Thermodynamic Analyses of Fuel Production via Solar-driven Non

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Thermodynamic Analyses of Fuel Production via Solar-driven Nonstoichiometric Metal Oxide Redox Cycling—Part II: Impact of Solid–Gas Flow Configurations and Active Material Composi-tion on System Level Efficiency Sha Li, VIncent Wheeler, Peter B. Kreider, Roman Bader, and Wojciech Lipi#ski Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b02082 • Publication Date (Web): 03 Sep 2018 Downloaded from http://pubs.acs.org on September 4, 2018

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Thermodynamic Analyse Analyses of Fuel Production via SolarSolar-driven NonNonstoichiometric stoichiometric Metal Oxide Redox Cycling— Cycling—Part II: Impact of Solid– Solid–Gas Flow Configurations and Active Material Composition on System Level Efficiency Sha Li, Vincent M. Wheeler, Peter B. Kreider, Roman Bader, and Wojciech Lipiński* Research School of Engineering, The Australian National University, Canberra, ACT 2601, Australia KEYWORDS: Solar fuels, ceria, thermodynamics, efficiency, optimization ABSTRACT: We present an advanced thermodynamic model for a water splitting solar reactor system employing Zr-doped ceria as the redox material and inert sweep gas to obtain the desired oxygen partial pressures in the reduction chamber. Conservation of mass and species, conservation of energy, and the Gibbs criteria are employed to predict solar-to-fuel efficiencies. Efficiencies vary widely with operating conditions—reactor temperatures and pressures—in addition to material thermodynamic properties making it difficult to compare the performance of proposed redox materials. We determine the maximum efficiencies theoretically achievable with selected redox materials by simultaneous multivariable optimization of all operational parameters within their meaningful ranges. For the baseline case of zero solid heat recovery and 75% gas heat recovery, the results demonstrate that a modest efficiency improvement can be achieved by doping ceria with 10% and 15% Zr as compared to pure ceria within a narrow reduction temperature range of 1700–1850 K. However, this efficiency benefit is achieved at the cost of low oxidation temperature operation, which may lower the realistic maximum efficiencies if the oxidation step is kinetically limited. Four different reactor flow configurations are considered, including a newly developed model for counter-current flow. It is found that a maximum solar-to-fuel efficiency of 7.8% for water splitting can be attained with state-of-the-art reactors operated at 1773 K, 95% gas heat recovery and no solid heat recovery, based on our model assumptions. In terms of potential efficiency enhancement, peak efficiencies of 26.4% and 25.2% can be achieved for inert gas sweeping and vacuum pumping, respectively, at reduction temperature of 1900K, 95% gas heat recovery and 90% solid heat recovery. The model results provide insights that help guide reactor design and operation as well as potential redox material selection.

1. INTRODUCTION

and an exothermic, typically off-sun steam-oxidation step,

Solar hydrogen production processes include thermo-, electro-, photochemical and hybrid pathways.1, 2 The solar thermochemical pathway holds promise due to its relatively high theoretical solar-to-fuel efficiency, utilization of the entire solar spectrum and inherent separation of the primary products (here H2 and O2).2-4 Two-step, nonstoichiometric, metal-oxide-based reduction/oxidation (redox) cycles have shown high theoretical efficiencies in solar thermochemical fuel production.4-6 Ceria has received the most attention as a redox material because of its fast oxidation kinetics, high selectivity, and good cycle stability.7-10 Other materials, such as perovskites,11-14 ferrites,15, 16 and doped ceria,17-19 offer lower reduction temperatures and increased fuel yield per mole of oxide per cycle as compared to pure ceria, making them strong candidates for high efficiency thermochemical cycling performance.1923 The two-step non-stoichiometric redox cycle for solar thermochemical water splitting consists of an endothermic, on-sun, reduction step,

1 1 M x O y − δ red + H 2 O → M x O y − δ ox + H 2 , ∆δ ∆δ

1 1 1 M x O y − δ ox → M x O y − δ red + O 2 , ∆δ ∆δ 2

(1)

(2)

where M x O y −δ red and M x O y −δ ox represent the reduced and oxidized metal oxides and ∆δ = δ red − δ ox is the difference in non-stoichiometry between the reduced and oxidized states. Generally, the reduction step requires high temperature and low oxygen partial pressure. To achieve the required low oxygen partial pressure, two common methods are employed: vacuum pumping or inert gas sweeping. Inert gas sweeping has been studied extensively in both experimental7, 10, 24, 25 and theoretical26-30 efforts, while vacuum pumping has also been employed to a much lesser extent31, 32. A number of comparative theoretical analyses27, 33-35 have drawn different conclusions regarding the better option for maintaining low oxygen partial pressure for the reduction step. A comprehensive performance metric considering both fuel output and total energy consumption should be adopted to fairly compare the solar thermochemical path-

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way to other technologies. Thus, we use the solar-to-fuel efficiency24, 36

η= & Q

n&H2 HHVH2 + Q&

solar,h

.

solar,pw

Here, HHVH 2 , n&H 2 , Q&solar,h and Q& solar,pw are the higher heating value of hydrogen, the molar flow rate of hydrogen, the solar energy input rate for all heating requirements, and the solar energy input rate for driving the necessary penalty work operations such as gas separation, respectively. Both Siegel et al.37 and Miller et al.38 suggested a commercialization threshold value of 35% for this efficiency. Numerous experimental and modelling studies have been undertaken to assess the solar-to-fuel efficiency of a reactor system undergoing two-step redox cycling with a selected material.24, 26, 28, 39 A small number of studies consider both thermodynamic and kinetic effects on reactor efficiency, while most focus more specifically on thermodynamic considerations, assuming fast kinetics due to lack of kinetic data or known material behavior.15, 40-42 A remarkable variation has been reported for predictions of the solar-to-fuel efficiency even when using the same materials, differing by four orders of magnitude from 0.04% to 40%.30, 41, 42 A number of thermodynamic modelling choices can explain such enormous deviations.15, 24, 30 (i) Solid–gas phase flow configurations. A reactor system implementing different solid–gas flow configurations requires differing amounts of sweep gas and oxidizer to aim for the same fuel output per mole of metal oxide. Four flow configurations have appeared in the literature: fixed-bed flow (FF)24, 36, 43, 44, counter-current flow (CF)15, 26, 30, mixed flow (MF)28, 33, and parallel flow (PF)30, 36. A reactor system operated under CF is widely recognized to offer the upper limit of the solarto-fuel efficiency.15, 30, 33, 34, 36 However, the solar-tofuel efficiencies for CF flow mode calculated by most prior work are unrealistically high due to an unsound assumption on thermodynamic equilibrium conditions, which leads to drastically underestimated predictions of sweep gas and oxidizer flow rate requirements.26, 30 An improved CF model has been developed in a parallel work45 and is incorporated into this work to offer a more accurate prediction on those flow rates and corresponding efficiencies. (ii) Treatment of exothermic reaction and solid sensible heat. Whether and how to use the heat transfer due to the exothermic oxidation step and the sensible heat from the metal oxide when cooled from reduction temperature to oxidation temperature has been disagreed upon in the literature, leading to differences in efficiency prediction.26, 28, 30, 35 (iii) Treatment of penalty work. Penalty work includes both the separation work for producing the sweep gas (or the pumping work for maintaining a vacuum environment) and purified product and the pumping work for transporting reactant gases. Some efforts totally ignore penalty work in solar-to-fuel efficiency predictions.17, 28 The studies that consider the penalty work

