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Thermodynamic analysis of isothermal redox cycling of ceria for solar fuel production Roman Bader, Luke J. Venstrom, Jane H. Davidson, and Wojciech Lipi#ski Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/ef400132d • Publication Date (Web): 31 May 2013 Downloaded from http://pubs.acs.org on June 19, 2013

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Thermodynamic Analysis of Isothermal Redox Cycling of Ceria for Solar Fuel Production Roman Bader, Luke J. Venstrom, Jane H. Davidson, and Wojciech Lipiński* Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA Keywords: solar, thermochemical, water, CO2, syngas, fuel, ceria, thermodynamic analysis Abstract

A thermodynamic analysis of continuous fuel production by redox cycling of ceria in a single solar reactor under isothermal conditions is presented. Ceria is partially reduced in a sweep flow of purified nitrogen and re-oxidized with either steam or carbon dioxide to produce hydrogen or carbon monoxide, respectively. The sweep gas and oxidizer flows are preheated by the product gases. The influence of selected process parameters, including operating temperature, pressure and the effectiveness of heat recovery, on the solar-to-fuel conversion efficiency is determined. For a solar concentration ratio of 3000, typical of state-of-the-art solar dish concentrators, an operating temperature of 1773 K, 95.5% of the available gas-phase heat must be recovered to reach conversion efficiencies of 10% and 18% for hydrogen and carbon monoxide production, respectively, assuming the flow rate of inert sweep gas is equivalent to that of counter-current flows of gas and ceria. The efficiency depends strongly on the gas-phase heat recovery *

Corresponding author. E-mail address: [email protected]; Fax: +1 (612) 625-6069. 1

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effectiveness and the sweep gas flow rate. Introducing a temperature swing of 150 K between reduction and oxidation steps strongly reduces the sweep gas flow rate and increases the efficiency from 10% to 31.6% for hydrogen production.

1. Introduction Liquid hydrocarbons are energy-dense, transportable, and storable fuels that will continue to be used in the foreseeable future. Developing a sustainable process for the production of hydrocarbon fuels is thus an important step towards a sustainable energy supply system. One intriguing approach is to convert CO2 and H2O, the primary products of liquid hydrocarbon combustion, back into liquid hydrocarbon fuels using solar energy. Sunlight is used to convert CO2 and H2O into H2 and CO, the components of synthesis gas (syngas), which can be further processed to liquid hydrocarbon fuels. The routes to produce H2 and CO using solar energy include semiconductor photocatalysis,1 solar-driven electrolysis,2 and thermochemical conversion in which concentrated sunlight is utilized as high-temperature process heat.3 Alternative routes to solar fuels include biological photosynthesis4 and thermochemical gasification of carbonaceous feedstocks.5,6 The present work focuses on solar thermochemical conversion of H2O and CO2. Metal oxide redox cycles are a promising pathway to convert H2O and CO2 to H2 and CO using solar energy.7–10 While H2O and CO2 can be thermally dissociated in a single hightemperature step, metal oxide cycles lower the requisite dissociation temperature and yield the products O2 and H2 and/or CO in separate steps.10 Many metal oxides have been considered for solar thermochemical fuel production, including zinc oxide,11,12 iron oxide,13 ferrites14–16 (mixed oxide systems based on iron), and cerium dioxide (ceria, CeO2). Ceria pertains to the sub-class of metal oxides that undergo only partial reduction.17–36 Here, we consider ceria because of 2


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numerous advantages outlined in the following discussion. The partial metal oxide redox cycle is comprised of the endothermic reduction of ceria using concentrated solar radiation,

2 2 CeO2δox  CeO2δred  O2 ,  

(1)

and the exothermic oxidation of ceria,

x x CeO2δred  xH 2O  CeO2δox  xH 2 δ δ

(2a)

2 x 2 x CeO2δred   2  x  CO2  CeO2δox   2  x  CO δ δ

(2b)

where the change in non-stoichiometry is δ  δred  δox and x  0

2 . The net effect is the

dissociation of H2O and CO2 into H2 and CO. In the partial redox cycle, ceria and other candidate non-stoichiometric metal oxides remain solid during the cycle,* which eliminates the need for a separation process to recover the metal oxide from the product gas mixture.37–39 Experiments have demonstrated the promise of ceria for solar fuel production. Ceria with various morphologies, including porous monoliths,18,22 felt,23 reticulated foam,36 powders,19,31 and powders featuring templated macroporosity32,33 all exhibit activity for fuel production, but the morphologies differ in their reactivity. Morphologies that retain specific surface area allow for more rapid fuel production.33 Thermodynamically, reduction is favored at high temperatures and low oxygen activities, and oxidation is favored at low temperatures and high oxygen activities. Thus, prior efforts to produce fuel using ceria have focused on a two-temperature cycle.18,21,36 Ceria is reduced at high *

The equilibrium vapor pressure of cerium dioxide has been estimated by Abanades et al.17, and has been found to be negligibly small up to 2400 K, which is 300 K above the highest temperature considered in the present study. 3


