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Heliostat field layout optimization for high-temperature solar thermochemical processing
Available online at www.sciencedirect.com
Solar Energy 85 (2011) 334–343 www.elsevier.com/locate/solener
Heliostat field layout optimization for high-temperature solar thermochemical processing Robert Pitz-Paal a,⇑, Nicolas Bayer Botero a, Aldo Steinfeld b,c b
a DLR, Institute of Technical Thermodynamics, Linder Ho¨he, D-51147 Ko¨ln, Germany ETH Zurich, Department of Mechanical and Process Engineering, 8092 Zurich, Switzerland c Paul Scherer Institute, Solar Technology Laboratory, 5232 Villigen, Switzerland
Received 6 July 2009; received in revised form 13 October 2010; accepted 18 November 2010 Available online 30 December 2010 Communicated by: Associate Editor L. Vant-Hull
Abstract The layout of the heliostat field of solar tower systems is optimized for maximum annual solar-to-chemical energy conversion efficiency in high-temperature thermochemical processes for solar fuels production. The optimization algorithm is based on the performance function that includes heliostat characteristics, secondary optics, and chemical receiver–reactor characteristics at representative time steps for evaluating the annual fuel production rates. Two exemplary applications for solar fuels production are selected: the thermal reduction of zinc oxide as part of a two-step water-splitting cycle for hydrogen production, and the coal gasification for syngas production. Ó 2010 Elsevier Ltd. All rights reserved. Keywords: Solar chemistry; Solar tower; Central receiver; Heliostat field; High temperature; Thermochemical
1. Introduction Solar thermochemical reactors for fuels production operating at above 1000 K are being designed for solar tower systems capable of delivering high solar flux densities in the multi-MW power scale (Steinfeld, 2005). The design and optimization of such receiver–reactors are usually performed on the basis of a pre-defined solar flux density as boundary condition (Pitman and Vant-Hull, 1986). Because of the high temperature requirement, the desired solar concentration ratios should be significantly higher than those encountered in solar power tower systems for Rankine-based electricity generation, which typically operate at an upper temperature of about 750 K and solar concentration ratios around 500 suns (1 sun = 1 kW/m2). In ⇑ Corresponding author. Tel.: +49 2203 601 2744; fax: +49 2203 601 4141. E-mail address: [email protected] (R. Pitz-Paal).
0038-092X/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2010.11.018
contrast, solar thermochemical plants usually operate at above 1000 K and require solar concentration ratios exceeding 1500 suns. Thus, as higher solar flux densities have a direct impact on the optical performance of the solar field, the overall optimization for maximum solarto-chemical energy conversion efficiency needs to consider the coupled field and receiver design parameters. Several authors have discussed the layout of central receiver concepts for applications requiring high-flux densities and high-temperature levels (Pitman and Vant-Hull, 1986; Segal and Epstein, 1999, 2003; Vant-Hull et al., 1999). In these previous studies, the energetic characteristics of the conceptual application were not integrated directly into the layout developing procedure. Instead, a fixed flux density was used as boundary condition. This paper presents a novel approach to optimize the heliostat field design and layout for high-temperature solar thermochemical processes that integrates the energetic behavior of the intended application. The approach is
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Nomenclature Ahelio reflective area of heliostat field (m2) Aaperture aperture area of cavity-receiver (m2) Areaction surface available to chemical reaction (m2) cp specific heat capacity of reacting stream (kJ kg1 K1) DHr specific enthalpy change of reaction (kJ kg1) EA apparent activation energy (kJ mol1) g0 optical efficiency gsolar-to-chemical solar-to-chemical energy conversion efficiency
based on the HFLCAL modeling code (Schwarzbo¨zl et al., 2009), originally developed for solar electricity generation systems. The optimization procedure is applied to two exemplary processes for solar fuels production, namely: the solar thermal reduction of zinc oxide at 2000 K as part of a two-step water-splitting cycle for hydrogen production (Schunk et al., 2009b), and the coal gasification at 1400 K for syngas production (Z’Graggen et al., 2006). The annual efficiency data obtained for the optimized high-flux solar tower systems are compared with those obtained with the conventional low-flux solar tower systems for power levels of 1, 10, and 100 MW. A sensitivity analysis is performed for the heliostat beam quality, tower height, and reactive surfaces. 2. Model description The calculation of the field performance is briefly sketched here; a more detailed description of the computing code has been previously presented (Schwarzbo¨zl et al., 2009). 2.1. Field performance The calculation of the annual field performance is based on the hourly performance on the 21st of every month with clear sky conditions. The sunshape is assumed as a circularnormal distribution with the same root-mean-square deviation from the central ray which has been shown to be an appropriate statistical approximation (Pettit et al., 1983). The code considers the changing solar position and accounts for cosine losses, imperfect reflections, atmospheric attenuation, shading and blocking, spillage transmissions losses in the secondary concentrator, and receiver losses. The determination of a specific field layout is depicted in Fig. 1. Starting with a set of hypothetical heliostat positions, the performance of each heliostat is calculated. Afterwards, the set of heliostats is ranked based on the annual energy performance per area of reflective surface to determine the best set of heliostats yielding a
greactor reactor efficiency DNI direct normal irradiance (W/m2) k0 pre-exponential kinetic factor (kg s1 m2) m reaction rate (kg s1) Preaction power consumed by chemical reaction (kW) Psolarin solar power into receiver aperture (kW) Pthermallosses reactor thermal losses (kW) R specific ideal gas constant (J kg1 K1) v chemical conversion
given design power. In earlier studies, the performance calculation for a single time point was compared to that obtained with complex ray-tracing software with good agreement (Schmitz et al., 2006). Temporal disturbances are not considered by the present quasi-dynamic approach. As the integration of irradiated solar energy during a typical meteorological year matches the sum of irradiated energy during the time step series, the annual performance estimation can be considered as a theoretical maximum achievable. 2.2. Receiver model The main fundamental difference between the present optimization applied for solar chemical tower systems using a specified chemical process and that applied for solar power tower systems using a specific heat transfer fluid (e.g. steam, salt, air) is that the chemical reaction rate cannot be controlled independently (e.g. by adjusting the mass flow rates), but strongly depends on the reaction temperature, which in turn is a function of the solar concentration ratio delivered by the heliostat field and the heat/mass transfer within the receiver–reactor. The receiver–reactor model links the intercepted solar radiation with the specific chemical reaction and computes the reactor efficiency in terms of greactor ¼
mðT Þ vðT Þ DH r ðT Þ P solarin
ð1Þ
with v being the chemical conversion. For the coal gasification case, v is calculated based on the chemical equilibrium. For the zinc oxide reduction case, v is set to zero below the boiling point of zinc otherwise to one. The nominal reaction temperature results from the energy balance in the reactor, g0 P solarin ¼ P reaction ðT Þ þ P thermallosses ðT Þ
ð2Þ
where Psolarin denotes the solar power input, and the two terms on the right hand side denote the power consumed by the endothermic chemical reaction and the thermal
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Fig. 1. Scheme of the layout developing procedure.
10 8 6 0.56
4 0.48
b
0.63
Flux Density [MW/m2]
Flux Density [MW/m2]
10
a
0.64
8 0.27 0.36
6 4
0.54
2
2 0.40 0.24
0.45
0.32 0.16
0.080
0
0
0.5
1.0 Aperture Area [m2]
1.5
0.72
0.45
2.0
0.5
0.36
1.0 Aperture Area [m2]
0.18
1.5
2.0
Fig. 2. Receiver–reactor model correlation of reactor efficiency, flux density and aperture area: (a) zinc oxide reduction; (b) coal gasification.
