As has been discussed in the previous section 2.3, multiple materials of distinct categories have been studied to develop the most the most suitable OC. However, no one material has yet been recognized as the most ideal. Non-stoichiometric Ceria has shown higher oxygen storage capacity at relatively lower reduction temperatures, with added advantages of good mechanical and physical properties. The typical reactions taking place in the reduction and the oxidation reactors are shown below in equations (3.1) and (3.2), in which, ceria releases oxygen and undergoes thermal reduction, in turn, to be oxidized by carbon dioxide and water producing carbon monoxide and hydrogen in the two reactors respectively.
1
2 1 2- 2
Reduction reactor : CeO CeO O 2
⎯⎯⎯
TH→
+
(3.1)
2
2- 2 2 2
Oxidation reactor : CeO +CO ⎯⎯⎯−TH →CeO +CO (3.2a)
2
2- 2 2 2 2
Oxidation reactor : CeO +H O⎯⎯⎯−TH→CeO +H (3.2b)
It needs to be mentioned that both the reactions are heterogeneous and non–catalytic. As with other metal oxides, the reduction and oxidation reactions are fundamentally different from the energy perspective, with the former being endothermic and the later, an exothermic reaction.
Hence, the two reactors are essentially operated at different temperature levels, with the reduction reactor being at a higher temperature than the oxidation reactor.
28
Due to the limited availability of the thermodynamic properties of non-stoichiometric ceria, a different approach was used using the fully reduced and stable form of Ceria, Ce2O3, widely available in the literature. The above reaction set (3.1-3.2) was therefore alternatively written as follows:
2 2 2 3 2
CeO (1-2 )CeO Ce O + O
⎯⎯→
kred + 2
(3.3)2 2 3 2 2
(1-2 )CeO
+ Ce O + CO
⎯⎯→koxd CeO CO+
(3.4)2 2 3 2 2 2
(1-2 )CeO
+ Ce O + H O
⎯⎯→koxd CeO H+
(3.5)The non-stoichiometry factor (δ) has been proposed to be defined as the ratio between the still-unreacted ceria and the completely reduced form, Ce2O3. Equation (3.3) represents the reduction reaction, while the CDS and WS reactions can be modelled as per the equations (3.4) and (3.5) respectively. The δ can hence be evaluated from equation (3.3) and can be written as per the following equation (3.6), whereby the value of δ can ideally between 0 and 0.5, the later corresponding to a fully reduced state of CeO2.
2 3
2 3 2
Ce O
Ce O CeO
= n
2 n +n
(3.6)
where, nis the molar flow of the respective components.
Nevertheless, a complete removal of all the available oxygen would cause the fluorite phase of CeO2 to destabilize, making phase transition inevitable beyond a certain degree of reduction [51]. Bulfin et al [51] reported the maximum achievable δ without changing the fluorite structure of CeO2 for redox recycling of ceria as limited to 0.35.
Proceeding accordingly, due to the limited availability of the thermodynamic properties of non-stoichiometric ceria, the degree of advancement of the reaction has been fundamentally used in the kinetics model developed instead of the non-stoichiometry coefficient. Therefore, a separate α parameter, indicating the degree of advancement of the reaction was defined for all the reactions in terms of the relative content of Ce2O3 and CeO2 in the solid mixture after respective reactions.
For the reduction of CeO2, the degree of advancement of reaction αred primarily describes the performance of the reduction reaction in terms of degree of reduction of the ceria powder and is represented by equation (3.7). The equation is based on its relationship with the non-stoichiometry coefficient δ, whereby a maximum extent of reaction is obtained at δmax of 0.35.
The numerator represents the current non-stoichiometry after reduction, while the denominator indicates the maximum possible non-stoichiometry.
max
α = αred =
(3.7)
29
A detailed discussion on the calculation of the degree of advancement of reaction is done in the following subsections. Indeed, such formulation of the degree of advancement of thermal reduction reaction (αred) agrees with the reduction kinetic model developed by Bulfin et al [51].
On the other hand, the oxidation of the reduced ceria inherently moves in the opposite direction to reduction, whereby, the extent of oxidation (αoxi) can be written according to the following equation (3.8).
oxd red
α =1-α
(3.8)Before delving in detail at the individual reaction kinetics, the pathways of reaction are worth discussing. Two primary pathways of reaction for the solid-gas systems have primarily been used in the literature [120]. In one method, the solid particle decreases in size as the reaction moves forward and leaves only a small portion of itself that contains impurities that are not able to react. An example being coal combustion, where the unreacted fraction of the initial fuel remains as ash. Another example of such mechanism might be a reduction of volatile OCs, whereby the metals get vaporized after the removal of oxygen by thermal reduction. The second mechanism assumes a constant reaction particle size during the entire reaction, even though the composition changes. The non-volatile OCs can essentially be considered to follow this reaction approach when the temperatures are low enough not to cause sublimation of the outer layers of the solid [121,122]. The schematic of the two different reaction model types is shown in the following Figure 3-1.
