Technical Note Entropy Analysis of Solar Two-Step Thermochemical Cycles for and Carbon Dioxide Splitting

Matthias Lange *, Martin Roeb, Christian Sattler and Robert Pitz-Paal

Received: 3 November 2015; Accepted: 7 January 2016; Published: 11 January 2016 Academic Editors: Michel Feidt, Daniel Tondeur, Jean-Noël Jaubert and Romain Privat

German Aerospace Center (DLR), Institute of Solar Research, Linder Höhe, 51170 Köln, Germany; [email protected] (M.R.); [email protected] (C.S.); [email protected] (R.P.-P.) * Correspondence: [email protected]; Tel.: +49-2203-601-4758; Fax: +49-2203-601-4141

Abstract: The present study provides a thermodynamic analysis of solar thermochemical cycles for splitting of H2O or CO2. Such cycles, powered by concentrated solar energy, have the potential to produce in a sustainable way. We extend a previous study on the of by also taking into account CO2 splitting and the influence of the solar absorption efficiency. Based on this purely thermodynamic approach, efficiency trends are discussed. The comprehensive and vivid representation in T-S diagrams provides researchers in this field with the required theoretical background to improve process development. Furthermore, results about the required entropy change in the used materials can be used as a guideline for material developers. The results show that CO2 splitting is advantageous at higher temperature levels, while water splitting is more feasible at lower temperature levels, as it benefits from a great entropy change during the splitting step.

Keywords: solar; thermochemical cycle; CSP; water splitting; CO2 splitting; T-S diagram; efficiency; entropy

1. Introduction Fossil depletion and the ongoing climate change lead to the need for a sustainable energy system. One important pillar of an energy system is the availability of fuels. Today, almost all fuels consumed worldwide are based on petroleum or natural gas, i.e., our mobility relies on unsustainable raw materials. In order to improve this situation in the future, great research effort is put into the production of sustainable fuels, mainly and synthetic hydrocarbons. One possible way to produce hydrogen and carbon monoxide is to apply solar-driven thermochemical cycles for water splitting or CO2 splitting. The obtained gases can be either used directly as a fuel or further processed in a Fischer–Tropsch plant to generate synthetic hydrocarbons. Many thermochemical cycles have been investigated and evaluated in the past [1–4]. The cycle which is subject to most research activities in this area today is the two-step cycle based on a redox reaction as follows [5]: 1. Endothermic reduction of a metal oxide (MO):

MOx Ñ MOx´δ ` δ{2 O2 (1)

2. Splitting step (for H2O or CO2)

MOx´δ ` CO2 Ñ MOx ` δ CO (2)

MOx´δ ` H2O Ñ MOx ` δ H2 (3)

Entropy 2016, 18, 24; doi:10.3390/e18010024 www.mdpi.com/journal/entropy Entropy 2016, 18, 24 2 of 12 Entropy 2016, 18, 24

SeveralSeveral thermodynamic evaluationsevaluations of of these these cycles, cycles, especially especially the the water-splitting water-splitting cycle cycle have have been beenconducted conducted [6–9 ].[6–9]. In our In our group, group, we intendwe intend to revive to revive the the thermodynamic thermodynamic analysis analysis of theseof these cycles cycles in ina differenta different way, way, based based on on vivid vivid graphical graphical representation. representation. Further,Further, wewe extendextend the existing by by analyzinganalyzing the the thermodynamic thermodynamic exigencies exigencies for for different different process process parameters parameters (temperatures, (temperatures, pressures). pressures). ThisThis way,way, wewe obtain obtain the the maximum maximum efficiency efficiency as well as well as the as required the required entropy entropy change change which thewhich material the materialneeds to needs undergo. to undergo. In a previous In a previous publication public [10ation], we [10], presented we presented the methodology the methodology of the analysis of the analysisbased on basedT-S diagram on T-S diagram representation. representation. The work The was work limited was tolimited the water-splitting to the water-splitting process process and the andinfluence the influence of the solar of the efficiency solar efficiency was not was taken not into taken account. into account. The present The paperpresent extends paper theextends analysis the analysisby considering by considering also CO2 alsosplitting CO2 andsplitting comparing and comparing it to water it splitting. to water Further, splitting. the Further, solar efficiency the solar is efficiencydiscussed is and discussed its influence and its on influence the theoretical on the process theoretical efficiency process is presented.efficiency is presented.

2.2. One-Step One-Step Cycle Cycle and and Solar Solar Efficiency Efficiency

2.1.2.1. Direct Direct Gas Gas Splitting—Thermolysis Splitting—Thermolysis

InIn reality, reality, direct splitting of of water water and and CO CO22 isis not not as as trivial trivial as as presented presented in in this this paragraph. paragraph. However,However, for the relevant temperature range this re representationpresentation is is sufficient, sufficient, especially because because the the presentpresent sectionsection hashas an an explanatory explanatory purpose purpose only. only. In orderIn order to completely to completely split watersplit water at 1 bar at into 1 bar into oxygenand hydrogen, and hydrogen, a temperature a temperature of about 4315of about K is 4315 necessary. K is necessary. This high temperatureThis high temperature is a result of is thea result large ofenthalpy the large of formationenthalpy of waterformation and theof water low entropy and the change low entropy between change H2O and between the product H2O gasesand the H2 T S productand O2. Thegases- Hrepresentation2 and O2. The of T one-step-S representation water splitting of one-step and subsequent water splitting recombination and subsequent at ambient recombinationtemperature is at shown ambient in Figuretemperature1. The is entropy shown in values Figure shown 1. The here entropy and values in all subsequent shown here figures and in allin thissubsequent paper are figures temperature-dependent in this paper are andtemp wereerature-dependent generated with and the thermochemistrywere generated with software the thermochemistryFactSage [11,12]. software FactSage [11,12].

Figure 1. T-S diagram of one step splitting of 1 mol H2O/CO2 at 1 bar and 100% conversion. Figure 1. T-S diagram of one step splitting of 1 mol H2O/CO2 at 1 bar and 100% conversion. The water-splitting curve in Figure 1 encloses an area which represents the energy of formation The water-splitting curve in Figure1 encloses an area which represents the energy of formation of of water (237 kJ/molH2O). This energy could be extracted from all water-splitting cycles, for example water (237 kJ/mol ). This energy could be extracted from all water-splitting cycles, for example by recombining hydrogenH2O and oxygen in an ideal fuel cell. In addition to the water-splitting cycle, by recombining hydrogen and oxygen in an ideal fuel cell. In addition to the water-splitting cycle, Figure 1 also shows the simplified T-S representation of direct CO2 splitting. Comparing the two Figure1 also shows the simplified T-S representation of direct CO splitting. Comparing the two cycles, CO2 splitting seems to be more feasible, because the maximum2 process temperature is lower. cycles, CO splitting seems to be more feasible, because the maximum process temperature is lower. The larger 2entropy change in the case of CO2 splitting leads to an increased width of the enclosed The larger entropy change in the case of CO splitting leads to an increased width of the enclosed area. Thus, the upper temperature being 33462 K is lower compared to H2O splitting. This is the case, area. Thus, the upper temperature being 3346 K is lower compared to H O splitting. This is the case, although the change is larger for CO2 splitting (257 kJ/mol2 CO), resulting in a larger enclosedalthough area the Gibbsin Figure free 1. energy change is larger for CO2 splitting (257 kJ/molCO), resulting in a larger enclosedDue areato the in high Figure process1. temperatures, the theoretical efficiency of direct splitting processes is Due to the high process temperatures, the theoretical efficiency of direct splitting processes is high. high. The splitting-cycle efficiency ηsc is based on the net . input assuming ideal heat recovery.The splitting-cycle This heat efficiency recovery ηissc theis based result on of the a pinch-point net heat input analysisQNET assumingwith minimum ideal heattemperature recovery. difference of 0 K. Such ideal heat recovery is assumed for all processes throughout this publication.

