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orcish name generator

ASME Turbo Expo Vancouver, June 6‐10 2011 Development of a model for the simulation of Organic Rankine Cycles based on group contribution techniques Enrico Saverio Barbieri Engineering Department University of Ferrara Mirko Morini MechLav Technopole of Ferrara Michele Pinelli Engineering Department University of Ferrara MechLav LABORATORIO PER LA MECCANICA AVANZATA Introduction Many industrial sectors and applications are characterized by the availability of low enthalpy thermal sources with temperatures lower than 400 °C. For example, the ones deriving from industrial processes (e.g. combustion products from gas turbines and internal combustion engines, technological processes and cooling systems) or renewable sources (e.g. solar and geothermal energy). The Organic Rankine Cycle (ORC) is a promising process for conversion of heat at low and medium temperature to electricity. A certain challenge is the choice of the organic working fluid and of the particular design of the cycle. For this reasons, a model for the simulation of ORC systems based on techniques for the estimation of thermodynamic properties from molecular structures can be a useful tool for ORC performance optimization. MechLav LABORATORIO PER LA MECCANICA AVANZATA The system 4 The ORC system is composed of three circuits. out heat source E T EC in 3 5 R 2 6 in cooling water C P out 1 E Evaporator T Turbine EC Electric Generator R Regenerator C Condenser P Pump MechLav LABORATORIO PER LA MECCANICA AVANZATA The system 4 EC The heat source circuit makes it possible to transfer heat from the heat source to the ORC unit. in Usually, the fluid is diathermal oil or pressurized water, but there are applications with direct heat transfer from hot gases. out heat source E T in 3 5 R 2 6 cooling water C P out 1 E Evaporator T Turbine EC Electric Generator R Regenerator C Condenser P Pump MechLav LABORATORIO PER LA MECCANICA AVANZATA The system 4 The ORC unit operates as a completely closed process. out heat source E T EC The pressurized organic working fluid is heated in the evaporator. in 3 5 The fluid then expands in a turbine which is directly connected to a generator. R 2 6 in cooling water C P out 1 E Evaporator T Turbine EC Electric Generator R Regenerator C Condenser P Pump The low enthalpy head in the turbine allows the use of a regenerator to increase the cycle efficiency. Then the fluid enters into the condenser. MechLav LABORATORIO PER LA MECCANICA AVANZATA The system 4 The cooling water circuit is the condensing fluid circuit. out heat source E T EC The low grade heat extracted from the ORC can be used for low temperature CHP applications (e.g. domestic heating). in 3 5 R 2 6 in cooling water C P out 1 E Evaporator T Turbine EC Electric Generator R Regenerator C Condenser P Pump MechLav LABORATORIO PER LA MECCANICA AVANZATA Thermodynamic cycles Two different thermodynamic cycles are considered: • the saturated cycle • the superheated cycle 650 toluene 600 3' Temperature [K] 550 4 500 450 5 3 400 5is 350 2is ≈ 2 300 1 6' 6 250 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Entropy [kJ/(kg K)] MechLav LABORATORIO PER LA MECCANICA AVANZATA Thermodynamic cycles Two different thermodynamic cycles are considered: • the saturated cycle • the superheated cycle 650 toluene 600 4' 3' 3' Temperature [K] 550 4 4 500 5 450 3 5 3 400 5is 5is 350 2is ≈≈ 22 2is 300 1 6' 6 250 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Entropy [kJ/(kg K)] MechLav LABORATORIO PER LA MECCANICA AVANZATA Property calculation The thermodynamic properties of the considered organic fluids are calculated from literature p‐v‐T tables in the case of saturated liquid or vapor. 