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differ in how they quantify the separation work for sweep gas production.15, 24, 26, 30, 35 (iv) Reactor operating conditions. The differences in temperature, oxygen partial pressures, (3) non-stoichiometric states of reactive materials, and gas and solid heat recovery conditions selected for modelling choices are another contributor to efficiency variation. The emergence of promising new materials along with their thermodynamic and kinetic data motivates the undertaking of thermodynamic analysis to understand their performance at a system level.11, 15, 19, 41, 46, 47 Numerous thermodynamic studies have compared the solar-to-fuel efficiencies of different materials under the same reduced or oxidized non-stoichiometric state.14, 17, 18, 41 For example, Takacs et al. predicted the efficiencies of 5 mol% Zr+4 doped ceria and pure ceria, assuming complete reoxidation with steam ( δ ox =0) for both materials.18 The same assumption was also employed by Ganzoury et al. when comparing the efficiencies among Ce-Zr mixtures.41 Scheffe and Steinfeld performed a thermodynamic analysis for ceria-based oxides with a number of different dopants (CaO, Y2O3, Gd2O3, and others) by keeping the reduced nonstoichiometric state constant ( δ red =0.1) for all selected materials.17 While these efforts are useful in offering a method for material comparison, the use of the same nonstoichiometric state for all materials will not necessarily demonstrate the highest possible efficiency for a given material. Thermodynamic properties differ from material to material as functions of non-stoichiometric state. A trade-off seems to exist between the ability to reduce and oxidize a material.19, 42 Allowing both non-stoichiometric states to vary freely for different materials is expected to yield a meaningful comparison of material performance. Reactor operational conditions must be allowed to change freely within their meaningful ranges in order to achieve optimal process conditions for a particular material.6 Expanding upon our prior effort,45 here we detail a comparative thermodynamic analysis of solar hydrogen production via two-step non-stoichiometric redox cycles with reduction reactions proceeding under inert sweep gas atmospheres. The selected model materials are zirconiadoped ceria with the dopant molar concentration of 0, 5, 10, 15 and 20% (denoted hereafter as ceria, Zr05, Zr10, Zr15 and Zr20). We aim to identify and compare the maximum efficiencies of these materials. This is achieved by simultaneous multivariable optimization of operating parameters using efficiency as the objective function. Four ideal plug flow configurations are considered representing all permutations of CF and PF in the reduction and oxidation chambers. They are denoted by CF–CF, CF–PF, PF–CF and PF–PF, with the first term representing the flow configuration in the reduction chamber and the second term representing that in the oxidation chamber. The notable outcomes of this study are: (i) identification of the peak efficiency of each material along with their corresponding optimal operating conditions for each flow configuration; (ii) exploration of the effect of free parameters on solar-tofuel efficiency; (iii) insight on future reactor design and new material development.

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2. PROCESS DESCRIPTION a)

b)

Figure 1. Schematic of the model reactor system for hydrogen production. Mass flow is indicated by thin arrows and energy flow by thick, grey arrows. An energy flow line pointing to or from a mass flow line indicates a heat addition or removal step, respectively: (a) a general schematic of the solar-driven, two-step non-stoichiometric metal-oxide based redox cycling for water splitting, (b) a detailed mass and energy flow for the reactor system.

A schematic of the reactor system under study for water splitting is shown in Figure 1; Figure 1(a) illustrates the general concept of the two-step non-stoichiometric metal oxide redox cycling while Figure 1(b) offers a detailed mass and energy flow diagram for the reactor system. The reactor system consists of a reduction chamber, an oxidation chamber, two gas–gas heat exchangers (HXg,red and HXg,ox), a solid–solid heat exchanger (HXs), and a gas separator (GS) to produce sweep gas from ambient air. Thermodynamic states are numbered 1–19. The thermodynamic processes that cause the changes to a state will be described in the following and indicated by the notation (initial state → Linal state). The solar power input Q& solar pro-

Purified nitrogen with low oxygen impurity ( 0 , additional solar input is

oxygen at the inlet and outlet of the sweep gas stream, and the molar flow rate of reactive material, respectively. The Dalton model is used to link the molar flow rates of gaseous phases and their partial pressures based on the assumption of ideal gas and an isobaric reduction system:

2

required in the oxidation chamber ( Q&solar,h,ox ). If the solar input is not required, the remaining power ( Q& recover,ox ) is used to preheat the sweep gas on the reduction side before the HXg,red (2→3); See eqs (32) and (33). Thermodynamic Model. The thermodynamic model is developed based on the following assumptions following the work of Bader et al.26: (i) the reactor system is operated under atmospheric pressure, i.e. psys=1 atm; (ii) quasisteady state is assumed; (iii) reaction kinetics and mass transport processes are so fast that the equilibrium state between gaseous and solid phases is only limited by thermodynamics; (iv) reduction and oxidation steps are assumed to proceed simultaneously in each reaction chamber for continuous hydrogen production; (v) the reduction chamber is treated as a blackbody cavity; (vi) the oxidation chamber is assumed to be a perfect oxygen exchange material in which the oxygen released from the water thermolysis reaction is totally absorbed by the metal oxide, thus creating a constant oxygen partial pressure along the flow path. Further discussion of this assumption can be found in our parallel work45; (vii) both gaseous and solid phases enter and exit the chambers at the corresponding reaction temperatures, i.e. T5=T6=T8=T9=Tred and T10=T11=T16=T17 =Tox; (viii) heat losses from the heat exchangers and piping are negligible; (ix) all gases are treated as ideal gases; (x) the heat recovery effectiveness of the gas heat exchangers are identical (εg,red=εg,ox=εg); (xi) the work to cycle the reactive material between reaction chambers and to pump the gases is not accounted for since they are strongly dependent upon the particular reactor design; (xii) the model materials are assumed to be 100% chemically reactive.

n&O2 ,red, j n&N2

=

pO2 ,red,j

( j = in,out),

psys − pO2 ,red,j

(7)

where pO 2 ,red,j is the oxygen partial pressure at the inlet or outlet of the reduction chamber. An energy balance for the reduction subsystem takes the form:

Q& solar,h,red − Q& rerad − Q& other = n&N2 [ hN (T6 ) − hN (T4 )] 2

(8)

2

+[ n&O2 ,6hO (T6 ) − n&O2 ,4 hO (T4 )] + n&MO [ hMOred (T9 ) − hMOox (T12 )] 2

2

where Q& rerad and Q& other are the re-radiation heat loss rate and heat loss rate via conduction and convection, respectively, given by26, 28 4 Q& rerad = AapertureσTred

(9)

and

Q&other = f (Q&solar,h − Q& rerad ).

(10)

Here f is the heat loss factor satisfying 0≤f≤1. Heat transfer from the net solar input is split into three contributions (depicted in Figure1(b)) for further analysis later and to facilitate the calculation of the heat input for reaction: (i) to preheat the sweep gas, Q& sweep,h = n& N 2 [ hN (T5 ) − hN (T4 )] 2

2

+ n&O 2 ,4 [ hO (T5 ) − hO (T4 )];

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2

2

(11)

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(ii) to preheat the metal oxide to the reduction temperature,

Q& MO = n&MO [hMOox (T8 ) − hMOox (T12 )];

(12)

and (iii) to drive the metal oxide reduction reaction, Q& chem,red = [n&O 2 ,6 − n&O 2 ,5 ]hO (Tred )

(13)

2

+ n&MO [ hMO red (Tred ) − hMO ox (Tred )].