2 Entropy 2016, 18, 24 3 of 12

ThisEntropy heat 2016 recovery, 18, 24 is the result of a pinch-point analysis with minimum temperature difference of 0 K. Such ideal heat recovery is assumed for all processes throughout this publication. In the case of water Insplitting, the case the of enumeratorwater splitting, in the the efficiency enumerator formulation in the efficiency is the Gibbs formulation free energy is the of Gibbs formation free energy of water of formation of water ΔGf,H2O. In the case of CO2 splitting, the benefit is (ΔGf,CO2 − ΔGf,CO). This leads to ∆Gf,H2O. In the case of CO2 splitting, the benefit is (∆Gf,CO2 ´ ∆Gf,CO). This leads to the general form: the general form: ∆Gf ηsc “ .Δ (4) =Q (4) NET

The efficiency efficiency of of direct direct CO CO22 splittingsplitting (η (ηscsc = =90.6%) 90.6%) is isadvantageous advantageous compared compared to tothe the efficiency efficiency of directof direct water water splitting splitting (n (scn =sc 82.8%).= 82.8%). This This advantage advantage is isdue due to to the the fact fact that that the the evaporation evaporation of of water takes place at a low temperature. Such a low temperaturetemperature input to a process decreasesdecreases itsits efficiency.efficiency.

2.2. Solar Absorption Efficiency Efficiency The solarsolar absorptionabsorption efficiency efficiency describes describes to whichto which extent extent the solar the radiationsolar radiation reaching reaching the receiver the receivercan be usedcan be by used a coupled by a coupled process process as thermal as thermal energy. energy. It isIt is strongly strongly dependent dependent on on thethe receiver temperature and the concentration ratio C [[13].13]. The concentration ratio describes the ratio between the collector aperture area and the absorber aperture area. Rising the receiver temperature as well as lowering thethe concentration concentration ratio ratio leads leads to increased to increa thermalsed thermal reradiation reradiation of the receiver. of the Highreceiver. reradiation High reradiationresults in low results solar in absorption low solar efficiencies.absorption efficien This relationcies. This is displayed relation is in displayed Figure2. in Figure 2.

Figure 2. Maximum absorption efficiency of a black body at different temperatures and Figure 2. Maximum absorption efficiency of a black body at different temperatures and concentration ratios. concentration ratios.

In the current analysis, whenever we take the solar absorption efficiency into account, we assumeIn thethe current receiver analysis, temperature whenever to be we the take reduct the solarion temperature, absorption efficiency because intoat this account, temperature we assume the endothermicthe receiver temperature reaction takes to be place. the reduction Further, temperature, we set the becauseconcentration at this ratio temperature to a constant the endothermic value of Creaction = 4000. takes This place.is a quite Further, high value, we set but the for concentration high temperature ratio to processes a constant itvalue should of beC =aimed 4000. at This such is higha quite values high to value, avoid but drastic for high thermal temperature losses. processesUsing solar it shouldtowers betogether aimed with at such secondary high values optics, to avoid such drastic thermal losses. Using solar towers together with secondary optics, such high concentration high concentration ratios can be reached [14]. Considering the absorption efficiency ηabs, the overall ratios can be reached [14]. Considering the absorption efficiency η , the overall solar to useful work solar to useful work efficiency ηtot is defined as: abs efficiency ηtot is defined as: = × (5) ηtottot “ ηabsabs ˆ ηsc (5) During the following study, the reader should keep in mind that this efficiencyefficiency formulation represents an ideal thermodynamic description far from real applications. With a concentration ratio of C = 4000, the required temperatures for the direct splitting cannot be reached.reached. The concentration ratios required to reach complete direct gas splitting are close to 8000 (CO2 splitting) and 20,000 ratios required to reach complete direct gas splitting are close to 8000 (CO2 splitting) and 20,000 (H2O (Hsplitting).2O splitting). Such highSuch concentrationhigh concentration ratios ratios are technically are technically not feasible. not feasible.

3 Entropy 2016, 18, 24 4 of 12

2.3. TwoEntropy Step 2016 Splitting, 18, 24 at Normal Pressure, Gas Phase Only

Direct2.3. Two splitting Step Splitting has been at Normal discussed Pressure, before Gas Phase and Only considered technically not feasible, even when aiming at lowerDirect conversion splitting has which been discussed would relax before the and temperature considered technically exigencies not but feasible, at the sameeven when time require high temperatureaiming at lower gas conversion separation whic [5].h Therefore,would relax thermochemicalthe temperature exigencies cycles which but at increasethe same thetime entropy differencerequire and high thus temperature widen the gas enclosed separation area [5]. in Ther theefore,T-S diagram thermochemical have beencycles introduced. which increase Out the of many possibleentropy cycles difference with different and thus numbers widen the of intermediateenclosed area in steps, the T two-step-S diagram cycling have been based introduced. on redox Out reactions of many possible cycles with different numbers of intermediate steps, two-step cycling based on has drawn most attention of the solar fuels research community [15,16]. In our previous paper we redox reactions has drawn most attention of the solar fuels research community [15,16]. In our explainprevious the two-step paper water-splittingwe explain the two-step process water-splitting in detail [10 process]. Here, in we detail directly [10]. Here, compare we directly it to the CO2 splittingcompare process. it to At the first, CO2 we splitting introduce process. only At thefirst, gas we introd phaseuce entropy only the change, gas phase as entropy this is mostchange, generic as and the basisthis of is all most processes generic independentand the basis of of all the proce redoxsses materialindependent choice. of the TheredoxT -materialS diagram choice. in FigureThe T-S3 shows diagram in Figure 3 shows the water-splitting and the CO2-splitting process. The oxidation the water-splitting and the CO2-splitting process. The oxidation temperature is set to 1600 K for both temperature is set to 1600 K for both processes. In the following, the CO2-splitting cycle is explained processes. In the following, the CO2-splitting cycle is explained in detail. in detail.

