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Solar Energy 85 (2011) 334–343

Heliostat field layout optimization for high-temperaturesolar thermochemical processing

Robert Pitz-Paal a,⇑, Nicolas Bayer Botero a, Aldo Steinfeld b,c

a DLR, Institute of Technical Thermodynamics, Linder Hohe, D-51147 Koln, Germanyb 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 2010Available 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 effi-ciency in high-temperature thermochemical processes for solar fuels production. The optimization algorithm is based on the performancefunction that includes heliostat characteristics, secondary optics, and chemical receiver–reactor characteristics at representative timesteps for evaluating the annual fuel production rates. Two exemplary applications for solar fuels production are selected: the thermalreduction of zinc oxide as part of a two-step water-splitting cycle for hydrogen production, and the coal gasification for syngasproduction.� 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 productionoperating at above 1000 K are being designed for solartower systems capable of delivering high solar flux densitiesin the multi-MW power scale (Steinfeld, 2005). The designand optimization of such receiver–reactors are usually per-formed on the basis of a pre-defined solar flux density asboundary condition (Pitman and Vant-Hull, 1986).Because of the high temperature requirement, the desiredsolar concentration ratios should be significantly higherthan those encountered in solar power tower systems forRankine-based electricity generation, which typically oper-ate at an upper temperature of about 750 K and solar con-centration ratios around 500 suns (1 sun = 1 kW/m2). In

0038-092X/$ - see front matter � 2010 Elsevier Ltd. All rights reserved.

doi:10.1016/j.solener.2010.11.018

⇑ Corresponding author. Tel.: +49 2203 601 2744; fax: +49 2203 6014141.

E-mail address: robert.pitz-paal@dlr.de (R. Pitz-Paal).

contrast, solar thermochemical plants usually operate atabove 1000 K and require solar concentration ratiosexceeding 1500 suns. Thus, as higher solar flux densitieshave a direct impact on the optical performance of thesolar field, the overall optimization for maximum solar-to-chemical energy conversion efficiency needs to considerthe coupled field and receiver design parameters.

Several authors have discussed the layout of centralreceiver concepts for applications requiring high-fluxdensities and high-temperature levels (Pitman andVant-Hull, 1986; Segal and Epstein, 1999, 2003; Vant-Hullet al., 1999). In these previous studies, the energetic charac-teristics of the conceptual application were not integrateddirectly into the layout developing procedure. Instead, afixed flux density was used as boundary condition.

This paper presents a novel approach to optimize theheliostat field design and layout for high-temperature solarthermochemical processes that integrates the energeticbehavior of the intended application. The approach is

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 kg�1

K�1)DHr specific enthalpy change of reaction (kJ kg�1)EA apparent activation energy (kJ mol�1)g0 optical efficiencygsolar-to-chemical solar-to-chemical energy conversion effi-

ciency

greactor reactor efficiencyDNI direct normal irradiance (W/m2)k0 pre-exponential kinetic factor (kg s�1 m�2)m reaction rate (kg s�1)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 kg�1 K�1)v chemical conversion

R. Pitz-Paal et al. / Solar Energy 85 (2011) 334–343 335

based on the HFLCAL modeling code (Schwarzbozl et al.,2009), originally developed for solar electricity generationsystems. The optimization procedure is applied to twoexemplary processes for solar fuels production, namely:the solar thermal reduction of zinc oxide at 2000 K as partof a two-step water-splitting cycle for hydrogen production(Schunk et al., 2009b), and the coal gasification at 1400 Kfor syngas production (Z’Graggen et al., 2006). The annualefficiency data obtained for the optimized high-flux solartower systems are compared with those obtained with theconventional low-flux solar tower systems for power levelsof 1, 10, and 100 MW. A sensitivity analysis is performedfor the heliostat beam quality, tower height, and reactivesurfaces.

2. Model description

The calculation of the field performance is brieflysketched here; a more detailed description of the comput-ing code has been previously presented (Schwarzbozlet al., 2009).

