process, while the temperature of working fluid remains constant during the evaporation process in RC (for non-azeotropic mixtures, there is a temperature glide in the evaporation process). This leads to an inherent heat transfer temperature difference between the exhaust gas and working fluid, which has a significant impact on the thermodynamic perfection of the cycle and the use of the waste heat. The conventional working fluid of RC is water [3–5]. Water is a typical wet fluid, hence a large superheat is needed for the initial state of the expansion process, to alleviate the liquid eroding on the
Energies 2019, 12, 4623; doi:10.3390/en12244623 www.mdpi.com/journal/energies Energies 2019, 12, 4623 2 of 22 turbine blades and to ensure the efficiency of the turbine. Therefore, under the given initial temperature of the waste heat source, the evaporating temperature of steam Rankine cycle (SRC) is restricted, which will affect the cycle’s thermal and exergy efficiencies. The latent heat of evaporation of water is much larger than its liquid and vapor sensible heat, which makes the temperature curve of the SRC’s heat addition process more non-smooth. In short, the thermophysical properties of water aggravate the thermodynamic deficiencies of the RC mentioned above. Also, an expensive multi-stage turbine is required for the SRC system owing to water’s large specific enthalpy drop and volume ratio in the adiabatic expansion process, and the steam turbine’s efficiency is reduced obviously under the low temperature and small capacity condition [6,7]. Many organic compounds are dry fluids (positive slope of saturation vapor curve) and isentropic fluids (vertical saturation vapor curve). The latent heat of evaporation of the organic compound is much smaller than that of water. Therefore, the temperature matching between the exhaust gas and working fluid in the organic Rankine cycle (ORC) is better than the SRC. Moreover, the positive-displacement expansion engines such as reciprocal piston expander, screw expander, and scroll expander can be used in the ORC system owing to the small volume ratio and enthalpy drop in the expansion process of organic working fluids with the lower critical temperature [8]. The cost of positive-displacement expanders is relatively low, and the expander’s efficiency can be guaranteed under small capacity. Therefore, it is generally acknowledged that the ORC system is suitable for low-moderate temperature and low-moderate capacity sources while the SRC system is more preferred for high temperatures and large capacity sources [9,10]. Performance improvement can be achieved by the modification of the cycle configuration. If the endothermic pressure of the working fluid is raised above the critical temperature, the isothermal evaporation process in RC will no longer exist and the cycle is named trans-critical cycle (TC). The TC shows a better temperature matching between exhaust gas and working fluid hence the heat source can be cooled down to a lower temperature. Although the high pressure ratio is detrimental to the turbine efficiency, organic trans-critical cycle (OTC) still outperforms ORC considering the detrimental effect [11]. Multiple evaporation pressure and flash are other possible options to improve the temperature match between exhaust gas and working fluid, so as to achieve better use of the available heat and smaller exergy loss in the heat absorption process [12,13]. The thermodynamic performance benefits of the modified cycles to the basic RC have been investigated in many studies. However, the comparative research between the modified cycles is rather scarce, especially between the water and organic working fluids. Wang et al. [14] performed the parameter optimization and exergy analysis of four cycles including steam flash cycle, steam dual-pressure cycle, ORC and Kalina cycle for recovering waste heat from the preheater exhaust and clinker cooler exhaust gases in cement plant. The result showed that the ORC has the lowest exergy efficiency and net power output. Pradeep Varma et al. [15] studied five plants (SRC, steam flash cycle, ORC, organic flash cycle, Kalina cycle) to select the best one that maximizes the power production from the exhaust gas. The organic flash cycle is recommended when the initial temperature of the heat source is 125 ◦C, while the Kalina cycle is recommended when the source temperature is 360 ◦C. Andreasen et al. [16] presented a design and off-design performance comparison between the steam dual-pressure cycle and ORC based on two diesel engine waste heat recovery cases. Results indicated that the steam dual-pressure cycle reaches higher net power outputs at high engine loads, while the ORC reaches higher performance at low engine loads when the two cycles are compared based on the same turbine efficiency. According to the authors’ knowledge, a clear performance comparison among steam flash cycle (SFC), steam dual-pressure cycle (SDC) and OTC have not been reported in the literature. The purpose of this study is to investigate and compare the thermodynamic performance of the SFC, SDC, and OTC based on the exhaust gas waste heat source from the cement industry with a medium temperature and capacity. The effect of parameters on the performance of the cycle is analyzed and the parameter optimization is performed by means of genetic algorithm to maximize the net power output. A three-stage axial turbine Energies 2019, 12, 4623 3 of 22 is considered for the OTC system and its efficiency is determined by the size parameter of the turbine Energies 2019, 12, x FOR PEER REVIEW 3 of 23 and the volume ratio of the working fluid [17]. As mentioned above, organic working fluid exhibits the Energies 2019, 12, x FOR PEER REVIEW 3 of 23 lowerabove, specific organic enthalpy working drop fluid than exhibits water the in thelower expansion specific enthalpy process. drop Therefore, than water the in organic the expansion turbine can be designedprocess.above, withorganicTherefore, a reducedworking the organic fluid number exhibits turbine of stages thecan lower be and designed specific higher with enthalpy efficiency a reduced drop compared thannumber water of with instages the the expansion and steam higher turbine. The steamefficiencyprocess. turbine’s Therefore, compared efficiency t he with organic isthe evaluated steam turbine turbine. can with be thedesignedThe correlations steam with turbine’s a reduced described efficiency number in Ref. isof evaluatedstages [18]. and withhigher the correlationsefficiency compareddescribed within Ref. the [18]. steam turbine. The steam turbine’s efficiency is evaluated with the 2. Descriptioncorrelations of described the System in Ref. [18]. 2. Description of the System 2.1. Heat2. Description Source Condition of the System 2.1. Heat Source Condition Typical2.1. Heat exhaust Source Condition gas condition from the clinker cooler for a cement kiln line of 5000 t/d capacity is Typical exhaust gas condition from the clinker cooler for a cement kiln line of 5000 t/d capacity considered in this study [14]. The waste heat is in the form of hot air, and the initial temperature and is consideredTypical inexhaust this study gas condition [14]. The from waste the heat clinker is in cooler the form for aof cement hot air kiln, and line the of initial 5000 t/d temperature capacity massand flowis consideredmass rate flow are 320 inrate this◦ Care study and 320 86.2 [14].°C and kg The/s. 86.2 waste The kg outlet /s.heat T heis temperature inoutlet the form temperature of of hot the air exhaustof, and the theexhaust gas initial is withoutgas temperature is without restriction sincerestriction thereand mass is no since flow danger thererate ofare is acidno 320 danger °C dew and corrosion.of 86.2 acid kg dew/s. T corrosion.he outlet temperature of the exhaust gas is without restriction since there is no danger of acid dew corrosion. 2.2. Organic2.2. Organic Trans-Critical Trans-Critical Cycle Cycle 2.2. Organic Trans-Critical Cycle The schematicThe schematic diagram diagram of of the the OTC OTC is is shown shown in Figure 11 andand the the T T-s-s diagram diagram of the of the OTC OTC is given is given in Figurein Figure2.The The 2. schematic generatedThe generated diagram high-pressure high of- pressurethe OTC and andis shown high-temperature high -intemperature Figure 1 and vapor vapor the T in- ins heat diagram heat recovery recovery of the vapor OTC vapor generatoris given generator (HRVG)(HRVGin expandsFigure) expands 2. The through generated through the the high turbine turbine-pressure to to output outputand high thethe-temperature powerpower (1 (1–2),–2), vapor and and inthe theheat shaft shaft recovery power power vaporis converted is generator converted into into (HRVG) expands through the turbine to output the power (1–2), and the shaft power is converted into electricityelectricity by theby generator.the generator. The The low-pressure low-pressure vaporvapor exhausted exhausted from from the the turbine turbine is condensed is condensed to the to the electricity by the generator. The low-pressure vapor exhausted from the turbine is condensed to the saturatedsaturated liquid liquid by by the the cooling cooling looploop in in the the condenser condenser (2–3). (2–3). The saturated The saturated liquid at liquid the condenser at the condenseroutlet is saturatedpressurized liquid above by the the cooling critical loop pressure in the of condenser the working (2–3). fluid The saturatedby the pump liquid (3 at–4) the and condenser then flows outlet into outlet is pressurized above the critical pressure of the working fluid by the pump (3–4) and then flows theis HRVGpressurized to absorb above the the heat critical from pressure exhaust of gas the (4 working–1) and afluid new by cycle the begins.pump (3 –4) and then flows into into thethe HRVG HRVG to to absorbabsorb the the heat heat from from exhaust exhaust gas (4 gas–1) (4–1)and a new and cycle a new begins. cycle begins. Exhaust gas Exhaust gas 1 Turbine 1 Turbine
HRVG G HRVG G Generator Generator 4 4 22 3 PPuump CCoonnddeennsseerr
FigureFigureFigure 1. Schematic 1. 1. Schematic Schematic diagram diagramdiagram ofof the organic organic transtrans trans-critical--criticalcritical cycle cycle cycle.. .