Figure 3. T-S diagram for splitting of one mole of water/CO2. Oxidation temperature is set to 1600 K, Figure 3.all Tpressures-S diagram are 1 forbar. splitting of one mole of water/CO2. Oxidation temperature is set to 1600 K, all pressures are 1 bar.

The cycle starts with heating CO2 from ambient to the oxidation temperature. Then each CO2 molecule loses one oxygen atom to the redox material resulting in the product gas carbon monoxide. The cycle starts with heating CO2 from ambient to the oxidation temperature. Then each CO2 In this step, the entropy decreases, because diatomic CO has lower degree of freedom than triatomic molecule loses one oxygen atom to the redox material resulting in the product gas carbon monoxide. CO2. In the next step, the redox material is heated to the reduction temperature. At this temperature, In this step,oxygen the evolves entropy from decreases, the redox material because leading diatomic to a strong CO has entropy lower increase. degree This of is freedom the endothermal than triatomic CO2. Inreduction the next step step, which the redoxrequires material solar energy is heated input. As to the the oxygen reduction and the temperature. CO evolve at Atdifferent this temperature, parts oxygenof evolves the process, from they the redoxare kept material separately leading so that to aentropy strong of entropy mixing increase.is not regarded This ishere. the In endothermal the reductionfollowing step which step, oxygen requires and solar CO are energy cooled input.to ambient As thetemperature. oxygen Then and thethey CO are evolvefinally recombined at different parts of the process,to CO2. In they this arerecombination kept separately step, useful so that work entropy equivalent of mixing to the enclosed is not regardedarea in the here.diagram In (Gibbs the following free energy of formation) can be extracted. There are three options to draw the T-S diagrams above step, oxygenthe oxidation and CO temperature: are cooled to ambient temperature. Then they are finally recombined to CO2. In this recombination step, useful work equivalent to the enclosed area in the diagram (Gibbs free 1. In real processes, the product gases (CO and H2 respectively for CO2/water splitting) are not energy of formation) can be extracted. There are three options to draw the T-S diagrams above the heated above oxidation temperature. Therefore, one could exclude their contribution to the oxidation temperature:overall entropy in the graphs. Then, the entropy would actually drop to zero at the reduction temperature and rise to the entropy of oxygen at the reduction temperature. When cooling the 1. In real processes, the product gases (CO and H2 respectively for CO2/water splitting) are not oxygen down from the reduction temperature, the product gas entropy would need to be added heatedleading above to oxidation a distorted temperature.graph, which would Therefore, be difficult one to couldcapture exclude for the reader. their Therefore, contribution we to the overalldid entropy not choose in thethis graphs.option. Then, the entropy would actually drop to zero at the reduction temperature2. The entropy and contribution rise to the entropyof the product of oxygen gases co atuld the also reduction be considered temperature. to stay constant When while cooling the oxygenthe down reduction from takes the reductionplace. In the temperature, T-S representation, the product this option gas would entropy result would in a straight need to line be added leadingupwards to a distorted after the graph, oxidation which reaction would and be difficultin a slight to change capture of for slope the reader.at Tox in Therefore, the curve we did representing the cooling of all gases. This kind of representation is easy to grasp visually, but not choose this option. 4 2. The entropy contribution of the product gases could also be considered to stay constant while the reduction takes place. In the T-S representation, this option would result in a straight line upwards after the oxidation reaction and in a slight change of slope at Tox in the curve representing the cooling of all gases. This kind of representation is easy to grasp visually, but may be confusing, Entropy 2016, 18, 24 5 of 12

because entropy terms from gases at different temperatures would be added and represented by Entropy 2016, 18, 24 only one line at Tred. Therefore, we also did not consider this way of representation. 3. In the T-S diagrams shown in this paper, the product gas is always heated to the reduction may be confusing, because entropy terms from gases at different temperatures would be added temperature to avoid the confusion which may come up with option 1 or 2. In real applications and represented by only one line at Tred. Therefore, we also did not consider this way this heatingof representation. would not take place. As long as ideal heat recovery is assumed, which is the case in 3.this study,In the T the-S diagrams heating of shown CO to in the this reduction paper, the temperature product gas does is always not influence heated to the the cycle reduction efficiency. Thus,temperature this is just to a avoid question the confusion of display which and hasmay no come effect up onwith the option outcome 1 or 2. of In the real analysis. applications this heating would not take place. As long as ideal heat recovery is assumed, which is the case In thein processes this study, shown the heating in Figure of 3CO, all to pressures the reduction are set temperature to 1 bar. Thus, does thenot onlyinfluence degree the of cycle freedom to adjustefficiency. the area enclosedThus, this is by just the a question curves isof thedispla reductiony and has temperatureno effect on the (the outcome oxidation of the analysis. temperature was set to a fixed value of 1600 K). Although the reduction temperatures still reach very high values In the processes shown in Figure 3, all pressures are set to 1 bar. Thus, the only degree of of above 2500 K, they could be radically reduced compared to the one-step process. Further, the freedom to adjust the area enclosed by the curves is the reduction temperature (the oxidation CO2-splittingtemperature cycle was still set to has a fixed a slightly value lowerof 1600 reduction K). Although temperature the reduction than temperatures the water-splitting still reach cycle.very Thehigh extentvalues toof whichabove 2500 the reductionK, they could temperature be radically can reduced be lowered compared due to to the the one-step two-step process. approach is determinedFurther, the by theCO2-splitting shaded areascycle instill Figure has3 alabelled slightly extra lower area reduction due to secondtemperature step. than These the areas representwater-splitting the difference cycle. between the one-step and the two-step splitting. It can be directly observed that the impactThe extent of the to which second the step reduction is larger temperature in the case ca ofn be water lowered splitting. due to Inthe the two-step following approach paragraph, is we givedetermined a possible by explanation the shaded forareas this in difference.Figure 3 labe However,lled extra for area a thorough due to second understanding, step. These an areas ab initio analysisrepresent is required, the difference which between is not within the one-step the scope and ofth thise two-step work. splitting. It can be directly observed that the impact of the second step is larger in the case of water splitting. In the following paragraph, Oxidizing the product gases CO and H to CO and H O respectively leads to an entropy decrease, we give a possible explanation for this difference2 2. However,2 for a thorough understanding, an ab mainly because the number of moles in the gas is reduced. However, the extent of this entropy change initio analysis is required, which is not within the scope of this work. differs remarkably between the two splitting processes. In the case of CO splitting, the entropy change Oxidizing the product gases CO and H2 to CO2 and H2O respectively2 leads to an entropy is moredecrease, than 80%mainly larger because than the in number the case of ofmoles water in splitting.the gas is reduced. This only Howeve appliesr, the for extent the temperature of this rangeentropy at which change water differs is gaseous remarkably (being between the relevant the two splitting temperature processes. range In inthe this case context). of CO2 splitting, A possible explanationthe entropy for this change discrepancy is more than is that 80% the larger CO 2thanmolecule in the case is linear, of water while splitting. the H 2ThisO molecule only applies is nonlinear. for Therefore,the temperature CO2 has tworange rotational at which andwater four is gaseous vibrational (being degrees the releva ofnt freedom, temperature while range H2O in has this three rotationalcontext). and A threepossible vibrational explanation degrees for this ofdiscrepancy freedom. is Asthat the the energyCO2 molecule spacing is linear, between while the the rotational H2O energymolecule states isis closernonlinear. compared Therefore, to vibrational CO2 has two energy rotational states, and molecules four vibrational with more degrees rotational of freedom, freedom while H2O has three rotational and three vibrational degrees of freedom. As the energy spacing have more possibilities to distribute energy resulting in larger entropy [17]. Nevertheless, CO has between the rotational energy states is closer compared to vibrational energy states, molecules with2 highermore absolute rotational entropy freedom than have H2 moreO, because possibilities it is a to larger, distribute heavier energy molecule. resulting Butin larger relative entropy to its [17]. weight, waterNevertheless, has high entropy CO2 has whichhigher absolute leads to entropy the low than entropy H2O, because decrease it is whena larger, recombining heavier molecule. H2 withBut O2. As a straightforwardrelative to its weight, consequence water has to high the above,entropy the which reduction leads to of the water low to entropy hydrogen decrease leads when to alarge entropyrecombining decrease H compared2 with O2. toAsreducing a straightforward CO2 to CO.consequence to the above, the reduction of water to Resultinghydrogen leads from to this a large difference entropy indecrease entropy compared change, to areducing large temperature CO2 to CO. gap between oxidation and reductionResulting leads from to this an advantagedifference in of entropy the water-splitting change, a large process temperature in terms gap between of potential oxidation to lower the reductionand reduction temperature. leads to an Anadvantage example of ofthe such water-splitting a case is displayedprocess in terms in Figure of potential4. Here, to thelower oxidation the temperaturereduction is temperature. set to 800 K andAn example all other of conditions such a case are is thedisplayed same as in in Figure Figure 4.3 .Here, the oxidation temperature is set to 800 K and all other conditions are the same as in Figure 3.