650 4' 600 Temperature [K] 550 4 3' 500 5 450 5is 3 400 350 2is ≈ 2 300 1 6' 6 250 2.0 2.5 3.0 3.5 Entropy [kJ/(kg K)] 4.0 4.5 5.0 Superheated vapor enthalpy is calculated by starting from the isobaric point on the saturated vapor curve and by using the specific heat at constant pressure. The specific heat at constant pressure is obtained when the molecular structure of the fluid is known and literature correlations named group contribution methods are used. This approach allows the model to be apply to each fluid whenever the p‐v‐T tables and molecule structure are known. MechLav LABORATORIO PER LA MECCANICA AVANZATA Group contribution methods A group contribution method is a technique to estimate and predict thermodynamic and other properties from molecular structures. It is based on the principle that some simple aspects of the structures of chemical components are always the same in many different molecules. This method is used to predict properties of pure components and mixtures by using group or atom properties. This reduces the number of needed data dramatically. Instead of needing to know the properties of thousands or millions compounds, only data for a few of groups have to be known. MechLav LABORATORIO PER LA MECCANICA AVANZATA Group contribution methods CH3 H H For example, the properties of the whole toluene molecule are the superposition of the properties of C C C C C C H H H MechLav LABORATORIO PER LA MECCANICA AVANZATA Group contribution methods CH3 H H For example, the properties of the whole toluene molecule are the superposition of the properties of • 5 aromatic carbons C C C C C C H H H MechLav LABORATORIO PER LA MECCANICA AVANZATA Group contribution methods CH3 H H For example, the properties of the whole toluene molecule are the superposition of the properties of • 5 aromatic carbons C C C C C C H H H MechLav LABORATORIO PER LA MECCANICA AVANZATA Group contribution methods CH3 H H For example, the properties of the whole toluene molecule are the superposition of the properties of • 5 aromatic carbons C C C C C C H H H MechLav LABORATORIO PER LA MECCANICA AVANZATA Group contribution methods CH3 H H For example, the properties of the whole toluene molecule are the superposition of the properties of • 5 aromatic carbons C C C C C C H H H MechLav LABORATORIO PER LA MECCANICA AVANZATA Group contribution methods CH3 H H For example, the properties of the whole toluene molecule are the superposition of the properties of • 5 aromatic carbons C C C C C C H H H MechLav LABORATORIO PER LA MECCANICA AVANZATA Group contribution methods CH3 H H For example, the properties of the whole toluene molecule are the superposition of the properties of • 5 aromatic carbons C C C C C C H • 1 substituted carbon in the aromatic ring H H MechLav LABORATORIO PER LA MECCANICA AVANZATA Group contribution methods CH3 H H For example, the properties of the whole toluene molecule are the superposition of the properties of • 5 aromatic carbons C C C C C C H • 1 substituted carbon in the aromatic ring • 1 methyl group H H MechLav LABORATORIO PER LA MECCANICA AVANZATA Group contribution methods In this work, group contribution methods are used for the calculation of the ideal gas heat capacity only, but these techniques can be used also for the latent heat of vaporization and, so, to generate p‐v‐T tables. Two methods are used for the calculation of the ideal gas heat capacity : • Joback method for halogenated hydrocarbons (e.g. refrigerants) ⎛ ⎞ ⎛ ⎞ 0 Cp (T ) = ⎜⎜ ∑ n jΔ j,a − 37.93⎟⎟ + ⎜⎜ ∑ n j Δ j,b + 0.210⎟⎟ T + ⎝ j ⎠ ⎝ j ⎠ ⎛ ⎞ ⎛ ⎞ + ⎜⎜ ∑ n jΔ j,c − 3.91⋅10−4 ⎟⎟ T 2 + ⎜⎜ ∑ n j Δ j,d + 2.06 ⋅10−7 ⎟⎟ T 3 ⎝ j ⎠ ⎝ j ⎠ • Thinh method for hydrocarbons in general (e.g. alkanes, aromatic hydrocarbons, etc.) [ ( Cp (T ) = ∑nj Aj + Bj,1 exp − Cj,1 / T 0 Dj,1 )− B exp (− C 2 j,2 / T Dj,2 )] j MechLav LABORATORIO PER LA MECCANICA AVANZATA Lee-Kesler method The heat capacity of the real gas is related to the value for the ideal gas state, at the same temperature by means of this equation Cp = Cp0 + ΔCp where ΔCp is a residual heat capacity calculated through the Lee‐Kesler method ΔC p ( ) () ( ) ( ) = ΔC + ω ΔC 0 p 1 p (ΔCp)(0) is the simple fluid contribution and (ΔCp)(1) is the deviation function. This parameters are given as a function of the reduced temperature Tr and