0.6
0.7
a
b 0.6
Efficiency [-]
Efficiency [-]
0.5
0.4 ηtotal ηreactor
0.3
ηtotal
0.5
ηreactor ηoptical
0.4
ηoptical
0.2
0.3 0
1
2 3 Thermal Losses [kW/m2 ]
4
0
1
2 3 Thermal Losses [kW/m2 ]
4
Fig. 3. Impact of thermal losses on overall, optical and reactor efficiencies: (a) zinc oxide reduction; (b) coal gasification.
losses. The reaction temperature varies with time as Psolarin varies along the day/year. Consequently, the heliostat field optimization cannot be performed under the generic assumption of a constant reactor temperature – and thereby independently of the chemical reaction – but needs to
consider the specific characteristics of the chemical process affecting Preaction and the specific reactor design that influences Pthermallosses. The following assumptions are made to estimate the upper performance limit of a reactor without detailed knowledge of the reactor design:
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Fig. 4. Design parameter for (a) heliostat field position; (b) solar receiver–reactor.
the reactor temperature is uniform, convection and conduction heat losses are neglected, transient heat losses during start-up and shut-down are neglected, reaction achieves completion, e.g. there are no chemical side products considered, no purge gases are used. Thus, Z P reaction ðT Þ ¼ mðT Þ DH r ðT Þ þ
T
cp dT
ð3Þ
T in
P thermalloss ðT Þ ¼ Aaperture erT 4
ð4Þ
The generic solar chemical reactor, schematically depicted in Fig. 4b, consists of a cylindrical cavity-receiver containing a windowed aperture and a CPC. It has been scaled up in size based on data obtained from solar furnace tests and numerical simulations (Schunk et al., 2009a,b; Z’Graggen et al., 2006; Schunk and Steinfeld, 2009). Scaling up to higher design power levels was performed by keeping the reaction surface Areaction linearly increasing with Psolarin. The reaction rate is given by EA mðT Þ ¼ Areaction k 0 exp ð5Þ RT For the zinc oxide reduction: ZnO ! Zn þ 0:5O2
ð6Þ
the Arrhenius parameters are EA = 361 kJ/mol and k0 = 14.03 106 kg/(s m2) (Schunk et al., 2009b). For coal gasification, C þ H2 O ! CO þ H2
ð7Þ
the Arrhenius parameters are EA = 43.154 kJ/mol and k0 = 0.2846 kg/s m2 (where carbon is available in the form of petcoke) (Z’Graggen et al., 2006). The receiver–reactor models yield a correlation between reactor efficiency, flux density, and aperture area, which is
depicted in Fig. 2 for zinc oxide reduction (Fig. 2a) and coal gasification (Fig. 2b). We assume that the presented formulation for the receiver–reactor gives an estimation of the theoretical upper limit of the radiation to the reactor efficiency depending on the solar flux density. To ensure that the further results concerning the optical subsystem are not influenced by the idealizations within the receiver model we introduced a thermal loss per unit reactor surface varying from 0 (baseline case) to 4 kW/m2. The results are shown in Fig. 3 and follow the method described in Section 3: each data point represents the arithmetic average of 10 optimizations runs and is subject to a small spread, expressed in terms of the standard deviation. In both cases, the decrease in the overall efficiency traces back to the decrease in the reactor efficiency: the standard deviation of the optical efficiency of the five data points (losses greater zero) is of the same magnitude as the standard deviation of the corresponding baseline design point (no thermal loss) (ZnO: 0.0048 vs. 0.0040 ; coal: 0.0012 vs. 0.0048). Hence, our results concerning the optical efficiency are independent of the idealizations within the thermal model of the receiver–reactor, but the energetic characteristics of the receiver–reactor impose constrains on the field efficiency. 3. Optimization The task of finding an optimum value of an objective function in a multidimensional parameter space is challenging (Carrol et al., 1999). There is a strong indication that the objective function exhibits a highly multimodal behavior with a high number of local maxima within a small spread. 3.1. Optimization problem Target function for the optimization is the average annual solar-to-chemical energy conversion efficiency, defined as: P all time steps mðT ÞDH r ðT Þ gsolar-to-chemical ¼ P ð8Þ all time steps DNI AHelio
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This definition considers the sensible heat as an energetic by-product without value. This is due to the fact that some chemical reactions require a fast cool-down (quenching) of the product gases to avoid recombination. We chose the main design parameters determining the layout of the heliostat field, the shape of the secondary concentrator, and reactor geometry to be free parameters subject to optimization. The selected parameters are: heliostat field spacing parameters (AR, BR and AU, BU see Fig. 4), angle of sight of the secondary concentrator (a generic CPC), that also defines the ratio of inlet and outlet aperture, angle between the horizontal and the optical axis of the secondary concentrator and receiver–reactor compound of the aperture U. aperture radius of the reactor, which matches the outlet radius of the CPC (Fig. 4b). Other design parameters which are kept fixed or are subject to the sensitivity analysis are given in Table 1 according to the specific design power level. 3.2. Optimization approach Three different optimization algorithms and their combinations were applied for the optimization of this sevendimensional problem, namely: an implementation of a genetic algorithm (Carrol et al., 1999), the Nelder–Mead algorithm (Press et al., 1992), and the Powell algorithm (Press et al., 1992). Since the latter showed poor performance, the coupled genetic algorithm with the Nelder– Mead algorithm was selected. The genetic algorithm is a heuristic optimization approach. It initially discretizes the allowed parameter space and creates a number of parameter vectors (called population) distributed randomly over the parameter space. Afterwards, the value of the objective function (called fitness) for each individual parameter vector is calculated. From this population, a certain number of individuals with the best fitness are selected, recombined, and subject to random mutation to form the subsequent generation. The random number generator is based on an initial arbitrary seed value and therefore allows creating
different optimization runs within the same parameter space. The termination criterion is a given population size and number of generations. Due to the discretization of the parameter space, finding the actual value of the optimum is highly unlikely. This part is addressed by the Nelder–Mead algorithm, which belongs to the hill climbing search methods and can be used for non-linear unimodal functions. The algorithm most likely converges directly into the local maximum next to its starting point. The termination criterion in this case is a given minimum change between two function evaluations. Our approach is to set-up the genetic algorithm to explore the parameter extensively and search for a parameter vector close to the global maximum. The result is fed as starting point to the Nelder–Mead algorithm for further improvement. 3.3. Optimization performance For the assessment of the best parameter set-up of the chosen optimization algorithms, a series of optimization runs with distinct set-ups was performed. Each set-up of parameters for the optimization algorithm was run against repeated optimizations varying the seed number for the random number generator. During the tests, the objective functions was highly multimodal, e.g. it formed a great number of local maxima. Furthermore, these maxima showed a very small difference in the value of the objective function, e.g. the solar-to-chemical conversion efficiency might come up with nearly equal values despite different parameter vectors for the system design. Fig. 5 exemplarily outlines this behavior. As a consequence of this behavior the goal was to find a parameter set-up for the optimization algorithm that produces the highest arithmetic mean out of a certain number of repeated optimization runs and simultaneously achieves a low spread between the lowest and highest value of the objective function. Fig. 6 depicts the optimization performance in terms of the arithmetic mean and the spread of 10 optimization runs for four different configurations of the genetic algorithm in stand-alone mode (denoted GA1– GA4) and three different configuration of the downhill simplex, each with a tighter termination tolerance specification combined with the genetic algorithm working under the configuration GA2 (denoted GA2DS1–GA2DS3). The
Table 1 Baseline design parameters. Design powera (MW)
Tower height (m)
Heliostat size (facet size) (m2)
Product of av. heliostat reflectivity and av. heliostat availability
Beam error (incl. sunshape) (mrad)
Areaction Zn/ZnO (m2)
Areaction C gasif (m2)
1 10 100b S + SW + SE (36 + 32 + 32)
40 120
10 (1) 120 (4.3)
0.87 0.87
3.3 3.3
250
120 (4.3)
0.87
3.3
21.7 217 2170 S + SW + SE (784 + 693 + 693)
11 110 1100 S + SW + SE (396 + 352 + 352)
a
Thermal power into receiver at 21.3. Solar noon with direct normal irradiation at design point of 873.33 W/m2 and an annual average of 645.17 W/m2. A multiple aperture design is introduced, consisting of three separate fields in north (N), northeast (NE) and northwest (NW) direction, to increase the optical efficiency. b
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Fig. 5. Comparison of two heliostat field layouts with nearly the same solar-to-chemical conversion efficiency.
