Factors Affecting the Efficiency of Solar Driven ... - ACS Publications

Commentary pubs.acs.org/IECR

Factors Affecting the Efficiency of Solar Driven Metal Oxide Thermochemical Cycles 1. INTRODUCTION The use of thermal energy derived from concentrated sunlight to produce hydrogen or carbon monoxide from water and carbon dioxide, respectively, in thermochemical reactions has long been touted as a pathway to efficient production of sustainable fuels. Many individual thermochemical cycles have been identified1−4 with the majority of research today focusing on two step reactions involving the successive thermal reduction and reoxidation of materials containing oxides of iron5 or cerium.6,7 In many cases the same oxide, under similar operating conditions, can decompose water to produce hydrogen or carbon dioxide to produce carbon monoxide. The ability to convert both water and carbon dioxide into usable chemical intermediates (gaseous fuels) avoiding energy losses from water gas shift or reverse water gas shift is critical to the efficient and cost-effective production of solar-derived liquid hydrocarbon fuels.8−10 Solar thermochemical fuel (H2 or CO) production fundamentally requires two processes: the collection and delivery of concentrated solar energy to a thermochemical reactor, and the conversion of thermal energy to chemical energy (fuel or fuel precursors) within the reactor. Figure 1 graphically displays these steps, associated hardware, and energy flows. In practice a solar concentrator, either a field of heliostats or a parabolic dish (Figure 1A), tracks the sun and reflects its energy, while also focusing it, to a thermochemical reactor (Figure 1B). Inside the reactor, chemical reactions occur that result in the decomposition of water or carbon dioxide into hydrogen or carbon monoxide, respectively, and oxygen, with all other materials recycled within the system (Figure 1C). Energy losses incurred during both collection and conversion are, as we will show, of similar magnitude. A reasonable question to ask is “what level of performance is required of solar thermochemical fuel production systems to demonstrate commercial viability?” A somewhat simplistic but nonetheless discerning answer to this question is that any new technology must offer compelling advantages over existing or competing technologies that solve the same problem. Commercial scale solar fuel production systems currently do not exist. However, many demonstrated and commercially available approaches can convert solar energy to electricity. Coupling one of these technologies to a commercially available alkaline electrolyzer represents a technically feasible, low risk, and commercially deployable means to produce hydrogen from solar energy. Table 1 summarizes several approaches and indicates component efficiencies as well as estimated values for commercially achievable annual average solar to f uel eff iciency AASFE (solar to H2). AASFE is the ratio of the annual average chemical energy (HHV) of the fuel produced to the annual average solar energy incident on the collector. The efficiency values in Table 1 include both collection and conversion losses with the solar to hydrogen efficiency defined as the energy content of hydrogen (HHV) produced by these © 2013 American Chemical Society

systems over a year of operation divided by the solar energy available to the collectors. This annual average efficiency is lower than the design point efficiency evaluated at only one point in time, usually peak performance. We contend that solar thermochemical hydrogen (or carbon monoxide) production technologies must either achieve a minimum level of performance in excess of the values shown in Table 1, or similar performance at a much lower cost, to be considered a competitive alternative. That is, it is our assertion that a reasonable minimum target AASFE of thermochemical processes is 20% for hydrogen or carbon monoxide production. We use a common target for both hydrogen and carbon monoxide production since many thermochemical cycles currently under development can yield either product under similar conditions and energy input requirements; to date we have not seen any evidence that the decomposition of water to produce hydrogen is preferred relative to carbon dioxide decomposition to produce carbon monoxide, or vice versa. We define the thermochemical conversion efficiency as the ratio of the net heating value of the fuel product (the higher heating value (HHV) is used when applicable), ΔHfuel, to the net thermal input, QTC, required to produce it: ηconv =

ΔHfuel QTC

(1)

The collection efficiency is defined as the ratio of heat supplied to the thermochemical reactor, QTC, to the available solar resource, Qsolar,a ηcoll =

QTC Q solar, a

(2)

Energy loss associated with processing of the fuel product, for example, separations, may also be included and is defined as

ηproc =

ΔHfuel,net ΔHfuel

(3)

The multiplicative combination of the thermochemical, collection, and processing efficiencies thus provides an AASFE value for comparison to Table 1. The focus on efficiency, with respect to collection and conversion performance, is appropriate given that in solar energy systems cost typically ties closely to system efficiency. This is because the bulk of capital expenses are associated with the solar collection system, for example, heliostats, photovoltaic modules, and associated installation costs;12 the less efficient the process is the more collection hardware and associated costs are required to produce a unit of product, be it fuel or electricity. As the technology to produce solar fuels becomes more mature, it will be necessary to perform detailed cost analyses to compare different technologies. However, given that solar thermochemical technology is in the Published: January 29, 2013 3276

dx.doi.org/10.1021/ie400193q | Ind. Eng. Chem. Res. 2013, 52, 3276−3286

Industrial & Engineering Chemistry Research

Commentary

Figure 1. A graphical illustration of a solar thermochemical fuel production system based on a parabolic dish collector (A), along with a detailed view of the thermochemical receiver/reactor (B) configured for a two-step, nonvolatile metal oxide cycle producing carbon monoxide from carbon dioxide. The two reactions occur at different temperatures (C) and must be separated to prevent product recombination. Internal heat recovery (recuperation) is used to limit the amount of thermal energy needed for sensible heating of the reactive material. The term δ is the oxygen deficiency, a measure of the degree to which the solid reactant is thermally cycled.

early stages of development, we contend that an emphasis on efficiency offers a more meaningful basis for comparison at this point. In 2005 Kolb and Diver13 conducted a screening analysis of prospective solar thermochemical hydrogen production cycles in support of the U.S. DOE funded Solar Thermochemical Hydrogen (STCH) production program. They evaluated many thermochemical concepts ranging from multistep, relatively low temperature cycles such as Hybrid Cu−Cl14 to two-step, high temperature cycles such as ZnO/Zn.15 The method of evaluation was to first perform an idealized cycle performance analysis to estimate thermochemical efficiency and then to couple the cycle with a suitable solar interface and perform an assessment of solar collection efficiency over the course of a typical operating year. Table 2 provides a summary of the estimated performance of several prospective thermochemical cycles from ref 13. In the Kolb and Diver screening analysis, several cycles, including the two-step, nonvolatile metal oxide cycles, showed

