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Improved kinetic model for water splitting thermochemical cycles using Nickel Ferrite
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 6 3 1 7 e6 3 2 7
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Improved kinetic model for water splitting thermochemical cycles using Nickel Ferrite Margaritis Kostoglou a,b, Souzana Lorentzou a, Athanasios G. Konstandopoulos a,c,* a
Aerosol & Particle Technology Laboratory, CPERI/CERTH, 6th km Charilaou-Thermi Rd, P.O. Box 60361, 57001 Thessaloniki, Greece b Department of Chemistry, Aristotle University of Thessaloniki, P.O. Box 116, 54124 Thessaloniki, Greece c Department of Chemical Engineering, Aristotle University, P.O. Box 1517, 54006 Thessaloniki, Greece
article info
abstract
Article history:
In a previous work of the authors (AIChE Journal 2013; 59(4): 1213-1225) on the character-
Received 17 September 2013
ization of the performance of redox material compositions during two-step thermo-
Received in revised form
chemical splitting of water, it was observed that fitting of the obtained hydrogen and
7 January 2014
oxygen concentration profiles with a reaction model based on simple first order reaction
Accepted 19 January 2014
rates could describe adequately only the first part of the evolution curves. This suggested
Available online 5 March 2014
that more complicated reaction models taking into account the structure of the redox material are needed to describe the whole extent of the experimental data. Based on the
Keywords:
above, a minimum set of experiments for water splitting thermochemical cycles over a
Ferrites
Nickel-ferrite was deigned and performed involving an increased duration of the reaction
Hydrogen
steps. A new extended model was derived for the water splitting and thermal reduction
Solar energy
reactions, which considers two oxygen storage regions of the redox material communi-
Water splitting
cating to each other by a solid state diffusion mechanism. The inclusion of two state
Reaction kinetics
variables instead of one has a significant effect on the reaction dynamics and renders the model capable to explain the dynamics of the convergence of the thermochemical cycles to a periodic steady state, observed experimentally in the previous work. Copyright ª 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
During the last years the subject of hydrogen production by employing water splitting thermochemical cycles is examined intensively in the literature [1,13]. The efficient implementation of the process in practice requires the appropriate (optimal) redox material, an optimized reactor design and an optimized operation strategy [14,15]. In order to be able to scale-up the results from the testing of redox materials in
laboratory reactors to the production reactor the kinetics of the reactions must be derived. This kinetics can be incorporated in the mathematical models of the application reactor, which will be used to optimize the reactor design and the operation strategy. In this spirit an effort is made to derive a descriptive reaction kinetic model for a particular redox material, a Ni-ferrite, which was found to be an active watersplitting material. The thermochemical production of hydrogen from water splitting based on redox-pair cycles comprises of two
* Corresponding author. Aerosol & Particle Technology Laboratory, CPERI/CERTH, 6th km Charilaou-Thermi Rd, P.O. Box 60361, 57001 Thessaloniki, Greece. Tel.: þ30 2310 498 192; fax: +30 2310 498 190. E-mail address: [email protected] (A.G. Konstandopoulos). 0360-3199/$ e see front matter Copyright ª 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhydene.2014.01.121
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reactions, the thermal reduction (regeneration of the material) (Reaction (1)) and the water splitting reaction (oxidation of the material) (Reaction (2)): MOox / MOred þ 1/2O2 (g)
(1)
MOred þ H2O (g) / MOox þ H2 (g)
(2)
where MOox is the oxidized form of the redox material and is usually the higher-valence oxide of a metal exhibiting multiple oxidation states. The thermal reduction step is the highertemperature step during which the oxidized form of the material releases a quantity of oxygen and “falls” to a more reduced (lower-valence) state. During the water splitting step the reduced material is oxidized from water back to the higher-valence state by taking oxygen from water and producing hydrogen, establishing thus a cyclic process. Among the compositions that have been extensively tested for such applications are the ferrites [16e21]. However, it is observed that the conditions that are employed for the synthesis and the characterization of the materials, such as the temperature, are moderate when compared to the water splitting and the thermal reduction cyclic operation of the materials. This may lead to phenomena such as sintering of the materials causing a modification of their structure and some times also reduction of their surface area which subsequently leads to the degradation of the performance of the material. In addition, evaluation conditions that are not representative of the actual application may obstruct the proposal of appropriate reaction mechanisms or the extraction of reliable water splitting e thermal reduction kinetic data. In Ref. [13], a variety of redox materials were synthesized and then calcined under air and under nitrogen at 1400 C to establish a common background for relevant comparisons. It was found e and corroborated by other studies reported in the literature [18e21] e that among the many ferrite materials tested for the targeted application, Zn-containing ones exhibit Zn-volatilization problems and Mn-containing ones suffer from phase stability problems under air atmosphere at high temperatures. These facts practically leave only NiFe2O4 and CoFe2O4 as the most “robust” among the ferrites, capable to operate reliably at the real conditions of a solar-aided process. Between these two, NiFe2O4 was the first material selected as a “model system” for a thorough parametric study of the water splitting e thermal reduction reactions in order to quantify the effects of various operating parameters presented and to extract reaction kinetics. In Ref. [22] a simple mathematical model was formulated describing the water splitting e thermal reduction cyclic studies with NiFe2O4 redox materials via the heterogeneous surface reactions of water vapor with the redox powder material, from which, in conjunction to the experiments above, the kinetic parameters of the water splitting and thermal reduction reactions were extracted. The effective water splitting kinetic constant exhibited weak temperature dependence between 700 and 1100 C. Fitting of the hydrogen and oxygen evolution profiles from these experiments with simple first order reaction rates could not describe adequately the entire profile. The inability of the model to describe the whole extend of the experimental data
was attributed to relatively short reaction times (i.e. the duration of activation, water splitting and thermal reduction steps) that led to insufficient: i) exhaustion of the oxygen uptake capability of the material and ii) liberation of the oxygen storage sites, during the water splitting and the thermal reduction steps respectively. In order to be able to describe the experimental data with an extended reaction model, NiFe2O4 was employed for the realization of experiments that involved an increased duration of the reaction steps. In this way, the hydrogen and oxygen concentration evolution curves corresponding to conditions close to the exhaustion of the storage sites were obtained. These long-term experiments were carried out at different combinations of water splitting and thermal reduction temperatures. The structure of the present work is the following: At first the kinetic model is described. Then the experimental conditions and results are presented. The strategy followed to fit the model to the experimental results is explained in detail. Finally a parametric study of the model is performed in order to demonstrate the effect of several parameters such as the cycling period and the initial state of the redox material.
2.