Figure 2. T-s diagram of the organic trans-critical cycle. FigureFigure 2. 2.T-s T- diagrams diagram ofof thethe organic trans trans-critical-critical cycle cycle..
2.3. Steam Flash Cycle 2.3. Steam2.3. Ste Flasham Flash Cycle Cycle
Figures 3 and4 show the schematic diagram and T-s diagram of the steam flash cycle. In contrast to the basic SRC, A portion of saturated water from the high-pressure economizer expands in the Energies 2019, 12, x FOR PEER REVIEW 4 of 23
Energies 2019, 12, 4623 4 of 22 Figures 3 and 4 show the schematic diagram and T-s diagram of the steam flash cycle. In contrast to Energiesthe basic 2019 , SRC12, x FOR, A PEERportion REVIEW of saturated water from the high-pressure economizer expands4 of 23 in the flasher (7–8) into saturated vapor (10) and liquid (9) of lower pressure. The vapor is sent to the turbine flasher (7–8)Figures into 3 saturated and 4 show vapor the schematic (10) and diagram liquid (9) and of T lower-s diagram pressure. of the Thesteam vapor flash iscycle. sent In to contrast the turbine 2 to generate power (10–11) and the liquid is mixed with water from low-pressure economizer and 2 to generateto the basic power SRC, (10–11)A portion and of thesaturated liquid water is mixed fromwith the high water-pressure from low-pressureeconomizer expands economizer in the and reenterreenterflasher the the high-pressure(7– high8) into-pressure saturated economizer economizer vapor (10) (6–7) and (6 liquid– after7) after being(9) obeingf lower pressurized pressurized pressure. by The the by vapor high-pressurethe highis sent-pressure to the pump turbine pump (5,9–6). (5,9– The6). rest2 The to ofgenerate res thet saturatedof powerthe saturated (10 water–11) fromandwater the the fromliquid high-pressure the is mixed high- pressurewith economizer water economizer from is low heated-pressure is to heated the economizer superheated to the superheated and vapor byvapor thereenter exhaust by thethe gashigh exhaust (12–1)-pressure andgas economizer flows(12–1) into and the(6 flows–7) turbine after into being 1 the to generatepressurized turbine power1 toby generatethe (1–2). high- Thepressure power turbine (1pump–2). exhausts (5,9The– turbine are condensedexhaust6). Thesin resare thet ofcondensed condenserthe saturated in (2,11–3) the water condenser from and pressurizedthe (2,11high-–pressure3) and to the pressurizedeconomizer flash pressure is to heated th bye flash the to the low-pressure pressure superheated by pumpthe low- (3–4),pressurevapor and thenby pump the flows exhaust (3–4), through and gas then(12 the–1) flows low-pressureand flows through into the economizerthe lowturbine-pressure 1 toto absorbgenerate economizer heat power to to the(1 absorb–2). state The heat ofturbine saturated to the state exhausts are condensed in the condenser (2,11–3) and pressurized to the flash pressure by the low- liquidof saturated (4–5) and liquid a new (4 cycle–5) and begins. a new cycle begins. pressure pump (3–4), and then flows through the low-pressure economizer to absorb heat to the state of saturated liquid (4–5) and a new cycle begins. Exhaust gas 1 Exhaust gas 1 Turbine 1 Steam drum Turbine 1 Superheater Steam drum Superheater 12 Evaporator 12 10 Turbine 2 Evaporator 13 10 Turbine 2 2 13 11 2 11 7 High-pressure 7 8 Flasher eHciognho-pmreiszseurre 8 Flasher economizer 6 6 5 5 CondenCsoerndenser LoLwow-p-preressssuurree 9 9 eceocnonoommiizzeerr 3 3 HHRRSSGG HigHh-ipgrhe-spsrueres spuurme p ump 4 4 Low-pressure pump Low-pressure pump
FigureFigure 3. 3.Schematic Schematic diagramdiagram of of the the steam steam flash flash cycle cycle.. Figure 3. Schematic diagram of the steam flash cycle.
FigureFigure 4. 4.T-s T-s diagram diagram of the the steam steam flash flash cycle cycle..
Figure 5 reveals the T-Q diagram of exhaust gas and working fluid in the heat recovery steam Figure5 reveals the T-Q diagramFigure of4. T exhaust-s diagram gas of and the steam working flash fluid cycle. in the heat recovery steam generatorgenerator (HRSG) (HRSG) of of the the SFC. SFC. ToTo avoid the the vapor vapor generation generation in the in high the-pressure high-pressure economizer, economizer, the temperature of the fluid at the outlet of the economizer is lower than the evaporation temperature, the temperatureFigure 5 ofreveals the fluid the atT- theQ diagram outlet of of the exhaust economizer gas and is lower working than fluid the evaporationin the heat recovery temperature, steam and the temperature difference is named approach temperature difference. The minimum andgenerator the temperature (HRSG) di offf erencethe SFC. is namedTo avoid approach the vapor temperature generation diff inerence. the high The-pressure minimum economizer, temperature the temperature difference in the process of heat exchange between the exhaust gas and working fluid is difftemperatureerence in the of process the fluid of at heat the exchange outlet of betweenthe economizer the exhaust is lower gas than and workingthe evaporation fluid is temperature called the , pinchand point the temperature temperature di ff differenceerence, which is usuallynamed occurs approach at the temperature saturated liquid difference. point of working The minimum fluid. temperature difference in the process of heat exchange between the exhaust gas and working fluid is
Energies 2019, 12, x FOR PEER REVIEW 5 of 23 calledEnergies the2019 pinch, 12, 4623 point temperature difference, which usually occurs at the saturated liquid point5 of of 22 working fluid.
FigureFigure 5.5. T-QT-Q diagramdiagram of flueflue gas and working fluid fluid in in the the HRSG HRSG of of steam steam flash flash cycle cycle..
2.4. St Steameam Dual Dual-Pressure-Pressure Cycle Figures 66 andand7 7are are the the schematic schematic diagram diagram and and T-s T-s diagram diagram of of the the steam steam dual-pressure dual-pressure cycle.cycle. The T-QT-Q diagramdiagram ofof exhaustexhaust gas gas and and working working fluid fluid in in the the HRSG HRSG is shownis shown in Figurein Figure8. The 8. T layouthe layout of the of theheat heat exchangers exchangers has significant has significant effects in effects the performance in the performance of the HRSG of [ 19the]. In HRSG view of [19]. maximizing In view the of maximizingamount of waste the amount heat recovered of waste from heat the recovered exhaust gas,from the the layout exhaust considered gas, the inlayout this study considered is as depicted in this studyin Figure is 6 as. Water depicted leaving in Figure the low-pressure 6. Water leaving economizer the low is divided-pressure into economizer two streams. is One divided stream into enters two streams.the low-pressure One stream drum enters (5–6), the and low another-pressure stream drum is (5 pumped–6), and toanother the high-pressure stream is pumped economizer to the (5–10).high- pressureHigh-pressure economizer stream (5 and–10). low-pressure High-pressure stream stream successively and low- absorbpressure the stream heat of successively exhaust gas (10–1,absorb 6–8), the heatand theof exhaust generated gas high-pressure (10–1, 6–8), and vapor the generated and low-pressure high-pressure vapor entervapor the and steam low- turbinepressure 1 vapor and turbine enter the2 respectively steam turbine (1–2, 1 8–9).and turbine The turbine 2 respectively exhausts (1 enter–2, 8– the9). condenserThe turbine together exhaust tos enter release the heat condenser (2,9–3). togetherThe water to inrelease the saturated heat (2,9 liquid–3). The state water at the in the outlet saturated of the condenser liquid state is at pumped the outlet by theof the low-pressure condenser ispump pumpedEnergies (3–4) 2019 and by, 12 the sent, x FOR low to PEER the-pressure low-pressure REVIEW pump economizer (3–4) and sent (4–5) to to the complete low-pressure the cycle. economizer (4–5)6 of to 23 complete the cycle. Exhaust gas 1
High-pressure High pressure Turbine 1 superheater drum
High-pressure evaporator 12 Turbine 2 11 High-pressure 2 economizer 8 9
Low-pressure Low pressure superheater drum Condenser Low-pressure 6 10 evaporator 7
5 Low-pressure High pressure pump economizer 3 Low pressure pump HRSG 4
Figure 6. Schematic diagram of the steam dual-pressure cycle. Figure 6. Schematic diagram of the steam dual-pressure cycle.