Figure 3-1 Different behaviours for the reacting solid particles [120]
As can be seen from the above Figure 3-1, the first mode of reaction, also called the Progressive Conversion Model (PCM), assumes that the concentration of unreacted solid in the particle is distributed quasi-uniformly during the reaction. However, the second, or the Shrinking Core Model (SCM) assumes that the front of the reaction advances into the solid as the reaction progresses, leading to gradual consumption of the unreacted material. Levenspiel [120]
commented that the SCM represents reality much better than the PCM, though the PCM can be simplified under certain conditions to the SCM. Mainly such situation can be observed when
30
the surface reaction rate is the rate determining step of the process and the diffusion rates in solid and in gas film are much faster.
The thermal reduction of metal oxides comprises several reaction steps. Of the five reaction steps of thermal reduction of ceria, as proposed by Levenspiel [120], these steps can be limited to three, since there is no additional reactant transport towards the reaction surface. The steps can be elaborated as i) the release of oxygen particles from the surface of the ceria; ii) the diffusion of oxygen vacancies towards the particle core and iii) the diffusion of oxygen particles through the gas film
Like the reduction reaction, the oxidation reaction can also be fully described through four steps as i) the transport of oxygen vacancies towards the reaction surface, ii) the diffusion of oxidant through the gas film towards reaction surface, iii) the filling the vacancies with oxygen and iv) the diffusion of the spent oxidant through the gas film
The additional step of oxidant (CO2/H2O) diffusion towards reaction surface needs to be considered. The second and the fourth steps of the oxidation reaction are much faster with respect to the other reactions. Literature reveals that the primary focus on studies in the related field focuses on expanding the reaction mechanism associated with filling the vacancies of the OC by oxygen (Step 3) through multiple reaction pathways [123,124] and on the transport of oxygen vacancies in the particle [125].
SCM can be used to model the redox kinetics of ceria, though not often used due to its higher complexity. Most of the studies focused on the kinetics of the OCs tend to describe possible reaction pathways for the material and later try to fit experimental data into various reaction models, based on the rate-limiting step in the reaction. Thus, the rate-determining step of the reaction pathway is included in the general formulation of the reaction rate. Between the two reactions, the reduction reaction is inherently slower, resulting in the reduction reaction to be the rate-determining step for the entire cycle, also directly influencing the yield from the oxygen reactor. Therefore, based on the above discussions, as well as the consideration that the crystal structure of the OC, especially for non-volatile and non-stoichiometric ceria remains constant throughout the redox cycle, a simplified approach was considered for modelling the reaction kinetics for the solar thermochemical cycle as described in the following sub-section.
3.1.1 Reduction kinetics
Bulfin et al [51] investigated ceria reduction kinetics at a wide range of temperature, between 1000oC and 1900oC and a wide range of oxygen partial pressures of 10-2 to 10-8 bar. The partial pressure of oxygen is developed from the presence of removable oxygen produced by the reduction of CeO2 as per equation (3.3).
The proposed reduction kinetic model by Bulfin et al [51] is essentially based on the Arrhenius equation, assuming an equilibrium reaction. This causes both forward and backward reactions from the release of oxygen and recombination of the released oxygen respectively, to occur together (CeO2 ↔ CeO2-δ + 0.5δO2). Unlike the previous argument of measuring the extent of non-stoichiometry, the authors proposed moles of oxygen vacancies per mole of cerium per
31
second or simply per second to be used as the measure of the non-stoichiometry of the reduced ceria, as shown in the following equation (3.9).
[O ]vac
[Ce] = (3.9)
The forward reduction reaction is driven by the concentration of removal of oxygen, while the backward recombination (or oxidation) reaction is influenced by the concentration of both the vacancies and the oxygen gas [51]. Thus, the rate of the total change of the non-stoichiometry, which in other terms is also the rate of change of the oxygen vacancy concentration can be written as difference of the rate at which oxygen leaves CeO2 (reduction) and the rate at which it recombines (oxidation) as per the following equation (3.10)
2
red max
E E
d =( - ) exp - exp
-dt RT RT
−
nr ox
red O ox
A P A
(3.10)
Where A represents the Arrhenius constant, E is the activation energy in kJ/mol-K, PO2 is the partial pressure of oxygen, nr is the reaction order, R is the universal gas constant and T is the absolute temperature in kelvin with subscript f and b as forward and backward reaction respectively.