Accurate enthalpy or specific heat data are not readily available for the metal oxides at varying nonstoichiometric states considered in the present study. Thus, we follow the method found in prior work26, 28, 30 to evaluate eq (13) by using an integral average of the stand° ard enthalpy of the reduction reaction (see eq (1)) ∆H red obtained from the experimental data of Panlener et al.48 for ceria and Hao et al.19 for Zr-doped ceria, δ red ° dδ . Q& chem,red = n&MO ∫ ∆H red

(14)

δ ox

Substituting eqs (11)–(14) into eq (8) yields

Q&solar,h,red − Q&rerad − Q&other = Q&chem,red + Q&sweep,h + Q&MO

(15)

Next consider the oxidation subsystem. The steam oxidation (eq (2)) can be modelled by combining the water thermolysis (WT) reaction, 1 H 2 O(g) → H 2 + O 2 , 2

(16)

with an oxidation reaction of the reduced material with oxygen 1 1 1 M x O y −δ red + O 2 → M x O y −δ ox . ∆δ ∆δ 2

(17)

We assume that the WT reaction is at equilibrium at the oxidizer inlet (state point 16) before it reacts with the metal oxide flow stream. The equilibrium compositions of inlet gaseous phase are characterized by the equation of reaction equilibrium for WT reaction at Tox, 1

n&H2 ,ox,in n&O2 2 ,ox,in  psys / pref  n&H2 O,ox,in  n&total,ox,in

1

o 2  ∆GWT (Tox )   = exp    RTox  

(18)

o where ∆GWT is the standard molar Gibbs free energy for WT reaction, eq (16),

∆G

o WT

1 (Tox ) = hH2 (Tox ) + hO2 (Tox ) − hH2O (Tox ) 2   1   −Tox  sHo 2 ( Tox ) + sOo 2 (Tox ) − sHo 2 O (Tox )  . 2  

(19)

The reference pressure pref is held at pref=patm in this study. Again we use the Dalton model and the assumptions of ideal gas and an isobaric oxidation system to link the oxygen partial pressures with their corresponding flow rates at both inlet and outlet of the oxidation chamber:

pO2 ,ox,j =

n&O2 ,ox,j n& total,ox,j

psys ( j = in,out).

(20)

We simplify the species and mass conservation at both the gas inlet and outlet by introducing the chemical conversion of water to hydrogen Xj as defined by

Xj =

n&H2 ,ox, j n&H2O,14

( j = in, out) .

(21)

The molar flow rates of all species entering and leaving the oxidation chamber are then related to the molar flow rate of water into the system n&H 2 O = n&H 2 O,14 by

n&O 2 ,ox , j

1  X in n&H 2 O,14  2 = 1  1 X n& − (δ − δ ox ) n&MO  2 out H 2 O,14 2 red

( j = in)

(22) ( j = out),

n&H2O,ox,j = (1− X j ) n&H2O,14 ( j = in,out) ,

(23)

n&H2 ,ox,j = X j n&H 2 O,14 ( j = in,out) ,

(24)

and, n& total,ox,j = n&H 2 ,ox,j + n&O 2 ,ox,j + n&H 2 O,ox,j ( j = in,out) .

(25)

The fuel output n&H 2 from the oxidation chamber appearing in eq (3) is then expressed as: n&H 2 = ∆δ n&MO = n&H 2 ,ox,out − 2n&O 2 ,ox,out

(26)

The energy balance equation for the oxidation subsystem is

Q&solar,h,ox − Q& recover,ox = [n&H2 O,17hH O (T17 ) + n&H2 ,17hH (T17 ) + n&O2 ,17 hO (T17 )] 2

2

2

(27)

−n&H2 O,15hH O (T15 ) + n&MO [hMOox (T11 ) − hMOred (T13 )]. 2

As with the reduction side, three energy contributions are introduced here to help understand how the solar input is used in the system and to facilitate the calculation of the metal oxide enthalpy terms: (i) the heat transfer necessary to heat the water to oxidation temperature, Q& H 2 O = n&H 2 O,15 [ hH O (T16 ) − hH O (T15 )]; 2

(28)

2

(ii) the heat transfer due to cooling of the reduced material after HXs to get the metal oxide to the oxidation temperature,

Q& MO,cool = n&MO[hMOred (T10 ) − hMOred (T13 )] ;

(29)

and (iii) the heat transfer due to the steam-oxidation reaction, Q& chem,ox = n&H 2 [ hH (Tox ) − hH O (Tox )] 2

2

+ n&MO [ hMOox (Tox ) − hMO red (Tox )].

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(30)

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(30) in terms of the heat released by the oxidation with oxygen, eq (17), and the heat required to drive the WT reaction, eq (16)),

tion (PSA), and cryogenic separation.50 When extremely low oxygen content in nitrogen is required, for example 1 ppm, cryogenic separation becomes the most efficient choice and a guideline for its work requirement is offered ranging from 12 to 21 kJ mol-1N2 .50 Authors in the solar

δ red o Q& chem,ox = n&MO ∫ ∆H ox dδ + n&H 2 ∆H Wo T (Tox )

thermochemistry field have used values varying in the range 12–16 kJ mol-1N2 .26, 30, 35 Though cryogenic separation

The exothermic heat transfer of the steam oxidation reaction Q& chem,ox is found using an expression alternative to eq

(31)

δ ox

o o where ∆H ox and ∆H WT are the standard enthalpy for the oxidation with oxygen, eq (17), and for the WT reaction, eq o (16), respectively. Data of ∆H ox are the negative values of o experimentally determined ∆H red since these two have the same expression but proceed in opposite directions (see eq (17) and eq (1)). The second term on the left-hand side of eq (27) is defined as:

Q& recover,ox = n&N2 [ hN (T3 ) − hN (T2 )] + n&O2 ,2 [hO (T3 ) − hO (T2 )] 2

2

(

2

)

2

( (

) )

& & & & &  &  − QH2O + Qchem,ox + QMO,cool  if QH2O + Qchem,ox + QMO,cool < 0 =  0 if Q& H2 O + Q& chem,ox + Q& MO,cool ≥ 0  (32) Substituting eqs (28)–(32) into eq (27), we obtain

(

(33)

)

Statements of conservation of energy for the three heat exchangers yields:

n&N2 [hN (T4 ) − hN (T3 )] + n&O2 ,3[hO (T4 ) − hO (T3 )] 2

2

2

2

= ε g{n&N2 [hN (T6 ) − hN (T3 )] + n&O2 ,6[hO (T6 ) − hO (T3 )]}, 2

2

2

(34)

2

2

2

2

(35)

2

+ n&H 2 ,17 [ hH (T17 ) − hH (T14 )] + n&O 2 ,17 [ hO (T17 ) − hO (T14 )]}, 2

2

2

2

and

n&MO[hMOox (T12 ) − hMOox (T11 )]

{

}

= ε s n&MO[hMOred (T9 ) − hMOred (T10 )] .

