designs Article
Energetic and Financial Optimization of Solar Heat Industry Process with Parabolic Trough Collectors Evangelos Bellos *
ID
, Ilias Daniil and Christos Tzivanidis
Thermal Department, School of mechanical engineering, National Technical University of Athens, Heroon Polytechniou 9, Zografou, 15780 Athens, Greece;
[email protected] (I.D.);
[email protected] (C.T.) * Correspondence:
[email protected] Received: 14 June 2018; Accepted: 13 July 2018; Published: 16 July 2018
Abstract: The objective of this work is the investigation of a solar heat industry process with parabolic trough solar collectors. The analysis is conducted for the climate conditions of Athens (Greece) and for five load temperature levels (100 ◦ C, 150 ◦ C, 200 ◦ C, 250 ◦ C, and 300 ◦ C). The examined configuration combines parabolic trough solar collectors coupled to a storage tank and an auxiliary heat source for covering the thermal need of 100 kW. The solar thermal system was optimized using the collecting area and the storage tank volume as the optimization variables. There are three different optimization procedures, using different criteria in every case. More specifically, the solar coverage maximization, the net present value maximization, and the payback period minimization are the goals of the three different optimization procedures. Generally, it is found that the payback period is between five and six years, the net present value is between 500–600 k€, and the solar coverage is close to 60%. For the case of the 200 ◦ C temperature level, the optimum design using the net present value criterion indicates 840 m2 of solar collectors coupled to a storage tank of 15.3 m3 . The optimization using the solar cover indicates the use of 980 m2 of solar collectors with a tank of 28 m3 , while the payback period minimization is found for a 560 m2 collecting area and an 8-m3 storage tank volume. The results of this work can be used for the proper design of solar heat industry process systems with parabolic trough collectors. Keywords: Solar energy; heat process; parabolic trough collector; optimization; solar industry
1. Introduction There are several problems in the domain of energy, which are mainly associated with fossil fuel depletion [1], increasing energy demand [2] and global warming [3]. The industrial sector is a high energy-consuming sector with around 50% of the worldwide energy consumption [4]. The majority of the energy consumption in the industries is for the heat process; this percentage reaches up to 70% [5]. The usual way for obtaining the demanded heat is by using fossil fuels [6], which has negative environmental impacts, as well a high operational cost. The use of solar energy for covering totally or partially the heat process demand of the industries is not a novel idea, but it is revisited [7,8] due to the serious environmental problems, as well as the fossil fuel depletion in the future [9–11]. The processes in the industries cover a great range of low, medium, and high temperatures [12,13]. Below, usual industries with the respective typical temperature ranges for the demanded heat are given [7,8]:
• • •
Dairy: 60–180 ◦ C Food: 60–120 ◦ C Paper: 60–120 ◦ C
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Chemical: 60–260 ◦ C Bricks and plastics: 60–220 ◦ C Automobile: 50–120 ◦ C Agriculture: 80–90 ◦ C Metal: 160–180 ◦ C
It is essential to state that every industry may need heat for more than one process. For instance, the dairy industry needs process heat for pressurization at 60–80 ◦ C, sterilization at 100–120 ◦ C, and drying at 120–180 ◦ C [7]. The parabolic trough solar collector (PTC) is the most mature solar concentrating technology [14,15] that is able to cover all of the previously presented temperature levels for the heat process in the industries [7]. The PTC can efficiently produce useful heat for temperatures up to 400 ◦ C with thermal oil as a working fluid, and up to 550 ◦ C with molten salts [15]. So, the use of PTC is a promising choice in the solar heat for an industrial process (SHIP). Moreover, other kinds of solar collectors are the flat plate collectors (FPC) for temperatures up to 100 ◦ C, the evacuated tube collector (ETC) for temperatures up to 150 ◦ C, and the linear Fresnel reflector (LFR) up to 300 ◦ C [16]. In the literature, there are various studies for SHIP in various locations over the world. Table 1 summarizes all of the investigated studies. In 2001, Kalogirou [17] theoretically examined a solar system with PTC for hot water production at 85 ◦ C for Cyprus. He found the optimum collecting area to be 300 m2 and the optimum storage tank for this collecting area at 25 m3 . The solar coverage for this energetically optimized system was around 50% for Spain. Guerro and Quijano [18] studied the use of PTC for heat production at 100 ◦ C for a cork industry. Their system has a nominal capacity of 260 kW with a 432 m2 collecting area and 15 m3 , while the solar coverage was 65%. Abdel-Dayem [19] investigated a steam production system with PTC for Egypt. The system includes 1958 m2 , that cover a load of 175 ◦ C in a 10% percentage. Pietruschka et al. [20] examined the use of different systems in different locations. Firstly, they investigated a system with FPC for a food industry in Austria. This system produces heat at 95 ◦ C and includes 1200 m2 of collectors that cover a load of 650 kW. The second system includes LFR for a brick industry in Italy. This system produces heat at 180 ◦ C and includes 2640 m2 of collectors that cover a load of 1.5 MW. The last system includes a PTC for a dairy in Spain. This system produces heat at 180 ◦ C and includes 2040 m2 of collectors that cover a load of 1.0 MW. Silva et al. [21] studied a heat production system at 150 ◦ C with PTC in Spain. The nominal heat production was 100 kW that is covered in a percentage of 67% with a 1000 m2 collecting area and 100 m3 of storage tank volume. Vittoriosi et al. [22] studied the use of LFR in a 1.2-MW installation in Italy. They found that the total system coverage was 20% with 2700 m2 of collectors for heat production at 260 ◦ C. El Ghazzani et al. [23] found that the use of 39,760 m2 of PTCs with a storage tank of 3300 m3 were able to cover 57% of a 10.5-MW load at 160 ◦ C in Morocco. Recently, in 2018, the combination of PTCs and FPCs was recently examined by Tian et al. [24] for Denmark. They used 5960 m2 of FPCs for heat production at 75 ◦ C, and 4039 m2 of PTCs for heat production at 75 ◦ C. There is also a storage volume of 2430 m3 . The load of the districting heating was covered by both collector types, with the FPC producing a bit lower than 5 kWh/m2 , and the PTC producing a bit more than 5 kWh/m2 . The previous literature review indicates that the use of PTC for producing heating for industrial processes or other heat applications is a promising choice. Various systems have been studied worldwide, especially in locations with relatively high solar potential. Greece is a country with high solar potential, which ranges from 1400 kWh/m2 up to 1800 kWh/m2 yearly. Athens is the largest city in Greece; it is located approximately in the middle of Greece (about 38◦ latitude), and it is a representative location for investigation with about 1600 kWh/m2 solar potential [25]. The objective of this work is to design an optimum industrial process heat system for the climate conditions of Athens (Greece). This system includes PTCs and an auxiliary system for covering the heating load during the period without solar irradiation. This system has a nominal load demand
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of 100 kW, and it is investigated theoretically for temperature levels between 100–300 ◦ C with a 50 ◦ C step. This work is a theoretical approach for a solar-assisted industrial heat process, and the results can be applied in different industrial processes. This system is studied energetically and financially for different design scenarios. More specifically, different combinations of solar collecting areas and storage tank volumes are tested for all the years and periods. The system is optimized with three different criteria: the maximization of the solar coverage, the maximization of the net present value (NPV), and the minimization of the payback period (PP) of the investment. The results of this work clearly show the coverage of a solar system with PTC for heat process, as well as its financial sustainability. Moreover, the optimum system size is variable with the different optimization goals, which is discussed in this work. The innovation of this paper is based on the investigation of the present system in Greece, as well as the optimization with different criteria. The comparison of the optimization with energy and financial criteria separately is something that is not found in the present literature, and so this work has to add something new to this domain. The final conclusions of this work can clearly prove if the use of PTCs for heating production is a promising choice for Greece, and whether they can be utilized by various researchers and engineers. Finally, it has to be said that the innovation of this work is mainly associated with the investigation of a solar heat industrial process system in Greek climate conditions, as well as the optimization of the system with different criteria. Table 1. Summary of solar heat industrial process studies. PTC: parabolic trough solar collector, FPC: flat plate collectors, LFR: linear Fresnel reflector. T
Aa
V
f
Q
(◦ C)
(m2 )
(m3 )
(%)
(MW)
PTC PTC PTC
85 100 175
300 432 1958
25 15 -
50 65 10
0.26 -
Food Bricks Dairy
FPC LFR PTC
95 180 185
1200 2640 2040
-
-
0.65 1.5 1.0
Spain Italy Marocco
Heat Bricks Hot air
PTC LFR PTC
150 260 160
1000 2700 39,760
100 3300
67 20 57
0.1 1.2 10.5
Denmark
District heating
FPC PTC
75 95
5960 4039
2430
-
-
Application or Industry
Collector Type
Cyprus Spain Egypt
Hot water Cork Steam
Pietruschka et al. [20]
Austria Italy Spain
Silva et al. [21] Vittoriosi et al. [22] El Ghazzani et al. [23] Tian et al. [24]
Study
Country
Kalogirou [17] Guerro and Quijano [18] Abdel-Dayem [19]
2. Material and Methods 2.1. The Examined System-General Description Figure 1 depicts the examined configuration with the proper details. Parabolic trough solar collectors are used in order for the solar irradiation to be converted into useful heat. Thermal oil flows in the PTC field, and it is stored in the storage tank. The thermal oil from the tank feeds the heat exchanger, while there is a boiler in order for the proper heat amount to be given in the load. More specifically, the examined solar field is assumed to have the modules to parallel connection. So, all of the pipes from the PTC outlets are connected, and they are delivered in the upper part of the tank, which is the hot tank region. Cold oil from the tank bottom leaves the tank, and it is separated in different smaller pipes that feed the various modules. In the other side of the tank, hot thermal oil leaves the tank, and it goes to the heat exchanger in order to put heat into the load. The colder oil from the heat exchanger outlet returns to the storage tank bottom region. In the present work, for a specific combination of collecting area and storage tank volume, the inputs in the system are the solar direct beam irradiation (Gb ), the ambient temperature (Tam ), and the load temperature (Tl ). The developed program, which is presented in the following subsections, calculates the other parameters as the inlet fluid temperature in the solar field (Tc,in ), the outlet fluid
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temperature for the solar field (Tc,out ), the fluid inlet temperature in the heat exchanger (Ts,in ), the outlet temperature of the heat exchanger (Ts,out ), as well as the various heat rates (Q). Designs 2018, 2, x
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Figure1.1. The The examined examined configuration. Figure configuration.
