Thermodynamic Analysis of Isothermal CO2 Splitting and CO2-H2O Co-Splitting for Solar Fuel Production

Accepted Manuscript Thermodynamic Analysis of Isothermal CO2 Splitting and CO2-H2O Co-Splitting for Solar Fuel Production Yong Hao, Jian Jin, Hongguang Jin PII: DOI: Reference:

S1359-4311(18)35460-7 https://doi.org/10.1016/j.applthermaleng.2019.04.010 ATE 13600

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

4 September 2018 19 February 2019 2 April 2019

Please cite this article as: Y. Hao, J. Jin, H. Jin, Thermodynamic Analysis of Isothermal CO2 Splitting and CO2H2O Co-Splitting for Solar Fuel Production, Applied Thermal Engineering (2019), doi: https://doi.org/10.1016/ j.applthermaleng.2019.04.010

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Thermodynamic Analysis of Isothermal CO2 Splitting and CO2-H2O Co-Splitting for Solar Fuel Production

Yong Haoa,b*, Jian Jina,b, Hongguang Jina,b a

Institute of Engineering Thermophysics, Chinese Academy of Sciences, 11 Beisihuanxi Rd., Beijing 100190, P. R. China b

University of Chinese Academy of Sciences, No.19A Yuquan Rd., Beijing 100049, P. R. China Email: [email protected]

ABSTRACT

Isothermal solar thermochemistry is a promising approach for deriving solar fuels from concentrated solar energy with potential advantages in reactor design and heat recovery. Previous work has demonstrated the feasibility of isothermal water splitting with ceria, but the solar-to-fuel efficiencies and operating temperature range are relatively undesirable. In this study, thermodynamic analysis is performed on the isothermal solar thermochemical splitting of CO2 as well as co-splitting of CO2 and H2O. The cycling reactions are found to exhibit considerably higher solar-to-fuel efficiencies than that of H2O due to the favorable Gibbs free energy change in the CO2 splitting reaction at elevated temperatures and the lower thermal energy requirement for gas heating due to the lack of phase change in CO2. Through the comparison of the conventional two-temperature cycling strategy, the advantages and disadvantages of both methodologies, as well as indications on system and reactor design, are discussed. Strategies for controlling the composition of solar-syngas derived from isothermal co-splitting of CO2 and H2O mixtures are also proposed.

Keywords: solar fuel, isothermal, thermochemical cycling, carbon dioxide, syngas

1. Introduction Solar energy is a clean, sustainable and renewable energy source. Among a wide spectrum of solar energy

technologies, one promising method is the direct synthesis of chemical fuels by dissociating H 2O or CO2, through which solar energy may be transformed into chemical energy of gaseous fuels (such as H2 or CO) [1] and liquid fuels [2]. Solar fuels, which are produced from thermochemical processes driven by concentrated solar energy, offer an effective means of solar energy storage for the following advantages: (1) the energy density of fuels (e.g., H2, CO) is high [3], typically 1-2 orders of magnitude higher than Li-ion batteries [4]; (2) the major drawbacks of sunlight, including intermittency and low density, are eliminated for subsequent applications; and (3) solar fuels can readily adapt to existing energy infrastructure, which offers an enormous potential in addressing real-world energy challenges and savings in investment. With high energy density, cost-effectiveness, versatility and potentially higher efficiencies, solar fuels have attracted growing attention, and considerable amounts of research have been accomplished in recent years [5,6].

Although there exists a wide range of methods to achieve solar fuel synthesis, low solar-to-fuel efficiency appears to be one of the major barriers towards practicality for many of them, such as photosynthesis, photocatalysis and photoelectrochemistry, partially due to their preferences towards specific ranges of the solar spectrum. In comparison, chemical reactions driven by solar thermal energy (via concentration) are potentially more efficient and more practical – owing not only to the utilization of the entire solar spectrum but also to a reasonable combination of thermodynamics and kinetics [7]. For example, the theoretical maximum solar-to-fuel efficiency of a solar thermal reactor operating at 1500°C with 5000 suns of incoming solar energy flux is 73% [8], whereas the maximum solar-to-fuel efficiency of a two-step solar thermochemical cycle could be as high as 65% [9]. Such processes involve a sequence of reduction and oxidation (redox) reactions, proceed cyclically and produce both oxygen and fuel (e.g., H 2, CO) in separate steps. Compared with the direct thermal dissociation of H2O or CO2 (i.e., thermolysis), thermochemical cycles could involve as few as only two steps [10] but benefit from significantly decreased reaction temperatures. For example, the thermochemical splitting of CO2 with 83% molar conversion at the reduction temperature of 1450°C has been experimentally demonstrated [11], significantly lower than the temperature required for direct thermal dissociation of CO2 to reach the same decomposition rate (3436°C) [12]. Additionally, thermochemical cycles avoid the fuel and O2 separation problem of direct thermolysis. Twostep thermochemical cycling MOx (M represents certain metals, e.g., Ce, Fe or Ni) is used for the splitting of H2O and/or CO2 to produce H2 and/or CO. The thermochemical cycle processes are described as follows: first, the metal oxide releases oxygen driven by concentrated solar energy in the reduction step (endothermic); then, the reduced metal/metal oxide is re-oxidized by H2O and/or CO2 to produce H2 and/or CO in the oxidation step (exothermic).

