Abstract
Synthesis of solar thermochemical hydrogen (STCH) production redox materials with engineered structures, for example, replica foams, can enable efficient heat and mass transport and are critical for scaled-up systems. Prior work has motivated the use of lanthanum strontium manganese (LSM)-type perovskites as foamed STCH materials, but the effect of their morphology on bulk and kinetic behavior has not been reported. In this work, replica and direct foamed samples of La0.65Sr0.35MnO3-δ (LSM35) were fabricated and compared to synthesized powders and dense monoliths, and similarly synthesized CeO2-δ (ceria) foams, regarding their specific reaction rates and bulk oxygen capacity/H2 yields. Changes in oxygen capacity (Δδ) and reaction rates were measured between 1200 °C and 1400 °C by using fixed ratios of steam and hydrogen during both reduction and oxidation steps, allowing for analysis under practical high conversion conditions. Results suggest bulk behavior and reaction rates of the foamed LSM materials are comparable to their powder analogues. Differences in reaction rates were observed only when replica foamed samples were subjected to rapid laser heating (emulating conditions expected in solar furnaces), which is expected but has not been demonstrated at such a small scale. Foamed samples were further subjected to 50 redox cycles at 1400 °C to evaluate their stability. Results show no statistically significant decrease in hydrogen production for any of the foamed samples, but the direct foamed samples became brittle with time. Together, these results demonstrate the viability of replica foamed LSM perovskites for integration in scaled-up STCH systems.
1 Introduction
The state-of-the-art solar thermochemical hydrogen (STCH) metal oxide is nonstoichiometric cerium dioxide or ceria (CeO2−δ). Ceria exhibits stable morphology at high temperatures, reduction at moderate pO2 (e.g., <10−3 atm above 1500 °C), favorable H2O splitting thermodynamics, and fast surface exchange kinetics and/or bulk oxygen transport, making it an excellent candidate for redox cycling [6–8]. Typically, reduction is performed at relatively high temperatures (≥1500 °C) and oxygen partial pressure (pO2) between 10−6 and 10−3 atm using either inert sweep gas or vacuum. Oxidation is usually performed at lower temperatures (≤1000 °C) and pO2 between 10−20 and 10−10 atm, where oxidation is most thermodynamically favorable [8,9]. Ceria undergoes a large entropy change during oxygen exchange, which is thermodynamically favorable when performing redox cycling at different temperatures. The large change in entropy limits the required change in temperature, and thus the required sensible heating, between reduction and oxidation steps [7,10]. These favorable properties have resulted in record solar-to-fuel efficiencies as high as 5.25% as demonstrated by Marxer et al. using a 4 kW solar reactor and 5.6% by Zoller using a 50 kW solar reactor, each demonstrated under CO2 splitting conditions [11–13].
The perovskite (ABO3-δ) class of materials has been identified as a potential pathway for decreasing the reduction temperature [14]. Perovskites have tunable thermodynamic properties as they can be doped with a wide range of elemental combinations [15]. As a result, their partial molar enthalpy can be varied greatly [15–17]. However, perovskites generally experience notably lower entropy changes than ceria, leading to larger temperature changes between reduction and oxygen to achieve similar fuel conversions at the expense of solar-to-fuel efficiency [18]. Some notable perovskites that have been investigated in recent years, namely strontium doped lanthanum-manganese perovskites (La-Sr-Mn or LSM and La-Sr-Mn-Al or LSMA), have demonstrated greater yields than ceria, at the expense of CO2/H2O conversion [19], and also under near-isothermal cycling conditions [18,20]. In near-isothermal cycling conditions, where relatively high oxidation temperatures close to the reduction temperature (e.g., 1400 °C) are used, solar-to-fuel efficiencies using perovskites can be superior to ceria when integrated with high-temperature gas-phase heat recuperation [14,20,21].