2.2. The Solar Field 2.2. The Solar Field The Eurotrough module is used in this work, which is a PTC with an evacuated tube receiver The Eurotrough module is used in this work, which is a PTC with an evacuated tube receiver [26–28]. [26–28]. This module has a collecting area of 70 m2 and various modules in parallel connection from 2 and various modules in parallel connection from three up to This module a collecting area of 70 mThe three up tohas 14 have been investigated. working fluid is Therminol VP-1 [29], and the mass flow 14 rate haveinbeen investigated. The working Therminol [29], and the mass flow rate in every every module is selected at 4 kg/sfluid [30]. is Moreover, it isVP-1 important to state that the collectors are module isin selected at 4 kg/s [30]. Moreover, is important that the collectors are2located in a located a north–south direction, and they it track the sun into thestate east–west direction. Table includes north–south direction, and they track the sun in the east–west direction. Table 2 includes the main the main data about the examined module. data about the examined module. Table 2. Basic data about the solar collector [26–28]. Table 2. Basic data about the solar collector [26–28].
Parameter Symbol Module area Amod Parameter Symbol Number of solar modules Nmod Module area Amod mc Number ofFlow solarrate modules Nmod Module length Flow rate mLc Module length LDr Receiver diameter Receiver diameter D Concentration ratio Cr Concentration ratio
C
Value 70 m2 Value 3 to 14 modules 70 m2 4∙N mod (kg/s) 3 to 14 modules m 4·N12 mod (kg/s) 12 m 70 mm 70 mm 26.2 26.2
The solar irradiation in the collector aperture (Qs) is calculated as:
The solar irradiation in the collector aperture = (Qs⋅ ) is calculated as: Qs = A a · Gb where the total collecting area (Aa) is given as:
(1)
(1)
(2) = ⋅ where the total collecting area (Aa ) is given as: The thermal efficiency of the solar collector (ηth) is defined as: A a = Nmod · Amod (2) = (3) The thermal efficiency of the solar collector (η th ) is defined as: The useful heat production (Qu) is calculated as: Qu = η⋅th =⋅ ( − ) (4) (3) Qs The thermal efficiency (ηth) can be estimated using the following literature formula for the Eurotrough model [30]:
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The useful heat production (Qu ) is calculated as: Qu = m · c p · ( Tout − Tin )
(4)
The thermal efficiency (η th ) can be estimated using the following literature formula for the Eurotrough model [30]: ηth = 0.7408 · K (θ ) − 0.0432 ·
Tc,in − Tam ( T − Tam )2 − 0.000503 · c,in Gb Gb
(5)
The incident angle modifier (K) is calculated for this collector, according to the literature [31], as below with the solar angle (θ) in degrees: K (θ ) = cos(θ ) − 5.25091 · 10−4 · θ − 2.859621 · 10−5 · θ 2
(6)
The present tracking system makes the PTC follow the sun in the east–west direction, while the PTC axis is in the north–south direction. In this case, the incident angle (θ) is calculated as below [30,32]: cos(θ ) =
q
cos2 (θz ) + cos2 (δ) · sin2 ( ϕ)
(7)
More details about the calculation of the solar angles can be found in [30,32]. 2.3. Storage Tank The storage tank is assumed to be a cylindrical insulated tank with a thermal loss coefficient equal to 0.8 W/m2 K. The storage tank is an open tank without heat exchangers that is modeled with five thermal zones, and all of the zones have the same thickness in every case. More details about this modeling can be found in [30,32,33]. The diameter of the tank is assumed to be the same as its length [30]. This assumption has been checked with a simple sensitivity analysis, and it is found that it has no practical impact on the results. Moreover, it is assumed that the stream temperature to the load (Ts,in ) is the temperature in the upper zone, while the temperature to the solar field (Tc,in ) is equal to the temperature of the last node. The general energy balance in the storage tank is given below: Qst = Qu − Qloss − Ql,s
(8)
The stored energy (Qst ) is the difference between the heat input from the solar field (Qu ) and the heat output to the load (Ql,s ), and the thermal losses to the ambient of the tank (Qloss ). The stored energy can be expressed as: dTst Qst = ρ · c p · V · (9) dt The volume of the storage tank (V) is a parameter of this work, and it is investigated for a great range in order to determine its optimum value. More details will be given in the following sections. 2.4. Load Heat Exchanger The load heat exchanger is used in order for the heat to be transfered from the load to the industrial stream. In this work, the industrial stream is assumed to have a constant temperature (Tl ) that is examined parametrically from 100 ◦ C up to 300 ◦ C, with a step of 50 ◦ C. The energy balance in the heat exchanger is given below: Ql,s = ms · c p · ( Ts,in − Ts,out ) (10) The heat exchanger effectiveness (η hex ) was selected at 70%, and it is defined as: ηhex =
Ts,in − Ts,out Ts,in − Tl
(11)
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The mass flow rate in every case is selected to be the one that gives the maximum load (Ql ), which is 100 kW for this case. Generally, the minimum pinch difference in the heat exchanger was about ~5 K in all of the cases. The pressure level in the thermal oil circuit is selected to be at 15 bar in order to keep the oil in its liquid phase. Moreover, it has to be said that in every case, the thermal oil has temperature levels similar to the load temperature, and there are not extremely high deviations between them, because this would increase the exergy destruction losses of the system. 2.5. System Operation The system is assumed to operate about 350 days per year, or 8400 h per year. The heat demand is 100 kW, which is covered from the solar energy or the boiler. The energy parameters (E) can be calculated by integrations of the energy rates (Q) for the entire year: Designs 2018, 2, x 6 of 23 2.5. System Operation
The
t=8760 Z h
E=
Q dt
(12)
The system is assumed to operate about 350 days per year, or 8400 h per year. The heat demand t =0 h is 100 kW, which is covered from the solar energy or the boiler. The energy can be calculated the energy rates (Q) for the entire solar cover (f ) isparameters a critical(E) parameter, andbyit integrations is definedofas: year:
f =
=
El,s El
(12)
(13)
2.6. Weather DataThe solar cover (f) is a critical parameter, and it is defined as: ,
= (13) The system is investigated with a usual methodology by investigating 12 typical days, one for every month. Moreover, the system is assumed to operate only on the sunny days of every month. 2.6. weather Weather Datadata regards the climate conditions of Athens (Greece) with 38◦ latitude. The examined system is investigated a usual by investigating 12 typical days, one for in Figure 3. The direct solar The beam irradiation iswith given in methodology Figure 2, and the ambient temperature every month. Moreover, the system is assumed to operate only on the sunny days of every month. These resultsThe have been also given in [30], which is one previous work about PTC. The methods for examined weather data regards the climate conditions of Athens (Greece) with 38° latitude. The obtaining these weather data are given in [30], and 2,it and is essential totemperature state that in the followed direct solar beam irradiation is given in Figure the ambient Figure 3. Thesemethodology results have been also givenstandards in [30], which is one previous work about PTC. Thedays methods for is in accordance with the ASHRAE [34]. Figure 4 exhibits the sunny of every month, as obtaining these weather data are given in [30], and it is essential to state that the followed they have been calculated using real-averaged meteorological data for the years 2010–2016 [35–37]. methodology is in accordance with the ASHRAE standards [34]. Figure 4 exhibits the sunny days of Totally, the solar 219 days per year, which is a reasonable percentage of 60%. every system month, asoperates they have about been calculated using real-averaged meteorological data for the years 2010–2016 [35–37]. Totally, the solar system operates about 219 days per year, which is a reasonable This strategy has been also followed in [38] for a system with PTC. percentage of 60%. This strategy has been also followed in [38] for a system with PTC.
