Development of a model for the simulation of Organic Rankine Cycles based on group contribution techniques

Transcription

1 ASME Turbo Expo Vancouver, June Development of a model for the simulation of Organic Rankine ycles based on group contribution techniques Enrico Saverio Barbieri Engineering Department University of Ferrara Mirko Morini Technopole of Ferrara Michele Pinelli Engineering Department University of Ferrara LABORATORIO PER LA MEANIA AVANZATA

2 Introduction Many industrial sectors and applications are characterized by the availability of low enthalpy thermal sources with temperatures lower than 400. 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 ycle (OR) 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 OR systems based on techniques for the estimation of thermodynamic properties from molecular structures can be a useful tool for OR performance optimization. LABORATORIO PER LA MEANIA AVANZATA

3 The system heat source out E 4 T E The OR system is composed of three circuits. in P 3 R in out cooling water E Evaporator T Turbine E Electric Generator R Regenerator ondenser P Pump LABORATORIO PER LA MEANIA AVANZATA

4 The system heat source out in P 4 E 3 R 2 1 T 6 5 E in out cooling water The heat source circuit makes it possible to transfer heat from the heat source to the OR unit. Usually, the fluid is diathermal oil or pressurized water, but there are applications with direct heat transfer from hot gases. E Evaporator T Turbine E Electric Generator R Regenerator ondenser P Pump LABORATORIO PER LA MEANIA AVANZATA

5 The system heat source out in E 4 T E The OR unit operates as a completely closed process. The pressurized organic working fluid is heated in the evaporator. E Evaporator T Turbine E Electric Generator R Regenerator ondenser P Pump P 3 R in out cooling water The fluid then expands in a turbine which is directly connected to a generator. 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. LABORATORIO PER LA MEANIA AVANZATA

6 The system heat source out in P 4 E 3 R 2 1 T 6 5 E in out cooling water The cooling water circuit is the condensing fluid circuit. The low grade heat extracted from the OR can be used for low temperature P applications (e.g. domestic heating). E Evaporator T Turbine E Electric Generator R Regenerator ondenser P Pump LABORATORIO PER LA MEANIA AVANZATA

7 Thermodynamic cycles Two different thermodynamic cycles are considered: the saturated cycle the superheated cycle toluene 550 3' 4 Temperature [K] is 2 1 6' 6 5is Entropy [kj/(kg K)] LABORATORIO PER LA MEANIA AVANZATA

8 Thermodynamic cycles Two different thermodynamic cycles are considered: the saturated cycle the superheated cycle toluene 4' Temperature [K] ' 3' 3 3 2is 2 1 6' is 5is Entropy [kj/(kg K)] LABORATORIO PER LA MEANIA AVANZATA

9 Property calculation Temperature [K] ' 550 3' is is 2 1 6' Entropy [kj/(kg K)] The thermodynamic properties of the considered organic fluids are calculated from literature p v T tables in the case of saturated liquid or vapor. 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. LABORATORIO PER LA MEANIA AVANZATA

10 Group contribution methods Agroup 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. LABORATORIO PER LA MEANIA AVANZATA

11 Group contribution methods 3 For example, the properties of the whole toluene molecule are the superposition of the properties of LABORATORIO PER LA MEANIA AVANZATA

12 Group contribution methods 3 For example, the properties of the whole toluene molecule are the superposition of the properties of 5 aromatic carbons LABORATORIO PER LA MEANIA AVANZATA

17 Group contribution methods 3 For example, the properties of the whole toluene molecule are the superposition of the properties of 5 aromatic carbons 1 substituted carbon in the aromatic ring LABORATORIO PER LA MEANIA AVANZATA

18 Group contribution methods 3 For example, the properties of the whole toluene molecule are the superposition of the properties of 5 aromatic carbons 1 substituted carbon in the aromatic ring 1 methyl group LABORATORIO PER LA MEANIA AVANZATA

19 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 p + ( T) j = n Δ j j,c j n Δ j j,a T 2 + j j n Δ j n Δ j j,b j,d T T 3 Thinh method for hydrocarbons in general (e.g. alkanes, aromatic hydrocarbons, etc.) 0 p Dj,1 Dj,2 ( T) = n [ A + B exp ( / T ) B exp ( / T )] j j j j,1 j,1 2 j,2 LABORATORIO PER LA MEANIA AVANZATA

20 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 p = 0 p + Δ p where Δ p is a residual heat capacity calculated through the Lee Kesler method Δ p = ( ) ( 0 Δ ) + ω ( Δ ) ( 1) p p (Δ p ) (0) is the simple fluid contribution and (Δ p ) (1) is the deviation function. This parameters are given as a function of the reduced temperature T r and pressure P r, and ω is the acentric factor. LABORATORIO PER LA MEANIA AVANZATA

21 The regenerator T T 5 T 3 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. T 6 T 2 ΔT PP,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 LABORATORIO PER LA MEANIA AVANZATA

