Accepted Manuscript Exergy and Exergoeconomic analysis and optimization of a solar double pressure organic Rankine cycle Milad Ashouri, Mohammad H. Ahmadi, S. Mohsen Pourkiaei, Fatemeh Razi Astaraei, Roghaye Ghasempour, Tingzhen Ming, Javid Haj Hemati PII: DOI: Reference:
S24519049(17)301981 https://doi.org/10.1016/j.tsep.2017.10.002 TSEP 66
To appear in:
Thermal Science and Engineering Progress
Received Date: Revised Date: Accepted Date:
10 July 2017 2 October 2017 3 October 2017
Please cite this article as: M. Ashouri, M.H. Ahmadi, S.M. Pourkiaei, F.R. Astaraei, R. Ghasempour, T. Ming, J.H. Hemati, Exergy and Exergoeconomic analysis and optimization of a solar double pressure organic Rankine cycle, Thermal Science and Engineering Progress (2017), doi: https://doi.org/10.1016/j.tsep.2017.10.002
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Exergy and Exergoeconomic analysis and optimization of a solar double pressure organic Rankine cycle Milad Ashouri1, Mohammad H. Ahmadi2*,S.Mohsen Pourkiaei1 , Fatemeh Razi Astaraei1, Roghaye Ghasempour1, Tingzhen Ming3, javid Haj Hemati1
1
Department of Renewable Energies, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran 2
Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran 3
School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan 430070, P.R.China Email address:
[email protected] Abstract: This study presents an exergoeconomic analysis and optimization of a double pressure organic Rankine cycle coupled with a solar collector via a thermal storage tank. Numerical analysis has been done to perform the exergetic analysis along with economic analysis. The performance of the system was examined during a day. Results showed that the system is capable of generating stable power during the day with a solar fraction of 100%. In nights and overcasts, the system can still generate power with the help of storage tank and an auxiliary heater. A parametric analysis examined the effect of key parameters on the system performance including exergy efficiency and product cost rate. The effective parameters included turbine inlet pressure and temperature. Exergoeconomic criteria revealed that solar collector has the most value of + which is due to both high exergy destruction and high investment costs of the collector. Following the collector, the storage tank, condenser, turbine, recuperator and evaporators had the highest destruction. To perform the optimization process, two objective functions including exergy efficiency and product cost rate were considered. Ten decision variable including inlet temperature and pressure of the turbines, heat exchanger minimum temperature differences and the mass flow rate of solar collector and tank and pressure of condenser were chosen according to the parametric analysis. Also, with the aid of a reliable decisionmaking technique called TOPSIS method, the optimal point was selected among the Pareto frontier of the genetic algorithm. Results show that system can reach the efficiency of 22.7% and product cost rate of 2.66 million dollars per year. Keywords: Exergoeconomic; Organic Rankine Cycle; Solar collector; Optimization, decision making.
1. Introduction Different researchers studied the thermodynamic cycle. Among them, Genetic Algorithms (GAs) have been utilized for optimizing the performance of Atkinson engine by Ahmadi et al [1]. Solar powered cycles have gained lots of attention. According to normalized power and thermal efficiency, a solar multistep irreversible Brayton cycle has been optimized by Ahmadi et al [2]. In their study, a solar dish Stirling for maximizing thermal efficiency and power was designed. The economic parameter is considered in their study by performing a thermoeconomic maximization design process [3,4]. Organic Rankine cycles (ORCs) follow fundamental rules of typical Rankine cycle working with water; however, it is popular due to some advantages over water Rankine cycle. This kind of cycles can work under low temperature and pressure and are showing better performance comparing to typical Rankine cycle. This advantage is considerable in comparison with water Rankine cycle specifically from lowgrade heat resources because of including various hydrocarbons and refrigerants. Different outputs can concur by utilizing proper working fluids based on a range of available heat source temperatures. In addition, simplicity and low cost can be obtained through working without feedwater heaters and multistage turbines. Among lots of sources of thermal energy are solar parabolic trough collectors; however, they only suitable for generating electricity in the scale of kilowatts to few megawatts. They are also reliable in rural areas or places close to factories because of evading from network connectivity which imposes an extra cost. As explained earlier, organic fluids in ORCs are categorized based on hydrocarbons and refrigerants. Among them, there are some dry fluids demonstrating positive slope in the TS diagram in the saturation vapor area. This advantage helps to protect turbine because of not superheating utilizing some organic fluids. According to this study, performance and efficiency of the cycle are studied through comparison of different dry organic fluids with and without superheating and recuperation. Therefore, this study helps us to choose a condition according to our demands. The ORC is studied by many researchers. A supercritical ORC based on lowgrade heat was analyzed and optimized by Le et al [5]. Basic and regenerative ORC are studied in their investigation. Accordingly, R1234ze demonstrated the best performance. Rayegam and Tao [6] introduced a methodology for finding the suitable working fluids in a solar ORC. They illustrated that 11 working fluids under low to mediumtemperature solar collectors are appropriate. Wang et al [7] performed studies on ORC together with solar collector containing a thermal storage system during an entire day. A solarthermal ORC with different working fluids were designed and optimized by McMahan [8]. An optimization and sizing methodology for a heat exchanger in a small scale solardriven ORC was presented by Quoilin et al [9] utilizing pinch and pressure drop. They also optimized the system based on turbine input pressure and evaporator temperature. Different organic fluids were compared by Ferrara et al [10] in a 20 kWe solar plant. They selected acetone as the best organic fluid with supercritical pressure. A thermodynamic and economic analysis was conducted by Le et al [11] for a
subcritical ORC utilizing zeotropic working fluids and water at 1508C. In their study, the best exergetic performance and the lowest cost of electricity were illustrated by Pentane. Moreover, the working fluid mixture with the minimum temperature glide led to the bestmaximized exergy efficiency. In addition, higher thermodynamic performance is obtained through pure fluidbased ORCs for maximizing exergy efficiency. A multiobjective optimization of ORC considering waste heat was performed by Wang et al [12]. They set the exergy efficiency and total capital costs of the system as the objectives for optimization. In their optimization process, turbine inlet temperature, turbine inlet pressure, pinch, and approach point of the heat exchanger were chosen as key parameters of the system. An exergy analysis of a parabolic trough solar collector on a steam Rankine cycle and an ORC bottoming cycle as the condenser was presented by AlSulaiman [13]. Accordingly, the main sources of the destruction are trough collectors and the vapor generator. Notably, the exergy efficiency is increased by bottoming cycle in comparison with a steam Rankine cycle without bottoming cycle. The abovementioned works are concentrated on one kind of ORCs. In this paper, thermoeconomic analysis on a Solar
ORC is investigated, as it has not been studied in past researches with such configuration. The goal of this study is to optimize the Organic solar Rankine cycle by considering the exergetic and thermoeconomic functions as the objectives with varying the key parameters of the cycle.
