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fuel assisted Rankine cycle for power generation
Energy 88 (2015) 555e562
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Exergoeconomic analysis of a solar-powered/fuel assisted Rankine cycle for power generation Eduardo J.C. Cavalcanti a, *, Henrique Pereira Motta b a b
Department of Mechanical Engineering, Federal University of Rio Grande do Norte, 59072-970, Natal, RN, Brazil Engineer of Mechanical Engineering, PB, Brazil
a r t i c l e i n f o
a b s t r a c t
Article history: Received 25 November 2014 Received in revised form 1 May 2015 Accepted 28 May 2015 Available online 19 June 2015
A Rankine System assisted for solar radiation and fuel combustion which produces 57 kW electrical power are evaluated from exergoeconomic point of view. The Parabolic trough collector efficiency has been performed to investigate its effect as heat source. The exergoeconomic parameters as the relative cost difference and the exergoeconomic factor for each component are evaluated. The analysis is based on the SPECO (Specific Exergy Costing) approach. The simulation of system on March, June, September and December 21st from 7 am to 4 pm for Natal/Brazil using real data was carried out. The results reveal the daily average values of collector efficiencies, ratio of the useful solar energy, electricity produced, the specific cost per exergy unit of the produced electricity and others heat rates. The system is advantageous for higher solar radiation. The outcome of the analysis can be useful in design, optimization of operating parameters and help to take decision of investment. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Exergoeconomic analysis Rankine cycle Solar collector Cost
1. Introduction The requirement to supply the demand for energy and the substitution of fossil energy by renewable sources drive the development of alternative renewable energy sources. A great deal of effort has been devoted to development of power system more efficient from a thermodynamics and economic point of view. The solar energy is a growing alternative in many countries, where there is abundant solar irradiation at nearby locations of the equator line. The SPFASRE (solar-powered/fuel assisted Rankine engine) is a green system which uses the solar energy and reduces the associated environmental impact. Some solar assisted Rankine engines use organic fluid as a working fluid called OCR (Organic cycle Rankine), even thought the efficiency is low. The Rankine cycle efficiency is about 50% of the Carnot cycle efficiency (e.g., [1,2]). The OCR efficiency is limited due to the organic fluids decomposition at high temperatures. Rankine engine which operates between temperature of 93 C and 27 C will expect to have an efficiency of 9% and if the higher temperature is increased to about 200 C, the efficiency can rise to 19%, [3]. The water is the original working fluid in Rankine engine. It can be
* Corresponding author. E-mail addresses: [email protected] (E.J.C. Cavalcanti), henriquepmotta@ gmail.com (H.P. Motta). http://dx.doi.org/10.1016/j.energy.2015.05.081 0360-5442/© 2015 Elsevier Ltd. All rights reserved.
superheated to a practical limit of 600 C. The water is used in large power plants to provide power and electricity due to the higher efficiency around double value of cycle efficiency. The SPFASRE has been simulated for Jeddah's climate in Saudi Arabia [3]. The system generates a 36 kW steady electrical power. Evacuated tube collector with an area of 400 m2 generates water steam at 230 C and the LPG fired superheater produces steam at 400 C. The results indicate that the system is driven from 80% to 85% of the energy required for solar energy during the summer, fall and spring seasons and 70% of the energy required for solar energy during the winter season. The engine operates between 8 am and 5 pm. The collectors were PTCs (parabolic trough collectors) which can produce heat until 400 C and its efficiency was steady of 78%. The development of thermal system consists of modifying the system and component design parameters. One approach to improve the performance is exergy analysis. Exergy analysis provides an effective method for the measuring and optimizing performance of a thermal system by accounting for the energy quality. The exergy analysis permits to identify the greatest loss of available energy which is taking place. Plants have been described in order to indicate the irreversibilities, i.e. evaluate the loss of available energy [4,5]. When higher the irreversibility in a plant or component, lower will be its efficiency. The purpose is reduce the irreversibility. The exergy analysis of thermal systems is widely gaining acceptance over traditional energy methods in both industry and
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academia. The exergoeconomy combines exergy analysis and economic principles which has assisted the decision making in economic objective. This methodology calculates the cost associated with each material and exergy stream with the aid of cost balances for each component and auxiliary cost equations. It aims to minimize total cost of the system products, which implicitly includes in the fuel cost rate. There are many currently systems to produce electricity and its cost can be evaluated. These systems include steam turbine, gas turbine, combined cycle, cogenerative cycle, reciprocating engines and research of new technologies. Among these researches, the currently exergoeconomic values of electricity cost per exergy unit have been evaluated [6, 17e21]. A CHP (combined heat and power) system derived by diesel engine has been studied by Ref. [17]. A gas/ steam combined cycle cogenerative plant which has a HRSG (heat recovery steam generator) has been evaluated by Ref. [18]. A basic Rankine cycle classic has been investigated to recover heat from low temperature heat sources (140 C) [19]. The values of electricity cost per exergy unit at CCHP (combined cooling, heating and power) system or trigeneration system have been studied. In paper
[20], the system has worked with gas turbine as prime mover and in paper [21] has worked with (gas-diesel) dual fuel reciprocating engine. However, there are not enough publications for exergoeconomic analysis of power cycle assisted for solar energy to produce electricity. According [6], nine commercial Solar Electric Generating Systems power plants that are operating in the California Mojave desert are proven solar technologies. These plants utilize parabolic trough collectors with steam Rankine cycle system. The authors state that in the field of exergoeconomic analysis and optimization of solar combined cycle systems, there is a lack of investigation and research. An integrated solar combined cycle system has been optimized by Ref. [6]. The exergoeconomic analysis needs to use current data, therefore the data of collector cost [16] were used. They evaluated the technology development of components as parabolic trough solar technology and its cost during years 1990 until 2020. The costs are reducing from $300 to $110 per meters square during these years. The summarized results are given in Table 1. Therefore, the aim of this study is exergoeconomic analysis in order to evaluate the specific cost per exergy unit of electricity,
Table 1 Electricity cost per exergy unit of systems. Cost per exergy unit
Feature
Reference Year
Electricity 4.48 $/GJ Electricity GT 13.96 $/GJ; ST 37.69 $/GJ; Average 18.89 $/GJ Electricity 26.75 $/GJ
Combined heat and power (CHP) system Electrical power 11.5 MW, vapor 2.5 kg/s steam at 140 C Gas/steam combined cycle Electrical power GT 23.7 MW þ ST 6.3 MW Overall 29.0 MW
[17] (2012) [18] (2006)
Rankine Cycle, Steam turbine inlet temp ¼ 140 C Electrical power 1.0 MW Gas Turbine, heat recovery steam generator (HRSG), absorption chiller Electrical power 19.23 MW, cooling 6.96 MW, heating (steam) 24.65 MW
[19] (2014)
Trigeneration dual fuel reciprocating engine (RE) with turbo air charger, absorption chiller. Electrical Power 5.9 MW, cooling 0.54 MW, hot water and steam 2.46 þ 1.82 MW
[21] (2010)
Integrated solar combined cycle system gas turbine 2 125.0 MW steam turbine 150.0 MW, overall 400.0 MW, useful energy of field collector 51.76 MW
[6] (2010)
Electricity of GT 20.9 $/GJ, Cooling 45.4 $/GJ, Heating 11.4 $/GJ Electricity of engine 45.95 $/GJ, Cooling 167.52 $/GJ, Hot water 29.98 $/GJ, Steam 42.42 $/GJ Electricity ST 76.75 $/GJ; GT 60.89 $/GJ
Fig. 1. Schematic of the solar-powered/fuel assisted Rankine engine (adapted from Ref. [3]).
[20] (2011)
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Fig. 2. Average of direct irradiation for March, June, September and December.
daily collector efficiency and the ratio between the useful solar energy of collector and the total rate of heat required for the system (Fss). The SPFASRE was simulated at Natal/Brazil. This study is the first of its kind for the Natal/Brazil solar irradiation during all seasons.
2. Methodology The system is similar to [3]. The difference is the present system has only one gas fired. It has collectors field that assist the Rankine engine. The working fluid at PTC is thermal oil which supply the heat required for preheating, evaporating and superheating of the water in the Rankine engine. The steam is then superheated with an LPG-fired superheater to improve the Rankine efficiency. The steam flows in turbine with 60,000 rpm. The turbine shaft speed is reduced to 3600 rpm by a gearbox which drives a generator. The heat is rejected at air cooler condenser. The generator supply the two pumps and two fans at point 23 and then generates the net electric power at point 13. Fig. 1 shows the schematic of SPFASRE. The next step in evaluation is to select the typical weather at city. Natal/Brazil is a tropical savanna climate. It is located at Brazil northeast with latitude 05 470, longitude 35 120 and height 30 m. The city is located nearby of equator line and has high solar irradiation. The February month has the higher solar insolation at Natal/Brazil during the year. In this month, the beam solar indices in normal angle with the Natal surface. The following data of an average year is based on the historical records from 1999 to 2012 according weatherspark [7]. The temperature typically varies from 22 C to 31 C and is rarely below 20 C or above 33 C. The probability that precipitation will be observed at this location varies throughout the year. Precipitation is most likely around June 13,
Fig. 3. Schematic of a parabolic trough collector: Adapted from Ref. [9].