Kinetic model description
There are two basic approaches for the derivation of rate expressions of water splitting and the corresponding regeneration (thermal reduction) reactions. The first approach is based on the consideration of kinetic expressions from works conducted in the field of solid phase reactions [23,24]. The expressions are fitted to the experimental rate-conversion curves to find the optimum expression and subsequently the mechanism that dominates the reaction rate. The disadvantage in this case is that the experimental results are typical for partial conversion and since the dominant reaction mechanisms (like the shrinking core one [25] or the three dimensional diffusion dominated [26]) have non-linear rates, a question about the validity of the approach arises. Other solid state reaction mechanisms proposed for the water splitting/thermal reduction reactions is the simple constant radial retraction rate [27] and the two-dimensional growth of nuclei model [28]. A linear reaction rate (the second approach) does not have the disadvantage associated to the incomplete conversion however the actual data do not support such a linear rate [22]. On the other hand the initial period of the reaction can be approximated by a linear form up to a point of 30% reduction of the initial rate. At longer reaction times the actual rate deviates from the linear behavior implying that there is a second reaction step which sustains the reaction. A phenomenological model will be developed here to be valid for the whole reaction duration met in the experiments. The new model does not cancel the previous linear model described in Ref. [22] but naturally extends it to longer reaction times. The general idea is that the redox material can be considered to consist of two distinct regions. The first region is in contact with the gas phase (outer region). This region includes the pore structure that is filled with gas. It is noted that the
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 6 3 1 7 e6 3 2 7
experimental reaction rates are in general small so the mass transfer resistance for gas phase diffusion in the pores can be ignored. The water splitting and regeneration reactions occur directly in this first region of the redox material. The second region (inner region) is the internal region (bulk material) which has no direct access to the gas phase. The oxygen atoms can move in this region through the dislocation system. Based on the solid state physics theories [29] it is more probable that vacancies and not atoms move in the solid. Nevertheless, the diffusion based mathematical formulation is the same in both cases. The intrinsic reaction rate is higher than the diffusion rate which is the dominant mechanism in this region, so the following assumption can be made: the free oxygen concentration in the dislocation system is in local equilibrium with the amount of oxygen oxidizing the redox material. In principle, a diffusion equation formalism must be employed for the oxygen transfer in the internal region. Given the complexity of the geometry of the redox material, it is not easy to define a domain for the solution of the diffusion equation. This difficulty can be overcome by replacing the diffusion problem with a lumped linear rate equation in the spirit of the so-called linear driving force formula used in modeling of adsorption kinetics [30]. Let us denote as 4 the instantaneous amount of gratoms of oxygen in the external region of the material (in the oxidized state of the material). The rate of hydrogen production (moles/s/g of redox material) is assumed to be given as (in consistency to the model developed in the previous work [22]): RH2 ¼ k1 Xnw ð4tot 4Þ
(3)
where k1 is the reaction rate constant (1/s), 4tot is the total oxygen capacity of the external region (gratoms/g) and Xw is the local water vapor molar fraction. It is more convenient to use molar fraction instead of concentration because in this way all the temperature effect is included in the kinetic constant k1. The units’ consistency in Equation (3) is based on the equivalence between moles of hydrogen and gratoms of oxygen in the vapor molecule. The exponent n accounts for the saturation of the external redox material region in vapor and can take values smaller than 1 in case of Xw values close to 1 being of interest. Such a Freundlich type function is preferred instead of a Langmuir type function because it permits easier analytical manipulation for use in reactor codes. Let us denote j the instantaneous amount of oxygen in the internal region (in the oxidized state of the material) and jtot (gratoms/g) the total capacity of this region in oxygen. The oxygen transfer from the internal to the external region through a diffusion mechanism can be described by the following linear relation: RT ¼ km1 ðKj 4Þ
(4)
where km1 is the mass transfer coefficient and K is the partition coefficient for oxygen in oxidized state among the two regions. In particular K ¼ 4tot/jtot. The evolution of the quantities 4 and j will be given by the following balances: d4 ¼ RH2 þ RT ¼ k1 Xnw ð4tot 4Þ þ km1 ðKj 4Þ dt
(5)
dj ¼ RT ¼ km1 ð4 KjÞ dt
(6)
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The rate of thermal reduction reaction (in moles/s/g) is given in consistency with the previous work model as: RO2 ¼ k2 4
(7)
The evolution of the quantities 4 and j during regeneration is given as: d4 ¼ 2RO2 þ RT ¼ 2k2 4 þ km2 ðKj 4Þ dt
(8)
dj ¼ RT ¼ km2 ð4 KjÞ dt
(9)
It is noted that in the general case, the mass transfer coefficient is not the same in the water splitting and the thermal reduction steps due to the structural changes of the internal region of the redox material related to the increased volume of the oxidized state. In addition 4tot is not a fixed parameter of the material but it depends on the temperature. It is obvious that K is in principle temperature dependent since 4tot is temperature dependent. The above system of equations can be solved for the evolution of the hydrogen and oxygen production given the initial conditions at t ¼ 0 i.e. 4(0) ¼ 40, j(0) ¼ j0. In general the number of the problem parameters (k1, k2, km1, km2, K, 4tot, 40, j0) is too large for their unique determination from the experimental data (underdetermined problem). A reduction of the parameters can be achieved by the appropriate pretreatment of the redox material in order to almost eliminate the oxidized state. In this case it can be set approximately 40 ¼ j0 ¼ 0 and the underdetermined parameter fitting problem is transformed to a determined one.
3.
Experimental procedure and results
3.1.
Experimental procedure
The redox material that is employed for the long-term experiments is NiFe2O4 synthesized by solid-phase Self-propagating High-temperature Synthesis (denoted hereafter as SHS). A detailed description of the synthesis conditions has been given in previous studies [7]. The parametric water splittingethermal reduction experiments were performed in a laboratory test rig consisting of an alumina tubular reactor enclosed within a high-temperature programmable furnace (Thermcraft Inc.) capable of reaching temperatures of 1500 C. The redox material powder (a quantity of 10 g) to be tested was supported by quartz wool in the middle of the reactor. The thickness of the redox material bed was approximately 1 cm. The evaluation procedure of the water splittingethermal reduction ability of the redox material involved three steps [13]. The first step, the activation, involved heating of the powder under nitrogen with a flow rate of 2 l/min and temperature increase ramp of 15 C/min up to 1400 C. The dwell time at the activation temperature varied from 3 to 5 h. During this initial “activation”, which is actually a thermal reduction step, oxygen was released from the material that e as already shown in previous relevant studies [13,22] e caused its transformation into an oxygen-deficient/reduced form of
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NiFe2O4d spinel structure, where d is the fraction of oxygen atoms removed from the lattice with respect to the fully oxidized form of the material. Subsequently the material was cooled under nitrogen to the desired water splitting temperature level; in the present study water splitting temperatures of 900, 1000 and 1100 C were tested. When the targeted temperature level was reached, water vapor was introduced in the nitrogen stream (mole fraction of vapor employed was 32%) flowing continuously over the heated sample with the aid of a heated pressurized water tank. The dwell time at the water splitting temperature was approximately 3 h. After the completion of the water splitting step the vapor flow was switched off and the reactor was heated again with the same ramp of 15 C/min to the thermal reduction temperature level, under pure nitrogen, where it remained for approximately 3 h. For each set of water splittingethermal reduction temperatures, “fresh” NiFe2O4 powder was used. A summary of the conditions that were employed in all experiments is shown in Table 1. The hydrogen and oxygen concentrations in the effluent gas stream were continuously recorded via a mass spectrometer (Pfeiffer, Omnistar Quadruple Mass Spectrometer). The long duration of the activation, the water splitting and the thermal reduction steps allowed the reaction to approach completion. To maximize the extracted information from a minimum set of experiments, the water splitting and the thermal reduction temperatures were varied from experiment to experiment (Table 1). For the set of water splittingethermal reduction experiments with the highest temperatures three thermochemical cycles were performed, whereas for the other two sets of experiments at lower reaction temperatures only one cycle was performed. The experiments performed here constitute the minimum set of experiments that allows complete identification of the model parameters.
3.2.
Results
Fig. 1 illustrates the evolution of H2 and O2 concentration during the long-term experiments that were conducted at different water splitting and thermal reduction temperatures. As mentioned earlier, in experiments that were presented in previous studies [22], the duration of the activation, water splitting and thermal reduction steps was not sufficient to provide a representative picture of the exhaustion of the oxygen uptake or liberation of oxygen from the storage sites. In the present experiments it is observed that with the increase of the duration of each step (water splitting and thermal
Table 1 e Long-term activation, water splitting and thermal reduction experiments. 1st set
2nd set
3rd set
T Dwell T Dwell T Dwell ( C) time (h) ( C) time (h) ( C) time (h) Activation 1400 Water splitting 900 (WS) Thermal 1300 reduction (TR)
5 w3
1400 1000 1350
5 w3
1400 1100 1400
w3
Fig. 1 e Evolution of H2 and O2 production rates during the long-term experiments for (a) the first (900e1300 C); (b) the second (1000e1350 C) and (c) the third (1100e1400 C) sets of temperature for water splitting/reduction steps.
reduction) the concentration of H2 and O2 is reduced to very low values. Although, the longer dwell time of 3e5 h is also not adequate for the concentration of the products to drop to zero, they provide a more clear picture of the exhaustion of the oxygen storage sites in the case of the water splitting step, while in the case of thermal reduction the longer dwell time allows the material to release almost all the O2 that can be released at a given temperature. In this way, the material approaches its initial state. Also, it can be concluded from these experiments that, in the case of NiFe2O4, the most favorable set of temperatures was 1100 C in terms of water splitting and 1400 C in terms of thermal reduction. At that
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specific pair of temperatures the material produces approximately 428 mmoles H2/gredox during the water splitting step and releases approximately 148 mmoles O2/gredox during the thermal reduction which corresponds to about 70% of the amount of O2 that was absorbed from the splitting of water. This regeneration efficiency is by no means a fundamental property of the particular redox material since it depends on the time of the two reaction steps. The extraction of fundamental quantities from the experimental data requires the use of the appropriate mathematical model. Based on the results presented in Fig. 1, in the particular operating temperature window, H2 yield showed better cycleto-cycle stability and, therefore, higher overall production.
4.
Data analysis
At first, it must be examined if the laboratory reactor can be assumed as a differential reactor which will greatly facilitate the analysis. The instantaneous degree of conversion is very small, which means that the water vapor concentration along the bed can be assumed constant and equal to its inlet value. Regarding the question if the reaction is kinetically controlled, the mass transfer coefficient for the catalyst particles was computed and it was found to correspond to mass fluxes of vapor much larger than those corresponding to measured reaction rates, so diffusion limitations can be ignored. The final issue to be considered is the temperature in the bed. If the heat of the water splitting reaction is DH (per mole of vapor), then a global heat balance in the bed gives the following raise of the gas temperature (which implies a gradual increase of the temperature along the bed): DT ¼ XwxcDH/cpg where cpg is the specific heat capacity of the gas and xc the fractional conversion of water vapor. It seems that in the particular longterm experiments, the temperature raises a few degrees at some instants but this increase can be ignored considering the broad range of temperatures covered by the experiments. The consideration of the actual reactor as a differential one leads to the following key relation for the water splitting step: RH2 ¼ FH2
(10)
The corresponding governing equation for the thermal reduction step is: RO2 ¼ FO2
(11)
The procedure followed to adjust the model to the experimental data will be presented here. It should be mentioned that only the part of the hydrogen and oxygen concentration profiles after their respective peak is included in the analysis procedure. According to the model, the product gas (hydrogen or oxygen) concentration should reach instantaneously its highest value and thereafter decrease; however in the experimental configuration the diffusion of the evolved gas in the line to the analyzer has as a result the gradual increase of the measured product gas concentration from zero to its maximum value. A sound indication for this is that the time interval required for hydrogen concentration to reach its highest value was always of the order of a few tens of seconds for all the experiments that were conducted.