Jan Jul 1000
Feb Aug
Mar Sep
Apr Oct
May Noe
Jun Dec
900 800
Gb (W/m2)
700 600 500 400 300 200 100 0 0
3
6
9
12
15
18
21
24
Hours Figure 2. Daily variation of the solar beam irradiation for all the months in Athens (Greece). Figure 2. Daily variation of the solar beam irradiation for all the months in Athens (Greece).
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35 35
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Jan Jan Jul Jul
Feb Feb Aug Aug
Mar Mar Sep Sep
Apr Apr Oct Oct
May May Noe Noe
Jun Jun Dec Dec
30 30 25 25 oC) Tam Tam(o(C)
20 20 15 15 10 10 5 5 0 0
0 0
3 3
6 6
9 9
12 12
Hours Hours
15 15
18 18
21 21
24 24
Figure 3. Daily variation of the ambient temperature for all the months in Athens (Greece).
FigureFigure 3. Daily variation of the ambient forall allthe themonths months in Athens (Greece). 3. Daily variation of the ambienttemperature temperature for in Athens (Greece).
Sunny SunnyDays Daysofofevery everymonth month
30 30 25 25 20 20 15 15 10 10 5 5 0 0
Jan Feb Mar Apr May Jun Jan Feb Mar Apr May Jun
Jul Aug Sep Oct Noe Dec Jul Aug Sep Oct Noe Dec
Figure 4. The number of equivalent sunny days for every month in Athens (Greece).
Figure 4. The number of equivalentsunny sunny days days for in Athens (Greece). Figure 4. The number of equivalent forevery everymonth month in Athens (Greece).
2.7. Financial Analysis 2.7. Financial Analysis In the present work, the financial analysis is a critical part because the industries are interested In the present work, the financial analysis is a critical part because the industries are interested in financially viable investments. This work is investigates the system with various financial indexes Ininthe present viable work, the financialThis analysis a critical part because thevarious industries are indexes interested in financially investments. work investigates the system with financial that are defined in this section. First of all, the total cost of the system (K tot) is calculated. This financially viable investments. This work investigates the system with various financial indexes that that are defined in this section. First of all, the total cost of the system (Ktot) is calculated. This parameter is depended on the collector field cost, the storage tank cost, and the heat exchanger cost: are defined in this section. First ofcollector all, the total cost the of the system is calculated. This parameter is parameter is depended on the field cost, storage tank(K cost, the heat exchanger cost: tot ) and (14) = ⋅ + cost, ⋅ + depended on the collector field cost, the storage and the heat exchanger cost: (14) = ⋅ tank + ⋅ +
2.7. Financial Analysis
Ktot = A a · Kc + V · KV + Khex
(14)
The yearly cash flow (CF) is calculated by the energy that the solar collector gives to the industry (El,s ), the cost of the heat (Kheat ), and the cost of the operation and maintenance (KO&M ).
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CF = El,s · Kheat − KO&M
(15)
The cost of the operation and maintenance (KO&M ) is assumed to be the 1% of the capital cost of Designs[39]: 2018, 2, x 8 of 23 the system KO&M = 0.01 · Ktot (16) The yearly cash flow (CF) is calculated by the energy that the solar collector gives to the industry (E l,s), the cost of the heat (Kheat), and the cost of the operation and maintenance (KO&M). The net present value (NPV) of the investment is calculated as: =
,
⋅
−
(15)
&
NPV = −Ktot + R · CF
The cost of the operation and maintenance (KO&M) is assumed to be the 1% of the capital cost of the system [39]:
The equivalent years of the investment (R) are calculated as below: &
= 0.01 ⋅
(17)
(16)
N
r )calculated −1 (1 + is The net present value (NPV) of the investment as: R=
(18)
N
= r−· (1 + r )⋅
(17)
Thepayback equivalent years of the of investment (R) are calculated as below: The period (PP) the investment is calculated as: =
PP =
(1 + ) −1 CF ln⋅ (1 CF+−r ·)Ktot
(18)
(19)
The payback period (PP) of the investment islncalculated (1 + r ) as:
The internal rate of return (IRR) of the lninvestment can be calculated by using the(19) following − ⋅ = ln(1 + ) (non-linear) expression: ! CFinvestment can be1 calculated by using the following (nonThe internal rate of return (IRR) of the IRR = (20) · 1− linear) expression: Ktot (1 + IRR) N = the ⋅storage 1 − ( tank (20) In this work, the collecting area (Aa ) and ) volume (V) are examined parametrically. According In to this the economy scale theory, a a)higher quantity a product lower specific cost work, the of collecting area (A and the storageoftank volume has (V) aare examined for reasonable production. So, curves of forscale thetheory, specific cost of the collecting arehas and the storage parametrically. According to two the economy a higher quantity of a product a lower specific are costgiven for reasonable production. So, two curvesThese for thedata specific cost of the to collecting are and tank volume in Figures 5 and 6 respectively. correspond reasonable selections the storage tank volume are given in Figures 5 and 6 respectively. These data correspond according to the market prices. In the real installations, standard equipment has to be usedtofor both reasonable selections according to the market prices. In the real installations, standard equipment has too small or too great installations, which makes the specific cost lower for greater installations. to be used for both too small or too great installations, which makes the specific cost lower for greater For example, the control system, the piping, the tracking mechanism, etc., are not so different for small installations. For example, the control system, the piping, the tracking mechanism, etc., are not so and great installations, andgreat this is the main reason using the costsfor listed inthe Figures 5 andin6 in this different for small and installations, and thisfor is the main reason using costs listed work. These costs correspond to reasonable market costs, in which costs are really different between Figures 5 and 6 in this work. These costs correspond to reasonable market costs, in which costs are really different between small and great installations [39–41]. small and great installations [39–41].
Specific collector cost - Kc (€/m2)
800 700 600 500 400 300 200 100 0 0
200
400
600
800
Collecting area - Aa (m2)
Figure 5. The specific cost of the solar collectors.
Figure 5. The specific cost of the solar collectors.