η total
0.31
0.30
0.29 GA1
GA2
GA3
GA4
GA2 DS1 GA2 DS2 GA2 DS3
optimization configuration
Fig. 6. Optimization performance for different parameter set-up for of the optimization algorithms (10 MW-ZnO).
coupling of both algorithms (GA2 vs. GA2DS2) shows a considerable performance gain (relative gain: 1.79% – absolute gain: 0.53%) with respect to the arithmetic mean. The relative spread e.g. the spread related to the arithmetic mean is reduced from 3.25% to 1.38%. The assumption of a highly multimodal objective function is supported by the fact that in the Fig. 6 an increase of the Nelder–Mead tolerance (from DS1: 1E-3 to DS3: 1E-10) has hardly any effect: the local maxima found cannot be further improved. Due to computational constrains, we limit the number of optimization runs to 10. To ensure that the results of 10 optimization runs are representative for the objective function, we chose the optimization configuration 0.31
(GA2DS2) and performed 450 optimization runs on both the zinc oxide reduction and coal gasification cases. The results of a statistical analysis are presented in Fig. 7. The 10 MW base cases give the following results: arithmetic mean: 0.30177 with standard deviation of 0.00329 for the zinc oxide reduction, and 0.40649 ± 0.00206 for the coal gasification case. These values differ only slightly from those resulting from only 10 optimization runs (ZnO: 0.3022 ± 0.0011; coal gasification: 0.4075 ± 0.0021) concerning the solar-to-chemical conversion efficiency. This does not hold for the partial efficiencies within the solar concentration subsystem which hence will be omitted during the analysis. We observed that selecting the maximum efficiency found in 10 repetitive optimization runs yields a distorted relation among comparable cases due to the impact of outliers. Hence, results are expressed in terms of the arithmetic average rather than the maximum found. 4. Results We studied conceptual applications for solar tower systems with solar reactors for the reduction of zinc oxide and for the gasification of coal. The plant is located on 36.12°N geographic latitude. Three power levels were considered, defined as the intercept power on the aperture of the secondary concentrator. For comparison, a typical field layout for a Rankine-based solar power plant was optimized using the same parameters expected for a fixed solar concentration ratio of 500 suns at the design point over a cir-
a
b 0.410
1 SD 50%
1 SD
-1 SD
50%
ηtotal
ηtotal
0.30 0.405
-1 SD
0.29 0.400 0.28
Fig. 7. Result of 450 optimization runs performed with different initialization of the random number generator (left) and the descriptive statistical analysis (right) for 10 MW zinc oxide-system (a) and coal gasification-system (b).
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Table 2 Baseline case optimization for solar ZnO dissociation and coal gasification and for a constant solar concentration ratio of 500 suns (typical for Rankinebased solar power plants). Efficiencies (%)
Reactor operating conditions
Field
Intercept
Secondary
Optical
Reactor
Total
Average operating temperature (K)
Peak operating temperature (K)
Flux density (MW/m2)
ZnO dissociation 1 MW, 10 m2 heliostat 10 MW, 120 m2 heliostat 100 MW, three cavities 120 m2 heliostat
66.7 67.3 63.7
86.4 86.0 88.7
92.1 92.2 91.7
53.1 53.4 51.8
55.5 55.9 57.0
29.5 29.8 29.2
1910 1912 1920
2014 2013 2017
4.5 4.6 4.8
Coal gasification 1 MW, 10 m2 heliostat 10 MW, 120 m2 heliostat 100 MW, three cavities 120 m2 heliostat
69.9 69.4 65.4
95.4 95.2 96.2
92.9 93.1 93.1
61.9 61.5 58.6
66.0 66.3 66.8
40.9 40.8 39.9
1308 1307 1308
1469 1470 1483
2.2 2.9 2.5
Thermal receiver 500 kW/m2 1 MW, 10 m2 heliostat 72.4 10 MW, 120 m2 heliostat 70.0 100 MW, northfield 64.5 120 m2 heliostat
96.5 97.5 99.5
– – –
69.9 68.2 64.2
–
– – –
n/a
–
cular aperture without CPC. The baseline parameters are given in Table 1. 4.1. Baseline results The results of the baseline case optimization are presented in Table 2. The field efficiency accounts for heliostat reflectivity and availability, cosine losses, losses due to blocking/shading and atmospheric attenuation. The intercept efficiency accounts for the spillage at the entrance aperture of the secondary concentrator. The optical efficiency summarizes the previous efficiencies. The definition of the reactor efficiency is given in Eq. (1) and covers the losses due to radiation. The average flux density refers to aperture area of the reactor. The selected chemical process has a strong impact on the field design and performance. The use of secondary concentrator limits the ground area where heliostats can be positioned due to its acceptance and inclination angles. The ZnO dissociation case achieves the highest solar-to-chemical energy conversion efficiency at an average operating temperature of about 1900 K. The design leads to small apertures, dense solar fields, and relatively high optical losses to achieve flux densities on the reactor aperture of above 4.5 MW/m2. The coal gasification case reaches the highest solar-to-chemical efficiency at average temperatures of approx. 1300 K and flux densities of around 2.5 MW/m2. This leads to lower field losses as well as lower radiation losses of the reactor, allowing 30% more solar energy per square meter of reflective surface to be stored in chemical form, as compared to the zinc oxide reduction case. These figures are theoretical upper limits; in practice the values will be considerably lower due to heat losses during start-up and shut-down, cloud passages, additional thermal losses due to convection
and conduction heat transfer, and the use of purge gases. In addition, incomplete reactions and the generation of by-products will further reduce the chemical yield and consequently the energy conversion efficiency. Scaling up from 1 to 100 MW leads to relatively small drops in the optical efficiency of about 2–3% points. The relative comparison is also influenced by the tower height that was fixed and not used as an optimization parameter. In the 1 MW case, 120 m2 heliostats cannot be used efficiently as they generate excessive spillage, therefore 10 m2 heliostats have been considered. For 10 MW and 100 MW cases, only 120 m2 heliostats were considered as the impact of spillage is significantly smaller and a very large number of small 10 m2 heliostats is expected to increase the operation and maintenance effort. 4.2. Sensitivity analysis A sensitivity analysis is carried out for the heliostat beam quality, the tower height, and the reactor radius on an interval of ±30% around the baseline value. The results are shown in Fig. 8a–f in terms of the change of the solarto-chemical energy conversion efficiency, the optical efficiency, and the flux density. The heliostat beam quality was varied from 4.3 to 2.3 mrad. As the sunshape (2.24 mrad) is already included in this figure, a 2.3 mrad beam quality represents a theoretical perfect heliostat. Heliostats with excellent optical qualities would be represented by a beam error of around 2.7 mrad. Both applications benefit strongly by the increased heliostat beam quality: the share of the gain in total efficiency compared to the gain in beam quality is about 64% on average in case of the zinc oxide reduction system and about 22% in case of the coal gasification-system. Both applications
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1.1
ref
1.0 1.1 ref SIG / SIG
1.2
1.0 0.9
0.6 0.9
1.0
0.8
0.8
0.6 0.7
1.3
1.2
1.1
1.1
1.0
1.0
e
0.8
0.9
1.0 1.1 ref SIG / SIG
1.2
1.3
1.2
1.2
1.1
1.1
1.0
1.0
ηtotal
0.9
ηoptical
ref
ref
η/η
Conc / Conc
η/η
ref
ref
1.2
ηtotal
0.9
0.9
ηoptical
c
0.8
0.8 0.7
0.8
0.9
1.0 1.1 ref ATH / ATH
1.2
0.8 0.7
1.3
1.2
f
2000 ηtotal
0.8
0.9
1.0 1.1 ref ATH / ATH
1.2
1500 ηtotal
0.9
0.8
0.6
0.8
1.0 1.2 ref Areactor / Areactor
1.4
1.6
1800
T
ref
1400 η/η
1900
Temperature [K]
ref
η/η
ηoptical
1.1
T
1.0
1.3
1.2
ηoptical
1.1
0.9
Conc
Conc
0.8
ref
1.2
0.8
0.8
1.4
Conc
ref
1.0
0.7
b
Conc / Conc
η/η
ref
1.2 1.0
0.8
ηoptical
1.4
Conc
0.9
1.6 ηtotal
1.0 1300 0.9
0.8
Temperature [K]
ηoptical
1.1
1.2
Conc / Conc
ηtotal
Conc / Conc
d
1.6
1.2
η/η
a
341
1200 0.6
0.8
1.0 1.2 ref Areactor / Areactor
1.4
1.6
Fig. 8. (a–f) Sensitivity analysis of solar-to-chemical energy conversion efficiency for the 1 MW concept for zinc oxide dissociation (a–c), and coal gasification (d–f). Parameters are the heliostat beam quality (a and d), tower height (b and e) and reactive surface.