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temperature, typically 1673–1873 K, and then cooled 400 to 800 degrees to split H2O and CO2. Prototype ceria-based solar reactors without recuperation of solid and gas phase sensible heat have produced H2 and CO at average solar-to-fuel efficiencies of up to 1.7%.21,23,36 Significant efficiency gains can be achieved in the two-temperature cycle, if, in addition to gas-phase heat recovery, a portion of the sensible heat released by the ceria during cooling from the higher to the lower cycle temperature is recovered.28,38 For example, with a concentration of 3000 suns, reduction temperature of 1800 K, oxidation temperature of 1073 K, and 90% gasphase heat recovery effectiveness, the theoretical cycle efficiency is 4.8% without solid-phase heat recovery, and 7.9% with 50% solid-phase heat recovery. The cycle efficiency is defined as the higher heating value (HHV) of the produced fuel divided by the solar power input to the cycle. Existing solid-phase heat recuperation strategies rely on radiative heat transfer and include the use of counter-rotating reactive rings39 or cylinders.40 Recuperating solid-phase sensible heat presents practical challenges associated with the construction and mechanical stability of hightemperature moving parts, and the isolation of the gas atmospheres in the reduction and oxidation zones of the reactor. Hence, eliminating the requirement for solid phase heat recuperation by operating both cycle steps at equal temperature would substantially simplify the reactor design and operation. Fuel production via isothermal redox cycling of undoped ceria has been demonstrated experimentally by Hao et al.41 In section 2, we discuss the operating conditions under which isothermal redox cycling of ceria is thermodynamically favored. In section 3, we formulate a thermodynamic model of redox cycling of ceria for syngas production in a solar reactor with gas-phase heat recovery. The results of a parametric study conducted with the thermodynamic model are presented in section 4, to show the influence of various process parameters on the cycle efficiency.

4


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2. Limit of Fuel Production for Isothermal Operation To elucidate the possibility of isothermal non-stoichiometric redox cycling of ceria, consider ceria contained in an isobaric and isothermal reacting volume through which gases flow continuously to remove products. As a result of sweeping products out of the system, ceria equilibrates with the gas entering the reacting volume. In the reduction step, the reactor is assumed to be purged with nitrogen with a low O2 -impurity; in the oxidation step, pure oxidizer (H2O or CO2) enters the reactor. In both cycle steps, gases and ceria are assumed to be at equal temperatures. As shown by the state diagram of ceria, Figure 1 (a), the equilibrium nonstoichiometry of ceria is a function of temperature and of the oxygen partial pressure in the gas only. Hence, in the reduction step, ceria equilibrates with the oxygen partial pressure in the nitrogen sweep gas; in the oxidation step, ceria equilibrates with the oxygen partial pressure in the oxidizer due to partial thermal dissociation of the oxidizer at elevated temperatures. The calculations of the oxygen partial pressure in the oxidizer are presented in section 3. Figure 1 (a) has been obtained by using the partial molar enthalpy hOo 2 and entropy sOo 2 of lattice-bound O2 determined experimentally by Panlener et al.42, together with the equilibrium condition for the O2-uptake/-release reaction of ceria, eq. (4) below. Panlener et al. obtained





hOo 2 and sOo 2 by experimentally determining  pO2 , T . Experiments were performed with pO2 , T , and  in the ranges [ 1022 atm, 102 atm], [1023K, 1773 K], and [0.001, 0.27],

respectively. hOo 2 and sOo 2 were found to be functions of  only. Based on this finding, the experimentally determined functions hOo 2 and sOo 2 can be used to calculate  at pO2 - and T values outside the above T - and pO2 - ranges, as long as  remains within the measured range.

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In the present analysis,  is restricted to values in the range [0, 0.25]. Between  = 0 and 0.001, polynomial curve fits are used to extrapolate hOo 2 and sOo 2 . The locus of ceria non-stoichiometry points for equilibrium with an oxidizer flow of H2O at atmospheric pressure in Figure 1 (a) corresponds to the lower non-stoichiometry in the cycle operated with H2O. The curve for pCO2 = 1.0 atm is similar. The higher cycle non-stoichiometry is established by the oxygen partial pressure in the sweep gas. Hence, the unshaded region of the state diagram in Figure 1 (a) depicts the operational window of the isothermal cycle. In the shaded region, the pO2 established during oxygen removal is higher than the oxygen activity of H2O at the desired operating temperature, and H2 is not produced upon H2O addition. Note that the two-temperature cycle operational window is substantially wider and includes the entire range of oxygen partial pressures and non-stoichiometries displayed in Figure 1 (a) because at temperatures less than ~1400 K, ceria fully re-oxidized. Figure 1 (b) shows the H2 produced at equilibrium for isothermal operation at temperatures between 1473 and 2073 K, with pO2 of 10-6–10-3 atm during reduction, and with pH2O = 1.0 atm during oxidation. Again, the result is similar for pCO2 = 1.0 atm. Hydrogen production increases monotonically with temperature. It is thus advantageous to operate the isothermal cycle at as high a temperature as possible from a fuel production standpoint. A more comprehensive thermodynamic model of the process that takes into account heat losses from the reactor and gasphase heat recovery is developed in the following section.

6


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Figure 1. (a) The δ–T– pO2 state diagram for undoped ceria based on the data in Panlener et al.42; the locus of the equilibrium points with pure H2O at 1 atm corresponds to the lower  in the cycle; the higher  is established by the oxygen partial pressure in the sweep gas; (b) The amount of H2 produced at equilibrium for isothermal operation with pH2O = 1.0 atm during oxidation in a flow-through system.

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Figure 2. Model system for the thermodynamic analysis of solar isothermal ( Tred = Tox ) redox cycling of ceria with N2 as inert sweep gas in the reduction zone and steam as the oxidizer in the oxidation zone. Numbers denote state points (SP). The products on the oxidation side are assumed to exit the process at T0 (SP13); any unrecovered excess energy is assumed to be removed by the HEXout outside the system boundary.