Replica ceria foams that promote improved heat and mass transfer via macro- and micro-porous geometries have been used in some notable demonstrations, resulting in record-setting solar-to-fuel efficiencies [11,22–24]. To date, the use of foams as the redox material (as opposed to inert foams coated with active material) has only widely been applied to ceria, focusing more on improving the geometry and manufacturing techniques of the ceria system due to its known structural integrity and redox performance. Earlier efforts to integrate perovskites into foamed structures involved coating an inert scaffold, such as Parvanian et al.’s La0.6Ca0.4 Mn0.7Al0.3O3 (LCMA)-coated SiC foam, or a ceria foam with a thin layer of perovskite, such as the La0.5Sr0.5Mn0.9Mg0.1O3 (LSMMg)-coated ceria system from Haeussler et al. [25–27]. These systems resulted in mechanical instability at extreme temperatures in the case of the inert structures and the creation of diffusional barriers during oxidation in the case of the ceria-coated system. Recently, solid CaMnO3 perovskite porous structures were fabricated and tested by Pein et al., demonstrating promising redox behavior and mechanical integrity for full perovskite foams [28]. Following this, Gager et al. presented a foaming strategy for solid La0.65Sr0.35MnO3-δ (LSM35) replica foams, which demonstrated stable hydrogen production over 50 cycles while maintaining structural integrity [29]. Overall, however, there is limited understanding of LSM foamed structures as redox materials and how their structures may impact bulk behavior, reaction rates, and cycling stability. Therefore, in the present work, LSM35 is synthesized as two different promising foam morphologies, namely direct foams and replica foams, along with ceria, as a basis for comparison. We compare their bulk redox behavior and reaction rates to powders and dense monoliths and evaluate their suitability for scaled-up operation.
2 Material Synthesis
For synthesis and powder-based experiments, commercial CeO2 (99.9%; Sigma Aldrich, St. Louis, MO) with d50 = 1.6 µm and LSM35 powders (Fuel Cell Materials, Lewis Center, OH) with 5% A-site deficiency, i.e., (La0.65Sr0.35)0.95MnO3 and d50 = 1.8 µm were used.
2.1 Direct Foam Synthesis.
CeO2 and LSM35 direct foams were fabricated using a two-part polyurethane (PU) system, FOAM-iT! 10 (Smooth-On, Easton, PA). A two-pot process was used with half the ceramic content mixed in the Part A (isocyanate based) and half in the Part B (polyol based) compounds. A 25 vol% and 27.5 vol% total ceramic content was used for the CeO2 and LSM35 foams, respectively. A higher ceramic content was used for the LSM35 foams to reduce cracking seen during burnout with lower ceramic contents. After mixing the ceramic powder into the respective parts, the two mixtures were combined and mixed at approximately 350 rpm for 15 s. The foams were then dried at room temperature for 24 h. After drying was completed, the foams were sectioned and placed in the furnace for burnout. All heat treatments were performed in the air. The foams were heated to 600 °C using a 60 °C/h ramp rate and held for 1 h to complete the removal of all organics. The subsequent thermal process was slightly different for each composition. Using a 200 °C/h ramp rate, the foams were held at 1050 °C for CeO2 and 900 °C for LSM35 for 2 h to stabilize the foams prior to sintering. The CeO2 foams were then sintered at 1650 °C for 2 h, and the LSM35 foams were sintered using a two-step sintering profile with T1 = 1300 °C and T2 = 1030 °C. A 30 min hold was performed at T1 and 5 h at T2. The optical image of each foam after sintering is presented in Figs. 1(a) and 1(d), along with relevant dimensions and mass.
2.2 Replica Foam Synthesis.
CeO2 and LSM35 replica foams were fabricated using 20 pores per inch (PPI) PU templates. An optical image of the foams is shown in Figs. 1(b) and 1(e), along with relevant dimensions and mass. A detailed description of the fabrication method can be found in our previously reported work on LSM35 [29]. Briefly, two water-based suspensions were fabricated for the dip coating steps. The suspension used for the first coating consisted of 75 wt% ceramic, while the second and third coatings used a 65 wt% suspension. The suspensions were prepared using a planetary ball mill. The ceramic powder, water, dispersant, and wetting agent were added to the mill and thoroughly mixed at 300 rpm. After mixing for 1 h 30 min, the suspension was removed from the ball mill. Binder and thickening agents were added and mixed using a stand stirrer at 250 rpm until homogeneity was achieved, typically after 10 min. PU templates were then dipped in the 75 wt% suspension and manually compressed to remove excess suspension. The CeO2 foams were then dried at 80 °C for 30 min, while the LSM35 foams were dried at room temperature for 24 h. The second and third coatings were then performed with the 65 wt% suspension, and compressed air was used to remove excess suspension and maintain open pores. After three coats, the CeO2 and LSM35 foams were heat treated following the profile used for the direct foams.