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occurring in 56% of days. Precipitation is least likely around November 23, occurring in 17% of days. Over the course of the year typical wind speeds vary from 1 m/s to 9 m/s (light air to fresh breeze), rarely exceeding 11 m/s (strong breeze). The irradiation has strong variation due to cloud and precipitation. The average direct irradiation during the hours for the nineteenth, twenty-first and twenty-thirty of March, June, September and December were calculated. The data represent the days of fall, winter, spring and summer 2010 according Inpe [8]. The PTC (parabolic trough collector) can utilize only direct radiation beam due to concentrating collector. These values were calculated by difference between total radiation and diffuse radiation. Fig. 2 shows the direct irradiation during the day for 4 month for each 5 min. The used collector was the PTCs (parabolic trough collectors). It is made by a sheet of reflective material into a parabolic shape, where the beam irradiation incident are reflected into the receiver tube. The receiver tube is a black metal tube placed along the focal line of the receiver where flow inside the work fluid. The PTC efficiency are not steady, it is affect by the heat losses to environmental and the useful heat removed by working fluid. The heat losses at air side are determinated by cover temperature, environmental temperature and wind velocity. The useful heat at working fluid side is determinate by temperature difference between work fluid and surface and flow configuration. To reduce the heat losses, an evacuated concentric glass tube (cover) is employed around the receiver. The PTC efficiency is calculated by ratio between the useful energy (Qu) and the beam radiation versus aperture area of the parabola (GB$Aa) [9]. The useful energy is calculated from an energy balance of its receiver as follows:
Q_ u ¼ GB $ho $Aa UL $Ar $ðTr Ta Þ ¼ hi $Ai $ðTr Toil Þ
(1)
The useful energy is equal the difference between the incident radiation on receiver and the heat losses on receiver (cover glass tube) to environmental or also equal the heat rate by convection between the receiver surface and the thermal fluid. The heat losses on receiver to environmental is estimated by the overall coefficient of heat exchange (UL). It is composed for the losses due to radiation and convection between the cover and the environment, and the radiation between the receiver and the cover of glass concentric evacuated. The overall coefficient of heat exchange is evaluated using the following equation:
" UL ¼ hair
Ar 1 þ þ hr;ca Ac hr;rc
#1 (2)
The coefficient can be determinated according [9]. The mass flow rate is divided in the row tube at collector field of 10. The air wind speeds was the years average of 5 m/s. The parameter of parabolic trough Collector are given in Fig. 3. The characteristics of Parabolic trough Collector are given in Table 2. The input parameters of components as efficiency and collector area are showed in Table 3. The collector field limitation is the maximum allowed temperature of the heat transfer oil used inside the collector. The working fluid was the Paratherm HR manufactured by Paratherm. The temperature should not exceed 343 C to work a long time to avoid the fluid degradation. In order to avoid fire hazards due to selfignition of the heat transfer oil, the temperature should not exceed the autoignition temperature of 416 C. Data of this fluid is available in Ref. [10]. The heat of combustion is 46.3 MJ/kg. Some input parameters were similar to [3]. The author carried out a simulation of this cycle for Saudi Arabia's climate. In this work, the operation data for maximum irradiation of 910 W/m2 at march is designed. The temperature of evaporator and pre-heater
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Table 2 Characteristics of PTC. Parameter
Value
Collector rim angle Collector aperture Receiver outside diameter Receiver inside diameter Glass cover diameter Mirror reflectivity Glass cover transmittance Glass cover emittance Receiver absorptivity Receiver emittance Collector orientation Mode of tracking Row tube collector
70 2.0 m 13.72 mm 9.24 mm 33.72 mm 0.98 0.96 0.87 0.97 0.92 Axis in NeS direction EeW horizontal 10
Table 3 The input parameters of system. Parameter
Value
Steam turbine efficiency Gas fired superheater efficiency Generator efficiency Gearbox efficiency Collector area
72% 60% 90% 90% 400 m2
on oil side is maintained steady by oil mass flow rate. The incoming turbine temperature is maintained by LPG consume. The maximum and minimum temperature of oil is 330 C and 200 C. The temperature of condenser is 55 C. The steam is maintained at 300 C at point 8 and 400 C at point 9 thought gas burning. The minimum pinch point between point 4 and 7 is 10 C. The pump is isentropic. The input parameters are defined as follows: The gas fired superheater is the place where burns LPG. The composition of natural gas is given in Table 4. The ratio between the useful solar energy of collector and the total rate of heat required for the system is calculated as the following equation:
Fss ¼
Q_ u _ Q u þ Q_ Gas
(3) fired
The thermodynamic model was built based on the mass, energy and exergy balance between each component. The Exergy balance for each component evaluated the destruction exergy as follows:
EF ¼ EP þ ED
(4)
The second law efficiency or exergetic efficiency at each component is the ratio between the product exergy and the fuel supplied exergy according to the equation:
ε¼
EP EF
The thermoeconomic analysis combines the exergetic analysis with the economic constraints for the optimization of the thermal system [5]. Its is useful to understand the cost formation process and calculate the specific unit exergetic cost of each product. The analysis reveals which equipment should be possible and economically feasible invest in order to improve the system. Different approaches for formulating efficiencies and auxiliary costing equations have been suggested in the literature. The SPECO (specific exergy costing method) works with their approach, fuels and products. This method was initially suggested by Refs. [11,12]. The rigorous discussion of fuel and product definitions that also consider the components of exergy (mechanical, thermal and chemical) has been made [13]. The product Ep and the fuel Ef are defined considering the desired result produced by the component and the resources expended to generate this result. The product is defined to be equal to the sum of all the exergy values to be considered at the outlet plus all the exergy increases between inlet and outlet that are in accord with the purpose of the component. The fuel is defined to be equal to all the exergy values to be considered at the inlet plus all the exergy decreases between inlet and outlet minus all the exergy increases that are not in accord with the purpose of the component. Decisions need to be made to implement the definitions [13]. The fuel and product exergy for all components of system are given in the following table (see Table 5). The basic thermoeconomic equation is shown as follows:
cp $Ep ¼ cf $Ef þ Z_
(6)
cP and cf represent the average costs per exergy unit of product and fuel, respectively. This equation states that the cost rate associated with the product of the system is equal to the sum of cost rate of fuel and capital cost. The purchase cost function of the component (Zi) is determinated by Refs. [5,6,14,15]. The solar field is comprised of collectors parabolic-trough from type of LS-3 which are single axis tracking and aligned on a northesouth line, thus tracking the sun from east to west [16]. Various purchase cost functions of this system are given in Appendix A. The capital investment of a component is converted into the cost rate considering the CRF (capital recovery factor):
Z_ i ¼ Zi $CRF$4 ½$=s
(7)
4 represents the maintenance factor 1.06. The CRF (capital recovery factor) is an economical parameter that depends on the interest rate as well as on the estimated equipment lifetime. CRF is calculated using the following equation:
ð1 þ iÞnyears 1 $ CRF ¼ i$ nyears ð1 þ iÞ 1 nyears $nh $3600
(8)
The years number (nyears) is 20, hour for solar Field is 9. The interest rate i is 12.4%. The fuels are solar radiation and natural gas.
(5) Table 5 Definition of fuel and product.
Table 4 Composition and typical properties of natural gas. Component
% Volume
Methane Ethane Propane Nitrogen Carbon dioxide Higher calorific value
88.82% 8.41% 0.55% 1.62% 0.60% 47.574 MJ/kg
Component
Exergy rate of product EP
Exergy rate of fuel EF
Collector Evaporator Pre-heater Pump 1 Pump 2 Gas fired SH Turbine Gear Box Induct. Gener. Air cooler Cond.
E3-E2 E8-E7 E7-E6 E2-E1 E6-E5 E16-E15 E11 E12 E13 þ E23 E18-E17
Eirrad E3-E4 E4-E1 E19 E20 E14 E9-E10 E11 E12 E10-E5
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Their costs are null and 0.3281 $/kg, respectively. Beside the purchased equipment cost, there are other DC (direct costs) and IC (indirect costs), according [17]. These costs involved in the project are showed in Table 6: The cost rate of the exergy destruction rate is defined as:
C_ D ¼ cf $E_ D
(9)
The relative cost difference rk and exergoeconomic factor fk are calculated as follows:
rk ¼
cp cf cf
(10)
fk ¼
Z_ _ cf $ED þ Z_
(11)
The exergoeconomic factor compares the rate of investment cost _ with the rate of cost of irreversibility (c $E_ D ). Low values of this (Z) f factor indicate that the cost of irreversibility is meaningful compared to the cost of investment. The lowest value of exergoeconomic factor indicates that this component has the greatest potential for improvement.