3. Thermodynamic Model The model system is shown in Figure 2. It consists of a non-stoichiometric redox reactor and two heat exchangers, HEXred and HEXox. Thermodynamic states in the system are denoted by the numbers 1–13, and are designated as SP1−SP13. Mass flows are indicated by thin arrows, and thick arrows indicate flows of energy. Concentrated solar radiation, Qsolar , is the source of high-temperature process heat. Reduction and oxidation of ceria are assumed to occur simultaneously in separated reduction and oxidation zones in the reactor. Purified nitrogen with low oxygen partial pressure is used to sweep away oxygen during the reduction step and 8


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maintain a low pO2 . The sweep gas is preheated in HEXred by the reduction effluent, and any remaining heat input to the sweep gas is provided by the solar radiation. This paper is focused on results with steam as the oxidizer. The analysis for CO2 as oxidizer is analogous, and selected results are included for CO2. Steam is generated and preheated in HEXox by the oxidation effluent, and any remaining heat input to the steam is provided by the solar radiation. Ceria is continuously cycled between reduction and oxidation at the constant rate nceria . In practice, the constant flow rate of ceria between the two zones may be realized, for example, by incorporating or forming it into a rotating cylinder that passes through both reactor zones. Alternatively, falling ceria particles may be used in a vertical particle-flow reactor. Finally, it is also conceivable that the two reactor zones are formed by two alternating groups of stationary ceria elements. In this case, only the gaseous atmosphere is switched between a low oxygen partial pressure atmosphere during reduction and a flow of oxidizer during oxidation. The thermodynamic analysis of the model redox system is based on the following assumptions. The system operates at steady-state. Solar radiation is absorbed by a blackbody receiver. Cavities with apparent absorptance/emittance > 0.9 can be readily designed, even with wall emissivity/absorptivity as low as 0.25.43 The reactive material is undoped ceria. Dopants have been identified which increase the achievable non-stoichiometry at given temperature.34 However, due to a lack of thermodynamic data and practical experience with doped ceria, undoped ceria is used as the reactive material in the present analysis. Ceria and gases are at uniform temperatures Tred and Tox in the reduction and oxidation zones, respectively, with

Tred  Tox for isothermal cycling. The preheated gases are further heated inside the reactor to the respective reaction zone temperatures with solar energy before they enter the reaction zones. For two-temperature cycling, ceria is heated/cooled to the respective reaction zone temperature 9


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before it enters the reaction zone. Heat losses from the heat exchangers and piping are expected to be small and are lumped into the heat loss term Qheat loss in the energy balance. All gases are treated as ideal gases. The system is in chemical equilibrium. Variations of the gas composition in flow direction only occur due to chemical reactions, whereas mixing of the gases due to convection and diffusion in the flow direction is neglected, i.e. plug flow is assumed. The results by Keene et al.44 indicate that the gas composition is nearly uniform over the flow cross-section. The dissociation of water and the recombination of products are neglected in the energy balance of HEXox, i.e. the inlet gas compositions remain unchanged inside HEXox. Ceria flow is countercurrent with the gas flow in the reaction zones. Thus, on the reduction side, ceria leaving the reduction zone (SP5) is in equilibrium with the sweep gas entering the reduction zone (SP3), resulting in the largest possible  red for given temperature Tred and initial sweep gas purity pO2 ,3 . At the gas outlet (SP4) of the reduction zone, the sweep gas is in equilibrium with the ceria entering at  ox (SP8). Since  ox corresponds to the highest equilibrium pO2 in the reduction zone for given Tred (Figure 1 (a)), a counterflow arrangement of ceria and sweep gas maximizes the increase of pO2 in the sweep gas and hence minimizes the amount of sweep gas used per mole of oxygen removed from the reduction zone. In the oxidation zone, the equilibrium pO2 in the gas flow ( H 2O , H 2 , and O 2 ) decreases as O 2 is removed from the gas flow by the ceria (cf. eq. (7) below). Hence, minimizing pO2 at the gas outlet of the oxidation zone (SP12) corresponds to maximizing the conversion of the oxidizer into fuel. Since  red corresponds to the lowest equilibrium pO2 in the oxidation zone for given Tox , a counterflow arrangement of the ceria flow and the gas flow also minimizes pO2 at the gas outlet and hence maximizes the

10


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conversion of the oxidizer into fuel. The assumption of counterflow of ceria and gas is equivalent to minimizing the amount of excess oxidizer and based on experimental data in our laboratory (not reported) is consistent with flow through tube filled with ceria pellets. Recognizing the variety of possible flow configurations, we include an analysis assuming perfect mixing of the gases, consistent with the analysis of the temperature swing cycle in Lapp et al.28 The non-stoichiometries of ceria,  red and  ox , are calculated from the chemical equilibrium condition:42 hOo 2    T sOo 2    RT ln

pO2

(4)

po

where hOo 2 and sOo 2 denote the partial molar enthalpy and entropy of O2 in the ceria. Figure 1



(a) shows  T , pO2

 calculated from eq. (4). Ceria is reduced to a nonstoichiometry  

red

as it



equilibrates at Tred with the sweep gas entering the reactor,  red   Tred , pO2 ,3 . Similarly, ceria is oxidized to a non-stoichiometry  ox as it equilibrates at Tox with the steam flow entering the





reactor,  ox   Tox , pO2 ,11 . The oxidation of ceria by steam is modeled by combining thermochemical data for thermolysis of H2O and incorporation of oxygen into vacant lattice sites in ceria: 2H2O  g   2H2  O2

(5)

2 2 CeO2 red  O2  CeO2ox  

(6)

