The most advanced solar thermochemical cycles in terms of demonstrated reactor efficiencies are based on temperature swing operated receiver-reactors with open porous ceria foams as a redox material. The demonstrated efficiencies are encouraging but especially for cycles based on ceria as the redox material, studies have pointed out the importance of high solid heat recovery rates to reach competitive process efficiencies. Different concepts for solid heat recovery have been proposed mainly for other types of reactors, and demonstration campaigns have shown first advances. Still, solid heat recovery remains an unsolved challenge. In this study, chances and limitations for solid heat recovery using a thermal storage unit with gas as heat transfer fluid are assessed. A numerical model for the reactor is presented and used to analyze the performance of a storage unit coupled to the reactor. The results show that such a concept could decrease the solar energy demand by up to 40% and should be further investigated.

## Introduction

Renewable chemical energy carriers could replace fossil fuels in the transportation sector and provide a means for long term storage if an efficient and economic production path is identified, that can be scaled to industrial levels. One candidate path which shows a high theoretical potential and for which a significant progress was experimentally demonstrated in the last years is based on two step solar thermochemical cycles for water and carbon dioxide splitting [1]. In these cycles, a redox material is reduced at high temperatures for which concentrated solar radiation is used to provide the necessary high temperature heat. In a second step, the reduced redox material is used to split water or carbon dioxide and provide renewable energy carriers which can be further processed.

Ceria was identified more than 10 years ago as a possible redox material which can be used in this cycle [2]. Positive characteristics of ceria are its physical stability and a reaction enthalpy which is large enough to reach significant conversion ratios during the splitting step. Unfortunately, the high reaction enthalpy of the reduction reaction leads at the same time to high reduction temperatures, typically at around 1500 °C. Intensive efforts have been made to identify a redox material with better properties, but when considering all material aspects and their implications for the process, until now ceria still remains one of the most promising material candidates [3].

The energy analysis of cycles based on ceria reveals that a large share of the energy input is used to heat the redox material after the splitting step (<1000 °C) to the reduction temperature (>1500 °C). Therefore, recovering sensible heat from the reduced redox material to preheat the redox material after the splitting step can significantly increase the process efficiency. Several approaches for solid heat recovery concepts for solar thermochemical cycles have been described theoretically in literature. At the same time only very little information is published about experimental campaigns in this area, mainly because the required high temperatures make such studies already at laboratory scale very challenging.

A first attempt to combine a receiver-reactor with integrated heat recovery is reported by Diver et al. [4] considering ferrites as redox material. Here, the redox material was placed on the outer surface of concentric rings. Through the counter-rotation of adjacent rings heat can be directly transferred from the hot redox material to the cold material. A system performance model predicted a recuperator effectiveness of 85.6%. The highly integrated system involved numerous design issues and tradeoffs. Unfortunately, during the experimental campaign parts of the system failed before reaching steady-state conditions [5]. Another theoretical study for direct heat transfer between monolithic structures was presented by Falter et al. [6]. Also here the monolithic redox material structures are transported as countercurrent streams between two reactors where the different reactions of the process take place. The theoretical study predicted high heat recovery rates above 70% but many technical challenges for the design and its implementation of such a system have precluded experimental studies so far.

Indirect concepts for sensible heat recovery make use of a heat transfer medium. In these concepts the heat transfer medium and the redox material have to be moved relatively to each other. Moving monolithic solids has been proposed by Lapp et al. [7] and heat transfer between redox particles via a separating wall has been proposed by Ermanoski et al. [8] and Falter et al. [6]. These concepts are limited by the effective thermal conductivity of the porous structures and particle beds, especially at low total pressures. In a different concept the use of particles as heat transfer medium was proposed [911]. In this concept binary particle beds of heat transfer particles and redox particles are formed where heat is directly transferred between the two types of particles. The main advantages of such binary particle beds are large surface exchange areas and the resulting high heat exchange rates. First experimental studies of this concept are reported by Felinks et al. [12] and Felinks [13]. Liquid metals as heat transfer medium have been proposed by Yuan et al. [14] predicting high theoretical process efficiencies. While theoretically promising also in case of this concept technical challenges seem significant and are likely to slow down experimental progress. So far no experimental results are reported for such a system.

Gas as heat transfer medium has been presented and tested by Hathaway et al. [15]. In contrast to the reactors considered in the other systems, this reactor is mainly proposed to work isothermally and is therefore rather recovering heat of the heated product stream. For a temperature difference driven redox cycle, the use of gas as heat transfer medium to recover heat of the redox material using a thermal storage has not been assessed so far. Despite of the drawbacks related to the use of gas as heat transfer medium, the concept could be combined with monolithic receiver-reactors and is expected to be technically less challenging compared to the previously discussed systems where solids have to be transported at high temperatures. These benefits are the motivation for the assessment presented here.

## Simulation Model

In this study the benefit of a thermal storage for heat recovery of the solid redox material in a solar thermochemical process is assessed. Therefore, a reactor model is developed and in a second step, coupled to a thermal storage by a gas as heat transfer medium. The reactor modeled in this work is based on the reactor type and operational conditions presented in Marxer et al. [16]. This reactor type uses a receiver cavity with ceria as redox material in the form of a reticulated porous ceramic (RPC) with dual porosity. The reactor is operated in batch mode: In a first phase (reduction) the RPC is heated by concentrated solar radiation and the released oxygen is removed by pulling a vacuum. In the second phase (oxidation) the reactor cools down and the reduced redox material is used to split water or carbon dioxide. This kind of receiver-reactor is the most elaborated type from a demonstrated reactor efficiency perspective and further improvements and a scale up of this reactor type are objectives of the current EU H2020 project SUN-to-LIQUID. A similar approach of a directly irradiated reactive RPC is followed within the series of HYDROSOL projects [17].