2. Methodology Fig.1 depicts the schematic of the cycle. In this study, the analysis is done by a written computing code and the thermoeconomic model is designed by exergoeconomic and optimization. The economic and exergetic optimization of the ORC is done by assuming that the needed heat of the cycle is provided by the sun collectors. The optimized performance condition is presented at last, and also thermodynamic analysis on the whole cycle is done to determine the effects of main parameters of the cycle. This analysis helps to determine the importance of the cycle parameters. In this study, Genetic Algorithm method of optimization is utilized for multiobjective optimization.
Figure1. Scheme of the cycle
2.1.Exergy Analysis In exergy analysis, by combining mass and conservation of energy equations with the Second Law of Thermodynamics, we make economic design and the optimization of the energy systems possible. By the exergy analysis of the subsystems and determining the exergy losses of the defined system, and economic design, system efficiency will increase and get closer to the ideal value. This information could not be provided by any other method such as energy analysis or the first law. This method is also very useful for increasing the whole efficiency of the system, economic performance of the system and comparison of the performance of different systems. Analysis of the Thermodynamic systems by the second law of thermodynamics is called Exergy analysis. By this law in any real process, the created entropy is related to exergy destruction. In this type of analysis, the goals are, identifying the location, type and amount of the entropy within different thermodynamic processes and effective parameters on creating these irreversibilities. This will provide the performance assessment of the system components and exploration of the efficiency increasing methods [14,15]. 2.1.1. Exergy Concept In thermodynamic and energy studies, exergy is called the ability or the maximum efficient work which is provided by a certain amount of the available energy. In other words, exergy is a part of the energy which is able to be transferred to mechanical work. The useless part of the energy is called Anergy [16]. Talking about regular energies, if the intended process be reversible (Entropy Creation equal to zero) the amount of anergy will be equal to zero. Hence the amount of exergy is the definer of the quality of the exergy. The balance of the exergy is as same as that of the energy in studying a heating system. The only difference is that the balance of the energy expresses the conservation of the energy and the balance of the exergy contains expressing terms of quality of the energy. The exergy expresses the diversion of the system from the balance state. Exergy could be count as a common property of the system and the environment. Exergy expresses the quality and value of the energy, thermodynamically and economically respectively [17]. 2.2.Restriction Restrictions which were considered in this study for simplification of the problem are as follows (some may be far from ideal state): • • • • • •
Steadystate system modeling Complete mixing of oil in the tank Constant pressure drop for different cycle parts equal to 5% Different cycle parts except heat storage tank and collector are adiabatic. Saturated liquid condenser outlet 80% efficiency of pump and turbine
• Saturated liquid economizer outlet in defined pressure • Onedimensional modeling for sun collector • No significant pressure loss in the sun collector instruments 2.3.Thermodynamic model of the sun collector The chosen collector for this research is a parabolic type due to its higher temperature range than flat collectors. The inner oil of the collector is a commercial one named Terminal. The heat capacity of the oil which is utilized is presented as [18]: Cp =
0.002414T 2
T T T + 5.9591 × 10 −6 × ( ) 2 − 2.9879 × 10−8 × ( )3 + 4.4172 × 10 −11 × ( ) 4 + 1.498 2 2 2
The absorbed radiation by the collector is [19,20]: Do ) S = I b ρ Rb γ (τα )b + I b R b (τα )b ( (2) W a − Do In this equation, the first term is related to the absorbed radiation by the tube and the second term is related to the reflected energy by the collector.
Rb in the equation 2 is presented as: cos θ sin La sin δ s + cos La cos δ s cosh s In Which: Rb =
(3)
sin δs = 23.45cos[0.986(N + 284)]
(4)
N is the number of the days and is counted from first of January. hs is the hour angle which is calculated by the rotational motion of the earth [21]. Hence 1 hour equals to 15 degrees. La is the latitude, according to the city selected Eshtehard, which the data of its radiation, temperature, and air velocity were available. Useful energy absorbed by the tube is calculated by the law of conservation of energy:
Qu = m f C P (T f
,out
− T f ,in )
(5)
f are the heat where the input and output temperatures of the tube are specified. Cp and m capacity and the flow of the oil fluid in the tube. The useful absorbed heat, based on the heat loss is also calculated as [22]: S − U L (T f ,in − T a ) ) Qu = FR (W a − D o ) L ( C W − Do C = a π Do m f C p − F ′π Do LU L (1 − exp( )) FR = π Do LU L m f C p
(6) (7) (8)
F′ =
1
1 D (9) UL[ + o ] U L D i hf FR is the ratio of heat transfer in the tube to the maximum heat transfer in which the whole temperature of the tube was equal to input temperature of the tube. Qu = (W a − D o ) Ls − U L π Do L (T P −T a )
(10)
UL is calculated by the heat transfer between the outer surface of the tube and the environment. Tp is the bulk temperature of the tube. Other parameters of the equation 10 are related to the dimensions of the parabolic collector. The heat transfer is assumed to be steady state and one dimensional. Tube and its cover are assumed to be perfectly concentric. Figure 2 depicts the model designed for the collector. The energy balance equations are solved based on the balance between the tube and the cover. The equations are repeated in a loop in MATLAB software as far as the energy transferred from the tube to the cover becomes equal to the energy transfers from the cover to the environment. In the next step amount of the useful heat of the collector is been calculated and temperatures of different points such as output temperature, inner and outer temperatures of the cover and the tube are achieved.
Figure.2 The diagram of the modeled tube in the sun collector
The network of the governing equations of the collector, considering onedimensional perpendicular heat transfer of the tube is shown in Figure 3.
Figure.3 Schematic of thermal resistance
Radiation heat transfer and energy balance equations which are used to balance the energy inside the tube are presented in Table 1.
Table.1. Radiation heat transfer and energy balance equations
Heat transfer type Heat transfer equation 12
Convection
q12conv = h1D 2π (T 2 −T1 ) q23cond =
32
Conduction
2π k 23 (T 2 − T 3 ) ln( D 3 D 2 )
k 23 = (0.013)T 23 + 15.2 for tube material [1]
σπ D 3 (T 34 −T 44 ) 1 (1 − ε 4 )D 3 + ε3 ε 4D 4
34
Radiation
q34rad =
34
Convection
q34conv =
2.425k 34 (T 3 −T 4 )(Pr RaD 3 (0.861 + Pr34 ))1/4 (1 + (D 3 D 4 )3/5 )5/4
q45cond =
2π k 45 (T 4 − T 5 ) ln( D 5 / D 4 )
45
Conduction
k 45 = 1.04 for glass [2] 56
Convection
q56conv = h56D5π (T 5 −T 6 )
57
Radiation
q57 rad = σπ D 5ε 5 (T 54 −T 74 )
2.4.Heat storage tank A complete mixing tank is used to model the reservoir tank. Figure 4 shows the schematic of the tank. In the process, the useful energy from collectors enters the reservoir tank and flows to the power system. Hence as the system is storing the heat, it is also feeding the energy to the power system. Also, some energy from the tank to the surrounding environment is given. It is assumed that in a definite time range, the tank temperature is constant and it will be counted by determining input and output heat flows to the tank [23]. As the sun radiation data were available in onehour time ranges, the time range in this study is chosen equal to one hour. The tank temperature in each hour is assumed to be constant.