11


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The enthalpy of reaction (5) is slightly temperature dependent, and varies between 500 kJ mol-1 and 504 kJ mol-1 for Tox in the range of 1400K to 2100K. The enthalpy of reaction (6) depends only on the non-stoichiometry  and varies between -972 and -780 kJ mol-1 for  in the range of 0 to 0.25. The steam oxygen activity ( pO2 ) is calculated from the equilibrium condition for reaction (5) at temperature T : 12

K

o p ,R 5

n n1 2  p  T   H2 O2  systemo  nH2O  ntotal p 

(7)

Figure 3 shows the oxygen activity pO2 as a function of temperature. By introducing the extent of reaction (5),  R 5 , the molar flow rates in eq. (7) can be expressed as:

Figure 3. Equilibrium pO2 that establishes when H 2 O is heated to temperature T .

nH2O  nH2O,9  R5

(8a)

nH2  nH2 ,9  R5

(8b)

12


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1 nO2  nO2 ,9  R5  nsink 2

(8c)

ntotal  nH2O  nH2  nO2

(8d)

nH2 ,9  nO2 ,9  0

(8e)

where nH2O,9 is the molar flow rate of water entering the system (SP9). The term nsink in equation (8c) accounts for the O 2 -removal from the oxidizer flow by ceria in the oxidation zone; hence, for SP9-SP11 nsink  0 , and for SP12-SP13 nsink   red   ox  nceria 2 . The extent of reaction (5) is determined iteratively such that eq. (7) is fulfilled. The equilibrium constant K po,R5 T  is obtained as: o  K po,R5 T   T hR T   5 ln  o dT    K p ,R T0   T0 RT 2 5  

(9)

with: T  1  hRo5 T     f hHo 2O g  T0     c op ,H2  c op ,O2  c op ,H2O g  dT  T0 2  

(10)

and:

K

o p ,R 5

  f g o H2O g  T0    T0   exp   RT 0  

For chemical equilibrium between ceria entering and gases leaving the oxidation zone (SP6/SP12), eq. (4) yields pO2 ,12  pO2  red , Tox  . The inlet oxidizer flow rate nH2O,9 is

13


(11)

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determined such that pO2 in the gas mixture at SP12, calculated from eqs. (7)−(8), matches

pO2 ,12 . The gas composition at SP13 is calculated from eqs. (7)−(8) at T0 . The molar flow rate of N2 through the reduction zone is calculated from:   pO2 ,4 pO2 ,3 nO2 ,red  nO2 ,4  nO2 ,3  nN2    psystem  pO ,4 psystem  pO ,3   2 2 

(12)

where: nO2 ,red 

 red   ox 2

(13)

nceria

is the rate of O2-release by ceria in the reduction zone, and pO2 ,4 is the equilibrium pO2 at SP4, pO2 ,4  pO2  ox , Tred  , obtained from eq. (4). Previous analyses assumed that the sweep gas and the released oxygen in the reduction zone are perfectly mixed.28 In this case, the sweep gas flow rate is calculated from:

nN2 ,ideal mixing 

psystem pO2 ,red

nO2 ,red

(14)

where pO2 ,red is the uniform O 2 -partial pressure in the reduction zone. For comparison, the cycle efficiency is recalculated for selected cases using eq. (14) instead of eq. (12). Temperatures T2 and T10 are found from energy balances for the heat exchangers HEXred and HEXox:

 red 



    T    n  h T   h T  

nN2 hN2 T2   hN2 T0   nO2 ,1 hO2 T2   hO2 T0 



nN2 hN2 Tred   hN2

0

O2 ,1

O2

red

14


O2

0

(15a)

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







 ox  nH O,9 hH O l g  T10   hH Ol  T0   nH Ol ,13 hH Og  Tox   hH Ol  T0  ... 2

2

2



2



2

2





 nH2O g ,13 hH2O g  Tox   hH2Og  T0   nH2 ,12 hH2 Tox   hH2 T0  ...





 nO2 ,12 hO2 Tox   hO2 T0  

(15b)

1

The subscipt  l g  in hH2O l g  indicates that H2O may exit HEXox as liquid, gas, or a 2-phase mixture. The enthalpy of liquid H 2 O is calculated at 1 bar. nH2O g ,13 is the molar flow rate of

H 2O that remains in the gas phase at T0 and p0  psystem , and nH Ol,13  nH Og ,13  nH Og ,12 . 2

2

2

The overall energy balance of the reactor is: Qsolar  Qrerad  Qheat loss  Qchem,red  Qgases,red  Qchem,ox  Qgases,ox  Qcool,ox  Qceria  0

(16)

where the solar power absorbed by a blackbody receiver is, Qsolar  Aaperture C G0

(17)

C is the solar concentration ratio and G0  1kW m-2 is the nominal solar flux incident on the concentrator. The reradiation losses from the cavity aperture are: 4 Qrerad  Aaperture Tred

(18)

The heat losses over the reactor walls are assumed to be a constant fraction of the net solar power absorbed by the reactor:



Qheat loss  F Qsolar  Qrerad



(19)

where 0  F  1 is an arbitrary heat loss factor. The energy source due to the chemical reaction in the reduction zone is: 15


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Qchem,red  nceria

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 hOo2  ox ,  red  2

(20)

where: hOo2  ox ,  red  

1 

 red



ox

hOo 2   d

(21)

The energy requirement to heat the sweep gas from the HEXred-outlet temperature T2 to the reduction zone temperature Tred is:







Qgases,red  nN2 hN2 Tred   hN2 T2   nO2 ,2 hO2 Tred   hO2 T2 



(22)