2.3 Dense Monolith Synthesis.
Dense Monoliths were uniaxially pressed, at approximately 150 MPa, into 1.4 g cylindrical pellets 13 mm in diameter using 1 wt% polyvinyl alcohol binder. The unfired ceramic pellets were obtained with a geometrical density between 50% and 60%. The pellets were then heat treated with a binder burnout step at 450 °C and 600 °C for 2 and 4 h. The CeO2 pellets were then sintered at 1650 °C for 2 h, and the LSM35 pellets were sintered using a two-step profile with T1 = 1300 °C and T2 = 1030 °C with 30 min and 5 h hold times. The geometrical density of each pellet was measured to be greater than 95% of the theoretical density. An optical image of each monolith after sintering can be seen in Figs. 1(c) and 1(f), along with relevant dimensions and mass.
3 Redox Cycling Experiments
3.1 Horizontal Water Splitting Reactor.
Here, ε is the reaction coordinate, nH2O, i is the input moles of steam, nH2,i is the input moles of hydrogen, ntotal is the total moles of species in the system, and Ptotal is the total system pressure. Kf,H2O is the water formation equilibrium constant, which was obtained from NIST-JANAF Thermochemical Tables [32].
During experimentation, the total Ar flowrate was 599.6 sccm, H2 flowrate was 0.4 sccm, such that the total noncondensable flowrate was maintained at 600 sccm, and steam flowrate varied between 0.658 and 8.718 g/h, depending on the desired ratio of steam to H2, or [nH2O/nH2]in. The RGA was calibrated via 3-point calibration prior to the start of each experiment. Then, the furnace temperature was increased to 300 °C, at which point an initial [nH2O/nH2]in was set. The initial ratio was set such that the reduction pO2 was 10−6.5 atm for all reduction temperatures—i.e., it decreases with increasing temperature. Temperature was increased to the set point (between 1200 and 1400 °C) at a rate of 20 °C/min. Once the prescribed temperature was reached, and the hydrogen signal stabilized, the redox material was isothermally cycled by varying [nH2O/nH2]in. Oxidation was initiated by a stepwise increase of steam flowrate according to the desired [nH2O/nH2]in and indicated by an increase in hydrogen signal in the RGA. After the H2 signal was stabilized, the [nH2O/nH2]in was reversed to repeat reduction at 10−6.5 atm before continuing to the next oxidation, and so on. After final oxidation, the temperature was decreased at a rate of 20 °C/min to 900 °C and exposed to a flow of air for 60 min to allow for complete re-oxidation. Following this dwell, the sample temperature was decreased further to room temperature under a flow of air, to ensure the sample re-oxidized completely (i.e., δ = 0). Δδ over the course of each reaction was determined by time integration of the calibrated H2 signal measured by the RGA. Reduction is characterized by a consumption of H2 and a decrease below the delivered baseline, and oxidation by the production of H2 and an increase above the delivered baseline.
For longer-term cycling of the foams, samples were subjected to two initial cycles to precondition the material and obtain oxidation and reduction rate data for the entire duration of the reaction, until equilibrium was approached. Using this experimental data, the minimized sum of reduction time (tred) and oxidation time (tox) to achieve 50% of the equilibrium predicted Δδ, or Δδmax, was determined through a numerical optimization routine [29]. Then, the subsequent reduction was performed until equilibrium approached, and for the following oxidation and reduction steps, tox and tred were set to these prescribed values to limit the total time required for cycling. Following five isothermal cycles under these controlled times, the material was cooled under Ar atmosphere back to ambient temperature to preserve oxygen nonstoichiometry—this was done because of experimental constraints limiting 24/7 operation. The experimental procedure was repeated for a total of 50 isothermal cycles. A linear regression analysis was performed to detect any significant change in Δδ over the course of the cycles.