Figure.4 Schematic of a thermal storage tank
dT ( m C p )w = Qu − Q l − Q loss dt
(11)
T is the tank and evaporator input temperature. Qu is the useful captured heat from the sun
is the input heat flow to the organic Rankine cycle and collector. Q l
Qloss is the heat loss of
the tank and is calculated by:
Qloss = (UA )t (Ts −Tamb )
(12)
(UA)t is related to the heat transfer coefficient of the tank which is dependent on tank dimensions and its body material. It is normally equal to 1113, but the accurate value could also be calculated [24]. By using equations 11 and 12 simultaneously in order to calculate the new temperature, we have: ∆t [Qu − Q l − Q loss ] (13) (mCp )w Where T s ,new is the new temperature of the tank. ∆t is equal to 1 hour. It is assumed that the T s ,new = T s +
heat losses in onehour time range are constant.
2.5.Double pressure Organic Rankine cycle with recovery As shown in Figure 1, the ORC with two stages and a recovery is investigated in this study. The balance of energy is the base of the modeling, as each of the cycle part is assumed to be a control volume. The assumptions are as below:
• The cycle is operating in a steady state condition. • A constant pressure drops for components of the cycle such as evaporators, condenser, and recovery are assumed. This amount is equal to 5%. • Cycle components other than the storage tank and collector are adiabatic and have no heat transfer with the environment. • Condenser output is considered to be saturated liquid. • Pump and turbine efficiency of 80 percent is considered. • Economizer outlet is assumed to be saturated liquid at the desired pressure. The general form of energy balance is [25]: n
n
i =1
i =1
Q − W = ∑ m o ho − ∑ m i hi
(14)
The mass balance equation is as follows: n
n
i =1
i =1
∑ m o = ∑ m i
(15)
After calculating Enthalpies and flows in a different point of the cycle to determine the heat transfer of each part, we have: Evaporators and recovery
Qeva = m i (ho − hi )
(16)
Turbine:
WT ,a hi − ho,a ηT = = WT ,s hi − ho ,s
(17)
The output work of high and lowpressure turbines: n
n
i =1
i =1
WT = ∑ m i hi − ∑ m o ho
(18)
We also have for the condenser [29,30]: n
n
i =1
i =1
Q Cond = ∑ m i hi − ∑ m o ho = UAcond ∆TLMTD In this regard, the logarithmic temperature difference is calculated from the following equation:
(19)
∆TLMTD =
∆T1 − ∆T2 ∆T log( 1 ) ∆T2
(20)
These relationships for each component of the system are applied to all enthalpy, entropy, temperature, and pressures are determined. After that by exergy analysis equations, all exergies are computable. To obtain a cost estimate of all the converters were supposed tubular shell. In economic relations, it is necessary to calculate the heat transfer area. For this reason, UA for each heat exchanger should be calculated from equations 18, 19, 20. Then shall U coefficient of each converter is obtained by heat transfer relations of the tube and shell. Dividing these two values provide heat transfer surface of heat exchangers. Relationships and details required to obtain the heat transfer coefficient are in [26]. 3. Thermoeconomic Analysis According to the definition in [3], thermoeconomic analysis mixes economic and thermodynamic analysis by applying the concept of cost (economic property), to exergy. The exergy is and adequate is a thermodynamic property to which we set the cost because it accounts for the energy quality. The exergy of a thermodynamic flow is the minimum amount of work needed for its production, from the reference environment. Once the reference environment is defined, exergy is a thermodynamic function of state which makes it possible to formulate the equivalence between different energy and/or matter flow streams of a plant. Two flows are thermodynamically equivalent, that is, it is theoretically possible to get one from the other without additional consumption of energy resources if, and only if, they have the same exergy. Exergetic efficiency compares a real process to an ideal process, i.e. reversible, of the same type. An exergy analysis locates and quantifies irreversibilities in a process. This analysis is essential in the design and operation of costly systems, because we
take into account both the efficiency and cost of the system. Exergoeconomic is actually a cost minimizing tool by exergy. On the other hand, Exergoeconomic is known as a powerful tool to understand the relationships between thermodynamic and economy or behavior of a system by the economic view. To assess the causes of the low efficiency of energy systems some methods have been developed which need to know the costs of nonproductivity. Having the knowledge of these costs is very useful to improve the economic efficiency of the system and in fact leads to cost reduction of the final products produced by the system [27]. In this type of analysis, using economic concepts with definitions of thermodynamics and by giving economic value to the Exergy, the balance between investment costs and exergyenergy flow costs will be established in a way which production of goods and services of thermodynamic cycle cost at a minimum price. For this reason, the LCOE method which is developed by ERRI in 1993 will be utilized. In this method, any costs associated with a project will be counted and a required minimum return of capital is included. Based on the overall investment cost and for economic, financial, operational and commercial input parameters assumptions, total income needs will be calculated annually. At last, calculated nonuniform amounts of annual fees related to investment, performance (excluding fuel costs), and maintenance and system fuel costs will be leveled and balanced. 4. Exergoeconomic Analysis
In exergoeconomic analysis the cost of any product that is produced by a multiproduct system is calculated separately. Price forming processes and streaming costs are determined in the system. All the parameters are optimized independently in a separate component. The cost of the entire system is minimized. Due to changes in annual costs when designing a heating system from the economic point of view, we must evaluate our way of leveling costs. Hence cost balance is needed in exergy balance [27].
= , , + +
(21)
Where the Z parameter denotes the costs (capital and investment costs). C denotes the costs associated to flow of exergy in and out of the system. For a control volume, fuel is the source of exergy which is consumed to generate the product and is different with actual fuel, such as natural gas, diesel, etc. Also, the product is the desired result generated by using the fuel [4]. This equation is written for all components of the system. More detail are described by the following section. 4.1. Calculation of Annual Total Revenue Requirement Annual Total Revenue Requirement is the amount of income in a year that the revenue must be obtained through the sale of goods in such a way that all costs of the system be compensated during the operation in the same year. These costs are consisting of two parts: • •
Carrying Charges (CC) Expenses
In calculating leveled costs, recovery factor has a great importance which is: i (1 + i ) (22) (1 + i ) − 1 In order to have a single basis of calculation nonuniform costs should be leveled. In exergoeconomic a parameter named ratio of costs refers to each flow. For each control volume cost balance is as follows: CRF =
+ + = +
(23)
= !
(24)
Z parameter is also defined as: =
. #$. % &
(25)
Where the maintenance factor φ is equal to 1.06. H the working hours of the system is considered to be 7446 hours. C is the investment cost which is calculated for each component by thermodynamic analysis of the before mentioned. Details of these relationships are shown in the table below.