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The gas production rate curves are fitted with a double exponential curve of the form F ¼ a1 ða2 ea3 t þ ð1 a2 Þea4 t Þ in order to smooth the experimental data. In general the degree of noise in the data is very small and the above functions fit the data very well. It is noted that the model equation for the gas production constitutes a system of two linear ordinary differential equations and their solution has the same general form with the function used to fit the data. Nevertheless, the relations between the fitting function parameters and the kinetic parameters are too complex for their use to offer any advantage. It was found much more convenient to estimate the model parameters by solving numerically the corresponding ordinary differential equations and comparing the results with the values of the equation fitted to the data. From the above, it is obvious that trying to fit the numerically solved kinetic model to the double exponential function for F leads always by definition to 100% success. It must be kept in mind that the parameter values resulting in this way are not always physically sound since their value is based on pure mathematical requirements without taking into account any physical constraint. The model parameter extraction, in the present case, must be conducted via the simultaneous consideration of consecutive cycles, so it is a much more demanding procedure than the one used for the linear model considered in Ref. [22] where each cycle was analyzed separately. The procedure for the derivation of the parameters from one experiment is described in the following paragraph. The first water splitting hydrogen production curve must be approached by assuming 40 ¼ j0 ¼ 0 and changing the values of the k1, K, 4tot, km1 parameters in order to approximate the fitted experimental data. At the end of the simulation of the particular cycle, the model gives some values for the variables 4 and j. These values must be the initial values in the attempt to simulate the first thermal reduction curve using the parameters k2, K, km2. The model predictions for 4 and j at the end of this cycle must be used as initial conditions for the simulation of the second water splitting cycle. It is noted that, as the water splitting in the case of the second cycle occurs at the same temperature with the first cycle, all the model parameters must be the same. The procedure continues by using the final values of 4, j that were extracted from the second water splitting cycle, as initial values to the second thermal reduction cycle. The model parameters must be the same as the ones of the first thermal reduction cycle. The whole procedure is repeated for each set of parameters, taking the cycles sequentially until a set of parameters, which can reasonably describe the experimental cycles, is found. Using this process, parameter values corresponding to the different temperatures can be found by analyzing the data from the long-term experiments (Fig. 1). A value for exponent n must be assumed. This cannot be based on the present work data since the experiments were conducted under the same vapor molar fraction. Experiments with different vapor fractions presented in Ref. [22] reveal that up to the fraction that was employed in the long-term experiments, the exponent value n ¼ 1 is a good approximation. The data taken at different temperatures are interpolated using Arrhenius temperature dependence or fitting by simple functions depending on the data form. The final set of
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parameters as a function of temperature is presented in Tables 2 and 3 for the case of water splitting and thermal reduction reactions respectively. Regarding water splitting, the total oxygen capacity of the external layer seems to increase linearly with temperature in the range of the water splitting experiments (900e1100 C). More surprising is the behavior of the kinetic rate constant k1 which appears to decrease with the increase of temperature. This behavior of the kinetic rate cannot be interpreted on an elementary basis but suggests that even the basic steps of the composite reaction mechanism proposed here consist of other simpler steps. A possible explanation of the reduction of k1 with temperature is that due to the thermal expansion of the material, the external surface area of the redox material (included in the effective coefficient k1) is reduced (e.g. by reduction of its roughness). The combination of the 4tot and k1 that gives the external region reaction rate corresponds to a very modest temperature dependence that led us, in the previous work [22], to suggest a temperature independence of the first linear stage of the water splitting reaction. The more detailed model presented here reveals a much more complex temperature dependence. It is very interesting that the ratio K of the external to the internal region oxygen capacity appears to be constant for water splitting on the temperature range considered. This is reasonable, since 4tot and jtot are intrinsic thermodynamic quantities and may vary similarly with the temperature. The difference between the two regions is not in their thermodynamics but in their accessibility by the gas phase. The mass transfer coefficient km1 appears to be constant from 900 to 1000 C and then increase up to 1100 C. The situation is simpler for the case of thermal reduction in the temperature range considered. The reaction constant k2 and the mass transfer coefficient km2 follow an Arrhenius dependence. The parameter K is constant at a value of about 35% of the one found for water splitting. It is noted that K, in principle, denotes the same variable, independently of the direction of the oxygen motion. So, it is considered the same for water splitting and thermal reduction. The difference observed is not attributed to the different phenomena occurring but to the difference of prevalent temperature implying a transition from 0.85 to 0.3 somewhere between 1100 C and 1300 C. The experimental and theoretical gas production rates for three cycles for the case of water splitting at 1100 and thermal reduction at 1400 C are shown in Fig. 2. It is obvious that the model describes the data adequately. The comparisons
Table 3 e Thermal reduction kinetic parameters as a function of temperature (in K). Thermal reduction k2 km2 K
e(41.594-83,334/T) e(74.507-136,000/T) 0.3
(1/s) (1/s)
for one cycle in the case of 1000e1350 C is shown in Fig. 3. In the case of 900e1300 C the thermal reduction at 1300 C produced negligible O2 and is therefore not presented in the diagram (Fig. 4). It must be noted that the results presented here cannot be considered as an absolute determination of the process kinetics but as an attempt to quantify in some way the experimental data in order to scale-up the results to solar reactors. Several complications not considered by the above described model will be discussed here. There is a “dead” period between water splitting and thermal reduction steps needed for the temperature to reach the desired value for the two steps. During this period, oxygen may be transferred from one region to another. Unfortunately, this process cannot be included to the data approximation procedure due to the lack of knowledge of the parameters km and K for the intermediate temperatures. Additionally it must be noted that in no case the present model is considered to describe in detail the phenomena occurring on the redox material. It is just a phenomenological model developed on the basis of experimental observations and capable to represent the experimental results. This model features are enough to allow the scale up of the laboratory reactor data to the industrial scale monolithic reactor through the appropriate reactor modeling. Another issue has to do with the aging of the material after each cycle. The temperature effect on the reaction kinetics has two components: a reversible one (e.g. due to structural changes from thermal expansion) and an irreversible one (e.g. sintering/melting of the material). It is well known that at high temperatures (larger than 1400 C used
Table 2 e Water splitting kinetic parameters as a function of temperature (in K). Water splitting k1 4tot km1
K
0.07098.851$105 T þ 2.786$108 T2 1.025 T-1136.8 2.83$104 2.83$104-0.95$104$(T1273)/100 0.85
(1/s) (Gratoms solid phase [O]/g of redox material) (1173 < T < 1273) (T > 1273)
Fig. 2 e Comparison of the experimental H2 and O2 production rate profiles (points) with the theoretical curves (solid lines) for the case of water splitting at 1100 Cethermal reduction at 1400 C.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 6 3 1 7 e6 3 2 7
5.
Fig. 3 e Comparison of the experimental H2 and O2 production rate profile (points) with the theoretical curves (solid lines) for the case of water splitting at 1000 Cethermal reduction at 1350 C.
here) redox materials may melt and lose their activity. At the temperatures employed here, it is possible that some deactivation of the material may occur after each cycle. This deterioration of the performance of the redox material was studied previously [13] where the redox material was subjected to grinding after the first water splitting step and also after the third thermal reduction step. It was observed that sintering of the redox material that took place at high temperatures was alleviated by grinding which had as an effect the modification of the structure of the redox material and the enhancement of the surface directly accessible for oxygen adsorption from the gas phase. However, in the present study, the data are not enough to quantify the degree of deactivation and the model parameters are derived ignoring such deactivation phenomena.
Fig. 4 e Comparison of the experimental H2 production rate profiles (points) with the theoretical curve (solid line) for the case of water splitting at 900 C.