3. Results and discussion The PTC performance is assessed using the model described. The system was designed initially for maximum solar irradiation of 910 W/m2. The output and input temperature of oil are steady and their values are 330 C and 200 C. Fig. 3 shows the effect of the solar irradiation on the PTC efficiency. The oil mass flow rate is higher when the solar irradiation is high for that the oil temperature not exceed 330 C. The receiver temperature is close the oil temperature due to turbulent flow, therefore the losses rates are steady. When the solar irradiation (GB) is decreased, the losses rates remain steady thus, the useful energy and efficiency are decreasing. In addition, for lower irradiation values, the efficiency decreases meaningfully due to the lower internal convective coefficient at laminar flow. For values below 230 W/m2, the output and input temperature of oil were changed to 270 C and 220 C to increase the efficiency. For new situation, the temperature of cover glass tube is reduced and decreasing his losses rates. However, the efficiency is again decreasing below 0.5 for lower solar irradiation (140 W/m2) (see Fig. 4). Table 7 shows the fluid temperature, mass flow rate, exergetic and thermoeconomic performance of the collector field and Rankine engine for solar irradiation of 910 W/m2. The mass flow rate of thermal oil is 8 times the steam mass flow rate. The thermal oil exergy is high due to the chemical exergy. The electrical net power is 56.6 kWe. The products of the system (collector field and Rankine engine) are steam hot thermal oil and electrical energy. The specific cost per exergy unit of fuel solar irradiation and LPG gas are null and 6.687 $/GJ. The electricity cost per exergy unit is of 10.42 $/GJ. The cost rate is high at collector field due to higher purchase cost. The specific cost per exergy unit of oil
Fig. 4. Efficiency Collector versus Direct Irradiation for two situation of oil temperature.
is low because its high exergy. The losses cost rate of the system is 0.1447 and 0.8654 $/h at 16 and 18, respectively. Thermoeconomic variables of cogenerative system, exergy destruction, exergy efficiency, average unit cost of fuel and product, the cost rate of exergy destruction rate, total cost rate, relative cost difference and exergoeconomic factor for each component are given in Table 8. The collector field has higher values of exergy destruction. The air cooler and collector have lower exergetic efficiency. The exergoeconomic analysis reveals that the higher average unit cost of fuel is at generator, and the higher average unit cost of product is at air cooler. Also, the gas fired superheater has a higher cost rate for
Table 7 Data of temperature, mass flow rate, exergy, costs rates and specific costs per exergy at each stream for solar irradiation of 0.91 kW/m2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
T [ C]
m_ [kg/s]
200.0 200.0 330.0 235.7 55.0 55.1 224.0 300.0 400.0 54.97
0.9083 0.9083 0.9083 0.9083 0.1063 0.1063 0.1063 0.1063 0.1063 0.1063
25.0 25.0 350.0 25.0 45.0
0.00086 0.04632 0.04718 12.240 12.240
Ex [kW]
_ C[$/h]
c [$/GJ]
44,651 44,651 44,777 44,681 0.90 1.16 22.06 110.0 122.70 23.40 73.41 66.07 56.64 42.24 0 6.01 0 7.86 0.44 0.27 0.04 2.07 2.92
305.90 305.90 306.70 306.10 0.01 0.03 0.26 0.95 1.88 0.36 2.23 2.23 2.13 1.02 0 0.14 0 0.87 0.02 0.01 0.001 0.08 0.11
1.90 1.90 1.90 1.90 1.90 4.24 3.32 2.41 4.24 4.24 8.44 9.38 10.42 6.69 0 6.69 0 30.58 10.42 10.42 10.42 10.42 10.42
Table 6 Cost of project. Direct costs (DC) Purchased equipment cost Installation Piping Instrumentation and controls
Indirect costs (IC) (PEC) 50% of PEC 30% of PEC 20% of PEC
Engineering and supervision Construction costs
50% of PEC 15% of DC
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Table 8 The thermoeconomic variables of the system. Component
ED [kW]
ε [%]
cf [$/GJ]
cP [$/GJ]
cD [$/h]
ZT [$/h]
rk [%]
G [%]
Collector Evaporator Preheater Gas fired Steam Turb Gear Box Generator Air cooler
213.70 8.11 8.79 23.45 25.94 7.34 6.61 14.64
36.96 91.55 70.38 35.28 73.89 90.00 90.00 34.93
0.000 1.903 1.903 6.687 4.242 8.437 9.375 4.242
1.848 2.183 3.080 20.010 8.437 9.375 9.930 30.58
0.000 0.056 0.060 0.565 0.396 0.223 0.223 0.224
0.8333 0.0331 0.0283 0.0483 0.7123 0.0001 0.0015 0.5217
e 14.72 61.84 199.2 98.87 11.12 5.921 620.7
100.00 37.30 31.95 7.88 64.26 0.06 0.68 69.99
exergy destruction rate due to its inherent nature. The higher cost rates are at collector and steam turbine which have higher purchase cost. Similar result has also been reported in integrated solar combined cycle system in Iran which the higher cost rate is at collector [6]. The higher relative cost difference is at air cooler. The lower value of exergoeconomic factor is at gear box and generator, revealing these two components should be increased his thermodynamic efficiency to improve the global efficiency. The solar radiation affects the performance of collector efficiency and the Rankine engine. Table 9 shows the direct solar irradiation, collector output temperature, collector efficiency, oil flow rate, output evaporator temperature, water flow rate, ratio useful solar energy, produced electricity (Ex[13]) and the specific unit exergetic cost. The output oil temperature changes from 330 to 270 when the irradiation is below 230 W/m2. The collector efficiency decreased while the irradiation is reduced. The thermal oil mass flow is high when the irradiation is high for control the maximum oil temperature at collector exit. The water flow rate is steady to produce a steady flow rate, and thus to hold the same rotation. Otherwise, the variation of water flow rate will reduce the steam turbine efficiency. The high solar irradiation provides higher rate useful solar energy. The produced electricity should be steady, although the electricity is reduced slightly due to increase of fan consumed electricity at point 21 related at air consumed in combustion. Therefore, the electricity cost per exergy unit is increasing due to the higher LPG fuel consume. Table 10 makes a comparison with the electricity cost per exergy unit between other power systems and shows the solar radiation to produces the same cost per exergy unit. Result of electricity cost per exergy unit has been reported in combined cycle cogeneration plant i.e. 13.96 $/GJ for gas turbine and 37.69 $/GJ for steam turbine and average of 18.89 $/GJ (Colpan and Yesin, [19]). Other system is for steam turbine with has heat source with low temperature 140 C to recover heat according Shokati et al. [20]. Its result of electricity cost per exergy is 26.75 $/ GJ. The solar-powered/Fuel assisted Rankine cycle reaches the value
of combined cycle when the irradiation is higher 750 W/m2. It means that the studied case changes the first system when the direct irradiation is higher than 750 W/m2. For the second system the stied system should has the direct irradiation higher than 600 W/m2 to reach the same cost per exergy unit. The difficult of comparative analysis is that the parameters of all system as work fluid temperature, power net produced. Comparison with same parameters may improve the accuracy of the results. The system was simulated to evaluate the effect of year seasons on performance parameters. The calculations of collector efficiencies, ratio of the useful solar energy of collector, specific unit exergetic cost of electricity, heat rates and cost rates were carried out for four month from 7 am to 16 pm using the data from Fig. 2. The results are shown at Table 11. The solar irradiation is higher in March and lower in June due to rainy winter season. The total electricity is steady. The useful energy of collector is higher in March when there is the higher collector efficiency. This is because the higher value of collector efficiency happens when the solar irradiation is higher, it can be showed at Fig. 2. The June and September months have the higher heat production at gas fired superheater due to low solar irradiation. The collector efficiency varies between 70 and 74%, such values are lower of collector efficiency of Gary et al. [3] of 78% due the control system of mass flow rate of thermal oil described Fig. 3. The range of ratio the useful solar energy of collector is between 37.7% and 50.3, which has higher value in March. The total fuel consume is higher in June due to low solar radiation. The higher losses cost during all day are in June due to high fuel consume. Therefore the lower costs per exergy unit happen at March when it happens higher solar irradiation. The daily values of electricity cost per exergy unit vary between 29.98 $/GJ and 35.83 $/GJ. All results of electricity cost per exergy unit daily for four month are higher of average value of 18.89 $/GJ [18], even thought the combined system of [19] works with gas turbine and the values are higher of average value of 26.75 $/GJ [19] of Steam turbine which works with low temperature of heat source. Therefore, the system in present study is not an advantageous system from an exergoeconomic point of view.