3.2 Rationale for Co-Delivery of H2 and H2O During Reduction and Oxidation Steps.
As mentioned, both reduction and oxidation steps were performed with controlled ratios of steam to H2, or [nH2O/nH2]in, where only the steam delivery was changed during redox cycling, and the H2 delivery remained constant. There are several benefits and subtleties of this methodology, which have been discussed prior by Carrillo et al. but are nevertheless briefly mentioned here [30]. First, as mentioned, one benefit is that oxidation can be performed under conditions more representative of high steam conversions, in which the reactive gas stream may become diluted with the product, which limits oxidation extents that are often overestimated because of excess steam delivery. Co-introducing H2 and H2O during oxidation, however, can lead to experimental artifacts from gas switching following reduction (typically only inert gas or inert gas and O2). This is because the product gas that should be quantified (i.e., H2) is also delivered, leading to difficulties accurately separating the product signal from the signal change caused as a result of switching. To circumvent these complications, we alternatively performed reduction with the same input H2 flowrate as used during oxidation but with less H2O. Thus, any deviations from the H2 baseline signal are solely due to reduction (H2 consumption) and oxidation (H2 production) reactions. By controlling the steam flowrate, we can ensure that the pO2 during reduction is still comparable to that which is expected with inert gas. Another benefit of this experimental strategy is that thermodynamic maps can be rendered by readily controlling pO2 over a much wider range of values than is possible from O2 gas mixing strategies. Finally, it is noted that this is not an operational strategy expected to be employed in scaled reactor systems but rather a method to ensure accuracy during the analysis of experimental data.
3.3 Stagnation Flow Reactor.
Laser-heated experiments were performed using Sandia National Laboratories (SNL), Livermore, CA, stagnation flow reactor (SFR). The capabilities of the experimental apparatus are described elsewhere [19,33,34]. To try and elucidate the effect that sample morphology has on reduction reaction rates at this smaller scale, ceria replica foam of two different masses (1.016 g and 0.546 g) and a deep bed of ceria powder of two different masses (1.186 g and 0.618 g) were compared via a temperature swing cycle with a change in temperature of ΔT = 200 °C and the maximum reduction temperature (Tred) reaching 1300 °C. Experimentation began with a 3-point calibration of oxygen and hydrogen via residual gas analysis. A mixture of pure Ar, 5% H2 balanced in Ar, and steam was used to control [nH2O/nH2]in according to the above-described rationale. The Ar flowrate was 360 sccm, H2 flowrate was 0.525 sccm, and steam was delivered at a constant 62.4 sccm. Prior to redox cycling, the sample was heated via indirect heat flux from a vertically oriented tube furnace to a temperature of 1100 °C, and the [nH2O/nH2]in ratio was set to 119. Following stabilization of the H2 signal, reduction was initiated by rapidly heating to 1300 °C at 12.5 °C/s using a 500 W continuous-wave near-infrared diode laser, keeping flowrates unchanged and the [nH2O/nH2]in constant at 119. The total system pressure was sub-ambient at 75 Torr, corresponding to pO2 of 10−8.9 atm and 10−6.5 atm during oxidation and reduction, respectively. This procedure was then repeated for the desired number of redox cycles. The oxygen evolution rate during reduction was derived from the output rate of hydrogen consumption, or deviation from the hydrogen baseline, during each reduction reaction. We assume all oxygen evolved from the reactive material reacted with hydrogen in the gas stream to form H2O, and thus, the rate of evolution of monotonic oxygen from the material is equal to the rate of hydrogen consumption measured by residual gas analysis.
3.4 Results and Discussion
3.4.1 Structural Impacts on Bulk Behavior.
Bulk behavior was investigated by analyzing the H2 yield (Δδ) during long redox cycling times. Exemplary molar flowrates of H2 during redox cycling of ceria and LSM35 direct foams at 1400 °C in the HWSF are shown in Figs. 2 and 3, respectively. The initial temperature ramp is shown in the left subplot under a constant [nH2O/nH2]in of 38, while the redox cycling at constant temperature is shown in the right subplot. The resulting H2 profile in response to stepwise changes in steam to hydrogen input ratio can be observed by deviation of the H2 flowrate signal from the input H2 baseline, shown as a constant dashed line. These increases and decreases from the baseline represent oxidation and reduction, respectively. Reduction of both ceria and LSM35 begins near 700 °C, indicated by the consumption of H2 by the liberated oxygen. Δδ during this initial reduction were 0.197 and 0.073 for LSM35 and ceria, respectively, and are qualitatively consistent with prior works where LSM35 reduced to a greater extent than ceria, and the peak reduction rate was achieved once the isothermal temperature was reached [20]. Subsequent Δδ (normalized per number of atoms) during oxidation under all temperatures considered (1200 °C–1400 °C), and overlayed with predictions based on data from Panlener et al. and Mizusaki et al. (La0.6Sr0.4MnO3, LSM40), are shown in Fig. 4 [7,35]. Here, LSM35 experimental data have been compared to LSM40 due to the lack of LSM35 thermodynamic models in the literature. It has been shown that these materials cycle similarly to each other in prior works, with LSM35 experiencing slightly lower Δδ than LSM40 under most conditions [18,20].