Table 1. Electrochemical Routes to Solar Hydrogen Production. Efficiency Values Are Based on the Annual Average Conversion of Solar Energy on the Primary Collector to Energy Contained (Higher Heating Value (HHV) in the Hydrogen Product technology

solar to electricityb

electricity to hydrogenc

solar to hydrogen

15% 18%

73% 73%

11% 13%

24%

73%

18%

photovoltaic/AEa molten salt tower/ AE dish stirling/AE a

b

Alkaline electrolysis. These are estimated annual average efficiency values.11 cThis performance value is at the high end for an alkaline electrolyzer, is dependent on system operation as well as size, and is based on the higher heating value (HHV) of the hydrogen product.11

Table 2. Estimated Efficiency of Solar Thermochemical Hydrogen Production Processes13 cycle name

temperature [°C]

solar interface

thermochemical efficiency (HHV)a

optical efficiencyb

receiver efficiencyc

annual efficiency

hybrid sulfur sulfur iodine copper chloride (hybrid) zinc oxide two-step MOxe

850 850 600 1800 1800

tower tower tower tower dish

50% 45% 44% 45% 52%

57% 57% 57% 51% 77%

76% 76% 83% 72% 62%

22% 19% 21%d 17% 25%

a Conversion of heat in the reactor to chemical energy measured as HHV of hydrogen. bThe ratio of energy striking the concentrator to energy entering the aperture. cThe ratio of energy entering the aperture to the thermal energy available to the reactor. dThe efficiency of the Cu−Cl cycle is currently under revision and may be reduced by as much as 50%. eNonvolatile metal oxide cycles.

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potential for conversion efficiencies in excess of the more conventional technologies listed in Table 1. All of the thermochemical conversion efficiency estimates include penalties associated with nonideal operation. Today, most R&D efforts in solar thermochemistry focus on the two-step metal oxide cycles. We now turn our attention to these cycles in particular with the discussion centered on a general system-level efficiency analysis for solar thermochemical fuel (CO or H2) production. In doing this we have four purposes in mind: (1) providing rigor in determining technical potential, (2) demonstrating that two-step nonvolatile metal oxide cycles can achieve an ambitious AASFE target, (3) providing a meaningful basis for comparison with alternative solar-to-fuel approaches, and (4) identifying specific areas where targeted research can be most beneficial.

2. SOLAR ENERGY COLLECTION Energy losses associated with solar collection occur along the path from available solar radiation to solar heat delivered to the thermochemical reactor. Specifically, collection system inefficiencies are associated with solar resource availability and utilization, operational losses, optical losses, and receiver thermal losses. There is no single ideal solar collection system, and the specific configuration used in a given application is dependent on technical and economic factors. For the purpose of facilitating a general discussion of solar thermochemical fuel production, we consider a parabolic dish collector (the most optically efficient collection platform) located in an area with excellent solar resource, Daggett, CA. In this way, we are essentially defining the most optimistic solar collection scenario. The amount of solar energy available for collection is based on geographically specific hourly data available in Typical Meteorological Year (TMY2) data files. The fraction of this energy input utilized by the system depends in part on that resource exceeding a minimum value of direct normal insolation (DNI) needed to offset thermal losses and parasitic loads within the system. This criterion is a function of thermal radiation losses at the operating temperature of the thermal reduction reaction, additional parasitic losses (e.g., pumping), and the collector area and optical efficiency. We have based our parabolic dish configuration on precommercial units produced by Stirling Energy Systems, which were under evaluation at Sandia National Laboratories. These units have a collection area, Acoll, of 88 m2 and an aperture diameter of 15 cm. For a thermal reduction temperature of 1500 °C, the minimum insolation required for system operation is 142 W/m2. This is the DNI needed to overcome optical and radiative losses in the system; that is, operating the system at a DNI less than this value does not result in net fuel production. We take a conservative value of 300 W/m2 in our analysis to account for additional parasitic losses. At Daggett, and at similar locations with an excellent solar resource, roughly 95% of the available solar energy is above the minimum threshold of 300 W/m2. The variation of DNI at Daggett on the Spring Equinox (March 20th) is shown in Figure 2. The DNI fails to meet the minimum insolation value in the early morning, late afternoon, and during periods of extensive cloud cover. Operational losses are associated with the layout of the field and its operability. Four factors contribute to operational losses: equipment availability, blocking and shading (B&S), wind outages, and continuous versus batch operation. The result of these performance-limiting factors is that not all of the solar resource above the minimum DNI is actually collected. Equipment availability for dish concentrators includes outages

Figure 2. The DNI in Daggett, CA, on March 20th based on hourly TMY2 data.

associated with maintenance. We assume a value of 97%, meaning that the system is operating for 97% of the time that the conditions are suitable for operation, based on past dish development experience at Sandia National Laboratories. The blocking of one concentrator by another also reduces the amount of sunlight collected. This parameter depends on field layout. We assume 2% of the solar energy beyond the minimum value is lost to blocking on an annual average basis. All CSP systems stow automatically when the local wind speed exceeds a value beyond which could damage the system. Stowing when the solar resource is available represents an energy loss. The wind outage parameter is geographically dependent. Assuming a conservative wind stow value of 25 mph this represents a loss of 1% of the energy above the minimum DNI. The mode of operation of the thermochemical reactor can also lead to losses. For example, systems that function in batch mode may be taken off-sun during the exothermic reoxidation reaction (see Figure 1C and text below for a description of the two-step process). In this mode, the solar energy above the minimum DNI during the off-sun reaction period is wasted. A batch flow system might minimize this loss if the time spent off-sun is relatively short, that is, the reaction kinetics of the reoxidation reaction are fast relative to thermal reduction, which is generally not the case. Conversely, a continuous flow reactor can utilize all of the solar energy above the minimum DNI since it remains on-sun at all times. Grouping the operational losses together and assuming the reactor operates continuously, the primary concentrator can intercept approximately 94% (0.94 = 0.97 × 0.98 × 0.99) of the solar energy available above the minimum DNI of 300 W/m2. Optical losses are associated with transferring solar energy from the primary concentrator into the aperture of the receiver/ reactor. We include the following terms in the optical loss calculation: • Primary concentrator reflectivity: The typical reflectivity of a modern thin glass mirror is 93%.16 • Secondary reflectivity: Some concepts may need to use secondary concentrators or reflectors (e.g., beam down platforms). Generally, the reflectivity of secondary concentrators is approximately equal that of the primary concentrator, hence, we assume 93%. • Soiling: The concentrators accumulate dirt over time and it would be likely unrealistic to clean continuously. As a 3278