show the same relative increase in the estimated solar flux density on the reactor aperture. The contribution of the receiver efficiency gain to the total efficiency gain is by 32% (zinc oxide) and 40% (coal gasification) larger than the contribution of the gain in the optical efficiency. Concerning the tower height, both applications suffer to a greater extent from a reduction than the gain from an increase. The loss in the overall efficiency is by a factor of 2.0 for zinc oxide reduction case and 2.4 for the coal gasification. In the zinc oxide reduction case, both optical and receiver efficiency contributes equally to the overall efficiency change. In the coal gasification case, the contribution of the change in the optical efficiency exceeds the
contribution of the receiver efficiency by 56%. An increase in the available reactive surface and, consequently, on the reaction rate, results in the same chemical conversion rate but at a lower temperature, leading to smaller radiation losses and hence to higher reactor efficiencies. Therefore, the overall efficiency is mainly influenced by the reactor efficiency: the change in the reactor efficiency is – on average – a factor of 2.7 and 2.4 larger than the change in the optical efficiency for the zinc oxide reduction and coal gasification cases, respectively. Thus, accurate kinetic data are critical to identify the optimized field and reactor design. The impact of the inlet temperature and hence of heat recovery to a certain degree is shown in Fig. 9. Note that
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ηtotal
1925
1900
0.25 400
600 800 1000 Inlet Temperature [K]
1400
b
ηtotal
T
0.30
0.50
1950
1200
T
1350
0.45
0.40 200
Operating Temperature [K]
a
ηtotal
ηtotal
0.35
Operating Temperature [K]
342
1300 400
600 800 Inlet Temperature [K]
1000
Fig. 9. Impact of reactor inlet temperature: (a) zinc oxide reduction; (b) coal gasification.
the range of the inlet temperatures shown here exceeds the reachable values by heat recovery from the products and serves the purpose of clarifying upper bounds of the applications. By increasing the inlet temperature of reactants from 298 K to 1273 K, a gain in the solar-to-chemical efficiency from 4% points (zinc oxide reduction) to 7% points (coal gasification) is observed. In the case of zinc oxide reduction, quenching of the product gases is required to avoid recombination, so that an efficient heat recovery might not be possible unless products are separated at high temperatures, e.g. using semi-permeable ceramic membranes. In the case of coal gasification, a heat recovery would increase the performance and is therefore worthwhile to consider.
the fixed flux density system (of 500 suns) usually applied in Rankine-based applications. Due to the higher concentration levels of the chemical applications, penalties of 15% points (zinc oxide reduction) and 7% points (coal gasification) are obtained. A sensitivity analysis on the optical design parameters shows that the zinc oxide reduction case benefits to a greater extend from an increase of the optical performance than the coal gasification case. Further, the benefit from an increase in inlet temperature, e.g. by measures of heat recovery, is – on average – 0.3% and 0.7% points per 100 K for the zinc oxide reduction and coal gasification, respectively.
5. Summary and conclusion
This work was performed during the sabbatical stay of Prof. Robert Pitz-Paal at the Department of Mechanical and Process Engineering of ETH Zurich in summer 2008.
We presented a methodology for the optimization of main design parameters of solar tower systems for performing high-temperature solar thermochemical processes. The optimization is based on maximizing the solar-tochemical energy conversion efficiency and accounts for the thermodynamics and kinetics of the reaction applied. A detailed investigation on the optimization problem showed a highly multimodal objective function that makes it difficult to identify the global optimum with a reasonable effort. We have therefore chosen a statistical approach to identify a reasonably good local optimum for our analysis. We carried out optimizations on two exemplarily thermochemical processes subject to current research: the zinc oxide reduction and the coal gasification. Both processes are modeled as ideal reactors for determining the theoretical maximum efficiency of storing solar energy in chemical form. Our results indicate that such a system is best designed for a solar flux density of 4600 suns operating at 1900 K for the zinc oxide reduction, and of 2500 suns at 1300 K for the coal gasification. The solar-to-chemical energy conversion efficiencies are estimated to be 30% and 40% for zinc oxide reduction and coal gasification, respectively. In that regard, we compared the resulting optical efficiencies of several system designs with that of
Acknowledgements
References Carrol, D.L., 1999. Fortran Genetic Algorithm Driver. Pettit, R.B., Vittitoe, C.N., Biggs, F., 1983. Simplified calculation procedure for determining the amount of intercepted sunlight in an imaging solar concentrator. Journal of Solar Energy Engineering 105, 101–107. Pitman, C.L., Vant-Hull, L.L., 1986. Performance of optimized solar central receiver systems as a function of receiver thermal loss per unit area. Solar Energy 37, 457–468. Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T., 1992. Numerical Recipies in C, Press Syndicate of the University of Cambridge. Schmitz, M., Schwarzbo¨zl, P., Buck, R., Pitz-Paal, R., 2006. Assessment of the potential improvement due to multiple apertures in central receiver systems with secondary concentrators. Solar Energy 80, 111–120. Schunk, L.O., Steinfeld, A., 2009. Kinetics of the thermal dissociation of ZnO exposed to concentrated solar irradiation using a solar-driven thermogravimeter in the 1800–2100 K range. AIChE Journal 55, 1497– 1504. Schunk, L.O., Lipinski, W., Steinfeld, A., 2009a. Heat transfer model of a solar receiver–reactor for the thermal dissociation of ZnO – experimental validation at 10 kW and scale-up to 1 MW. Chemical Engineering Journal 150, 502–508.
R. Pitz-Paal et al. / Solar Energy 85 (2011) 334–343 Schunk, L.O., Haeberling, P., Wepf, S., Meier, A., Steinfeld, A., 2009b. A solar receiver–reactor for the thermal dissociation of zinc oxide. Journal of Solar Energy Engineering 130. Schwarzbo¨zl, P., Pitz-Paal, R., Schmitz, M., 2009. Visual HFLCAL – A Software Tool for Layout and Optimization of Heliostats Fields. Presented at SolarPACES 2009. Segal, A., Epstein, M., 1999. Comparative performances of tower-top and tower-reflector central solar receivers. Solar Energy 65, 207–226. Segal, A., Epstein, M., 2003. Optimized working temperatures of a solar central receiver. Solar Energy 75, 503–510.