pressure Pr, and ω is the acentric factor. MechLav LABORATORIO PER LA MECCANICA AVANZATA The regenerator T5 T T3 The use of high molecular mass organic fluids as working fluids implies an expansion in the turbine with a small enthalpy head, which corresponds to a small change in terms of temperature. T6 T2 ΔTPP,R q Then, it is possible to use superheated steam leaving the turbine to heat the compressed fluid from the pump through the regenerator. This implies a reduction in thermal power which is necessary to provide the evaporation of the organic fluid. The regenerator is a surface counter‐flow heat exchangers . The minimum difference of temperature (pinch point) is located at the inlet liquid side MechLav LABORATORIO PER LA MECCANICA AVANZATA Heat exchangers Temperature profile of evaporator T Tout,HS T3’ T3 ΔTPP,E Tin,HS Ti1,HS Ti1,HS T4 Tout,HS T3’ T3 saturated cycle Tin,HS Ti2,HS T4’ T4 T ΔTPP,E superheated cycle q q Temperature profile of condenser T T6 T6’ Tout,CW T1 Ti,CW ΔTPP,C Tin,CW The external heat sources and sinks are considered non‐isothermal. Evaporator and condenser are considered as surface counter‐flow heat exchangers. q MechLav LABORATORIO PER LA MECCANICA AVANZATA Model implementation The model is implemented in Matlab environment. The structure of the model is traditional. Component parameters (pump and turbine efficiencies, heat exchangers pinch point, etc.) saturated cycle vaporization temperature condensation temperature Component energy and mass balances superheated cycle vaporization pressure turbine inlet temperature stream properties (heat source circuit, cooling water circuit and ORC), heat exchanged, pumping power, turbine specific work, system power output, system efficiency MechLav LABORATORIO PER LA MECCANICA AVANZATA Model analysis Six working fluids (commonly used in ORC applications and widely studied in literature) were considered: four hydrocarbons and two refrigerants. The working fluids considered are Propane (C3H8), Butane (C4H10), Benzene (C6H6), Toluene (C7H8), R134a (C2H2F4), R123 (C2HCl2F3). MW Tc [kg/kmol] [K] 44.1 369.8 pc vc [bar] [m3/kmol] 42.5 0.203 name typology Propane alkane Butane alkane 58.1 425.16 38.0 0.255 Benzene aromatic 78.1 562.2 49.0 0.212 Toluene aromatic 92.1 591.8 41.1 0.316 R134a halogenated 102.0 374.2 40.6 0.198 R123 halogenated 152.9 456.9 36.7 0.287 MechLav LABORATORIO PER LA MECCANICA AVANZATA Model analysis - Vaporization 35 η [%] The beahviour of the model is analyzed by starting from the saturated cycle. 30 25 Propane 20 Butane Benzene 15 By increasing the vaporization temperature the cycle efficiency increases. Different fluids covers different ranges of temperature, and the envelope of the curves define a general trend. Toluene R134a 10 R123 5 340 370 400 430 460 490 520 550 580 Tv [K] 35 Propane η [%] Butane 30 Benzene Toluene 25 R134a Efficiency also increases by increasing the vaporization pressure. Also in this case, each fluid covers a different range of pressure according to its critical properties. R123 20 15 10 5 - 5 10 15 20 25 30 35 40 pv [bar] pk [bar] Tk [K] Propane 10 300 Butane 2.6 300 Benzene 0.14 300 Toluene 0.042 300 R134a 7.0 300 R123 0.98 300 MechLav LABORATORIO PER LA MECCANICA AVANZATA Model analysis - Condensation 35 η [%] Propane 30 Butane Benzene 25 Toluene R134a 20 R123 15 10 5 300 350 400 450 Tk [K] 35 500 Propane η [%] Butane 30 The behavior of the model agrees with literature: by decreasing condensation temperature and pressure, the efficiency of the cycle increases. Benzene 25 Toluene R134a 20 R123 15 10 5 - pv [bar] Tv [K] 5 10 Propane 36.9 362 15 20 Butane 32.1 415 25 pk [bar] Benzene 32.3 529 30 Toluene 26.2 555 R134a 35.8 368 R123 28.0 440 vaporization conditions @ best efficiency MechLav LABORATORIO PER LA MECCANICA AVANZATA Model analysis - Superheating 35 η [%] 30 pr < 0.5 Then it is analyzed the effect of the superheating temperature on the Hirn cycle efficiency for two values of vaporization pressure. 