Commentary

important to also consider the field packing density, which is the ratio of collection area to total field area, and is generally above 20% for parabolic dishes. If a central receiver (power tower) collection platform is used instead of a parabolic dish, the collection efficiency will be lower on an annual basis due to several factors. Among these factors is the cosine loss incurred at the primary concentrator (heliostat), atmospheric attenuation, and the nonideal shape of the collection field (it is not a paraboloid of revolution, while a dish concentrator is). The cosine loss refers to a decrease in the optical efficiency of the field resulting because heliostats do not point directly at the sun (unlike a parabolic dish), but rather at a position between the sun and the central receiver. Martinek et al. show that the collection efficiency of a multicavity central receiver can approach 40%, or about 30% less than our estimate here for a parabolic dish collector.18 Pitz-Paal et al. present results for a heliostat field optimization developed specifically for the unique characteristics of solar thermochemical processes (in contrast to previous work focusing on solar electric systems). They show that ηcoll = 30% is possible for a zinc oxide process operating at 2000 K at a scale between 1 and 100 MWth.19

result, a 5% (on average) reduction in the reflectivity of the primary concentrator is to be expected. • Window reflection: Many thermochemical receiver/ reactor concepts require a controlled atmosphere and utilize fused silica (quartz) windows on the aperture in order to isolate the reactor from ambient conditions. The transparency of a window is not perfect, and only ninetyfive percent (95%) of the concentrated light incident on the window generally passes through it. This level of performance is achievable with an antireflective coating.17 • Intercept: Aperture sizing is based on a trade-off between maximizing intercept (how much of the concentrated light falls within the aperture) and minimizing thermal losses. A larger aperture allows more sunlight into the reactor, but also allows additional losses from thermal radiation. An aperture optimally sized for 1500 °C operation on an 88 m2 dish intercepts 95% of the energy passing through the window. • Tracking: Inaccurate tracking results in spillage of useful energy. On the basis of operational experience, this is approximately a 1% loss for modern parabolic dish systems. The combination of the optical losses reduces the amount of solar energy reaching the aperture to ηopt = 79% of that incident on the primary concentrator in a system that does not include secondary optics. Receiver losses include thermal losses from the receiver to the surroundings in the form of conduction, convection, and thermal radiation. In the case of a well-insulated thermochemical receiver/reactor with a quartz window on the aperture, it is reasonable to assume that convection and conduction losses are negligible. Thermal radiation losses are calculated at the operating temperature of the thermal reduction reaction. In the case of a two-step metal oxide reaction this temperature can be 1500 °C or higher, although lower temperatures would be preferred for operational purposes. At 1500 °C and a cavity emissivity of 0.9, 83% of the energy entering the aperture of the receiver/reactor (on an annual basis) remains inside the device and is available for conversion into chemical energy. This estimate is based on an hourly energy balance (summed over an entire operating year) that accounts for variations in DNI and ambient temperature; low DNI leads to relatively lower receiver efficiency (heat available/heat input), and vice versa. When considering all of the collection losses together in our “ideal” optical configuration we find that, on an annual basis, 59% percent of the available solar resource is converted into heat that is available to produce chemical energy within the thermochemical reactor. The total collection efficiency is a product of individual losses.

3. THERMOCHEMICAL CONVERSION MODEL DEVELOPMENT The thermochemical reactor operates by dividing a difficult and thermodynamically unfavorable reaction (e.g., water or carbon dioxide thermolysis) into two more favorable reactions based on the cyclic reduction and reoxidation of a metal oxide.

Typically heat is applied at high temperature (TTR) to drive the endothermic reduction reaction R.1; the reoxidation reaction R.2 is carried out at a lower temperature (TOX) and is mildly exothermic so does not require external energy input. The term, δ, is the degree of oxygen deficiency of the reduced metal oxide relative to the oxidized state as the reactive material is cycled through R.1 and R.2. It is a direct measure of the capacity of the reactive material to produce fuel, on a per cycle basis. The net output of the reaction cycle R.3 is a fuel that can be used to do work. Thermochemical reactors can be thought of as heat engines producing chemical fuel instead of mechanical work, but subject to the same thermodynamic constraints as thermal power cycles (i.e., Carnot limitation). In practice, the total energy demand of a thermochemical reactor per mole of fuel produced, qTC shown in eq 5, is, at a minimum, a function of (a) the energy demand of the thermal reduction reaction (qTR), (b) the sensible energy input (qsens) needed to heat the reactive material from the reoxidation reaction temperature, TOX, to the reduction reaction temperature, TTR, and if one elects to do so, (c) the energy required to operate the thermal reduction reaction at reduced oxygen partial pressure, qp,eq. Although reduced pressure operation is not a necessity, it is generally common practice, used to promote the reduction reaction, that is, to increase δ for a given TTR. qp,eq is the thermal equivalent of this pump work input. This thermal input is a consequence of our assumption that all energy inputs will be provided by a solar flux.

solar > DNI min solar primary net heat delivered = · · solar available solar available solar > DNI min solar in aperture net heat delivered · solar on primary solar in aperture (4)

ηcoll (59%) = ηres(95%) ·ηoper (94%) ·ηopt(79%) ·ηrec(83%) (5)

Note that the basis for the aggregate collection efficiency is the collection area of the solar concentrator, and not the total field area. To compare total solar energy collection from a field of parabolic dishes to, for example, a field of fuel crops, it is

qTC = qTR + qsens + qp,eq 3279

(6)



Commentary

additional temperature in the work producing thermochemical heat engine is T0, ambient temperature. An accounting of energy flows (kJ/s) at the system boundary for the case of minimum energy input (Wp = 0) yields

Other energy inputs may also be included, but these are in general much smaller in magnitude. We consider the energy associated with product separation, which can be significant in the case of CO2 decomposition to produce CO, as part of the overall system below (section 4). The minimum energy input required to produce a mole of fuel product, that is, assuming no energy is required for pumping or sensible heating, is the enthalpy change of the thermal reduction reaction. This is a known quantity, as a function of temperature and, to a lesser extent, the degree of reduction (i.e., x−δ in R.1 and R.2, as defined by the equilibrium with a given oxygen partial pressure) for commonly used reactive materials such as cerium oxide and iron oxide.20 In both cases, the enthalpy change of thermal reduction exceeds that of carbon dioxide or water thermolysis by a considerable margin, indicating room for improvement using better designed materials; however, the enthalpy change of thermal reduction of any hypothetical viable material is constrained by the laws of thermodynamics.21,22 (The heat of reaction for water thermolysis is 251 kJ/mol-H2 while the enthalpy change of thermal reduction of cerium oxide at 1500 °C and PO2 = 1 × 10−6 atm is 401 kJ/mol-H2.) To illustrate this point we present, in Figure 3, a construct that includes a two-step