(36)

for HXg,red, HXg,ox, and HXs, respectively. We have introduced the heat exchanger effectiveness, ε , using its standard definition and subscripts denoting a gas or solid heat exchanger.49 Finally, the solar power input used for providing the penalty work for sweep gas production can be determined by

n&N wsep,N 2 Q& solar,pw = 2 ,

ηsolar-ele

wsep,N

2

 12000 J mol −1  2 =   pO ,air  2 × 1000 J mol −1 ln      p   O2 ,red,in 

pO2 ,red,in < 5 × 10−4 atm pO2 ,red,in ≥ 5 × 10−4 atm

where pO2 ,air represents the oxygen partial pressure in atmospheric air. The possibility of using vacuum pumping to achieve low oxygen partial pressures also has merit and is explored in detail in a following section. Reactor Solid–Gas Flow Configurations. The above analysis only offers a single relationship between n& N2 n&MO ,

∆δ and pO2 ,red,out for the reduction subsystem and between

n&H2 O n&MO , ∆δ , pO2 ,ox,out and X out for the oxidation subsys-

n&H 2 O [ hH O (T15 ) − hH O (T14 )] = ε g {n&H 2 O,17 [hH O (T17 ) − hH O (T14 )]

content range following the work by Krenzke and Davidson30 and Ganzoury et al.41. Therefore, a piecewise function30, 41 is adopted to calculate the molar separation work:

(38)

Q&solar,h,ox − Q& recover,ox = Q& H2O + Q&chem,ox + Q& MO,cool

requires less energy at lower oxygen impurities, membrane separation and PSA become more efficient when oxygen impurities become higher than 500 ppm.30, 41 In general, the lower oxygen impurities in the sweep gas production, the more separation work should be required.51, 52 However, due to a lack of data for cryogenic separation at low oxygen impurities below 500 ppm, a constant value of 12 kJ mol-1N2 at 1ppm is assumed here for this low oxygen

(37)

where ηsolar-ele and wsep,N 2 are the efficiency of solar energy converted to electricity and the required molar separation work, respectively. Three common air separation technologies exist: membrane separation, pressure swing adsorp-

tem, respectively, leaving the mass and species conservation analyses undetermined. Additional relationship(s) between those parameters relies on the specific solid-gas flow patterns implemented in the reactor. Different reactor flow configurations will result in a different distribution of oxygen partial pressure in the reduction chamber, water conversion in the oxidation chamber, and nonstoichiometry profiles of the redox material for both chambers along the flow path. These differences lead to different chemical equilibrium conditions established within the chambers. Two specific, ideal steady-state flow configurations are considered here: CF and PF. The FF model is excluded from consideration in the present study due to its transient process operation. The system under consideration is a reactor implementing CF or PF configuration with prescribed inlet conditions of reactant flow rates and thermodynamic states. A schematic of the reduction system is shown in Figure 2 with Figure 2(a) representing the CF configuration and Figure 2(b) representing the PF. Based on conservation of mass and species as well as Gibbs’ criterion, a revised CF model for both the reduction and oxidation chambers has been developed in a parallel effort.45 The PF model30, 36 assumes chemical equilibrium at the gas outlet. It will also be employed for comparison with the revised CF model regard-

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ing the optimal reduction and oxidation extent possible. The undetermined mass and species conservation analyses mentioned above can be closed using the PF and revised CF models and will not be detailed here. Readers interested in these two specific models can consult our parallel work45. When combining the flow choices in both reduction and oxidation chambers, we obtain four reactor flow configurations which we will refer to as CF–CF, CF–PF, PF–CF, and PF–PF. For these abbreviations, the flow configuration implemented in the reduction chamber appears on the left and that implemented in the oxidation chamber appears on the right. To determine the solar-to-fuel efficiency of the whole reactor system, analyses on the reduction and oxidation chambers need to be coupled together. The key to the coupling lies in the flow loop of the redox material, whose inlet non-stoichiometry state of one chamber is the outlet non-stoichiometry state of the other. As a result, both the reduced and oxidized non-stoichiometry states of the working material, δ red and δ ox , are affected by the flow streams of sweep gas and oxidizer to each individual chamber. Therefore, different combinations of sweep gas and oxidizer streams at varying inlet conditions ( n& N2 n&MO ,

are selected as working materials based on their readily ° ° ° , ∆S red , ∆H ox available thermodynamic data including ∆H red ° and ∆ S ox from the studies of Panlener et al.48 for ceria ( 0.001 < δ < 0.25 ) and of Hao et al.19 for Zr-doped ceria ( 0.01 < δ < 0.2 ), respectively. These materials have been heavily studied in the literature for solar thermochemical fuel production, and varying conclusions have been drawn regarding the most efficient redox material. This is mainly due to the different modelling choices as well as the varying common non-stoichiometry states between materials, as mentioned above.18, 41, 42 For example, Takacs et al.18 concluded that pure ceria has higher efficiency than Zr20, while a study by Bulfin et al.42 claimed better performance for Zr20 than pure ceria.

a)

pO2 ,red,in , n&H 2 O n&MO , pO2 ,ox,in (Tox ) and X in ) will result in dif-

ferent reduced and oxidized non-stoichiometry states. This leads to different fuel outputs, which may eventually lead to different solar-to-fuel efficiency predictions. Here, we term those varying inlet parameters as free parameters since their values can be chosen freely within their meaningful ranges. To identify their optimal values, we use the solar-to-fuel efficiency defined by eq (3) as the objective function, and define a constrained optimization problem as given by

max

η (y)

subject to

yL < y < yU,

b)

(39)

where y is a vector of length four whose components are the

unknown

free

parameters: pO2 ,red,in , n& N2 n&MO ,

n&H 2 O n&MO and Tox . The inlet oxygen partial pressure p O2 ,ox,in and water conversion X in are pure functions of Tox

from eqs (18)–(25)) and are thus excluded from the candidates of free parameters. The constraints in eq (39) are defined by the operating ranges of interest for the reactor system under study where the subscripts L and U represent lower and upper limits of the operating parameters, respectively. Choices for these limits are elucidated in the next section. Note that the determination of free parameters is not unique. Our choice of free parameters is motivated by relevance to reactor design from the viewpoint of practical operation. Both temperature-swing and isothermal operation are possibly included in our analysis.

3. RESULTS AND DISCUSSION A summary of the prescribed and free parameters selected for the baseline case study is presented in Table 1. These parameters apply to all results unless stated otherwise. Pure ceria and Zr-doped ceria (Zr05, Zr10, Zr15 and Zr20)

Figure 2. Schematic flow configurations implemented in the reduction chamber: (a) CF, (b) PF (the dashed line boundaries denote a certain chemical equilibrium state).

The prescribed parameters are set by practical estimates. The concentration ratio is set to obtain the highest operating temperature realizable with a solar dish concentrator system or a heliostat field plus a secondary concentrating device.53, 54 Atmospheric pressure is assumed for both reference pressure and reactor system pressure based on assumption (i). The heat loss factor f and the efficiency of solar to electricity are set to be consistent with previous studies.26, 28, 30 Conservative values of gas and solid heat recovery effectiveness are employed to enable realistic operation: the solid heat recovery effectiveness εs is set to zero considering the practical challenges in operating high-

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temperature moving parts as in existing solid heat recovery designs.55, 56 The gas heat recovery effectiveness is set to be εg=0.75.35, 57 A range of 1400–1900 K is considered for Tred to allow for both realistic and extreme cases of the reactor operating temperature. The selected lower temperature limit is a typical value used in previous studies,26, 28 while the upper limit is determined by Zr15; the highest value of δ in the literature (0.2) limits Tred to 1919 K at pO2 ,red,in =10-6 atm.19 The constraints of selected free parameters appearing in eq (39) are set to ensure two physically meaningful bounds. The partial pressures of oxygen are constrained to behave Table 1. Summary of prescribed and free parameters for baseline case thermodynamic analyses Parameters C

Prescribed

Free yL < y < yU

Values 3000

DNI

1000 W m-2

pref

1 atm

psys

1 atm

f

0.2

ηsolar-ele

0.25

εs

0

εg

0.75

Tred

1400–1900 K at 50 K intervals

pO2 ,red,in

[10-6, 0.1] atm

n& N2 n&MO

[0, 105]

n&H 2 O n&MO

[0, 105]