1000
1200
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Table 3 includes thethe other parameters ofof this work. The heat exchanger selected 1010 k€k€ [42], Table 3 includes other parameters this work. The heat exchangercost costis is selectedatat the project is 25and years, the discount factor is 3% [38]. costheat of the heat is the[42], project lifetimelifetime (N) is 25(N) years, theand discount factor (r) is 3%(r)[38]. The costThe of the is estimated to be 0.10 €/kWh [43]. Moreover, theof range the specific about solar collectorsand andthe to estimated be 0.10 €/kWh [43]. Moreover, the range the of specific costscosts about the the solar collectors the storage are given in this table, they havealso alsopresented presented in in Figures Figures 55and essential to to storage tank tank are given in this table, as as they have and6.6.ItItis is essential state thatthe theinstallation installationcost cost is is assumed the specific costs of Figures 5 and 6. 6. state that assumedto tobe beincluded includedinin the specific costs of Figures 5 and
Specific tank cost - KV (€/m3)
1400 1200 1000 800 600 400 200 0 0
20
40
60
Storage tank volume - V
80
100
(m3)
Figure 6. The specific cost of the storage tank. Figure 6. The specific cost of the storage tank. Table 3. Data for the financial analysis. Table 3. Data for the financial analysis.
Parameter Parameter Heat exchanger cost Specific collector Heat exchanger costcost Specific tank cost Specific collector cost Specific tank cost Heat cost Heat cost life Project Project lifefactor Discount Discount factor O&M costs O&M costs
Symbol Symbol Khex c KKhex K V Kc KKheat V KN heat N r r KO&M KO&M
Value 10 Value k€ 225~70010€/m k€ 2 3 2 475~1200 €/m 225~700 €/m 3 475~1200 €/m 0.10 €/kWh 0.10 €/kWh 25 years 25 years 3% 3% 1%∙Ktot 1%·Ktot
2.8. Followed Methodology 2.8. Followed Methodology In this work, the industrial heat process system is optimized for five different heat production In this work, the industrial heat process optimized five heat variables production temperature levels (100 °C, 150 °C, 200 °C, 250system °C, 300 is °C). For everyfor case, thedifferent optimization ◦ C, 150 ◦ C, 200 ◦ C, 250 ◦ C, 300 ◦ C). For every case, the optimization variables temperature levels (100 are the collecting area (Aa) and the ratio of the collecting area to the storage tank (Aa/V). The collecting 2 (14 modules), arearea the ranged collecting area the ratioto of980 the m collecting area towhile the storage tank Thefrom collecting a )2 and a /V). from 210(Am (3 modules) the ratio (A(A a/V) ranged 10 2 2 2 3 2 3 area ranged m. The (3 modules) 980ism (14 modules), while the ratioof (Amodules, m /m up tofrom 100 210 m /m collecting to area examined for a different number and from so a /V) ranged 3 up to 100 m2 /m3 . The collecting 10every m2 /mextra is examined forarea. a different number of modules, module adds an extra 70 m2 toarea the total collecting The reason for using the ratioand 2 to the a/V) and not directlyadds the volume ontotal the collecting examination of the in the every so(A every extra module an extra(V) 70 is mbased area. Theproper reasonvolumes for using ratio specifically, there is no reason examining extremely great for the case ofin three (Acase. and not directly the volume (V) isfor based on the an examination of thetank proper volumes every a /V) More modules, because these tanks arereason suitable cases withan10extremely modules, great for instance. present case. More specifically, there is no forfor examining tank forSo, thethe case of three technique leads tothese the examination of the proper cases. Figure 7 shows the examined in modules, because tanks are suitable for cases with 10 modules, for instance.combination So, the present a two-dimensional (2D) depiction. technique leads to the examination of the proper cases. Figure 7 shows the examined combination in a two-dimensional (2D) depiction.
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Designs 2018, 2, x
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The optimization is performed by examining all of the depicted cases in Figure 7, and then Thefor optimization is performed all value of thefor depicted cases function. in Figure Three 7, anddifferent then searching which combinations leadsby toexamining the optimum the objective searching for which combinations leads to the optimum value for the objective function. Three optimization procedures are performed: different optimization procedures are performed: (a) Maximization of the solar cover (f ) (a) Maximization of the solar cover (f) (b) Maximization of the net present value (NPV) (b) Maximization of the net present value (NPV) (c) Minimization of the payback period (PP) (c) Minimization of the payback period (PP) More specifically, threethree independent optimization procedures are performed, and the optimization More specifically, independent optimization procedures are performed, and the goals in every case are given in the previous bullets (a to c). In every procedure, totally cases optimization goals in every case are given in the previous bullets (a to c). In every procedure, 228 totally are228 investigated, which are depicted in Figure 7. More specifically, 12 different collecting areas cases are investigated, which are depicted in Figure 7. More specifically, 12 different collectingare examined, for every collecting period, 19 different tanks are investigated. all of the areas areand examined, and for every collecting period,storage 19 different storage tanks areFinally, investigated. Finally, all of the cases and the the oneoptimization that satisfies the goal selected asone. cases are evaluated, and are theevaluated, one that satisfies goaloptimization is selected as theisoptimum the optimum for theprocedure, first optimization procedure, optimum case is the that For instance, forone. theFor firstinstance, optimization the optimum casethe is the one that leads to one maximum leads to maximum solaroptimization cover. In the procedure, second optimization procedure, optimum casemaximum is the onenet solar cover. In the second the optimum case is the one with the with the maximum net present value, while in the third optimization present value, while in the third optimization procedure, the optimumprocedure, case is thethe oneoptimum with the case lowest is the one with the lowest payback period. payback period.
Storage tank volume - V (m3)
100
80
60
40
20
0 200
400
600
Collecting area -Aa
800
1000
(m2)
Figure (2D) depiction depictionofofthe theexamined examinedcases. cases. Figure7.7.Two-dimensional Two-dimensional (2D)
Thelast laststep stepisisthe thediscussion discussion of of the the optimum optimum designs solar The designs with withthe thedifferent differentcriteria. criteria.The The solar coverage is an energy criterion that indicates the amount of useful energy production by the sun. coverage is an energy criterion that indicates the amount of useful energy production by the sun. Higher values of this parameter indicate that higher amounts of the heat process load are cover by Higher values of this parameter indicate that higher amounts of the heat process load are cover by the solar energy, and so the auxiliary energy consumption is lower. The (NPV) and the (PP) are the the solar energy, and so the auxiliary energy consumption is lower. The (NPV) and the (PP) are the financial criteria that evaluate the viability of the project. The (NPV) evaluates the total net gain of the financial criteria that evaluate the viability of the project. The (NPV) evaluates the total net gain of the investment if the capital cost, the yearly cash flow, the discount factor, and the total life of the project investment if the capital cost, the yearly cash flow, the discount factor, and the total life of the project are are taken into consideration. The payback period takes into account the capital cost, the yearly cash taken consideration. payback takes into account the considered capital cost,inthethis yearly cash flow, flow,into and the discount The factor, whileperiod the total project life is not index. The and the discount factor, while the total project life is not considered in this index. The optimization with optimization with these criteria is important in order to investigate the system by different points of these criteria is important in order to investigate the system by different points of view. The optimum view. The optimum designs are different because the solar cover maximization generally indicates designs different because solaruseful coverenergy maximization indicatesOn greater systems inthe order greaterare systems in order forthe higher amountsgenerally to be produced. the other hand, forfinancial higher useful energy amounts to be produced. On the other hand, the financial criteria usually criteria usually indicate smaller systems, which presents an efficient relationship between indicate smaller which production. presents an efficient relationship between the system scale and the the system scalesystems, and the energy energy production.