The reactor is modeled using a simplified one-dimensional (1D) representation. The obvious benefit of a simplified 1D model is the reduced computational demand compared to geometrically accurate three-dimensional representations of the reactor geometry [18] and even more to simulations with locally resolved RPC structure [19,20]. The simplified model approach allows simulations for a larger number of design and operational parameter combinations. As the model is intended to provide data for an overall plant simulation for yearly yield calculations, low computational demand is important. At the same time, the model still has to be able to reasonably represent the main features of the system and the physical and chemical mechanisms and transport phenomena in order to capture the general behavior of the receiver-reactor. Fortunately, the main aspects of the reactor behavior can be captured in a 1D model as will be presented below.

Figure 1 shows a schematic view of a realistic reactor geometry as well as the features of the 1D model. The real receiver-reactor has a cylindrical cavity surrounded by a ceria RPC, which itself is surrounded by high temperature insulation and a stainless steel shell. The cavity has a circular aperture through which concentrated radiation enters into the cavity. Inlets at the front and outlets at the back of the reactor allow establishing a flow field from the front to the back. In addition vacuum can be pulled by using a connected vacuum pump.

Fig. 1
Fig. 1
Close modal

The 1D model is providing a spatially resolved representation of the RPC in direction from the irradiated surface to the back side of the RPC which is also the general gas flow direction. To capture the thermal inertia of the reactor also the insulation surrounding the RPC is considered. The 1D RPC structure is a volume-averaged porous medium comprised of two phases (solid and fluid) with a local nonthermal equilibrium condition [21]. It is exposed to concentrated radiation with a flux of the same integral power as for a corresponding three-dimensional reactor geometry with cavity (see Fig. 1(a)). Also the integral value of the reradiation is consistent with the reradiation leaving the cavity through the aperture. In the 1D model the RPC thickness is the same as in the real reactor and also the total mass of the RPC is maintained. The RPC has been modeled using the effective properties provided by Ackermann et al. [20] which are based on geometrical properties of the RPC. In the following study only the RPC type will be analyzed, which was used in the experimental campaign [16]. Nevertheless, in future work the analysis can be extended to RPCs with other properties.

In the porous domain the heat transfer is modeled using the transient energy equation
$ρscp∂Ts∂t=∂∂xkeffs∂Ts∂x+αAVTf−Ts+q˙chem+q˙rad$
(1)
For the effective thermal conductivity $keffs$ the Rossland diffusion approximation is used, $αAV$ is the volumetric heat transfer coefficient, $q˙chem$ describes the reaction enthalpy (only during the reduction step - the oxidation is treaded separately as discussed below) and $q˙rad$ contains the incoming radiation and the radiative heat exchange with the surrounding. The penetration of the incoming radiation into the porous structure is approximated using the effective extinction coefficient [20]. Both redox reactions are modeled assuming local equilibrium between the redox material with the given temperature and the partial pressure of oxygen in the reactor based on the correlation given by Ackermann et al. [20]. The fluid phase is assumed to be transparent and all the reaction enthalpy is attributed to the solid phase. The contribution of conduction in the fluid phase is omitted. Therefore, the energy equation for the fluid phase is defined as
$ρfcp∂Tf∂t+uTf=αAVTs−Tf$
(2)

Due to the high permeability of the considered RPC and the low mass flow rates at moderate total pressures during the reduction step the pressure drop over the RPC is neglected. The pressure in the reactor during the reduction is calculated using a pressure dependent pumping speed of a pump. Mass conservation was respected for the different gas species involved in the different phases. The superficial mean velocity $u$ is determined at the front of the porous domain. The governing equations are spatially discretized using the finite volume method and calculated using an in-house Python 3.6 code.

The calculation of the re-oxidation is done in an independent step, after the heat transfer simulation. The thermodynamics of the oxidation of ceria by CO2 can be modeled by the gas-phase-reaction (3) and the surface reaction (4)
$CO2→CO+12O2$
(3)
$CeO2−δred+δred−δox2O2→CeO2−δox$
(4)
This approach was also chosen by Warren et al. [22] and Venstrom et al. [23] in their studies of ceria-based redox cycles. All reactions are assumed to be fast enough to establish equilibrium at each point in time and location in the reactor. The equilibrium state of reaction (3) was calculated with the law of mass action given in the following equation, as reported in detail by the aforementioned studies [22,23]:
$KGR=exp−∑iνi⋅Gi0R⋅T=pCOp0⋅pO2p012pCO2p0$
(5)
where $Gi0$ are the free Gibbs energies of gaseous species i at standard pressure and $νi$ are the according stoichiometric factors from reaction (3). Thermodynamic data to calculate the equilibrium constant $KGR$ was obtained from Aspen Custom Modeler V10, assuming ideal gases. A polynomial of the form
$Gi0=a2⋅Tc2+a1⋅Tc+a0$
(6)
was fitted to the data. Herein $Tc$ is the temperature in ° C. Values for the parameters $ai$ in Eq. (6) are given in Table 1.
Table 1