Table 9 Effect of solar irradiation on system parameter. Irrad [kW/m2]
T3 [ C]
hcoll
m_ oil [kg/s]
T8 [ C]
m_ w [kg/s]
Fss [%]
Ex[13] [kW]
celet [$/GJ]
0.91 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10
330 330 330 330 330 330 330 330 270 270
0.8103 0.8089 0.7947 0.7805 0.7552 0.7298 0.6695 0.6091 0.5574 0.1130
0.9083 0.8968 0.7831 0.6730 0.5581 0.4495 0.3299 0.2251 0.3637 0.0369
300.4 286.1 224.0 224.0 224.0 224.0 224.0 215.0 154.6 65.31
0.1064 0.1064 0.1064 0.1064 0.1064 0.1064 0.1064 0.1064 0.1064 0.1064
92.33 91.16 79.59 68.39 56.70 45.66 33.50 22.66 13.95 1.41
56.71 56.70 56.67 56.64 56.62 56.60 56.57 56.53 56.18 55.25
10.40 10.95 16.33 21.42 26.71 31.66 37.15 42.05 47.16 54.87
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Table 10 The electricity cost per exergy unit of three systems. Cost per exergy unit $/GJ
Feature
Turb inlet temp C
Power MW
Irradiation dir equivalent W/m2
18.89 26.75 Studied case-Table 8
Steam turb/gas turb Steam turb Steam turb
450/733 140 400
6.29/23.72 ¼ 29.02 1.0 0.057
750 600 Table 8
Table 11 Simulation of performance system for 4 year month. GB [MJ] March June Sept Dec
6970 5515 5805 6290
and and and and
537.8 425.6 447.9 485.3
2
W/m W/m2 W/m2 W/m2
W[13] [MJ]
Qu [MJ]
hcoll [%]
Qgas
1828 1826 1829 1829
5204 3905 4125 4571
74.66 70.80 71.06 72.67
5152 6453 6232 5786
fired
[MJ]
Fss [%]
mfuel [kg]
C[13] [$]
C[16] þ C[18] [$]
50.25 37.70 39.83 44.13
180.5 226.1 218.3 202.1
54.81 65.43 63.45 59.81
5.66 7.07 7.29 6.74
4. Conclusions HRSG: A system solar-powered/fuel assisted rankine engine for power generation has been evaluated using the thermoeconomic method described by Ref. [5] in order to investigate the effect of solar radiation. The collector efficiency is higher while the solar irradiation values are high. The system was simulated from 7 am to 4 pm at March, June, September and December 21st for 2010 year. The electrical net power is steady of 56.6 kWe. The study reveals the thermodynamic inefficiencies, cost rates, average unit cost of fuel and product for each components, specific cost per exergy unit of electricity and ratio useful solar energy. As a result, the components with highest potential for improvement are identified. The method indicates whether improvement should be obtained by increasing the thermodynamic efficiency or by reducing investment cost. The rainy winter of June has the lower solar irradiation and, thus the lower collector efficiency, higher fuel consume and higher specific cost per exergy unit of electricity. In contrast, the March month has the opposite results of winter. The system is not an advantageous system from an exergoeconomic point of view. It has been observed that the electricity cost rate per exergy unit is significantly higher compared to other system as the combined system. Thus, it is important to put efforts to improve the overall efficiency of SPFASRE. In other hand, other aspect as environmental impact is important for analysis of effect of solar collector assisting Rankine cycle for electricity production because this system burns less fuel and should reduce the environmental impact.
Acknowledgment The knowledge of this method was sponsored for CAPES. The author would like to thanks for George Tsatsaronis for his supporting at pos-doc project. And Propesq/UFRN for scholarship of bachelor
Appendix A. Cost function 1 Air compressor: PECc ¼ 71:1$m_ air $ 0:92h $PPei $ln PPei c
Combustion
PECcc ¼ 46:08$m_ ar $
chamber:
#
1 0:995PPe i
$ð1 þ eð0:018$T26:4Þ Þ Gas turbine: PECt ¼ 479:34$
m_ g 0:93ht
$ln PPei $ð1 þ eð0;036$T54:4Þ Þ
Q_ ec DTec
16.38 18.93 18.41 17.56
!0:8 þ
¼ ¼ ¼ ¼
22.04 26.00 25.70 24.30
Q_ ev DTev
29.98 35.83 34.69 32.67
!0:8 þ
Q_ sh DTsh
!0:8
þ21276$m_ w þ 1184:4$m_ 1:2 g Solar Field: PECcoll ¼ 355 $/m2 _ 0:71 Pump: PECpump ¼ 3540$W _ SteamTurbine: PECST ¼ 6000$W
0:7
0:89 A Condenser: PECaircooler ¼ 156000$ 200 Fan: PECF ¼ 12300$
W_ 50
!0:76
Generator/Motor: PECGen ¼ 500$
!0:89 1h_ $ h p
W_ 10
P
!0:6
Heat Exchanger: PECHE ¼ 12000$
A_ 100
Nomenclature Aa Ac Ai Ar C C_
D
cp cf ED EF EP fk Fss GB hair hr,c-a hr,r-c
"
PECHRSG ¼ 6570$
þ þ þ þ
c[13] [$/GJ]
hi i m_ oil m_ w nyears nh
aperture area of collector m2 glass cover area m2 receiver internal area m2 receiver area m2 cost $ cost rate of the exergy destruction rate $/s average costs per exergy unit of product $/kJ average costs per exergy unit of fuel $/kJ destruction exergy rate kW fuel exergy rate kW product exergy rate kW exergoeconomic factor ratio between the useful solar energy of collector and the total rate of heat required for the system beam solar radiation W/m2 external coefficient of air convection at cover W/(m2 K) radiation coefficient from glass cover to ambient W/ (m2 K) radiation coefficient from receiver to glass cover W/ (m2 K) internal coefficient of convection W/(m2 K) interest rate thermal oil mass flow rate kg/s water mass flow rate kg/s years number hour number
562
Q_ u Q_
Gas fired
E.J.C. Cavalcanti, H.P. Motta / Energy 88 (2015) 555e562
useful energy rate at collector W energy rate produced at gas fired superheater W relative cost difference receiver temperature K air temperature K thermal oil temperature K global coefficient of heat exchanger W/(m2.K)
rk Tr Ta Toil UL Z_
cust rate of component $/s
Z_ T Zi W
total cust rate (purchase, direct and indirect cost) $/s purchase component cost electric energy MJ
Greek symbols ε exergetic efficiency 4 maintenance factor ho optical efficiency of collector Abbreviation CRF capital recovery factor DC direct costs IC indirect costs LPG liquefied petroleum gas PEC purchased equipment cost PTC parabolic trough collector SPFASRE solar-powered/fuel assisted Rankine engine References [1] Barber RE. Current costs of solar power organic rankine cycle engines. Sol Energy 1978;20(1):1. ~ es-Moreira JR. Analise Exerge tica de um Ciclo Rankine [2] Cavalcanti EJC, Simo Organico com Fonte Solar, CIBIM 10. 2011. Oporto, Portugal. [3] Gari H, Khalifa A, Radhwan A. Design and simulation of a solar-powered/fuelassisted rankine engine for power generation. Appl Energy 1988;30:245e60.
[4] Kotas TJ. The exergy method of thermal plant analysis. 1st ed. London: Anchor Brendon Ltd; 1985. [5] Bejan A, Tsatsaronis G, Moran M. Thermal design and optimization. USA: John Wiley & Sons, Inc.; 1996. [6] Baghernejad A, Yaghoubi M. Multi-objective exergoeconomic optimization of an integrated solar combined cycle system using evolutionary algorithms. Int J Energy Res 2010;35(7):601e15. [7] WeatherSpark. weatherspark.com/averages/33461/Natal-Rio-Grande-doNorte-Brazil, access sept/08/2014 at10:20hr. ~ DE TEMPO E ESTUDOS CLIMATICO. [8] Inpe e CENTRO DE PREVISAO www.cptec. inpe.br/, access april/08/2011 at 11:30 hr. [9] Kalogirou S. Solar energy engineering: processes and systems. 1st ed. Elsevier Inc; 2009. [10] Paratherm Corporation e Heat Transfer Fluids. http://www.paratherm.com/ heat-transfer-fluids/high-temperature-heat-transfer-fluids/paratherm-hr/. Acess em sept/01/2010 at 9:30hr. [11] Tsatsaronis G, Lin L. On exergy costing in exergoeconomics. In: Computeraided energy systems analysis, American Society of Mechanical Engineers. AES; 1990. p. 21. [12] Lazzaretto A, Tsatsaronis G. On the calculation of efficiencies and costs in thermal systems. In: Proceedings of the ASME advanced energy systems division. Nashville, Tennessee: AES; 1999. p. 39. [13] Lazzaretto, Tsatsaronis. SPECO: a systematic and general methodology for calculating efficiencies and costs in thermal systems. Energy 2006;31: 1257e89. [14] Misra RD, Sahoo PK, Gupta A. Thermoeconomic optimization of a single effect H2O/LiBr absorption chiller system. Int J Refrig 2003;26:158e69. [15] Smith R. Chemical process design and integration. John Wiley; 2005. [16] Kearney D, Price H. Parabolic-trough technology roadmap a pathway for sustained commercial development and deployment of parabolic-trough technology. SunLab NREL; 1999. [17] Yildirim U, Gungor A. An application of exergoeconomic analysis for a CHP system. Electr Power Energy Syst 2012;42:250e6. [18] Colpan CO, Yesin T. Energetic, exergetic and thermoeconomic analysis of Bilkent combined cycle cogeneration plant. Int J Energy Res 2006;30:875e89. [19] Shokati N, Ranjbar F, Yari M. A comparative analysis of rankine and absorption power cycles from exergoeconomic viewpoint. Energy Convers Manag 2014;88:657e68. [20] Graebi H, Amidpour M, Karimkashi S, Rezayan O. Energy, exergy and thermoeconomic analysis of a combined cooling, heating and power (CCHP) system with gas turbine prime mover. Int J Energy Res 2011;35:697e709. [21] Balli O, Aras H, Hepbasli A. Thermodynamic and thermoeconomic analyses of a trigeneration (TRIGEN) system with a gasediesel engine: part II e an application. Energy Convers Manag 2010;51:2260e71.