Figure 4. T-S diagram for splitting of one mole of water/CO2. Oxidation temperature is set to 800 K, Figure 4. T-S diagram for splitting of one mole of water/CO . Oxidation temperature is set to 800 K, all pressures are 1 bar. 2 all pressures are 1 bar. 5 Entropy 2016, 18, 24 6 of 12 Entropy 2016, 18, 24

Entropy 2016, 18, 24

Figure 5. Reduction temperatures corresponding to oxidation temperature with all gases at 1 bar. At Figure 5. Reduction temperatures corresponding to oxidation temperature with all gases at 1 bar. oxidation temperatures below 1100 K, water splitting can be performed at lower reduction At oxidation temperatures below 1100 K, water splitting can be performed at lower reduction temperatures than CO2 splitting. temperatures than CO2 splitting. Figure 5. Reduction temperatures corresponding to oxidation temperature with all gases at 1 bar. At Concludingoxidation fromtemperatures the above, below it is1100 instructive K, water tosplitting show canthe beresulting performed reduction at lower temperature reduction when Concluding from the above, it is instructive to show the resulting reduction temperature when changingtemperatures the oxidation than COtemperature.2 splitting. This dependency is displayed in Figure 5. At an oxidation changingtemperature the of oxidation about 1100 temperature. K, the two This processes dependency have the is displayedsame reduction in Figure temperature.5. At an oxidationAt higher temperatureConcluding of about from 1100 the K, above, the twoit is instructive processes to have show the the same resulting reduction reduction temperature. temperature when At higher oxidation temperatures, CO2 splitting leads to lower reduction temperatures, while water splitting is changing the oxidation temperature. This dependency is displayed in Figure 5. At an oxidation oxidationadvantageous temperatures, at lower oxidation CO2 splitting temperatures. leads to lower reduction temperatures, while water splitting is temperature of about 1100 K, the two processes have the same reduction temperature. At higher advantageousThe impact at lowerof this oxidation trend on temperatures.the efficiency is displayed in Figure 6. It shows the ideal process oxidation temperatures, CO2 splitting leads to lower reduction temperatures, while water splitting is The impact of this trend on the efficiency is displayed in Figure6. It shows the ideal process efficiencyadvantageous ηsc as well at lower as the oxidation total efficiency temperatures. ηtot which includes solar absorption losses. Regarding the efficiency η as well as the total efficiency η which includes solar absorption losses. Regarding the process efficiencyThesc impact ηsc of, the this CO trend2-splitting on the efficiencyprocesstot is is advantageous displayed in Figure in the 6. complete It shows therange ideal subject process to this process efficiency η , the CO -splitting process is advantageous in the complete range subject to this analysis.efficiency This ηissc canas scwell be explainedas the2 total byefficiency the fact ηtot that which the includes extra area solar due absorption to the second losses. Regardingstep (as shown the in analysis. This is can be explained by the fact that the extra area due to the second step (as shown in Figureprocess 3) is smaller efficiency in η thesc, the case CO of2-splitting CO2 splitting. process This is advantageous area itself has in the a poor complete efficiency, range subject because to thisheat at a Figurehigh analysis.temperature3) is smaller This is level incan the be is caseexplained dumped. of CO by Thus,2 thesplitting. fact the that proc Thistheess extra area with area itself the due hassmaller to athe poor second extra efficiency, steparea (as has shown because the inhigher heat at a highFigure temperature 3) is smaller levelin the iscase dumped. of CO2 splitting. Thus, the This process area itself with has the a poor smaller efficiency, extra because area has heat the at higher a efficiency ηsc. This trend is reversed when taking the solar absorption efficiency into account. A large high temperature level is dumped. Thus, the process with the smaller extra area has the higher efficiencyextra areaη scwhich. This trendconsiderably is reversed reduces when takingthe upper the solar process absorption temperature efficiency is intorewarded account. by A largegood efficiency ηsc. This trend is reversed when taking the solar absorption efficiency into account. A large extraabsorption area which efficiencies. considerably Thus, at reduces low oxidation the upper temper processatures temperature which typically is rewarded lead byto large good extra absorption areas, efficiencies.extra area Thus, which at low considerably oxidation temperaturesreduces the upper which process typically temperature lead to large is rewarded extra areas, by thegood overall the overallabsorption efficiency efficiencies. ηtot of Thus, water at lowsplitting oxidation is higher temper comparedatures which to typicallyCO2 splitting. lead to large extra areas, efficiency ηtot of water splitting is higher compared to CO2 splitting. the overall efficiency ηtot of water splitting is higher compared to CO2 splitting.