Parameters for the polynomial fit in Eq. (6)

Compounda2 in (J mol−1° C−2)a1 in (J mol−1° C−1)a0 in (J mol−1)
CO2−1.978 × 10−2−3.151 × 10−3.854 × 105
CO−1.191 × 10−2−1.100 × 102−1.289 × 105
O2−1.238 × 10−2−2.166 × 106.448 × 103
Compounda2 in (J mol−1° C−2)a1 in (J mol−1° C−1)a0 in (J mol−1)
CO2−1.978 × 10−2−3.151 × 10−3.854 × 105
CO−1.191 × 10−2−1.100 × 102−1.289 × 105
O2−1.238 × 10−2−2.166 × 106.448 × 103
The time-step width has to be small enough to ensure
$n˙Gas⋅Δt≪ΔnGas$
(7)
holds, i.e., the amount of matter transported through a finite element per time-step is small compared to the matter stored in the element. Otherwise the change of gas-composition over time would not be considered sufficiently in the equilibrium calculations.

As will be discussed later, the simulation of the oxidation step is only poorly representing the real behavior during the re-oxidation. It has been shown experimentally that the oxidation rate is limited by the active surface but so far not enough information is available to accurately capture this aspect in the model for different RPC structures. By choosing a RPC temperature value of 750 °C as condition for the end of the oxidation and the start of the preheating or reduction step, and by assuming a negligible impact of the reaction-heat and an almost complete re-oxidation at this stage, the following study can be reasonably conducted without details about the oxidation kinetics.

The storage model is using similar governing equations as the thermal model of the reactor but omitting the reaction enthalpy term and the radiative term. As a reasonable first assumption it considers a porous structure as heat storage medium with the same effective properties as the RPC in the receiver-reactor but chemically inert during the cycle. In contrast to the RPC in the reactor a porous medium with smaller cross section and larger thickness is assumed for the storage. In this study the ratio between cross section areas of the RPC of the reactor and of the porous storage material is 5. As the physical properties are the same for both structures and $cp$ is assumed constant a heat capacity ratio ($HCR$) can be defined as
$HCR=mstmreac$
(8)

This value describes the ratio of the thermal capacity of the storage material to the thermal capacity of the RPC in the reactor. The $HCR$ will be varied in the following study to analyze the impact of relative storage sizing.

## Model Results and Discussion

### Reactor Without Storage.

For the validation of the receiver-reactor model simulation results are compared to experimental data published by Marxer et al. [16]. The geometrical representation in the model agrees with the experimental values for the total amount of ceria in the reactor, the RPC thickness (25 mm), the aperture radius (20 mm) and the average concentration ratio at the aperture (2790). The boundary conditions of the simulation were chosen to match the information provided in the paper wherever possible. This includes the volumetric flow rates and the start and end temperatures of the reduction and oxidation phases. In Fig. 2 the experimental data (extracted from Fig. 2 of Marxer et al. [16]) and simulation results are depicted, including the temperature evolution and the production rates of O2 during the reduction and CO during the oxidation.

Fig. 2
Fig. 2
Close modal

First, the temperature evolution is discussed: In general the simulation results show a good agreement with the experimental temperatures during the heating (reduction) and cooling (oxidation) phases. Still, certain differences are highlighted and discussed: The onset of the temperature increase is much stronger in the simulation, while the experimental data shows a significant time delay before the temperature increases. One reason for this might be that the simulation results are showing the average temperature of the RPC structure, while for the experimental results it is not clear how exactly this temperature was obtained. One possible explanation is that for the determination of the “nominal” reactor temperature thermocouple signals primarily at the back side of the RPC were used. This would be in line with the description of the experimental settings in a similar campaign [24].

To further investigate this aspect the simulated temperature evolution is shown also for the front as well as for the back of the RPC in Fig. 3. The simulation results of the back side of the RPC show also a delayed temperature increase, but still not as pronounced as the experimental results. This will be further analyzed in the context of the oxygen release.

Fig. 3
Fig. 3
Close modal

The second aspect in the validation is the reduction of the RPC and the resulting release of O2. In Fig. 2 the evolution of the O2 release rate is shown for the experiment as well as for the simulation. The results obtained in the simulation are smaller throughout the whole reduction step. Only at the end of the reduction step, similar values are reached (0.37 mL min−1 gCeO2−1 in the experiment compared to 0.30 mL min−1 gCeO2−1 in the simulation). Also the shapes of the release rate curves are different. The experimental rate reaches a level, which stays constant for about 5 min until the end of the reduction step. In comparison the simulated release rate is constantly increasing. For the interpretation of these differences, the integral value of the released oxygen is calculated. The total amount of released O2 in the experiment is about 3 mL gCeO2−1 which results in 0.21 molO2. If one calculates the equilibrium δ for T = 1500 °C (nominal temperature at end of reduction) and pO2 = 10 mbar (measured total pressure at end of reduction) for 10 mol of ceria (as used in the reactor), one would expect a release of about 0.077 molO2. This shows that the released amount O2 is significantly higher than expected at these conditions, even if the whole RPC is reduced homogenously. Higher temperatures or lower partial pressures are needed to reach the observed amount of O2. Looking at the pressure evolution shown in Fig. 2 of Marxer et al. [16] one would assume that the O2 share in the atmosphere in the reactor at the end of the reduction cycle is significant even if the reactor is swept during the reduction at $V˙Ar=0.625Lmin−1$. Assuming a lower limit of pO2 min = 2.5 mbar, one would need at least an average temperature of 1600 °C to obtain an O2 release above 0.2 mol. Since at least the back of the RPC is at temperatures close to 1500 °C parts of the RPC will have to be heated during the reduction phase to temperatures significantly above 1600 °C. This could be a result of a rather inhomogeneous flux distribution of the incoming radiation which is realistic considering that at most seven lamps have been used during the experiment. In such a case, the RPC would locally reach temperatures well above the nominal temperature of the reactor. Due to the highly nonlinear temperature dependence of the oxygen release characteristic of ceria, this could lead to a higher overall O2 release. At the same time a higher local flux density could also explain the early and stronger onset of the O2 release. Due to radiative heat exchange in the cavity the temperature distribution would be more homogenized at later stages during the reduction.