Tox

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with their corresponding optimal operating conditions for all materials and reactor flow configurations; and (ii) investigate the effect of each free parameter on the solar-tofuel efficiency to elucidate which physical mechanisms lead to losses/gains in efficiency. Then, varying solid and gas heat recovery parameters are further considered to explore how far inert gas sweeping can go in terms of solar-to-fuel efficiency. The option of vacuum pumping is also considered to serve as a comparison case, which may offer insight on the more efficient choice under a specific operating condition. Baseline Case. The maximum solar-to-fuel efficiencies for selected redox materials under different flow configurations are found via simultaneous optimization of all free parameters as listed in Table 1. The effect of different flow configurations on solar-to-fuel efficiency is similar for all working materials and hence only the result of ceria is shown here in Figure 3. The maximum solar-to-fuel efficiency for ceria occurs under CF–CF and is 9.4% for water splitting at Tred=1900 K. As expected, CF outperforms PF in terms of the maximum solar-to-fuel efficiency when applied to the same reaction chamber. The better performance of CF is caused either by achieving similar optimal non-stoichiometry swings with lower sweep gas and oxidizer flow rates or using similar sweep gas and oxidizer flow rates to achieve higher non-stoichiometry swings, as can be found from the Supporting Information. It is interesting to note that CF–PF is more efficient than PF–CF, suggesting a CF-like configuration within the reduction chamber is more important. This offers guidance for reactor design and realistic operation. The maximum efficiency for carbon dioxide splitting using ceria under CF–CF is 9.0% at Tred=1900 K, εs=0, εg=0.75. Results for CO2 splitting under other flow configurations are similar to that of H2O splitting; interested readers can refer to the Supporting Information.

[600 K, Tox,max]

as expected in the system operation: pO2 ,red,in < pO2 ,red,out < psys . The limit of pO2 ,red,in is chosen based on current air separation technologies30, 50. Note that this limit is not absolute and it can be overcome with other, less mature separation technologies such as thermochemical pumps to achieve a much lower oxygen partial pressure at lower energy cost.32, 58 A wide meaningful range of flow rate ratios of sweep gas to metal oxide and oxidizer to metal oxide, from zero to 105, is considered to find their optimal values. The lower limit of Tox is chosen to show a broad range of thermodynamic efficiency prediction and may not be achievable when considering other requirements such as realistic oxidation kinetics. The upper limit of Tox is derived from the condition δ ox < δ red where an extreme equilibrium condition of δ ox = δ red = δ eq (Tox,max ) for

Figure 3. Maximum efficiencies of ceria under different flow configurations with εs=0, εg=0.75 for water splitting.

the oxidation reaction by oxygen, eq (17), at the gas inlet. In the following section, we first focus on the baseline case to (i) report the maximum solar-to-fuel efficiencies along

Similar trends of the maximum solar-to-fuel efficiency are found for all flow configurations when comparing different materials. Therefore, only the result for the CF–CF configu-

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ration is displayed in Figure 4. The doped ceria Zr10 and Zr15 demonstrate a modest efficiency benefit over pure ceria at higher temperature range of 1700–1850 K. However, both Zr05 and Zr20 are less efficient than pure ceria over the same temperature range. At lower temperatures below 1650 K, a much less significant efficiency benefit is predicted for materials of all doping levels. This can be understood by noting that all doping materials achieve higher non-stoichiometry swings under their optimal operating conditions but at the cost of higher sweep gas and water flow rates as well as larger temperature swings, resulting in higher fuel output as well as higher solar power input. The competing effects of increase in both numerator and denominator of the solar-to-fuel efficiency (see eq (3)) make their efficiencies not necessarily higher than that of pure ceria. However, this minor efficiency gain of Zr-doped ceria is accompanied by lower oxidation temperature operation due to their larger temperature swings, which may lead to lower achievable maximum efficiencies if the redox cycling is kinetically limited. Therefore, we urge caution in drawing conclusion about the efficiency promise of Zrdoped ceria over that of pure ceria.

CF, and the magnitude of the temperature swing is shown to increase significantly with Zr-doping levels, indicating that different materials favor different temperature cycling choices. The optimal reduced and oxidized nonstoichiometry values are found to increase with higher Zr doping levels in general, suggesting oxidation is more difficult with higher Zr content, in agreement with experimental evidence for CO2 splitting.59 The maximum efficiencies under CF–CF via multivariable optimization based on a revised CF model45 reported here are more realistic (below 10%) than the previous study by Krenzke and Davidson30, whose maximum efficiency is around 40% at εs=0.75, εg=0.8, Tred=1773 K under CF–CF. This is mainly due to the unsound assumption of enforcing equilibrium at both gas inlet and outlet in their work,30 which we demonstrate can violate the second law of thermodynamics in a parallel work.45 The unsoundness of their assumption has also been recognized by Brendelberger et al.54, Hathaway et al.24, and Ehrhart et al.29. In addition, their assumption of 75% solid heat recovery effectiveness30 may also have a large effect on the efficiency difference. Herein, we revisit their work by using the same energy balance model while employing the revised CF model45 to predict the optimized efficiency under CF– CF. Results are shown in Figure 5 using their definition of efficiency. The reproduction of their results, using their CF model, confirms the employment of the same energy balance model. Note that unlike the CF model used in their work30 which only has one single free parameter ( pO2 ,red,in ), the revised CF model45 offers the same number of free parameters ( pO2 ,red,in , pO2 ,red,out and δ ox ) as chosen in their PF–PF model. As a result, the revised CF–CF model yields the optimized efficiencies over a full range of the oxidation temperature under consideration (Tox=1073–1773 K) whereas their results were truncated when the sweep gas became unphysically low. The revised CF–CF model predicts much lower optimum efficiencies, with the highest value of 15.9% achieved under an optimal condition of pO2 ,red,in = 1.4 × 10−4 atm, pO2 ,red,out =0.045 atm, Tox =1292 K.

Figure 4. Maximum efficiencies for water splitting of all materials under CF–CF flow configuration with εs=0, εg=0.75.

The peak efficiencies are listed in Table 2 along with their corresponding optimal operating conditions for each material under CF–CF and PF–PF to offer upper and lower bounds. Results at a common experimental temperature case, Tred=1773 K, can be found in the Supporting Information. All optima are found when the system undergoes a combination of both temperature and pressure swing operation, which is in agreement with results of previous studies.26, 42, 57 The optimal oxygen partial pressure entering the reduction chamber varies widely for all materials and flow configurations since it has little effect on the solar-to-fuel efficiencies over a wide range of values as explored in the next subsection. A general trend of higher demands of sweep gas and water flow rates is found when the flow choice transfers from CF–CF to PF–PF and when the Zr content in materials increases. PF–PF requires a higher temperature swing for optimal operation than CF–

The difference in peak efficiencies between our work (9.4%) and the revisited work by Krenzke and Davidson30 (15.9%) is due to the differences in modelling choices: (i) the heat release from exothermic reaction and solid sensible heat is used to preheat the oxidizer in our work, while this same heat release is used to provide the penalty work in theirs; (ii) an operating condition of Tred=1900 K, εs=0, εg=0.75 is prescribed in our model while a different condition of Tred=1773 K, εs=0.75, εg=0.8 is assumed in their work. Another significant finding from Figure 5 is that temperature-swing is predicted to be more efficient than isothermal operation, which agrees well with the results shown in Table 2. Expanding upon on the maximum efficiencies and their corresponding optimal operating conditions reported above for the baseline case, the dominating energy requirements behind these optimal results are further explored here. Understanding the energetic constituents of efficiency and losses can offer insight on reactor design and operation. To facilitate our discussion here, the solar-

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to-fuel efficiency is reformulated via the introduction of dimensionless energy factor terms (Fi) as defined in the work by Jarrett et al.6:

η=

1 Fchem,red + Floss + FMO + Fsolar,h,ox + Fsweep

(40)

Table 2. Peak efficiencies for water splitting using selected reactive materials and optimum values of operating condition parameters. Flow configuration

Optimum parameter

η pO

CF–CF

Zr10

Zr15

Zr20

7.6%

9.4%

9.5%

9.0%

1.0×10-5

3.4×10-5

1.7×10-3

2.3×10-4

1.5×10-3

Tred (K)