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Exergoeconomic analysis of a solar-powered/fuel assisted Rankine cycle for power generation Eduardo J.C. Cavalcanti a, *, Henrique Pereira Motta b a b
Department of Mechanical Engineering, Federal University of Rio Grande do Norte, 59072-970, Natal, RN, Brazil Engineer of Mechanical Engineering, PB, Brazil
a r t i c l e i n f o
a b s t r a c t
Article history: Received 25 November 2014 Received in revised form 1 May 2015 Accepted 28 May 2015 Available online 19 June 2015
A Rankine System assisted for solar radiation and fuel combustion which produces 57 kW electrical power are evaluated from exergoeconomic point of view. The Parabolic trough collector efficiency has been performed to investigate its effect as heat source. The exergoeconomic parameters as the relative cost difference and the exergoeconomic factor for each component are evaluated. The analysis is based on the SPECO (Specific Exergy Costing) approach. The simulation of system on March, June, September and December 21st from 7 am to 4 pm for Natal/Brazil using real data was carried out. The results reveal the daily average values of collector efficiencies, ratio of the useful solar energy, electricity produced, the specific cost per exergy unit of the produced electricity and others heat rates. The system is advantageous for higher solar radiation. The outcome of the analysis can be useful in design, optimization of operating parameters and help to take decision of investment. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Exergoeconomic analysis Rankine cycle Solar collector Cost
1. Introduction The requirement to supply the demand for energy and the substitution of fossil energy by renewable sources drive the development of alternative renewable energy sources. A great deal of effort has been devoted to development of power system more efficient from a thermodynamics and economic point of view. The solar energy is a growing alternative in many countries, where there is abundant solar irradiation at nearby locations of the equator line. The SPFASRE (solar-powered/fuel assisted Rankine engine) is a green system which uses the solar energy and reduces the associated environmental impact. Some solar assisted Rankine engines use organic fluid as a working fluid called OCR (Organic cycle Rankine), even thought the efficiency is low. The Rankine cycle efficiency is about 50% of the Carnot cycle efficiency (e.g., [1,2]). The OCR efficiency is limited due to the organic fluids decomposition at high temperatures. Rankine engine which operates between temperature of 93 C and 27 C will expect to have an efficiency of 9% and if the higher temperature is increased to about 200 C, the efficiency can rise to 19%, [3]. The water is the original working fluid in Rankine engine. It can be
* Corresponding author. E-mail addresses: [email protected] (E.J.C. Cavalcanti), henriquepmotta@ gmail.com (H.P. Motta). http://dx.doi.org/10.1016/j.energy.2015.05.081 0360-5442/© 2015 Elsevier Ltd. All rights reserved.
superheated to a practical limit of 600 C. The water is used in large power plants to provide power and electricity due to the higher efficiency around double value of cycle efficiency. The SPFASRE has been simulated for Jeddah's climate in Saudi Arabia [3]. The system generates a 36 kW steady electrical power. Evacuated tube collector with an area of 400 m2 generates water steam at 230 C and the LPG fired superheater produces steam at 400 C. The results indicate that the system is driven from 80% to 85% of the energy required for solar energy during the summer, fall and spring seasons and 70% of the energy required for solar energy during the winter season. The engine operates between 8 am and 5 pm. The collectors were PTCs (parabolic trough collectors) which can produce heat until 400 C and its efficiency was steady of 78%. The development of thermal system consists of modifying the system and component design parameters. One approach to improve the performance is exergy analysis. Exergy analysis provides an effective method for the measuring and optimizing performance of a thermal system by accounting for the energy quality. The exergy analysis permits to identify the greatest loss of available energy which is taking place. Plants have been described in order to indicate the irreversibilities, i.e. evaluate the loss of available energy [4,5]. When higher the irreversibility in a plant or component, lower will be its efficiency. The purpose is reduce the irreversibility. The exergy analysis of thermal systems is widely gaining acceptance over traditional energy methods in both industry and
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academia. The exergoeconomy combines exergy analysis and economic principles which has assisted the decision making in economic objective. This methodology calculates the cost associated with each material and exergy stream with the aid of cost balances for each component and auxiliary cost equations. It aims to minimize total cost of the system products, which implicitly includes in the fuel cost rate. There are many currently systems to produce electricity and its cost can be evaluated. These systems include steam turbine, gas turbine, combined cycle, cogenerative cycle, reciprocating engines and research of new technologies. Among these researches, the currently exergoeconomic values of electricity cost per exergy unit have been evaluated [6, 17e21]. A CHP (combined heat and power) system derived by diesel engine has been studied by Ref. [17]. A gas/ steam combined cycle cogenerative plant which has a HRSG (heat recovery steam generator) has been evaluated by Ref. [18]. A basic Rankine cycle classic has been investigated to recover heat from low temperature heat sources (140 C) [19]. The values of electricity cost per exergy unit at CCHP (combined cooling, heating and power) system or trigeneration system have been studied. In paper
[20], the system has worked with gas turbine as prime mover and in paper [21] has worked with (gas-diesel) dual fuel reciprocating engine. However, there are not enough publications for exergoeconomic analysis of power cycle assisted for solar energy to produce electricity. According [6], nine commercial Solar Electric Generating Systems power plants that are operating in the California Mojave desert are proven solar technologies. These plants utilize parabolic trough collectors with steam Rankine cycle system. The authors state that in the field of exergoeconomic analysis and optimization of solar combined cycle systems, there is a lack of investigation and research. An integrated solar combined cycle system has been optimized by Ref. [6]. The exergoeconomic analysis needs to use current data, therefore the data of collector cost [16] were used. They evaluated the technology development of components as parabolic trough solar technology and its cost during years 1990 until 2020. The costs are reducing from $300 to $110 per meters square during these years. The summarized results are given in Table 1. Therefore, the aim of this study is exergoeconomic analysis in order to evaluate the specific cost per exergy unit of electricity,
Table 1 Electricity cost per exergy unit of systems. Cost per exergy unit
Feature
Reference Year
Electricity 4.48 $/GJ Electricity GT 13.96 $/GJ; ST 37.69 $/GJ; Average 18.89 $/GJ Electricity 26.75 $/GJ
Combined heat and power (CHP) system Electrical power 11.5 MW, vapor 2.5 kg/s steam at 140 C Gas/steam combined cycle Electrical power GT 23.7 MW þ ST 6.3 MW Overall 29.0 MW
[17] (2012) [18] (2006)
Rankine Cycle, Steam turbine inlet temp ¼ 140 C Electrical power 1.0 MW Gas Turbine, heat recovery steam generator (HRSG), absorption chiller Electrical power 19.23 MW, cooling 6.96 MW, heating (steam) 24.65 MW
[19] (2014)
Trigeneration dual fuel reciprocating engine (RE) with turbo air charger, absorption chiller. Electrical Power 5.9 MW, cooling 0.54 MW, hot water and steam 2.46 þ 1.82 MW
[21] (2010)
Integrated solar combined cycle system gas turbine 2 125.0 MW steam turbine 150.0 MW, overall 400.0 MW, useful energy of field collector 51.76 MW
[6] (2010)
Electricity of GT 20.9 $/GJ, Cooling 45.4 $/GJ, Heating 11.4 $/GJ Electricity of engine 45.95 $/GJ, Cooling 167.52 $/GJ, Hot water 29.98 $/GJ, Steam 42.42 $/GJ Electricity ST 76.75 $/GJ; GT 60.89 $/GJ
Fig. 1. Schematic of the solar-powered/fuel assisted Rankine engine (adapted from Ref. [3]).
[20] (2011)
E.J.C. Cavalcanti, H.P. Motta / Energy 88 (2015) 555e562
Fig. 2. Average of direct irradiation for March, June, September and December.
daily collector efficiency and the ratio between the useful solar energy of collector and the total rate of heat required for the system (Fss). The SPFASRE was simulated at Natal/Brazil. This study is the first of its kind for the Natal/Brazil solar irradiation during all seasons.
2. Methodology The system is similar to [3]. The difference is the present system has only one gas fired. It has collectors field that assist the Rankine engine. The working fluid at PTC is thermal oil which supply the heat required for preheating, evaporating and superheating of the water in the Rankine engine. The steam is then superheated with an LPG-fired superheater to improve the Rankine efficiency. The steam flows in turbine with 60,000 rpm. The turbine shaft speed is reduced to 3600 rpm by a gearbox which drives a generator. The heat is rejected at air cooler condenser. The generator supply the two pumps and two fans at point 23 and then generates the net electric power at point 13. Fig. 1 shows the schematic of SPFASRE. The next step in evaluation is to select the typical weather at city. Natal/Brazil is a tropical savanna climate. It is located at Brazil northeast with latitude 05 470, longitude 35 120 and height 30 m. The city is located nearby of equator line and has high solar irradiation. The February month has the higher solar insolation at Natal/Brazil during the year. In this month, the beam solar indices in normal angle with the Natal surface. The following data of an average year is based on the historical records from 1999 to 2012 according weatherspark [7]. The temperature typically varies from 22 C to 31 C and is rarely below 20 C or above 33 C. The probability that precipitation will be observed at this location varies throughout the year. Precipitation is most likely around June 13,
Fig. 3. Schematic of a parabolic trough collector: Adapted from Ref. [9].