Under all conditions, Δδ/atom was larger for LSM35 compared to ceria. These experimental results are presented in Fig. 4 and agree well with thermodynamic model calculations. Foamed samples generally agree well with the powdered sample. This suggests that the foam structure synthesis procedures do not affect the bulk material properties. The ceria replica foam underwent a slightly lower Δδ than the powder, with a 17% difference, just outside of the 16.3% measured system error determined by repeated measurements, discussed later. This could be explained by the observed slower oxidation rate of the replica foam seen in Fig. 5. Although the sample appeared to approach equilibrium based on the RGA signal during oxidation reaching zero, it could be that the measured rate was below the detection limit.
Here, cp is the specific heat in J mol−1 K−1, ci is the elemental contribution, Ni is the number of occurrences of each element i in the chemical formula, cmisc is the constant associated with elements not having a specific constant from Hurst and Harrison’s analysis, Nmisc is the number of occurrences of the miscellaneous element in the chemical formula, and n is the number of different elements in the compound with specified elemental contributions [37]. Using elemental contribution coefficients from Hurst and Harrison, it can be determined that ceria’s estimated heat capacity is 53.47 J mol−1 K−1, and LSM35’s estimated heat capacity is 95.57 J mol−1 K−1. The estimated heat capacity for ceria agrees well with the predicted value at standard conditions of 60.39 J mol−1 K−1 using correlations from Riess et al. [38]. The ratio of estimated heat capacities between ceria and LSM35 is 0.56, which is represented quite well by the ratio of atoms in the chemical formula of 0.6. The specific heats presented here have been taken from correlations at 298 K; however, trends hold at higher temperatures for ceria and LSM at high temperatures, with a ratio of heat capacities of 0.55 at 1200 K [10,39,40].
3.4.2 Structural Impacts on Reaction Rates.
Oxidation rates at 1400 °C with [nH2O/nH2]in = 500 for ceria and LSM35 samples are shown in Fig. 5 as first-order time derivative curves of delta to qualitatively compare the reaction rates of each material. Powder and replica foam reaction rates were comparable for both samples, with the ceria peak rate for powder being greater than the replica foam for the first 150 s but similar for the rest of the reaction. Direct foam reaction rates were greater than both powder and replica foams. Thus, there is no obvious negative kinetic impact resulting from the use of either of these foamed structures when compared to powders. The dense monoliths of ceria and LSM35 reacted significantly slower than all other morphologies, as expected, likely because of oxygen mass transport limitations through the solid [6]. Also, the LSM35 dense monolith reduced less compared to the other structures, suggesting that the reaction was not given sufficient time to reach equilibrium and demonstrating the significant mass transport limitations associated with the morphology.
Differences in reaction rate were observed when subjecting replica foams and powders to rapid heating in a laser-driven reduction. It is empirically well known and has been experimentally demonstrated that heat transfer is usually reaction rate limiting during reduction in larger-scale solar reactors [41]. This is one of the primary motivating factors behind the utilization of ceria-based replica foams in past reactor demonstrations. They have been used successfully in scaled-up reactors and resulted in improved efficiencies compared to monolithic bricks or felts [41–43]. This is demonstrated in Fig. 6, which shows reduction rates for ceria replica foam and powders of different masses. In these experiments, samples were heated from 1100 °C to 1300 °C at a constant [nH2O/nH2]in of 119. The replica foam (0.546 g or 50% Mass) shown in the left subplot reduced at a peak mass-specific oxygen evolution rate of 0.11 µmol g−1 s−1 and decayed toward equilibrium over time until the laser was powered off. This procedure was repeated with double the mass loading (1.016 g or 100% Mass), and the resulting reduction rate profile was nearly identical to the smaller mass loading, suggesting near mass independence of reaction rate at this scale. This is in stark contrast to trends observed with the ceria powder bed shown in the right subplot. Here, when doubling the mass from 0.618 g to 1.186 g, the peak reduction rate decreased from 0.275 µmol g−1 s−1 to 0.146 µmol g−1 s−1. These rates decrease almost proportionally with increasing sample mass. These results can be explained by the replica foam’s macro-porosity, which promotes volumetric radiative heat transfer and subsequent absorption through the entirety of the sample. The powder bed heat transfer rates, on the other hand, likely rely more on conduction and/or convection through the particle bed.