Efficient solar thermochemical cycles rely critically on materials [13], cycling strategies [14] and reactor design [11,15,16]. In recent years, ceria has attracted considerable attention and is regarded as a benchmark material for two-step H2O and/or CO2 splitting cycles [9,17,18]. Conventional temperature-swing cycling thermally reduces the oxide material at a high temperature (e.g., 1500°C) to release oxygen and oxidizes it with H2O or CO2 at a lower temperature (e.g., 800°C) to generate fuel. However, such mode inevitably incurs a high energy penalty because the greatest portion of the total thermal energy input of the entire cycle is usually dumped into the environment by the (solid) material during cooling. Although attempts at highefficacy heat recovery from solids were made by a few research groups and encouraging progress was achieved [17,19–22], such processes are inherently limited by challenges ranging from the material to system levels, and their practicality particularly for scale-up is unclear. The isothermal thermochemical cycling strategy was proposed by a few groups [23,24], in which the temperature difference in the T-swing cycling mode is eliminated, and reaction steps proceed by merely swinging the oxygen partial pressure. In particular, the same author of this work discovered ceria-based isothermal thermochemistry and performed detailed thermodynamic analysis to reveal the underlying mechanisms for this unconventional approach; by combining oxygen-starved, pre-reduced ceria with partial thermolysis of water in the oxidation step, oxygen is

partially removed from water by ceria and a net production of hydrogen follows. Highlights of this novel approach lie mainly in its potential for simpler reactor design (no heat is exchanged through walls) and better heat recovery (unused thermal energy is completely carried away by gases). Despite the advantages of isothermal thermochemical cycling, there is still a lack of theoretical and experimental studies in terms of both cycling strategies and reactor design to fulfill its potential for high solar-to-fuel efficiencies.

Nonetheless, there is special significance in the solar thermochemical dissociation of CO2 because it provides a beneficial approach for converting a major greenhouse gas into useful fuels driven by a major renewable energy source. In addition to the cost advantages of using CO2 as a feedstock, the value of this approach is also underscored by its complementary nature with carbon sequestration and storage where the storage is unsuitable [25], as well as its indispensability as a provider of carbon elements for liquid fuel synthesis [11]. For solar thermal applications, CO2 has advantages over H2O as it does not involve the heat of evaporation of water and can be utilized more easily [1]. Moreover, it is well known that CO2 is thermodynamically less stable than water at elevated temperatures, resulting in a more pronounced thermolysis effect of CO2. Such factors, when combined, result in higher solar-to-fuel efficiencies for CO2 splitting than that for H2O. A pinch point analysis by Lange et al. showed that the splitting of CO2 is more advantageous than that of H2O at higher temperature levels [26], which is also confirmed by several experimental studies [27,28]. Furthermore, when CO2 is co-split with water [29–31], the synthesis gas produced can be transformed into liquid (such as the Fischer-Tropsch synthesis [32,33]) transportable fuels with well-established industrial routes. Such reactions are analogous to photosynthesis in terms of storing solar energy and fixing carbon but are much more efficient [18]. The rapid dissociation of both H2O and/or CO2 was reported by several research groups with pure or doped ceria [15,34–37] using a conventional temperature swing cycling strategy.

Most studies on thermochemical splitting of CO2 to date still focus on T-swing cycles. Furler et al. [38] demonstrated a cavity reactor operated in a temperature-swing mode driven by a solar simulator for CO2 splitting. A reticulated porous ceramic (RPC) foam made of undoped ceria was investigated and the experimental results showed that the average and peak efficiency of solar-to-fuel were 1.73% and 3.53%, respectively. The latest experiment at the lab-level for CO2 splitting, which was carried out by the same research group [11], showed that the average efficiency of solar-to-fuel reached 5.25% by optimizing the reactor design and RPC structure. Takacs et al. [39] performed thermochemical CO2 splitting in a solardriven thermogravimetric analyzer. Different structures of undoped and Zr4+-doped ceria were studied and the results showed that the 10 ppi ceria with dual-scale RPC offered the best performance by considering heating rates, temperature uniformity, reaction rates, and specific fuel yields. However, doped Zr 4+ can lead to unfavorable thermodynamics and slow the kinetic rates, hence its performance was not as good as undoped ceria under the same experimental conditions. Additionally, other solar thermochemical reactors

were proposed for CO2 splitting via isothermal ceria redox cycle [40] and under temperature-swing conditions [41].

For the thermodynamic analysis of isothermal CO2 splitting cycles, the same author of this work was among the first to point out that the isothermal splitting of CO2 exhibits considerably higher solar-to-fuel conversion efficiency than that of H2O (e.g., 12% for CO2 and 3% for H2O at 1500°C, no heat recovery) [42]. Bader et al. [43] investigated the effects of temperature, heat recovery, and concentration ratio on the solar-to-fuel conversion efficiency of isothermal CO2 splitting cycles and indicated that the efficiency depends strongly on the gas-phase heat recovery effectiveness. Furthermore, the effects of gas flow rates on the operation of the reactor were explored using a computational fluid dynamics model [44]. In addition to the conventional two-step isothermal cycle, a new type of isothermal CO2 splitting using a dense ceramic membrane reactor was also recently reported [45,46], but the efficiency was estimated to be low. From both thermodynamic and practical points of view, the potential of achieving high solar-to-fuel efficiencies with isothermal splitting of CO2 requires further discussion and clarification. Theoretical analysis on both isothermal and T-swing solar thermochemical splitting of CO2 are presented in this work.