Designs 2018, 2, 24
11 of 23
It is useful to state that the IRR has not be used as an optimization goal because its maximization was equivalent to the minimization of the payback period, and thus there was not any reason for presenting a fourth optimization procedure. Now, it is important to state how the dynamic analysis in general and the yearly simulation has been conducted. Every combination (collecting area, storage tank, and temperature level of the load) was examined separately for 12 typical days during the year. The sunny days for every month have been used, and finally, the total yearly operation was developed. For every day, the system was examined with a time step of 30 seconds. The differential equations of the storage tank have been solved, and the procedure was performed for three days in order for the results to converge. The initial values in the tank were assumed to be the same as the load temperature level, but these values are converged after running the code for some consecutive days. Moreover, it is important to state that the collector loop was operating when the thermal efficiency was positive. Furthermore, the solar system feeds the load when the temperature of the thermal oil is higher than the load and there is a minimum pinch point of ~5 K in the heat exchanger. The proper control functions have been used in the code for respecting these constraints. It is essential to state that this work has been performed with a developed program in FORTRAN. Similar programs for the simulation of solar-driven systems in time-depended conditions have been performed in [39,41]. It is also useful to state that the developed model is based on the differential equation in the storage tank, while the other parts have been modeled with simple formulas, which makes the present analysis a pseudodynamic problem. In the end, Table 4 is given, which includes the main information about this work. This table summarizes information that was previously given in Section 2. Table 4. General information about this work. Description/Parameters
Data/Information
Location Collector type Tracking system Storage type Working fluid Heat process load Yearly operation period Load temperature level Collecting area (Aa ) Aa /V Heat exchanger efficiency (η hex ) Tank thermal loss coefficient (UT )
Athens (Greece), latitude φ = 38◦ PTC, Eurotrough module One-axis, follow the sun east–west Sensible storage Thermal oil (Therminol VP-1) 100 kW 350 days–8400 h From 100 to 300 ◦ C (variable) From 210 to 980 m2 From 10 to 100 m2 /m3 70% 0.8 W/m2 K
3. Results and Discussion The examined configuration is optimized with three different procedures, and the optimization results are given in Sections 3.1–3.4. The summary and the deeper discussion of the results are given in Section 3.4. 3.1. Optimization for Maximum Solar Cover The first optimization procedure is performed with the maximization of the solar coverage as the goal. Figure 8 is a three-dimensional (3D) depiction of the solar coverage for the various examined cases with the load temperature level at 200 ◦ C. This temperature level is selected as a representative intermediate temperature level. Generally, a higher collecting area leads to higher solar cover, which is reasonable. However, the optimum storage tank changes in every case. Figure 9 illustrates the optimum storage tank volumes for different collecting areas, and for the six examined load temperature levels. The general sense is that higher collecting areas need higher storage tanks. Moreover, it is found that loads of higher temperatures need smaller tanks.
Designs 2018, 2, x
12 of 23
Designs Designs 2018, 2018, 2, 2, 24 x
12 12 of of 23 23
The yearly load production from the solar energy is given in Figure 10, and the respective solar coverThe is given inload Figure 11. Thesefrom results the cases with in theFigure optimum storage tank, as itsolar has yearly production theregard solar energy is given 10, and the respective The yearly load production from the solar energy is given in Figure 10,higher and thecover respective solar been given in Figure 9. It is obvious that higher collecting areas lead to and great cover is given in Figure 11. These results regard the cases with the optimum storage tank, as it has cover is given in Figure These results regard the is cases with optimum storage tank, as it has been production sun.9.11. Moreover, the solar lower in the higher load to temperatures because the been givenby in the Figure It is obvious that cover higher collecting areas lead higher cover and great given in Figure 9. Ittemperatures is obvious that higher collecting areas leadsolar to higher cover and great production operation at higher leads to the reduction of the thermal efficiency. It can be said production by the sun. Moreover, the solar cover is lower in higher load temperatures because the by the sun. Moreover, the solar cover lower incover higher load temperatures the operation at that after 560 m2, thetemperatures increasing rate inisthe solar isof lower compared tobecause the collecting areas for operation at higher leads to the reduction the solar thermal efficiency. It can be said 2 higher temperatures leads to the reduction of the solar thermal efficiency. It can be said that after up toafter 560 m . m2, the increasing rate in the solar cover is lower compared to the collecting areas for that 560 2 , the increasing rate in the solar cover is lower compared to the collecting areas for up to 560 m2 . 560 m It is remarkable that the solar coverage reaches up to 60% approximately. This “upper limit” is up to 560 m2. It is remarkable that the solaroperation coverage reaches to 60% approximately. This reasonable if the maximum yearly areup considered. In other words, the“upper sunny limit” days ofis It is remarkable that the solar coverage days reaches up to 60% approximately. This “upper limit” is reasonable the maximum operation days considered. other words, sunny daysthe of the year areif for Athens,yearly and according to theare used data, theIn daysthe are 350 for reasonable if 219 the maximum yearly operation days are considered. Inoperation other words, the sunny days of the year are 219 for of Athens, according to the used data, the operation days are is 350 for higher the industry. industry. ratio 219 toand 350 gives a maximum 62.57%, which the year The are 219 for Athens, and according to thesolar usedcover data,ofthe operation daysa bit are 350 forthan the The ratio of 219 to 350 gives a maximum solar cover of 62.57%, which is a bit higher than the obtained the obtained results. So, it is found that the examined configuration is able to cover the heat load on industry. The ratio of 219 to 350 gives a maximum solar cover of 62.57%, which is a bit higher than results.days So, itinisafound thatway. the examined configuration ismonthly able to cover the heat load on sunny daysare in sunny suitable More results about the variation of the solar coverage the obtained results. So, it is found that the examined configuration is able to cover the heat load on a suitable way. More results about the monthly variation of the solar coverage are given in Section 3.4, given Section whichway. follows. sunnyindays in a3.4, suitable More results about the monthly variation of the solar coverage are which follows. given in Section 3.4, which follows. 60%
50%-60%
50% 40%
50%-60% 40%-50%
40% 30%
40%-50% 30%-40%
30% 20%
30%-40% 20%-30%
20% 10%
20%-30% 10%-20%
10% 0%
10%-20% 0%-10%
Solar cover Solar cover -f -f
60% 50%
0%
0%-10% 910 40 630 770 55 10 350 490 70 2 3 210 25 Aa/V (m /m )40 Collecting area910 - Aa (m2) 85 100 350 490 630 770 55 70 2 3) 210 Aa/V (m Collecting area - Aa (mTl2=) 200 °C. 85 of (A Figure 8. Solar coverage for /m the examined combinations a) and (Aa/V) for load temperature 100 Figure 8. Solar coverage for the examined combinations of (Aa ) and (Aa /V) for load temperature 10
25
Figure 8.◦Solar coverage for the examined combinations of (Aa) and (Aa/V) for load temperature Tl = 200 °C. T l = 200 C.
45 40
T = 100 ˚C 100˚C ˚C TT==250
T = 150 ˚C 150˚C ˚C TT==300
40 35
T = 250 ˚C
T = 300 ˚C
Optimum storage volume Optimum storage tanktank volume 3) 3 (m (m )
45
T = 200 ˚C T = 200 ˚C
35 30 30 25 25 20 20 15 15 10 10 5
05 0210
280
350
420
490
560
630
700
770
840
910
980
Collecting area - A (m2) 210 280 350 420 490 560 630 a 700 770 840 910 980 2) Collecting area - Aa (m Figure 9. Optimum storage tank volumes for different collecting areas with the maximization of the solar coverage as the optimization criterion. Figure 9. Optimum storage tank volumes for different collecting areas with the maximization of the Figure 9. Optimum storage tank volumes for different collecting areas with the maximization of the solar coverage as the optimization criterion. solar coverage as the optimization criterion.
Designs 2018, 2, 24 Designs 2018, 2018, 2, 2, xx Designs
13 of 23
13 of of 23 23 13
100 ˚C ˚C TT == 100
150 ˚C ˚C TT == 150
200 ˚C ˚C TT == 200
250 ˚C ˚C TT == 250
300 ˚C ˚C TT == 300
Yearly heat production (MWh)
600 600 500 500 400 400 300 300 200 200 100 100 00 210 210
280 280
350 350
420 420
490 490
560 560
630 630
Collecting area area -- AAaa Collecting
700 700
770 770
840 840
910 910
980 980
(m22)) (m
Figure 10. Yearly heat productionfor fordifferent differentcollecting collecting areas areas and and optimum storage tank inin order toto Figure Yearly heat production for different collecting in order to Figure 10.10. Yearly heat production areas andoptimum optimumstorage storagetank tank order achieve maximum maximum solar solar cover. cover. achieve achieve maximum solar cover.