Taking this into consideration the CO release curve is analyzed. The simulation shows a much higher and narrower CO peak. As can be easily observed also the total amount of produced CO is significantly smaller in the case of the simulation. The lower total amount is in line with the smaller O2 release and therefore with the achieved reduction extent at the end of the reduction step. In contrast to the reduction, the oxidation reaction rate is expected to be limited by the surface area of the RPC [26]. Since the simulation result just considers the temperature, gas phase composition and local reduction extent, a limitation by the surface exchange is not included and the peak rate is overestimating the real evolution. This is in line with similar results for the thermodynamic limit of CO release rates presented in Fig. 3 of Marxer et al. [16].

In total, the analysis of the experimental data and the simulation results suggest that the model captures reasonably well the main transport mechanisms in the reactor and the RPC structure for the thermal analysis. Especially if a homogenous flux is applied the average temperature evolution of the RPC structure is expected to be in good agreement. The total amounts of produced O2 and CO differ roughly by a factor of 2; the reason for this is attributed to a larger inhomogeneity of the local flux densities of the incoming radiation. Since the experimental reactor efficiency is in the order of 5%, the reaction enthalpies still have a minor impact on the overall thermal behavior of the reactor and the model can be applied for the investigation of the coupling of storage unit and reactor.

### Coupling of Storage Unit and Reactor.

As described in the introduction, heat recovery of the reactive material is crucial to improve the system efficiency. In this study the option of using a gas as heat transfer medium will be analyzed using the simplified 1D reactor model coupled to a thermal storage model (Fig. 4).

Fig. 4
Fig. 4
Close modal

While in the case without storage there are mainly two phases—reduction and oxidation—two more phases have to be considered if a thermal storage is used: preheating and cooling. In the preheating phase a heat transfer fluid (HTF) is heated in the storage unit and used to heat the RPC in the reactor. During the cooling phase the HTF is used to transfer heat from the hot reduced RPC to the storage.

The conditions for the end of the different phases are summarized in Table 2. The preheating is stopped as soon as the temperature in the reactor ($Trc$) decreases. In case of the cooling phase a temperature decline in the storage ($Tst$) is used as stopping criteria. At the start of the simulation all parts of the reactor and the storage unit are at the oxidation end temperature (750 °C).

Table 2

Phase end conditions

PhaseEnd condition
PreheatingMean $Trc$ is decreasing
ReductionMean $Trc>1500 °C$
CoolingMean $Tst$ is decreasing
OxidationMean $Trc<750 °C$
PhaseEnd condition
PreheatingMean $Trc$ is decreasing
ReductionMean $Trc>1500 °C$
CoolingMean $Tst$ is decreasing
OxidationMean $Trc<750 °C$

The relative durations of the four phases with respect to the corresponding converged phase durations are displayed for consecutive cycles in Fig. 5. After an initial phase of changing durations the system converges to a state where the durations of the different phase have reached constant values. For the case shown in Fig. 5 this constant state is reached after about eight cycles. Especially for lower HTF flow rates and larger storage sizes a constant state is reached rather at larger cycle numbers. A maximum of 16 cycles were simulated if the durations did not converge beforehand. The situation changes when heat losses in the pipes connecting the storage and the reactor are considered. This is discussed in further detail in the context of Fig. 6.

Fig. 5
Fig. 5
Close modal
Fig. 6
Fig. 6
Close modal

While the preheating phase could be done in principle on sun, here the case without irradiation during the preheating phase is considered. Heat losses could be lowered by closing the aperture for the duration of the preheating phase but since the reactors described in this study do not have an adaptable aperture it is also not considered in this study and the aperture is assumed to remain open during the whole cycle.

Unintended oxidation of the reduced ceria during the cooling phase has to be avoided, but if a reasonably clean inert gas is used, the total amount of O2 which is present in the HTF and which might be absorbed by the ceria should not be worrisome. A blower is used to provide the necessary pressure increase to maintain the required gas flow rate in the circuit connecting the reactor and the storage. In this study purified nitrogen is considered as HTF.

Since heat losses of a storage unit typically become relatively less important for larger scales, the considered reactor will be a scaled version of the model geometry (3.5 kW) described in Sec. 2. In order to respect size limiting factors like the window size, a conservative estimate of 300 kW for the scale up version is used. Properties like the aperture area, the ceria mass load, the volumetric flow rates of the gases, the oxidizer and the pumping speed of the vacuum pump are scaled by the same factor. The insulation thickness is increased from 60 mm to 0.2 m.