Figure 6. Comparison of efficiencies of water splitting and CO2 splitting. Total efficiency is strongly FigureFigure 6.6. ComparisonComparison ofof efficienciesefficiencies ofof waterwater splittingsplitting andand COCO2 splitting. Total efficiencyefficiency isis stronglystrongly dependent on reduction temperature. 2 dependentdependent onon reductionreduction temperature.temperature. 2.4. Two Step Splitting at Reduced Pressure, Gas Phase Only 2.4.2.4. Two StepStep SplittingSplitting atat ReducedReduced Pressure,Pressure, GasGas PhasePhase OnlyOnly Up to now, the pressure of all gases was kept at 1 bar in order to introduce the concepts and UpUpshow toto general now,now, the thedependencies. pressure pressure of of allHowever, all gases gases was real was keptapplicat kept at 1ionsat bar 1 work inbar order in with order to reduced introduce to introduce oxygen the conceptspressure the concepts in and the show and generalshowreduction general dependencies. dependencies.step. This However, is accomplished However, real applications by real either applicat sw workeepingions with withwork reduced inert with gas oxygenreduced reducing pressure oxygen the oxygen inpressure the partial reduction in the reduction step. This is accomplished by either sweeping with inert gas reducing the oxygen partial

6 6 Entropy 2016, 18, 24 7 of 12 step. This is accomplished by either sweeping with inert gas reducing the oxygen partial pressure or by reducing the total pressure with vacuum pumps. Thermodynamically, these two options are Entropy 2016, 18, 24 equivalent, so they will not be treated separately in the following. Entropy 2016, 18, 24 Typically,pressure or the by oxygenreducing pressure the total duringpressure reduction with vacuum is reduced pumps. to Thermo aboutdynamically, 10´4–10´5 barthese in two order to options are equivalent, so they will not be treated separately in the following. furtherpressure lower or the by reduction reducing temperature.the total pressure The Twi-Sthdiagram vacuum representationspumps. Thermodynamically, of the two cycles these withtwo low Typically, the oxygen pressure during reduction is reduced to about 10−4–10−5 bar in order to oxygenoptions pressure are equivalent, during reduction so they will are not shown be treated in Figure separately7. In in the the figure, following. the entropy of the products further lower the reduction temperature.´4 The T-S diagram representations of the two cycles with low with oxygenTypically, pressure the of oxygen 1 bar andpressure 10 duringbar is labelledreduction to is show reduced the benefitto about of 10 lowering−4–10−5 bar the in pressure:order to the oxygen pressure during reduction are shown in Figure 7. In the figure, the entropy of the products oxygenfurther entropy lower is the increased reduction and temperature. thus the enclosedThe T-S diagram area of representations the cycle increases, of the two too. cycles This with results low in the with oxygen pressure of 1 bar and 10−4 bar is labelled to show the benefit of lowering the pressure: possibilityoxygen to pressure considerably during decreasereduction theare reductionshown in Figure temperature. 7. In the figure, In the casethe entropy of Figure of the7, the products reduction the oxygen entropy is increased and thus the enclosed area of the cycle increases, too. This results in with oxygen pressure of 1 bar and 10−4 bar is labelled to show the benefit of lowering the pressure: can takethe placepossibility below to 2000considerably K, while decrease at ambient the pressurereduction thetemperature. reduction In temperature the case of wouldFigure need7, the to be the oxygen entropy is increased and thus the enclosed area of the cycle increases, too. This results in well abovereduction 2400 can K. take place below 2000 K, while at ambient pressure the reduction temperature would the possibility to considerably decrease the reduction temperature. In the case of Figure 7, the Theneed effect to be well of this above temperature 2400 K. reduction on the efficiency is shown in Figure8, exemplarily for reduction can take place below 2000 K, while at ambient pressure the reduction temperature would T =The 1000 effect K. of The this process temperature efficiency reductionη is on hardly the efficiency affected is by shown reducing in Figure the pressure,8, exemplarily because for the oxidationneed to be well above 2400 K. sc Toxidation = 1000 K. The process efficiency ηsc is hardly affected by reducing the pressure, because the dominatingThe effecteffect limitingof this temperature the efficiency reduction is the on heat the efficiency dump at is oxidation shown in Figure temperature. 8, exemplarily Only for a slight dominating effect limiting the efficiency is the heat dump at oxidation temperature. Only a slight decreaseToxidation can = be1000 observed K. The process when efficiency lowering η thesc is hardly pressure, affected because by reducing the heat the input pressure, takes because place atthe lower decrease can be observed when lowering the pressure, because the heat input takes place at lower temperatures.dominating In effect strong limiting contrast the to efficiency that, reducing is the heat the pressuredump at bringsoxidation quite temperature. a large benefit Only whena slight taking temperatures. In strong contrast to that, reducing the pressure brings quite a large benefit when into accountdecrease thecan solarbe observed absorption when efficiency. lowering the From pressu 1 barre, tobecause 10´5 bar,the heat the totalinput efficiencytakes place can at lower almost be taking into account the solar absorption efficiency. From 1 bar to 10−5 bar, the total efficiency can doubled,temperatures. because theIn strong reduction contrast temperature to that, reducing is decreased the pressure by about brings 600 quite K. a large benefit when almost be doubled, because the reduction temperature is decreased by about 600 K. taking into account the solar absorption efficiency. From 1 bar to 10−5 bar, the total efficiency can almost be doubled, because the reduction temperature is decreased by about 600 K.

Figure 7. T-S diagram of splitting one mole of H2O/CO2 with reduced pressure. Oxidation Figuretemperature 7. T-S diagram is set ofto splitting1000 K. Entropy one mole lin ofes H of2O/CO oxygen2 with release reduced at 1 bar pressure. and 10−4 Oxidation bar are shown temperature to Figure 7. T-S diagram of splitting one mole of H2O/CO2 ´with4 reduced pressure. Oxidation is setvisualize to 1000 K.the Entropy effect of linesreduced of oxygenpressure. release at 1 bar and 10 bar are shown to visualize the effect temperature is set to 1000 K. Entropy lines of oxygen release at 1 bar and 10−4 bar are shown to of reduced pressure. visualize the effect of reduced pressure.