2.1. Field performance

The calculation of the annual field performance is basedon the hourly performance on the 21st of every month withclear sky conditions. The sunshape is assumed as a circular-normal distribution with the same root-mean-square devi-ation from the central ray which has been shown to bean appropriate statistical approximation (Pettit et al.,1983). The code considers the changing solar positionand accounts for cosine losses, imperfect reflections, atmo-spheric attenuation, shading and blocking, spillage trans-missions losses in the secondary concentrator, andreceiver losses. The determination of a specific field layoutis depicted in Fig. 1. Starting with a set of hypotheticalheliostat positions, the performance of each heliostat is cal-culated. Afterwards, the set of heliostats is ranked based onthe annual energy performance per area of reflectivesurface to determine the best set of heliostats yielding a

given design power. In earlier studies, the performance cal-culation for a single time point was compared to thatobtained with complex ray-tracing software with goodagreement (Schmitz et al., 2006). Temporal disturbancesare not considered by the present quasi-dynamic approach.As the integration of irradiated solar energy during a typ-ical meteorological year matches the sum of irradiatedenergy during the time step series, the annual performanceestimation can be considered as a theoretical maximumachievable.

2.2. Receiver model

The main fundamental difference between the presentoptimization applied for solar chemical tower systemsusing a specified chemical process and that applied forsolar power tower systems using a specific heat transferfluid (e.g. steam, salt, air) is that the chemical reaction ratecannot be controlled independently (e.g. by adjusting themass flow rates), but strongly depends on the reaction tem-perature, which in turn is a function of the solar concentra-tion ratio delivered by the heliostat field and the heat/masstransfer within the receiver–reactor.

The receiver–reactor model links the intercepted solarradiation with the specific chemical reaction and computesthe reactor efficiency in terms of

greactor ¼mðT Þ � vðT Þ � DHrðT Þ

P solarin

ð1Þ

with v being the chemical conversion. For the coal gasifica-tion case, v is calculated based on the chemical equilibrium.For the zinc oxide reduction case, v is set to zero below theboiling point of zinc otherwise to one. The nominal reac-tion temperature results from the energy balance in thereactor,

g0P solarin ¼ P reactionðT Þ þ P thermallossesðT Þ ð2Þ

where Psolarin denotes the solar power input, and the twoterms on the right hand side denote the power consumedby the endothermic chemical reaction and the thermal

Fig. 1. Scheme of the layout developing procedure.

0.0800.160.240.32

0.40

0.48

0.56

0.64

0.5 1.0 1.5 2.00

2

4

6

8

10

Flux

Den

sity

[M

W/m

2 ]

Aperture Area [m2]

0.180.360.45

0.45

0.54

0.36

0.63

0.72

0.27

0.5 1.0 1.5 2.00

2

4

6

8

10Fl

ux D

ensi

ty [

MW

/m2 ]

Aperture Area [m2]

a b

Fig. 2. Receiver–reactor model correlation of reactor efficiency, flux density and aperture area: (a) zinc oxide reduction; (b) coal gasification.

0 1 2 3 40.2

0.3

0.4

0.5

0.6

Eff

icie

ncy

[-]

Thermal Losses [kW/m2 ]

ηtotal

ηreactor

ηoptical

0 1 2 3 40.3

0.4

0.5

0.6

0.7

Eff

icie

ncy

[-]

Thermal Losses [kW/m2 ]

ηtotal

ηreactor

ηoptical

a b

Fig. 3. Impact of thermal losses on overall, optical and reactor efficiencies: (a) zinc oxide reduction; (b) coal gasification.

336 R. Pitz-Paal et al. / Solar Energy 85 (2011) 334–343

losses. The reaction temperature varies with time as Psolarin

varies along the day/year. Consequently, the heliostat fieldoptimization cannot be performed under the genericassumption of a constant reactor temperature – and there-by independently of the chemical reaction – but needs to

consider the specific characteristics of the chemical processaffecting Preaction and the specific reactor design that influ-ences Pthermallosses. The following assumptions are made toestimate the upper performance limit of a reactor withoutdetailed knowledge of the reactor design:

Fig. 4. Design parameter for (a) heliostat field position; (b) solar receiver–reactor.