Figure 7. T-s diagram of the steam dual-pressure cycle.
Energies 2019, 12, x FOR PEER REVIEW 6 of 23
Exhaust gas 1
High-pressure High pressure Turbine 1 superheater drum
High-pressure evaporator 12 Turbine 2 11 High-pressure 2 economizer 8 9
Low-pressure Low pressure superheater drum Condenser Low-pressure 6 10 evaporator 7
5 Low-pressure High pressure pump economizer 3 Low pressure pump HRSG 4
Energies 2019, 12, 4623 6 of 22 Figure 6. Schematic diagram of the steam dual-pressure cycle.
Energies 2019, 12, x FOR PEER REVIEWFigure 7. TT-s-s diagram of the steam dual dual-pressure-pressure cycle.cycle. 7 of 23
Figure 8. TT-Q-Q diagram of flue flue gas and working fluid fluid in the HRSG of SDC.SDC.
3. Methodology Methodology 3.1. Thermodynamic Modeling 3.1. Thermodynamic Modeling In the present study, the parameters are optimized with the objective of maximizing the net power In the present study, the parameters are optimized with the objective of maximizing the net output of the system, and the exergy analysis is also performed since it can tell us in which process the power output of the system, and the exergy analysis is also performed since it can tell us in which available energy is dissipated and show the direction for the enhancement of system performance. process the available energy is dissipated and show the direction for the enhancement of system The energy and exergy analysis are based on the first and second laws of thermodynamics, respectively. performance. The energy and exergy analysis are based on the first and second laws of For simplicity, the system is considered in a steady state. The heat loss and pressure drop in the heat thermodynamics, respectively. For simplicity, the system is considered in a steady state. The heat loss exchangers and pipes are ignored, and the variation of the kinetic and potential energy of working and pressure drop in the heat exchangers and pipes are ignored, and the variation of the kinetic and fluid in each component can also be ignored. potential energy of working fluid in each component can also be ignored. The energy equation in each component can be described as: The energy equation in each component can be described as: . X . X . . Q =Qm minh hin mmout hhout W+ W (1(1)) in in− out out . wherewhere mmand andh areh a there the mass mass flow flow rate rate and and enthalpy enthalpy of theof the streams; streams; the the subscript subscript in in and and out out refer refer to tostreams streams entering entering and and leaving leaving the the component; component;in andin andout referout torefer the to heat the addition heat addition capacity capacity and work and . . workoutput output of the process.of the process.Q and WQ referand toW therefer heat to additionthe heat capacityaddition andcapacity work and output work of theoutput process. of the process. The exergy of the steady flow stream is the maximum amount of useful work that can be obtained in the process of stream changing from the given state to the environmental equilibrium state in a reversible way. The specific exergy of a stream can be given as:
ex h h0 T 0() s s 0 (2) where h and s are the enthalpy and entropy of the stream; T0 refers to the ambient temperature; h0 and s0 are the enthalpy and entropy of the stream under ambient condition. The exergy loss in each component can be calculated as:
I min e x,, in m out e x out W (3) For the waste heat recovery system, the exergy balance equation is:
EIWx, g tot net (4)
Energies 2019, 12, 4623 7 of 22
The exergy of the steady flow stream is the maximum amount of useful work that can be obtained in the process of stream changing from the given state to the environmental equilibrium state in a reversible way. The specific exergy of a stream can be given as:
ex = h h T (s s ) (2) − 0 − 0 − 0 where h and s are the enthalpy and entropy of the stream; T0 refers to the ambient temperature; h0 and s0 are the enthalpy and entropy of the stream under ambient condition. The exergy loss in each component can be calculated as:
. X . X . . I = m e moutex,out W (3) in x,in − − For the waste heat recovery system, the exergy balance equation is:
. . . Ex,g = Itot + Wnet (4)
. . where Itot is the total exergy loss of all components in the system; Wnet is the net power output of the . system. Ex,g refers to the exergy contained in the heat released from the exhaust gas to the system, which can be calculated as follows:
. . Ex,g = mg[h hg,out T (s sg,out)] (5) g,in − − 0 g,in − . where mg is the mass flow rate of the exhaust gas; hg,in and hg,out are the enthalpy of exhaust gas entering and leaving the HRVG/HRSG; sg,in and sg,out are the entropy of exhaust gas entering and leaving the HRVG/HRSG. The exhaust gas is directly discharged to the environment at a temperature higher than the ambient temperature after releasing heat to the system, and the exergy loss caused by this process is as follows: . . Igas = mg[hg,out hg T (sg,out sg )] (6) − ,0 − 0 − ,0 The thermal efficiency and exergy efficiency of the system are defined as:
. Wnet ηth = . (7) mg(h hg,out) g,in − . Wnet ηe = . (8) Ex,g The mass and energy balance equations and exergy loss in each component of OTC, SFC, and SDC systems are listed in Table1. The number subscript corresponds to the state point in Figures1 and2 for the OTC, Figures3–5 for the SFC and Figures6–8 for the SDC. Energies 2019, 12, 4623 8 of 22
Table 1. Mass and energy balance equations, and exergy loss in each component.
Component Equations OTC . . . Q = mg(hg,in hg,in) = mw f (h1 h4) HRVG . . − . − I = T0[mw f (s1 s4) mg(sg,in sg,out)] . . − − . − Wturb = mw f (h1 h2) = mw f (h1 h2s)ηturb Turbine . . − − I = T0mw f (s2 s1) . . − Q = mw f (h2 h3) Condenser . . − I = mw f [h2 h3 T0(s2 s3)] . . − − . − Wpump = mw f (h4 h3) = mw f (h4s h3)/ηpump Pump . . − − I = T0mw f (s4 s3) . − . . Net power output Wnet = W Wpump turb − SFC . . . . . Q = mg(hg,in hg,in) = mw f ,4(h5 h4) + mw f ,6(h7 h6) + mw f ,1(h1 h7) . . − . − − − mw f ,4 = mw f ,1 + mw f ,10 HRSG . . . . . mw f ,6 = mw f ,5 + mw f ,9 = mw f ,1 + mw f ,8 . . . . . I = T0[mw f ,4(s5 s4) + mw f ,6(s7 s6) + mw f ,1(s1 s7) mg(sg,in sg,out)] − . − . − − − Wturb,1 = mw f ,1(h1 h2) Turbine 1 . . − I = T0mw f ,1(s2 s1) . . − Wturb,2 = mw f ,10(h10 h11) Turbine 2 . . − I = T0mw f ,10(s11 s10) . . . − Q = mw f ,1(h2 h3) + mw f ,10(h11 h3) Condenser . . − −. I = mw f ,1[h2 h3 T0(s2 s3)] + mw f ,10[h11 h3 T0(s11 s3)] − −. − . − − − Wpump,LP = mw f ,4(h4 h3) Low-pressure Pump . . − I = T0mw f ,4(s4 s3) . . − Wpump,HP = mw f ,6(h6 h5) High-pressure Pump . . − I = T m (s s ) 0 w f ,6 6 − 5 hw f ,8 = hw f ,7 . . mw f ,10 = mw f ,8xw f ,8 Flasher . . mw f ,9 = mw f ,8(1 xw f ,8) . . − I = T0mw f ,8(s8 s7) . . . −. . Net power output Wnet = W + W W W turb,1 turb,2 − pump,LP − pump,HP SDC . . . . . Q = mg(hg,in hg,in) = mw f ,5(h5 h4) + mw f ,6(h8 h6) + mw f ,1(h1 h10) . . − . − − − HRSG mw f ,5 = mw f ,6 + mw f ,1 . . . . . I = T0[mw f ,5(s5 s4) + mw f ,6(s8 s6) + mw f ,1(s1 s10) mg(sg,in sg,out)] − . − . − − − Wturb,1 = mw f ,1(h1 h2) Turbine 1 . . − I = T0mw f ,1(s2 s1) . . − Wturb,2 = mw f ,6(h8 h9) Turbine 2 . . − I = T0mw f ,6(s9 s8) . . . − Q = mw f ,1(h2 h3) + mw f ,6(h9 h3) Condenser . . − − . I = mw f ,1[h2 h3 T0(s2 s3)] + mw f ,6[h9 h3 T0(s9 s3)] − −. − . − − − Wpump,LP = mw f ,5(h4 h3) Low-pressure Pump . . − I = T0mw f ,5(s4 s3) . . − Wpump,HP = mw f ,1(h10 h5) High-pressure Pump . . − I = T0mw f ,1(s10 s5) . . . −. . Net power output Wnet = W + W W W turb,1 turb,2 − pump,LP − pump,HP Energies 2019, 12, 4623 9 of 22
3.2. Organic Working Fluid Selection
Li et al. [20] indicated that working fluids with critical temperatures slightly lower (40–60 ◦C) than the initial temperature of the heat source will achieve higher net power output for the OTC driven by waste heat. The conclusion is based on the assumption that the isentropic expansion efficiency of all working fluids is 0.8, whereas the fact is that the fluid with the high critical temperature usually shows low condensing pressure and high volume ratio, which will result in a sharp efficiency drop of the turbine [17,21]. In addition to the thermodynamic performance, some other characteristics of the working fluid such as environmental characteristics, toxicity, corrosiveness, and thermal stability should also be evaluated. Four pure organic fluids, R245fa, n-pentane, cyclopentane, and hexamethyldisiloxane (MM), which have been widely used in commercial ORC installations [22], are selected as the working fluid for OTC in the present study. All the studied fluids are dry or isentropic fluids, and they are hydrofluorocarbon (HFC), alkane, hydrocarbon, and siloxane, respectively. Table2 lists the major thermophysical properties of the fluids.