100 ˚C ˚C TT == 100
150 ˚C ˚C TT == 150
200 ˚C ˚C TT == 200
250 ˚C ˚C TT == 250
300 ˚C ˚C TT == 300
70% 70% 60% 60%
Solar cover - f
50% 50% 40% 40% 30% 30% 20% 20% 10% 10% 0% 0% 210 210
280 280
350 350
420 420
490 490
560 560
630 630
Collecting area area -- AAaa Collecting
700 700
770 770
840 840
910 910
980 980
(m22)) (m
Figure 11. Maximum solar cover for different collecting areas (the storagetank tankisis isthe theoptimum optimumone onefor Figure Maximum solar cover different collecting areas (the storage tank the optimum one Figure 11.11. Maximum solar cover forfor different collecting areas (the storage for every every point). point). for every point).
3.2. Optimization Optimization for for Maximum Maximum NPV NPV 3.2. 3.2. Optimization for Maximum NPV The second second optimization optimization procedure procedure is is based based on on the the maximization maximization of of the the NPV. NPV. This This parameter parameter is is The The second optimization procedure is based on the maximization of the NPV. This parameter crucial for for the the investigation investigation of of the the investment, investment, and and Figure Figure 12 12 illustrates illustrates its its variation variation with with the the crucial is crucial for the investigation thetemperature investment,to Figure 12 illustrates its variation withto the optimization variables with the theofload load temperature toand be 200 200 °C. Generally, Generally, the NPV NPV reaches close close to optimization variables with be °C. the reaches ◦ C. Generally, the NPV reaches close to optimization variables with the load temperature to be 200 600 k€, k€, and and itit is is higher higher for for great great collecting collecting areas. areas. Also, Also, the the storage storage tank tank seems seems to to play play an an important important 600 600 k€, and it is higher for great collecting areas. Also, the storage tank seems to play an important role in the results. Thus, Figure 13 gives the optimum storage tank volumes for different collecting
Designs 2018, 2, x Designs 2018, 2, x Designs 2018, 2, 24
14 of 23 14 of 23
14 of 23
Netpresent presentvalue value- -NPV NPV(k€) (k€) Net
role in the results. Thus, Figure 13 gives the optimum storage tank volumes for different collecting role in the results. Thus, Figure 13 gives the optimum storage tank volumes for different collecting areas and temperature levels. Generally, a higher collecting area needs a higher storage tank, but after areas and temperaturelevels. levels. Generally,aahigher higher collecting area tank, but after areas temperature area needs needsaahigher higherstorage storage tank, but after 3. 490and m2, the optimum storageGenerally, tank is close to 15 mcollecting 490 2m2, the optimum storage tank is close to 15 m33. 490 m ,Figure the optimum storage tank is close to 15 m . 14 depicts the NPV for different temperature levels and collecting areas with the Figure 14 depicts the NPV for different temperature levels and collecting areas with the Figure 14 depicts theas NPV different temperature levels areas with the optimum optimum storage tanks theyfor have been defined in Figure 13. and The collecting NPV has an increasing rate with optimum storage tanks as they have been defined in Figure 13. The NPV has an increasing rate with 2 (for storage tanks asarea, they haveisbeen defined Figure 13. The NPV 770 has m an increasing rate with the collecting which maximized forincollecting areas between T l = 100 °C) and 980the the collecting area, which is maximized for collecting areas between 7702 m2 (for Tl = 100 °C) and 980 2 ◦ C) 2 2 collecting area, which is maximized for collecting areas between 770 m (for T = 100 and 980 m 2 (for Tl = 300 °C). It is important to state that after 630 m 2, the NPV has smalll variations with them m (for Tl = ◦300 °C). It is important to state that after 630 m2 , the NPV has small variations with the collecting it has to saidthat thatafter the cases with higher levels have with lowerthe (for Tl = 300area. C).Moreover, It is important to be state 630 m , the NPVtemperature has small variations collecting area. Moreover, it has to be said that the cases with higher temperature levels have lower NPV, because the heat costit is thetosame in allthat of the cases, and the collector thermal efficiency is lower collecting area. Moreover, has be said the cases with higher temperature levels have lower NPV, because the heat cost is the same in all of the cases, and the collector thermal efficiency is lower at higher temperature levels. NPV, because the heat cost is the same in all of the cases, and the collector thermal efficiency is lower at higher temperature levels. at higher temperature levels. 600 600 500 500 400 400
500-600 500-600 400-500 400-500 300-400 300-400 200-300 200-300 100-200 100-200 0-100 0-100
300 300 200 200 100 100 0 0 10 10 25 25 40 40
55 55
2 3 A Aaa/V /V (m (m2/m /m3))
70 70
85 85
210 210 100 100
350 350
490 490
630 630
770 770
910 910
2 Collecting Collecting area area -- A Aaa (m (m2))
Figure 12. Net present value for the examined combinations of (Aa) and (Aa/V) for load temperature Tl = Figure Netpresent presentvalue value for for the the examined of of (A(A a) and (Aa/V) for load temperature Tl = Figure 12.12.Net examinedcombinations combinations a ) and (Aa /V) for load temperature 200 °C. 200 °C.◦ C. T = 200
Optimumstorage storagetank tankvolume volume(m (m3)3) Optimum
l
18 18 16 16 14 14 12 12 10 10 8 8 6 6 4 4 2 2 0 0
TT == 100 100 ˚C ˚C TT == 250 ˚C 250 ˚C
210 210
280 280
350 350
420 420
490 490
TT == 150 150 ˚C ˚C TT == 300 ˚C 300 ˚C
560 560
630 630
TT == 200 200 ˚C ˚C
700 700
2 Collecting Collecting area area -- A Aaa (m (m2))
770 770
840 840
910 910
980 980
Figure 13. Optimum storage tank volumes for different collecting areas with the maximization of the Figure 13. Optimum storage tank volumes for different collecting areas with the maximization of the net present value asstorage the optimization criterion. Figure 13. Optimum tank volumes for different collecting areas with the maximization of the net present value as the optimization criterion. net present value as the optimization criterion.
Designs 2018, 2, 24 Designs 2018, 2, x
15 of 23
15 of 23
Designs 2018, 2, x
15 of 23
700
NetNet Present Value - NPV (k€)(k€) Present Value - NPV
700 600
T = 100 ˚C TT==100 250˚C˚C
T = 150 ˚C TT==150 300˚C˚C
T = 250 ˚C
T = 300 ˚C
T = 200 ˚C T = 200 ˚C
600 500 500 400 400 300 300 200 200 100 100 0 0 210 280 350 420 490 560 630 700 770 840 910 980 (m2) 770 840 910 980 210 280 350 420 Collecting 490 560 area 630- Aa700 2
Collecting - Aa (m Figure 14. Maximum net present value for differentarea collecting areas) (the storage tank is the optimum Figure 14. Maximum net present value for different collecting areas (the storage tank is the optimum one for every point). Figure 14. Maximum one for every point). net present value for different collecting areas (the storage tank is the optimum one for every point).
3.3. Optimization for a Minimum Payback Period 3.3. Optimization for a Minimum Payback Period 3.3. Optimization for a Minimum Payback Period The third optimization procedure is conducted with the minimization of the payback period as The third optimization procedure is conducted with in the minimization of the period as the The criterion. parameter is important, and it iswith used cases inof order to payback evaluate choices third This optimization procedure is conducted the many minimization the payback period as thesuch criterion. This parameter is important, and it is used in many cases in order to evaluate choices as the use of parameter solar energy coveringand a load and substituting the conventional fuel the criterion. This is for important, it is used in many partially cases in order to evaluatefossil choices such as the use of solar energy for covering a load and substituting partially the conventional fossil boiler. such as the use of solar energy for covering a load and substituting partially the conventional fossil fuel fuel boiler. boiler.Figure 15 is a 3D depiction of the simple payback period with the optimization variables when aa3D of simple payback periodwith with the optimization variables when theFigure load is15 atisis 200 °C.depiction This Figure clearly shows the existence of a the global minimumvariables point at 560 m2 Figure 15 3D depiction of the the simple payback period optimization when ◦ 2 3 2 3 collecting area an 8-m storage tank volume (Aa/V) of =of70 m /m ]. In this case, the the load 200 C. This Figure clearly shows the[or existence global minimum point at 560 the loadisisatat 200with °C. This Figure clearly shows the existence a aglobal minimum point at payback 560 m2 m 3 2 3 period isarea 4.88with years, which a promising value, especially for technologies. collecting 8-m storage tank [or /V) /m ]. this In this case, payback 2/m 3]. energy collecting area withan an 8-m3is storage tank volume volume [or (A (Aaa/V) ==renewable 7070mm In case, thethe payback period value, especially especiallyfor forrenewable renewableenergy energy technologies. periodisis4.88 4.88years, years,which whichis is aa promising promising value, technologies. 9-10 7-9 5-7 3-5
7-9
5-7
3-5
9 9 7 7 5 5 3 3 10 25 40 55
Collecting area - Ac (m2) Collecting area - Ac (m2)
70 85 100
85
70
55
10
25
Payback period - PP- PP (years) Payback period (years)
9-10
40/V (m2/m3) A a Aa/V (m2/m3)
Figure 15. Payback period for the examined 100 combinations of (Aa) and (Aa/V) for load temperature Tl = 200 °C. Figure 15. Payback period for the examined combinations of (Aa) and (Aa/V) for load temperature Tl = Figure 15. Payback period for the examined combinations of (Aa ) and (Aa /V) for load temperature 200 °C.◦ Tl = 200 C.