R. Pitz-Paal et al. / Solar Energy 85 (2011) 334–343 337

� 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,

P reactionðT Þ ¼ mðT Þ � DH rðT Þ þZ T

T in

cpdT� �

ð3Þ

P thermallossðT Þ ¼ AapertureerT 4 ð4Þ

The generic solar chemical reactor, schematicallydepicted in Fig. 4b, consists of a cylindrical cavity-receivercontaining a windowed aperture and a CPC. It has beenscaled up in size based on data obtained from solar furnacetests and numerical simulations (Schunk et al., 2009a,b;Z’Graggen et al., 2006; Schunk and Steinfeld, 2009). Scal-ing up to higher design power levels was performed bykeeping the reaction surface Areaction linearly increasingwith Psolarin.

The reaction rate is given by

mðT Þ ¼ Areactionk0 exp�EA

RT

� �ð5Þ

For the zinc oxide reduction:

ZnO! Znþ 0:5O2 ð6Þ

the Arrhenius parameters are EA = 361 kJ/mol andk0 = 14.03 � 106 kg/(s m2) (Schunk et al., 2009b).

For coal gasification,

CþH2O! COþH2 ð7Þ

the Arrhenius parameters are EA = 43.154 kJ/mol andk0 = 0.2846 kg/s m2 (where carbon is available in the formof petcoke) (Z’Graggen et al., 2006).

The receiver–reactor models yield a correlation betweenreactor efficiency, flux density, and aperture area, which is

depicted in Fig. 2 for zinc oxide reduction (Fig. 2a) andcoal gasification (Fig. 2b).

We assume that the presented formulation for the recei-ver–reactor gives an estimation of the theoretical upperlimit of the radiation to the reactor efficiency dependingon the solar flux density. To ensure that the further resultsconcerning the optical subsystem are not influenced by theidealizations within the receiver model we introduced athermal loss per unit reactor surface varying from 0 (base-line case) to 4 kW/m2. The results are shown in Fig. 3 andfollow the method described in Section 3: each data pointrepresents the arithmetic average of 10 optimizations runsand is subject to a small spread, expressed in terms of thestandard deviation. In both cases, the decrease in the over-all efficiency traces back to the decrease in the reactor effi-ciency: the standard deviation of the optical efficiency ofthe five data points (losses greater zero) is of the same mag-nitude as the standard deviation of the corresponding base-line design point (no thermal loss) (ZnO: 0.0048 vs. 0.0040 ;coal: 0.0012 vs. 0.0048). Hence, our results concerning theoptical efficiency are independent of the idealizationswithin the thermal model of the receiver–reactor, but theenergetic characteristics of the receiver–reactor imposeconstrains on the field efficiency.

3. Optimization

The task of finding an optimum value of an objectivefunction in a multidimensional parameter space is challeng-ing (Carrol et al., 1999). There is a strong indication thatthe objective function exhibits a highly multimodal behav-ior with a high number of local maxima within a smallspread.

3.1. Optimization problem

Target function for the optimization is the averageannual solar-to-chemical energy conversion efficiency,defined as:

gsolar-to-chemical ¼P

all time stepsmðT ÞDH rðT ÞPall time stepsDNI AHelio

ð8Þ

338 R. Pitz-Paal et al. / Solar Energy 85 (2011) 334–343

This definition considers the sensible heat as an energeticby-product without value. This is due to the fact that somechemical reactions require a fast cool-down (quenching) ofthe product gases to avoid recombination. We chose themain design parameters determining the layout of theheliostat field, the shape of the secondary concentrator,and reactor geometry to be free parameters subject to opti-mization. The selected parameters are:

� heliostat field spacing parameters (AR, BR and AU, BUsee Fig. 4),� angle of sight of the secondary concentrator (a generic

CPC), that also defines the ratio of inlet and outletaperture,� angle between the horizontal and the optical axis of the

secondary concentrator and receiver–reactor compoundof the aperture U.

� aperture radius of the reactor, which matches the outletradius of the CPC (Fig. 4b).

Other design parameters which are kept fixed or are sub-ject to the sensitivity analysis are given in Table 1 accordingto the specific design power level.