557
occurring in 56% of days. Precipitation is least likely around November 23, occurring in 17% of days. Over the course of the year typical wind speeds vary from 1 m/s to 9 m/s (light air to fresh breeze), rarely exceeding 11 m/s (strong breeze). The irradiation has strong variation due to cloud and precipitation. The average direct irradiation during the hours for the nineteenth, twenty-first and twenty-thirty of March, June, September and December were calculated. The data represent the days of fall, winter, spring and summer 2010 according Inpe [8]. The PTC (parabolic trough collector) can utilize only direct radiation beam due to concentrating collector. These values were calculated by difference between total radiation and diffuse radiation. Fig. 2 shows the direct irradiation during the day for 4 month for each 5 min. The used collector was the PTCs (parabolic trough collectors). It is made by a sheet of reflective material into a parabolic shape, where the beam irradiation incident are reflected into the receiver tube. The receiver tube is a black metal tube placed along the focal line of the receiver where flow inside the work fluid. The PTC efficiency are not steady, it is affect by the heat losses to environmental and the useful heat removed by working fluid. The heat losses at air side are determinated by cover temperature, environmental temperature and wind velocity. The useful heat at working fluid side is determinate by temperature difference between work fluid and surface and flow configuration. To reduce the heat losses, an evacuated concentric glass tube (cover) is employed around the receiver. The PTC efficiency is calculated by ratio between the useful energy (Qu) and the beam radiation versus aperture area of the parabola (GB$Aa) [9]. The useful energy is calculated from an energy balance of its receiver as follows:
Q_ u ¼ GB $ho $Aa UL $Ar $ðTr Ta Þ ¼ hi $Ai $ðTr Toil Þ
(1)
The useful energy is equal the difference between the incident radiation on receiver and the heat losses on receiver (cover glass tube) to environmental or also equal the heat rate by convection between the receiver surface and the thermal fluid. The heat losses on receiver to environmental is estimated by the overall coefficient of heat exchange (UL). It is composed for the losses due to radiation and convection between the cover and the environment, and the radiation between the receiver and the cover of glass concentric evacuated. The overall coefficient of heat exchange is evaluated using the following equation:
" UL ¼ hair
Ar 1 þ þ hr;ca Ac hr;rc
#1 (2)
The coefficient can be determinated according [9]. The mass flow rate is divided in the row tube at collector field of 10. The air wind speeds was the years average of 5 m/s. The parameter of parabolic trough Collector are given in Fig. 3. The characteristics of Parabolic trough Collector are given in Table 2. The input parameters of components as efficiency and collector area are showed in Table 3. The collector field limitation is the maximum allowed temperature of the heat transfer oil used inside the collector. The working fluid was the Paratherm HR manufactured by Paratherm. The temperature should not exceed 343 C to work a long time to avoid the fluid degradation. In order to avoid fire hazards due to selfignition of the heat transfer oil, the temperature should not exceed the autoignition temperature of 416 C. Data of this fluid is available in Ref. [10]. The heat of combustion is 46.3 MJ/kg. Some input parameters were similar to [3]. The author carried out a simulation of this cycle for Saudi Arabia's climate. In this work, the operation data for maximum irradiation of 910 W/m2 at march is designed. The temperature of evaporator and pre-heater
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Table 2 Characteristics of PTC. Parameter
Value
Collector rim angle Collector aperture Receiver outside diameter Receiver inside diameter Glass cover diameter Mirror reflectivity Glass cover transmittance Glass cover emittance Receiver absorptivity Receiver emittance Collector orientation Mode of tracking Row tube collector
70 2.0 m 13.72 mm 9.24 mm 33.72 mm 0.98 0.96 0.87 0.97 0.92 Axis in NeS direction EeW horizontal 10
Table 3 The input parameters of system. Parameter
Value
Steam turbine efficiency Gas fired superheater efficiency Generator efficiency Gearbox efficiency Collector area
72% 60% 90% 90% 400 m2
on oil side is maintained steady by oil mass flow rate. The incoming turbine temperature is maintained by LPG consume. The maximum and minimum temperature of oil is 330 C and 200 C. The temperature of condenser is 55 C. The steam is maintained at 300 C at point 8 and 400 C at point 9 thought gas burning. The minimum pinch point between point 4 and 7 is 10 C. The pump is isentropic. The input parameters are defined as follows: The gas fired superheater is the place where burns LPG. The composition of natural gas is given in Table 4. The ratio between the useful solar energy of collector and the total rate of heat required for the system is calculated as the following equation:
Fss ¼
Q_ u _ Q u þ Q_ Gas
(3) fired
The thermodynamic model was built based on the mass, energy and exergy balance between each component. The Exergy balance for each component evaluated the destruction exergy as follows:
EF ¼ EP þ ED
(4)
The second law efficiency or exergetic efficiency at each component is the ratio between the product exergy and the fuel supplied exergy according to the equation:
ε¼
EP EF
The thermoeconomic analysis combines the exergetic analysis with the economic constraints for the optimization of the thermal system [5]. Its is useful to understand the cost formation process and calculate the specific unit exergetic cost of each product. The analysis reveals which equipment should be possible and economically feasible invest in order to improve the system. Different approaches for formulating efficiencies and auxiliary costing equations have been suggested in the literature. The SPECO (specific exergy costing method) works with their approach, fuels and products. This method was initially suggested by Refs. [11,12]. The rigorous discussion of fuel and product definitions that also consider the components of exergy (mechanical, thermal and chemical) has been made [13]. The product Ep and the fuel Ef are defined considering the desired result produced by the component and the resources expended to generate this result. The product is defined to be equal to the sum of all the exergy values to be considered at the outlet plus all the exergy increases between inlet and outlet that are in accord with the purpose of the component. The fuel is defined to be equal to all the exergy values to be considered at the inlet plus all the exergy decreases between inlet and outlet minus all the exergy increases that are not in accord with the purpose of the component. Decisions need to be made to implement the definitions [13]. The fuel and product exergy for all components of system are given in the following table (see Table 5). The basic thermoeconomic equation is shown as follows:
cp $Ep ¼ cf $Ef þ Z_
(6)
cP and cf represent the average costs per exergy unit of product and fuel, respectively. This equation states that the cost rate associated with the product of the system is equal to the sum of cost rate of fuel and capital cost. The purchase cost function of the component (Zi) is determinated by Refs. [5,6,14,15]. The solar field is comprised of collectors parabolic-trough from type of LS-3 which are single axis tracking and aligned on a northesouth line, thus tracking the sun from east to west [16]. Various purchase cost functions of this system are given in Appendix A. The capital investment of a component is converted into the cost rate considering the CRF (capital recovery factor):
Z_ i ¼ Zi $CRF$4 ½$=s
(7)
4 represents the maintenance factor 1.06. The CRF (capital recovery factor) is an economical parameter that depends on the interest rate as well as on the estimated equipment lifetime. CRF is calculated using the following equation:
ð1 þ iÞnyears 1 $ CRF ¼ i$ nyears ð1 þ iÞ 1 nyears $nh $3600
(8)
The years number (nyears) is 20, hour for solar Field is 9. The interest rate i is 12.4%. The fuels are solar radiation and natural gas.
(5) Table 5 Definition of fuel and product.
Table 4 Composition and typical properties of natural gas. Component
% Volume
Methane Ethane Propane Nitrogen Carbon dioxide Higher calorific value
88.82% 8.41% 0.55% 1.62% 0.60% 47.574 MJ/kg
Component
Exergy rate of product EP
Exergy rate of fuel EF
Collector Evaporator Pre-heater Pump 1 Pump 2 Gas fired SH Turbine Gear Box Induct. Gener. Air cooler Cond.
E3-E2 E8-E7 E7-E6 E2-E1 E6-E5 E16-E15 E11 E12 E13 þ E23 E18-E17
Eirrad E3-E4 E4-E1 E19 E20 E14 E9-E10 E11 E12 E10-E5
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559
Their costs are null and 0.3281 $/kg, respectively. Beside the purchased equipment cost, there are other DC (direct costs) and IC (indirect costs), according [17]. These costs involved in the project are showed in Table 6: The cost rate of the exergy destruction rate is defined as:
C_ D ¼ cf $E_ D
(9)
The relative cost difference rk and exergoeconomic factor fk are calculated as follows:
rk ¼
cp cf cf
(10)
fk ¼
Z_ _ cf $ED þ Z_
(11)
The exergoeconomic factor compares the rate of investment cost _ with the rate of cost of irreversibility (c $E_ D ). Low values of this (Z) f factor indicate that the cost of irreversibility is meaningful compared to the cost of investment. The lowest value of exergoeconomic factor indicates that this component has the greatest potential for improvement.