Table 2. Thermophysical properties of the four considered fluids.
Fluid Tboil [◦C] Tcrit [◦C] Pcrit [MPa] ODP GWP Thermal Stability Limit [◦C] R245fa 15.14 154.01 3.65 0 1030 300 [23] n-pentane 36.06 196.55 3.37 0 4 2 280 [24] ± Cyclopentane 49.25 238.54 4.52 0 < 25 275 [25] MM 100.25 245.55 1.94 0 0 300 [26]
3.3. Optimization Variables and Specified Parameters The turbine inlet pressure and temperature are selected as the optimization variables for the OTC. The turbine inlet pressure and temperature, flash pressure and the mass flow ratio of the flash stream to the main stream are optimized for the SFC. The variables chosen for optimizing the SDC are the turbine inlet pressure and temperature of the main steam, turbine inlet pressure, and temperature of the low-pressure steam. The boundaries of each variable for OTC, SFC, and SDC are listed in Table3. The system may become unsteady near the critical region since the small fluctuations of temperature result in a greater pressure variation. Hence the lower limit of turbine inlet pressure for OTC and the upper limit of turbine inlet pressure for SFC and SDC are set as 1.1Pc and 0.9Pc, respectively. For the OTC, the expansion process cannot pass through the two-phase region; for the SFC and SDC, the vapor quality of the steam exiting turbine should be higher than the minimum allowable value to alleviate the cavitation of turbine blades, which is set as 0.88 in the present study. Table4 details the specified parameters of the OTC, SFC, and SDC systems. The turbine e fficiency is computed based on the operation parameters by using the correlations presented in Ref. [17,18]. For the organic axial turbine, the isentropic efficiency is determined by the size parameter (SP), volume ratio (Vr), specific speed (Ns) and the number of stages.
0.5 Vout,is SP = 0.25 ∆his V Vr = out,is (9) Vin 0.5 RPM Vout,is Ns = 60 0.75 ∆his
Higher SP and smaller Vr are beneficial to reduce the leakage and secondary losses and the Mach number in the nozzle, thus making the turbine more efficient. In operation, the specific speed can be optimized by adjusting the turbine’s revolutions per minute (RPM). Considering the turbine efficiency and the equipment complexity, a three-stage axial turbine is adopted for the OTC system. For the steam turbine, the isentropic efficiency is the function of the turbine rating and rated speed, and the steam inlet superheat and pressure. The steam turbine with the higher rating, the lower Energies 2019, 12, 4623 10 of 22 rated speed, the lower steam inlet pressure, and the greater steam inlet superheat will achieve higher efficiency.
Table 3. Boundaries of the optimized parameters for the OTC, SFC, and SDC.
Optimized parameters Lower limit Upper limit OTC
Turbine inlet pressure (TIP), p1 1.1pc 15 MPa No liquid formation during Turbine inlet temperature (TIT), T T 1 expansion process stable, limit SFC
Turbine inlet pressure, p1 Pcon + 100 kPa 0.9pc Vapor quality at turbine outlet Turbine inlet temperature, T T ∆Tpp 1 higher than 0.88 g,in − Mass flow ratio, MFR 0 6 Min {p1 50 kPa, Vapor quality at Flash pressure, p Pcon + 50 kPa − 10 turbine outlet higher than 0.88} SDC
Turbine 1 inlet pressure, p1 Pcon + 100 kPa 0.9pc Vapor quality at turbine outlet Turbine 1 inlet temperature, T T ∆Tpp 1 higher than 0.88 g,in − Turbine 2 inlet pressure, p Pcon + 50 kPa p 50 kPa 8 1 − Vapor quality at turbine outlet Turbine 2 inlet temperature, T T ∆Tpp 8 higher than 0.88 g,in −
Table 4. Specified parameters of the OTC, SFC, and SDC system.
Parameter Value
Exhaust gas initial temperature, Tg,in 320 ◦C . Exhaust gas mass flow rate, mg 86.2 kg/s Exhaust gas pressure, pg 101.325 kPa Ambient temperature, T0 20 ◦C Condensing temperature, T3 30 ◦C Pinch point temperature difference in 15 ◦C HRVG/HRSG, ∆Tpp Approach temperature difference in HRSG, ∆Tap 5 ◦C Working fluid pump efficiency, ηpump 0.8
3.4. Optimization Strategy The parameter optimization is performed based on the MATLAB platform by employing the genetic algorithm (GA). The thermodynamic properties of the working fluids and the exhaust gas are calculated based on REFPROP NIST 9.0 [27]. The GA is a stochastic global search method that simulates natural biological evolution, and it is suitable for the highly nonlinear or discrete problem since it involves a search for many individuals distributed within the domain rather than a single point. The GA is a conventional optimization algorithm and its specific operations such as initialization of population, calculation of fitness, crossover, and mutation will not be described here. For improving the computational efficiency, the population is divided into several subpopulations. The individual migration between the subpopulations can accelerate the convergence process since the different subpopulations may have different evolutionary trends. The control parameters in GA are shown in Table5, which can reach a good trade-o ff between algorithm accuracy and computational time. Energies 2019, 12, 4623 11 of 22
Table 5. Control parameters in GA.
Tuning Parameters Value Tuning Parameters Value Number of individuals 100 Generation interval for migration 20 Number of subpopulations 5 Fraction of subpopulation for migration 0.2 Energies 2019The, 12 probability, x FOR PEER of REVIEW crossover 0.7 Minimum number of generation limit 150 12 of 23 The probability for mutation 0.1 Objective function tolerance 0.01 4. Results and Discussion 4. Results and Discussion 4.1. Performance Analysis of the OTC 4.1. Performance Analysis of the OTC The variation of the performance of the OTC with the turbine inlet pressure and temperature will beThe detailed variation in ofthis the section performance. For different of the OTCworking with fluids, the turbine the variation inlet pressure is similar and and temperature n-pentane will is takenbe detailed as an inexample this section. to introduce For diff theerent variation. working fluids, the variation is similar and n-pentane is taken as anFigure example 9 shows to introduce the effect the of variation. the turbine inlet pressure and temperature on the thermal efficiency of theFigure cycle9. showsGiven thethe e turbineffect of the inlet turbine pressure, inlet pressure the average and heattemperature absorption on the temperature thermal effi andciency heat of releasethe cycle. temperature Given the turbine of the cycle inlet pressure, increase the with average the increase heat absorption of the turbine temperature inlet temperature. and heat release The variationtemperature of the of thethermal cycle efficiency increase with is a thecombined increase action of the of turbine the average inlet temperature. heat absorption The temperature variation of andthe thermalaverage eheatfficiency release is a temperature. combined action When of the the turbine average inlet heat pressure absorption is low, temperature the system and efficiency average increasesheat release first temperature. and then decrease When as the the turbine turbine inlet inlet pressure temperatur is low,e increases; the system when effi theciency turbine increases inlet pressurefirst and thenis high, decrease the variation as the turbineof average inlet heat temperature absorption increases; temperature when has the a turbinestronger inlet effect pressure on the systemis high, thermal the variation efficiency of averagethan the heatvariation absorption of the average temperature heat release has a temperature, stronger effect hence on thethe system thermal eefficiencfficiencyy thantends the to variationincrease with of the the average increase heat of release the turbine temperature, inlet temperature. hence the system thermal efficiency tends to increase with the increase of the turbine inlet temperature.