343
Steinfeld, A., 2005. Solar thermochemical production of hydrogen – a review. Solar Energy 78, 603–615. Vant-Hull, L.L., Izygon, M.E., Imhof, A., 1999. Optimization of central receiver fields to interface with applications requiring high flux density receivers. Journal De Physique IV France 09, Pr3-65–Pr3-70. Z’Graggen, A., Haueter, P., Trommer, D., Romero, M., de Jesus, J.C., Steinfeld, A., 2006. Hydrogen production by steam-gasification of petroleum coke using concentrated solar power – II reactor design, testing, and modeling. International Journal of Hydrogen Energy 31, 797–811.
Solar Energy 85 (2011) 334–343 www.elsevier.com/locate/solener
Heliostat field layout optimization for high-temperature solar thermochemical processing Robert Pitz-Paal a,⇑, Nicolas Bayer Botero a, Aldo Steinfeld b,c b
a DLR, Institute of Technical Thermodynamics, Linder Ho¨he, D-51147 Ko¨ln, Germany ETH Zurich, Department of Mechanical and Process Engineering, 8092 Zurich, Switzerland c Paul Scherer Institute, Solar Technology Laboratory, 5232 Villigen, Switzerland
Received 6 July 2009; received in revised form 13 October 2010; accepted 18 November 2010 Available online 30 December 2010 Communicated by: Associate Editor L. Vant-Hull
Abstract The layout of the heliostat field of solar tower systems is optimized for maximum annual solar-to-chemical energy conversion efficiency in high-temperature thermochemical processes for solar fuels production. The optimization algorithm is based on the performance function that includes heliostat characteristics, secondary optics, and chemical receiver–reactor characteristics at representative time steps for evaluating the annual fuel production rates. Two exemplary applications for solar fuels production are selected: the thermal reduction of zinc oxide as part of a two-step water-splitting cycle for hydrogen production, and the coal gasification for syngas production. Ó 2010 Elsevier Ltd. All rights reserved. Keywords: Solar chemistry; Solar tower; Central receiver; Heliostat field; High temperature; Thermochemical
1. Introduction Solar thermochemical reactors for fuels production operating at above 1000 K are being designed for solar tower systems capable of delivering high solar flux densities in the multi-MW power scale (Steinfeld, 2005). The design and optimization of such receiver–reactors are usually performed on the basis of a pre-defined solar flux density as boundary condition (Pitman and Vant-Hull, 1986). Because of the high temperature requirement, the desired solar concentration ratios should be significantly higher than those encountered in solar power tower systems for Rankine-based electricity generation, which typically operate at an upper temperature of about 750 K and solar concentration ratios around 500 suns (1 sun = 1 kW/m2). In ⇑ Corresponding author. Tel.: +49 2203 601 2744; fax: +49 2203 601 4141. E-mail address: [email protected] (R. Pitz-Paal).
0038-092X/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2010.11.018
contrast, solar thermochemical plants usually operate at above 1000 K and require solar concentration ratios exceeding 1500 suns. Thus, as higher solar flux densities have a direct impact on the optical performance of the solar field, the overall optimization for maximum solarto-chemical energy conversion efficiency needs to consider the coupled field and receiver design parameters. Several authors have discussed the layout of central receiver concepts for applications requiring high-flux densities and high-temperature levels (Pitman and Vant-Hull, 1986; Segal and Epstein, 1999, 2003; Vant-Hull et al., 1999). In these previous studies, the energetic characteristics of the conceptual application were not integrated directly into the layout developing procedure. Instead, a fixed flux density was used as boundary condition. This paper presents a novel approach to optimize the heliostat field design and layout for high-temperature solar thermochemical processes that integrates the energetic behavior of the intended application. The approach is
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Nomenclature Ahelio reflective area of heliostat field (m2) Aaperture aperture area of cavity-receiver (m2) Areaction surface available to chemical reaction (m2) cp specific heat capacity of reacting stream (kJ kg1 K1) DHr specific enthalpy change of reaction (kJ kg1) EA apparent activation energy (kJ mol1) g0 optical efficiency gsolar-to-chemical solar-to-chemical energy conversion efficiency
based on the HFLCAL modeling code (Schwarzbo¨zl et al., 2009), originally developed for solar electricity generation systems. The optimization procedure is applied to two exemplary processes for solar fuels production, namely: the solar thermal reduction of zinc oxide at 2000 K as part of a two-step water-splitting cycle for hydrogen production (Schunk et al., 2009b), and the coal gasification at 1400 K for syngas production (Z’Graggen et al., 2006). The annual efficiency data obtained for the optimized high-flux solar tower systems are compared with those obtained with the conventional low-flux solar tower systems for power levels of 1, 10, and 100 MW. A sensitivity analysis is performed for the heliostat beam quality, tower height, and reactive surfaces. 2. Model description The calculation of the field performance is briefly sketched here; a more detailed description of the computing code has been previously presented (Schwarzbo¨zl et al., 2009). 2.1. Field performance The calculation of the annual field performance is based on the hourly performance on the 21st of every month with clear sky conditions. The sunshape is assumed as a circularnormal distribution with the same root-mean-square deviation from the central ray which has been shown to be an appropriate statistical approximation (Pettit et al., 1983). The code considers the changing solar position and accounts for cosine losses, imperfect reflections, atmospheric attenuation, shading and blocking, spillage transmissions losses in the secondary concentrator, and receiver losses. The determination of a specific field layout is depicted in Fig. 1. Starting with a set of hypothetical heliostat positions, the performance of each heliostat is calculated. Afterwards, the set of heliostats is ranked based on the annual energy performance per area of reflective surface to determine the best set of heliostats yielding a
greactor reactor efficiency DNI direct normal irradiance (W/m2) k0 pre-exponential kinetic factor (kg s1 m2) m reaction rate (kg s1) Preaction power consumed by chemical reaction (kW) Psolarin solar power into receiver aperture (kW) Pthermallosses reactor thermal losses (kW) R specific ideal gas constant (J kg1 K1) v chemical conversion
given design power. In earlier studies, the performance calculation for a single time point was compared to that obtained with complex ray-tracing software with good agreement (Schmitz et al., 2006). Temporal disturbances are not considered by the present quasi-dynamic approach. As the integration of irradiated solar energy during a typical meteorological year matches the sum of irradiated energy during the time step series, the annual performance estimation can be considered as a theoretical maximum achievable. 2.2. Receiver model The main fundamental difference between the present optimization applied for solar chemical tower systems using a specified chemical process and that applied for solar power tower systems using a specific heat transfer fluid (e.g. steam, salt, air) is that the chemical reaction rate cannot be controlled independently (e.g. by adjusting the mass flow rates), but strongly depends on the reaction temperature, which in turn is a function of the solar concentration ratio delivered by the heliostat field and the heat/mass transfer within the receiver–reactor. The receiver–reactor model links the intercepted solar radiation with the specific chemical reaction and computes the reactor efficiency in terms of greactor ¼
mðT Þ vðT Þ DH r ðT Þ P solarin
ð1Þ
with v being the chemical conversion. For the coal gasification case, v is calculated based on the chemical equilibrium. For the zinc oxide reduction case, v is set to zero below the boiling point of zinc otherwise to one. The nominal reaction temperature results from the energy balance in the reactor, g0 P solarin ¼ P reaction ðT Þ þ P thermallosses ðT Þ
ð2Þ
where Psolarin denotes the solar power input, and the two terms on the right hand side denote the power consumed by the endothermic chemical reaction and the thermal
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Fig. 1. Scheme of the layout developing procedure.