Figure 8. Influence of reducing the pressure on the reduction temperature and the efficiency; Tox = 1000 K. Figure 8. Influence of reducing the pressure on the reduction temperature and the efficiency; Figure 8. Influence of reducing the pressure on the reduction temperature and the efficiency; Tox = 1000 K. Tox =However, 1000 K. when interpreting this increase of the total efficiency, one should consider that applying a vacuum as well as flushing with inert gas bring along large irreversibilities reducing the However, when interpreting this increase of the total efficiency, one should consider that efficiency [8,18,19]. Therefore, the pressure reduction should mainly be considered as a technical However,applying a vacuum when interpretingas well as flushing this with increase inert ofgas thebring total along efficiency, large irreversibilities one should reducing consider the that advantage rather than an efficiency boost. applyingefficiency a vacuum [8,18,19]. as Therefore, well as flushing the pressure with reduction inert gas should bring mainly along be large considered irreversibilities as a technical reducing advantage rather than an efficiency boost. 7 7 Entropy 2016, 18, 24 8 of 12

theEntropy efficiency 2016, 18, [248 ,18,19]. Therefore, the pressure reduction should mainly be considered as a technical advantage rather than an efficiency boost. 2.5. Two Step Splitting at Reduced Pressure, Gas and Solid Phase 2.5. Two Step Splitting at Reduced Pressure, Gas and Solid Phase A possible approach in system design is to define the temperature limits which are technically A possible approach in system design is to define the temperature limits which are technically reasonable and then use a material which can work at these temperatures. A typical material reasonable and then use a material which can work at these temperatures. A typical material candidate candidate for such an approach is ceria. It can be reduced from CeO2 to CeO2-δ with values of δ for such an approach is ceria. It can be reduced from CeO to CeO with values of δ reaching from reaching from 0 to 0.5. In the relevant temperature range, 2ceria does2´ notδ undergo a phase change, but 0 to 0.5. In the relevant temperature range, ceria does not undergo a phase change, but δ increases δ increases steadily with increasing temperature and decreasing oxygen pressure. The entropy steadily with increasing temperature and decreasing oxygen pressure. The entropy change in the change in the material per mole of oxygen released is considerably higher at low values of δ [20]. The material per mole of oxygen released is considerably higher at low values of δ [20]. The explanation for explanation for this effect is the higher configurational disorder caused by the first oxygen atoms this effect is the higher configurational disorder caused by the first oxygen atoms leaving the crystal leaving the crystal structure. The drawback of low values of δ is a high thermal mass which needs to structure. The drawback of low values of δ is a high thermal mass which needs to be cycled between be cycled between oxidation and reduction temperature at low fuel generation rates. Thus, the lower oxidation and reduction temperature at low fuel generation rates. Thus, the lower the δ, the more the δ, the more important becomes solid phase heat recovery [7,21]. important becomes solid phase heat recovery [7,21]. For a complete analysis of a specific redox material, it is important to also consider the For a complete analysis of a specific redox material, it is important to also consider the enthalpy of reaction. Only then, it can be determined if a certain process can be accomplished at selected of reaction. Only then, it can be determined if a certain process can be accomplished at selected temperature levels. But in this analysis we want to point out the entropy requirement and discuss it temperature levels. But in this analysis we want to point out the entropy requirement and discuss it in a vivid way together with the efficiency. The enthalpy of reaction is assumed to be always of the in a vivid way together with the efficiency. The enthalpy of reaction is assumed to be always of the value which is necessary to make the reaction feasible. This idealization should be kept in mind value which is necessary to make the reaction feasible. This idealization should be kept in mind when when dealing with specific materials. Thus, in this paper we show the highest possible efficiency dealing with specific materials. Thus, in this paper we show the highest possible efficiency which which could be reached with materials perfectly matching the process conditions. could be reached with materials perfectly matching the process conditions. Figure 9 shows the T-S diagram with typical process parameters in the range of recent projects Figure9 shows the T-S diagram with typical process parameters in the range of recent projects realizing solar thermochemical cycles [22]. The reduction takes place at 1700 K and a pressure of 10−5 realizing solar thermochemical cycles [22]. The reduction takes place at 1700 K and a pressure of 10´5 bar. The oxidation temperature is set to 1300 K. In order to keep the representation of the T-S bar. The oxidation temperature is set to 1300 K. In order to keep the representation of the T-S diagrams diagrams consistent and generic, we do not include the absolute entropy value of a possible redox consistent and generic, we do not include the absolute entropy value of a possible redox material. material. Instead, we only include the entropy difference during oxidation and reduction. The Instead, we only include the entropy difference during oxidation and reduction. The dashed lines in dashed lines in Figure 9 represent the gas phase entropy only. The required extra entropy change Figure9 represent the gas phase entropy only. The required extra entropy change which needs to be which needs to be undergone by the redox material in order to reach the necessary ΔG is also undergone by the redox material in order to reach the necessary ∆G is also marked in the figure. marked in the figure.

Figure 9. T-S diagram of splitting one mole of H2O/CO2 at defined reaction temperatures. The Figure 9. T-S diagram of splitting one mole of H2O/CO2 at defined reaction temperatures. The entropy entropy change required by the redox material is marked. change required by the redox material is marked.

Analogous to the example in Figure 9, we determined the required entropy change in the redox materialAnalogous for different to the process example conditions, in Figure9 ,see we Figure determined 10. The the oxidation required temperature entropy change is varied in the on redox the materialx-axis, the for reduction different temperature process conditions, is varied see by Figure setting 10 the. The temperature oxidation difference temperature between is varied oxidation on the xand-axis, reduction the reduction to dT = temperature 200 K and dT is = varied 400 K. by The setting results the are temperature shown for a difference reduction betweenpressure oxidationof 0.1 bar and reduction10−5 bar. The to d graphsT = 200 show K and that dT =at 400oxidation K. The temp resultseratures are shown above for 1100 a reduction K, the entropy pressure exigencies of 0.1 bar regarding the redox material are less demanding in the case of CO2.

8 Entropy 2016, 18, 24 9 of 12 and 10´5 bar. The graphs show that at oxidation temperatures above 1100 K, the entropy exigencies regarding the redox material are less demanding in the case of CO2. Entropy 2016, 18, 24 Entropy 2016, 18, 24

Figure 10. Required entropy change in the redox material per mole of H2O/CO 2. Figure 10. Required entropy change in the redox material per mole of H2O/CO2. Figure 10. Required entropy change in the redox material per mole of H2O/CO2. However, at oxidation temperatures below 1100 K, the opposite is the case: water-splitting does However, at oxidation temperatures below 1100 K, the opposite is the case: water-splitting does not requireHowever, such at a oxidation high entropy temperatures change in below the redo 1100x material.K, the opposite This trend is the can case: again water-splitting be explained does by not require such a high entropy change in the redox material. This trend can again be explained thenot extrarequire area such which a high the entropysecond stepchange generates in the redoin thex material.T-S diagram This (see trend Figure can again3). If that be explained area plays by a by the extra area which the second step generates in the T-S diagram (see Figure3). If that area dominantthe extra area role—which which the issecond the case step atgenerates low proces in thes temperatures—theT-S diagram (see Figure water-splitting 3). If that area process plays is a advantageous,playsdominant a dominant role—which because role—which theis theentropy iscase the caseatchange low at low procesin processthe sgas temperatures—the temperatures—thephase during oxidation water-splitting water-splitting is larger. process process Further, is loweradvantageous, reduction becausebecause pressures thethe also entropy entropy lead changeto change a decrease in thein the gasof thegas phase required phase during during redox oxidation materialoxidation is larger. entropy is larger. Further, change. Further, lower reductionlowerThe reduction total pressures efficiency pressures also leadof also the to leadprocess a decrease to a isdecrease shown of the required ofin the Figure required redox 11 formaterial redox the materialsame entropy parameter entropy change. setchange. used in FigureThe 10. total The efficiencyefficiencyeffect of the of oxidation the process temperature is shownshown inon FigureFigure the efficiency 11 forfor thethe has samesame been parameterparameterdiscussed before set used [10]. in ItFigure can be 1010. summarized. The effect of as the follows: oxidation at low temperature oxidation temperatures on the the efficiency efficiency the heathas has been beenloss accompanied discussed discussed before before with [10]. [the10]. oxidationIt cancan bebe summarizedsummarized step is dominating asas follows:follows: the efficiency. at low oxidationoxidation If that temperaturestemperaturesheat loss takes the place heatheat at lossloss higher accompaniedaccompanied temperatures, withwith the the efficiencyoxidation drops. step is However, dominating at theone efficiency.efficiency. point the Ifinfluenc thatthat heatheate of lossloss that takestakes heat placeplaceloss is atat overruled higherhigher temperatures,temperatures, by the positive the effectefficiencyefficiency of rising drops. heat However, input temperatures. at one point Then, the influenceinfluenc the efficiencye of that rises heat again loss wi is th overruledoverruled rising temperatures. by thethe positivepositive effect ofof risingrising heatheat inputinput temperatures.temperatures. Then,Then, thethe efficiencyefficiency risesrises againagain withwith risingrising temperatures.temperatures.