Figure 9. Effects of the turbine inlet pressure and temperature on the system thermal efficiency. Figure 9. Effects of the turbine inlet pressure and temperature on the system thermal efficiency. Given the turbine inlet temperature, the thermal efficiency of the cycle first increases and then decreasesGiven as the the turbine turbine inlet pressuretemperature, increases, the thermal whichis efficiency mainly due of tothe the cycle decrease first incre of theases average and then heat decreasesrelease temperature as the turbine and inlet the decrease pressure of increases, the turbine which efficiency. is mainly The due variation to the ofdecrease the turbine of the e ffiaverageciency heatunder release different temperature turbine inlet and pressure the decrease and temperature of the turbine is shown efficiency. in Figure The 10 variation. It can be of seen the that turbine the efficiencyincrease of under the turbine different inlet turbine pressure inlet will pressure result in and a sharp temperature reduction is ofshown the turbine in Figure effi ciency.10. It can The be e seenffect thatof the the turbine increase inlet of temperaturethe turbine inlet on the pressure turbine will effi ciencyresult in is weaka sharp than reduction that of theof the turbine turbine inlet efficiency pressure.. The effect of the turbine inlet temperature on the turbine efficiency is weak than that of the turbine inlet pressure.
Energies 2019, 12, x FOR PEER REVIEW 13 of 23
EnergiesEnergies 20192019,, 1212,, 4623x FOR PEER REVIEW 1312 of 2223
Figure 10. Effects of the turbine inlet pressure and temperature on the turbine efficiency. Figure 10. Effects of the turbine inlet pressure and temperature on the turbine efficiency. FigureFigure 11 illustrates 10. Effects the of effectsthe turbine of the inlet turbine pressure inlet and pressure temperature and on temperature the turbine efficiency on the exhaust. gas outletFigure temperature. 11 illustrates The pinch the eff pointects of temperature the turbine inletdifference pressure between and temperature the exhaust on gas the and exhaust working gas outletfluid Figureoccurs temperature. 11during illustrates the The heat pinchthe exchangeeffects point of temperature processthe turbine when inlet di fftheerence pressure turbine between andinlet temperature temperature the exhaust on is gas thehigh, and exhaust as working shown gas fluidinoutlet Figure occurs temperature. 12(a), during and the Thethe heat higherpinch exchange pointturbine temperature process inlet pressure when difference the can turbine achieve between inlet better temperature the thermal exhaust is matching high,gas and as shown workingand the in Figurelowerfluid occurs outlet 12a, and duringtemperature the higherthe heat of turbine theexchange exhaust inlet processpressure gas than when can that achievethe of turbinethe lower better inlet turbine thermal temperature inlet matching pressure. is high, and However, theas shown lower outletwhenin Figure the temperature turbine12(a), and inlet of the the temperature higher exhaust turbine gas is than low, inlet that the pressure ofpinch the lowerpoint can turbinetemperatureachieve inlet better pressure.difference thermal However, occursmatching at when theand inlet thethe turbineoflower the workingoutlet inlet temperature temperature fluid, as shown of is the low, in exhaust Figure the pinch gas12(b). pointthan Therefore, that temperature of the a higher lower diff turbineerenceturbine occursinletinlet pressure pressure. at the inletresults However, of in the a workinghigherwhen the inlet fluid, turbine temperature as showninlet temperature inof Figurethe working 12 isb. low, Therefore, fluid, the pinchwhich a higher pointwill further temperature turbine cause inlet differencea pressure higher outlet resultsoccurs temperature inat athe higher inlet inletofof thethe temperature exhaustworking gas. fluid, of theas shown working in fluid,Figure which 12(b). willTherefore, further a cause higher a turbine higher outletinlet pressure temperature results of in the a exhausthigher inlet gas. temperature of the working fluid, which will further cause a higher outlet temperature of the exhaust gas.
Figure 11. Effects of the turbine inlet pressure and temperature on the exhaust gas outlet temperature. Figure 11. Effects of the turbine inlet pressure and temperature on the exhaust gas outlet temperature. The net power output of the cycle is equal to the thermal efficiency multiplied by the heat absorptionFigure capacity.11. Effects Figureof the turbine 13 shows inlet thepressure effects and of temperature the turbine on inlet the pressureexhaust gas and outlet temperature temperature on. the net power output. There exists an optimal turbine inlet pressure to maximize the net power output for a given turbine inlet temperature, and the optimal turbine inlet pressure increases as the turbine inlet temperature increases. Similarly, the optimal turbine inlet temperature increases with the increase of the turbine inlet pressure, but its increment decreases when the turbine inlet pressure is higher than 10 MPa.
Energies 2019, 12, x FOR PEER REVIEW 14 of 23
.
Figure 12. Temperature matching between the heat source and working fluid for the OTC: (a) Turbine inlet temperature = 280 °C; (b) Turbine inlet temperature = 230 °C .
The net power output of the cycle is equal to the thermal efficiency multiplied by the heat absorption capacity. Figure 13 shows the effects of the turbine inlet pressure and temperature on the net power output. There exists an optimal turbine inlet pressure to maximize the net power output for a given turbine inlet temperature, and the optimal turbine inlet pressure increases as the turbine
Energiesinlet temperature2019, 12, 4623 increases. Similarly, the optimal turbine inlet temperature increases with13 of the 22 increaseEnergies 2019 of , the12, x turbine FOR PEER inlet REVIEW pressure, but its increment decreases when the turbine inlet pressure14 of 23 is higher than 10 MPa. Table 6 lists the optimization results for the four working fluids. n-pentane achieves the maximum power output, and the MM shows the worst performance from the perspective of thermal efficiency and net power output. Due to the large Vr in the expansion process of cyclopentane and MM (223 and 454, respectively), their turbine efficiency is lower than that of n-pentane and R245fa. MM is ‘too dry’, resulting in a higher temperature of the fluid exiting the turbine, which is detrimental to the thermal efficiency of the cycle.
Table 6. Optimized variables and the system performance of the OTC.
̇ Fluid TIP [MPa] TIT [°C ] Tg,out [°C ] ηturb [%] ηth [%] 푾풏풆풕 [kW]
R245fa 14.56 275.47 52.81 85.39 20.61 4851.76
n-pentane 5.14 240.55 48.66 85.41 20.42 4884.73 286 Cyclopentane 6.31 266.54 64.66 82.27 21.59 4860.20
287 FigureFigureMM 12. 12. Temperature Temperature2.13 matchingmatching betweenbetween265.55 the heat 54.91 source source and and working working80.01 fluid fluid for for the16.51 the OTC: OTC: (a ()a Turbine)3855.92 Turbine 288 inletinlet temperature temperature= = 280280 ◦°C;C; (b) Turbine inlet temperature == 230230 °C.◦C.
289 The net power output of the cycle is equal to the thermal efficiency multiplied by the heat 290 absorption capacity. Figure 13 shows the effects of the turbine inlet pressure and temperature on the 291 net power output. There exists an optimal turbine inlet pressure to maximize the net power output 292 for a given turbine inlet temperature, and the optimal turbine inlet pressure increases as the turbine 293 inlet temperature increases. Similarly, the optimal turbine inlet temperature increases with the 294 increase of the turbine inlet pressure, but its increment decreases when the turbine inlet pressure is 295 higher than 10 MPa. 296 Table 6 lists the optimization results for the four working fluids. n-pentane achieves the 297 maximum power output, and the MM shows the worst performance from the perspective of thermal 298 efficiency and net power output. Due to the large Vr in the expansion process of cyclopentane and 299 MM (223 and 454, respectively), their turbine efficiency is lower than that of n-pentane and R245fa. 300 MM is ‘too dry’, resulting in a higher temperature of the fluid exiting the turbine, which is detrimental 301 to the thermal efficiency of the cycle. Figure 13. Effects of turbine inlet pressure and temperature on the system net power output. 302 Table 6. Optimized variables and the system performance of the OTC. Table6 lists the optimization results for the four working fluids. n-pentane achieves the maximum Fluid TIP [MPa] TIT [°C] Tg,out [°C] η [%] η [%] 𝑾 [kW] power output, and the MM shows the worst performance fromturb the perspectiveth of thermal𝒏𝒆𝒕 efficiency and net powerR245fa output. Due 14.56 to the large275.47Vr in the expansion52.81 process85.39 of cyclopentane20.61 and4851.76 MM (223 and 454, respectively),n-pentane their turbine5.14 efficiency240.55 is lower48.66 than that of n-pentane85.41 and20.42 R245fa. MM4884.73 is ‘too dry’, resulting in a higher temperature of the fluid exiting the turbine, which is detrimental to the thermal Cyclopentane 6.31 266.54 64.66 82.27 21.59 4860.20 efficiency of the cycle. MM 2.13 265.55 54.91 80.01 16.51 3855.92 Table 6. Optimized variables and the system performance of the OTC.