The energy source due to the chemical reactions in the oxidation zone is: Qchem,ox  nceria

 hOo2  ox ,  red  nH2 ,12 hRo5 Tox  2

(23)

QR5

Qoxid

The energy requirement to heat the oxidizer from the HEXox-outlet temperature T10 to the oxidation zone temperature Tox is:



Qgases,ox  nH2O,9 hH2O g  Tox   hH2Og  T10 



(24)

It is assumed that any net heat release from the chemical reactions in the oxidation zone, Qchem,ox , is used to heat the oxidizer. If Qgases,ox  Qchem,ox , the heat released by the chemical reactions is less than the energy needed to heat the oxidizer from T10 to Tox , and solar energy is used to provide the difference. If Qgases,ox  Qchem,ox , the heat released by the chemical reactions in the oxidation zone exceeds the energy needed to heat the oxidizer from T10 to Tox . In this case, the 16


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Energy & Fuels

excess heat is assumed to be cooled actively from the oxidation side of the reactor. This cooling is accounted for in the energy balance by the term Qcool,ox : Q  Qgases,ox  Qcool,ox   chem,ox 0  

if Qchem,ox  Qgases,ox if Qchem,ox  Qgases,ox

(25)

For two-temperature cycling, Qceria accounts for the energy requirement to heat ceria from the lower to the higher cycle temperature:

Qceria  nceria



Tred

Tox

cceria  , T  dT

(26)

hceria

where the molar heat capacity of non-stoichiometric undoped ceria, cceria  , T  , is estimated by extrapolating the correlation given by Riess et al.45 The solar-to-fuel efficiency of the process is defined as the ratio of the higher heating value of the produced fuel to the solar energy input through the reactor aperture:



nH2 ,13HHVHo 2 Qsolar

(27)

Additional energy is needed outside the system to purify the sweep gas (nitrogen). Assuming the sweep gas is obtained by air separation in a commercial cryogenic rectification plant, the electric work needed to produce nitrogen with O 2 impurity of 1 ppm is estimated to be

wsg  16 kJ mol1 .46 Assuming that the electric work is produced by a state-of-the-art dish/Stirling solar power system with a solar-to-electric conversion efficiency of 0.25,47 the additional solar heat rate needed to produce the amount of sweep gas that is used in the process is: 17


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Qsg 



wsg nN2 ,1  nO2 ,1

Page 18 of 43



solar-to-electric

(28)

For comparison, the theoretical minimum work Wsg,min is calculated to recycle the sweep gas, i.e. to decrease the O 2 -molar fraction in the sweep gas from xO2 ,4 to xO2 ,1 . The process path for the calculation of Wsg,min is shown schematically in Figure 4. In process step 1→2, the sweep gas is separated into its components, requiring a minimum work input of: W12  T0 R nN2 ,4 ln xN2 ,4  nO2 ,4 ln xO2 ,4 

(29)

Figure 4. Sweep gas purification process.

In step 2→3, nO2 ,red is removed from the process. Since O 2 has been separated, no work is associated with this step. In step 3→4, the separated N 2 and O 2 that remain in the system are mixed, releasing the work: W34  T0 R nN2 ,1 ln xN2 ,1  nO2 ,1 ln xO2 ,1 

The net work input Wsg,min required to recycle the sweep gas is:

18


(30)

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Wsg,min  W12  W34

(31)

Table 1. Baseline parameters. Direct normal solar irradiance, G0 Solar concentration ratio, C Total pressure in system, psystem

1 kW m 3000 1 atm

Inlet O2 –mole fraction in sweep gas, xO2 ,1

106

Heat recovery effectiveness, Heat loss factor, F Ambient temperature, T0 Flow arrangement

 red ,  ox

-2

0.955 0.2 298 K Counter-flow

4. Results and Discussion The baseline set of process parameters listed in Table 1 has been selected based on the following considerations. A solar concentration ratio of C = 3000 is typical for commercial solar dish concentrators.47 Cryogenic rectification is commonly used to purify nitrogen, and can achieve an O 2 purity of pO2 psystem = 106 .46 The reactor heat loss factor, F, has been selected based on previous heat transfer analyses of hightemperature solar thermochemical reactors.48–51 The gas phase heat recovery effectiveness of 95.5% has been set such that a solar-to-fuel efficiency of 10% is attained with the baseline parameters in the isothermal cycle operated at Tred  Tox  1773K . Effectiveness values ≥ 95% have been reported for regenerators.52–54 All results are calculated for a solar heat input to the reactor of Qsolar  1 kW, but can be scaled to different reactor sizes, as long as the baseline

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parameters remain representative for the scaled reactor size. All results are presented for Tred in the range 1400 to 2100 K,* and with H2O as the oxidizer, except where stated. Isothermal cycling. For isothermal cycling of ceria, ceria remains at constant temperature throughout the cycle, Tred  Tox  Tceria , and no energy is required to heat ceria, Qceria  0 . The solar-to-fuel efficiency  for the isothermal cycle with 100% heat recovery effectiveness,

 red   ox  1 , and a perfectly insulated reactor, F = 0, is plotted in Figure 5 for solar concentration ratios encountered in commercial solar towers,55 commercial solar dishes,47 prototype dish systems,56 and peak concentration ratios of state-of-the art dish systems.47,56 Parameters not varied in the plot are kept at the baseline values listed in Table 1. The operating temperature, Tceria , is limited to 2100 K to avoid a change of phase of ceria.18 Figure 5 shows the high potential of the isothermal cycle to efficiently convert solar energy into storable fuel. For C = 3000 and Tceria = 1773 K, efficiency of 54% is achieved.