Table2. Exergoeconomic equations of the Organic Rankine cycle based on solar collector Component SolarCollector [5]
' = (150 + 90)+'
Storage Tank [5]
, = 35$/01ℎ
Economizer_HP
3' _5 = 45.7+3' 5
Evaporator_HP
389_5 = 34.9+3895
Superheater_HP
,:;5 = 96.2+,:;5
Economizer_LP
3' _> = 45.7+3' >
Evaporator_LP
389_> = 34.9+389>
Superheater_LP
,:;> = 96.2+,:;>
Pump1[6]
:?;@ = 35401:?;@ A.B@
Pump2
:?;C = 35401:?;C A.B@
Auxiliary Heater[6]
Recuperator[6]
D:E = 28$/01ℎ
G3' = (+G3' /0.093)A.BH
' I = 1773JK93L
Condenser [6]
Z ٌ◌
M:LN3 =
[email protected] UVW(X)YA.@BBO(UVW())
Turbine[6]
The next step to exergoeconomic analysis is to apply the equations 2324 for each of the components of the cycle and solve the equations in order to obtain Cs. Then through the equation 25 and Exergy Analysis, any flow rate and subsequently the cost of each component would provide fuel prices and products rate. The equations required to solve a system of equations are given below: Table3. Exergoeconomic equations of the solar Rankine cycle components component
Cost rate balance
Auxiliary equation
Solar collector
+ [: + ' = CS CT
[: =0
Storage Tank
+ H + [ = @ + CT + >,[ CS
@ CT = = !@ !CT >,[
Auxiliary Heater
= C @ + ^_ + ^_
= ^_
Superheater_HP
+ ,:;5 = T + @Q C + @H
C T = !C !T
Evaporator_HP
+ 3895 = S + @H T + @B
T S = !T !S
Economizer_HP
+ 3' 5 = P + @B S + @O
P S = !P !S
Superheater_LP
+ ,:;> P + @T = O + @S
P O = !P !O
Evaporator_LP
+ 389> = B + @T O + @C
O B = !O !B
\ ]>,[
\ !^_
+ 3' > = H + @@ B + CB
B H = !B !H
Pump2
+ K;:?;C + K;:?;C = @O @P
,;:?;C ,M:L5 = 1 ;:?;C 1M:L5
Pump1
Q + K;:?;@ + K;:?;@ = @A
,;:?;C ,:?;@ = 1 ;:?;C 1:?;@
Economizer_LP
= @C + @P @@
Separator
Turbine_HP
+ M5 = CA + ,M5 @Q
@Q CA = !@Q !CA
Turbine_LP
+ M> = CC + ,M> C@
C@ CC = !C@ !CC
+ CA = C@ @S
Mixer
Recuperator
+ @A + G3' = CB + CH CC
Condenser
+ CP + I = Q + CO CH
CC CH = !CC !CH CH Q = !CH !Q =0 CP
For comparison exergoeconomic performance of the system, various parameters are defined. The average cost of fuel per kilowatt for each component Exergy is defined as follows: ,`
= =
,` ! ,` ,`
(26)
!,` By combining the above equations, the relative cost difference is equal to: ,`
a` =
,`
− ,`
,`
(27)
(28)
This parameter shows the difference between the cost of production and the product which is due to the exergy destruction and investment. The cost flow rate of the exergy destruction is equal to: ,`
a` =
−
,`
(29)
,`
Exergoeconomic factors that reflect the initial cost impact of a component to its exergy damage is calculated as follows [29,31]: b` = a` =
`
(30)
` + ,` − ,` ,`
(31)
,`
5. Result and Discussion
The designed cycle was run for a complete 24hour time range. Tank and collector temperature profile, absorbed solar radiation by the collector and the useful heat transferred to the collector fluid (heat oil) is calculated. For the sensitivity analysis on effective parameters of the cycle and also performing the optimization, a constant solar radiation working condition was selected as a design point. Other working points of the cycle are off design conditions. It should be noticed that this is exactly the same as real fossil or renewable energy plant working condition. The results of the study are presented in figures and tables. 5.1 System performance during the day
In this part, the thermoeconomic simulation results of the double pressure with recovery organic Rankine cycle of a parabolic solar collector are presented. First, simulation of the system was done for a full day of Eshtehard city based on weather data and then the system was optimized for designed conditions.
T_St
350
T_o
Q_u
S_abs
9 8
300
Temperature (ºC)
6
200
5
150
4 3
100 2 50
1
0
0 0
5
10
15
Time (hr)
20
25
Sabs (MW)/ Qu(MW)
7 250
Figure.5 Changes of the thermal storage tank parameters with temperature during the day
Figure 5 shows the changes of tanks and solar collector parameters throughout a day. As the figure shows, collector outlet temperature of from about 7 am rises with receiving useful radiant energy from the sun by the collector. This useful energy gets into a thermal storage tank and leads to increase of the tank temperature. As the figure depicts, tank temperature is always lower than collector output temperature and the tank temperature is used for the Rankine cycle. Despite a reduction in delivered temperature to the system with storage tank, the heat will continuously be delivered to Rankine power generation system during the day. If it was no storage tank in the whole system, this would not be possible. With increasing intensity of solar radiation during the day as well as the air temperature rises, the heat received from the collector and hence tank temperature rises further. The maximum temperature of the tank occurs around 16:00 due to heat accumulation from the tank at this time, however, the intensity of the sunlight at this time of the day does not have its maximum value (according to the figure). As a result, the collector and the tank maximum temperatures have shifted to the right of the graph. Moreover, the maximum tank temperature has a delay to a maximum temperature of collector output. With the progress of activities during the day and reduction of solar radiation, the plant tank temperature reduces and reaches its lowest level. This process will continue during the next day. As it is shown in the figure, the thermal storage tank makes the continuous power production per day and night possible. With increasing the tank fluid (heating oil) weight, fluctuations of the tank temperature could be significantly reduced, which reduces the operating temperature of the tank and increases its size. In this figure, tank temperature fluctuations during the day and night are about 130 degrees. This is necessary for proper functioning of the power generation cycle and pinches considerations. Net Work
Mass Flow Rate
2000
13 12 11
1600
10 9
1400 8 1200
7 6
1000 5 800
4 10
12
14
16
18
20
Time (hr)
Figure.6 turbine output power and fluid flow changes during the day and night
Mass Flow Rate (kg/s)
Net Power Output (kW)
1800
Figure 6 shows the turbine output power changes with time during the day. As it was expected, with increasing of the radiation in the daylight and tank temperature as well, the heat amount entering the cycle is increased. Thus, the cycling fluid flow rate is increased which leads to increase of the work output of the turbine. It should be mentioned that the cycle parameters such as turbine inlet temperature and pressure, remains constant due to the stability of the turbine performance. It is only the input flow rate to the cycle that changes; because by changing other parameters such as turbine inlet temperature turbine blades may be damaged. Results are shown in the figure. As it is shown, minimum and maximum turbine output work is equal to 1.34 MW and 1.89 MW, respectively. 5.2. The effect of key parameters on the performance of the system 5.2.1. Changes of inlet pressure of the highpressure turbine
Figure 7 depicts the effect of changing the inlet pressure of the highpressure turbine on the production cost rate and exergy efficiency. As it is obvious, turbine work output increases with increasing the pressure which is due to rising input enthalpy and input energy content to the turbine. On the other hand, increasing the pressure increases the turbine and heat exchangers sizes which affect and raise the production cost rate. The rate of increase in yield is about 0.9% but the cost increase rate was 0.7%. Hence increasing the pressure is cost efficient. Exergy Efficiency
2515000
15.85
2510000
15.8
2505000
15.75
2500000
15.7
2495000
15.65
ƞ (%)
CP ($/year)
Product cost rate
2490000
15.6 14
15
16
17
18
19
PHRSG1 (bar)
Figure.7 Highpressure evaporator pressure changes effect, on the production cost rate.
