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

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Entropy Analysis of Solar Two-Step Thermochemical Cycles for Water and Carbon Dioxide Splitting entropy Technical Note Entropy Analysis of Solar Two-Step Thermochemical Cycles for Water 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 fuels in a sustainable way. We extend a previous study on the thermodynamics of water splitting 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 redox 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 fuel 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 hydrogen 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 work 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 oxygen 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 Gibbs free energy 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 heat. input assuming ideal heat recovery.The splitting-cycle This heat efficiency recovery hissc 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 DGf,H2O. In the case of CO2 splitting, the benefit is (DGf,CO2 ´ DGf,CO). This leads to the general form: the general form: DGf hsc “ .Δ (4) =Q (4) NET The efficiency efficiency of of direct direct CO CO22 splittingsplitting (η (hscsc = =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.
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