3.2. Optimization approach

Three different optimization algorithms and their com-binations were applied for the optimization of this seven-dimensional problem, namely: an implementation of agenetic algorithm (Carrol et al., 1999), the Nelder–Meadalgorithm (Press et al., 1992), and the Powell algorithm(Press et al., 1992). Since the latter showed poor perfor-mance, the coupled genetic algorithm with the Nelder–Mead algorithm was selected. The genetic algorithm is aheuristic optimization approach. It initially discretizes theallowed parameter space and creates a number of parame-ter vectors (called population) distributed randomly overthe parameter space. Afterwards, the value of the objectivefunction (called fitness) for each individual parameter vec-tor is calculated. From this population, a certain number ofindividuals with the best fitness are selected, recombined,and subject to random mutation to form the subsequentgeneration. The random number generator is based on aninitial arbitrary seed value and therefore allows creating

Table 1Baseline design parameters.

Designpowera (MW)

Towerheight (m)

Heliostat size(facet size) (m2)

Product of av. heliostat refleand av. heliostat availability

1 40 10 (1) 0.8710 120 120 (4.3) 0.87

100b

S + SW + SE 250 120 (4.3) 0.87(36 + 32 + 32)

a Thermal power into receiver at 21.3. Solar noon with direct normal irradiatib A multiple aperture design is introduced, consisting of three separate fields i

optical efficiency.

different optimization runs within the same parameterspace. The termination criterion is a given population sizeand number of generations. Due to the discretization of theparameter space, finding the actual value of the optimum ishighly unlikely. This part is addressed by the Nelder–Meadalgorithm, which belongs to the hill climbing search meth-ods and can be used for non-linear unimodal functions.The algorithm most likely converges directly into the localmaximum next to its starting point. The termination crite-rion in this case is a given minimum change between twofunction evaluations. Our approach is to set-up the geneticalgorithm to explore the parameter extensively and searchfor a parameter vector close to the global maximum. Theresult is fed as starting point to the Nelder–Mead algorithmfor further improvement.

3.3. Optimization performance

For the assessment of the best parameter set-up of thechosen optimization algorithms, a series of optimizationruns with distinct set-ups was performed. Each set-up ofparameters for the optimization algorithm was run againstrepeated optimizations varying the seed number for therandom number generator. During the tests, the objectivefunctions was highly multimodal, e.g. it formed a greatnumber of local maxima. Furthermore, these maximashowed a very small difference in the value of the objectivefunction, e.g. the solar-to-chemical conversion efficiencymight come up with nearly equal values despite differentparameter vectors for the system design. Fig. 5 exemplarilyoutlines this behavior.

As a consequence of this behavior the goal was to find aparameter set-up for the optimization algorithm that pro-duces the highest arithmetic mean out of a certain numberof repeated optimization runs and simultaneously achievesa low spread between the lowest and highest value of theobjective function. Fig. 6 depicts the optimization perfor-mance in terms of the arithmetic mean and the spread of10 optimization runs for four different configurations ofthe genetic algorithm in stand-alone mode (denoted GA1–GA4) and three different configuration of the downhill sim-plex, each with a tighter termination tolerance specificationcombined with the genetic algorithm working under theconfiguration GA2 (denoted GA2DS1–GA2DS3). The

ctivity Beam error (incl.sunshape) (mrad)

Areaction Zn/ZnO(m2)

Areaction

C gasif (m2)

3.3 21.7 113.3 217 110

2170 11003.3 S + SW + SE S + SW + SE

(784 + 693 + 693) (396 + 352 + 352)

on at design point of 873.33 W/m2 and an annual average of 645.17 W/m2.n north (N), northeast (NE) and northwest (NW) direction, to increase the

Fig. 5. Comparison of two heliostat field layouts with nearly the same solar-to-chemical conversion efficiency.

GA1 GA2 GA3 GA4 GA2 DS1 GA2 DS2 GA2 DS30.29

0.30

0.31

ηto

tal

optimization configuration

Fig. 6. Optimization performance for different parameter set-up for of theoptimization algorithms (10 MW-ZnO).

R. Pitz-Paal et al. / Solar Energy 85 (2011) 334–343 339

coupling of both algorithms (GA2 vs. GA2DS2) shows aconsiderable performance gain (relative gain: 1.79% – abso-lute gain: 0.53%) with respect to the arithmetic mean. Therelative spread e.g. the spread related to the arithmetic meanis reduced from 3.25% to 1.38%. The assumption of a highlymultimodal objective function is supported by the fact thatin the Fig. 6 an increase of the Nelder–Mead tolerance(from DS1: 1E-3 to DS3: 1E-10) has hardly any effect: thelocal maxima found cannot be further improved.