*

If, in practice, volatilization of ceria occurs below this temperature, either the reactor design will have to allow for the recovery of the vaporized material, or the reactor operating temperature will have to be limited to avoid volatilization. 20


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Figure 5. Solar-to-fuel efficiency  as a function of solar concentration ratio C, and process temperature Tceria , for isothermal cycling, Tred  Tox  Tceria , ideal heat recovery,  red   ox  1 , and perfectly insulated reactor, F  0 ; all other parameters as given in Table 1; solid curves for H2O splitting, dashed curves for CO2 splitting. Figure 6 shows the values of the individual terms of the energy balance, eq. (16), for C = 3000. Figures 7 and 8 show the corresponding molar flow rates of all species in the reactor, and non-stoichiometries of the ceria after reduction,  red , and after oxidation,  ox . On the oxidation side of the reactor, the net rate of heat release by the exothermic oxidation of ceria and the endothermic water-splitting reaction, Qoxid  QR5 , exceeds the rate of heat transfer required to raise the temperature of the oxidizer from T10 to Tox for any temperature Tceria between 1400−2100 K. As a result, heat must be actively removed from the oxidation zone. Since the heat capacity rate of the gas flow on the hot side of HEXred exceeds that of the gases on the cold side, Qgases,red  0 , and Qsolar is used exclusively to provide the heat needed to reduce ceria in the

reduction zone, Qchem,red , and to compensate for the reradiation losses Qrerad .

21


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Figure 6. Energy balance terms for isothermal cycling, Tred  Tox  Tceria , ideal heat recovery,

 red   ox  1 , perfectly insulated reactor,

F  0 , and a solar concentration ratio of C = 3000;

solid curves for H2O splitting, dashed curves for CO2 splitting.

Figure 7. Molar flow rates, for isothermal cycling, Tred  Tox  Tceria , ideal heat recovery,

 red   ox  1 , perfectly insulated reactor, F = 0, and a solar concentration ratio of C = 3000.

22


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Energy & Fuels

Figure 8. Non-stoichiometries after the reduction and oxidation steps,  red and  ox , respectively, as functions of process temperature Tceria , for isothermal cycling of ceria,

Tred  Tox  Tceria , with the inlet O 2 content in the sweep gas xO2 ,1  106 . With increasing Tceria , Qrerad increases and the net heat rate that remains available for the reduction of ceria decreases. However, as Tceria increases, ceria is cycled at higher nonstoichiometries (Figure 8). Since the enthalpy of reduction of ceria, hOo2 , decreases with increasing non-stoichiometry,42 less energy is needed to reduce ceria per mole of O 2 released. The increase of Qrerad is approximately compensated for by the decrease of hOo2 between

Tceria =1400−1800 K. Hence, the molar rate of O 2 release in the reduction zone, nO2 ,red , shown in Figure 7, remains approximately constant in this range of Tceria . Since, the molar fuel production rate, nH2 , is proportional to nO2 ,red , the efficiency  is also nearly constant for

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Tceria = 1400−1800 K. For Tceria > 1800 K, the increase of Qrerad with Tceria is no longer compensated by the decrease of hOo2 , and the fuel production rate and hence  decrease. Figure 9 (solid curves) shows  for isothermal cycling, with C in the range 1000−10,000, and all other parameters set to the baseline values of Table 1. Comparison of Figure 5 and Figure 9 shows the strong dependence of  on gasphase heat recovery. The increase of  with C is due to the decrease of the reradiation losses,

Qrerad . For the results with C  3000 , the energy balance terms are plotted in Figure 10, and the molar flow rates are plotted in Figure 11. Heating the sweep gas from T2 to Tceria requires 22−57% of Qsolar (Figure 10). Increasing Tceria increases Qrerad but decreases the heat rates to heat the gases, Qgases,red and Qgases,ox , over most of the Tceria range under consideration, resulting in increasing  . Since the equilibrium constant of the water-splitting reaction, K po,R5 T  , and hence pO2 ,4  pO2 ,11 increase with Tceria (Figure 3), nN2 nO2 ,red decreases (eq. (12)), i.e. less sweep gas is used per mole of O 2 removed from the reduction zone, resulting in decreasing Qgases,red . On the oxidation side, the increase of K po,R5 T  leads to a larger ratio nH2 ,12 nH2O,12 , i.e.

to a lower oxidizer flow per mole of produced fuel, which reduces Qgases,ox . For Tceria  1775K , the heat rate to heat the oxidizer exceeds the net heat release by the chemical reactions, Qgases,ox  Qchem.ox , and solar energy input is needed to heat the oxidizer to Tox . For Tceria  1775 K,

the excess energy on the oxidation side of the reactor, Qchem.ox  Qgases,ox , reaches up to 5% of

Qsolar . For comparison, the dashed lines in Figure 9 show the predicted efficiency if eq. (14), with

24


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Energy & Fuels

pO2 ,red = 104 atm, is used instead of eq. (12) to calculate the sweep gas flow rate. Comparison of the solid and dashed curves highlights the importance of efficient use of the sweep gas.

Figure 9. Solar-to-fuel efficiency  as a function of process temperature Tceria for selected values of solar concentration ratio C and for isothermal cycling, Tred  Tox  Tceria ; all other parameter as given in Table 1; solid lines: sweep gas flow rate calculated with eq. (12); dashed lines: sweep gas flow rate calculated with eq. (14) with pO2 ,red = 104 atm.