2. Theoretical analysis

A ceria-based thermochemical cycle for CO2 splitting (e.g., for two-T) can be expressed as

Oxidation (at TOx):  1CeO2  CO2   1CeO2  CO

(1)

Reduction (at TRe):  1CeO2-   1CeO2- + 0.5 O2

(2)

Combined: CO2  CO  0.5 O2

(3)

i

f

f

i

where  stands for the oxygen nonstoichiometry (i.e., deviation from the stoichiometry of 2 for oxygen) of ceria, and a fluorite structure can be maintained up to  = 0.35 [17];  i and  f stand for  values at the beginning and end of the oxidation step, respectively (  i >  f ); and    i   f is the net change in oxygen nonstoichiometry as well as a numerical equivalent of the amount of fuel produced per mole of ceria per cycle; TOx and TRe are the temperatures at which oxidation and reduction reactions occur, respectively. For two-T cycling, TOx < TRe, and for isothermal cycling, TOx = TRe.

The thermodynamic efficiency of CO2 solar thermochemical splitting cycles, for both two-T and isothermal cycling, is analyzed and compared. The significance of the thermodynamic efficiency analysis mainly resides in its capability of screening out material systems or reactions that are incapable of producing fuels beyond a

certain performance threshold but may fall short in predicting those that would excel in reality. However, given that solar thermochemical technology is still under development, discussions about thermodynamic efficiency still offer a meaningful theoretical basis for comparison [47]. For the thermodynamic efficiency analysis of two-T cycling, the formalism of Chueh et al. is adopted [48]; for the thermodynamic efficiency analysis of isothermal cycling, the formalism of the previous work of the same author [24] is adopted. The first-law thermodynamic efficiency of the cycling is derived based on a zero-dimensional thermodynamic model. For such purpose, a closed system for the oxidation reaction only is assumed, which considers the thermodynamic equilibrium reached by coexistence of an amount of readily reduced ceria and another amount of CO2 (energy penalties due to oxygen removal and heat losses are calculated separately), during which the nonstoichiometry of ceria starts at  i and ends at  f . The thermodynamic efficiency is defined as the heating value of the fuel derived to the minimum solar thermal energy required for the ceria-CO2 system to complete the cycle, taking solar re-radiation losses into account. The thermodynamic efficiency of the two cycling strategies can be unified as



abs  HHVCO

(4)

Qredu  QCO2  Qceria  Qpump

where

abs  1 

 T 4

(5)

I C

is the solar absorption efficiency of an ideal blackbody reactor in which the cycling reactions are assumed to take place [8],  is Boltzmann’s constant, T is the temperature of the reactor, I is solar irradiation, and C is the concentration ratio; HHVCO is the heating value of CO defined at 25°C; Qredu , QCO and Qceria represent 2

the thermal energy required to reduce ceria, heat CO2 and heat ceria, respectively. In particular, the thermal energy for extracting 1 mole of oxygen atoms from ceria (i.e., to produce 1 mole of CO) is calculated by

i

Qredu   1  Hceria   d f

(6)

where Hceria   is the molar enthalpy change of the ceria oxidation reaction. The nonstoichiometry terms  i and  f are solved from the thermodynamic equilibrium of oxygen between the gas phase and ceria (Eq. (2)):

G  ,T   Hceria    T Sceria    RT ln pO2

(7)

where Sceria   is the entropy change of the ceria oxidation reaction [49], and pO is the oxygen partial 2

pressure in the gas phase during thermal reduction. The other two heating terms are

QCO2  1  fg  nCO2 

TOx

25C

Qceria  1  fs   1 

TRe

TOx

Cp,CO2 dT

(8)

Cp,ceriadT

(9)

where fg and fs are the fraction of heat recovery from gas and solid phases, respectively; nCO is the 2

amount of CO2 used to actually produce 1 mole of CO; Cp,CO and Cp,ceria are the specific heat of CO2 and ceria under 1 atm, respectively. During the reduction step, vacuum pumping is applied to removing oxygen. 2

Energy required for vacuum pumping is calculated by

Qpump 

1

heat-to-work

n

oxygen

RT ln pO2 dt

(10)

where heat-to-work is the heat-to-work efficiency (assumed 0.4 [13]) and noxygen is the molar flow rate of O2 released by ceria during the reduction step. To avoid redundancy, only key equations, Eq. (4) to Eq. (9), are outlined above for comprehension. More details can be found in the two references mentioned above.