10 8 6 0.56
4 0.48
b
0.63
Flux Density [MW/m2]
Flux Density [MW/m2]
10
a
0.64
8 0.27 0.36
6 4
0.54
2
2 0.40 0.24
0.45
0.32 0.16
0.080
0
0
0.5
1.0 Aperture Area [m2]
1.5
0.72
0.45
2.0
0.5
0.36
1.0 Aperture Area [m2]
0.18
1.5
2.0
Fig. 2. Receiver–reactor model correlation of reactor efficiency, flux density and aperture area: (a) zinc oxide reduction; (b) coal gasification.
0.6
0.7
a
b 0.6
Efficiency [-]
Efficiency [-]
0.5
0.4 ηtotal ηreactor
0.3
ηtotal
0.5
ηreactor ηoptical
0.4
ηoptical
0.2
0.3 0
1
2 3 Thermal Losses [kW/m2 ]
4
0
1
2 3 Thermal Losses [kW/m2 ]
4
Fig. 3. Impact of thermal losses on overall, optical and reactor efficiencies: (a) zinc oxide reduction; (b) coal gasification.
losses. The reaction temperature varies with time as Psolarin varies along the day/year. Consequently, the heliostat field optimization cannot be performed under the generic assumption of a constant reactor temperature – and thereby independently of the chemical reaction – but needs to
consider the specific characteristics of the chemical process affecting Preaction and the specific reactor design that influences Pthermallosses. The following assumptions are made to estimate the upper performance limit of a reactor without detailed knowledge of the reactor design:
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Fig. 4. Design parameter for (a) heliostat field position; (b) solar receiver–reactor.
the reactor temperature is uniform, convection and conduction heat losses are neglected, transient heat losses during start-up and shut-down are neglected, reaction achieves completion, e.g. there are no chemical side products considered, no purge gases are used. Thus, Z P reaction ðT Þ ¼ mðT Þ DH r ðT Þ þ
T
cp dT
ð3Þ
T in
P thermalloss ðT Þ ¼ Aaperture erT 4
ð4Þ
The generic solar chemical reactor, schematically depicted in Fig. 4b, consists of a cylindrical cavity-receiver containing a windowed aperture and a CPC. It has been scaled up in size based on data obtained from solar furnace tests and numerical simulations (Schunk et al., 2009a,b; Z’Graggen et al., 2006; Schunk and Steinfeld, 2009). Scaling up to higher design power levels was performed by keeping the reaction surface Areaction linearly increasing with Psolarin. The reaction rate is given by EA mðT Þ ¼ Areaction k 0 exp ð5Þ RT For the zinc oxide reduction: ZnO ! Zn þ 0:5O2
ð6Þ
the Arrhenius parameters are EA = 361 kJ/mol and k0 = 14.03 106 kg/(s m2) (Schunk et al., 2009b). For coal gasification, C þ H2 O ! CO þ H2
ð7Þ
the Arrhenius parameters are EA = 43.154 kJ/mol and k0 = 0.2846 kg/s m2 (where carbon is available in the form of petcoke) (Z’Graggen et al., 2006). The receiver–reactor models yield a correlation between reactor efficiency, flux density, and aperture area, which is
depicted in Fig. 2 for zinc oxide reduction (Fig. 2a) and coal gasification (Fig. 2b). We assume that the presented formulation for the receiver–reactor gives an estimation of the theoretical upper limit of the radiation to the reactor efficiency depending on the solar flux density. To ensure that the further results concerning the optical subsystem are not influenced by the idealizations within the receiver model we introduced a thermal loss per unit reactor surface varying from 0 (baseline case) to 4 kW/m2. The results are shown in Fig. 3 and follow the method described in Section 3: each data point represents the arithmetic average of 10 optimizations runs and is subject to a small spread, expressed in terms of the standard deviation. In both cases, the decrease in the overall efficiency traces back to the decrease in the reactor efficiency: the standard deviation of the optical efficiency of the five data points (losses greater zero) is of the same magnitude as the standard deviation of the corresponding baseline design point (no thermal loss) (ZnO: 0.0048 vs. 0.0040 ; coal: 0.0012 vs. 0.0048). Hence, our results concerning the optical efficiency are independent of the idealizations within the thermal model of the receiver–reactor, but the energetic characteristics of the receiver–reactor impose constrains on the field efficiency. 3. Optimization The task of finding an optimum value of an objective function in a multidimensional parameter space is challenging (Carrol et al., 1999). There is a strong indication that the objective function exhibits a highly multimodal behavior with a high number of local maxima within a small spread. 3.1. Optimization problem Target function for the optimization is the average annual solar-to-chemical energy conversion efficiency, defined as: P all time steps mðT ÞDH r ðT Þ gsolar-to-chemical ¼ P ð8Þ all time steps DNI AHelio
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This definition considers the sensible heat as an energetic by-product without value. This is due to the fact that some chemical reactions require a fast cool-down (quenching) of the product gases to avoid recombination. We chose the main design parameters determining the layout of the heliostat field, the shape of the secondary concentrator, and reactor geometry to be free parameters subject to optimization. The selected parameters are: heliostat field spacing parameters (AR, BR and AU, BU see Fig. 4), angle of sight of the secondary concentrator (a generic CPC), that also defines the ratio of inlet and outlet aperture, angle between the horizontal and the optical axis of the secondary concentrator and receiver–reactor compound of the aperture U. aperture radius of the reactor, which matches the outlet radius of the CPC (Fig. 4b). Other design parameters which are kept fixed or are subject to the sensitivity analysis are given in Table 1 according to the specific design power level. 3.2. Optimization approach Three different optimization algorithms and their combinations were applied for the optimization of this sevendimensional problem, namely: an implementation of a genetic algorithm (Carrol et al., 1999), the Nelder–Mead algorithm (Press et al., 1992), and the Powell algorithm (Press et al., 1992). Since the latter showed poor performance, the coupled genetic algorithm with the Nelder– Mead algorithm was selected. The genetic algorithm is a heuristic optimization approach. It initially discretizes the allowed parameter space and creates a number of parameter vectors (called population) distributed randomly over the parameter space. Afterwards, the value of the objective function (called fitness) for each individual parameter vector is calculated. From this population, a certain number of individuals with the best fitness are selected, recombined, and subject to random mutation to form the subsequent generation. The random number generator is based on an initial arbitrary seed value and therefore allows creating
different optimization runs within the same parameter space. The termination criterion is a given population size and number of generations. Due to the discretization of the parameter space, finding the actual value of the optimum is highly unlikely. This part is addressed by the Nelder–Mead algorithm, which belongs to the hill climbing search methods and can be used for non-linear unimodal functions. The algorithm most likely converges directly into the local maximum next to its starting point. The termination criterion in this case is a given minimum change between two function evaluations. Our approach is to set-up the genetic algorithm to explore the parameter extensively and search for a parameter vector close to the global maximum. The result is fed as starting point to the Nelder–Mead algorithm for further improvement. 3.3. Optimization performance For the assessment of the best parameter set-up of the chosen optimization algorithms, a series of optimization runs with distinct set-ups was performed. Each set-up of parameters for the optimization algorithm was run against repeated optimizations varying the seed number for the random number generator. During the tests, the objective functions was highly multimodal, e.g. it formed a great number of local maxima. Furthermore, these maxima showed a very small difference in the value of the objective function, e.g. the solar-to-chemical conversion efficiency might come up with nearly equal values despite different parameter vectors for the system design. Fig. 5 exemplarily outlines this behavior. As a consequence of this behavior the goal was to find a parameter set-up for the optimization algorithm that produces the highest arithmetic mean out of a certain number of repeated optimization runs and simultaneously achieves a low spread between the lowest and highest value of the objective function. Fig. 6 depicts the optimization performance in terms of the arithmetic mean and the spread of 10 optimization runs for four different configurations of the genetic algorithm in stand-alone mode (denoted GA1– GA4) and three different configuration of the downhill simplex, each with a tighter termination tolerance specification combined with the genetic algorithm working under the configuration GA2 (denoted GA2DS1–GA2DS3). The
Table 1 Baseline design parameters. Design powera (MW)
Tower height (m)
Heliostat size (facet size) (m2)
Product of av. heliostat reflectivity and av. heliostat availability
Beam error (incl. sunshape) (mrad)
Areaction Zn/ZnO (m2)
Areaction C gasif (m2)
1 10 100b S + SW + SE (36 + 32 + 32)
40 120
10 (1) 120 (4.3)
0.87 0.87
3.3 3.3
250
120 (4.3)
0.87
3.3
21.7 217 2170 S + SW + SE (784 + 693 + 693)
11 110 1100 S + SW + SE (396 + 352 + 352)
a
Thermal power into receiver at 21.3. Solar noon with direct normal irradiation at design point of 873.33 W/m2 and an annual average of 645.17 W/m2. A multiple aperture design is introduced, consisting of three separate fields in north (N), northeast (NE) and northwest (NW) direction, to increase the optical efficiency. b
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Fig. 5. Comparison of two heliostat field layouts with nearly the same solar-to-chemical conversion efficiency.