QTR = Q OX + Q FC + WFC

(7)

An exergy balance of the system results in the following expression. ⎛ ⎛ T ⎞ T ⎞ QTR ⎜1 − o ⎟ = Q OX ⎜1 − o ⎟ + WFC TTR ⎠ TOX ⎠ ⎝ ⎝

(8)

The first two terms in eq 8 account for the exergy entering the thermochemical reactor (at the thermal reduction temperature), and the exergy leaving the reactor (at the reoxidation temperature). Both eqs 7 and 8 include a term for the work production from the fuel cell defined as WFC = n fuel ̇ ΔGfo

(9)

where ṅfuel is the molar flow rate of fuel into the fuel cell and ΔGof is the Gibbs free energy of formation at standard pressure of carbon dioxide (or water). Combining eqs 7 through 9 and further setting QFC = ṅfuelToΔsof , QTR = ṅfuelΔHTR leads to an expression for the minimum enthalpy change per mole of fuel product of a hypothetical material with thermal reduction at TTR, reoxidation at TOX, and oxygen partial pressure of 1 atm during thermal reduction of PO2. QTR n fuel ̇

(

ΔHfo = ΔHTR = qTR =

To TOX

(

To

)

− 1 + ΔGfo

1 TOX

−

1 TTR

)

(10)

ΔHof is the enthalpy of formation of the fuel cell product (either water or carbon dioxide) at To. Equation 10 shows that the minimum enthalpy change of the thermal reduction reaction is achieved for materials that operate with the maximum separation between the thermodynamically defined TTR and TOX during thermal cycling. The lower limit on the enthalpy change of thermal reduction happens when TOX = To and TTR is equal to the temperature at which the change in the Gibbs free energy of reaction for water (or carbon dioxide) decomposition is zero. In other words, the maximum efficiency is characterized by the exotherm of the reoxidation reaction as well the endotherm of the reduction (they are not independent of one another) and therefore the maximum theoretical efficiency is defined by the thermodynamics of the thermolytic reaction of the gas (H2O or CO2) in question. The second term in eq 6 accounts for the common case when the reduction reaction is carried out below TTR. (Since the fuel cell in Figure 2 is not included in the actual thermochemical reactor system, the pump work must be supplied externally.) This might be advantageous or necessary for example if TTR is beyond the material limit of a given reactor concept. In this case, decreasing the reactor pressure, and thus the oxygen partial pressure, can enable thermal reduction at a lower temperature. Alternately, decreasing the oxygen partial pressure will increase the oxygen deficiency, δ, at a given temperature. Essentially, reducing the thermal reduction pressure enables a given reactive material to liberate more oxygen during thermal reduction and hence have the capacity to produce more fuel during reoxidation. Figure 4 graphically illustrates both of these applications of reduced thermal reduction pressure.

Figure 3. An illustration of a work producing thermochemical heat engine.

thermochemical cycle and a reversible fuel cell. The presence of the fuel cell is computationally expedient as it allows the combined system to be modeled as a work producing power cycle; the fuel cell would not be present in an actual thermochemical fuel production system. We include both steps of the thermochemical cycle and also include a pump for the reduction side, which we consider below, although it is not required in the derivation of the minimum enthalpy term. The evaluation of the minimum enthalpy change of thermal reduction for a hypothetical reactive material requires both an energy and exergy balance to be performed at the system boundary. In the following analysis, we assume that the temperature of heat input, TTR, and that of heat output from the reoxidation reaction, TOX, correspond to the temperatures at which the change in Gibbs free energy of these reactions is zero. That is, for derivation of the enthalpy term, these are thermodynamically defined temperatures, which do not necessarily coincide with operating temperatures. The one 3280



Commentary

heats, Cp, for both, taken as the average between TH and TL. Thus, Qsens may be determined from qsens =

(1 − εR ) Cp(TH − TL) δFR

(13)

To simplify this further, we introduce a new parameter, the utilization factor, χ, which groups δ, εR, and FR into a convenient and meaningful figure of merit defined as χ=

For simplicity, we do not consider sweep gases as a practical means for reducing the oxygen partial pressure as Lapp et al.23 and Ermanoski et al.24 have shown sweep gases to be energetically costly. The thermal energy input required to supply the pump work for operation at subambient pressure is qp,eq RTpump 2ηh − w

ln

Po PO2

qTC =

⎛ Po ⎞ + R ln⎜ P ⎟ ⎝ O2,H ⎠

To TOX

1 Cp(TH − TL) χ

(

)

− 1 + ΔGfo

1 To T OX

+

(14)

RTpump 2ηh − w

−

ln

1 TTR

Po PO2

)

+

1 Cp(TH − TL) χ

(15)

assuming that the sensible energy required to heat and cool the reactant and product gases is recuperated and roughly balances. (The exothermic heat from reoxidation (R.2) is not available for reuse in the cycle (i.e., to reheat the oxide for reduction) as it is liberated at the lowest temperature in the cycle.) Thermal energy in the reactor not converted to fuel must be actively removed from the reactor. For example, the reactive material may be cooled with excess CO2 or H2O flow prior to reoxidation. The heat carried away by these coolants is a loss and not recovered in this analysis. Similarly, we do not assume that the thermal energy content of the product oxygen stream is recoverable.

ΔHTR

ΔHTR TTR

(

ΔHfo

(11)

where R is the molar gas constant, Tpump is the operating temperature of the pump hardware, PO2 is the reduced oxygen partial pressure, Po is 1 atm, and ηh−w is the conversion efficiency of heat to pump work. Finally, we consider the third term in eq 6. The cycle requires sensible heat, qsens, to increase the temperature of the metal oxide reactant, along with any inert support, from TOX to TTR. As already indicated, the temperature of heat addition, TH, may be lower than TTR. We must also acknowledge that the temperature of heat rejection, TL, may be greater than TOX, for kinetic or other reasons. Thus, we define the actual operating temperatures as TH and TL. TH relates to the thermodynamically defined reduction enthalpy, temperature, and oxygen partial pressure through TH =

qsens =

With the assumption that FR is 1 (e.g., cerium oxide), the limits of the utilization factor are 0 ≤ χ ≤ ∞ as 0 ≤ εR ≤ 1, and 0 ≤ δ ≤ 0.5. More practically 0 ≤ εR ≤ 0.95, and 0.001 ≤ δ ≤ 0.5; therefore the region of interest is 0.001 ≤ χ ≤ 10. The utilization factor couples materials and reactor considerations in a quantitative and consequential manner. Maximizing efficiency requires minimizing qsens and hence, from eq 14, maximizing χ. That is, to maximize efficiency, thermochemical cycles based on materials with small values of δ must also have high recuperation values, εR. In the absence of recuperation, maximizing δ becomes critical. Furthermore, eq 13 includes an important subtlety; δ is not an independent variable and remains a function of the thermodynamics of the solid and the partial pressure of oxygen. Combining all of the preceding terms into a single expression gives the total thermal energy requirement for each mole of product gas. (These are the energy inputs common to most thermochemical reactors. Some concepts include additional energy inputs such as solar heating of the exothermic reoxidation reaction24,25 that must also be accounted for.)