Due to computational constrains, we limit the numberof optimization runs to 10. To ensure that the results of10 optimization runs are representative for the objectivefunction, we chose the optimization configuration

-1 SD

1 SD

50%

0.28

0.29

0.30

0.31

η tota

l

a

Fig. 7. Result of 450 optimization runs performed with different initialization o(right) for 10 MW zinc oxide-system (a) and coal gasification-system (b).

(GA2DS2) and performed 450 optimization runs on boththe zinc oxide reduction and coal gasification cases. Theresults of a statistical analysis are presented in Fig. 7.The 10 MW base cases give the following results: arithme-tic mean: 0.30177 with standard deviation of 0.00329 forthe zinc oxide reduction, and 0.40649 ± 0.00206 for thecoal gasification case. These values differ only slightly fromthose resulting from only 10 optimization runs (ZnO:0.3022 ± 0.0011; coal gasification: 0.4075 ± 0.0021) con-cerning the solar-to-chemical conversion efficiency. Thisdoes not hold for the partial efficiencies within the solarconcentration subsystem which hence will be omitted dur-ing the analysis. We observed that selecting the maximumefficiency found in 10 repetitive optimization runs yields adistorted relation among comparable cases due to theimpact of outliers. Hence, results are expressed in termsof the arithmetic average rather than the maximum found.

4. Results

We studied conceptual applications for solar tower sys-tems with solar reactors for the reduction of zinc oxide andfor the gasification of coal. The plant is located on 36.12�Ngeographic latitude. Three power levels were considered,defined as the intercept power on the aperture of the sec-ondary concentrator. For comparison, a typical field lay-out for a Rankine-based solar power plant was optimizedusing the same parameters expected for a fixed solar con-centration ratio of 500 suns at the design point over a cir-

-1 SD

1 SD

50%

0.400

0.405

0.410

η tota

l

b

f the random number generator (left) and the descriptive statistical analysis

Table 2Baseline case optimization for solar ZnO dissociation and coal gasification and for a constant solar concentration ratio of 500 suns (typical for Rankine-based solar power plants).

Efficiencies (%) Reactor operating conditions

Field Intercept Secondary Optical Reactor Total Average operatingtemperature (K)

Peak operatingtemperature (K)

Flux density(MW/m2)

ZnO dissociation

1 MW, 10 m2 heliostat 66.7 86.4 92.1 53.1 55.5 29.5 1910 2014 4.510 MW, 120 m2 heliostat 67.3 86.0 92.2 53.4 55.9 29.8 1912 2013 4.6100 MW, three cavities

120 m2 heliostat63.7 88.7 91.7 51.8 57.0 29.2 1920 2017 4.8

Coal gasification

1 MW, 10 m2 heliostat 69.9 95.4 92.9 61.9 66.0 40.9 1308 1469 2.210 MW, 120 m2 heliostat 69.4 95.2 93.1 61.5 66.3 40.8 1307 1470 2.9100 MW, three cavities

120 m2 heliostat65.4 96.2 93.1 58.6 66.8 39.9 1308 1483 2.5

Thermal receiver 500 kW/m2

1 MW, 10 m2 heliostat 72.4 96.5 – 69.9 – – n/a10 MW, 120 m2 heliostat 70.0 97.5 – 68.2 –100 MW, northfield

120 m2 heliostat64.5 99.5 – 64.2 – –

340 R. Pitz-Paal et al. / Solar Energy 85 (2011) 334–343

cular aperture without CPC. The baseline parameters aregiven in Table 1.