Designs 2018, 2, 24
16 of 23
Designs 2018, 2, x Designs 2018, 2, x
16 of 23 16 of 23
Optimum Optimumstorage storagetank tankvolume volume(m (m3)3)
Figure 16 16 exhibits thethe optimum storage tanks for different loadload temperatures andand collecting areas. Figure exhibits optimum storage tanks for different temperatures collecting Figure 16 exhibits the optimum storage tanks for different load temperatures and collecting 3 for the 3 Theareas. optimum storage tank is about 10 m majority of the cases. Figure 17 gives the payback The optimum storage tank is about 10 m for the majority of the cases. Figure 17 gives the areas. The optimum storage tank is about 10 m3 for the majority of the cases. Figure 17 gives the period for allperiod of the for loadalltemperatures, and for the examined areascollecting with the optimum storage payback of the load temperatures, and for collecting the examined areas with the payback period for all of the load temperatures, and for the examined areas with the 2 for all collecting tanks in every case. tanks The payback is minimized at 560 of optimum storage in every period case. The payback period is m minimized at the 560temperature m22 for all of levels the optimum◦ storage tanks in every case. The payback is minimized at 560 m for all of the 2 . These period 2 except 300 C, which is minimized for 630 m results indicate that there is a great influence temperature levels except 300 °C, which is minimized for 630 m . These results indicate that there is temperature levels except 300 °C, which is minimized for 630 m2. These results indicate that there is a great influence of the collecting area to the the payback period.was Thisnot result wasin not of the collecting area to the minimization ofminimization the payback of period. This result found the a great influence of the collecting area to the minimization of the payback period. This result was not found in theofoptimization of thethe system with the maximization of the NPV, because inthere this case, there optimization the system with maximization of the NPV, because in this case, was a great found in the optimization of the system with the maximization of the NPV, because in this case, there was a great “optimum area” where the NPV presented a small variation. “optimum area” where the NPV presented a small variation. was a great “optimum area” where the NPV presented a small variation.
100 ˚C ˚C TT == 100 250 ˚C ˚C TT == 250
14 14 12 12
150 ˚C ˚C TT == 150 300 ˚C ˚C TT == 300
200 ˚C ˚C TT == 200
10 10 8 8 6 6 4 4 2 2 0 0
210 210
280 280
350 350
420 420
490 490
560 560
630 630
700 700
Collecting area area -- A Ac (m (m22)) Collecting c
770 770
840 840
910 910
980 980
Figure 16. Optimum storage tank volumes for different collecting areas with the minimization of the Figure Optimum storagetank tankvolumes volumesfor for different different collecting collecting areas ofof thethe Figure 16.16. Optimum storage areaswith withthe theminimization minimization payback period as the optimization criterion. payback period optimizationcriterion. criterion. payback period as as thethe optimization
100 ˚C ˚C TT == 100 250 ˚C ˚C TT == 250
Payback Paybackperiod period- -PP PP(years) (years)
8.0 8.0 7.5 7.5
150 ˚C ˚C TT == 150 300 ˚C ˚C TT == 300
200 ˚C ˚C TT == 200
7.0 7.0 6.5 6.5 6.0 6.0 5.5 5.5 5.0 5.0 4.5 4.5 4.0 4.0
210 210
280 280
350 350
420 420
490 490
560 560
630 630
700 700
Collecting area area -- A Ac (m (m22)) Collecting c
770 770
840 840
910 910
980 980
Figure 17. Minimum payback period for different collecting areas (the storage tank is the optimum Figure 17. Minimum payback period for different collecting areas (the storage tank is the optimum one for point). Figure 17. every Minimum payback period for different collecting areas (the storage tank is the optimum one one for every point). for every point).
Designs 2018, 2, 24
17 of 23
3.4. Summary and Discussion The last step in this investigation is the comparisons and the discussion of the obtained results. Tables 5–7 include the results of the global optimum cases with the three performed optimization procedures, as they have been described in Sections 3.1–3.3 in detail. These tables give results about the optimum design (collecting area and storage tank), as well as the values of the crucial parameter for these cases. These results regard all of the examined load temperature levels. It can be said that the optimum design is different when the different optimization criteria are used. This creates many optimum scenarios, and this result needs more investigation. The optimization with the solar cover lead to the maximum examined collecting areas (980 m2 ), while the NPV gives values that are a bit lower, from 770 m2 to 980 m2 . The optimization with the PP gives significantly lower collecting areas between 560–630 m2 . At this point, the case of 200 ◦ C is selected as an example in order to make a suitable analysis. Using the solar cover as a criterion (scenario A), the solar cover is 59.89%, the NPV is 572 k€, and the payback period is 6.01 years. Using the NPV as a criterion (scenario B), the solar cover is 58.37%, the NPV is 582 k€, and the payback period is 5.44 years. Moreover, using the payback period as a criterion (scenario C), the solar cover is 52.26%, the NPV is 543 k€, and the payback period is 4.88 years. These results show that the use of solar cover as criterion leads to a relatively high payback period (6.01 years from 4.88 years), while the use of the payback period leads to lower solar cover (52.26% from 59.89%). However, the use of NPV as criterion leads to a small sacrifice in solar cover (58.37% from 59.89%) and payback period (5.44 years from 4.88 years). So, the optimum design according to the NPV seems to be the most suitable case. In this scenario, the collecting area is 840 m2 , and the storage tank volume is 15.3 m3 . It is also useful to state that the optimum collecting areas are generally higher for higher load temperatures. Moreover, the optimum storage tanks are lower in higher temperatures for optimization with solar cover, while they are higher for optimization with financial criteria. The optimization with the solar cover leads generally to greater storage tanks (24.5 m3 to 39.2 m3 ), the optimization with the NPV leads to intermediate storage tanks volumes (12.8 m3 to 16.3 m3 ), while the optimization with the payback period leads to the smallest tanks (8 m3 to 9 m3 ). At this point, it is important to state that the literature results of Table 1 are generally found with energetic optimizations, and thus the found storage tanks are generally great, which is also obvious from the previous comparative discussion. Table 5. Optimization results for solar cover maximization (Scenario A). NPV: net present value, PP: payback period, IRR: internal rate of return. Tl
Aa,opt
(Aa /V)opt
Vopt
NPV
PP
IRR
fmax
(◦ C)
(m2 )
(m2 /m3 )
(m3 )
(k€)
(Years)
(%)
(%)
100 150 200 250 300
980 980 980 980 980
25 25 35 40 40
39.2 39.2 28.0 24.5 24.5
589 578 572 562 549
5.95 6.03 6.01 6.06 6.16
18.32 18.09 18.15 18.00 17.71
61.34 50.65 59.89 59.08 58.21
Designs 2018, 2, 24
18 of 23
Table 6. Optimization results for NPV maximization (Scenario B). Tl ◦ ( C)
Aa,opt
(Aa /V)opt
Vopt
NPVmax
PP
IRR
f
(m2 )
(m2 /m3 )
(m3 )
(k€)
(years)
(%)
(%)
100 150 200 250 300
770 840 840 910 980
60 70 55 55 60
12.8 12.0 15.3 16.6 16.3
603 593 582 569 552
5.07 5.31 5.44 5.75 6.06
21.38 20.64 19.99 18.95 18.01
58.78 58.91 58.37 58.35 58.02
Designs 2018, 2, x Table 7. Optimization results for payback period minimization (Scenario C).