Figure 4. In the absence of pressure reduction, the thermal reduction reaction is defined by line 1 to point a where it intersects the horizontal line corresponding to ΔGTR = 0. If the oxygen partial pressure is reduced, it is possible to run the thermal reduction reaction at a lower temperature while achieving the same gas phase equilibrium composition (and δ) by following line 1′ and intersecting ΔGTR = 0 at point b. Reduced pressure operation may also be used to increase the equilibrium fraction of oxygen (and δ). This is the case when following line 1′ to point c; the temperature of thermal reduction in this case is TTR. The reoxidation reaction is shown as line 2, while thermolysis is shown as line 3.

qp,eq =

δFR ; (1 − εR )

(12)

4. SYSTEM LEVEL ANALYSIS Equation 15 may now be combined with the solar collection analysis and applied to determine the potential AASFE for a given set of operational assumptions, that is, to map out the performance space of solar thermochemical reactors based on two-step, nonvolatile metal oxide chemistry. To begin, we define the thermodynamic behavior of a candidate material through the specification of TTR, TOX, PO2, and the utilization factor, χ. We further specify, for simplicity, that TH = TTR and TL = TOX (i.e., that the reactor is operated such that the change in Gibbs free energy for the reoxidation and reduction reactions is zero). The specification of these parameters allows the calculation of qTC

where PO2,H is the oxygen partial pressure at which the reactor is operated. The additional work that must be added to the system for the reduction case has already been considered in the second term. For the reoxidation case, the additional work will be treated below in the form of a separation. The amount of solid that must be heated in the reactor is a function of the redox extent per cycle, δ, and the molar fraction of the solid material that is reactive (as opposed to inert, for example in the case of a carrier phase), FR. The sensible energy demand is also a function of the effectiveness of sensible heat recovery (recuperation, εR) between the reduced and reoxidized solids. For simplicity, we assume equal and constant specific 3281



Commentary

consideration, is dependent on χ, which is treated here as the independent variable. Therefore, each curve defines the efficiency achievable with a particular material or family of materials as a function of utilization, which encompasses a combination of materials and reactor characteristics. Figure 5A illustrates several key points. First, the figure verifies the strong dependence of the efficiency on the utilization factor. For very large utilizations (i.e., as recuperation effectiveness approaches unity) only the heat of reduction, qTR, limits the maximum achievable efficiency. This can be seen in the flattening of the curves at high utilizations. Hence, for high utilization factors, efficiencies are best for materials that operate over the largest temperature swing wherein the endotherm is smaller. Simply put, high utilization minimizes sensible heat losses. The opposite is true for the low utilization regime. Then the magnitude of the sensible heat loss becomes significant relative to the endotherm, which favors smaller temperature swings. As an example of the interplay of reaction extent and recuperation, and the importance of recuperation when δ is small, consider the TL = 100 °C curve in Figure 5A. If a particular material has a δ equal to 0.05 under the conditions of this curve (a realistic value for commonly studied materials), then decreasing the recuperation from 95% (χ = 1) to just 50% (χ = 0.1) decreases the possible efficiency from 65% to only 19%. Alternately if δ = 0.5 could be achieved, then the efficiency could reach 65% (χ = 1) with only 50% recuperation. In Figure 5B, the effects of reducing the operating pressure to drive the reaction as described above are examined with TH set at 1500 °C and TL at 1150 °C. We assume an isothermal pump operating at 100 °C; that is, the gases are cooled to minimize pump work, and the efficiency of converting heat to pump work is 20%. For a given material pumping may or may not be beneficial. If pumping does not appreciably change the oxygen deficiency, δ, then the performance at reduced pressure can be estimated from Figure 5B by following a vertical line down from the 0.21 atm curve to the point where it intersects the curve corresponding to the oxygen partial pressure during thermal reduction. Pumping is, in this case, a losing proposition. Conversely, if oxygen deficiency increases with reduced pressure, as is typically the case, so does the utilization factor, thus reducing the sensible energy demand and improving performance. As an example, consider a reactor operating at PO2 = 0.21 atm with a fixed level of sensible energy recuperation of εR = 20% and with δ = 0.02 (χ = 0.025). This point is indicated in Figure 5B as point 1 and corresponds to an AASFE of 9%. Assuming further that δ = 0.5 for this particular material when PO2 is reduced to 1 × 10−6 atm (point 2 in Figure 4B), the AASFE increases to nearly 20% despite the penalty incurred for providing pump work to the reactor. Taken together, the results shown in Figure 5 panels A and B support the conclusion that an AASFE greater than 20% may be achieved through the combination of a well-designed reactor (high recuperation), favorable material thermodynamics (reaction extent), and operation of the thermal reduction reaction at reduced pressure. This is true even for reactive materials that might have very large heats of reduction. In Figure 5, TL= 1150 °C corresponds to ΔHTR = 747 kJ/mol CO, much larger than that of ceria (Table 3) or the ferrites commonly used. This is something of an upper limit as it is unlikely that any material having a higher reduction endotherm will achieve an AASFE much in excess of 20%. Many of the parameters used in the development of Figure 5 are listed in Table 3.

and ηconv via eq 1. Both of these parameters are assumed to be independent of DNI. That is, the operating conditions within the reactor, and the extent of recuperation, do not vary with DNI although the flow of reactants and products do. The collection efficiency for all subsequent results is assumed to be a constant value of ηcoll = 59%, consistent with location specific reactor operation at TH = 1500 °C averaged over an operating year. Finally, the energy expended to separate product carbon monoxide from carbon dioxide in the exhaust stream of the reactor is accounted for through a processing efficiency, ηproc = 94%. This quantity represents the net energy content of the fuel stream after separation losses are subtracted, and is based on the minimum work needed to separate carbon monoxide from carbon dioxide assuming a 1:3 mixing ratio. A detailed discussion of CO/CO2 separation losses in solar fuel production system had been developed in refs 9 and 10. The variation of both thermochemical conversion efficiency and AASFE as a function of the utilization factor is shown graphically in Figure 5 panels A and B for a range of operating conditions. To be clear on what Figure 5A represents, each set of thermodynamic operating conditions (TTR, TOX) fixes a value for the endothermic heat of reaction for the metal oxide, ΔHoTR. By virtue of setting PO2 to Patm, there is no pump work required to drive the reaction in this case. The remaining term in the efficiency calculation, which derived from the sensible heat