1900

1900

1900

1900

1900

Tox (K)

1458

1322

1205

1152

1109

442

578

695

748

791

0.037

0.042

0.054

0.065

0.066

0.0048

0.0091

0.0082

0.015

0.016

0.032

0.033

0.046

0.050

0.050

0.18

0.34

0.26

0.29

0.43

2 ,red,in

(atm)

∆T (K)

δ red δ ox

n&H2 O n&MO

η pO

1.6

1.9

2.7

2.9

2.9

5.5%

4.0%

5.5%

5.1%

4.7%

6.9×10-3

4.5×10-3

4.8×10-3

3.3×10-3

2. ×10-3

Tred (K)

1900

1900

1900

1900

1900

Tox (K)

1266

991

980

789

888

634

909

920

1111

1012

0.027

0.029

0.041

0.049

0.051

0.0045

0.0064

0.010

0.014

0.020

0.023

0.023

0.031

0.035

0.031

0.30

0.40

0.34

0.45

0.67

3.9

4.1

5.7

4.1

2 ,red,in

(atm)

∆T (K)

δ red δ ox ∆δ n&N 2 n&MO

n&H2 O n&MO

2.3

with  Q& i   n&H2 HHVH2  &  Qrerad + Q& other Fi =   n&H2 HHVH2 & &  Qsweep,h + Qsolar,pw  n&H HHVH  2 2

Zr05

9.4%

∆δ n&N 2 n&MO

PF–PF

Ceria

(i = chem, red; MO; solar,h,ox) (i =loss) (i = sweep)

This enables the sum of all dimensionless energy factors to be the reciprocal of the solar-to-fuel efficiency. First, we look at the optimized case, where all free parameters are at their optimal values, to identify the dominating energy factors at varying prescribed reduction temperatures. This is conducted using pure ceria under CF–CF configuration as an example case. Figure 6 shows the maximum solar-to-fuel efficiencies along with their associated energy factor terms as a function of the reduction temperature for the baseline case. The zero solar input to the oxi-

dation chamber Fsolar,ox suggests that the oxidation step performs best when no solar input is required. Except for the energy factor to drive the reduction reaction, Fchem,red, which remains basically constant, all other energy factors including Fsweep, FMO, and Floss decrease with increasing reduction temperature. This is due(41) to the dominating effect of the increase in fuel output over the increase in the respective solar power requirements for heating and producing the sweep gas, for heating the metal oxide and for heat losses via reradiation and other modes. The most dominating energy factor is FMO and its share of the total solar input decreases from 58% to 39% as the reduction temperature increases from 1500 K to 1900 K. The second-most important energy factor shifts from Fsweep at low reduction temperatures to Floss at high reduction temperatures due to the dramatic increase of the heat loss rate with increased reduction temperature (see eqs (9) and (10)). If higher reduction temperatures beyond this range are considered, the increase in the heat loss share of the total solar input may become so predominate that it could outperform the increase in fuel production and an efficiency decline will be expected. This is seen in the work by Lapp et al.28 where

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the solar-to-fuel efficiency begins to decrease at very high reduction temperature for pure ceria.

tures for water splitting using ceria under CF–CF configuration with εs=0, εg=0.75.

Next, the effect of free parameters on solar-to-fuel efficiency is investigated to elucidate how changing each free parameter causes deviation from the optimized efficiency conditions. The investigation is performed using ceria under CF–CF at the reduction temperature of 1900 K as a reference case with one parameter being varied within a selected range to ensure efficiencies above 1% while holding other free parameters constant at the optimal values as listed in Table 2.

In the subsequent discussion on the effect of a certain free parameter, the energy factor Fchem,red remains essentially unchanged at a specific value for each varying free parameter case due to its pure reliance on the integral average of ° (δ i ) , a relatively constant value over a range of δ ox – ∆H red

δred for ceria (see eq (14)). Another term worth noting is Floss. Though its value changes with the free parameters, it is not directly affected by them (see eq (9) and (10)) and hence will not be discussed in the coming analysis. As to the term of Fsolar,h,ox, it will become apparent that the use of solar energy to preheat the oxidizer to Tox in the oxidation chamber always indicates a dramatic decrease in process efficiency. While this conclusion may seem intuitive, exactly how Fsolar,ox appears is often not. It becomes non-zero when the energy cost to preheat the oxidizer becomes larger than can be supplied by the heat recovered from the cooling of the metal oxide and the heat released from oxidation; see eqs (31)–(33). This is caused by a number of reasons that are often difficult to separate: (i) A lower temperature difference between the oxidation and reduction chambers means less heat rate recovery from the metal oxide leaving the reduction chamber, Q& MO,cool . (ii) Lower fuel production rate leads to less heat rate released from steam oxidation, Q& chem,ox . Thus, any decrease in fuel

Figure 5. Optimized efficiency comparison with Krenzke and Davidson30 under Tred=1773 K at εs=0, εg=0.8 for PF–PF and at εs=0.75, εg=0.8 for CF–CF, respectively. Legend text “reproduced” is in reference to the effort to reproduce the work by Krenzke and Davidson30, and “revised” refers to using the revised CF model45 to revisit, modify, and optimize the work by Krenzke and Davidson30. The displayed percentages showcase the highest predicted solar-to-fuel efficiencies using the respective CF–CF models.

Figure 6. Maximum solar-to-fuel efficiencies along with their associated energy factor terms at varying reduction tempera-

production rate can have a compounding, negative effect on the process efficiency if Q&solar,h,ox becomes non-zero. (iii) The heat rate required to preheat the incoming oxidizer, Q& H 2 O , becomes large because of a high oxidation temperature or a high oxidizer flow rate in the oxidation chamber.

Figure 7. Effect of inlet oxygen partial pressure in the reduction chamber on energy factors and solar-to-fuel efficiency for water splitting using ceria at Tred=1900 K, εs=0, εg=0.75 under CF–CF. The values of other constant free parameters are given in Table 2.

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All flow configurations display similar trends and hence only the result of CF–CF is reported here due to its high efficiency performance. The effect of changes in the oxygen partial pressure entering the reduction chamber is illustrated in Figure 7. The solar-to-fuel efficiency is insensitive to changes in pO2 ,red,in over a broad range and remains relatively constant in its optimum range from 1 × 10 −6 to 5.6 × 10 −3 atm, after which the efficiency begins to decrease gradually. This is not surprising since the optimal reduced non-stoichiometry state is always achieved over the above wide range, creating a constant high fuel output rate. On the other hand, the penalty work required to produce the sweep gas is assumed constant as long as cryogenic separation can be used (see eq (38)), making the solar input also constant. Once pO2 ,red,in crosses the threshold value, both the fuel production rate and the penalty work begin to decrease due to the decreased δ red and the employment of PSA for sweep gas production. The latter effect is more dominating than the former, resulting in slight decrease in Fsweep as observed. The first-constant-then-increasing trend of FMO is owing to the first-constant-then-increased fuel production rate since the energy rate to heat the metal oxide Q& MO stays unchanged. Therefore, a wide range of

Page 12 of 17

results in a non-trivial efficiency trend. The dramatic decrease in efficiency at high sweep gas flow rates is due to the significant increase in Fsweep relative to the fuel output. As a result, a range of sweep gas flow rates near and below the optimal value is suggested for practical operation. The effect of water flow rate to the oxidation chamber is illustrated in Figure 9. With increasing water flow rates, an increase in non-stoichiometry swing as well as fuel production rate is expected. On the other hand, the increase in the water flow rate also results in an increase in the energy rate Q& H 2 O to heat the water to Tox. Once the growth in Q& H 2 O becomes too large, the two constant energy terms Q& MO,cool + Q& chem,ox will not be able to meet this demand and extra solar input will be required. Consequently a dramatic increase in Fsolar,h,ox and a sharp decline in efficiency will be expected. These results indicate that the oxidation is best conducted auto-thermally at off-sun conditions.

inlet partial pressures well below 5.6 × 10 −3 atm is operable for high reactor performance.