### Theoretical Heat Recovery Potential of an Ideal System With Storage.

Before looking into the simulation results of the reactor model coupled to a storage unit, the theoretical potential of different sized storage units for recovering heat is briefly discussed assessing the energy balance. Considering repeated ideal co-current heat transfer from one unit (reactor) with alternating start temperatures of Tred (1500 °C) and Tox (750 °C) to a second unit (storage) and back, a theoretical maximum heat recovery rate ($HRR$) can be reached. Assuming a constant heat capacity the heat recovery rate can be defined, using the temperature of the reactor after the recovery step $Thr$, as
$HRR=Thr−ToxTred−Tox$
(9)

The heat recovery rate is shown in Fig. 7 for different sized storage units represented by the $HCR$.

Fig. 7
Fig. 7
Close modal

While for a $HCR$ of 1 the heat recovery rate is limited to 1/3, it approaches a heat recovery rate close to 0.5 for larger $HCR$ values. This result suggests that the storage unit should be as large as possible. In a real system, different other effects are important and will limit the reasonable size of the storage unit as discussed below. A first drawback of large storage units is shown in Fig. 8. Larger storage units reach higher heat recovery rates only after an increasing number of iterations. Taking the limited number of hours during a day for the operation of a solar thermochemical process into account at typical cycle durations in the order of 40 min for this reactor design (see Fig. 2) a reasonable storage unit will probably have a $HCR$ below 5. Larger storage units can be advantageous if the heat losses are low and heat is stored overnight. In such a case, the storage unit can also be used to decrease the start-up time of the system and help prevent large temperature gradients.

Fig. 8
Fig. 8
Close modal

### Performance Analysis of a Coupled System.

In the following analysis the reactor is coupled to a storage unit with the 1D modeling approach described above. Two different cases are assessed: First, heat losses of the storage as well as heat losses in the pipes connecting the receiver-reactor to the storage unit are neglected. Since the heat losses can in principle be reduced significantly by using thicker layers of insulation with lower thermal conductivity values, this often has to be balanced by economic factors which are not discussed in this study. Therefore, the results without heat losses are included to indicate the potential of the technology. Second, heat losses for the storage are estimated for an insulation layer thickness $lins=0.25m$ and a thermal conductivity $kins=0.25W/(mK)$ at the front and back side of the heat storage medium as
$q˙loss=kinslinsAinsTst−Tamb$
(10)
The ambient temperature $Tamb$ is set to 20 °C. Losses to the sides are neglected. The heat losses in the piping are approximated by assuming a fixed temperature difference over the insulation of the pipe of 1200 K. The corresponding temperature loss $Tloss$ of the HTF between the reactor and the storage as a function of the flow rate factor $FRF$ can then be calculated as
$Tloss=31.72KFRF$
(11)
where $FRF$ is defined as
$FRF=V˙V˙basic$
(12)

Since the storage is only used to preheat the reactor if there is actually a temperature increase in the reactor, the heat losses in the pipes can cause the preheating phase to stop directly if the temperature increase of the HTF in the storage is too low. In this case the preheating phase is skipped which can result in cyclic fluctuations of the durations for preheating and cooling (see Fig. 6). For the investigated cases this phenomenon is observed for low $FRF$ (<4) and large $HCR$ (>3.5). In these cases the reduction duration does not stabilize and the results are not included in the following analysis.

In addition it is assumed that the storage unit does not have an idle time. For the storage unit the preheating step is directly followed by a cooling step. This could be achieved in practice, if several phase shifted reactors share the same storage unit.

In Fig. 9 the mean temperature of the RPC in a reactor is shown for a complete cycle without storage and for a complete cycle with storage. For the case with storage, the different phases of the cycle—preheating, reduction, cooling, and oxidation—are indicated. As can be seen the storage is used to increase the temperature of the RPC after the oxidation and before the irradiation starts. With this, the duration of the irradiation and therefore the required heat input can be decreased. The duration from the end of the oxidation to the end of the reduction is increased since the preheating is only slowly increasing the temperature of the RPC in comparison to the reduction phase with irradiation. During the cooling typically higher gas flow rates are used compared to the oxidizer flow rate, but at the same time the temperature of the gas entering the reactor is higher compared to oxidizer inlet temperature. Therefore, the total duration of cooling and oxidation depends on the design and operational conditions.

Fig. 9
Fig. 9
Close modal

In the following parametric study mainly two parameters will be assessed. The first one is the flow rate of the HTF, the second one the storage size. The changes will be represented by changing $FRF$ and $HCR$ values. General parameters of the analyzed system are summarized in Table 3.