Oftentimes the energy cost of mechanical vacuum pumps is the dominating energy penalty term for the solarto-fuel efficiency (Eq. 4) because the efficiency of vacuum pumps is extremely low when they work at low pressure [50]; however, lower pressure is desired for higher fuel productivity per cycle. Nevertheless, several novel approaches for oxygen removal have been proposed recently to address this bottleneck problem for potentially high thermodynamic efficiencies [51]. For example, electrochemical oxygen pump, a device using electric potential to drive the transport of oxygen ions across an oxygen permeation membrane, offers the advantage of high efficiency and low energy consumption [52] without the heat recovery problem, which can be used at high-temperature conditions (e.g., 1500 °C) [53]. An oxygen pump with yttria-stabilized zirconia (YSZ) membrane is assumed for this study. The conductivity of oxygen ions of YSZ is about four orders of

magnitude higher than that of electrons at 1600°C [54], so that electronic leakage through the membrane is negligible. The Faradaic efficiency is thus assumed to be 100% for electrochemical oxygen removal. The energy consumption of an electrochemical oxygen pump is calculated as follows:

Qelectro-pump 

4FEcell

heat-to-work

n

oxygen

(11)

dt

where is Faraday’s constant and

c ll

is the applied potential, which is approximately 0.75 V in 1000°C

[55]. It was found from our recent studies that the consumption of an electrochemical oxygen pump is much less than that of a vacuum pump and inert gas sweeping for oxygen removal [12]. Thus, it is possible to achieve a much lower oxygen partial pressure (e.g., 1 Pa) with an energy cost much lower than that of mechanical vacuum pumps. Therefore, we consider the process of oxygen removal as one that has sufficient room of energy cost reduction to a degree that is comparable to other energy cost terms in Eq. 4. For the convenience and simplicity of thermodynamic analysis on both isothermal and two-T solar thermochemical CO2 splitting processes, we take the ideal (i.e., minimum) energy cost for oxygen removal (i.e., Eq. 10) for subsequent discussions, only considering the (solar) heat-to-work efficiency.

3. Results and discussion First, this work focuses on evaluating the thermodynamic efficiency of isothermal solar thermochemical

splitting of CO2. Conditions common to all cases are given in Table 1. Other conditions are case-specific. Thermodynamic calculations are performed by HSC software [12] and an in-house python code.

Table 1. Common conditions for all calculation cases. C

pO2 ，Re

5000

1.0 Pa

I 2

1000 W/m

pO2 ，Re is the oxygen partial pressure for thermal reduction, Eq. (2).

The key factors affecting the solar-to-fuel efficiency of isothermal thermochemical splitting of CO2 are first analyzed. As shown in Fig. 1 (a), the Gibbs free energy change of CO2 splitting reaction water splitting reaction

is smaller than that of

above 817°C, resulting in a significantly higher partial pressure of oxygen in

the case of CO2 (partial) thermolysis. Because a thermodynamic equilibrium is first reached between the lattice oxygen in ceria and oxygen in the gas phase ( pO2 ，Re ) in the reduction step (Eq. (2)), the driving force for the oxidation step (Eq. (1)), i.e., the difference in chemical potentials of oxygen between the gas phase and solid phase, is higher for CO2 than that for H2O. Consequently, a higher fuel productivity and higher solar-to-fuel efficiency can be expected, this has also been proved by experiments using an isothermal tubular ceria membrane reactor [56]. Another important factor is the

thermal energy required to heat the reactant (CO2 or H2O) to the operation temperature of the isothermal reactions. As shown in Fig. 1 (b), although the specific heat of CO2 is higher than that of H2O for the majority of the temperature range, the latent heat of H2O due to phase change at 100°C dramatically boosts the energy cost such that heating CO2 is 0

500

1000

2000 2.8

(a)

250

2.4 H2O

225

G (kJ/mol)

1500

2.0

CO2

200

1.6

175 1.2

150

0.8

125

0.4

100 817

75 0

500

1000

1500

0.0 2000

Temperature (°C)

140

0

500

(b) 120

1000

1500

2000 100

H2O

80

CO2

100 80

60

60

40

40

Cp (J/mol/K)

275

O2 Partial Pressure (x103 Pa) Energy for Heating Gas to TH (kJ/mol)

more energy-efficient. For example, heating 1 mole of CO2 to 1500°C costs 26% less energy than for H2O.

20 20 0 0

500

1000

1500

0 2000

TH (°C)

Figure 1. Key factors affecting the efficiency of isothermal thermochemical splitting of CO2; (a) Gibbs free energy change and pO2 due to thermolysis at the thermodynamic equilibrium of CO2 and H2O; (b) specific heat and thermal energy required to heat CO2 or H2O to a given temperature TH.

The thermodynamic efficiency (Eq (4), also called “

V efficiency”) is then calculated For the convenience of

discussion, the ratio of CO2 to available oxygen vacancies upon reduction is defined as

rCO2 

nCO2

 i nceria

(11)

Fig. 2 (a) shows the efficiency at various operating temperatures from 1300 to 1900°C. The overall trend is very similar to that of isothermal H2O splitting [24]: 1) the maximum efficiency is achieved in the limit of rCO2 → ; ) efficiency increases with increasing temperature; 3) the plateau region in which the efficiency virtually keeps constant is rCO2 ~ 1. However, closer inspection reveals quantitative differences – the efficiency of CO2 splitting is much higher. For example, at 1500°C, the efficiency reaches 12%, whereas the value is only 3% for isothermal splitting of H2O.