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Model parametric study
A parametric analysis of the kinetic model with the parameters derived from fitting the experimental data follows. The conditions that were considered for the simulation are the same with those employed in the experiments. Several operation scenarios are provided below to reveal details on the modeling approach which were not evident by the directly experimentally measured quantities. Initial conditions very close to those of the experiments shown in Fig. 2 are considered. In the first case (base case) a temperature switch between 1100 C and 1400 C every 104 s is considered. Initially there is no solid phase oxygen 40 ¼ j0 ¼ 0. The gas production rates are shown in Fig. 5 for five cycles. There is an initial reduction of the hydrogen production from the first to the second cycle (similar to the one observed experimentally). The system comes practically to a periodic operation at the second cycle for the hydrogen production and at the first cycle for oxygen release. The corresponding evolution of the solid phase oxygen is shown in Fig. 6. The external region oxygen amount 4 follows the expected behavior: increases during water splitting and decreases during thermal reduction. The internal region oxygen shows a more complex behavior. It increases during water splitting step but it continues to increase during the first stage of the thermal reduction step. This is due to the shift of the partition coefficient K from 0.85 to 0.3 between splitting and reduction. When 4 decreases considerably, j starts decreasing after passing through a maximum. The number of cycles in which the periodic steady state is reached depends on the degree of completeness of the reaction occurring in each step and this in turn depends on the step duration. In the limit of infinite duration for each step the reactions are completed so the periodicity is reached instantaneously. The large step time of 104 s of the base case
Fig. 5 e Modeling the H2 and O2 production for temperature switches between 1100 C and 1400 C every 104 s.
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considered here is close to the infinite duration and this explains the fast approach to periodicity. In the case of a small reaction extent during each step of water splitting and thermal reduction, the approach to periodicity is slow. According to the second scenario studied, temperature switches between 1100 C and 1400 C every 3000 s. The gas production rates for the same conditions with the base case but a time interval of 3000 s for each step is shown in Fig. 7. It is obvious that the convergence to the periodic steady state is much slower. The hydrogen production rate decreases and the oxygen production rate increases for five cycles before
convergence to be achieved. The corresponding evolution of the adsorbed oxygen is shown in Fig. 8. In this case the internal region oxygen amount j is always larger than the external region oxygen amount 4 during the periodic steady state. It seems that the slow convergence to the periodicity is due mainly to the slow dynamics of the internal region oxygen. In order to study the effect of the initial conditions 40, j0 (amount of solid phase oxygen) on the gas production rates three cases are considered: (a) case A: 40 ¼ 200, j0 ¼ 0, (b) case B: 40 ¼ 100, j0 ¼ 100, (c) case C: 40 ¼ 0, j0 ¼ 200 (the units are gratoms [O]/g of redox). The gas production rates for step period of 104 s are shown in Fig. 9. The initial condition in this case influences only the first hydrogen production cycle. In particular, only the external region oxygen has an effect since the effect of j0 is negligible small. The situation is different for the case of step duration of 3000 s. The influence of the initial conditions remains for several cycles of hydrogen and oxygen production as it is shown in Fig. 10. The gas production rate decreases with the increase of 40. The influence of j0 is again very small. So the general conclusion from the above results is that i) the number of cycles required for establishment of the periodic steady state depends on the extent of reaction in each step and ii) the influence of initial conditions 40, j0 on gas production increase as the reaction extent in each step increases. This is in agreement with the respective finding of the previous version of the kinetic model in Ref. [22]. The small reaction time for each step prevented the approach to a periodic steady state. In addition, the idea to perform experiments with a longer reaction extent to avoid the influence of the initial conditions is justified. In the solar reactor it is very difficult to keep the temperature constant in time and the reactions may partially occur during the increase and decrease of the temperature [10]. In order to simulate such a situation, model results for the differential reactor considered here for linear temperature
Fig. 7 e Modeling of the H2 and O2 production for temperature switches between 1100 C and 1400 C every 3000 s.
Fig. 8 e Evolution of the solid phase oxygen for temperature switches between 1100 C and 1400 C every 3000 s.
Fig. 6 e Evolution of the solid phase oxygen for temperature switches between 1100 C and 1400 C every 104 s.
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Fig. 9 e Effect of the initial conditions 40, j0 on H2 and O2 production for three different 40, j0 cases (A, B, C) and step period of 104 s.
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Fig. 11 e Modeling H2 and O2 production for linear temperature increase (water splitting 900e1100 C, thermal reduction 1300e1400 C).
increase between 900 and 1100 C (water splitting) and between 1300 and 1400 C (thermal reduction) in 3000, 6000 and 104 s are presented in Figs. 11 and 12. The gas production rates are shown in Fig. 11. The combination between the dependence of the reaction rate on 4, j and the temperature leads to the particular shapes of gas rate curves shown in Fig. 11. An initial stage of large time variation of the gas production rate is followed by a period of slow variation. The corresponding solid phase oxygen evolution curves are shown in Fig. 12. External region oxygen undergoes a well defined maximum at the
moment of switching from water splitting to thermal reduction where internal region oxygen j increases during most of the time. The findings of the present work are capable to explain the behavior observed in Ref. [22] where the variations in the activation time and in the reaction time from experiment to experiment led to seemingly uncorrelated reaction rates between the experiments and between the cycles, raising questions about the stability of the redox material. The present model suggests that the observed behavior is not due to material instability rather than to the difference of the state variables 4 and j at the onset of each cycle.
Fig. 10 e Effect of the initial conditions 40, j0 on H2 and O2 production for three different 40, j0 cases (cases A, B, C) and step period of 3000 s.
Fig. 12 e Solid phase oxygen evolution curves for linear temperature increase (water splitting 900e1100 C, thermal reduction 1300e1400 C).
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Conclusions [12]
A new extended model is derived for water splitting and thermal reduction reactions on a redox material. The new model considers two oxygen storage regions communicating to each other by a solid state diffusion mechanism. A minimum set of experiments for water splitting thermochemical cycles over a Ni-ferrite was designed and performed in order to derive the model parameters. The particular model is a direct extension for higher reaction extents of the linear model proposed previously [22]. The distinct difference of the proposed model over the typical solid reaction models used in the literature is the inclusion of two state variables instead of one. This has a significant effect on the reaction dynamics and renders the model capable to explain the dynamics of the convergence of the thermochemical cycles to a periodic steady state, observed previously.
[13]
[14]
[15]
[16]
Acknowledgments The authors would like to thank the European Commission and the Fuel Cells and Hydrogen Joint Undertaking for funding part of this work through the project “HYDROSOL-3D”.
[17]
[18]
references
[1] Nakamura T. Hydrogen production from water utilizing solar heat at high temperatures. Sol Energy 1977;19(5):467e75. [2] Tamaura Y, Steinfeld A, Kuhn P, Ehrensberger K. Production of solar hydrogen by a novel 2-step water-splitting thermochemical cycle. Energy 1995;20(4):325e30. [3] Perkins C, Weimer AW. Likely near-term solar-thermal water splitting technologies. Int J Hydrogen Energy 2004;29:1587e99. [4] Steinfeld A. Solar thermochemical production of hydrogen e a review. Solar Energy 2005;78:603e15. [5] Kodama T, Kondoh Y, Yamamoto R, Andou H, Satou N. Thermochemical hydrogen production by a redox system of ZrO2-supported Co(II)-ferrite. Sol Energy 2005;78(5):623e31. [6] Kaneko H, Gokon N, Hasegawa N, Tamaura Y. Solar thermochemical process for hydrogen production using ferrites. Energy 2005;30(11e12):2171e8. [7] Agrafiotis C, Roeb M, Konstandopoulos AG, Nalbandian L, Zaspalis VT, Sattler C, et al. Solar water splitting for hydrogen production with monolithic reactors. Sol Energy 2005;79(4):409e21. [8] Abanades S, Charvin P, Flamant G, Neveu P. Screening of water-splitting thermochemical cycles potentially attractive for hydrogen production by concentrated solar energy. Energy 2006;31:2805e22. [9] Kaneko H, Yokoyama T, Fuse A, Ishihara H, Hasegawa N, Tamaura Y. Synthesis of new ferrite, AleCu ferrite, and its oxygen deficiency for solar H2 generation from H2O. Int J Hydrogen Energy 2006;31(15):2256e65. [10] Agrafiotis C, Pagkoura C, Lorentzou S, Kostoglou M, Konstandopoulos AG. Hydrogen production in solar reactors. Catal Today 2007;127(1e4):265e77. [11] Roeb M, Sa¨ck JP, Rietbrock P, Prahl C, Schreiber H, Neises M, et al. Test operation of a 100 kW pilot plant for solar
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hydrogen production from water on a solar Tower. Sol Energy 2011;85(4):634e44. Konstandopoulos AG, Pagkoura C, Lorentzou S. Solar Fuel and industrial solar chemistry. In: Lovegrove K, Stein W, editors. Concentrating solar power technology: principles, developments and applications. Part 3 Optimisation, improvements and applications. Cambridge: Woodhead Publishing Series in Energy No. 21; 2011. pp. 620e61. Agrafiotis C, Pagkoura C, Zygogianni A, Karagiannakis G, Kostoglou M, Konstandopoulos AG. Hydrogen production via solar-aided water splitting thermochemical cycles: combustion synthesis and preliminary evaluation of spinel redox-pair materials. Int J Hydrogen Energy 2012;37(11):8964e80. Kostoglou M, Lekkos C, Konstandopoulos AG. On mathematical modeling of solar hydrogen production in monolithic reactors. Comput Chem Eng 2011;351:915e22. Roeb M, Neises M, Sa¨ck JP, Rietbrock P, Monnerie N, Dersch J, et al. Operational strategy of a two-step thermochemical process for solar hydrogen production. Int J Hydrogen Energy 2009;34(10):4537e45. Gokon N, Takahashi S, Yamamoto H, Kodama T. Thermochemical two-step water-splitting reactor with internally circulating fluidized bed for thermal reduction of ferrite particles. Int J Hydrogen Energy 2008;33(9):2189e99. Miller JE, Allendorf MD, Diver RB, Evans LR, Siegel NP, Stuecker JN. Metal oxide composites and structures for ultrahigh temperature solar thermochemical cycles. J Mater Sci 2008;43:4714e28. Fresno F, Ferna´ndez-Saavedra R, Go´mez-Mancebo MB, Vidal A, Sa´nchez M, Rucandio MI, et al. Solar hydrogen production by two-step thermochemical cycles: evaluation of the activity of commercial ferrites. Int J Hydrogen Energy 2009;34(7):2918e24. Fresno F, Yoshida T, Gokon N, Ferna´ndez-Saavedra R, Kodama T. Comparative study of the activity of nickel ferrites for solar hydrogen production by two-step thermochemical cycles. Int J Hydrogen Energy 2010;35(16):8503e10. Tsuji M, Togawa T, Wada Y, Sano T, Tamaura Y. Kinetic study of the formation of cation-excess magnetite. J Chem Soc Faraday Trans 1995;91:1533e8. Rosmaninho MG, Herreras S, Lago RM, Araujo MH, Navarro RM, Fierro JLG. Effect of the partial substitution of Fe by Ni on the structure and activity of nanocrystalline NixFe3xO4 ferrites for hydrogen production by two-step water-splitting. Nanosci Nanotechnol Lett 2011;3(5):705e16. Agrafiotis C, Zygogianni A, Pagkoura C, Kostoglou M, Konstandopoulos AG. Hydrogen production via solar-aided water splitting thermochemical cycles with nickel ferrite: experiments and modeling. AIChE J 2013;59(4):1213e25. Gotor FJ, Criado JM, Malek J, Koga N. Kinetic analysis of solidstate reactions: the universality of master plots for analyzing isothermal and non-isothermal experiments. J Phys Chem A 2000;104(46):10777e82. Khawam A, Flanagan D. Solid-state kinetic models: basics and mathematical fundamentals. J Phys Chem B 2006;110(35):17315e28. Neises M, Roeb M, Schmuecker M, Sattler C, Pitz-Paal R. Kinetic investigations of the hydrogen production step of a thermochemical cycle using mixed iron oxides coated on ceramic substrates. Int J Energy Res 2010;34(8):651e61. Go KS, Son SR, Kim SD. Reaction kinetics of reduction and oxidation of metal oxides for hydrogen production. Int J Hydrogen Energy 2008;33:5986e95.