Figure 9. Effect of oxidizer flow rate on energy factors and solar-to-fuel efficiency for water splitting using ceria at Tred=1900 K, εs=0, εg=0.75 under CF–CF configuration. The values of other constant free parameters are given in Table 2.

Figure 8. Effect of sweep gas flow rate on energy factors and solar-to-fuel efficiency for water splitting using ceria at Tred=1900 K, εs=0, εg=0.75 under CF–CF configuration. The values of other constant operational parameters are given in Table 2.

The effect of variations in sweep gas supply to the reduction chamber is shown in Figure 8. As the sweep gas flow rate increases, the reduced non-stoichiometry increases, leading to an increasing fuel production rate n&H2 . The power to heat and produce the sweep gas ( Q& sweep,h + Q& solar,pw ) is also increased since it is proportional to n& N2 . The simultaneous increase in fuel output and energy consumption

The effect of oxidation temperature variations is shown in Figure 10. The initial increase in efficiency at higher oxidation temperatures is due to the decline of FMO; smaller temperature swings require less heat rate to preheat the working material. However, if the temperature swing is too low (Tox is too high), the energy rate necessary to preheat the oxidizer becomes so large that Fsolar,ox will appear. The later increase in the factor of Fsweep is due to the decline of the fuel output at high oxidation temperature under a constant energy consumption to heat and produce the sweep gas. The peak efficiency occurs at the optimal temperatureswing condition and further demonstrates its better performance than that of isothermal operation. Potential Efficiency Improvement. The efficiencies reported above for the baseline case do not account for solar collection losses. If one now takes into account the annual average collection efficiency of a parabolic dish collector system, for example, to be 59%37, the overall solar-to-fuel

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efficiencies in most circumstances for the baseline case would then be less than 5%. This value is indeed quite low and may make the solar thermochemical pathway appear unpromising. However, recall that the baseline case is limited to a conservative condition of zero solid heat recovery and 75% gas heat recovery. Recent solar thermochemical reactor design efforts have shown that gas heat recovery of up to 0.9524 and solid heat recovery of over 0.760, 61or 0.862 are realistic and possible, which may improve the solar-tofuel efficiency to a great deal. In recognition of this potential for efficiency enhancement, we aim to investigate the effect of varying solid and gas heat recovery conditions on solar-to-fuel efficiency to explore the upper limits of efficiency for the option of inert gas sweeping. The option of vacuum pumping is also considered to satisfy our curiosity as to which is the more efficient choice to maintain low oxygen partial pressure in the reduction chamber.

 pO ,red  1 o ° ∆H red (δ red ) − Tred ∆Sred (δ red ) = − RTred ln  2  , 2  pref  and the oxygen release rate in the reduction chamber is determined by: 1 n&O2 ,red = n&MO (δ red − δ ox ) 2

The solar energy requirement corresponding to the penalty work for pumping the released oxygen from the vacuum pressure to ambient pressure at ambient temperature condition is given by33-35: W&pw,vp n&O2 ,red RTabm  pamb  = Q& solar,pw = ln    pO ,red  ηsolar-vp ηsolar-vp  2  where ηsolar-vp is the conversion efficiency of solar to vacuum pumping work, which is the product of solar-toelectricity efficiency and electricity-to-pump efficiency. The solar-to-electricity efficiency is assumed to be 25% as shown in Table 1 to be consistent with the analysis for inert gas sweeping. Regarding the electricity-to-pump efficiency, the analytical model developed by Bulfin et al.35 is adopted here in recognition of the fact that the electricityto-pump efficiency declines with decreasing pressure. Consequently, the mathematical expression for the solar to vacuum pumping efficiency is:

 pO2 ,red    pref 

0.544

ηsolar-vp = ηsolar-ele ×ηele-vp = 0.25 × 

Figure 10. Effect of oxidation temperature on energy factors and solar-to-fuel efficiency for water splitting using ceria at Tred=1900 K, εs=0, εg=0.75 under CF–CF configuration. The values of other constant free parameters are given in Table 2.

Prior efforts27, 33-35 have compared inert gas sweeping and vacuum pumping under different operating conditions and model assumptions, with different conclusions drawn regarding the more efficient operating choice. Herein, the option of vacuum pumping is also analyzed using the same methodology as developed for inert gas sweeping. Much of the thermodynamic model described in section 3 will remain unchanged and we only highlight changes made necessary for vacuum pumping operation. The oxygen partial pressure within the reduction chamber is identical to the system pressure maintained by the vacuum pump, pO2 ,red = psys,vp .33-35 Since no sweep gas is employed, the sweep gas flow rate and the energy requirement to preheat the sweep gas become zero in eq (15), i.e., n&N 2 = 0, and Q& sweep,h = 0 . As a result, a CF flow configuration between solid and the released oxygen is unlikely to occur, and a PF configuration is thus assumed with the final reduction extent of the metal oxide being determined under equilibrium condition:

Based on this modified thermodynamic model developed for the option of vacuum pumping, its solar-to-fuel efficiency can then be determined and further optimized using the same multivariable optimization scheme as defined by eq (39). Note that unlike the option of inert gas sweeping which contains four free parameters ( pO2 ,red,in , n& N2 n&MO , n&H 2 O n&MO and Tox ), the option of vacuum pumping only

yields three free parameters that can be optimized— pO2 ,red , n&H 2 O n&MO and Tox due to the absence of inert gas. The range of these three free parameters are set to be consistent with those under inert gas option as listed in Table 1. The result of maximum solar-to-fuel efficiency employing inert gas at varying gas and solid heat recovery conditions (εg=0, 0.95; εs=0, 0.5, 0.75, 0.9) is shown in Figure 11 under CF–CF configuration using pure ceria as the model material. The corresponding results for vacuum pumping at the same heat recovery conditions are also illustrated in Figure 11 to facilitate a direct comparison with the option of inert gas. Note that the gas heat recovery conditions under vacuum pumping only refer to those of the heat exchanger on the oxidation side (HXg,ox in Figure 1(b)). All efficiencies reported here are achieved via simultaneous multivariable optimization (see eq (39)) of all free parameters as summarized in Table 1. Overall, the efficiencies achieved under both options are quite similar and comparable. The optimal solar-to-fuel efficiency predicted for current “state-ofthe-art” reactor systems (Tred=1773K, εs=0, εg=95%) is

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7.8% and 8.3% for inert gas sweeping and vacuum pumping, respectively. The peak efficiencies via inert gas sweeping and vacuum pumping are predicted to be 26.4% and 25.2%, respectively, at Tred=1900K, εs=0.9, εg=0.95. For both cases, solid heat recovery plays a more critical role in improving the maximum solar-to-fuel efficiency than gas heat recovery. For example, at Tred=1900 K, εg=0.95, the maximum efficiency under inert gas option is more than doubled from 11.0% to 26.4% when the solid heat recovery effectiveness

Figure 11. Effect of solid and gas heat recovery parameters on maximum solar-to-fuel efficiency for water splitting at varying reduction temperatures using ceria as the model material. Black dotted lines: the option of using inert gas under CF–CF configuration; red dashed lines: the option of using a vacuum pump in the reduction chamber. The maximum efficiency is achieved via multivariable optimization of all free parameters. Parameters not varied in the figure are set by the baseline case as listed in Table 1.