40

HHV Efficiency (%)

50

30 1700°C 25

1600°C

20 15

1500°C

10 5

1400°C

10-3

1800°

H2O

C 1900°

40 30

C

0°C 190

C 1700°

°C 00 17

C 1600°

20 1500°C

00

10-2

10-1

100

101

102

103

104

0

°C

15

10 1400°C 1300°C 0 1200°C

1300°C

0 10-4

(b)

CO2

0% heat recovery

35 1800°C

HHV Efficiency (%)

60

(a)

1900°C

0°C

130

20

40

60

80

100

Heat Recovery (%)

rCO2

Figure 2. Thermodynamic efficiency of isothermal solar thermochemical splitting of CO2; (a) without heat recovery; (b) maximum efficiency at different heat recovery percentages, in comparison with H2O.

An efficiency of 12% is attained with an ideal energy cost (i.e., minimum work of separation) for oxygen removal. For practical consideration, an electrochemical oxygen pump is assumed to replace a mechanical vacuum pump to obtain more realistic efficiencies under the common conditions in Table 1 and at a 1500°C operating temperature. The applied voltage (i.e.,

c ll )

of the pump is 1.32 V [57]. The heat energy cost for

removing 0.5 mol of O2 is 636.8 kJ, and the corresponding solar-to-fuel efficiency is 9.44%. In contrast, if a mechanical vacuum pump is used to remove oxygen [50], the efficiency is less than 0.01%. Furthermore, the energy cost is not sensitive to oxygen partial pressures, hence the efficiency can remain considerably higher even under lower oxygen partial pressures.

As mentioned above, one of the major advantages for isothermal thermochemical cycling is the convenience of heat recovery from gas phases. The maximum efficiencies for isothermal splitting of CO2 and H2O as functions of the heat recovery percentage of the gas phase are shown in Fig. 2 (b) for comparison. CO 2 outperforms H2O for all temperatures shown, and the same efficiencies can be achieved with CO2 at temperatures of 100-200°C lower than that of H2O, a significant and beneficial decrease for operations at such a high temperature range. In particular, both panels in Fig. 2 show that the best sensitivity of efficiency versus temperature is achieved between 1500 and 1700°C. The underlying reason for this is twofold: when the temperature is relatively low, the exponential increase of pO2 due to thermolysis dominates; when the temperature is high, the decrease in solar absorption efficiency (Eq. (5)) excels. Even without any heat recovery, the maximum efficiencies for temperatures from 1500 to 1700°C, namely, 12%, 22% and 31%, are already attractive. A not unreasonable heat recovery rate of 80% would increase the efficiencies to 33%, 45% and 51%, respectively. Under circumstances with significant heat recovery, the most sensitive temperature region is shifted down to 1300 to 1600°C. Considering the tradeoffs between efficiency and the requirements on materials at high temperatures, the optimum temperature window for isothermal CO2 splitting is approximately 1500-1600°C.

Additionally, due to the absence of phase change in CO2 in the temperature range of operation, the heat exchanger required for achieving the desired recovery rate is expected to be much simpler.

It would then be instructive to obtain quantitative understanding of the major causes of the much higher efficiency of CO2 splitting. Corresponding to the possible causes shown in Fig. 1, the conversion rate (of reactant to fuel) and thermal energy costs for producing 1 mole of fuel are plotted in Fig. 3 in the temperature range of 1300-1700°C for isothermal splitting without any heat recovery. The fundamental reason for the higher efficiency of CO2 splitting is ascribed to its thermodynamic nature, i.e., a higher conversion rate due to a higher pO by thermolysis, which in turn is due to the more favorable Gibbs free energy change at elevated 2

temperatures (Fig. 1 (a)). Take 1500°C as an example, the G for CO2 and H2O splitting reactions is 129 and 149 kJ/mol, respectively, and the pO resulting from thermolysis is 181 and 75 Pa, respectively. Based on the 2

analysis mentioned above, the conversion rate of CO2 is 3.67 times that of H2O. A higher conversion implies more fuel production per cycle; therefore, the total thermal energy cost for producing 1 mole of fuel is much less, only 2.4×103 kJ for CO2 (compared with 9.8×103 kJ for H2O). A lower thermal energy cost for heating reactant gas is proved to be the second reason for the higher efficiency of CO2. Still taking 1500°C as an example, due to the lack of phase transition, the percentage of heating in the total thermal energy cost for CO2 splitting is 71%, which is significantly lower than 85% for H2O splitting. Overall, the conversion rate of reactants increases exponentially with temperature. The total thermal energy cost per mole of fuel and the

Conversion rate to fuel (%)

30

Thermal Energy (x104 kJ/mol-fuel)

percentage of heating both exhibit exponential decays accordingly.

(a)

25

H2O CO2

20 15 10 5 0

(b)

8 7.12 7

92%

6 5 4 3 2

1.68 90%

2.45 89%

1 0

1300

1400

1500

1600

1700

1300

Temperature (oC)

0.98 0.56 85% 0.46 0.24 78% 0.13 0.25 0.09 83% 71% 55% 68% 40%

1400

1500

1600

1700

Temperature (oC)

Figure 3. Conversion rate and energy cost for isothermal solar thermochemical H2O and CO2 splitting at selected temperatures without heat recovery. (a) conversion rate of reactant gas to fuel; (b) thermal energy required for producing 1 mole of fuel. For panel (b), black/gray represents H2O splitting, and orange/yellow represent CO2 splitting; the number on top of each column is the total thermal energy cost for producing one mole of fuel (H2 for H2O; CO for CO2), and the percentage underneath each column is the fraction of thermal energy required to heat the reactant gas to the isothermal reaction temperature.