3. Results and discussion The PTC performance is assessed using the model described. The system was designed initially for maximum solar irradiation of 910 W/m2. The output and input temperature of oil are steady and their values are 330 C and 200 C. Fig. 3 shows the effect of the solar irradiation on the PTC efficiency. The oil mass flow rate is higher when the solar irradiation is high for that the oil temperature not exceed 330 C. The receiver temperature is close the oil temperature due to turbulent flow, therefore the losses rates are steady. When the solar irradiation (GB) is decreased, the losses rates remain steady thus, the useful energy and efficiency are decreasing. In addition, for lower irradiation values, the efficiency decreases meaningfully due to the lower internal convective coefficient at laminar flow. For values below 230 W/m2, the output and input temperature of oil were changed to 270 C and 220 C to increase the efficiency. For new situation, the temperature of cover glass tube is reduced and decreasing his losses rates. However, the efficiency is again decreasing below 0.5 for lower solar irradiation (140 W/m2) (see Fig. 4). Table 7 shows the fluid temperature, mass flow rate, exergetic and thermoeconomic performance of the collector field and Rankine engine for solar irradiation of 910 W/m2. The mass flow rate of thermal oil is 8 times the steam mass flow rate. The thermal oil exergy is high due to the chemical exergy. The electrical net power is 56.6 kWe. The products of the system (collector field and Rankine engine) are steam hot thermal oil and electrical energy. The specific cost per exergy unit of fuel solar irradiation and LPG gas are null and 6.687 $/GJ. The electricity cost per exergy unit is of 10.42 $/GJ. The cost rate is high at collector field due to higher purchase cost. The specific cost per exergy unit of oil
Fig. 4. Efficiency Collector versus Direct Irradiation for two situation of oil temperature.
is low because its high exergy. The losses cost rate of the system is 0.1447 and 0.8654 $/h at 16 and 18, respectively. Thermoeconomic variables of cogenerative system, exergy destruction, exergy efficiency, average unit cost of fuel and product, the cost rate of exergy destruction rate, total cost rate, relative cost difference and exergoeconomic factor for each component are given in Table 8. The collector field has higher values of exergy destruction. The air cooler and collector have lower exergetic efficiency. The exergoeconomic analysis reveals that the higher average unit cost of fuel is at generator, and the higher average unit cost of product is at air cooler. Also, the gas fired superheater has a higher cost rate for
Table 7 Data of temperature, mass flow rate, exergy, costs rates and specific costs per exergy at each stream for solar irradiation of 0.91 kW/m2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
T [ C]
m_ [kg/s]
200.0 200.0 330.0 235.7 55.0 55.1 224.0 300.0 400.0 54.97
0.9083 0.9083 0.9083 0.9083 0.1063 0.1063 0.1063 0.1063 0.1063 0.1063
25.0 25.0 350.0 25.0 45.0
0.00086 0.04632 0.04718 12.240 12.240
Ex [kW]
_ C[$/h]
c [$/GJ]
44,651 44,651 44,777 44,681 0.90 1.16 22.06 110.0 122.70 23.40 73.41 66.07 56.64 42.24 0 6.01 0 7.86 0.44 0.27 0.04 2.07 2.92
305.90 305.90 306.70 306.10 0.01 0.03 0.26 0.95 1.88 0.36 2.23 2.23 2.13 1.02 0 0.14 0 0.87 0.02 0.01 0.001 0.08 0.11
1.90 1.90 1.90 1.90 1.90 4.24 3.32 2.41 4.24 4.24 8.44 9.38 10.42 6.69 0 6.69 0 30.58 10.42 10.42 10.42 10.42 10.42
Table 6 Cost of project. Direct costs (DC) Purchased equipment cost Installation Piping Instrumentation and controls
Indirect costs (IC) (PEC) 50% of PEC 30% of PEC 20% of PEC
Engineering and supervision Construction costs
50% of PEC 15% of DC
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Table 8 The thermoeconomic variables of the system. Component
ED [kW]
ε [%]
cf [$/GJ]
cP [$/GJ]
cD [$/h]
ZT [$/h]
rk [%]
G [%]
Collector Evaporator Preheater Gas fired Steam Turb Gear Box Generator Air cooler
213.70 8.11 8.79 23.45 25.94 7.34 6.61 14.64
36.96 91.55 70.38 35.28 73.89 90.00 90.00 34.93
0.000 1.903 1.903 6.687 4.242 8.437 9.375 4.242
1.848 2.183 3.080 20.010 8.437 9.375 9.930 30.58
0.000 0.056 0.060 0.565 0.396 0.223 0.223 0.224
0.8333 0.0331 0.0283 0.0483 0.7123 0.0001 0.0015 0.5217
e 14.72 61.84 199.2 98.87 11.12 5.921 620.7
100.00 37.30 31.95 7.88 64.26 0.06 0.68 69.99
exergy destruction rate due to its inherent nature. The higher cost rates are at collector and steam turbine which have higher purchase cost. Similar result has also been reported in integrated solar combined cycle system in Iran which the higher cost rate is at collector [6]. The higher relative cost difference is at air cooler. The lower value of exergoeconomic factor is at gear box and generator, revealing these two components should be increased his thermodynamic efficiency to improve the global efficiency. The solar radiation affects the performance of collector efficiency and the Rankine engine. Table 9 shows the direct solar irradiation, collector output temperature, collector efficiency, oil flow rate, output evaporator temperature, water flow rate, ratio useful solar energy, produced electricity (Ex[13]) and the specific unit exergetic cost. The output oil temperature changes from 330 to 270 when the irradiation is below 230 W/m2. The collector efficiency decreased while the irradiation is reduced. The thermal oil mass flow is high when the irradiation is high for control the maximum oil temperature at collector exit. The water flow rate is steady to produce a steady flow rate, and thus to hold the same rotation. Otherwise, the variation of water flow rate will reduce the steam turbine efficiency. The high solar irradiation provides higher rate useful solar energy. The produced electricity should be steady, although the electricity is reduced slightly due to increase of fan consumed electricity at point 21 related at air consumed in combustion. Therefore, the electricity cost per exergy unit is increasing due to the higher LPG fuel consume. Table 10 makes a comparison with the electricity cost per exergy unit between other power systems and shows the solar radiation to produces the same cost per exergy unit. Result of electricity cost per exergy unit has been reported in combined cycle cogeneration plant i.e. 13.96 $/GJ for gas turbine and 37.69 $/GJ for steam turbine and average of 18.89 $/GJ (Colpan and Yesin, [19]). Other system is for steam turbine with has heat source with low temperature 140 C to recover heat according Shokati et al. [20]. Its result of electricity cost per exergy is 26.75 $/ GJ. The solar-powered/Fuel assisted Rankine cycle reaches the value
of combined cycle when the irradiation is higher 750 W/m2. It means that the studied case changes the first system when the direct irradiation is higher than 750 W/m2. For the second system the stied system should has the direct irradiation higher than 600 W/m2 to reach the same cost per exergy unit. The difficult of comparative analysis is that the parameters of all system as work fluid temperature, power net produced. Comparison with same parameters may improve the accuracy of the results. The system was simulated to evaluate the effect of year seasons on performance parameters. The calculations of collector efficiencies, ratio of the useful solar energy of collector, specific unit exergetic cost of electricity, heat rates and cost rates were carried out for four month from 7 am to 16 pm using the data from Fig. 2. The results are shown at Table 11. The solar irradiation is higher in March and lower in June due to rainy winter season. The total electricity is steady. The useful energy of collector is higher in March when there is the higher collector efficiency. This is because the higher value of collector efficiency happens when the solar irradiation is higher, it can be showed at Fig. 2. The June and September months have the higher heat production at gas fired superheater due to low solar irradiation. The collector efficiency varies between 70 and 74%, such values are lower of collector efficiency of Gary et al. [3] of 78% due the control system of mass flow rate of thermal oil described Fig. 3. The range of ratio the useful solar energy of collector is between 37.7% and 50.3, which has higher value in March. The total fuel consume is higher in June due to low solar radiation. The higher losses cost during all day are in June due to high fuel consume. Therefore the lower costs per exergy unit happen at March when it happens higher solar irradiation. The daily values of electricity cost per exergy unit vary between 29.98 $/GJ and 35.83 $/GJ. All results of electricity cost per exergy unit daily for four month are higher of average value of 18.89 $/GJ [18], even thought the combined system of [19] works with gas turbine and the values are higher of average value of 26.75 $/GJ [19] of Steam turbine which works with low temperature of heat source. Therefore, the system in present study is not an advantageous system from an exergoeconomic point of view.