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[27] Le Gal A, Abanades S. Catalytic investigation of ceriaezirconia solid solutions for solar hydrogen production. I J Hydrogen Energy 2011;36(8):4739e48. [28] Abanades S. Thermogravimetry analysis of CO2 and H2O reduction from solar nanosized Zn powder for thermochemical Fuel production. Ind Eng Chem Res 2012;51(2):746e55.
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[29] Sirdeshmukh DB, Sirdeshmukh L, Subhadra KG. Atomistic properties of solids. Berlin Heidelberg: Springer Series in Materials Science; 2011. [30] Tien C. Adsorption calculations and modeling. Boston: Butterworth-Heinemann; 1994.
Available online at www.sciencedirect.com
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Improved kinetic model for water splitting thermochemical cycles using Nickel Ferrite Margaritis Kostoglou a,b, Souzana Lorentzou a, Athanasios G. Konstandopoulos a,c,* a
Aerosol & Particle Technology Laboratory, CPERI/CERTH, 6th km Charilaou-Thermi Rd, P.O. Box 60361, 57001 Thessaloniki, Greece b Department of Chemistry, Aristotle University of Thessaloniki, P.O. Box 116, 54124 Thessaloniki, Greece c Department of Chemical Engineering, Aristotle University, P.O. Box 1517, 54006 Thessaloniki, Greece
article info
abstract
Article history:
In a previous work of the authors (AIChE Journal 2013; 59(4): 1213-1225) on the character-
Received 17 September 2013
ization of the performance of redox material compositions during two-step thermo-
Received in revised form
chemical splitting of water, it was observed that fitting of the obtained hydrogen and
7 January 2014
oxygen concentration profiles with a reaction model based on simple first order reaction
Accepted 19 January 2014
rates could describe adequately only the first part of the evolution curves. This suggested
Available online 5 March 2014
that more complicated reaction models taking into account the structure of the redox material are needed to describe the whole extent of the experimental data. Based on the
Keywords:
above, a minimum set of experiments for water splitting thermochemical cycles over a
Ferrites
Nickel-ferrite was deigned and performed involving an increased duration of the reaction
Hydrogen
steps. A new extended model was derived for the water splitting and thermal reduction
Solar energy
reactions, which considers two oxygen storage regions of the redox material communi-
Water splitting
cating to each other by a solid state diffusion mechanism. The inclusion of two state
Reaction kinetics
variables instead of one has a significant effect on the reaction dynamics and renders the model capable to explain the dynamics of the convergence of the thermochemical cycles to a periodic steady state, observed experimentally in the previous work. Copyright ª 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
During the last years the subject of hydrogen production by employing water splitting thermochemical cycles is examined intensively in the literature [1,13]. The efficient implementation of the process in practice requires the appropriate (optimal) redox material, an optimized reactor design and an optimized operation strategy [14,15]. In order to be able to scale-up the results from the testing of redox materials in
laboratory reactors to the production reactor the kinetics of the reactions must be derived. This kinetics can be incorporated in the mathematical models of the application reactor, which will be used to optimize the reactor design and the operation strategy. In this spirit an effort is made to derive a descriptive reaction kinetic model for a particular redox material, a Ni-ferrite, which was found to be an active watersplitting material. The thermochemical production of hydrogen from water splitting based on redox-pair cycles comprises of two
* Corresponding author. Aerosol & Particle Technology Laboratory, CPERI/CERTH, 6th km Charilaou-Thermi Rd, P.O. Box 60361, 57001 Thessaloniki, Greece. Tel.: þ30 2310 498 192; fax: +30 2310 498 190. E-mail address: [email protected] (A.G. Konstandopoulos). 0360-3199/$ e see front matter Copyright ª 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhydene.2014.01.121
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reactions, the thermal reduction (regeneration of the material) (Reaction (1)) and the water splitting reaction (oxidation of the material) (Reaction (2)): MOox / MOred þ 1/2O2 (g)
(1)
MOred þ H2O (g) / MOox þ H2 (g)
(2)
where MOox is the oxidized form of the redox material and is usually the higher-valence oxide of a metal exhibiting multiple oxidation states. The thermal reduction step is the highertemperature step during which the oxidized form of the material releases a quantity of oxygen and “falls” to a more reduced (lower-valence) state. During the water splitting step the reduced material is oxidized from water back to the higher-valence state by taking oxygen from water and producing hydrogen, establishing thus a cyclic process. Among the compositions that have been extensively tested for such applications are the ferrites [16e21]. However, it is observed that the conditions that are employed for the synthesis and the characterization of the materials, such as the temperature, are moderate when compared to the water splitting and the thermal reduction cyclic operation of the materials. This may lead to phenomena such as sintering of the materials causing a modification of their structure and some times also reduction of their surface area which subsequently leads to the degradation of the performance of the material. In addition, evaluation conditions that are not representative of the actual application may obstruct the proposal of appropriate reaction mechanisms or the extraction of reliable water splitting e thermal reduction kinetic data. In Ref. [13], a variety of redox materials were synthesized and then calcined under air and under nitrogen at 1400 C to establish a common background for relevant comparisons. It was found e and corroborated by other studies reported in the literature [18e21] e that among the many ferrite materials tested for the targeted application, Zn-containing ones exhibit Zn-volatilization problems and Mn-containing ones suffer from phase stability problems under air atmosphere at high temperatures. These facts practically leave only NiFe2O4 and CoFe2O4 as the most “robust” among the ferrites, capable to operate reliably at the real conditions of a solar-aided process. Between these two, NiFe2O4 was the first material selected as a “model system” for a thorough parametric study of the water splitting e thermal reduction reactions in order to quantify the effects of various operating parameters presented and to extract reaction kinetics. In Ref. [22] a simple mathematical model was formulated describing the water splitting e thermal reduction cyclic studies with NiFe2O4 redox materials via the heterogeneous surface reactions of water vapor with the redox powder material, from which, in conjunction to the experiments above, the kinetic parameters of the water splitting and thermal reduction reactions were extracted. The effective water splitting kinetic constant exhibited weak temperature dependence between 700 and 1100 C. Fitting of the hydrogen and oxygen evolution profiles from these experiments with simple first order reaction rates could not describe adequately the entire profile. The inability of the model to describe the whole extend of the experimental data
was attributed to relatively short reaction times (i.e. the duration of activation, water splitting and thermal reduction steps) that led to insufficient: i) exhaustion of the oxygen uptake capability of the material and ii) liberation of the oxygen storage sites, during the water splitting and the thermal reduction steps respectively. In order to be able to describe the experimental data with an extended reaction model, NiFe2O4 was employed for the realization of experiments that involved an increased duration of the reaction steps. In this way, the hydrogen and oxygen concentration evolution curves corresponding to conditions close to the exhaustion of the storage sites were obtained. These long-term experiments were carried out at different combinations of water splitting and thermal reduction temperatures. The structure of the present work is the following: At first the kinetic model is described. Then the experimental conditions and results are presented. The strategy followed to fit the model to the experimental results is explained in detail. Finally a parametric study of the model is performed in order to demonstrate the effect of several parameters such as the cycling period and the initial state of the redox material.