25 Propane 20 Butane Benzene 15 Toluene R134a 10 R123 5 350 400 450 500 550 600 650 700 750 TIT[K] By increasing the superheating temperature the efficiency of the cycle increases both for low and high vaporization pressure. 45 η [%] 40 pr > 0.5 35 30 Propane 25 Butane 20 Benzene 15 Toluene R134a 10 R123 5 350 400 450 500 550 600 650 700 750 TIT [K] MechLav LABORATORIO PER LA MECCANICA AVANZATA Model validation To evaluate the validity of the model, the results of the current model (CM) are compared with the results of a model presented in literature (LM) and the results of a commercial code (CC) widely used for energy system modelling and analysis. A saturated cycle using toluene as the working fluid is considered. Property Tv Tk Tin,CW ηis, turbine ηis, pump ΔTPP,E ΔTPP,R ΔTPP,C Value 548 K 311 K 288 K 0.85 0.65 30 K 10 K 7 K MechLav LABORATORIO PER LA MECCANICA AVANZATA Model validation Pe [kW] η [%] pv [bar] pk [bar] h4‐h5is [kJ/kg] Pt,R [kW] Pt,E [kW] Pt,C [kW] CM LM e [%] CC e [%] 349 31 24.2 0.07 224 234 1140 778 345 31 23.9 0.07 221 222 1124 779 1.2 0.0 1.0 0.0 1.4 5.4 1.4 ‐0.1 339 30 24.3 0.07 221 204 1124 775 2.9 3.3 ‐0.5 0.0 1.4 15 1.4 0.4 The relative error is in general lower than 5 %, with the exception of the thermal power transferred in the regenerator Pt,R. This can be due to the fact that the heat exchange in the regenerator is not constrained by an external fluid, and, therefore, its determination has a higher degree of freedom. MechLav LABORATORIO PER LA MECCANICA AVANZATA Model application To evaluate the capabilities of the model, it is applied to the calculation of the performance of a unit ORC that is positioned as a bottomer of a micro gas turbine (MGT). The exhaust gases from the micro gas turbine are used directly as the heat source for the ORC. The fluid used is the Toluene and the saturated cycle is taken into consideration. The considered micro gas turbine is a Capston C30 characterized by a power output of 30 kW. Property Tin,HS Tout,HS mHS Tin,CW ηis, turbine ηis, pump ΔTPP, E ΔTPP, R ΔTPP, C Value 548 K 413 K 0.31 kg/s 288 K 0.85 0.65 10 K 10 K 10 K MechLav LABORATORIO PER LA MECCANICA AVANZATA Model application Results of model application to MGT‐ORC combined cycle Pe [kW] 10.8 ηcycle [%] 24.57 pv [bar] 5.22 pk [bar] 0.05 h4‐h5is [kJ/kg] 224 Pt,R [kW] 4 Pt, E [kW] 44 Pt,C[kW] 34 It can be highlighted that the MGT‐ORC combined cycle allows to increase the electrical power of the plant from 30 kW to approximately 41 kW and the global efficiency from 26 % to 35 %. This result is in agreement with other analyses presented in literature. MechLav LABORATORIO PER LA MECCANICA AVANZATA Conclusions • A model for the simulation of saturated and superheated organic Rankine cycles was developed. The model is based on thermodynamic tables for the determination of saturated liquids and vapors while it uses thermodynamic correlation to calculate the specific heat. The structure of the model allows the simulation of any fluid whenever p‐v‐T tables and molecule structure are known. • A sensitivity analysis on the main process parameters was performed. The model proved to capture the physics of the phenomena . • The model is validated by comparing it with model found in literature and commercial software. The model proved to be capable of correctly simulating an organic Rankine cycle with relative errors generally lower than 5 %. • Finally, the model was applied to a micro gas turbine/ORC combined cycle. MechLav LABORATORIO PER LA MECCANICA AVANZATA Future developments The model is corrently used in the optimization of a ThermoPhotoVoltaic generator and an Organic Rankine Cycle integrated system. A preliminary analysis is presented in A. De Pascale, C. Ferrari, F. Melino, M. Morini, M. Pinelli, 2011, “Integration between a Thermo‐Photo‐Voltaic generator and an Organic Rankine Cycle”, Proc. of the 3rd International Conference on Applied Energy, pp. 2571‐86 MechLav LABORATORIO PER LA MECCANICA AVANZATA Questions? Mirko Morini, PhD [email protected] phone/FAX +39 0532 974966 MechLav LABORATORIO PER LA MECCANICA AVANZATA