Table 3

Baseline parameters

Parameter nameValueUnit
Concentration ratio at aperture2790
RPC thickness reactor0.025m
Number of pores per inch10
Insulation thickness reactor0.2m
Insulation thickness storage0.25m
Insulation thickness pipe0.15m
Thermal conductivity insulation0.25W m−1 K−1
Ratio of cross section areas of reactor and storage5
Oxidizer flow rate600L min−1
HTF flow rate ($V˙basic)$6000L min−1
Length of pipes in HTF circuit5m
Pipe diameter0.1m
Pipe roughness0.0001m
Number of bends in HTF circuit4
Isentropic blower efficiency0.5
Heat to electricity efficiency0.4
Parameter nameValueUnit
Concentration ratio at aperture2790
RPC thickness reactor0.025m
Number of pores per inch10
Insulation thickness reactor0.2m
Insulation thickness storage0.25m
Insulation thickness pipe0.15m
Thermal conductivity insulation0.25W m−1 K−1
Ratio of cross section areas of reactor and storage5
Oxidizer flow rate600L min−1
HTF flow rate ($V˙basic)$6000L min−1
Length of pipes in HTF circuit5m
Pipe diameter0.1m
Pipe roughness0.0001m
Number of bends in HTF circuit4
Isentropic blower efficiency0.5
Heat to electricity efficiency0.4
Heat recovery of the redox material is the main objective of the application of a storage unit. In addition, the storage has an effect on other parts of the system like the heat stored in the insulation and the heat lost to the ambient. Therefore, instead of the heat recovery rate a new metric based on the solar energy input demand is introduced to analyze the benefit of the coupled system with storage. Solar radiation is only considered as energy source during the reduction step. Since the flux at the aperture is assumed constant throughout the reduction step the solar input is determined by the duration of the respective reduction steps. From this a relative energy benefit ($REB$) can be derived when comparing the reduction step duration of the case with storage $tredst$ to the case without storage $tredno−st$
$REB=1−tredsttredno−st$
(13)

The resulting $REB$ for different multiples of the baseline HTF flow rate value are shown in Fig. 10. The figure contains two sets of simulation results: The first set is obtained for an ideal storage without heat losses in the storage and the HTF circuit to show the potential of the approach and the second set is obtained considering heat losses as described above for a more realistic perspective.

Fig. 10
Fig. 10
Close modal

For the cases shown in the figure the $REB$ is increasing with increasing $HCR$ promoting larger storage units. If losses are considered, $REB$ values close to 40% are predicted. If several storage units are combined and the operation is adjusted to establish a quasi-countercurrent heat flow, even higher $REB$ values seem possible [10].

The $REB$ is also increasing with the HTF flow rate. This can be seen in more detail in Fig. 11. For values up to a $FRF$ of 6 the $REB$ is strongly increasing. Above this value a saturation effect can be noticed and large increases in mass flow rate lead to diminishing improvements of the $REB$. Larger $HCR$ have a positive effect on the $REB$, especially for larger factors of the HTF flow rate. Also for the $HCR$ a saturation effect can be noticed, comparable to the results shown in Fig. 7. The comparison of the values with and without heat losses shows that a storage unit with heat losses leads to significantly lower $REB$ values for lower HTF flow rates (below a flow rate factor of 4). For higher values the effect of heat losses on the $REB$ is significantly reduced. This is mainly caused by the lower temperature decrease of the HTF in the piping at larger flow rates.

Fig. 11
Fig. 11
Close modal

While the $REB$ increase for higher HTF flow rates the parasitic power demand for pumping the HTF through the circuit increases as well—negatively influencing the overall system efficiency. In order to quantify this effect the pressure loss in the circuit and the blower performance are calculated for different HTF flow rates.

For the pressure loss calculation of the RPC in the reactor and of the storage medium permeability and Dupuit–Forchheimer coefficient correlations given by Ackermann et al. [20] in combination with Darcy's law are used. For the calculation of the pressure loss in the pipes and bends the properties given in Table 3 and the correlations described in the chapter “Fluid Dynamics and Pressure Drop” of the VDI Heat Atlas [27] are used. The corresponding power demand of the blower is then determined in the simulation software aspenplus with the model “Compr” from the Aspen Model library and operated in “Isentropic” mode, in which the outlet temperature is determined by specifying the isentropic efficiency of the compressor. As property method the Peng–Robinson equation of state is used. The fluid temperature at the inlet of the blower is set to 1225 °C.

The electrical energy demands of the blower during the preheating and cooling phases are added and converted to an equivalent heat demand using a heat to electricity efficiency. These values are compared in Fig. 12 to the savings in required solar energy input due to the use of the storage. To put these values into perspective the endotherm reaction energy of reactors without storage and with the demonstrated 5% efficiency and a hypothetical 20% efficiency are included.

Fig. 12
Fig. 12
Close modal

As can be seen, the savings in required solar energy input are significant and they are converging for large flow rates. At the same time the equivalent heat demand for pumping the HTF through the cycle is strongly increasing with the flow rate and surpasses the reaction energies and also the energy savings per cycle, limiting the benefits of a storage at large flow rates. Nevertheless, there seems to be a flow rate range where the demand of the pump is significantly below the energetic benefits of the coupled storage system. In this flow rate range the use of such a storage system seems to be highly valuable and should be further investigated in more detail.

## Summary and Conclusions

This study assesses the use of a thermal storage unit for recovering sensible heat of a redox material in a solar thermochemical cycle for water and carbon dioxide splitting using gas as heat transfer medium. A 1D reactor model is presented for the simulation of consecutive sequences of solar thermochemical cycles. By comparing the simulation results to experimental results differences primarily of the reduction reaction rates and oxidation reaction rates can be noticed. For the reduction reaction, inhomogeneous flux conditions at the RPC front are seen as a main cause for these differences. In the oxidation reaction, limitations of the surface reaction rate are not yet integrated in the model leading to an overestimation of the oxidation rate. For a more accurate description of the oxidation reaction further experimental and numerical studies for different RPC structures will be required. Despite these differences between the 1D model and the experiment, the general thermal behavior of the model agrees well with the experimental results justifying the use of the model for the heat recovery analysis.

When coupling the reactor to the storage unit, two new phases for the process are added: a preheating phase where heat is transferred from the storage to the reactor after the oxidation and a cooling phase where heat is transferred from the hot reactor after the reduction to the storage. For the analysis the change in duration of the reduction phase is used to calculate a relative energy benefit.