Figure 11. Total theoretical efficiency of solar water splitting at different process conditions. Figure 11. Total theoretical efficiency of solar water splitting at different process conditions. Figure 11. Total theoretical efficiency of solar water splitting at different process conditions. Further, lower reduction pressures are beneficial for the absorption efficiency, as discussed aboveFurther, when considering lower reduction the gas pressures phase only. are Reducing beneficial the for temperature the absorption difference efficiency, to dT as = 200discussed K, the efficiencyaboveFurther, when drops considering lower remarkably. reduction the Thisgas pressures phaseis again areonly. due beneficial Reducingto the large for the theinfluence temperature absorption of the efficiency,difference heat loss asduring to discussed dT =oxidation. 200 aboveK, the whenefficiencyFigure considering drops 12 shows remarkably. the gasan example phase This only. is of again Reducingsuch due a process to the the temperature large with influencelow d differenceT. Theof the strong heat to dT lossinfluence= 200 during K, the of oxidation. efficiencythe large areadrops associatedFigure remarkably. 12 showsto the This secondan is example again step due ofis to clearlysuch the largea visible.process influence Inwith this oflow case, the d heatT the. The lossheat strong duringreleased influence oxidation. during of oxidation the large shouldarea associated be coupled to the to seconda secondary step is process. clearly visible.Energe tically,In this case,the thermochemical the heat released cycle during could oxidation surely alwaysshould bebe extendedcoupled towith a secondarysecondary process.processes Energe usingtically, all waste the heatthermochemical and thus leading cycle to could the Carnot surely efficiencyalways be extendedbetween withthe secondaryreduction processestemperatur usinge and all wasteambient heat temperature.and thus leading Technically to the Carnot and economicallyefficiency between however, the such reduction an approach temperatur is not alwayse and feasible. ambient temperature. Technically and economically however, such an approach is not always feasible. 9 9 Entropy 2016, 18, 24 10 of 12

Figure 12 shows an example of such a process with low dT. The strong influence of the large area associated to the second step is clearly visible. In this case, the heat released during oxidation should be coupled to a secondary process. Energetically, the thermochemical cycle could surely always be extended with secondary processes using all waste heat and thus leading to the Carnot efficiency between the reduction temperature and ambient temperature. Technically and economically however, such an approach is not always feasible. Entropy 2016, 18, 24

Figure 12. T-S diagram of splitting one mole of H2O/CO2 at an oxidation temperature of 1300 K and a Figure 12. T-S diagram of splitting one mole of H2O/CO2 at an oxidation temperature of 1300 K and reduction temperature of 1500 K. a reduction temperature of 1500 K.

3. Conclusions 3. Conclusions We have conducted a comprehensive study on the efficiency of solar thermochemical splitting We have conducted a comprehensive study on the efficiency of solar thermochemical splitting cycles. The study is based on an approach using mainly T-S diagrams, hence emphasizing graphical cycles. The study is based on an approach using mainly T-S diagrams, hence emphasizing explanations rather than the underlying equations. A previous study analyzing the purely graphical explanations rather than the underlying equations. A previous study analyzing the purely thermochemical process efficiency of water splitting was extended. On the one hand, CO2-splitting thermochemical process efficiency of water splitting was extended. On the one hand, CO -splitting cycles were analyzed and compared to the previous results. On the other hand, the solar absorption2 cycles were analyzed and compared to the previous results. On the other hand, the solar absorption efficiency was included in the overall efficiency calculation. efficiency was included in the overall efficiency calculation. CO2 splitting is in many cases advantageous compared to water splitting regarding the CO splitting is in many cases advantageous compared to water splitting regarding the efficiency. efficiency.2 This is due to the higher entropy change which occurs when recombining CO with This is due to the higher entropy change which occurs when recombining CO with oxygen compared to oxygen compared to H2. However, when splitting CO2, the low entropy change in the gas phase H . However, when splitting CO , the low entropy change in the gas phase during the oxidation step during2 the oxidation step can lead2 to higher demands regarding the redox material. The entropy can lead to higher demands regarding the redox material. The entropy difference in the solid between difference in the solid between the oxidized and the reduced state needs to be higher in some cases, the oxidized and the reduced state needs to be higher in some cases, especially when operating at especially when operating at low temperatures. low temperatures. The study has theoretical thermodynamic character only and should therefore only help The study has theoretical thermodynamic character only and should therefore only help understanding the general principles of the analyzed cycles. Real applications have to cope with understanding the general principles of the analyzed cycles. Real applications have to cope with many many other factors like heat recovery from solids, efficiency cutbacks due to means to create an other factors like heat recovery from solids, efficiency cutbacks due to means to create an oxygen oxygen deficient atmosphere and many more. This should be kept in mind when interpreting the deficient atmosphere and many more. This should be kept in mind when interpreting the efficiency efficiency values. Furthermore, the redox material entropy values shown here are only valid in values. Furthermore, the redox material entropy values shown here are only valid in combination combination with certain of reaction. Therefore, no specific material analysis was with certain enthalpies of reaction. Therefore, no specific material analysis was conducted here. conducted here. Also especially at low temperatures, slow kinetics may impede the process to Also especially at low temperatures, slow kinetics may impede the process to practical infeasibility. practical infeasibility. Thus, this study does not intend to present real process efficiencies, but rather Thus, this study does not intend to present real process efficiencies, but rather to provide the relevant to provide the relevant thermodynamic background every process developer should have when thermodynamic background every process developer should have when trying to bring theory trying to bring theory into practice. into practice. Acknowledgments: The research leading to these results has received funding from the European Union's Acknowledgments:Seventh Framework TheProgramme research (FP7/2007-2013) leading to these for results the Fuel has Cells received and Hydrogen funding from Joint the Technology European Initiative Union’s Seventhunder grant Framework agreement Programme n° 325361 (FP7/2007-2013)and from the Initiative for the and Fuel Networking Cells andHydrogen Fund of the Joint Helmholtz Technology Association Initiative of German Research Centers (Grant Identifier VH-VI-509).