Figure 8 shows changing the evaporator heat transfer area with changing the high pressure of the turbine. With increasing the pressure, the heat transfer area of the highpressure evaporator will increase. Raising pressure of the inner fluid of heat exchanger tubes reduces
the fluid velocity and increases the need for heat transfer area. Changes in the gas phase characteristics and liquid fluid properties such as conductivity, heat transfer coefficient, density, viscosity, and etc. are effective in determining the overall heat transfer coefficient and fluids heat transfer area changes. On the other hand, with increasing the higher pressure of the cycle, the received heat from oil decreases. This will lead to higher oil inlet temperature to lowtemperature evaporator and as a result, the heat transfer area of lowpressure evaporator decreases. These changes are less than highpressure evaporator changes, which is depicted in figure 20. A_HRSG1
A_HRSG2
14000 12000 10000 8000 6000 4000 2000 0 14
14.5
15
15.5
16
16.5
17
17.5
18
18.5
PHRSG1 (bar)
Figure.8 Highpressure changes of the evaporator among heat transfer area changes of the high and lowpressure evaporator.
Figure 9 shows the effect of the high pressure of the turbine on organic fluid flow rate and output power. Despite increasing the pressure, the flow rate decreases. This should increase the overall power of the system, but the increase of pressure increases the enthalpy. Hence, its cumulative effect with flow rate decrease results in higher work output. The figure also shows that; inlet pressure of the turbine has a greater effect on enthalpy increase in comparison with flow rate decrease.
Mass flow rate
1602
10.6
1600
10.58
1598
10.56 10.54
1596
10.52 1594 10.5 1592 10.48 1590
10.46
1588
10.44
1586
10.42
1584
Mass Flow Rate (kg/s)
Net Output Power (kW)
Net Power
10.4 14
14.5
15
15.5
16
16.5
17
17.5
18
18.5
PHRSG1 (bar)
Figure.9 High pressure of evaporator changes effect on work output and operating fluid flow rate
Figures 1012 show the low pressure of evaporator effect on thermodynamic and economic parameters. As it is shown in figure 10 while increasing the pressure, both exergy and cost raise. Exergy efficiency is increased due to increased work output. Costs also increased due to enlargement of the heat exchanger size. The trend of output power increase and operating flow rate reduction is the same as highpressure turbine described in Figure 12. Product cost rate
Exergy Efficiency
2510000
15.8 15.75 15.7
2500000 15.65
ƞ (%)
CP ($/year)
2505000
2495000 15.6 2490000
15.55
2485000
15.5 7
8
9
10
11
PHRSG2 (bar)
Figure.10 The low pressure changes of highpressure evaporator effect on production cost rate
Mass flow rate
1590
10.6
1588
10.58
1586
10.56
1584
10.54
1582
10.52
1580
10.5
1578
10.48
1576
10.46
1574
10.44
1572
10.42
1570
Mass Flow Rate (kg/s)
Net Output Power (kW)
Net Power
10.4 7
7.5
8
8.5
9
9.5
10
10.5
11
PHRSG2 (bar)
Figur.11 The low pressure changes of evaporator effect work output and operating fluid flow rate A_HRSG1
A_HRSG2
16000 14000 12000 10000 8000 6000 4000 2000 0 7
7.5
8
8.5
9
9.5
10
10.5
11
PHRSG2 (bar)
Figure.12 Low pressure changes of evaporator effect on heat transfer areas of high and low pressure evaporator
5.2.2. Effect of high pressure turbine inlet temperature on the system
Figures 1315 show the effect of the high pressure turbine inlet temperature. As it is shown in the figures, the turbine inlet temperature has a great impact on the efficiency and the production cost rate. Figure 13 shows that, despite decreasing organic fluid flow rate by increasing the inlet high pressure turbine temperature, the work output increases. This is due to increasing of the fluid energy content by increasing its temperature. The cumulative impact
of increasing turbine inlet temperature is increased work output. It should be noticed that reducing the fluid flow rate reduces the increasing rate of turbine work output. Ouput power
Mass flow rate
1620
10.57 10.56 10.55 10.54
1580
10.53 1560
10.52 10.51
1540
10.5
Mass Flow Rate (kg/s)
Net Output Power (kW)
1600
10.49
1520
10.48 1500
10.47 225
227
229
231
233
235
237
239
241
TIT1 (C)
Figure.13 Turbine 1 temperature changes effect on work output and operating fluid flow rate
Figure 14 shows the increase in exergy efficiency and cost production rate by increasing the inlet temperature. Exergy efficiency has an increase of 1.47% while the cost rising amount is 1.42%. This indicates that temperature increase has a greater impact on increasing efficiency than increasing cost has. Figure 15 also shows a slow increasing rate of heat transfer area by temperature. This increase is due to changing properties of the warming fluid which cause Reynolds and other related parameters increase. Consequently, heat transfer coefficient reduces, but these changes amount are small.