The temperature range for isothermal splitting is relatively high; thus, the re-radiation from the reactor back to the environment is often non-negligible. In the expression for solar absorption efficiency defined by Eq. (5), in addition to the operating temperature, the concentration ratio is another factor that affects efficiency. As reflected by Fig. 4, a higher concentration ratio generally leads to higher efficiencies, but the efficiency curves level off at different concentration ratios at different rates, depending on the operating temperature. The efficiency at higher temperatures has a stronger dependence on the concentration ratio. Physically, this is because solar reactors require an increasingly smaller aperture (i.e., inlet for solar irradiation) area to reduce the re-radiation loss into the environment. In the optimum temperature range of 1500-1600°C for isothermal CO2 splitting, a concentration ratio of 3000 or above appears to be sufficient for achieving high enough efficiencies. For example, at 1500°C and 1600°C, the efficiency achieved at C=3000 is 86% and 83%, respectively, of that achieved at C=10000; at C=5000, the percentage increases to 92% for both cases. In the literature, even lower concentration ratios (e.g., 1500) were used [48] for the same temperature range (for two-T cycling). In Fig. 4, this corresponds to a highly reduced efficiency: 67% and 58% of the extreme efficiencies for 1500°C and 1600°C, respectively. Although the concentration ratio of 1500 and beyond is within the reach of dish concentrators [58], the determination of optimum concentration ratio is oftentimes an issue that must be resolved taking into account the reactor operation conditions (e.g., temperature and efficiency) and economic factors. 1900°C

HHV Efficiency (%)

40

1800°C 1700°C

30 1600°C

20 1500°C

10 1400°C 1300°C 1200°C

0 0

2000

4000

6000

8000

10000

Concentration Level Figure 4. Efficiency of isothermal solar thermochemical CO2 splitting at various concentration ratios and operating temperatures.

Considering the importance of a cycling strategy for practical efficiencies and reactor design, isothermal and two-T cycling modes are compared next in terms of efficiencies without heat recovery (Fig. 5). Consistent with previous work [24], the temperature of the oxidation step (Eq. 1) of two-T cycling is assumed to be 700°C lower than that for reduction (700°C is an approximate optimum temperature difference for two-T efficiency). With a two-T strategy, the efficiency for CO2 splitting is slightly higher than that of H2O, and the primary

reason for this is the lower energy cost of heating CO2 than that of H2O. Fu l productivity p r cycl (i. ., Δδ) is almost identical between the two cases for reduction temperatures of 1600°C and lower because the oxidation reaction of ceria (Eq. 1) at 900°C and below is dominated by the thermodynamics of ceria [48]. At even higher temperatures, CO2 exhibits a higher fuel productivity because the oxidation temperature (>1000°C) starts to play an increasingly important role in promoting thermolysis, which is more pronounced for CO2 than for H2O, resulting in a smaller  f and thus a larger  for CO2.

The efficiency of isothermal H2O splitting with ceria, under the circumstance of zero heat recovery, however, is much lower than that of two-T, primarily due to the unfavorable thermodynamics of H2O. As discussed previously, a heat recovery percentage of 50-90% is necessary to achieve comparable or higher efficiencies than two-T splitting [24]. However, the situation is different for isothermal CO2 splitting; the efficiency is roughly half the value of its two-T splitting for a reduction temperature of 1400°C and starts to exceed the efficiency at 1580°C, whereas the temperature range of 1500-1600°C is well within the reach of current solar thermochemical reactors [48]. Moreover, the ratio of efficiency between CO2 splitting and H2O splitting (Fig. 5, inset) shows that for isothermal cycling, CO2 splitting is much more efficient than H2O splitting, whereas the situation is completely different for two-T cycling for reasons stated above. At 1400°C where the peak ratio for isothermal cycling occurs, even though the efficiency is only half that of two-T, compensation comes from the savings in cycling time (because reactor heating/cooling is avoided), rendering the two strategies comparable.

The influence of high temperatures on efficiency is also different between the two cycling strategies. For twoT cycling, the efficiency for temperatures beyond 1600°C levels off and then slightly decreases due to the decrease in the solar absorption efficiency abs ; in the case of isothermal cycling, the adverse effect of a decreasing abs is partially canceled out by the exponential increase of pO with temperature due to 2

thermolysis, deferring the plateau region to 1800°C. With an effective gas-phase heat recovery, isothermal solar thermochemical CO2 splitting could be more advantageous than two-T strategy in general. The quantitative effect of heat recovery on efficiency enhancement is not discussed further because there is no significant difference between the CO2 and H2O cases.