Figure 5. (A) Reactor and system performance variation for a range of reoxidation reaction temperatures with PO2 = 0.21 atm, and (B) the effect of reduced oxygen partial pressure during thermal reduction for TH = 1500 °C and TL = 1150 °C. 3282



Commentary

Table 3. The Energy Burdens within a Solar Thermochemical Fuel Production System for Several Possible Reactive Materialsa reactive materials Figure 5A

TTR/Tox [°C] PO2 [atm] oxygen deficiency [δ] recuperation extent [εR] total collection eff. [ηcoll] QR for χ = 1 [kJ/mol CO] Qsens for χ = 1 [kJ/mol CO] Qp,eq for χ = 1 [kJ/mol CO] thermochemical eff. [ηR] separation penalty [ηsep] total efficiency, ηcoll·ηR·ηsep [AASFE] a

Figure 5B

Figure 6 CeO2, 1 × 10−3 atm

CeO2, 1 × 10−6 atm

model, 0.21 atm 1500/1150 0.21

100 °C

800 °C

1150 °C

0.21 atm

1 × 10−3 atm

1 × 10−6 atm

CeO2, 0.21 atm

1500/100 0.21

1500/800 0.21

1500/1150 0.21

1500/1150 0.21

1500/1150 1 × 10−3

1500/1150 1 × 10−6

1500/1150 0.001

1500/1150 1 × 10−3

1500/1150 1 × 10−6

0.007

0.025

0.093

1

0.97

0.91

59%

59%

59%

59%

59%

59%

59%

59%

59%

59%

313

458

747

747

747

747

452

476

452

401

120

60

30

30

30

30

120

91

47.8

51.4

0

0

0

0

54

107

54

0

53.6

107

65%

55%

36%

36%

34%

32%

45%

50%

51%

51%

94%

94%

94%

94%

94%

94%

94%

94%

94%

94%

36%

30%

20%

20%

19%

18%

25%

28%

28%

28%

Experimental data for the thermodynamic properties of ceria were taken from ref 24, and are based on the work of Panlener et al.20

In recent years a considerable amount of attention has been focused on the use of cerium oxide or doped cerium oxide as a reactive material suitable for two-step thermochemical production of either carbon monoxide or hydrogen.6,23−25 Ceria is relatively stable at temperatures up to 1500 °C and it does not require an inert support as do compounds based on the chemistry of iron oxide. However, the achievable reaction extent, δ, is relatively low compared to other materials at the conditions suitable for solar thermochemical reactors. The plot in Figure 6 shows the performance range possible using ceria as the reactive material. This plot was generated by modifying eq 15 to include

experimental data for the enthalpy change of thermal reduction, QR, and the oxygen deficiency δ in eq 12. Each curve in Figure 6 has a fixed value of QR and δ and the utilization factor is only a function of recuperation extent, εR. The values of these parameters are listed in Table 3. In a reactor without recuperation, a pure ceria reactant can achieve a maximum thermochemical efficiency of roughly 25% (at 1 × 10−6 atm) for the conditions simulated in Figure 6. This level of performance is not sufficient to achieve the 20% minimum AASFE target; recuperation is required. When operating in air, εR must be greater than 0.96. Operation at reduced oxygen partial pressure helps in the case of ceria, with a minimum required εR of 0.88 and 0.56 at 0.001 atm and 1 × 10−6 atm, respectively. There are practical constraints that limit the amount of pressure reduction that can be implemented in a solar fuel production reactor. Principal among these is the large volumetric flow rate (pumping speed) required for oxygen removal at low pressure. We discuss this in detail in another publication,24 and conclude that for a system size at the kilowatt scale (thermal basis) or beyond it is likely that the minimum allowable thermal reduction pressure will be in the range of 0.01 to 0.001 atm; any reactor using ceria as the reactive material must therefore be capable of recuperation near εR = 0.9 (90% sensible energy recovery) to be competitive with more conventional approaches to producing solar fuels, which also implies a need for new materials discovery.

5. DISCUSSION AND CONCLUSIONS The sustainable production of chemical fuels from solar energy can be accomplished in a number of ways. At a high level, the most important differentiation between various approaches is the annual average conversion efficiency of solar energy to chemical energy. Although this metric does not explicitly include cost, it does directly relate to the amount of collection area and associated conversion hardware needed to produce a certain quantity of fuel output; capital expenditures are the principal cost

Figure 6. The performance envelope for carbon dioxide splitting in a two-step solar thermochemical cycle with a cerium oxide reactive material. (Curves a, b) reduction in air (δ = 0.007); (curves c,d) reduction at 0.001 atm (δ = 0.025); (curves e,f) reduction at 1 × 10−6 atm (δ = 0.093). Points a, c, and e correspond to zero recuperation. Points b, d, and f correspond to 100% recuperation. The curve labeled “model” represents the predicted performance using reaction enthalpy as per eq 15. The operating conditions are the same as for curves a and b. 3283