Exergy efficiency
Product cost rate
2525000
15.9
2520000 15.85 2515000 15.8
2505000 15.75 2500000 2495000
ƞ (%)
CP ($/year)
2510000
15.7
2490000 15.65 2485000 2480000
15.6 226
228
230
232
234
236
238
240
242
239
241
TIT1 (C)
Figure.14 Inlet turbine1 temperature changes effect on production cost rate A_HRSG1
A_HRSG2
13200
AHRSG1(m2)/ AHRSG2(m2)
11200 9200 7200 5200 3200 1200 225
227
229
231
233
235
237
TIT1 (C)
Figure.15 Inlet turbine1 temperature changes effect on low and high pressure evaporator heat transfer areas
5.2.3. Effect of low pressure turbine inlet temperature on the system
According to Figure 16, while increasing the inlet low pressure turbine temperature, the work output increases due to inlet fluid enthalpy increase at turbine second stage. As it can be seen
in Figure 17, increasing the pressure increases the heat transfer area of low pressure heat exchanger which is normal. Ouput power 1600
Net Output Power (kW)
1595 1590 1585 1580 1575 1570 1565 1560 1555 1550 188
193
198
TIT2 (C)
Figure.16 Inlet turbine2 temperature changes effects on work output A_HRSG1
A_HRSG2
AHRSG1(m2)/ AHRSG2(m2)
13200 11200 9200 7200 5200 3200 1200 188
190
192
194
196
198
200
202
TIT2 (C)
Figure.17 Inlet turbine2 temperature changes effect on low and high evaporator heat transfer areas
5.2.4. The effect of condenser pressure on system performance
Figure 18 and Figure 19 shows the effect of condenser pressure on the area of heat exchangers with exergy efficiency and the rate of cost of production. With increasing condenser pressure heat transfer area of low pressure heat exchanger is reduced when it is
due to the low thermal load. Area of high pressure heat exchanger remains constant due to being independent. A_HRSG1
A_HRSG2
AHRSG1(m2)/ AHRSG2(m2)
12500 10500 8500 6500 4500 2500 0
0.1
0.2
0.3
0.4
0.5
0.6
Pcond (bar)
Figure.18 Condenser pressure changes effect on low and high pressure evaporator heat transfer areas
Figure 19 represented a reduction of exergy efficiency by condenser pressure increase, which is due to reducing work output by increasing fluid output pressure. On the other hand, there is an optimum cost at pressure 0.3 bar which cost will increase after that. It should be noticed that exergy efficiency is reduced more than 2% which is a significant amount in the whole system. Hence the selection of the optimal condenser pressure has a great importance to the turbines inlet pressure.
Exergy efficiency
Product cost rate
2500000
18
2490000
16 14 12
2470000
10 2460000 8 2450000
ƞ (%)
CP ($/year)
2480000
6
2440000
4
2430000
2
2420000
0 0
0.1
0.2
0.3
0.4
0.5
0.6
Pcond (bar)
Figure.19 Condenser pressure changes effect on production cost rate
5.2.5. Collector oil flow rate effect on system performance
Figures 20 to 22 represent the collector oil flow rate effect on system performance. According to figure 20, with increasing the collector flow rate, small exergy efficiency increase is seen which is due to collector exergy destruction reduction and more utilized useful sun energy. Moreover, it leads to a slight increase of cost in power plants by increasing work of the pump. As it is expected from Figure 21 change in heat transfer area is independent of the flow collector. The Figure 22 shows that by increasing the collector fluid flow rate, cycle working fluid flow rate is increased due to the increase in the available heat of the tank. As a result, output power increases with a low slope. It should be noted that figure 20 approved the figure 22 about any increase of exergy efficiency.
Exergy efficiency
Product cost rate
2503000
15.95
2502000 15.9 2501000 15.85
2499000 15.8 2498000 2497000
ƞ (%)
CP ($/year)
2500000
15.75
2496000 15.7 2495000 2494000
15.65 60
65
70
75
80
85
90
m_dot_col (kg/s)
Figure.20 Collector inlet oil flow rate changes effect on production cost rate A_HRSG1
A_HRSG2
AHRSG1(m2)/ AHRSG2(m2)
12500
10500
8500
6500
4500
2500 60
65
70
75
80
85
90
m_dot_col (kg/s)
Figure.21 Collector inlet oil flow rate changes effect on low and high evaporator heat transfer areas
Mass flow rate
1700
10.68
1680
10.66
1660
10.64
1640 1620
10.62
1600
10.6
1580
10.58
1560 10.56
Mass Flow Rate (kg/s)
Net Output Power (kW)
Ouput power
1540 10.54
1520 1500
10.52 60
65
70
75
80
85
90
m_dot_col (kg/s)
Figure.22 Collector flow rate changes effect on work output of operating fluid flow rate
5.2.6. Effect of steam generator flow rate on system performance
Figure 23 shows the generator flow rate effect on work output and cycle operating fluid flow rate. As it is expected with increasing the generator flow rate the entering heat to the cycle increases and lead to increase of cycle operating organic fluid flow rate in order to turbine inlet temperature remains constant. Hence an increase in work output will occur as depicted in the figure. Figure 24 shows the result of work output increase which is exergy efficiency increase. On the other hand, due to increasing heat transfer area, work output and turbine size, the production cost rate increases. Figure 25 shows the increasing heat transfer area of heat exchangers due to increasingly more available heat in the cycle. The results are depicted in Figures 2325.
Ouput power
Mass flow rate
1800
14 12
1700 10
1650 1600
8
1550 6
1500 1450
4
Mass Flow Rate (kg/s)
Net Output Power (kW)
1750
1400 2
1350 1300
0 14
16
18
20
22
24
26
m_dot_VG (kg/s)
Figure.23 Tank flow rate changes effect on turbine work output and operating fluid flow rate Exergy efficiency
Product cost rate
2564000
20
2544000
18 16
2524000 12
2484000
10
2464000
8 6
2444000 4 2424000
2
2404000
0 14
16
18
20
22
24
26
m_dot_VG (kg/s)
Figure.24 Thermal tank storage flow rate changes effect on production cost rate
ƞ (%)
CP ($/year)
14 2504000
A_HRSG1
A_HRSG2
15000
AHRSG1(m2)/ AHRSG2(m2)
13000 11000 9000 7000 5000 3000 1000 14
16
18
20
22
24
26
m_dot_VG (kg/s)
Figure.25 Thermal tank storage flow rate changes effect on low and high evaporator heat transfer areas
5.2.7. Minimum heat exchangers pinch temperatures effect on system performance
Figures 26 to 28 show the effect of different cycle heat exchangers minimum pinch temperatures, such as recovery, condenser, and generator on thermoeconomic organic double pressure Rankine cycle performance. As shown in Figure 26, with increasing in pinch temperature of the recovery, the exergy efficiency decreases. This is due to recovery efficiency decrease has a direct effect on generator heat demand decrease. On the other hand, as the transferred heat by the recovery decreases, the minimum pinch increases. As it is seen in Figure 27 due to the independence of heat transfer areas from recovery pinches, there is no change in their values. This is the proof of low production cost changes, as a large part of the costs are for generator heat exchangers. Exergy efficiency
Product cost rate
2564000
15.75
2544000 15.7
2504000
15.65
ƞ (%)
CP ($/year)
2524000
2484000 15.6
2464000 2444000
15.55
2424000 2404000
15.5 3
5
7
9
11
Pinch_Rec (kg/s)
Figure.26 Heat exchanger recovery pinch changes effect on production cost rate
A_HRSG1
A_HRSG2
15000
AHRSG1(m2)/ AHRSG2(m2)
13000 11000 9000 7000 5000 3000 1000 3
5
7
9
11
Pinch_Rec (kg/s)
Figure.27 Heat exchanger recovery pinch changes effect on low and high evaporator heat transfer areas
As it is shown in figure 28 by increasing pinch recovery the organic working fluid flow rate decreases because of reducing available heat by the generator heat exchangers. As a result, the reduction in flow rate leads to a reduction in work output. Mass flow rate
1800
10.58
1750
10.56
1700
10.54
1650
10.52
1600
10.5
1550 10.48
1500
10.46
1450 1400
10.44
1350
10.42
1300
Mass Flow Rate (kg/s)
Net Output Power (kW)
Ouput power
10.4 3
5
7
9
11
Pinch_Rec (kg/s)
Figure.28 Heat exchanger recovery pinch changes effect on turbine work output and operating fluid flow rate
Figure 29 shows the changes in exergy efficiency and exergoeconomic cost function versus condenser pinch changes. Increasing pinch at the beginning has little effect on efficiency and cost, while after that, increasing the amount of water required in the system, increases the
cost as well. As follows from the definition of exergy efficiency, it is almost constant and independent of the condenser pinch. Exergy efficiency
Product cost rate 18
2854000
16
2804000
14 12
2704000
10
2654000
8
2604000
ƞ (%)
CP ($/year)
2754000
6
2554000 2504000
4
2454000
2
2404000
0 4
5
6
7
8
9
10
Pinch_Cond (C)
Figure.29 Condenser pinch changes effect on production cost rate
Figures 3032 show the effect of high pressure evaporator pinch on system performance. Figure 30 shows that increasing the pinch have little effect on system performance at the beginning due to minimum pinch satisfaction in the system. But as the minimum pinch increases, oil temperature is needed to be increased as well which lead to auxiliary natural gas system demand. Because of high performance of the auxiliary system, exergy efficiency is increased and as a result, production cost rate increased too. As it is shown in Figure 31, little heat transfer area changes are due to fluid properties variations during temperature changes which lead to stability of heat transfer coefficient. Figure 32 confirms Figure 30. As it is shown operating fluid flow rate and work output increase by increasing of the pinch minimum.