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Figure 10. Energy balance terms for the baseline case and for isothermal cycling,

Tred  Tox  Tceria .

Figure 11. Molar flow rates, for the curve denoted C  3000 in Figure 9 (baseline case).

26


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Energy & Fuels

Figure 12 shows the energy demand for the production of the sweep gas that is used in the process, for the results shown in Figure 9. Solid curves show the solar thermal energy demand to generate the equivalent amount of electricity needed to produce the sweep gas used in the process by air separation in an existing cryogenic rectification plant. The solar energy demand for the sweep gas production is up to 23-times the solar power input to the reactor (1 kW). In contrast, if the sweep gas used in the process is recycled, the theoretical minimum work associated with the sweep gas separation amounts to less than 1% of the solar power input (dashed curves). Hence, sweep gas recycling is necessary to keep the parasitic energy use for the process low. The dashed curves in Figure 12 follow the same trends as the efficiency curves in Figure 9, because Wsg,min is dominated by the change of nO2 ,4 (eq. (29)), which is proportional to .

Figure 12. Energy demand to produce the sweep gas used in the process, for the results shown in Figure 9: Solid lines: solar energy demand to generate the electricity that is needed to produce the sweep gas (nitrogen) by air separation via cryogenic rectification; dashed lines: theoretical minimum work needed to recycle the sweep gas used in the process.

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Significantly higher efficiencies are achieved when using CO2 instead of H2O as the oxidizer (see Figures S1 and S2 in the Supporting Information). At any given temperature Tceria , the CO2-splitting reaction has a larger equilibrium constant than the H2O-splitting reaction. This fact leads to lower ratio nN2 nO2 ,red and higher ratio nH2 ,12 nH2O,12 , i.e. to lower heat rates to heat the sweep gas and the oxidizer per mole of produced fuel, resulting in higher  . The influence of the inlet O 2 -concentration in the sweep gas, xO2 ,1  xO2 ,3 , on  is shown in Figure 13. The benefit of decreasing xO2 ,1 decreases with decreasing xO2 ,1 . Decreasing xO2 ,1 below 106 has negligible effect on  . Decreasing xO2 ,1 reduces the amount of sweep gas needed per mole of O 2 removed from the reduction zone, nN2 nO2 ,red (eq. (12)), hence reducing Qgases,red and increasing  . The benefit of lowering xO2 ,1 vanishes, once the second term in

brackets in eq. (12) is much smaller than the first term.

28


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Figure 13. Influence of inlet O 2 -concentration in sweep gas and process temperature Tceria on solar-to-fuel efficiency  , for isothermal cycling; parameters not varied in the plot are set to the baseline values listed in Table 1.

The influence of gas-phase heat recovery effectiveness  on  is shown in Figures 14 (a) and 14 (b) for H2 and CO production, respectively. Solid lines are for  red   ox in the range 0.5−0.97, dashed lines are for  red  0.5−0.97 and  ox = 0. The results show the strong influence of gas-phase heat recovery on  . For example at Tceria = 1773 K, increasing  red   ox from 0.5 to 0.955 increases  from 1.1% to 10% for H2 production, and from 2.6% to 18% for CO production. Since nH2O,9 is significantly lower than nN2 , the impact of omitting heat recovery on the oxidation side, HEXox, is studied. The impact of omitting HEXox on  increases with increasing  red , and leads to a substantial reduction of  for  red  0.8 .

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Figure 14. Influence of heat recovery effectiveness and process temperature Tceria on solar-tofuel efficiency  for isothermal cycling: (a) H2O-splitting, (b) CO2-splitting; solid lines:

 red   ox as labeled, dashed lines:  red as labeled,  ox  0 ; parameters not varied in the plot are set to the baseline values listed in Table 1.

The influence of the total pressure in the system, psystem , on  is shown in Figure 15. From eq. (12), with pO2 ,4  pO2 ,11 from eqs.(7)–(8), it follows that within the range Tceria =1400-2100 K, decreasing psystem results in decreasing nN2 nO2 ,red -ratio. Decreasing psystem also decreases

pO2 ,12  pO2 ,3 and hence increases the conversion of the oxidizer, leading to less excess oxidizer. Both trends lead to increasing efficiency with decreasing psystem .

30


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Figure 15. Influence of total pressure psystem and process temperature Tceria on solar-to-fuel efficiency  , for isothermal cycling; parameters not varied in the plot are set to the baseline values listed in Table 1; 1) with psystem  102 atm,  = 0.25 is reached at 1918 K, with psystem  101 atm,  = 0.25 is reached at 2008 K.

Two-temperature cycling. The impact of small deviations from isothermal cycling up to 200 K is considered in recognition of the challenges to maintain isothermal conditions in a reactor and to show the potential benefit of maintaining a higher temperature during reduction. In each cycle, ceria is to be heated from the lower to the higher cycle temperature, requiring the heat input Qceria  0. Figure 16 shows  as a function of Tred for two-temperature cycling with temperature swing Tceria  Tred  Tox in the range  200 K, 200 K  . Increasing Tceria decreases

nN2 nO2 ,red and nH2O,9 nH2 ,13 , due to increasing pO2 ,4 and decreasing pO2 ,12 , respectively. Increasing the temperature swing Tceria increases the thermal energy demand to heat ceria from the lower to the higher cycle temperature. Qgases,red decreases strongly with increasing Tceria , due

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to decreasing nN2 nO2 ,red (Figure 17 (a)). Qgases,ox increases between Tceria = 0 and 50 K, due to the increase in efficiency  and hence of nH2 ,13 , and decreases between Tceria = 100 and 200 K, due to decreasing nH2O,9 nH2 ,13 (Figure 17 (b)). The net result of these trends is that  increases with Tceria in the range 0 to 150 K, and slightly decreases between Tceria = 150 and 200 K. For

Tceria  0,* most of Qsolar is used to heat the sweep gas from T2 to Tred and to compensate for the reradiation losses. Consequently, the fuel production rate and hence Qceria are low. For Tceria in the range −50 to −200 K, Qceria is below 2% of Qsolar .