Commentary

seemingly straightforward considerations for the reactor should at least include operating on-sun continuously, minimizing pathways for thermal and optical losses, and minimizing “parasitic” energy inputs to the thermochemical reactor, for example, pumps and purges. As shown herein, however, the addition of work to the reactor to reduce the operating pressure for the reduction reaction, for example, can provide a system benefit, again illustrating the complex connectedness of material and reactor. The Palette of Potential Materials Is Large and Largely Unexplored for This Application. Regarding materials, the examples included herein demonstrate that there is no single definition of an ideal material for achieving a desired efficiency. Nonetheless, there are some general insights to be drawn. At the simplest level, one should be aware that the stoichiometric reactions traditionally written to describe thermochemical conversions are a convenient, but misleading oversimplification. Although the conversion of one line compound to another is an attractive feature from the point of view of utilization (large δ), this frame of reference unnecessarily limits the pool of candidate materials. Materials that are capable of being reduced and reoxidized incrementally can potentially be implemented with relatively high efficiencies, provided the reactor is effective in internally recuperating sensible heat. Basic Thermodynamic Considerations for the Materials Reveal Important Trade-offs. The examples herein illustrate that theoretical upper limit on efficiency is greatest when the endothermic heat of reduction is smallest. As shown, this corresponds to materials that require a wide operating window (i.e., a large difference between TL and TH, smaller ΔS for R.1) to achieve a given level of conversion. However, to realize this advantage requires high utilization factors. That is, the cost for a high maximum theoretical efficiency is an increasing demand for high extents of reaction and/or very effective recuperation, which derives from the large sensible heat demand. Finally, regarding pumping, it is generally true that adding energy to the system as work rather than directly as heat will decrease the efficiency for a given material. When comparing one material to another though, the material that requires pumping may be a better choice overall. In this case, the smaller the reduction endotherms for the materials in question, the less likely that the choice to pump will be the more efficient option. Materials Considerations Must Extend beyond Thermodynamics. A minimum set of additional considerations for materials would include reaction kinetics and materials durability, which includes considerations such as volatility, chemical and physical compatibility with other reactor components (e.g., solid/solid reaction, thermal expansion, etc.), and physical degradation associated with thermal cycling. Reaction kinetics are tied directly to reaction extent and are particularly relevant. As thermodynamic considerations (maximum efficiency and reaction extent) drive one toward widening the temperature difference, and in particular decreasing TL (TL ≥ TOX), it becomes more and more likely that the reoxidation reaction R.2 will be kinetically limited. The use of catalysts to improve reaction rates is a possibility, but a challenging prospect given the high temperature generally required for thermal reduction. In light of this, it is likely that high surface area materials and reactor designs having flexibility with respect to the time allotted for individual reactions will be necessary to take full advantage of the thermodynamic improvements for advanced reactive materials. On the other hand increasing TH (TH ≤ TTR) is likely to have kinetic benefits. However, increasing TH will

driver for solar energy technologies across platforms. Hence, although thermochemical fuel production technologies offer the potential for relatively efficient operation, it is important to understand that these technologies should be evaluated against more conventional and low risk approaches based on electrolysis; that is, thermochemical routes to solar f uels must achieve a systemlevel AASFE ef f iciency in excess of 20% to be considered a viable alternative. Conclusions derived from our analysis in light of this metric are summarized below. Thermally Efficiency Reactors Are a Necessity. To meet the goal, one should not ignore the upstream components, and care should be taken to minimize collection losses for example by limiting the number of components in the optical pathway (reflectors, windows). That said, the upstream solar collection and concentrator technology is relatively mature and there is little opportunity for making large improvements to these components that will significantly impact the overall efficiency (or relax the thermal efficiency requirement for the reactor). The Necessary Efficiencies Are Challenging, but Plausible. Our analysis shows that meeting the viability metric requires a reactor thermochemical efficiency of at least 36% (heat to chemical energy in the reactor). While clearly a challenging problem, our analysis also suggests that solar fuel production with thermochemical systems could potentially exceed this metric and ultimately provide more than 30% system efficiency (solar to fuel) on an annual average basis using a parabolic dish collector. Reactors and Materials Should Be Considered As a System; Improvements Are Needed in Both. Reaching the 30% system level efficiency will require both advanced materials and reactors as more than 50% of the net heat input to the reactor must convert into chemical energy on an annual basis to reach the aggressive 30% system AASFE mark. As we have shown, the conversion of solar-derived heat into chemical energy is a strong function of both the thermodynamic behavior of the reactive material, and the reactor in which the thermochemical cycle is implemented. Utilization Factor Is a Valuable Metric; Recuperation and Reaction Extent Are Key Areas for Focus. At the highest level, the thermodynamics define what the maximum possible efficiency can be for a given material, but perhaps more directly and practically define the extent of reaction possible for that material under a given set of operating conditions. Similarly, at the highest level, the reactor design determines the extent to which the internal recuperation of thermal energy is made possible. We point to reaction extent and recuperation in particular because, as the analysis here clearly shows, the overall efficiency of the thermochemical conversion is heavily tied to the combination of these attributes. Furthermore, these attributes of materials and reactors are linked in such a way that if one sets a target efficiency it becomes clear that improvements in one aspect (e.g., materials), directly relaxes constraints on the other (recuperation) and vice versa. The utilization factor we have introduced here quantitatively captures this important interdependency. Other Reactor Attributes Are Important As Well. The design and operation of internally recuperative reactors is beyond the scope of this paper. We note however that due to the importance of recuperation we have solely focused our reactor development efforts on designs with the potential to achieve high levels of recuperation effectiveness (εR > 0.8).24,26 We also point out that there are other reactor considerations that should be addressed to maximize thermochemical efficiency. Briefly, 3284



Commentary

opinions and conclusions expressed, however, are those of the authors. This work was supported by the Laboratory Directed Research and Development program at Sandia National Laboratories, in the form of a Grand Challenge project entitled ‘‘Reimagining Liquid Transportation Fuels: Sunshine to Petrol”. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract No. DE-AC04-94AL85000.

introduce a new set of challenges, for example, volatilization of the reactive material and increased solar collection losses. Reduced pressure operation is one alternative that enables sidestepping such problems. A Note of Caution. As a final point regarding materials we note that our model is useful for evaluating the potential efficiency of known and hypothetical materials, although it provides no insight into whether a particular parameter set maps onto a “discoverable” material. It has long been recognized that the ΔS values exhibited by metal oxides for reduction are limited, and that these limits are directly tied to the absence of any simple two-step cycles that operate at the lower temperatures that are compatible with nuclear reactors, for example.21 In fact, the major contributor to the entropy term is typically the evolution of oxygen and not changes within the oxide itself.27 In light of the relatively low efficiencies possible with these types of materials, a lesson that can be gleaned here is that while finding a material that operates over a very narrow temperature window may seem attractive from an operational standpoint, in reality the search for such a material is likely to be unfruitful. Summary. In conclusion, we reiterate the importance of establishing benchmarks based on established technologies for evaluating the possible viability of new technologies aimed at achieving the same ends. Our analysis here suggests that thermochemical routes to solar fuels meet the metric of potential viability using existing photovoltaic/electrolytic technology as the benchmark. However, living up to the promise will require improvements in both reactors and materials. The utilization factor introduced herein provides a key metric for comparing materials/reactors combinations along the pathway to commercialization.