Exergy efficiency
Product cost rate 25
2754000 2704000
20
15 2604000
ƞ (%)
CP ($/year)
2654000
2554000
10
2504000 5 2454000 2404000
0 4
9
14
19
24
Pinch_Eva_HP (C)
Figure.30 Evaporator pinch changes effect on cost production rate A_HRSG1
A_HRSG2
15000
AHRSG1(m2)/ AHRSG2(m2)
13000 11000 9000 7000 5000 3000 1000 4
9
14
19
24
Pinch_Eva_HP (C)
Figure.31 Evaporator pinch changes effect on low and high evaporator heat transfer areas
Mass flow rate
2500
18
2400
16
2300
14
2200
12
2100
10
2000 8
1900
6
1800 1700
4
1600
2
1500
Mass Flow Rate (kg/s)
Net Output Power (kW)
Ouput power
0 4
9
14
19
24
Pinch_Eva_HP (C)
Figure.32 Evaporator pinch changes effect on turbine work output and operating fluid flow rate
5.3. Optimization results
In this section, the results of the multiobjective optimization are presented. As we resulted from the sensitivity analysis, all ten cycle key variables have increasing and decreasing or no changing impact on the two objective functions: Cost exergoeconomic function and Exergy efficiency function. Hence a twoobjective optimization is required to find the optimum level of decision variables so that the system can operate at the lowest possible cost and highest efficiency. Due to nonlinearity of the system and its discrete nature, a repetitive nature optimization algorithm was needed, which high and widely employed in energy systems Genetic Algorithm were selected. Due to the application of this algorithm, its MATLAB software toolbox is available that also was used in this research.
Pareto Frontier
2900000
Cp ($ × 106/Year)
2800000 2700000
Topsis method
2600000 2500000 2400000 2300000 2200000 0.05
0.1
0.15 ηex (%)
0.2
0.25
0.3
Figure.33. the Pareto of the twoobjective optimization genetic algorithm
Figure 33 shows the multiobjective optimization result. As it is shown two target exergy efficiency and cost production rate functions are simultaneously optimized by genetic algorithm. All tenstudied cycle key variables are considered as decision variables. Exergy efficiency is varied from 11 to 23% and exergoeconomic cost varied from 2.3 to 2.8 million dollars per year. These ranges are relatively large. Hence it is needed to choose the optimal points among them. A convenient and reliable method is TOPSIS. An orange dot on the graph is selected by this method. The resulting sets of points are selectable and the choice of optimal operation point is the responsibility of the user. Table 5 shows the different points of the operating cycle and also exergy and exergoeconomic functions for each part. Zero Exergy amounts corresponding to point 25 for water is due to the atmospheric pressure and temperature and is known as a reference. Oil pressure in all parts is equal to the atmospheric pressure. The rest operational points of the cycle are shown in the table. Table 5 Different operating points of the cycle with Exergy and operating fluid type
State Point
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Fluid type
Therminol oil
25 26
266.6
1.1
1008.6
20
227.8
266.6
1
1008.6
20
227.8
257.5
1
984.8
20
215.6
222.1
1
894.1
20
170.2
210
1
863.8
20
155.6
208
1
858.8
20
153.2
193.5
1
823.2
20
136.4
150
1
719.9
20
90.5
29.7
0.2
102.5
10.5
0.2
30.1
9.8
100.8
10.5
1.4
179.7
9.6
238.7
10.5
77.3
179.7
9.6
238.7
2.7
77.3
179.1
9.5
505.9
2.7
171.3
195
9.5
543.4
2.7
184.9
179.7
9.6
238.7
7.9
77.3
180.9
15.5
241.8
7.9
79.1
208.3
15.3
318.7
7.9
107.7
207.7
15.2
549
7.9
197.6
230
15
609.4
7.9
221.8
216.3
9.5
593.7
7.9
204.4
210.9
9.5
581
10.5
199.4
127.6
0.2
438.3
10.5
38
266.6
0
1008.6
65.5
227.8
318.5
0
1148.5
65.5
302.5
20
1
84
210.4
0
24.8
1
103.9
210.4
0.2
Therminol oil
Therminol oil Therminol oil Therminol oil
Cyclohexane Cyclohexane Cyclohexane Cyclohexane
Cyclohexane Cyclohexane Cyclohexane
Cyclohexane Cyclohexane Cyclohexane
20
24
ex [kJ/kg]
Therminol oil
Cyclohexane
23
J [kg/s]
h [kJ/kg]
Therminol oil
19
22
P [bar]
Therminol oil
Cyclohexane
21
T [℃]
Cyclohexane
Cyclohexane Therminol oil Therminol oil Water Water
Cyclohexane
27 28
100 35.3
Cyclohexane
9.7 0.2
42.9 294.3
10.5 10.5
20.5 12.6
Table 6 represents the exergoeconomic details of the process optimal point. As it is presented, the maximum amount of exergy destruction is caused by the sun collector and the heat storage tank after that. The great amount of exergy destruction caused by the sun collector is due to high loss of sun radiation by the collector surface, which could be eliminated by utilizing modern collectors. Mixing oils with different temperatures causes the exergy destruction of the heat storage tank as well. In general, high temperature difference causes exergy destruction which should be kept low by lowering the pinch temperature. As it is shown in the figure the exergy destruction cost of the collector and the exergy destruction cost of fuel are equal to zero which is due to free radiation of the sun. After the sun collector and the heat storage tank, heat exchangers of the evaporators have the greatest amount of the exergoeconomic cost which is due to high investment cost for this equipment. This cost could be decreased by utilizing high efficient heat exchangers such as plate heat exchangers. The amount of “f” which presents the investment effect on exergy destruction has the greatest value for the low pressure evaporator. This is because of low exergy destruction and high investment costs of low pressure evaporator. Among inflows to each part, the condenser has the highest output flow cost.