Figure 16. Influence of temperature swing Tceria  Tred  Tox and temperature Tred on solar-tofuel efficiency  , for two-temperature redox cycling; a positive Tceria corresponds to a higher temperature in the reduction zone than in the oxidation zone; parameters not varied in the plot are set to the baseline values listed in Table 1. *

Although Tox ˃ Tred is undesirable from a thermodynamics point of view, it may occur in practice due to excessive solar radiation absorption in the oxidation zone, insufficient heat exchange between the ceria in the oxidation zone and the gas flow, or insufficient cooling of the oxidation zone.

32


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Figure 17. Heat rates to heat the sweep gas from T2 to Tred (a), and to heat the oxidizer from T10 to Tox (b), in % of Qsolar , for the results in Figure 16.

5. Summary and Conclusions The thermodynamics of continuous fuel production by isothermal redox cycling of solid ceria in a solar reactor has been analyzed. In the model isothermal cycle, ceria was partially reduced in a low O 2 -partial pressure atmosphere created by a flow of purified nitrogen, and reoxidized with a flow of pure steam or carbon dioxide. The nitrogen and steam or carbon dioxide flows were preheated with the hot gaseous reaction products. The results elucidate the influence of operating temperature, pressure, sweep gas purity, gas-phase heat recovery effectiveness, solar concentration ratio, and modest temperature swings on the solar-to-fuel conversion efficiency. With a solar concentration ratio of C = 3000, operating temperature of Tceria  1773 K, and gas-phase heat recovery effectiveness of   95.5%, the conversion efficiency is 10% for hydrogen production and 18% for carbon monoxide production. Significantly higher efficiency 33


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can be reached by (i) raising the cycle temperature to beyond 1773 K, (ii) decreasing the total pressure in the reactor, or (iii) introducing a modest temperature swing of 100 K between reduction and oxidation step. These measures lead to a reduction of the sweep gas flow rate, the heating of which represents a substantial fraction of the energy budget. The efficiency also strongly depends on the heat recovery effectiveness; for example with C = 3000 and Tceria  1773 K, increasing the heat recovery effectiveness from 50% to 95.5%, increases the efficiency from 1.1% to 10% for H2 production, and from 2.6% to 18% for CO production. Increasing the solar concentration ratio beyond 3000 only has a significant impact on the efficiency at operating temperatures beyond 1800 K. Decreasing the inlet O 2 -content of the sweep gas to below 1 ppm has negligible effect on the efficiency. The energy penalty associated with the separation of the nitrogen strongly depends on whether the nitrogen is separated from air, or the sweep gas used in the process is recycled. In the former case, the energy demand for the sweep gas production is several times higher than the solar power input to the process. In contrast, the theoretical minimum work needed to recycle the sweep gas amounts to less than 1% of the solar power input to the reactor. The present analysis shows a possible alternative to the more widely considered twotemperature cycle. While two-temperature cycling is more favorable thermodynamically, the isothermal approach allows for a potentially simplified solar reactor design by eliminating the need for active solid-phase heat recovery, but at the cost of substantially more stringent requirements for affecting a large swing in oxygen partial pressure between reduction and oxidation and for gas phase heat recovery.

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Energy & Fuels

Acknowledgements The financial support by the U.S. Department of Energy’s Advanced Research Projects AgencyEnergy (award no. DE-AR0000182) is gratefully acknowledged. We thank Prof. Sossina M. Haile from the California Institute of Technology and Justin Lapp from the University of Minnesota for discussions of non-stoichiometric ceria cycles. Supporting Information This information is available free of charge via the Internet at http://pubs.acs.org/.

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Nomenclature

Aaperture

aperture area of reactor, m 2

C

solar concentration ratio

c , cp

specific heat capacity, J mol1 K1

F

heat loss factor

G0

direct normal irradiance, W m-2

HHV

higher heating value, J mol1

h

molar enthalpy, J mol1

Kp

equilibrium constant

n

molar flow rate, mols1

p

pressure, Pa

Q

heat rate, W

R

universal gas constant, 8.314 J mol-1 K-1

T

temperature, K

T , T 

dummy variable, K

x

mole fraction

Greek

f g

Gibbs energy of formation, J mol1

h

enthalpy of reaction, J mol1

fh

enthalpy of formation, J mol1 36


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s

entropy of reaction, J mol-1 K-1

Tceria

temperature swing, Tceria  Tred  Tox , K



change in non-stoichiometry



non-stoichiometry



heat recovery effectiveness



solar-to-fuel efficiency

solar-to-electric

solar-to-electric conversion efficiency



Stefan-Boltzmann constant, W m2 K 4



extent of reaction, mol

Subscripts 0

ambient

1,2,…

state point

chem

chemistry

cool

cooling

g

gas

in

inlet

l

liquid

min

minimum

out

outlet

ox

oxidation zone

oxid

oxidation

red

reduction zone

rerad

reradiation 37


Energy & Fuels

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R5

reaction given by eq. (5)

sg

sweep gas

Superscripts average o

standard conditions

Abbreviations HEX

heat exchanger

SP

state point

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