. Fluid TIP [MPa] TIT [◦C] Tg,out [◦C] ηturb [%] ηth [%] Wnet [kW] R245fa 14.56 275.47 52.81 85.39 20.61 4851.76 n-pentane 5.14 240.55 48.66 85.41 20.42 4884.73 Cyclopentane 6.31 266.54 64.66 82.27 21.59 4860.20 MM 2.13 265.55 54.91 80.01 16.51 3855.92
4.2. Performance Analysis of the SFC For the basic SRC driven by the waste heat, the pinch point temperature difference between working fluid and heat source usually occurs at the bubble point of the working fluid. The smaller heat absorption of the liquid water in the economizer results in a larger outlet temperature of the heat source. Aims to improving the use of the waste heat, in the SFC, a portion of the saturated water which is 303
Energies 2019, 12, x FOR PEER REVIEW 15 of 23
Figure 13. Effects of turbine inlet pressure and temperature on the system net power output.
4.2. Performance Analysis of the SFC For the basic SRC driven by the waste heat, the pinch point temperature difference between working fluid and heat source usually occurs at the bubble point of the working fluid. The smaller heat absorption of the liquid water in the economizer results in a larger outlet temperature of the heat Energies 2019, 12, 4623 14 of 22 source. Aims to improving the use of the waste heat, in the SFC, a portion of the saturated water which is supposed to enter the evaporator is directly flashed into the saturated liquid and saturated gassupposed, and the to satu enterrated the evaporatorliquid will isfurther directly absorb flashed heat into from the the saturated waste heat liquid source and saturated in the high gas,-pressure and the economizer.saturated liquid will further absorb heat from the waste heat source in the high-pressure economizer. FigureFigure 1414 presentspresents the the variation variation of of the the SFC’s SFC’s performance performance with with the the mass mass flow flow ratio ratio of of the the flash flash streamstream to to the the main main stream. stream. When When the the mass mass flow flow ratio ratio is is 0, 0, the the SFC SFC becomes becomes the the basic basic SRC. SRC. The The flashing flashing temperaturetemperature is is lower lower than than the evaporating the evaporating temperature, temperature, thus the thus average the heat average absorption heat temperature absorption temperatureof the working of the fluid working decreases fluid with decreases the increase with the of the increase mass flowof the ratio mass of flow the flashratio streamof the flash to the stream main tostream, the main which stream, leads whi to thech leads reduction to the in reduction the system in thermalthe system effi ciency.thermal Accordingly, efficiency. Accordingly, the exhaust the gas exhaustoutlet temperature gas outlet temperature will decrease will as thedecrease mass flowas the ratio mass increases flow ratio since increases more heat since of themore exhaust heat of gas the is exhaustreleased gas in theis released high-pressure in the high economizer.-pressure economizer. However,However, when when the the ma massss flow flow ratio ratio reaches reaches a a certain certain value, value, the the position position of of the the pinch pinch point point temperaturetemperature difference difference between between the the working working fluid fluid and and exhaust exhaust gas gas is is transferred transferred from from the the bubble bubble pointpoint of of the the main main stream stream to to the the inlet inlet of of the the high high-pressure-pressure economizer. economizer. If If the the mass mass flow flow r ratioatio is is further further increased,increased, the the outlet outlet temperature temperature of of the the exhaust exhaust gas gas will will remain remain almost almost unchanged. unchanged. Figure Figure 1515 revealsreveals thethe T T-Q-Q diagram diagram of of the the heat heat source source and and working fluid fluid with the mass flow flow ratio of 2.5 and 4.5. Due Due to to thethe combined eeffectffect of of the the system system thermal thermal effi efficiencyciency and and heat heat absorption absorption capacity, capacity, the net the power net power output outputof the systemof the system increases increases first and first then and decreases then decreases with the with increase the increase of the mass of the flow mass ratio. flow ratio.
Energies 2019, 12, x FOR PEER REVIEW 16 of 23 Figure 14. Figure 14. EffectEffect of of mass mass flow flow ratio ratio on on the the system system performance performance of of SFC SFC..
Figure 15. Thermal matching between the heat source and working fluid for the SFC. Figure 15. Thermal matching between the heat source and working fluid for the SFC. Figure 16 shows the effect of flashing temperature on the system performance. Please note that the Figure 16 shows the effect of flashing temperature on the system performance. Please note that corresponding mass flow ratio for each flashing temperature is taken as the optimal value to maximize the corresponding mass flow ratio for each flashing temperature is taken as the optimal value to maximize the system’s net power output. The average heat absorption temperature of the working fluid and the outlet temperature of the exhaust gas increase as the flash temperature increases. The maximum net power output is obtained after a comprehensive consideration of the heat input and thermal efficiency variation. The optimal parameters and the system performance are shown in Table 7.
Table 7. Optimized variables and the system performance of the SFC.
̇ Teva [°C] TIT [°C] Tflash [°C] MFR Tg,out [°C] ηturb [%] ηth [%] 푊푛푒푡 [kW]
177.83 305 105.93 3.59 95.68 74.12 20.07 3967.9
Figure 16. Effect of flashing temperature on the system performance of SFC.
4.3. Performance Analysis of the SDC In contrast to the SFC, the way of SDC to improve the use of the waste heat is to add a complete low-temperature circuit which includes the low-temperature preheating, evaporating and superheating. Same as the SFC, the increase of heat absorption of SDC is at the expense of the decrease of the thermal efficiency.
Energies 2019, 12, x FOR PEER REVIEW 16 of 23
Figure 15. Thermal matching between the heat source and working fluid for the SFC.
EnergiesFigure2019, 1216, 4623shows the effect of flashing temperature on the system performance. Please note15 that of 22 the corresponding mass flow ratio for each flashing temperature is taken as the optimal value to maximize the system’s net power output. The average heat absorption temperature of the working fluidthe system’s and the net outlet power temperature output. The of averagethe exhaust heat gas absorption increase temperature as the flash oftemperature the working increases. fluid and The the maximumoutlet temperature net power of output the exhaust is obtained gas increase after a as comprehensive the flash temperature consideration increases. of the The heat maximum input and net thermalpower output efficiency is obtained variation. after The a comprehensiveoptimal parameters consideration and the system of the heatperformance input and are thermal shown e ffiin ciencyTable 7.variation. The optimal parameters and the system performance are shown in Table7.
Table 7. Optimized variables and the system performance of the SFC. Table 7. Optimized variables and the system performance of the SFC. . Teva [◦C] TIT [◦C] Tflash [◦C] MFR Tg,out [◦C] ηturb [%] ηth [%] Wneṫ [kW] Teva [°C] TIT [°C] Tflash [°C] MFR Tg,out [°C] ηturb [%] ηth [%] 푊푛푒푡 [kW] 177.83 305 105.93 3.59 95.68 74.12 20.07 3967.9 177.83 305 105.93 3.59 95.68 74.12 20.07 3967.9
Figure 16. Effect of flashing temperature on the system performance of SFC. Figure 16. Effect of flashing temperature on the system performance of SFC. 4.3. Performance Analysis of the SDC 4.3. Performance Analysis of the SDC In contrast to the SFC, the way of SDC to improve the use of the waste heat is to add a completeIn contrast low-temperature to the SFC, the circuit way which of SDC includes to improve the low-temperature the use of the waste preheating, heat is to evaporating add a complete and lowsuperheating.-temperature Same circuit as the SFC, which the includesincrease of the heat low absorption-temperature of SDC preheating, is at the expense evaporating of the decrease and superheating.of the thermal Same efficiency. as the SFC, the increase of heat absorption of SDC is at the expense of the decrease of theFigure thermal 17 efficiency.shows the T-Q diagrams of exhaust gas and working fluid under the condition that the SDC system outputs the maximum power, as well as the condition that the basic SRC operates with the same main evaporating temperature and turbine inlet temperature as the SDC. Compared with the basic SRC, the SDC produces 25.24% more power with a lower thermal efficiency and a higher heat absorption. The optimal parameters and the system performance of the SDC are shown in Table8.