2.
Kinetic model description
There are two basic approaches for the derivation of rate expressions of water splitting and the corresponding regeneration (thermal reduction) reactions. The first approach is based on the consideration of kinetic expressions from works conducted in the field of solid phase reactions [23,24]. The expressions are fitted to the experimental rate-conversion curves to find the optimum expression and subsequently the mechanism that dominates the reaction rate. The disadvantage in this case is that the experimental results are typical for partial conversion and since the dominant reaction mechanisms (like the shrinking core one [25] or the three dimensional diffusion dominated [26]) have non-linear rates, a question about the validity of the approach arises. Other solid state reaction mechanisms proposed for the water splitting/thermal reduction reactions is the simple constant radial retraction rate [27] and the two-dimensional growth of nuclei model [28]. A linear reaction rate (the second approach) does not have the disadvantage associated to the incomplete conversion however the actual data do not support such a linear rate [22]. On the other hand the initial period of the reaction can be approximated by a linear form up to a point of 30% reduction of the initial rate. At longer reaction times the actual rate deviates from the linear behavior implying that there is a second reaction step which sustains the reaction. A phenomenological model will be developed here to be valid for the whole reaction duration met in the experiments. The new model does not cancel the previous linear model described in Ref. [22] but naturally extends it to longer reaction times. The general idea is that the redox material can be considered to consist of two distinct regions. The first region is in contact with the gas phase (outer region). This region includes the pore structure that is filled with gas. It is noted that the
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experimental reaction rates are in general small so the mass transfer resistance for gas phase diffusion in the pores can be ignored. The water splitting and regeneration reactions occur directly in this first region of the redox material. The second region (inner region) is the internal region (bulk material) which has no direct access to the gas phase. The oxygen atoms can move in this region through the dislocation system. Based on the solid state physics theories [29] it is more probable that vacancies and not atoms move in the solid. Nevertheless, the diffusion based mathematical formulation is the same in both cases. The intrinsic reaction rate is higher than the diffusion rate which is the dominant mechanism in this region, so the following assumption can be made: the free oxygen concentration in the dislocation system is in local equilibrium with the amount of oxygen oxidizing the redox material. In principle, a diffusion equation formalism must be employed for the oxygen transfer in the internal region. Given the complexity of the geometry of the redox material, it is not easy to define a domain for the solution of the diffusion equation. This difficulty can be overcome by replacing the diffusion problem with a lumped linear rate equation in the spirit of the so-called linear driving force formula used in modeling of adsorption kinetics [30]. Let us denote as 4 the instantaneous amount of gratoms of oxygen in the external region of the material (in the oxidized state of the material). The rate of hydrogen production (moles/s/g of redox material) is assumed to be given as (in consistency to the model developed in the previous work [22]): RH2 ¼ k1 Xnw ð4tot 4Þ
(3)
where k1 is the reaction rate constant (1/s), 4tot is the total oxygen capacity of the external region (gratoms/g) and Xw is the local water vapor molar fraction. It is more convenient to use molar fraction instead of concentration because in this way all the temperature effect is included in the kinetic constant k1. The units’ consistency in Equation (3) is based on the equivalence between moles of hydrogen and gratoms of oxygen in the vapor molecule. The exponent n accounts for the saturation of the external redox material region in vapor and can take values smaller than 1 in case of Xw values close to 1 being of interest. Such a Freundlich type function is preferred instead of a Langmuir type function because it permits easier analytical manipulation for use in reactor codes. Let us denote j the instantaneous amount of oxygen in the internal region (in the oxidized state of the material) and jtot (gratoms/g) the total capacity of this region in oxygen. The oxygen transfer from the internal to the external region through a diffusion mechanism can be described by the following linear relation: RT ¼ km1 ðKj 4Þ
(4)
where km1 is the mass transfer coefficient and K is the partition coefficient for oxygen in oxidized state among the two regions. In particular K ¼ 4tot/jtot. The evolution of the quantities 4 and j will be given by the following balances: d4 ¼ RH2 þ RT ¼ k1 Xnw ð4tot 4Þ þ km1 ðKj 4Þ dt
(5)
dj ¼ RT ¼ km1 ð4 KjÞ dt
(6)
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The rate of thermal reduction reaction (in moles/s/g) is given in consistency with the previous work model as: RO2 ¼ k2 4
(7)
The evolution of the quantities 4 and j during regeneration is given as: d4 ¼ 2RO2 þ RT ¼ 2k2 4 þ km2 ðKj 4Þ dt
(8)
dj ¼ RT ¼ km2 ð4 KjÞ dt
(9)
It is noted that in the general case, the mass transfer coefficient is not the same in the water splitting and the thermal reduction steps due to the structural changes of the internal region of the redox material related to the increased volume of the oxidized state. In addition 4tot is not a fixed parameter of the material but it depends on the temperature. It is obvious that K is in principle temperature dependent since 4tot is temperature dependent. The above system of equations can be solved for the evolution of the hydrogen and oxygen production given the initial conditions at t ¼ 0 i.e. 4(0) ¼ 40, j(0) ¼ j0. In general the number of the problem parameters (k1, k2, km1, km2, K, 4tot, 40, j0) is too large for their unique determination from the experimental data (underdetermined problem). A reduction of the parameters can be achieved by the appropriate pretreatment of the redox material in order to almost eliminate the oxidized state. In this case it can be set approximately 40 ¼ j0 ¼ 0 and the underdetermined parameter fitting problem is transformed to a determined one.
3.
Experimental procedure and results
3.1.
Experimental procedure
The redox material that is employed for the long-term experiments is NiFe2O4 synthesized by solid-phase Self-propagating High-temperature Synthesis (denoted hereafter as SHS). A detailed description of the synthesis conditions has been given in previous studies [7]. The parametric water splittingethermal reduction experiments were performed in a laboratory test rig consisting of an alumina tubular reactor enclosed within a high-temperature programmable furnace (Thermcraft Inc.) capable of reaching temperatures of 1500 C. The redox material powder (a quantity of 10 g) to be tested was supported by quartz wool in the middle of the reactor. The thickness of the redox material bed was approximately 1 cm. The evaluation procedure of the water splittingethermal reduction ability of the redox material involved three steps [13]. The first step, the activation, involved heating of the powder under nitrogen with a flow rate of 2 l/min and temperature increase ramp of 15 C/min up to 1400 C. The dwell time at the activation temperature varied from 3 to 5 h. During this initial “activation”, which is actually a thermal reduction step, oxygen was released from the material that e as already shown in previous relevant studies [13,22] e caused its transformation into an oxygen-deficient/reduced form of
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NiFe2O4d spinel structure, where d is the fraction of oxygen atoms removed from the lattice with respect to the fully oxidized form of the material. Subsequently the material was cooled under nitrogen to the desired water splitting temperature level; in the present study water splitting temperatures of 900, 1000 and 1100 C were tested. When the targeted temperature level was reached, water vapor was introduced in the nitrogen stream (mole fraction of vapor employed was 32%) flowing continuously over the heated sample with the aid of a heated pressurized water tank. The dwell time at the water splitting temperature was approximately 3 h. After the completion of the water splitting step the vapor flow was switched off and the reactor was heated again with the same ramp of 15 C/min to the thermal reduction temperature level, under pure nitrogen, where it remained for approximately 3 h. For each set of water splittingethermal reduction temperatures, “fresh” NiFe2O4 powder was used. A summary of the conditions that were employed in all experiments is shown in Table 1. The hydrogen and oxygen concentrations in the effluent gas stream were continuously recorded via a mass spectrometer (Pfeiffer, Omnistar Quadruple Mass Spectrometer). The long duration of the activation, the water splitting and the thermal reduction steps allowed the reaction to approach completion. To maximize the extracted information from a minimum set of experiments, the water splitting and the thermal reduction temperatures were varied from experiment to experiment (Table 1). For the set of water splittingethermal reduction experiments with the highest temperatures three thermochemical cycles were performed, whereas for the other two sets of experiments at lower reaction temperatures only one cycle was performed. The experiments performed here constitute the minimum set of experiments that allows complete identification of the model parameters.
3.2.