Author Contributions: Robert Pitz-Paal initiated the paper and did general consulting. Martin Roeb and Christian Sattler helped improving the manuscript and interpreting the results. Matthias Lange wrote the paper and conducted the numerical analysis. All authors have read and approved the final manuscript.

Conflicts of Interest: The authors declare no conflict of interest.

References

1. Kodama, T.; Gokon, N. Thermochemical Cycles for High-Temperature Solar . Chem. Rev. 2007, 107, 4048–4077.

10 Entropy 2016, 18, 24 11 of 12 under grant agreement n˝ 325361 and from the Initiative and Networking Fund of the Helmholtz Association of German Research Centers (Grant Identifier VH-VI-509). Author Contributions: Robert Pitz-Paal initiated the paper and did general consulting. Martin Roeb and Christian Sattler helped improving the manuscript and interpreting the results. Matthias Lange wrote the paper and conducted the numerical analysis. All authors have read and approved the final manuscript. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Kodama, T.; Gokon, N. Thermochemical Cycles for High-Temperature Solar Hydrogen Production. Chem. Rev. 2007, 107, 4048–4077. [CrossRef][PubMed] 2. Rosen, M.A. Advances in hydrogen production by thermochemical water decomposition: A review. Energy 2010, 35, 1068–1076. [CrossRef] 3. Bamberger, C.E. Hydrogen production from water by thermochemical cycles; a 1977 update. Cryogenics 1978, 18, 170–183. [CrossRef] 4. Abraham, B.; Schreiner, F. General Principles Underlying Chemical cycles which Thermally decompose Water Into the Elements. Ind. Eng. Chem. Fundam. 1974, 13, 305–310. [CrossRef] 5. Nakamura, T. Hydrogen production from water utilizing solar heat at high temperatures. Sol. Energy 1977, 19, 467–475. [CrossRef] 6. Diver, R.B.; Miller, J.E.; Allendorf, M.D.; Siegel, N.P.; Hogan, R.E. Solar thermochemical water-splitting ferrite-cycle heat engines. J. Sol. Energy Eng. 2008, 130, 041001. [CrossRef] 7. Lapp, J.; Davidson, J.; Lipi´nski,W. Efficiency of two-step solar thermochemical non-stoichiometric redox cycles with heat recovery. Energy 2012, 37, 591–600. [CrossRef] 8. Bader, R.; Venstrom, L.J.; Davidson, J.H.; Lipi´nski,W. Thermodynamic Analysis of Isothermal Redox Cycling of Ceria for Production. Energy Fuels 2013, 27, 5533–5544. [CrossRef] 9. Muhich, C.L.; Ehrhart, B.D.; Al-Shankiti, I.; Ward, B.J.; Musgrave, C.B.; Weimer, A.W. A review and perspective of efficient hydrogen generation via solar thermal water splitting. Wiley Interdiscip. Rev. Energy Environ. 2015.[CrossRef] 10. Lange, M.; Roeb, M.; Sattler, C.; Pitz-Paal, R. T–S diagram efficiency analysis of two-step thermochemical cycles for solar water splitting under various process conditions. Energy 2014, 67, 298–308. [CrossRef] 11. Bale, C.W.; Chartrand, P.; Degterov, S.A.; Eriksson, G.; Hack, K.; Mahfoud, R.B.; Melançon, J.; Pelton, A.D.; Petersen, S. FactSage thermochemical software and databases. Calphad 2002, 26, 189–228. [CrossRef] 12. Bale, C.W.; Bélisle, E.; Chartrand, P.; Decterov, S.A.; Eriksson, G.; Hack, K.; Jung, I.H.; Kang, Y.B.; Melançon, J.; Pelton, A.D.; et al. FactSage thermochemical software and databases—Recent developments. Tools Comput. Thermodyn. 2009, 33, 295–311. [CrossRef] 13. Fletcher, E.A.; Moen, R.L. Hydrogen and Oxygen from Water—The use of solar energy in a one-step effusional process is considered. Science 1977, 197, 1050–1056. [CrossRef][PubMed] 14. Steinfeld, A. Solar thermochemical production of hydrogen—A review. Sol. Energy 2005, 78, 603–615. [CrossRef] 15. Abanades, S.; Charvin, P.; Flamant, G.; Neveu, P. Screening of water-splitting thermochemical cycles potentially attractive for hydrogen production by concentrated solar energy. Energy 2006, 31, 2805–2822. [CrossRef] 16. Roeb, M.; Neises, M.; Monnerie, N.; Call, F.; Simon, H.; Sattler, C.; Schmücker, M.; Pitz-Paal, R. Materials-Related Aspects of Thermochemical Water and Carbon Dioxide Splitting: A Review. Materials 2012, 5, 2015–2054. [CrossRef] 17. Chabay, R.W. Matter and Interactions, 3rd ed.; Cram101 Incorporated: Moorpark, CA, USA, 2013.

18. Bulfin, B.; Call, F.; Lange, M.; Lübben, O.; Sattler, C.; Pitz-Paal, R.; Shvets, I.V. Thermodynamics of CeO2 Thermochemical Fuel Production. Energy Fuels 2015, 29, 1001–1009. [CrossRef] 19. Siegel, N.P.; Miller, J.E.; Ermanoski, I.; Diver, R.B.; Stechel, E.B. Factors Affecting the Efficiency of Solar Driven Metal Oxide Thermochemical Cycles. Ind. Eng. Chem. Res. 2013, 52, 3276–3286. [CrossRef] 20. Panlener, R.J.; Blumenthal, R.N.; Garnier, J.E. A thermodynamic study of nonstoichiometric cerium dioxide. J. Phys. Chem. Solids 1975, 36, 1213–1222. [CrossRef] Entropy 2016, 18, 24 12 of 12

21. Felinks, J.; Brendelberger, S.; Roeb, M.; Sattler, C.; Pitz-Paal, R. Heat recovery concept for thermochemical processes using a solid heat transfer medium. Appl. Therm. Eng. 2014, 73, 1004–1011. [CrossRef]

22. Furler, P.; Scheffe, J.; Gorbar, M.; Moes, L.; Vogt, U.; Steinfeld, A. Solar Thermochemical CO2 Splitting Utilizing a Reticulated Porous Ceria Redox System. Energy Fuels 2012, 26, 7051–7059. [CrossRef]

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