Table 8. Optimized variables and the system performance of the SDC.
. Teva,main [◦C] TITmain [◦C] Teva, LP [◦C] TITLP [◦C] Tg,out [◦C] ηturb [%] ηth [%] Wnet [kW] 177.19 305 97.57 158.61 91.58 74.15 19.75 3977.8 Energies 2019, 12, x FOR PEER REVIEW 17 of 23
Figure 17 shows the T-Q diagrams of exhaust gas and working fluid under the condition that the SDC system outputs the maximum power, as well as the condition that the basic SRC operates with the same main evaporating temperature and turbine inlet temperature as the SDC. Compared with the basic SRC, the SDC produces 25.24% more power with a lower thermal efficiency and a higher heat absorption. The optimal parameters and the system performance of the SDC are shown in Table 8.
Table 8. Optimized variables and the system performance of the SDC.
̇ Teva,main [°C] TITmain [°C ] Teva, LP [°C] TITLP [°C] Tg,out [°C ] ηturb [%] ηth [%] 푊푛푒푡 [kW] Energies 2019, 12, 4623 16 of 22 177.19 305 97.57 158.61 91.58 74.15 19.75 3977.8
FigureFigure 17. 17. TT-Q-Q diagram diagram of of the the heat heat source source and working fluid fluid for the SDC and basic SRC SRC..
4.4. Performance Performance Comparison Comparison of of OTC, OTC, SFC SFC,, and and SDC The comparison of the net power power output of OTC OTC using using n n-pentane,-pentane, SFC, SDC SDC,, the basic ORC with nn-pentane-pentane as the the working working fluid fluid and and SRC SRC is is shown shown in in Figure Figure 18. 18. The The corresponding corresponding thermal thermal efficiency, efficiency, exhaust gas outletoutlet temperaturetemperature and and turbine turbine e ffiefficiencyciency of of each each cycle cycle are are also also given given in thein the figure. figure. For For the theorganic organic working working fluid, fluid,when the when endothermic the endothermic pressure pressureis increased is from increase subcriticald from to subcritical supercritical, to supercritical,the turbine e ffitheciency turbine is reduced,efficiency but is reduced, the thermal but ethefficiency thermal and efficiency net power and output net power of the output system of the are systemimproved. are Comparedimproved. withCompared the basic with SRC, the SFC, basic and SRC, SDC SFC enhance, and SDC the netenhance power the output net power by improving output bythe improving use of the wastethe use heat. of the The waste thermal heat. e ffiTheciency thermal of the efficiency OTC, SFC, of the and OTC, SDC SFC is almost, and SDC equal is andalmost the equalmaximum and the net maximum power output net ofpower SDC output is slightly of SDC higher is thanslightly that higher of SFC. than Owing that to of the SFC. organic Owing working to the organicfluid giving working much fluid better giving temperature much better matching temperature with matching exhaust gas with in exhaust the heat gas addition in the heat process addition and processhigher turbineand higher efficiency turbine than efficiency water, thethan maximum water, the net maximum power output net power of OTC output is 19.74% of OTC higher is 19.74% than higherthatEnergies of than SDC.2019, that12, x FORof SDC. PEER REVIEW 18 of 23
FigureFigure 18. Performance com comparisonparison of of OTC, OTC, SFC SFC,, and and SDC SDC..
4.5. Cost Analysis of OTC, SFC, and SDC The cost of HRSG mainly depends on its heat transfer area, and the cost of HRSG accounts for a large proportion of the total cost of the system. In the heat transfer process of the exhaust gas and working fluid, the thermal resistance of the exhaust gas is much higher than that of the working fluid, hence the over-all heat transfer coefficient U of different working fluid has little difference. Therefore, the heat transfer requirement UA of the HRSG can approximately reflect its heat transfer area, and the UA can be evaluated by the following equation:
Q UA i (10) Tmi,
The heat transfer process between the exhaust gas and working fluid is divided into 100
segments subjected to identical heat flow. The Qi and Tmi, refer to the heat rate and logarithmic mean temperature difference between exhaust gas and working fluid in each segment. Figure 19 shows the UA of the HRSG when the cycles output the maximum power. It is not surprising that the UA of OTC is higher than that of SFC and SDC since the better temperature matching between the exhaust gas and working fluid means the higher heat absorption and smaller heat transfer temperature difference. The UA/W is further calculated, which means the UA per unit net power output. It can be seen that SDC achieves the minimum UA/W, followed by the SFC. However, we cannot conclude that the SFC and SDC are more economical than OTC, because the cost of other components in the system is not reflected in this indicator. SDC and SFC systems are more complex than the OTC system, and the number of stages of the steam turbine is more than that of the organic turbine, which entails the higher cost of the component.
Energies 2019, 12, 4623 17 of 22
4.5. Cost Analysis of OTC, SFC, and SDC The cost of HRSG mainly depends on its heat transfer area, and the cost of HRSG accounts for a large proportion of the total cost of the system. In the heat transfer process of the exhaust gas and working fluid, the thermal resistance of the exhaust gas is much higher than that of the working fluid, hence the over-all heat transfer coefficient U of different working fluid has little difference. Therefore, the heat transfer requirement UA of the HRSG can approximately reflect its heat transfer area, and the UA can be evaluated by the following equation:
. X Q UA = i (10) ∆Tm,i
The heat transfer process between the exhaust gas and working fluid is divided into 100 segments . subjected to identical heat flow. The Qi and ∆Tm,i refer to the heat rate and logarithmic mean temperature difference between exhaust gas and working fluid in each segment. Figure 19 shows the UA of the HRSG when the cycles output the maximum power. It is not surprising that the UA of OTC is higher than that of SFC and SDC since the better temperature matching between the exhaust gas and working fluid means the higher heat absorption and smaller heat transfer temperature difference. The UA/W is further calculated, which means the UA per unit net power output. It can be seen that SDC achieves the minimum UA/W, followed by the SFC. However, we cannot conclude that the SFC and SDC are more economical than OTC, because the cost of other components in the system is not reflected in this indicator. SDC and SFC systems are more complex than the OTC system, and the number of stages of the steam turbine is more than that of the organic Energiesturbine, 2019 which, 12, x entailsFOR PEER the REVIEW higher cost of the component. 19 of 23
Figure 19. TheThe UA UA and and UA/W UA/W of HRSG for the OTC, SFC SFC,, and SDC SDC..
4.6. Exergy Exergy A Analysisnalysis of OTC, SFC SFC,, and SDC The exergy analysisanalysis of of OTC OTC using using n-pentane, n-pentane SFC,, SFC, and and SDC SDC is shown is shown in Table in Table9. The 9. exergy The exergy input inpof theut of system the system plus the plus exergy the exergy loss in loss the outletin the gasoutlet is thegas totalis the exergy total exergy of the exhaustof the exhaust gas heat gas source. heat source.The exergy The input exergy of input OTC is of higher OTC isthan higher that of than SFC that and of SDC SFC due and to SDC its lower due tooutlet its lower temperature outlet temperatureof exhaust gas. of exhaust The net gas. power The output net power plus theoutput total plus exergy the total loss inexergy each componentloss in each iscomponent equal to the is equalexergy to input the exergy of the input system, of the and system the exergy, and the effi exergyciency efficiency of OTC, SFC,of OTC, and SFC SDC, and is 60.58%, SDC is 60.58%, 53.23%, 53.23%,and 52.85%, and 52.85%, respectively. respectively. The biggest exergy loss occurs in the condenser for OTC since the temperature of the fluid exiting turbine (121.5 °C ) is much higher than the ambient temperature. The exergy loss in HRSG of SFC and SDC is higher than that of OTC, because the temperature matching between exhaust gas and working fluid of SFC and SDC is not as good as that of OTC, resulting in a large heat transfer temperature difference. The turbine efficiency of SFC and SDC is lower than that of OTC (74.12%, 74.15% vs 85.41%), which makes the higher exergy loss in the steam turbine. Figure 20 shows the partition of the exergy loss in the HRSG of SFC and SDC. For the SFC, the biggest exergy loss occurs in the evaporator; for the SDC, the high-pressure evaporator amounts for the largest exergy loss, followed by the low-pressure evaporator. This tells us that the isothermal evaporating is the main cause of exergy destruction in the heating process.
Table 9. The exergy inputs, outputs, and losses in components for OTC, SFC, and SDC.