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(1) Pohl, P. I.; Brown, L. C.; Chen, Y.; Diver, R. B.; Besenbruch, G. E.; Earl, B. L.; Jones, S. A.; Perret, R. F. Evaluation of solar thermo-chemical reactions for hydrogen production. Proceedings of the 12th International Symposium Solar Power and Chemical Energy Systems 2004, Oaxaca, Mexico. (2) Steinfeld, A. Solar thermochemical production of hydrogenA review. Sol. Energy 2005, 78, 603−615. (3) Perkins, C.; Weimer, A. W. Likely near-term solar-thermal water splitting technologies. Int. J. Hydrogen Energy 2004, 29, 1587−1599. (4) Licht, S. Efficient solar-driven synthesis, carbon capture, and desalinization, STEP: solar thermal electrochemical production of fuels, metals, bleach. Adv. Mater. 2011, 20, 1−21. (5) Miller, J. E.; Allendorf, M. D.; Diver, R. B.; Evans, L. R.; Siegel, N. P.; Stuecker, J. N. Metal oxide composites and structures for ultra-high temperature solar thermochemical cycles. J. Mater. Sci. 2008, 43, 4714− 4728. (6) Abanades, S.; Flamant, G. Thermochemical hydrogen production from a two-step solar-driven water-splitting cycle based on cerium oxides. Solar Energy 2006, 80, 1611−1623. (7) Chueh, W. C.; Haile, S. M. Ceria as a thermochemical reaction medium for selectively generating syngas or methane from H2O or CO2. ChemSusChem 2009, 2, 735−739. (8) Miller, J. E. Initial case for splitting carbon dioxide to carbon monoxide and oxygen. Sandia National Laboratories: New Mexico, 2007; Report No. SAND07-8012. (9) Kim, J.; Henao, C. A.; Johnson, T. A.; Dedrick, D. E.; Miller, J. E.; Stechel, E. B.; Maravelias, C. T. Methanol production from CO2 using solar-thermal energy: process development and techno-economic analysis. Energy Environ Sci 2011, 4, 3122−3132. (10) Kim, J.; Johnson, T. A.; Miller, J. E.; Stechel, E. B.; Maravelias, C. T. Fuel production from CO2 using solar-thermal energy: system-level analysis. Energy Environ Sci 2012, 5, 8417−8429. (11) Ivy, J. Summary of Electrolytic Hydrogen Production. National Renewable Energy Laboratory: Golden, CO, 2004; Report No. NREL/ MP-560-36734. (12) Kolb, G. J.; Ho, C. K.; Mancini, T. R.; Gary, J. A. Power tower technology roadmap and cost reduction plan. Sandia National Laboratories: New Mexico, 2011; Report No. SAND2011-2419. (13) Kolb, G. J.; Diver, R. B. Screening analysis of solar thermochemical hydrogen concepts. Sandia National Laboratories: New Mexico, 2008; Report No. SAND2008-1900. (14) Lewis, M. A.; Ferrandon, M. S.; Tatterson, D. F.; Mathias, P. Evaluation of alternative thermochemical cyclesPart III further development of the Cu−Cl cycle. Int. J. Hydrogen Energy 2009, 34, 4136−4145. (15) Perkins, C.; Lichty, P. R.; Weimer, A. W. Thermal ZnO dissociation in a rapid aerosol reactor as part of a solar hydrogen production cycle. Int. J. Hydrogen Energy 2008, 33, 499−510. (16) Kennedy, C. E.; Terwilliger, K. Optical durability of candidate solar reflectors. J. Solar Energy Eng. 2005, 127, 262−268. (17) Gombert, A.; Glaubitt, W.; Rose, K.; Dreibholz, J.; Blasi, B.; Heinzel, A.; Sporn, D.; Doll, W.; Wittwer, V. Anti-reflective transparent covers for solar devices. Solar Energy 2000, 68, 357−360. (18) Martinek, J.; Channel, M.; Lewandowski, A.; Weimer, A. W. Considerations for the design of solar-thermal chemical processes. J. Solar Energy Eng. 2010, 132.

Nathan P. Siegel* Department of Mechanical Engineering, Bucknell University, Lewisburg, Pennsylvania 17837, United States

James E. Miller Advanced Materials Laboratory, Sandia National Laboratories, Albuquerque, New Mexico 87106, United States

Ivan Ermanoski Concentrating Solar Technologies Department, Sandia National Laboratories, Albuquerque, New Mexico 87106, United States

Richard B. Diver Diver Solar LLC, Albuquerque, New Mexico 87123, United States

Ellen B. Stechel

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REFERENCES

LightWorks and the Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287-7205, United States

AUTHOR INFORMATION

Corresponding Author

*Tel.: 1-570-577-3827. Fax: 1-570-577 7281. E-mail: nps004@ bucknell.edu. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We wish to thank our colleagues, Emily Carter, George Crabtree, James Klausner, and Peter Loutsenhizer for the time taken to review this manuscript and for their insightful feedback. The 3285



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(19) Pitz-Paal, R.; Bayer Botero, N.; Steinfeld, A. Heliostat field layout optimization for high-temperature solar thermochemical processing. Solar Energy 2011, 85 (2), 334−343. (20) Panlener, R. J.; Blumenthal, R. N.; Garnier, J. E. A thermodynamic study of nonstoichiometric cerium dioxide. J. Phys. Chem. Solids 1975, 36 (11), 1213−1222. (21) Funk, J. E.; Reinstrom, R. M. Energy requirements in the production of hydrogen from water. Ind. Eng. Chem. Process. Des. Dev. 1966, 5, 336−342. (22) Fletcher, E. A. Solarthermal processing: A review. J. Solar Energy Eng. 2001, 123, 63−74. (23) Lapp, J.; Davidson, J. H.; Lipinski, W. Efficiency of two-step solar thermochemical non-stoichiometric redox cycles with heat recovery. Energy 2012, 37, 591−600. (24) Ermanoski, I.; Siegel, N. P.; Stechel, E. B. Development of a moving packed bed reactor for solar thermochemical fuel production. J. Solar Energy Eng. 2012, in press. (25) Chueh, W. C.; Falter, C.; Abbott, M.; Scipio, D.; Furler, P.; Haile, S. M.; Steinfeld, A. High-flux solar-driven thermochemical dissociation of CO2 and H2O using nonstoichiometric ceria. Science 2010, 330, 1797−1801. (26) Diver, R. B.; Miller, J. E.; Allendorf, M. D.; Siegel, N. P.; Hogan, R. E. Solar thermochemical water-splitting ferrite-cycle heat engines J. Solar Energy Eng. 2008, 130. (27) Meredig, B.; Wolverton, C. First-principles thermodynamic framework for the evaluation of thermochemical H2O or CO2-splitting materials. Phys. Rev. B 2009, 80, 245119.

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