Results
Fig. 1 illustrates the evolution of H2 and O2 concentration during the long-term experiments that were conducted at different water splitting and thermal reduction temperatures. As mentioned earlier, in experiments that were presented in previous studies [22], the duration of the activation, water splitting and thermal reduction steps was not sufficient to provide a representative picture of the exhaustion of the oxygen uptake or liberation of oxygen from the storage sites. In the present experiments it is observed that with the increase of the duration of each step (water splitting and thermal
Table 1 e Long-term activation, water splitting and thermal reduction experiments. 1st set
2nd set
3rd set
T Dwell T Dwell T Dwell ( C) time (h) ( C) time (h) ( C) time (h) Activation 1400 Water splitting 900 (WS) Thermal 1300 reduction (TR)
5 w3
1400 1000 1350
5 w3
1400 1100 1400
w3
Fig. 1 e Evolution of H2 and O2 production rates during the long-term experiments for (a) the first (900e1300 C); (b) the second (1000e1350 C) and (c) the third (1100e1400 C) sets of temperature for water splitting/reduction steps.
reduction) the concentration of H2 and O2 is reduced to very low values. Although, the longer dwell time of 3e5 h is also not adequate for the concentration of the products to drop to zero, they provide a more clear picture of the exhaustion of the oxygen storage sites in the case of the water splitting step, while in the case of thermal reduction the longer dwell time allows the material to release almost all the O2 that can be released at a given temperature. In this way, the material approaches its initial state. Also, it can be concluded from these experiments that, in the case of NiFe2O4, the most favorable set of temperatures was 1100 C in terms of water splitting and 1400 C in terms of thermal reduction. At that
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specific pair of temperatures the material produces approximately 428 mmoles H2/gredox during the water splitting step and releases approximately 148 mmoles O2/gredox during the thermal reduction which corresponds to about 70% of the amount of O2 that was absorbed from the splitting of water. This regeneration efficiency is by no means a fundamental property of the particular redox material since it depends on the time of the two reaction steps. The extraction of fundamental quantities from the experimental data requires the use of the appropriate mathematical model. Based on the results presented in Fig. 1, in the particular operating temperature window, H2 yield showed better cycleto-cycle stability and, therefore, higher overall production.
4.
Data analysis
At first, it must be examined if the laboratory reactor can be assumed as a differential reactor which will greatly facilitate the analysis. The instantaneous degree of conversion is very small, which means that the water vapor concentration along the bed can be assumed constant and equal to its inlet value. Regarding the question if the reaction is kinetically controlled, the mass transfer coefficient for the catalyst particles was computed and it was found to correspond to mass fluxes of vapor much larger than those corresponding to measured reaction rates, so diffusion limitations can be ignored. The final issue to be considered is the temperature in the bed. If the heat of the water splitting reaction is DH (per mole of vapor), then a global heat balance in the bed gives the following raise of the gas temperature (which implies a gradual increase of the temperature along the bed): DT ¼ XwxcDH/cpg where cpg is the specific heat capacity of the gas and xc the fractional conversion of water vapor. It seems that in the particular longterm experiments, the temperature raises a few degrees at some instants but this increase can be ignored considering the broad range of temperatures covered by the experiments. The consideration of the actual reactor as a differential one leads to the following key relation for the water splitting step: RH2 ¼ FH2
(10)
The corresponding governing equation for the thermal reduction step is: RO2 ¼ FO2
(11)
The procedure followed to adjust the model to the experimental data will be presented here. It should be mentioned that only the part of the hydrogen and oxygen concentration profiles after their respective peak is included in the analysis procedure. According to the model, the product gas (hydrogen or oxygen) concentration should reach instantaneously its highest value and thereafter decrease; however in the experimental configuration the diffusion of the evolved gas in the line to the analyzer has as a result the gradual increase of the measured product gas concentration from zero to its maximum value. A sound indication for this is that the time interval required for hydrogen concentration to reach its highest value was always of the order of a few tens of seconds for all the experiments that were conducted.
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The gas production rate curves are fitted with a double exponential curve of the form F ¼ a1 ða2 ea3 t þ ð1 a2 Þea4 t Þ in order to smooth the experimental data. In general the degree of noise in the data is very small and the above functions fit the data very well. It is noted that the model equation for the gas production constitutes a system of two linear ordinary differential equations and their solution has the same general form with the function used to fit the data. Nevertheless, the relations between the fitting function parameters and the kinetic parameters are too complex for their use to offer any advantage. It was found much more convenient to estimate the model parameters by solving numerically the corresponding ordinary differential equations and comparing the results with the values of the equation fitted to the data. From the above, it is obvious that trying to fit the numerically solved kinetic model to the double exponential function for F leads always by definition to 100% success. It must be kept in mind that the parameter values resulting in this way are not always physically sound since their value is based on pure mathematical requirements without taking into account any physical constraint. The model parameter extraction, in the present case, must be conducted via the simultaneous consideration of consecutive cycles, so it is a much more demanding procedure than the one used for the linear model considered in Ref. [22] where each cycle was analyzed separately. The procedure for the derivation of the parameters from one experiment is described in the following paragraph. The first water splitting hydrogen production curve must be approached by assuming 40 ¼ j0 ¼ 0 and changing the values of the k1, K, 4tot, km1 parameters in order to approximate the fitted experimental data. At the end of the simulation of the particular cycle, the model gives some values for the variables 4 and j. These values must be the initial values in the attempt to simulate the first thermal reduction curve using the parameters k2, K, km2. The model predictions for 4 and j at the end of this cycle must be used as initial conditions for the simulation of the second water splitting cycle. It is noted that, as the water splitting in the case of the second cycle occurs at the same temperature with the first cycle, all the model parameters must be the same. The procedure continues by using the final values of 4, j that were extracted from the second water splitting cycle, as initial values to the second thermal reduction cycle. The model parameters must be the same as the ones of the first thermal reduction cycle. The whole procedure is repeated for each set of parameters, taking the cycles sequentially until a set of parameters, which can reasonably describe the experimental cycles, is found. Using this process, parameter values corresponding to the different temperatures can be found by analyzing the data from the long-term experiments (Fig. 1). A value for exponent n must be assumed. This cannot be based on the present work data since the experiments were conducted under the same vapor molar fraction. Experiments with different vapor fractions presented in Ref. [22] reveal that up to the fraction that was employed in the long-term experiments, the exponent value n ¼ 1 is a good approximation. The data taken at different temperatures are interpolated using Arrhenius temperature dependence or fitting by simple functions depending on the data form. The final set of
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parameters as a function of temperature is presented in Tables 2 and 3 for the case of water splitting and thermal reduction reactions respectively. Regarding water splitting, the total oxygen capacity of the external layer seems to increase linearly with temperature in the range of the water splitting experiments (900e1100 C). More surprising is the behavior of the kinetic rate constant k1 which appears to decrease with the increase of temperature. This behavior of the kinetic rate cannot be interpreted on an elementary basis but suggests that even the basic steps of the composite reaction mechanism proposed here consist of other simpler steps. A possible explanation of the reduction of k1 with temperature is that due to the thermal expansion of the material, the external surface area of the redox material (included in the effective coefficient k1) is reduced (e.g. by reduction of its roughness). The combination of the 4tot and k1 that gives the external region reaction rate corresponds to a very modest temperature dependence that led us, in the previous work [22], to suggest a temperature independence of the first linear stage of the water splitting reaction. The more detailed model presented here reveals a much more complex temperature dependence. It is very interesting that the ratio K of the external to the internal region oxygen capacity appears to be constant for water splitting on the temperature range considered. This is reasonable, since 4tot and jtot are intrinsic thermodynamic quantities and may vary similarly with the temperature. The difference between the two regions is not in their thermodynamics but in their accessibility by the gas phase. The mass transfer coefficient km1 appears to be constant from 900 to 1000 C and then increase up to 1100 C. The situation is simpler for the case of thermal reduction in the temperature range considered. The reaction constant k2 and the mass transfer coefficient km2 follow an Arrhenius dependence. The parameter K is constant at a value of about 35% of the one found for water splitting. It is noted that K, in principle, denotes the same variable, independently of the direction of the oxygen motion. So, it is considered the same for water splitting and thermal reduction. The difference observed is not attributed to the different phenomena occurring but to the difference of prevalent temperature implying a transition from 0.85 to 0.3 somewhere between 1100 C and 1300 C. The experimental and theoretical gas production rates for three cycles for the case of water splitting at 1100 and thermal reduction at 1400 C are shown in Fig. 2. It is obvious that the model describes the data adequately. The comparisons
Table 3 e Thermal reduction kinetic parameters as a function of temperature (in K). Thermal reduction k2 km2 K
e(41.594-83,334/T) e(74.507-136,000/T) 0.3
(1/s) (1/s)
for one cycle in the case of 1000e1350 C is shown in Fig. 3. In the case of 900e1300 C the thermal reduction at 1300 C produced negligible O2 and is therefore not presented in the diagram (Fig. 4). It must be noted that the results presented here cannot be considered as an absolute determination of the process kinetics but as an attempt to quantify in some way the experimental data in order to scale-up the results to solar reactors. Several complications not considered by the above described model will be discussed here. There is a “dead” period between water splitting and thermal reduction steps needed for the temperature to reach the desired value for the two steps. During this period, oxygen may be transferred from one region to another. Unfortunately, this process cannot be included to the data approximation procedure due to the lack of knowledge of the parameters km and K for the intermediate temperatures. Additionally it must be noted that in no case the present model is considered to describe in detail the phenomena occurring on the redox material. It is just a phenomenological model developed on the basis of experimental observations and capable to represent the experimental results. This model features are enough to allow the scale up of the laboratory reactor data to the industrial scale monolithic reactor through the appropriate reactor modeling. Another issue has to do with the aging of the material after each cycle. The temperature effect on the reaction kinetics has two components: a reversible one (e.g. due to structural changes from thermal expansion) and an irreversible one (e.g. sintering/melting of the material). It is well known that at high temperatures (larger than 1400 C used
Table 2 e Water splitting kinetic parameters as a function of temperature (in K). Water splitting k1 4tot km1
K
0.07098.851$105 T þ 2.786$108 T2 1.025 T-1136.8 2.83$104 2.83$104-0.95$104$(T1273)/100 0.85
(1/s) (Gratoms solid phase [O]/g of redox material) (1173 < T < 1273) (T > 1273)
Fig. 2 e Comparison of the experimental H2 and O2 production rate profiles (points) with the theoretical curves (solid lines) for the case of water splitting at 1100 Cethermal reduction at 1400 C.
