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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.
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
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
R Regenerator
C Condenser
P Pump
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
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.
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
R Regenerator
C Condenser
P Pump
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)]
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)]
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.
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.
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
CH3
H
H
• 5 aromatic carbons
C
C
C
C
C
C
H
H
H
CH3
H
H
C
C
C
C
C
C
H
H
H
CH3
H
H
C
C
C
C
C
C
H
H
H
CH3
H
H
C
C
C
C
C
C
H
H
H
CH3
H
H
C
C
C
C
C
C
H
H
H
CH3
H
H
C
C
C
C
C
C
H
• 1 substituted carbon in the aromatic ring
H
H
CH3
H
H
C
C
C
C
C
C
H
• 1 substituted carbon in the aromatic ring
• 1 methyl group
H
H
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
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.
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
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
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
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
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
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]
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
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.
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
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.
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.
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

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