η total
0.31
0.30
0.29 GA1
GA2
GA3
GA4
GA2 DS1 GA2 DS2 GA2 DS3
optimization configuration
Fig. 6. Optimization performance for different parameter set-up for of the optimization algorithms (10 MW-ZnO).
coupling of both algorithms (GA2 vs. GA2DS2) shows a considerable performance gain (relative gain: 1.79% – absolute gain: 0.53%) with respect to the arithmetic mean. The relative spread e.g. the spread related to the arithmetic mean is reduced from 3.25% to 1.38%. The assumption of a highly multimodal objective function is supported by the fact that in the Fig. 6 an increase of the Nelder–Mead tolerance (from DS1: 1E-3 to DS3: 1E-10) has hardly any effect: the local maxima found cannot be further improved. Due to computational constrains, we limit the number of optimization runs to 10. To ensure that the results of 10 optimization runs are representative for the objective function, we chose the optimization configuration 0.31
(GA2DS2) and performed 450 optimization runs on both the zinc oxide reduction and coal gasification cases. The results of a statistical analysis are presented in Fig. 7. The 10 MW base cases give the following results: arithmetic mean: 0.30177 with standard deviation of 0.00329 for the zinc oxide reduction, and 0.40649 ± 0.00206 for the coal gasification case. These values differ only slightly from those resulting from only 10 optimization runs (ZnO: 0.3022 ± 0.0011; coal gasification: 0.4075 ± 0.0021) concerning the solar-to-chemical conversion efficiency. This does not hold for the partial efficiencies within the solar concentration subsystem which hence will be omitted during the analysis. We observed that selecting the maximum efficiency found in 10 repetitive optimization runs yields a distorted relation among comparable cases due to the impact of outliers. Hence, results are expressed in terms of the arithmetic average rather than the maximum found. 4. Results We studied conceptual applications for solar tower systems with solar reactors for the reduction of zinc oxide and for the gasification of coal. The plant is located on 36.12°N geographic latitude. Three power levels were considered, defined as the intercept power on the aperture of the secondary concentrator. For comparison, a typical field layout for a Rankine-based solar power plant was optimized using the same parameters expected for a fixed solar concentration ratio of 500 suns at the design point over a cir-
a
b 0.410
1 SD 50%
1 SD
-1 SD
50%
ηtotal
ηtotal
0.30 0.405
-1 SD
0.29 0.400 0.28
Fig. 7. Result of 450 optimization runs performed with different initialization of the random number generator (left) and the descriptive statistical analysis (right) for 10 MW zinc oxide-system (a) and coal gasification-system (b).
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Table 2 Baseline case optimization for solar ZnO dissociation and coal gasification and for a constant solar concentration ratio of 500 suns (typical for Rankinebased solar power plants). Efficiencies (%)
Reactor operating conditions
Field
Intercept
Secondary
Optical
Reactor
Total
Average operating temperature (K)
Peak operating temperature (K)
Flux density (MW/m2)
ZnO dissociation 1 MW, 10 m2 heliostat 10 MW, 120 m2 heliostat 100 MW, three cavities 120 m2 heliostat
66.7 67.3 63.7
86.4 86.0 88.7
92.1 92.2 91.7
53.1 53.4 51.8
55.5 55.9 57.0
29.5 29.8 29.2
1910 1912 1920
2014 2013 2017
4.5 4.6 4.8
Coal gasification 1 MW, 10 m2 heliostat 10 MW, 120 m2 heliostat 100 MW, three cavities 120 m2 heliostat
69.9 69.4 65.4
95.4 95.2 96.2
92.9 93.1 93.1
61.9 61.5 58.6
66.0 66.3 66.8
40.9 40.8 39.9
1308 1307 1308
1469 1470 1483
2.2 2.9 2.5
Thermal receiver 500 kW/m2 1 MW, 10 m2 heliostat 72.4 10 MW, 120 m2 heliostat 70.0 100 MW, northfield 64.5 120 m2 heliostat
96.5 97.5 99.5
– – –
69.9 68.2 64.2
–
– – –
n/a
–
cular aperture without CPC. The baseline parameters are given in Table 1. 4.1. Baseline results The results of the baseline case optimization are presented in Table 2. The field efficiency accounts for heliostat reflectivity and availability, cosine losses, losses due to blocking/shading and atmospheric attenuation. The intercept efficiency accounts for the spillage at the entrance aperture of the secondary concentrator. The optical efficiency summarizes the previous efficiencies. The definition of the reactor efficiency is given in Eq. (1) and covers the losses due to radiation. The average flux density refers to aperture area of the reactor. The selected chemical process has a strong impact on the field design and performance. The use of secondary concentrator limits the ground area where heliostats can be positioned due to its acceptance and inclination angles. The ZnO dissociation case achieves the highest solar-to-chemical energy conversion efficiency at an average operating temperature of about 1900 K. The design leads to small apertures, dense solar fields, and relatively high optical losses to achieve flux densities on the reactor aperture of above 4.5 MW/m2. The coal gasification case reaches the highest solar-to-chemical efficiency at average temperatures of approx. 1300 K and flux densities of around 2.5 MW/m2. This leads to lower field losses as well as lower radiation losses of the reactor, allowing 30% more solar energy per square meter of reflective surface to be stored in chemical form, as compared to the zinc oxide reduction case. These figures are theoretical upper limits; in practice the values will be considerably lower due to heat losses during start-up and shut-down, cloud passages, additional thermal losses due to convection
and conduction heat transfer, and the use of purge gases. In addition, incomplete reactions and the generation of by-products will further reduce the chemical yield and consequently the energy conversion efficiency. Scaling up from 1 to 100 MW leads to relatively small drops in the optical efficiency of about 2–3% points. The relative comparison is also influenced by the tower height that was fixed and not used as an optimization parameter. In the 1 MW case, 120 m2 heliostats cannot be used efficiently as they generate excessive spillage, therefore 10 m2 heliostats have been considered. For 10 MW and 100 MW cases, only 120 m2 heliostats were considered as the impact of spillage is significantly smaller and a very large number of small 10 m2 heliostats is expected to increase the operation and maintenance effort. 4.2. Sensitivity analysis A sensitivity analysis is carried out for the heliostat beam quality, the tower height, and the reactor radius on an interval of ±30% around the baseline value. The results are shown in Fig. 8a–f in terms of the change of the solarto-chemical energy conversion efficiency, the optical efficiency, and the flux density. The heliostat beam quality was varied from 4.3 to 2.3 mrad. As the sunshape (2.24 mrad) is already included in this figure, a 2.3 mrad beam quality represents a theoretical perfect heliostat. Heliostats with excellent optical qualities would be represented by a beam error of around 2.7 mrad. Both applications benefit strongly by the increased heliostat beam quality: the share of the gain in total efficiency compared to the gain in beam quality is about 64% on average in case of the zinc oxide reduction system and about 22% in case of the coal gasification-system. Both applications