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results for payback NPV period minimization (Scenario C). f TlTable 7.AOptimization (Aa /V) Vopt PPmin IRR a,opt opt
(◦ C)
2 /m 3 ) opt (m 3) a/V) Tl(m2 )Aa,opt (m(A NPV Vopt (k€) PPmin (years)IRR (%) f (%) 2) 2/m3) 3) (°C) (m (m (m (k€) (years) (%) (%) 100 560 70 8.0 573 4.68 23.09 54.27 100560 560 8.0 573559 4.68 4.7823.09 22.79 54.27 53.30 150 7070 8.0 200 7070 8.0 150560 560 8.0 559543 4.78 4.8822.79 22.17 53.30 52.26 250 560 60 9.3 527 5.03 21.73 200 560 70 8.0 543 4.88 22.17 52.26 51.26 300 630 70 9.0 525 5.21 250 560 60 9.3 527 5.03 21.73 21.02 51.26 51.69 300 630 70 9.0 525 5.21 21.02 51.69 The IRR is also given in Tables 5–7. It takes values from 17.71 to 23.09%, which are satisfying is also given in Tables 5–7.as It an takes values fromgoal, 17.71 to 23.09%, which are satisfying values.The ThisIRR parameter has not been used optimization because the IRR maximization was values. This parametertohas been used asof anthe optimization goal, because the IRR maximization was found to be equivalent thenot minimization payback period. found be step equivalent the minimization of the payback period. results for the solar coverage of Theto last in thistowork is the presentation of the monthly The last step in this work is the presentation of the monthly results theoptimum solar coverage thethe the load. These results are depicted in Figure 18, and they regard the for three casesoffor load. These results are depicted in Figure 18, and they regard the three optimum cases for the load load temperature of 200 ◦ C. The solar cover has the same values among the three scenarios from temperature of 200 °C. The solar cover has the same values among the three scenarios from April to April to August. This shows that increasing the collecting area is not beneficial during these months. August. This shows that increasing the collecting area is not beneficial during these months. However, the greater collecting areas of scenario A and B gives higher solar cover than the scenario However, the greater collecting areas of scenario A and B gives higher solar cover than the scenario C for the rest of the year. During the winter, solar coverage of 20~30% is achieved, while in July and C for the rest of the year. During the winter, solar coverage of 20~30% is achieved, while in July and August, it reaches close to 90%. The main reason for these results is the number of the sunny days of August, it reaches close to 90%. The main reason for these results is the number of the sunny days of every month. withoutoperation operation(15 (15per peryear) year) are assumed every month.ItItisisimportant importantto tostate state that that the the days days without are assumed to to be be separated in all in thein same assumption gives thegives proper time for maintenance separated in of allthe of months the months the way. sameThis way. This assumption the proper time for during the entire year. Moreover, Table 8 includes the monthly energy production by the solar energy maintenance during the entire year. Moreover, Table 8 includes the monthly energy production by forthe thesolar threeenergy optimum scenarios. for the three optimum scenarios.
Scenario A : Aa = 980 m² - Aa/V = 35 m³ Scenario B : Aa = 840m² - Aa/V = 55m³
Monthly coverage of the load
100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Jan
Feb Mar Apr May Jun
Jul
Aug Sep
Oct Nov Dec
Figure 18. Monthly coverage of the load for the optimum cases for load temperature Tl = 200 °C. Figure 18. Monthly coverage of the load for the optimum cases for load temperature Tl = 200 ◦ C.
Designs 2018, 2, 24
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Table 8. Energy production during the months and the year for the three optimum scenarios. Energy Production by the Solar Energy (MWh) Period January February March April May June July August September October November December Year
Scenario A
Scenario B
Scenario C
25.23 24.00 36.00 43.20 45.60 50.40 67.20 67.20 45.60 40.80 32.09 25.75 503.07
21.49 24.00 36.00 43.20 45.60 50.40 67.20 67.20 45.60 39.99 27.41 22.20 490.29
14.84 17.10 32.17 43.20 45.60 50.40 67.20 67.20 39.47 27.43 18.94 15.39 438.95
4. Conclusions The objective of this work is the energetic and financial optimization of a solar heat industrial process system. Parabolic trough solar collectors coupled to a storage tank are used in order to cover a continuous industrial heat load. The temperature of this load is examined parametrically from 100 ◦ C to 300 ◦ C, covering a great range of possible applications as they have been described in the introduction section. The optimization is performed with three different procedures with the following criteria: maximization of the solar cover, maximization of the NPV, and minimization of the payback period. The optimization variables were the collecting area and the storage tank volume. This analysis regards the climate conditions of Athens (Greece) and the load was selected at 100 kW. The most important conclusions of this work are summarized below: -
-
Higher load temperatures lead to greater optimum collecting areas, lower solar cover, lower NPV, and a higher payback period. The optimum storage tank is greater when the system is optimized with energy criteria (solar cover) compared to the financial optimization (NPV and payback period). The solar cover was generally found close to 60%, which is a high value. This value is restricted by the number of the sunny days during the year. Different criteria lead to the different optimum scenario. Finally, the optimization with the NPV maximization is found to be the most suitable case. In this scenario with a temperature load of 200 ◦ C, the collecting area is 840 m2 , the storage tank volume is 15.3 m3 , the NPV is 582 k€, and the solar cover is 58.37%. The IRR was found to range from 17.71 to 23.09%, which are acceptable and promising values for the present technology.
In the end, it can be said that the use of PTC for industrial heat process of various temperature levels is a financially viable investment with good indexes and high solar coverage. Author Contributions: E.B. has the idea of this work, he wrote the main text and he made the last step of the calculations. I.D. made the greatest part of the calculations with the dynamic model. C.T. checked and corrected the work, as well as he helped in the proper organization of the simulations. Funding: This research has been funded by Bodossaki Foundation. Acknowledgments: Evangelos Bellos would like to thank “Bodossaki Foundation” for its financial support. Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.
Designs 2018, 2, 24
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Nomenclature Aa C CF cp Dr E f Gb IRR K Kc Kheat Khex KO&M Ktot Kv L m N NPV Nmod PP Q Qs R r T t UT V Greek symbols δ η het η th θ θz ρ φ Subscripts and superscripts am c c,in c,out hex l l,s l,b loss max min mod opt
Collector net area, m2 Concentration ratio Cash flow, €/year Specific heat capacity under constant pressure, J/kg K Absorber diameter, m Energy, kWh Solar cover Solar direct beam irradiation, W/m2 Internal Rate of Return, % Incident angle modifier Collector specific cost, €/m2 Cost of the heat energy, €/kWh Heat exchanger cost, € Operation and maintenance cost, € Total cost, € Tank specific cost, €/m3 Module length, m Mass flow rate, kg/s Project lifetime, years Net Present Value, € Number of modules Payback period, years Energy Rate, W Solar irradiation rate, W Equivalent investment years, years Discount factor, % Temperature, ◦ C Time, h Tank thermal loss coefficient, W/m2 K Storage tank volume, m3 Solar declination angle, ◦ Heat exchanger efficiency Thermal efficiency Solar incident angle, ◦ Zenith angle, ◦ Density, kg/m3 Local latitude, ◦ ambient collector collector inlet collector outlet heat exchanger to load load load from the solar energy load from the boiler thermal loss of the tank maximum minimum module optimum
Designs 2018, 2, 24
r s s,in s,out st u Abbreviations ETC FPC LFR O&M Operation and Maintenance PTC SHIP 2D 3D
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receiver sourse of the sourse of the load inlet sourse of the load outlet stored in the tank useful evacuated tube collector flat plate collector linear Fresnel reflector parabolic trough collector solar heat industrial process Two-dimensional depiction Three-dimensional depiction
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