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5.
Fig. 3 e Comparison of the experimental H2 and O2 production rate profile (points) with the theoretical curves (solid lines) for the case of water splitting at 1000 Cethermal reduction at 1350 C.
here) redox materials may melt and lose their activity. At the temperatures employed here, it is possible that some deactivation of the material may occur after each cycle. This deterioration of the performance of the redox material was studied previously [13] where the redox material was subjected to grinding after the first water splitting step and also after the third thermal reduction step. It was observed that sintering of the redox material that took place at high temperatures was alleviated by grinding which had as an effect the modification of the structure of the redox material and the enhancement of the surface directly accessible for oxygen adsorption from the gas phase. However, in the present study, the data are not enough to quantify the degree of deactivation and the model parameters are derived ignoring such deactivation phenomena.
Fig. 4 e Comparison of the experimental H2 production rate profiles (points) with the theoretical curve (solid line) for the case of water splitting at 900 C.
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Model parametric study
A parametric analysis of the kinetic model with the parameters derived from fitting the experimental data follows. The conditions that were considered for the simulation are the same with those employed in the experiments. Several operation scenarios are provided below to reveal details on the modeling approach which were not evident by the directly experimentally measured quantities. Initial conditions very close to those of the experiments shown in Fig. 2 are considered. In the first case (base case) a temperature switch between 1100 C and 1400 C every 104 s is considered. Initially there is no solid phase oxygen 40 ¼ j0 ¼ 0. The gas production rates are shown in Fig. 5 for five cycles. There is an initial reduction of the hydrogen production from the first to the second cycle (similar to the one observed experimentally). The system comes practically to a periodic operation at the second cycle for the hydrogen production and at the first cycle for oxygen release. The corresponding evolution of the solid phase oxygen is shown in Fig. 6. The external region oxygen amount 4 follows the expected behavior: increases during water splitting and decreases during thermal reduction. The internal region oxygen shows a more complex behavior. It increases during water splitting step but it continues to increase during the first stage of the thermal reduction step. This is due to the shift of the partition coefficient K from 0.85 to 0.3 between splitting and reduction. When 4 decreases considerably, j starts decreasing after passing through a maximum. The number of cycles in which the periodic steady state is reached depends on the degree of completeness of the reaction occurring in each step and this in turn depends on the step duration. In the limit of infinite duration for each step the reactions are completed so the periodicity is reached instantaneously. The large step time of 104 s of the base case
Fig. 5 e Modeling the H2 and O2 production for temperature switches between 1100 C and 1400 C every 104 s.
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considered here is close to the infinite duration and this explains the fast approach to periodicity. In the case of a small reaction extent during each step of water splitting and thermal reduction, the approach to periodicity is slow. According to the second scenario studied, temperature switches between 1100 C and 1400 C every 3000 s. The gas production rates for the same conditions with the base case but a time interval of 3000 s for each step is shown in Fig. 7. It is obvious that the convergence to the periodic steady state is much slower. The hydrogen production rate decreases and the oxygen production rate increases for five cycles before
convergence to be achieved. The corresponding evolution of the adsorbed oxygen is shown in Fig. 8. In this case the internal region oxygen amount j is always larger than the external region oxygen amount 4 during the periodic steady state. It seems that the slow convergence to the periodicity is due mainly to the slow dynamics of the internal region oxygen. In order to study the effect of the initial conditions 40, j0 (amount of solid phase oxygen) on the gas production rates three cases are considered: (a) case A: 40 ¼ 200, j0 ¼ 0, (b) case B: 40 ¼ 100, j0 ¼ 100, (c) case C: 40 ¼ 0, j0 ¼ 200 (the units are gratoms [O]/g of redox). The gas production rates for step period of 104 s are shown in Fig. 9. The initial condition in this case influences only the first hydrogen production cycle. In particular, only the external region oxygen has an effect since the effect of j0 is negligible small. The situation is different for the case of step duration of 3000 s. The influence of the initial conditions remains for several cycles of hydrogen and oxygen production as it is shown in Fig. 10. The gas production rate decreases with the increase of 40. The influence of j0 is again very small. So the general conclusion from the above results is that i) the number of cycles required for establishment of the periodic steady state depends on the extent of reaction in each step and ii) the influence of initial conditions 40, j0 on gas production increase as the reaction extent in each step increases. This is in agreement with the respective finding of the previous version of the kinetic model in Ref. [22]. The small reaction time for each step prevented the approach to a periodic steady state. In addition, the idea to perform experiments with a longer reaction extent to avoid the influence of the initial conditions is justified. In the solar reactor it is very difficult to keep the temperature constant in time and the reactions may partially occur during the increase and decrease of the temperature [10]. In order to simulate such a situation, model results for the differential reactor considered here for linear temperature
Fig. 7 e Modeling of the H2 and O2 production for temperature switches between 1100 C and 1400 C every 3000 s.
Fig. 8 e Evolution of the solid phase oxygen for temperature switches between 1100 C and 1400 C every 3000 s.
Fig. 6 e Evolution of the solid phase oxygen for temperature switches between 1100 C and 1400 C every 104 s.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 6 3 1 7 e6 3 2 7
Fig. 9 e Effect of the initial conditions 40, j0 on H2 and O2 production for three different 40, j0 cases (A, B, C) and step period of 104 s.
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Fig. 11 e Modeling H2 and O2 production for linear temperature increase (water splitting 900e1100 C, thermal reduction 1300e1400 C).
increase between 900 and 1100 C (water splitting) and between 1300 and 1400 C (thermal reduction) in 3000, 6000 and 104 s are presented in Figs. 11 and 12. The gas production rates are shown in Fig. 11. The combination between the dependence of the reaction rate on 4, j and the temperature leads to the particular shapes of gas rate curves shown in Fig. 11. An initial stage of large time variation of the gas production rate is followed by a period of slow variation. The corresponding solid phase oxygen evolution curves are shown in Fig. 12. External region oxygen undergoes a well defined maximum at the
moment of switching from water splitting to thermal reduction where internal region oxygen j increases during most of the time. The findings of the present work are capable to explain the behavior observed in Ref. [22] where the variations in the activation time and in the reaction time from experiment to experiment led to seemingly uncorrelated reaction rates between the experiments and between the cycles, raising questions about the stability of the redox material. The present model suggests that the observed behavior is not due to material instability rather than to the difference of the state variables 4 and j at the onset of each cycle.
Fig. 10 e Effect of the initial conditions 40, j0 on H2 and O2 production for three different 40, j0 cases (cases A, B, C) and step period of 3000 s.
Fig. 12 e Solid phase oxygen evolution curves for linear temperature increase (water splitting 900e1100 C, thermal reduction 1300e1400 C).
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Conclusions [12]
A new extended model is derived for water splitting and thermal reduction reactions on a redox material. The new model considers two oxygen storage regions communicating to each other by a solid state diffusion mechanism. A minimum set of experiments for water splitting thermochemical cycles over a Ni-ferrite was designed and performed in order to derive the model parameters. The particular model is a direct extension for higher reaction extents of the linear model proposed previously [22]. The distinct difference of the proposed model over the typical solid reaction models used in the literature is the inclusion of two state variables instead of one. This has a significant effect on the reaction dynamics and renders the model capable to explain the dynamics of the convergence of the thermochemical cycles to a periodic steady state, observed previously.
[13]
[14]
[15]
[16]
Acknowledgments The authors would like to thank the European Commission and the Fuel Cells and Hydrogen Joint Undertaking for funding part of this work through the project “HYDROSOL-3D”.
[17]
[18]
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