4.1. Baseline results

The results of the baseline case optimization are pre-sented in Table 2. The field efficiency accounts for heliostatreflectivity and availability, cosine losses, losses due toblocking/shading and atmospheric attenuation. The inter-cept efficiency accounts for the spillage at the entranceaperture of the secondary concentrator. The optical effi-ciency summarizes the previous efficiencies. The definitionof the reactor efficiency is given in Eq. (1) and covers thelosses due to radiation. The average flux density refers toaperture area of the reactor. The selected chemical processhas a strong impact on the field design and performance.The use of secondary concentrator limits the ground areawhere heliostats can be positioned due to its acceptanceand inclination angles. The ZnO dissociation case achievesthe highest solar-to-chemical energy conversion efficiencyat 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 densitieson the reactor aperture of above 4.5 MW/m2. The coal gas-ification case reaches the highest solar-to-chemical effi-ciency at average temperatures of approx. 1300 K andflux densities of around 2.5 MW/m2. This leads to lowerfield losses as well as lower radiation losses of the reactor,allowing 30% more solar energy per square meter of reflec-tive surface to be stored in chemical form, as compared tothe zinc oxide reduction case. These figures are theoreticalupper limits; in practice the values will be considerablylower 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 ofby-products will further reduce the chemical yield and con-sequently the energy conversion efficiency. Scaling up from1 to 100 MW leads to relatively small drops in the opticalefficiency of about 2–3% points. The relative comparisonis also influenced by the tower height that was fixed andnot used as an optimization parameter. In the 1 MW case,120 m2 heliostats cannot be used efficiently as they generateexcessive spillage, therefore 10 m2 heliostats have been con-sidered. For 10 MW and 100 MW cases, only 120 m2 helio-stats were considered as the impact of spillage issignificantly smaller and a very large number of small10 m2 heliostats is expected to increase the operation andmaintenance effort.

4.2. Sensitivity analysis

A sensitivity analysis is carried out for the heliostatbeam quality, the tower height, and the reactor radius onan interval of ±30% around the baseline value. The resultsare shown in Fig. 8a–f in terms of the change of the solar-to-chemical energy conversion efficiency, the optical effi-ciency, and the flux density. The heliostat beam qualitywas varied from 4.3 to 2.3 mrad. As the sunshape(2.24 mrad) is already included in this figure, a 2.3mrad beam quality represents a theoretical perfect helio-stat. Heliostats with excellent optical qualities would berepresented by a beam error of around 2.7 mrad. Bothapplications benefit strongly by the increased heliostatbeam quality: the share of the gain in total efficiency com-pared to the gain in beam quality is about 64% on averagein case of the zinc oxide reduction system and about 22% incase of the coal gasification-system. Both applications

0.7 0.8 0.9 1.0 1.1 1.2 .310.8

0.9

1.0

1.1

1.2

ηtotal

ηoptical

Conc

η /

ηref

SIG / SIGref

0.6

0.8

1.0

1.2

1.4

1.6

Con

c /

Co

ncre

f

0.7 0.8 0.9 1.0 1.1 1.2 1.30.8

0.9

1.0

1.1

1.2

ηtotal

ηoptical

Conc

η /

ηref

ATH / ATHref

0.8

0.9

1.0

1.1

1.2

Con

c /

Co

ncre

f

0.6 0.8 1.0 1.2 1.4 1.60.8

0.9

1.0

1.1

1.2η

total

ηoptical

T

η /

ηref

Areactor

/ Aref

reactor

1800

1900

2000

Tem

per

atur

e [K

]

0.7 0.8 0.9 1.0 1.1 1.2 1.30.8

0.9

1.0

1.1

1.2

ηtotal

ηoptical

Conc

η /

ηref

SIG / SIGref

0.6

0.8

1.0

1.2

1.4

1.6

Con

c /

Co

ncre

f

0.7 0.8 0.9 1.0 1.1 1.2 1.30.8

0.9

1.0

1.1

1.2

ηtotal

ηoptical

Conc

η /

ηref

ATH / ATHref

0.8

0.9

1.0

1.1

1.2

Con

c /

Co

ncre

f0.6 0.8 1.0 1.2 1.4 1.6

0.8

0.9

1.0

1.1

1.2η

total

ηoptical

T

η /

ηref

Areactor

/ Aref

reactor

1200

1300

1400

1500

Tem

per

atur

e [K

]

a

b

c

d

e

f

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 coalgasification (d–f). Parameters are the heliostat beam quality (a and d), tower height (b and e) and reactive surface.