increases from 0 to 0.9. While in comparison, a comparably modest efficiency increase is observed from 7.5% to 11.0% for the inert gas option as the gas heat recovery condition improves from 0 to 0.95 at Tred=1900 K, εs=0. More importantly, only solid heat recovery of over 75% can promise a solar-to-fuel efficiency higher than 20% based on our thermodynamic model. This emphasizes the importance of efficient solid heat recovery in current reactor design efforts. The more efficient choice to maintain low oxygen pressure in the reduction chamber relies on the specific heat recovery conditions as well as the operating temperatures. When no gas or solid heat recovery is implemented, vacuum pumping is predicted to be more efficient than inert gas sweeping, with 8.2% versus 7.5% at 1900 K, in agreement with the experimental demonstration by Marxer et al.31 However, when efficient gas heat recovery is achieved, such as 95%24, the performance via inert gas sweeping will surpass that of vacuum pumping, particularly at high solid heat recovery conditions and high reduction temperatures. Note that the relative performance displayed here for both inert gas and vacuum pump options is closely tied to our specific model assumptions, operating conditions and reactor flow configurations; this is solely a thermodynamic analysis that does not consider other ef-

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fects such as reaction rates, and hence is not absolute. At different operating conditions, the conclusions drawn here may change, but the methodology employed can serve as a general framework for relevant future analyses.

4. CONCLUSIONS CONCLUSIONS An advanced thermodynamic model has been developed based on conservation of mass and species as well as Gibbs’ criterion to predict the maximum efficiencies of a solar reactor system via simultaneous optimization of all variable parameters. Ceria doped with Zr at various concentrations were selected as the model materials under four reactor flow configurations. For each material, the peak efficiency along with its corresponding optimal operating conditions has been identified. The effect of variable operating parameters on the solar-to-fuel efficiency has been investigated using pure ceria as a reference case. For the baseline case of zero heat recovery and 75% gas heat recovery, the maximum solar-to-fuel efficiency using ceria has been found to be 9.4% at Tred=1900 K under CF– CF. The CF configuration outperforms PF when applied to the same reactor chamber. Another interesting finding is that a reactor system operated under CF–PF is more efficient than that under PF–CF. Thus, achieving a CF-like flow configuration within the reactor, especially within the reduction chamber, is worthy of significant attention for thermochemical reactor design. Doped ceria with 10% and 15% Zr demonstrate modest efficiency benefit over pure ceria for a reduction temperature range of 1700–1850 K for the baseline case. While, by contrast, both Zr05 and Zr20 are less efficient than pure ceria over the same temperature range. At lower reduction temperatures below 1650 K, only a minor efficiency gain over pure ceria is predicted for all doping materials. However, the modest efficiency improvement of these doping materials is accompanied by low oxidation temperature operation, which may lower the realistic maximum efficiencies if the oxidation step is kinetically limited. Therefore, we urge caution in drawing conclusion about the efficiency promise of doped materials over that of pure ceria. The optimal operating conditions were determined for each active material for the baseline case. Temperature swing operation has been demonstrated to be more efficient than isothermal cycling operation. The magnitude of the optimal temperature swing depends on the flow configuration and the choice of reactive material. Solar-to-fuel efficiencies were found to be insensitive to changes in inlet oxygen partial pressures below a certain value ( 5.6 × 10−3 atm ) based on our model. The optimal values of reduced and oxidized non-stoichiometry are found to increase with higher Zr doping concentrations in general. Thus, the optimal operating conditions in an actual reactor system should be systematically studied for particular designs employing a certain material. In terms of potential efficiency improvement, varying solid and gas heat recovery conditions are considered for both inert gas and vacuum pump options to achieve the low oxygen pressure required in the reduction chamber. Peak

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efficiencies of 26.4% and 25.2% for water splitting are predicted for inert gas sweeping and for vacuum pumping, respectively, at the reduction temperature of 1900 K, 95% gas heat recovery and 90% solid heat recovery. The impact of solid heat recovery on maximum solar-to-fuel efficiency is more significant than that of gas heat recovery, and a solid heat recovery of over 75% is required to aim for an efficiency higher than 20%. This points to the need for more efficient solid heat recovery in reactor design. The more efficient choice to maintain low oxygen pressure in the reduction chamber relies on the specific heat recovery conditions as well as the operating temperatures. When no gas or solid heat recovery is implemented, vacuum pumping is demonstrated to be more efficient, while at an efficient gas heat recovery condition of 95%, inert gas sweeping performs slightly better at high temperature and high solid heat recovery conditions.

X=chemical conversion y=free parameter vector1 Greek Symbols ° ∆GWT = standard molar Gibbs free energy for WT given by eq

(16), J mol−1 ∆Hox° = standard molar enthalpy for reaction (17), J mol-1O ° ∆Hred = standard molar enthalpy for reaction (1), J mol-1O o ∆H WT =standard molar enthalpy for WT reaction (16), J mol-1

∆Sox° = standard molar entropy for reaction (17), J K -1 mol-1O ° ∆Sred = standard molar entropy for reaction (1), J K -1 mol-1O ∆δ =non-stoichiometry swing ∆T =temperature swing, K δ =non-stoichiometry

ε =heat recovery effectiveness

ASSOCIATED CONTENT

η =solar-to-fuel efficiency ηele-vp =electricity to vacuum pumping conversion efficiency

Supporting Information

ηsolar-ele =solar to electricity conversion efficiency

Comparison of selected optimal results among four reactor flow configurations using ceria for water splitting, maximum efficiencies for CO2 splitting using ceria under different flow configurations, and optimal operating conditions for water splitting of all Zr-doped materials at a typical reduction temperature of 1773 K. This information is accessible free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *Email: [email protected].

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS ACKNOWLEDGMENTS The financial support of the China Scholarship Council (Sha Li, grant no. [2015]3022, 201506020092) and the Australian Research Council (Wojciech Lipiński, Future Fellowship, award no. FT140101213) is gratefully acknowledged.

NOMENCLATURE Aaperture=aperture area of reactor, m2 C= solar concentration ratio DNI=direct normal irradiance, W m-2 f=conduction and convection heat losses factor F=dimensionless energy factor introduced in eq (41) h =molar enthalpy, J mol-1 HHV= higher heating value, J mol−1 n& =molar flow rate, mol s-1 p=pressure, atm

ηsolar-vp =solar to vacuum pumping conversion efficiency

σ =Stefan–Boltzmann constant, W m-2 K-4 Subscripts 1,2…=state point amb=ambient condition chem,ox=chemical reaction in the oxidation chamber chem,red=chemical reaction in the reduction chamber cool=cooling heat release g=gas phase h=heating requirement i,j=variables in=inlet L=lower limit max=maximum min=minimum MO=metal oxide other=other heat losses mode out=outlet ox=oxidation chamber pw=penalty work recover,ox=heat recovered from the oxidation chamber red=reduction chamber rerad=reradiation heat loss s=solid phase sep=separation solar=solar heat rate input sweep=sweep gas U=upper limit vp=vacuum pump Superscripts

° =standard condition at T and patm Abbreviations CF=countercurrent flow

Q& =heat rate, W R = universal molar gas constant, 8.314 J mol−1 K−1 s = molar entropy, J mol-1 K-1 T=temperature, K w =molar separation work, J mol-1 W& =work rate, W

The units of this quantity depend upon the choice of parameter being optimized. 1

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FF=fixed-bed flow GS=gas separator HX=heat exchanger MF=mixed flow MO=metal oxide PF=parallel flow PSA=pressure swing adsorption WT=water thermolysis Zr05, Zr10…=Zr-doped ceria

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