1200 1300 1400 1500 1600 1700 1800 1900 40 0.20

25

isothermal CO2 splitting

2 1 0 1200

20

isothermal

3

0.15

two-T CO2 splitting

two-T

TRe (oC) 1400

1600

1800

0.10 two-T H2O splitting

15 10

isothermal H2O splitting

 = i - f

30

4

CO2 / H2O

HHV Efficiency,  (%)

35

0.05

5 0 0.00 1200 1300 1400 1500 1600 1700 1800 1900

TRe (°C) Figure 5. Comparison of efficiencies of two-temperature (i.e., two-T) and isothermal solar thermochemical splitting of CO2 and H2O at a given reduction temperature TRe and pO2 ，Re =1.0 Pa, without heat recovery; for two-T cycling, oxidation temperature TOx is 700°C lower than TRe individually, and fu l productivity Δδ is also plott d. Ins t: comparison of ffici ncy ratio of CO2-splitting to H2O-splitting for isothermal and two-T cycling strategies.

3

O2 Partial Pressure (x10 Pa)

3.0 2.5 2.0 1.5

H2O H2O:CO2=2:1 H2O:CO2=1:1 H2O:CO2=1:2 CO2

1.0 0.5 0.0 1200

1400

1600

1800

2000

Temperature (oC) Figure 6. Oxygen partial pressure due to thermolysis of pure H2O, pure CO2 and their mixtures at selected mixing ratios.

Figure 7. Calculated partial pressure of reactants as functions of temperature at the O2 partial pressure of 1 Pa and total pressure of 1 atm.

As noted by several authors in the literature, an important objective for CO2 chemical recycling is turning it into liquid fuels, for which the derivation of syngas is a key intermediate step. The feasibility of syngas production with ceria was experimentally demonstrated by Steinfeld et al. [35] by way of co-splitting H2O and CO2 with two-T thermochemical cycling. Driven by the oxygen partial pressure of simultaneous thermolysis of H2O and CO2, isothermal cycling is also capable of splitting H2O-CO2 mixtures and producing syngas. A preliminary analysis (Fig. 6) indicates that when such a mixture is subject to high temperatures, the pO in the 2

gas phase stays within the range demarcated by those from the thermolysis of pure H2O (lower limit) and pure CO2 (higher limit) and shows a monotonic increase with a decreasing H2O:CO2 ratio. By the thermodynamic analysis process demonstrated in this study, it can be qualitatively predicted that the energy conversion efficiency for the isothermal splitting of H2O-CO2 mixtures is higher than that for pure H2O but lower than that for pure CO2, with higher percentages of CO2 being more favorable. Furthermore, Fig. 7 shows the calculated partial pressure of products as functions of temperature at pO of 1 Pa (for thermal reduction) 2

and a total pressure of 1 atm. Both partial pressures of H2 and CO increase with the increment of temperature, and the pressure of CO rises faster than that of H2 due to the difference in Gibbs free energy change at higher temperatures (Fig. 1a). Additionally, the partial pressure of products (CO, H2) increase rapidly when the temperature exceeds 1700°C. For example, at 1800°C and pO of 1 Pa, the decomposition 2

percentages of H2O and CO2 are 13.2% and 42.9%, respectively.

Due to the difference between thermolysis of CO2 and that of H2O at elevated temperatures, the molar ratio of CO to H2 is expected to be higher than that of CO2 to H2O in the feed. For the purpose of a precise control of syngas composition, the quantitative correlation between products and reactants must be further examined. As shown in Fig. 8a, the CO:H2 ratio in the product scales linearly with the CO:H2 ratio in the feed for temperatures between 1200 and 2000°C, and the CO:H2 ratio in gaseous products is universally higher than the CO2:H2O ratio of the input, which is also consistent with Ref. [35]. Furthermore, the temperature has an interesting influence on the CO:H2 ratio, which increases before the temperature reaches 1600°C but decreases afterward. Such trend holds for all CO2:H2O ratios investigated. The linearity between CO:H2 (product) and CO2:H2O (reactant), as well as the influence of temperature on CO:H2 ratio can both be interpreted by simple thermodynamic relations. To this end, we assume that in a closed system in the oxidation step, the molar amount of CO2 and H2O to start with are m 0 and n 0 , respectively, and that at the equilibrium state after isothermal co-splitting of CO2 and H2O, the molar amounts of CO and H2 are m and n , respectively. By definition of the thermodynamic equilibrium constant, for the splitting of CO2, we obtain

m

m0



1  pO2 / p





 K CO2 T 

0.5

(12)

1

Similarly, for the splitting of water, we obtain

n

n0



1  pO2 / p





0.5

 KH2O T 

(13)

1

where pO2 is the partial pressure of oxygen in the gas phase (common for CO2 and H2O splitting), p  is standard pressure, and KCO2 T  KH2O T  are the thermodynamic equilibrium of a CO2 dissociation reaction (Eq. 3) and H2O dissociation reaction (H2 →

 

 m m0 1  pO2 / p  . n n0 1  p / p O2

 

2

+ 0.5O2), respectively. Then, we obtain

0.5

 KH2O T 

0.5

 K CO2 T 

1 1

(14)

Therefore, we obtain a linear correlation between the product and reactant as



CO CO2  .f pO2 ,T H2 H2O



(15)

where the slope of the line is a function of oxygen partial pressure pO2 and temperature T

 f  p ,T   1  p

1  pO2 / p

O2

O2

/ p

 