22 eat exchangers Temperature profile of evaporator T T in,s T i1,s T T i1,s T in,s T i2,s T out,s T out,s T 4 T 3 ΔTPP,E T 4 T 3 ΔT PP,E T 4 T 3 saturated cycle T 3 superheated cycle Temperature profile of condenser q q T T 1 T 6 T 6 The external heat sources and sinks are considered non isothermal. T i,w T in,w ΔT PP, T out,w Evaporator and condenser are considered as surface counter flow heat exchangers. q LABORATORIO PER LA MEANIA AVANZATA

23 Model implementation The model is implemented in Matlab environment. The structure of the model is traditional. omponent parameters (pump and turbine efficiencies, heat exchangers pinch point, etc.) saturated cycle condensation temperature omponent energy and mass balances vaporization temperature superheated cycle vaporization pressure turbine inlet temperature stream properties (heat source circuit, cooling water circuit and OR), heat exchanged, pumping power, turbine specific work, system power output, system efficiency LABORATORIO PER LA MEANIA AVANZATA

24 Model analysis Six working fluids (commonly used in OR applications and widely studied in literature) were considered: four hydrocarbons and two refrigerants. The working fluids considered are Propane ( 3 8 ), Butane ( 4 10 ), Benzene ( 6 6 ), Toluene ( 7 8 ), R134a ( 2 2 F 4 ), R123 ( 2 l 2 F 3 ). name typology MW [kg/kmol] T c [K] p c [bar] v c [m 3 /kmol] Propane alkane Butane alkane Benzene aromatic Toluene aromatic R134a halogenated R123 halogenated LABORATORIO PER LA MEANIA AVANZATA

25 Model analysis - Vaporization 35 η [%] Propane 20 Butane 15 Benzene Toluene 10 R134a R T v [K] 35 η [%] Propane Butane Benzene Toluene R134a R p v [bar] The beahviour of the model is analyzed by starting from the saturated cycle. 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. 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. Propane Butane Benzene Toluene R134a R123 p k [bar] T k [K] LABORATORIO PER LA MEANIA AVANZATA

26 Model analysis - ondensation 35 η [%] Propane Butane Benzene Toluene R134a R T k [K] η [%] Propane 30 Butane Benzene 25 Toluene R134a 20 R123 The behavior of the model agrees with literature: by decreasing condensation temperature and pressure, the efficiency of the cycle increases p k [bar] Propane Butane Benzene Toluene R134a R123 p v [bar] T v [K] vaporization best efficiency LABORATORIO PER LA MEANIA AVANZATA

27 Model analysis - Superheating 35 η [%] η [%] p r < 0.5 Propane Butane Benzene Toluene R134a R TIT[K] p r > 0.5 Then it is analyzed the effect of the superheating temperature on the irn cycle efficiency for two values of vaporization pressure. By increasing the superheating temperature the efficiency of the cycle increases both for low and high vaporization pressure Propane Butane Benzene Toluene 15 R134a 10 R TIT [K] LABORATORIO PER LA MEANIA AVANZATA

28 Model validation To evaluate the validity of the model, the results of the current model (M) are compared with the results of a model presented in literature (LM) and the results of a commercial code () widely used for energy system modelling and analysis. A saturated cycle using toluene as the working fluid is considered. Property Value T v T k T in,w 548 K 311 K 288 K η is, turbine 0.85 η is, pump 0.65 ΔT PP,E ΔT PP,R ΔT PP, 30 K 10 K 7 K LABORATORIO PER LA MEANIA AVANZATA

29 Model validation M The relative error is in general lower than 5 %, with the exception of the thermal power transferred in the regenerator P t,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. LM e [%] e [%] P e [kw] η [%] p v [bar] p k [bar] h 4 h 5is [kj/kg] P t,r [kw] P t,e [kw] P t, [kw] LABORATORIO PER LA MEANIA AVANZATA

30 Model application To evaluate the capabilities of the model, it is applied to the calculation of the performance of a unit OR 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 OR. The fluid used is the Toluene and the saturated cycle is taken into consideration. The considered micro gas turbine is a apston 30 characterized by a power output of 30 kw. Property Value T in,s T out,s m S T in,w 548 K 413 K 0.31 kg/s 288 K η is, turbine 0.85 η is, pump 0.65 ΔT PP, E ΔT PP, R ΔT PP, 10 K 10 K 10 K LABORATORIO PER LA MEANIA AVANZATA

31 Model application Results of model application to MGT OR combined cycle P e [kw] 10.8 η cycle [%] p v [bar] 5.22 p k [bar] 0.05 h 4 h 5is [kj/kg] 224 P t,r [kw] 4 P t, E [kw] 44 P t, [kw] 34 It can be highlighted that the MGT OR 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. LABORATORIO PER LA MEANIA AVANZATA

32 onclusions 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/or combined cycle. LABORATORIO PER LA MEANIA AVANZATA

33 Future developments The model is corrently used in the optimization of a ThermoPhotoVoltaic generator and an Organic Rankine ycle integrated system. A preliminary analysis is presented in A. De Pascale,. Ferrari, F. Melino, M. Morini, M. Pinelli, 2011, Integration between a Thermo Photo Voltaic generator and an Organic Rankine ycle, Proc. of the 3 rd International onference on Applied Energy, pp LABORATORIO PER LA MEANIA AVANZATA

34 Questions? Mirko Morini, PhD phone/fax LABORATORIO PER LA MEANIA AVANZATA