Two parameters are primarily assessed: the flow rate of the heat transfer fluid and the ratio between the overall heat capacity of the storage medium and the RPC in the reactor. Larger storage units seem to be capable to recover a larger share of the heat, but it takes more cycles to charge the storage before they outperform smaller storage units and they cause a larger pressure drop.

Larger flow rates of the heat transfer fluid increase the recovered heat and allow better usage of larger storage units. At the same time the power demand for pumping the heat transfer fluid is strongly increasing with the flow rate limiting the reasonable upper flow rate. While for a single storage unit a reduction of up to 40% of the required solar energy input seems possible, the combination of multiple storage units at different temperature levels might increase the energy benefit even further.

Besides these encouraging performance predictions, additional advantages of this approach compared to other heat recovery concepts discussed in literature are the expected lower technical complexity and its capability to be coupled to the currently most elaborated reactor type and thereby advancing this technology further.

## Funding Data

• European Union Horizon 2020 Research and Innovation Program (654408, Funder ID. 10.13039/100010661).

• Swiss State Secretariat for Education, Research and Innovation (Staatssekretariat für Bildung, Forschung und Innovation) (SERI) (15.0330, Funder ID. 10.13039/501100007352).

## References

1.
Nakamura
,
T.
,
1977
, “
Hydrogen Production From Water Utilizing Solar Heat at High Temperatures
,”
Sol. Energy
,
19
(
5
), pp.
467
475
.
2.
,
S.
, and
Flamant
,
G.
,
2006
, “
Thermochemical Hydrogen Production From a Two-Step Solar-Driven Water-Splitting Cycle Based on Cerium Oxides
,”
Sol. Energy
,
80
(
12
), pp.
1611
1623
.
3.
Muhich
,
C. L.
,
Blaser
,
S.
,
Hoes
,
M.C.
, and
Steinfeld
,
A.
,
2018
, “
Comparing the Solar-to-Fuel Energy Conversion Efficiency of Ceria and Perovskite Based Thermochemical Redox Cycles for Splitting H2O and CO2
,”
Int. J. Hydrogen Energy
,
43
(
41
), pp.
18814
18831
.
4.
Diver
,
R. B.
,
Miller
,
J. E.
,
Allendorf
,
M. D.
,
Siegel
,
N. P.
, and
Hogan
,
R. E.
,
2008
, “
Solar Thermochemical Water-Splitting Ferrite-Cycle Heat Engines
,”
ASME J. Sol. Energy Eng.
,
130
(
4
), pp.
41001
41008
.
5.
Diver
,
R. B.
,
Miller
,
J. E.
,
Siegel
,
N. P.
, and
Moss
,
T. A.
,
2010
, “
Testing of a CR5 Solar Thermochemical Heat Engine Prototype
,”
ASME
Paper No. ES2010-90093.
6.
Falter
,
C. P.
,
Sizmann
,
A.
, and
Pitz-Paal
,
R.
,
2015
, “
Modular Reactor Model for the Solar Thermochemical Production of Syngas Incorporating Counter-Flow Solid Heat Exchange
,”
Sol. Energy
,
122
, pp.
1296
1308
.
7.
Lapp
,
J.
,
Davidson
,
J.
, and
Lipiński
,
W.
,
2012
, “
Efficiency of Two-Step Solar Thermochemical Non-Stoichiometric Redox Cycles With Heat Recovery
,”
Energy
,
37
(
1
), pp.
591
600
.
8.
Ermanoski
,
I.
,
Siegel
,
N. P.
, and
Stechel
,
E. B.
,
2013
, “
A New Reactor Concept for Efficient Solar-Thermochemical Fuel Production
,”
ASME J. Sol. Energy Eng.
,
135
(
3
), p.
031002
.
9.
Brendelberger
,
S.
,
,
J.
,
Roeb
,
M.
, and
Sattler
,
C.
,
2014
, “
Solid Phase Heat Recovery and Multi Chamber Reduction for Redox Cycles
,”
ASME
Paper No. ES2014-6421.
10.
,
J.
,
Brendelberger
,
S.
,
Roeb
,
M.
,
Sattler
,
C.
, and
Pitz-Paal
,
R.
,
2014
, “
Heat Recovery Concept for Thermochemical Processes Using a Solid Heat Transfer Medium
,”
Appl. Therm. Eng.
,
73
(
1
), pp.
1006
1013
.
11.
Brendelberger
,
S.
, and
Sattler
,
C.
,
2015
, “
Concept Analysis of an Indirect Particle-Based Redox Process for Solar-Driven H2O/CO2 Splitting
,”
Sol. Energy
,
113
, pp.
158
170
.
12.
,
J.
,
Richter
,
S.
,
Lachmann
,
B.
,
Brendelberger
,
S.
,
Roeb
,
M.
,
Sattler
,