3.4.3 Stability Testing.
Δδ per atom of each LSM35 foam, replica and direct, over the course of 50 cycles with 50% Δδmax is shown in Fig. 7. From visual inspection, there is no obvious trend in Δδ as the cycles increase, which is supported by statistical linear regression analysis. Regression results indicate a slope of 0 with 95% confidence for all data sets aside from the replica foam reductions (see Fig. 7 inset), indicating that each foam structure did not experience any statistically significant decrease in hydrogen yield over the course of 50 cycles. The average Δδ per atom for the replica foam reduction and oxidation, respectively, was 0.0076 ± 0.0013 and 0.0092 ± 0.0014. The average Δδ per atom for the direct foam reduction and oxidation, respectively, was 0.0107 ± 0.0019 and 0.0112 ± 0.0016. Over the course of the 50 cycles, Δδ during oxidation and reduction for each set were equivalent within two standard deviations from the average Δδ, aside from the few data points which were skewed upward and downward during reduction and oxidation and can be seen in cycles 18-20 and 27-30 for direct foam and cycles 4-5, 34-35 for replica foam. This was caused by the drift of the residual gas signals over the course of the long experiments, which causes an overestimation of oxidation Δδ and an underestimation of reduction Δδ when the drift increases with time and an underestimation of oxidation Δδ and an overestimation of reduction Δδ when the drift decreases with time. The direct foam did not maintain mechanical integrity and became brittle following the extended time at temperature and repeated cycling. The replica foam, however, maintained its mechanical integrity, displaying excellent bulk thermodynamic and mechanical stability.
4 Conclusions
In this study, LSM35 direct and replica foams were synthesized and subjected to bulk behavior, reaction rate, and redox stability investigations in an HWSF in order to determine foam synthesis impact on redox behavior. Bulk behavior and reaction rates were compared to LSM35 dense monolith and powder analogues, as well as similar structures of ceria for a baseline comparison. Advantageous reduction rates using replica foam (ceria) were demonstrated from a new perspective using a laser-heated SFR to observe desirable radiative heat transfer through the foam at the lab scale.
It was observed that LSM35 powder, direct foam, and replica foams all experienced a similar Δδ per atom under a large shift in pO2 and high isothermal cycling temperature. This trend was also observed with the ceria structures. It was also shown that oxidation rates during water splitting were comparable between powders and foamed samples, with all being much greater than dense monoliths. Significant reaction rate dependence on structure was only observed when subjecting a ceria replica foam to a high heat flux source, resulting in near mass independence of reduction reaction rate, while powder reduction rate scaled inversely with mass. Both direct and replica foams of LSM35 demonstrated stable redox cycling over 50 isothermal cycles, validated by a linear regression analysis of each reduction and oxidation set; however, the direct foam did not maintain mechanical integrity. Overall, the work validates the continued use of LSM perovskite replica foam structures for redox cycling and motivates further development and optimization of foam geometries for efficient scalable hydrogen production.
Acknowledgment
We gratefully acknowledge financial support from the U.S. Department of Energy Hydrogen and Fuel Cell Technologies Office (Award Number: DE-EE0008840). Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC (NTESS), a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration (DOE/NNSA) under contract DE-NA0003525. This written work is authored by an employee of NTESS. The employee, not NTESS, owns the right, title, and interest in and to the written work and is responsible for its contents. Any subjective views or opinions that might be expressed in the written work do not necessarily represent the views of the U.S. Government. The DOE will provide public access to results of federally sponsored research in accordance with the DOE Public Access Plan.
Conflict of Interest
There are no conflicts of interest.
Data Availability Statement
The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.
Nomenclature
- c =
modified Kopp contribution
- d =
diameter (mm)
- h =
height (mm)
- i =
input
- m =
mass (g)
- n =
moles
- t =
time (s)
- w =
width (mm)
- K =
equilibrium constant
- L =
length (mm)
- N =
number of occurrences
- P =
pressure (atm)
- T =
temperature (°C)
- cp =
specific heat capacity (J mol−1 K−1)
- [nH2O/nH2]in =
input molar steam to hydrogen ratio
- pO2 =
oxygen partial pressure (atm)