Table 6 Exergoeconomic Organic Solar Rankine Cycle simulation results with individual components $ ) de
Solar collector Storage Tank Economizer_HP Evaporator_HP Superheater_HP Economizer_LP
$ ) de
(
component
(
$ ( ) fgha
! (01)
$ ( ) fgha
$ + ( ) fgha
f (%)
r (%)
0
2.8
5086
0
449030
449030
100
Inf
2.8
4.9
1895.3
169701.4
37727
207428.4
18.2
74.3
3
4.3
237.5
22431.7
12333
34764.7
35.5
44
3
4.2
549.3
51873.5
20634
72507.5
28.5
41.9
3
4.6
113.5
10720.4
5669.1
16389.5
34.6
53.3
3
5
636
60070.3
12667
72737.3
17.4
66.1
3
8.9
42.6
4021.1
49377
53398.1
108.9
397.4
3
7
5
474.1
1567.6
2041.7
76.9
134.2
7.2
20.5
33.6
7656.9
12529
20185.9
62.1
184.4
7.2
17.6
8.4
1907.7
6880
8787.7
78.3
144.3
4.9
7.2
43.6
6734.5
23228
29962.5
77.5
47.4
5.9
7.2
359.5
67090.5
46660
113750.5
41
22
Evaporator_LP Superheater_LP Pump2 Pump1 Turbine_HP Turbine_LP
Recuperator Condenser Auxiliary Heater
5.9
7.4
145.4
27126.7
57536
84662.7
68
25.1
5.9
47.2
271.8
50712
73813
124525
59.3
697.8
0.6
1.9
973
19815.8
33808
53623.8
63
192.1
Table 7 Genetic Algorithms results to optimize the system performance Parameter Population size Crossover probability Mutation probability
Unit 
Range
Optimal
150

80.0

50.0

1815
17.84
810
17.84
227240
414.8751
190200
196.22
0.160.50
90.1
825
24.64
410
9.71
1525
24.84
6585
84.27
59
7.23

2.66

22.7
bar TIP1 TIP2
bar
℃ TIT1
℃ TIT2 P_cond
bar
℃
Pinch_Eva
℃ Pinch_Rec
0i/j
mdot_VG
0i/j
Mdot_col
℃
Pinch_cond Product cost rate Exergy efficiency
10O × $/fgha %
The Table 7 shows the result of optimized organic Rankine cycle. Change interval of any of the 10 decision variables and their optimal values are shown. In design conditions, the system is able to generate power at a cost of 2.66 million dollars with a yield of 22.7% in a year.
Conclusion
In this study, exergetic and exergoeconomic performance of an organic double pressure Rankine cycle were investigated by analysis of sun collector and heat storage tank. Firstly, by means of energy analysis, exergy analysis was performed and all operational points of the cycle were modeled. Then, heat transfer coefficients were calculated by means of flows amount, and heat transfer areas were determined by means of logarithmic temperature differential approach. By means of exergy analysis, economic calculations of the cycle were performed. Finally, by the combination of exergy and economic concepts, thermoeconomic relations were determined which lead to determination of production cost rate of each part of the cycle and other exergoeconomic analysis parameters. By defining effective operational parameters of the cycle such as exergy efficiency and production cost rate, optimization was performed by Genetic Algorithm and TOPSIS decisionmaking method was employed to choose the optimal point. The results have shown that the organic Rankine cycle coupled by a sun collector is able to produce power all day long which is due to the presence of the heat storage tank. The heat storage tank decreases fluctuations of inlet oil temperature of the evaporator. The results have shown that there is no need of auxiliary boiler in the daylight for the cycle and the system performs by the sun ratio of 100%. In the following by the sunset, the auxiliary boiler helps the tank and the system produces continuous power. The sun collector has the greatest exergy destruction ratio which could be improved by decreasing heat losses of the collector and improving its efficiency. The heat storage tank and evaporators are in the next rank of exergy destruction ratio. This is due to high temperature difference between hot and cold sources which could be improved by designing lower pinch temperature evaporators. In the organic Rankine cycle, the lowpressure turbine has the greatest total cost of exergy destruction and investment + . Following that, there are heat recoveries, evaporators and condensers. Sensitivity analysis showed that higher inlet turbine and lower condenser pressures result in higher exergy efficiency. On the other hand, the production rate cost increases. Hence a multiobjective optimization was needed. By performing the optimization process the optimal point of the operating cycle was chosen and applied. In the optimal conditions of the performance, the system could reach to exergy efficiency of 22.7% and production cost rate of 2.66 million dollars per year. Nomenclature
Rb
the beam radiation tilt factor
A
Area [m2]
l
Heat [kW]
Cond
Condenser
α
Absorbance
ε
emissivity
Inner diameter [m]
η
Isentropic efficiency
Do
Outer diameter [m]
θ
Incident angle [degree]
FR
Heat Removal Factor
π
Pi number
g
Gravity acceleration [m/s2]
m
Dynamic viscosity [m2/s]
Specific enthalpy [kJ/kg];
ρ
Reflectivity; Density [kg/m3]
Cp
Specific heat capacity [J/kg.K]
Tp
the bulk temperature of the tube
Di
h
Convective heat transfer coefficient [W/m2K]
hw
wind heat transfer coefficient
ω
The hour angle
Ib
Beam radiation [W/m2]
τ
Transmittance
k
Thermal conductivity [W/mK]
β
The tilted angle
J
Mass flow [kg/s]
δ
The solar declination
m
Mass [kg]
ϕ
local latitude
N
Number of glass
Pr
Prandtl number
QTS
thermal storage load
lu
Useful heat gain [kW]
Ra
Rayleigh number
T
Temperature [°C; K]
TIT
Turbine Inlet Temperature
TIP
Turbine Inlet pressure
t
Time [hour]
col
Collector
U
Heat transfer coefficient [W/m2K]
1
Power [kW]
eva
Evaporator
References
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A small scale organic Rankine cycle is investigated exergoeconomic analysis and optimization of a double pressure organic Rankine cycle coupled with a solar collector A multiobjective optimization is done to gain optimal performance of organic Rankine cycle coupled with a solar collector