C.
, and
Pitz-Paal
,
R.
,
2016
, “
Particle–Particle Heat Transfer Coefficient in a Binary Packed Bed of Alumina and Zirconia-Ceria Particles
,”
Appl. Therm. Eng.
,
101
, pp.
101
111
.
13.
,
J.
,
2017
,
Heat Recovery From Particles Using Spherical Heat Transfer Media in Solar Thermochemical Cycles
,
RWTH Aachen
,
Aachen, Germany
.
14.
Yuan
,
C.
,
Jarrett
,
C.
,
Chueh
,
W.
,
Kawajiri
,
Y.
, and
Henry
,
A.
,
2015
, “
A New Solar Fuels Reactor Concept Based on a Liquid Metal Heat Transfer Fluid: Reactor Design and Efficiency Estimation
,”
Sol. Energy
,
122
, pp.
547
561
.
15.
Hathaway
,
B. J.
,
Bala Chandran
,
R.
,
,
A. C.
,
Chase
,
T. R.
, and
Davidson
,
J. H.
,
2016
, “
Demonstration of a Solar Reactor for Carbon Dioxide Splitting Via the Isothermal Ceria Redox Cycle and Practical Implications
,”
Energy Fuels
,
30
(
8
), pp.
6654
6661
.
16.
Marxer
,
D.
,
Furler
,
P.
,
Takacs
,
M.
, and
Steinfeld
,
A.
,
2017
, “
Solar Thermochemical Splitting of CO2 Into Separate Streams of CO and O2 With High Selectivity, Stability, Conversion, and Efficiency
,”
Energy Environ. Sci.
,
10
(
5
), pp.
1142
1149
.
17.
Säck
,
J. P.
,
Breuer
,
S.
,
Cotelli
,
P.
,
Houaijia
,
A.
,
Lange
,
M.
,
Wullenkord
,
M.
,
Spenke
,
C.
,
Roeb
,
M.
, and
Sattler
,
C.
,
2016
, “
High Temperature Hydrogen Production: Design of a 750 KW Demonstration Plant for a Two Step Thermochemical Cycle
,”
Sol. Energy
,
135
, pp.
232
241
.
18.
Kyrimis
,
S.
,
Le Clercq
,
P.
, and
Brendelberger
,
S.
,
2018
, “
3D Modelling of a Solar Thermochemical Reactor for MW Scaling-Up Studies
,”
SolarPACES
, Casablanca, Morocco, Oct. 2–5, Paper No. 25746.
19.
Haussener
,
S.
,
Jerjen
,
I.
,
Wyss
,
P.
, and
Steinfeld
,
A.
,
2012
, “
Tomography-Based Determination of Effective Transport Properties for Reacting Porous Media
,”
ASME J. Heat Transfer
,
134
(
1
), p. 012601.
20.
Ackermann
,
S.
,
Takacs
,
M.
,
Scheffe
,
J.
, and
Steinfeld
,
A.
,
2017
, “
Reticulated Porous Ceria Undergoing Thermochemical Reduction With High-Flux Irradiation
,”
Int. J. Heat Mass Transfer
,
107
, pp.
439
449
.
21.
Saito
,
M. B.
, and
de Lemos
,
M. J. S.
,
2005
, “
Interfacial Heat Transfer Coefficient for Non-Equilibrium Convective Transport in Porous Media
,”
Int. Commun. Heat Mass Transfer
,
32
(
5
), pp.
666
676
.
22.
Warren
,
K. J.
,
Reim
,
J.
,
Randhir
,
K.
,
Greek
,
B.
,
Carrillo
,
R.
,
Hahn
,
D. W.
, and
Scheffe
,
J. R.
,
2017
, “
Theoretical and Experimental Investigation of Solar Methane Reforming Through the Nonstoichiometric Ceria Redox Cycle
,”
Energy Technol.
,
5
(
11
), pp.
2138
2149
.
23.
Venstrom
,
L. J.
,
De Smith
,
R. M.
,
Chandran
,
R. B.
,
Boman
,
D. B.
,
Krenzke
,
P. T.
, and
Davidson
,
J. H.
,
2015
, “
Applicability of an Equilibrium Model to Predict the Conversion of CO2 to CO Via the Reduction and Oxidation of a Fixed Bed of Cerium Dioxide
,”
Energy Fuels
,
29
(
12
), pp.
8168
8177
.
24.
Marxer
,
D.
,
Furler
,
P.
,
Scheffe
,
J.
,
Geerlings
,
H.
,
Falter
,
C.
,
Batteiger
,
V.
,
Sizmann
,
A.
, and
Steinfeld
,
A.
,
2015
, “
Demonstration of the Entire Production Chain to Renewable Kerosene Via Solar Thermochemical Splitting of H2O and CO2
,”
Energy Fuels
,
29
(
5
), pp.
3241
3250
.
25.
Keene
,
D. J.
,
Davidson
,
J. H.
, and
Lipinski
,
W.
,
2013
, “
A Model of Transient Heat and Mass Transfer in a Heterogeneous Medium of Ceria Undergoing Nonstoichiometric Reduction
,”
ASME J. Heat Transfer
,
135
(
5
), p. 052701.
26.
Takacs
,
M.
,
Ackermann
,
S.
,
Bonk
,
A.
,
Neises‐von
,
M.
, Puttkamer, Haueter, Ph.,
Scheffe
,
J. R.
,
Vogt
,
U. F.
, and
Steinfeld
,
A.
,
2017
, “
Splitting CO2 With a Ceria-Based Redox Cycle in a Solar-Driven Thermogravimetric Analyzer
,”
AIChE J.
,
63
(
4
), pp.
1263
1271
.https://doi.org/10.1002/aic.15501
27.
Part L1.2
Kast
,
W.
, and
Nirschl
,
H.
,
2010
,
VDI Heat Atlas
, 2nd ed.,
Springer
,
Berlin
.