0.5

0.5

  T  1   p

 KH2O T 

1

 K CO2

1

1  pO2 / p  O2

/ p

 

0.5

 exp  GH2O T  / RT 

0.5

 exp  GCO2 T  / RT 

(16)





For temperatures higher than 817°C (Fig. 1a), GH2O  GCO2 , and thus, the slope f pO2 ,T  1 regardless of pO2 . We further define the ratio of conversions as the ratio of CO2 conversion to H2O conversion:

R



CO / CO2 m / m0   f pO2 ,T H2 / H2O n / n0



(17)

The ratio of conversion is plotted in Fig. 8b. For each pO2 , there exists a peak value of the ratio R at which the content of CO is the highest for all temperatures explored. The peak value of each curve and the corresponding temperature both decrease with decreasing pO2 , indicating that a higher degree of thermal reduction is in favor of operation at lower temperatures and higher H2 concentration in the syngas. By fixing either pO2 or T and varying the other, one could essentially control the content of the syngas for a wide range of CO2 and H2O input combinations. The significance of the ratio of conversions (Eq. 17) is that the composition of syngas as the output of an isothermal co-splitting system





with arbitrary CO2 and H2O inputs observes a simple dimensionless function .f pO2 ,T and could be controlled through pO2 and T, thereby making it possible to fine-tune the content of the feedstock for further synthesis of liquid fuels.

4.0

Ratio of conversions, R

3.5

3.0

2.5

2.0

pO2 (Pa) 1 0.1 0.01

1.5

(a)

(b)

1.0 1200

1400

1600

1800

2000

Temperature (oC)

Figure 8. Ratio of CO to H2 in the product of isothermal co-splitting of CO2 and H2O. (a) Calculated CO:H2 molar ratio as a function of the CO2:H2O molar ratio with pO2 of 1 Pa and total pressure of 1 atm at different temperatures. (b) Ratio of decomposition percentages of CO2 to H2O as a function of temperature with pO2 of 1 Pa and total pressure of 1 atm.

Finally, as an example to show the feasibility of the isothermal co-splitting scheme for practical syngas production, the solar-to-fuel efficiency (Eq. 4) is calculated for the conditions corresponding to the three peaks in Fig. 8b, i.e., ( pO , T) = (1.0 Pa, 1600°C), (0.1 Pa, 1500°C) and (0.01 Pa, 1400°C); the theoretical 2

efficiencies (assuming minimum work of separation) for the splitting of pure CO2 are 22.0%, 25.6%, 27.6%, respectively. If we assume electrochemical pumping as a means of effective oxygen removal (Eq. 11), then the efficiencies (1.0 Pa, 1600°C), (0.1 Pa, 1500°C) and (0.01 Pa, 1400°C) for the splitting of pure CO 2 become 14.5%, 15.7% and 16.2%, respectively, and efficiencies for the co-splitting of CO2 and H2O with a molar ratio of 1:1 are 10.8%, 12.1% and 12.8%, respectively. The operating temperatures of 1400-1600°C are reasonable for both CO2 and H2O to exhibit sufficient levels of thermolysis and are also well within the reach of solar dish concentrators. Thus, the approach of isothermal co-splitting of CO2 and H2O as proposed above may provide a practical method for solar-syngas production of liquid fuels.

4. Conclusions

In this paper, the analysis is performed on the isothermal solar thermochemical splitting of CO2 at elevated temperatures. The solar-to-fuel efficiency, conversion rate and fuel produced per cycle of isothermal CO2 splitting are considerably higher than that of isothermal splitting of H2O due to the favorable thermodynamic nature of CO2, which leads to higher oxygen partial pressures due to thermolysis and thus higher driving forces for the oxidation step of the splitting cycle. Being lack of phase change and thus of latent heat while heating CO2 is a secondary contributor to its efficiency enhancement. Isothermal CO2 splitting appears to be a more practical way of solar fuel production compared with isothermal H2O splitting because requirements for the concentration ratio of solar concentrators and operating temperature range of the reactors can be readily satisfied with state-of-the-art technologies in this field. Even when compared with conventional twotemperature splitting of CO2, the isothermal strategy is able to achieve comparable or higher efficiencies within the temperature range of 1500-1600°C without heat recovery. The high theoretical efficiency of isothermal CO2 splitting and its potential advantages for reactor design and heat recovery certainly provide a strong basis for it to be considered as a great approach for efficient solar fuel production. Furthermore, isothermal co-splitting of CO2 and H2O is analyzed, and the CO:H2 ratio in the product (syngas) shows a linear dependence on the CO2:H2O ratio on the feed side. The composition of the syngas product is tunable by adjusting the oxygen partial pressure for thermal reduction and temperature of isothermal operation, hereby facilitating control of solar-syngas production which is useful for producing liquid solar fuel afterwards.

Acknowledgments

This study was supported by the National Natural Science Foundation under award number 51676189, the Chinese Academy of Sciences International Collaboration Key Program under award number 182211KYSB20160043, and the Chinese Academy of Sciences Frontier Science Key Research and

Development under award number QYZDYSSW-JSC036. The author would also like to thank Professor Sossina M. Haile at the Northwestern University, U.S.A. for inspirational discussions.

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