R. Pitz-Paal et al. / Solar Energy 85 (2011) 334–343 341

show the same relative increase in the estimated solar fluxdensity on the reactor aperture. The contribution of thereceiver efficiency gain to the total efficiency gain is by32% (zinc oxide) and 40% (coal gasification) larger thanthe contribution of the gain in the optical efficiency. Con-cerning the tower height, both applications suffer to agreater extent from a reduction than the gain from anincrease. The loss in the overall efficiency is by a factorof 2.0 for zinc oxide reduction case and 2.4 for the coal gas-ification. In the zinc oxide reduction case, both optical andreceiver efficiency contributes equally to the overall effi-ciency change. In the coal gasification case, the contribu-tion of the change in the optical efficiency exceeds the

contribution of the receiver efficiency by 56%. An increasein the available reactive surface and, consequently, on thereaction rate, results in the same chemical conversion ratebut at a lower temperature, leading to smaller radiationlosses and hence to higher reactor efficiencies. Therefore,the overall efficiency is mainly influenced by the reactor effi-ciency: the change in the reactor efficiency is – on average –a factor of 2.7 and 2.4 larger than the change in the opticalefficiency for the zinc oxide reduction and coal gasificationcases, respectively. Thus, accurate kinetic data are criticalto identify the optimized field and reactor design.

The impact of the inlet temperature and hence of heatrecovery to a certain degree is shown in Fig. 9. Note that

400 600 800 1000 12000.25

0.30

0.35

ηtotal

T

η tota

l

Inlet Temperature [K]

1900

1925

1950

Op

erat

ing

Tem

per

atur

e [K

]

200 400 600 800 10000.40

0.45

0.50

ηtotal

T

η tota

l

Inlet Temperature [K]

1300

1350

1400

Op

erat

ing

Tem

per

atur

e [K

]

a b

Fig. 9. Impact of reactor inlet temperature: (a) zinc oxide reduction; (b) coal gasification.

342 R. Pitz-Paal et al. / Solar Energy 85 (2011) 334–343

the range of the inlet temperatures shown here exceeds thereachable values by heat recovery from the products andserves the purpose of clarifying upper bounds of the appli-cations. By increasing the inlet temperature of reactantsfrom 298 K to 1273 K, a gain in the solar-to-chemical effi-ciency from 4% points (zinc oxide reduction) to 7% points(coal gasification) is observed. In the case of zinc oxidereduction, quenching of the product gases is required toavoid recombination, so that an efficient heat recoverymight not be possible unless products are separated at hightemperatures, e.g. using semi-permeable ceramic mem-branes. In the case of coal gasification, a heat recoverywould increase the performance and is therefore worth-while to consider.

5. Summary and conclusion

We presented a methodology for the optimization ofmain design parameters of solar tower systems for per-forming high-temperature solar thermochemical processes.The optimization is based on maximizing the solar-to-chemical energy conversion efficiency and accounts forthe thermodynamics and kinetics of the reaction applied.A detailed investigation on the optimization problemshowed a highly multimodal objective function that makesit difficult to identify the global optimum with a reasonableeffort. We have therefore chosen a statistical approach toidentify a reasonably good local optimum for our analysis.

We carried out optimizations on two exemplarily ther-mochemical processes subject to current research: the zincoxide reduction and the coal gasification. Both processesare modeled as ideal reactors for determining the theoreti-cal maximum efficiency of storing solar energy in chemicalform. Our results indicate that such a system is bestdesigned for a solar flux density of 4600 suns operatingat 1900 K for the zinc oxide reduction, and of 2500 sunsat 1300 K for the coal gasification. The solar-to-chemicalenergy conversion efficiencies are estimated to be 30%and 40% for zinc oxide reduction and coal gasification,respectively. In that regard, we compared the resultingoptical efficiencies of several system designs with that of

the fixed flux density system (of 500 suns) usually appliedin Rankine-based applications. Due to the higher concen-tration levels of the chemical applications, penalties of15% points (zinc oxide reduction) and 7% points (coal gas-ification) are obtained. A sensitivity analysis on the opticaldesign parameters shows that the zinc oxide reduction casebenefits to a greater extend from an increase of the opticalperformance than the coal gasification case. Further, thebenefit from an increase in inlet temperature, e.g. by mea-sures of heat recovery, is – on average – 0.3% and 0.7%points per 100 K for the zinc oxide reduction and coal gas-ification, respectively.

Acknowledgements

This work was performed during the sabbatical stay ofProf. Robert Pitz-Paal at the Department of Mechanicaland Process Engineering of ETH Zurich in summer 2008.

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