OTC SFC SDC
Exergy input of system [kW] 8063.6 7454.9 7526.5
Exergy loss in outlet gas [kW] 107.9 716.7 645.1
Net power output [kW] 4884.7 3967.9 3977.8
Exergy loss in component [kW] HRVG 1084.1 1343.4 1720.7
Turbine 677.9 1352.7 1347.3
Condenser 1347.1 469.3 479.7
Pump 69.8
LP pressure 0.206 0.152
HP pressure 3.72 0.852
Flasher 317.7
Energies 2019, 12, 4623 18 of 22
The biggest exergy loss occurs in the condenser for OTC since the temperature of the fluid exiting turbine (121.5 ◦C) is much higher than the ambient temperature. The exergy loss in HRSG of SFC and SDC is higher than that of OTC, because the temperature matching between exhaust gas and working fluid of SFC and SDC is not as good as that of OTC, resulting in a large heat transfer temperature difference. The turbine efficiency of SFC and SDC is lower than that of OTC (74.12%, 74.15% vs 85.41%), which makes the higher exergy loss in the steam turbine. Figure 20 shows the partition of the exergy loss in the HRSG of SFC and SDC. For the SFC, the biggest exergy loss occurs in the evaporator; for the SDC, the high-pressure evaporator amounts for the largest exergy loss, followed by the low-pressure evaporator. This tells us that the isothermal evaporating is the main cause of exergy destruction in the heating process.
Table 9. The exergy inputs, outputs, and losses in components for OTC, SFC, and SDC.
OTC SFC SDC Exergy input of system [kW] 8063.6 7454.9 7526.5 Exergy loss in outlet gas [kW] 107.9 716.7 645.1 Net power output [kW] 4884.7 3967.9 3977.8 Exergy loss in component [kW] HRVG 1084.1 1343.4 1720.7 Turbine 677.9 1352.7 1347.3 Condenser 1347.1 469.3 479.7 Pump 69.8 LP pressure 0.206 0.152 HP pressure 3.72 0.852 Energies 2019, 12, x FOR PEER REVIEW Flasher 317.7 20 of 23
(a) (b)
Figure 20. Distribution of the exergy loss in HRSG.HRSG. (a) SFC;SFC; (b)) SDC.SDC.
4.7. Performance Comparison under Higher Heat Source Temperature The above results results are are based based on on the the given given waste waste heat heat source source with with an an initial initial temperature temperature of 320 of 320 °C ◦andC and a mass a mass flow flow rate rate of 86.2 of 86.2 kg/s. kg I/fs. the If theinitial initial temperature temperature of the of theexhaust exhaust gas gasis further is further increased, increased, the theoptimal optimal turbine turbine inlet inlettemperature temperature to maximize to maximize the net the power net o powerutput of output the cycle of the will cycle also be will increased also be increasedaccordingly. accordingly. However, However, the turbine the inlet turbine temperature inlet temperature of the OTC of the is OTC limited is limited by the by thermal the thermal stable stabletemperature temperature of the organic of the organic fluid, which fluid, will which result will in result greater in greaterexergy destruction exergy destruction in the heating in the heatingprocess. process.Figure 21 Figure presents 21 presents the maximum the maximum net power net output power of output OTC ofusing OTC n using-pentane n-pentane,, SFC, and SFC, SDC and under SDC undervarious various initial initialtemperatures temperatures of exhaust of exhaust gas. It gas. can It be can seen be seenthat thatthe themaximum maximum net netpower power output output of ofSDC SDC is always is always slightly slightly higher higher than than that that of of SFC. SFC. When When the the initial initial temperature temperature of of exhaust exhaust gas exceeds 415 ◦°CC,, the SDC can achieve more power output thanthan thethe OTC.OTC.
Figure 21. The maximum net power output of OTC, SFC, and SDC under the various initial temperature of exhaust gas.
5. Conclusions The OTC, SFC, and SDC systems can be used to recover the waste heat available in the industrial processes. This study focuses on the thermodynamic performance of OTC, SFC, and SDC based on the exhaust gas of an initial temperature of 320 °C and a mass flow rate of 86.2 kg/s which is from the clinker cooler for a cement kiln line of 5000 t/d capacity. Four organic fluids, including R245fa, n- pentane, cyclo-pentane and MM, are selected as working fluids for the OTC, and the optimized
Energies 2019, 12, x FOR PEER REVIEW 20 of 23
(a) (b)
Figure 20. Distribution of the exergy loss in HRSG. (a) SFC; (b) SDC.
4.7. Performance Comparison under Higher Heat Source Temperature The above results are based on the given waste heat source with an initial temperature of 320 °C and a mass flow rate of 86.2 kg/s. If the initial temperature of the exhaust gas is further increased, the optimal turbine inlet temperature to maximize the net power output of the cycle will also be increased accordingly. However, the turbine inlet temperature of the OTC is limited by the thermal stable temperature of the organic fluid, which will result in greater exergy destruction in the heating process. Figure 21 presents the maximum net power output of OTC using n-pentane, SFC, and SDC under various initial temperatures of exhaust gas. It can be seen that the maximum net power output of SDC is always slightly higher than that of SFC. When the initial temperature of exhaust gas exceeds Energies 2019, 12, 4623 19 of 22 415 °C , the SDC can achieve more power output than the OTC.
Figure 21. 21.The The maximum maximum net net power power output output of OTC, of SFC, OTC, and SFC SDC, and under SDC the under various the initial various temperature initial temperatureof exhaust gas. of exhaust gas. 5. Conclusions 5. Conclusions The OTC, SFC, and SDC systems can be used to recover the waste heat available in the industrial The OTC, SFC, and SDC systems can be used to recover the waste heat available in the industrial processes. This study focuses on the thermodynamic performance of OTC, SFC, and SDC based on processes. This study focuses on the thermodynamic performance of OTC, SFC, and SDC based on the exhaust gas of an initial temperature of 320 ◦C and a mass flow rate of 86.2 kg/s which is from the exhaust gas of an initial temperature of 320 °C and a mass flow rate of 86.2 kg/s which is from the the clinker cooler for a cement kiln line of 5000 t/d capacity. Four organic fluids, including R245fa, clinker cooler for a cement kiln line of 5000 t/d capacity. Four organic fluids, including R245fa, n- n-pentane, cyclo-pentane and MM, are selected as working fluids for the OTC, and the optimized pentane, cyclo-pentane and MM, are selected as working fluids for the OTC, and the optimized thermodynamic performance of the OTC, SFC, and SDC systems are compared. Main conclusions are summarized as follows:
The thermal efficiency of the three cycles is almost equal. The maximum net power output of SDC is slightly higher than that of SFC, while the OTC provides a 19.74% more net power output than the SDC since an improved temperature matching between the exhaust gas and the working fluid in the heat addition process and a higher turbine efficiency are achieved in OTC. For the OTC, the biggest exergy loss occurs in the condenser due to the higher turbine exiting temperature of the working fluid. For the SFC and SDC, the isothermal evaporating is the main cause of the exergy destruction in the heat addition process. SDC gives higher net power outputs than OTC does at the initial temperatures of exhaust gas exceeding 415 ◦C, since the turbine inlet temperature of OTC is limited by the thermal stability of the organic working fluid.
Author Contributions: Conceptualization, H.W.; Data curation, L.R.; Formal analysis, L.R.; Funding acquisition, H.W.; Investigation, L.R.; Methodology, L.R.; Project administration, H.W.; Software, L.R.; Writing—original draft, L.R.; Writing—review & editing, H.W. Funding: This research was funded by the National Natural Science Foundation of China (No. 51376134). Conflicts of Interest: The authors declare no conflict of interest. Energies 2019, 12, 4623 20 of 22
Nomenclature e exergy (J/kg) h enthalpy (J/kg) . I exergy loss (W) . m mass flow rate (kg/s) P pressure (kPa) . Q heat transfer rate (W) s entropy (J/kg/K) SP size parameter (m) T temperature (◦C) Vr volume ratio . W power (W) x quality of vapor-liquid mixture Greek letters η efficiency ∆ difference Subscript ap approach point eva evaporator c critical con condenser g gas in inlet out outlet pp pinch point th thermal turb turbine wf working fluid Abbreviations EC economizer EV evaporator HP high pressure HRVG heat recovery vapor generator HRSG heat recovery steam generator LP low pressure OTC organic trans-critical cycle RPM revolutions per minute SDC steam dual-pressure cycle SFC steam flash cycle SH superheater SRC steam Rankine cycle
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