Table 9 Effect of solar irradiation on system parameter. Irrad [kW/m2]
T3 [ C]
hcoll
m_ oil [kg/s]
T8 [ C]
m_ w [kg/s]
Fss [%]
Ex[13] [kW]
celet [$/GJ]
0.91 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10
330 330 330 330 330 330 330 330 270 270
0.8103 0.8089 0.7947 0.7805 0.7552 0.7298 0.6695 0.6091 0.5574 0.1130
0.9083 0.8968 0.7831 0.6730 0.5581 0.4495 0.3299 0.2251 0.3637 0.0369
300.4 286.1 224.0 224.0 224.0 224.0 224.0 215.0 154.6 65.31
0.1064 0.1064 0.1064 0.1064 0.1064 0.1064 0.1064 0.1064 0.1064 0.1064
92.33 91.16 79.59 68.39 56.70 45.66 33.50 22.66 13.95 1.41
56.71 56.70 56.67 56.64 56.62 56.60 56.57 56.53 56.18 55.25
10.40 10.95 16.33 21.42 26.71 31.66 37.15 42.05 47.16 54.87
E.J.C. Cavalcanti, H.P. Motta / Energy 88 (2015) 555e562
561
Table 10 The electricity cost per exergy unit of three systems. Cost per exergy unit $/GJ
Feature
Turb inlet temp C
Power MW
Irradiation dir equivalent W/m2
18.89 26.75 Studied case-Table 8
Steam turb/gas turb Steam turb Steam turb
450/733 140 400
6.29/23.72 ¼ 29.02 1.0 0.057
750 600 Table 8
Table 11 Simulation of performance system for 4 year month. GB [MJ] March June Sept Dec
6970 5515 5805 6290
and and and and
537.8 425.6 447.9 485.3
2
W/m W/m2 W/m2 W/m2
W[13] [MJ]
Qu [MJ]
hcoll [%]
Qgas
1828 1826 1829 1829
5204 3905 4125 4571
74.66 70.80 71.06 72.67
5152 6453 6232 5786
fired
[MJ]
Fss [%]
mfuel [kg]
C[13] [$]
C[16] þ C[18] [$]
50.25 37.70 39.83 44.13
180.5 226.1 218.3 202.1
54.81 65.43 63.45 59.81
5.66 7.07 7.29 6.74
4. Conclusions HRSG: A system solar-powered/fuel assisted rankine engine for power generation has been evaluated using the thermoeconomic method described by Ref. [5] in order to investigate the effect of solar radiation. The collector efficiency is higher while the solar irradiation values are high. The system was simulated from 7 am to 4 pm at March, June, September and December 21st for 2010 year. The electrical net power is steady of 56.6 kWe. The study reveals the thermodynamic inefficiencies, cost rates, average unit cost of fuel and product for each components, specific cost per exergy unit of electricity and ratio useful solar energy. As a result, the components with highest potential for improvement are identified. The method indicates whether improvement should be obtained by increasing the thermodynamic efficiency or by reducing investment cost. The rainy winter of June has the lower solar irradiation and, thus the lower collector efficiency, higher fuel consume and higher specific cost per exergy unit of electricity. In contrast, the March month has the opposite results of winter. The system is not an advantageous system from an exergoeconomic point of view. It has been observed that the electricity cost rate per exergy unit is significantly higher compared to other system as the combined system. Thus, it is important to put efforts to improve the overall efficiency of SPFASRE. In other hand, other aspect as environmental impact is important for analysis of effect of solar collector assisting Rankine cycle for electricity production because this system burns less fuel and should reduce the environmental impact.
Acknowledgment The knowledge of this method was sponsored for CAPES. The author would like to thanks for George Tsatsaronis for his supporting at pos-doc project. And Propesq/UFRN for scholarship of bachelor
Appendix A. Cost function 1 Air compressor: PECc ¼ 71:1$m_ air $ 0:92h $PPei $ln PPei c
Combustion
PECcc ¼ 46:08$m_ ar $
chamber:
#
1 0:995PPe i
$ð1 þ eð0:018$T26:4Þ Þ Gas turbine: PECt ¼ 479:34$
m_ g 0:93ht
$ln PPei $ð1 þ eð0;036$T54:4Þ Þ
Q_ ec DTec
16.38 18.93 18.41 17.56
!0:8 þ
¼ ¼ ¼ ¼
22.04 26.00 25.70 24.30
Q_ ev DTev
29.98 35.83 34.69 32.67
!0:8 þ
Q_ sh DTsh
!0:8
þ21276$m_ w þ 1184:4$m_ 1:2 g Solar Field: PECcoll ¼ 355 $/m2 _ 0:71 Pump: PECpump ¼ 3540$W _ SteamTurbine: PECST ¼ 6000$W
0:7
0:89 A Condenser: PECaircooler ¼ 156000$ 200 Fan: PECF ¼ 12300$
W_ 50
!0:76
Generator/Motor: PECGen ¼ 500$
!0:89 1h_ $ h p
W_ 10
P
!0:6
Heat Exchanger: PECHE ¼ 12000$
A_ 100
Nomenclature Aa Ac Ai Ar C C_
D
cp cf ED EF EP fk Fss GB hair hr,c-a hr,r-c
"
PECHRSG ¼ 6570$
þ þ þ þ
c[13] [$/GJ]
hi i m_ oil m_ w nyears nh
aperture area of collector m2 glass cover area m2 receiver internal area m2 receiver area m2 cost $ cost rate of the exergy destruction rate $/s average costs per exergy unit of product $/kJ average costs per exergy unit of fuel $/kJ destruction exergy rate kW fuel exergy rate kW product exergy rate kW exergoeconomic factor ratio between the useful solar energy of collector and the total rate of heat required for the system beam solar radiation W/m2 external coefficient of air convection at cover W/(m2 K) radiation coefficient from glass cover to ambient W/ (m2 K) radiation coefficient from receiver to glass cover W/ (m2 K) internal coefficient of convection W/(m2 K) interest rate thermal oil mass flow rate kg/s water mass flow rate kg/s years number hour number
562
Q_ u Q_
Gas fired
E.J.C. Cavalcanti, H.P. Motta / Energy 88 (2015) 555e562
useful energy rate at collector W energy rate produced at gas fired superheater W relative cost difference receiver temperature K air temperature K thermal oil temperature K global coefficient of heat exchanger W/(m2.K)
rk Tr Ta Toil UL Z_
cust rate of component $/s
Z_ T Zi W
total cust rate (purchase, direct and indirect cost) $/s purchase component cost electric energy MJ
Greek symbols ε exergetic efficiency 4 maintenance factor ho optical efficiency of collector Abbreviation CRF capital recovery factor DC direct costs IC indirect costs LPG liquefied petroleum gas PEC purchased equipment cost PTC parabolic trough collector SPFASRE solar-powered/fuel assisted Rankine engine References [1] Barber RE. Current costs of solar power organic rankine cycle engines. Sol Energy 1978;20(1):1. ~ es-Moreira JR. Analise Exerge tica de um Ciclo Rankine [2] Cavalcanti EJC, Simo Organico com Fonte Solar, CIBIM 10. 2011. Oporto, Portugal. [3] Gari H, Khalifa A, Radhwan A. Design and simulation of a solar-powered/fuelassisted rankine engine for power generation. Appl Energy 1988;30:245e60.
[4] Kotas TJ. The exergy method of thermal plant analysis. 1st ed. London: Anchor Brendon Ltd; 1985. [5] Bejan A, Tsatsaronis G, Moran M. Thermal design and optimization. USA: John Wiley & Sons, Inc.; 1996. [6] Baghernejad A, Yaghoubi M. Multi-objective exergoeconomic optimization of an integrated solar combined cycle system using evolutionary algorithms. Int J Energy Res 2010;35(7):601e15. [7] WeatherSpark. weatherspark.com/averages/33461/Natal-Rio-Grande-doNorte-Brazil, access sept/08/2014 at10:20hr. ~ DE TEMPO E ESTUDOS CLIMATICO. [8] Inpe e CENTRO DE PREVISAO www.cptec. inpe.br/, access april/08/2011 at 11:30 hr. [9] Kalogirou S. Solar energy engineering: processes and systems. 1st ed. Elsevier Inc; 2009. [10] Paratherm Corporation e Heat Transfer Fluids. http://www.paratherm.com/ heat-transfer-fluids/high-temperature-heat-transfer-fluids/paratherm-hr/. Acess em sept/01/2010 at 9:30hr. [11] Tsatsaronis G, Lin L. On exergy costing in exergoeconomics. In: Computeraided energy systems analysis, American Society of Mechanical Engineers. AES; 1990. p. 21. [12] Lazzaretto A, Tsatsaronis G. On the calculation of efficiencies and costs in thermal systems. In: Proceedings of the ASME advanced energy systems division. Nashville, Tennessee: AES; 1999. p. 39. [13] Lazzaretto, Tsatsaronis. SPECO: a systematic and general methodology for calculating efficiencies and costs in thermal systems. Energy 2006;31: 1257e89. [14] Misra RD, Sahoo PK, Gupta A. Thermoeconomic optimization of a single effect H2O/LiBr absorption chiller system. Int J Refrig 2003;26:158e69. [15] Smith R. Chemical process design and integration. John Wiley; 2005. [16] Kearney D, Price H. Parabolic-trough technology roadmap a pathway for sustained commercial development and deployment of parabolic-trough technology. SunLab NREL; 1999. [17] Yildirim U, Gungor A. An application of exergoeconomic analysis for a CHP system. Electr Power Energy Syst 2012;42:250e6. [18] Colpan CO, Yesin T. Energetic, exergetic and thermoeconomic analysis of Bilkent combined cycle cogeneration plant. Int J Energy Res 2006;30:875e89. [19] Shokati N, Ranjbar F, Yari M. A comparative analysis of rankine and absorption power cycles from exergoeconomic viewpoint. Energy Convers Manag 2014;88:657e68. [20] Graebi H, Amidpour M, Karimkashi S, Rezayan O. Energy, exergy and thermoeconomic analysis of a combined cooling, heating and power (CCHP) system with gas turbine prime mover. Int J Energy Res 2011;35:697e709. [21] Balli O, Aras H, Hepbasli A. Thermodynamic and thermoeconomic analyses of a trigeneration (TRIGEN) system with a gasediesel engine: part II e an application. Energy Convers Manag 2010;51:2260e71.