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1.1
ref
1.0 1.1 ref SIG / SIG
1.2
1.0 0.9
0.6 0.9
1.0
0.8
0.8
0.6 0.7
1.3
1.2
1.1
1.1
1.0
1.0
e
0.8
0.9
1.0 1.1 ref SIG / SIG
1.2
1.3
1.2
1.2
1.1
1.1
1.0
1.0
ηtotal
0.9
ηoptical
ref
ref
η/η
Conc / Conc
η/η
ref
ref
1.2
ηtotal
0.9
0.9
ηoptical
c
0.8
0.8 0.7
0.8
0.9
1.0 1.1 ref ATH / ATH
1.2
0.8 0.7
1.3
1.2
f
2000 ηtotal
0.8
0.9
1.0 1.1 ref ATH / ATH
1.2
1500 ηtotal
0.9
0.8
0.6
0.8
1.0 1.2 ref Areactor / Areactor
1.4
1.6
1800
T
ref
1400 η/η
1900
Temperature [K]
ref
η/η
ηoptical
1.1
T
1.0
1.3
1.2
ηoptical
1.1
0.9
Conc
Conc
0.8
ref
1.2
0.8
0.8
1.4
Conc
ref
1.0
0.7
b
Conc / Conc
η/η
ref
1.2 1.0
0.8
ηoptical
1.4
Conc
0.9
1.6 ηtotal
1.0 1300 0.9
0.8
Temperature [K]
ηoptical
1.1
1.2
Conc / Conc
ηtotal
Conc / Conc
d
1.6
1.2
η/η
a
341
1200 0.6
0.8
1.0 1.2 ref Areactor / Areactor
1.4
1.6
Fig. 8. (a–f) Sensitivity analysis of solar-to-chemical energy conversion efficiency for the 1 MW concept for zinc oxide dissociation (a–c), and coal gasification (d–f). Parameters are the heliostat beam quality (a and d), tower height (b and e) and reactive surface.
show the same relative increase in the estimated solar flux density on the reactor aperture. The contribution of the receiver efficiency gain to the total efficiency gain is by 32% (zinc oxide) and 40% (coal gasification) larger than the contribution of the gain in the optical efficiency. Concerning the tower height, both applications suffer to a greater extent from a reduction than the gain from an increase. The loss in the overall efficiency is by a factor of 2.0 for zinc oxide reduction case and 2.4 for the coal gasification. In the zinc oxide reduction case, both optical and receiver efficiency contributes equally to the overall efficiency change. In the coal gasification case, the contribution of the change in the optical efficiency exceeds the
contribution of the receiver efficiency by 56%. An increase in the available reactive surface and, consequently, on the reaction rate, results in the same chemical conversion rate but at a lower temperature, leading to smaller radiation losses and hence to higher reactor efficiencies. Therefore, the overall efficiency is mainly influenced by the reactor efficiency: the change in the reactor efficiency is – on average – a factor of 2.7 and 2.4 larger than the change in the optical efficiency for the zinc oxide reduction and coal gasification cases, respectively. Thus, accurate kinetic data are critical to identify the optimized field and reactor design. The impact of the inlet temperature and hence of heat recovery to a certain degree is shown in Fig. 9. Note that
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Fig. 9. Impact of reactor inlet temperature: (a) zinc oxide reduction; (b) coal gasification.
the range of the inlet temperatures shown here exceeds the reachable values by heat recovery from the products and serves the purpose of clarifying upper bounds of the applications. By increasing the inlet temperature of reactants from 298 K to 1273 K, a gain in the solar-to-chemical efficiency from 4% points (zinc oxide reduction) to 7% points (coal gasification) is observed. In the case of zinc oxide reduction, quenching of the product gases is required to avoid recombination, so that an efficient heat recovery might not be possible unless products are separated at high temperatures, e.g. using semi-permeable ceramic membranes. In the case of coal gasification, a heat recovery would increase the performance and is therefore worthwhile to consider.
the fixed flux density system (of 500 suns) usually applied in Rankine-based applications. Due to the higher concentration levels of the chemical applications, penalties of 15% points (zinc oxide reduction) and 7% points (coal gasification) are obtained. A sensitivity analysis on the optical design parameters shows that the zinc oxide reduction case benefits to a greater extend from an increase of the optical performance than the coal gasification case. Further, the benefit from an increase in inlet temperature, e.g. by measures of heat recovery, is – on average – 0.3% and 0.7% points per 100 K for the zinc oxide reduction and coal gasification, respectively.
5. Summary and conclusion
This work was performed during the sabbatical stay of Prof. Robert Pitz-Paal at the Department of Mechanical and Process Engineering of ETH Zurich in summer 2008.
We presented a methodology for the optimization of main design parameters of solar tower systems for performing high-temperature solar thermochemical processes. The optimization is based on maximizing the solar-tochemical energy conversion efficiency and accounts for the thermodynamics and kinetics of the reaction applied. A detailed investigation on the optimization problem showed a highly multimodal objective function that makes it difficult to identify the global optimum with a reasonable effort. We have therefore chosen a statistical approach to identify a reasonably good local optimum for our analysis. We carried out optimizations on two exemplarily thermochemical processes subject to current research: the zinc oxide reduction and the coal gasification. Both processes are modeled as ideal reactors for determining the theoretical maximum efficiency of storing solar energy in chemical form. Our results indicate that such a system is best designed for a solar flux density of 4600 suns operating at 1900 K for the zinc oxide reduction, and of 2500 suns at 1300 K for the coal gasification. The solar-to-chemical energy conversion efficiencies are estimated to be 30% and 40% for zinc oxide reduction and coal gasification, respectively. In that regard, we compared the resulting optical efficiencies of several system designs with that of
Acknowledgements
References Carrol, D.L., 1999. Fortran Genetic Algorithm Driver
R. Pitz-Paal et al. / Solar Energy 85 (2011) 334–343 Schunk, L.O., Haeberling, P., Wepf, S., Meier, A., Steinfeld, A., 2009b. A solar receiver–reactor for the thermal dissociation of zinc oxide. Journal of Solar Energy Engineering 130. Schwarzbo¨zl, P., Pitz-Paal, R., Schmitz, M., 2009. Visual HFLCAL – A Software Tool for Layout and Optimization of Heliostats Fields. Presented at SolarPACES 2009. Segal, A., Epstein, M., 1999. Comparative performances of tower-top and tower-reflector central solar receivers. Solar Energy 65, 207–226. Segal, A., Epstein, M., 2003. Optimized working temperatures of a solar central receiver. Solar Energy 75, 503–510.
343
Steinfeld, A., 2005. Solar thermochemical production of hydrogen – a review. Solar Energy 78, 603–615. Vant-Hull, L.L., Izygon, M.E., Imhof, A., 1999. Optimization of central receiver fields to interface with applications requiring high flux density receivers. Journal De Physique IV France 09, Pr3-65–Pr3-70. Z’Graggen, A., Haueter, P., Trommer, D., Romero, M., de Jesus, J.C., Steinfeld, A., 2006. Hydrogen production by steam-gasification of petroleum coke using concentrated solar power – II reactor design, testing, and modeling. International Journal of Hydrogen Energy 31, 797–811.