Assuming ideal gas behaviour, the concentration of O2 is directly proportional to the partial pressure of O2 (PO2) or the vacuum pressure of the total reactor, as applicable based on the reactor design. Based on the works of Panlener et al. [126] and Dawicke et al. [127] and through the plotting of log(δ) against log(PO2) with certain assumptions, the authors developed a reaction kinetic model for the net thermal reduction reaction of ceria. To fit the developed kinetic model with the experimental results, the shrinking core model was used. Considering a surface reaction to be the rate-determining step there would be a shrinking sphere of vacancies resulting in a restriction on the reaction rate with the advancement of the reaction. A third order model for the rate equation was found to be the best fit and the overall rate equation for the reduction reaction, based on Xred is obtained as per the following equation (3.11). The values of the parameters of the rate equation are summarized in Table 3-1.
d d 1/3
= (1- )
dt dt
d −
red
re
(3.11)
Table 3-1 Ceria reduction rate equation coefficients presented by Bulfin et al [51]
Parameter Value
δmax 0.35
n 0.218 ± 0.0013
Ered (kJ/mol) 232 ± 5 Eox (kJ/mol) 36 ± 4
Ared (s-1) 720,000 ± 360,000 Aox (s-1bar-n) 82 ± 41
32
However, the transition from the rate equation to the reaction rates of the concerned chemical species is done as per the equations (3.2) and (3.11) together with the available chemical species. Three distinct chemical species take part in the above reaction. For each mole of cerium (III) oxide (Ce2O3) generated, two moles of ceria (IV) oxide (CeO2) are consumed and half a mole of oxygen gets released. Aside from stoichiometric coefficients, knowledge of reaction time step is important. In the discrete kinetic model, the particle residence time is used as the time parameter, in terms of Δt, as can be seen from equations (3.12) through (3.14). The thermal reduction reaction rates for the three species taking part in the reaction are shown below.
2 2
redCeO CeO red
k = -2 n dα Δt
dt (3.12)
2 3 CeO2
red
redCe O n
k = 1 n dα Δt
dt (3.13)
2 CeO2
red
redO n
k = 0.5 n dα Δt
dt (3.14)
3.1.2 Oxidation kinetics
the The oxidation kinetics for ceria for H2O and CO2 splitting has been investigated for reactivity by different research groups [49]. The initial reduction state of the sample has been reported to strongly influence the subsequent oxidation reaction. Significant drop in the reaction rates were noticed when non–stoichiometry factor exceeded 0.18-0.2 values in the temperatures below 820oC [49]. It is reported that high variations in the reaction activation energies with non–stoichiometry of the sample in higher concentrations of the oxidizing gas.
As reported, the activation energy varied in range of 160-200 kJ/mol for non–stoichiometry between 0.01 and 0.09. For oxidation, the kinetics developed by Arifin [124], and Arifin and Weimer [128], who investigated redox kinetics of ceria for water and carbon dioxide splitting reaction. The reaction mechanism has been proposed in the general formulation for the reaction rate as equation (3.15) with the corresponding coefficients being listed in Table 3-2.
no
oxd oxd
oxd i oxd
dα E
=A exp - y (1-α )
dt RT
(3.15)
Where Aoxd is the Arrhenius constant, Eoxd is the activation energy degree and no is the order of the oxidation reaction and yi is the oxidant molar fraction, ψ represents the reaction model exponent.
The oxidation reaction of the reduced ceria with αred water vapour and CO2 splitting was found to behave similarly to a homogeneous reaction, i.e. its rate decelerates proportionally to the depletion of the reactants (1-αoxd). More so, the kinetics of the water splitting reaction are quite fast due to the relatively small activation energy of 29 kJ/mol. However, similar analyses revealed the dependence of the rate-determining step of the carbon dioxide splitting reaction on the on the temperature of the process [124]. It was also observed that with the increase in
33
temperature, carbon site blocking, and subsequent surface recombination stops. At 875oC only reaction pathway is direct desorption of carbon monoxide from the particle surface, which might result in significant changes to the reaction coefficients ψ and no as indicated in Table 3-2. It is worth noticing that in the discussed research, ceria sample was constantly cycled and reused in different conditions. Nevertheless Arifin [124], noted that the overall production of the fuel from the sample remained almost constant, though reaction times varied because of varying temperatures and molar fractions of reactants.
Table 3-2 Kinetic parameters of the oxidation reaction of reduced ceria obtained by Arifin [124]
Oxidant Temp (oC) A0 (1/s) E0 (KJ/mol) ψ (-) no(-) CO2 750-950
650-725
1.0 4.2
29 47
0.89 0.53
1.0 1.0 H2O 750-800
825-875
3.4 2.5
45 41
0.65 0.7
1.2 1.7
To determine the reaction rates for splitting reactions, the degree of advancement of oxidation reaction was calculated as per mentioned in equation (3.8). Following the aforementioned equation, independent to the use of CO2 or H2O, when one mole of each is consumed, it leads to simultaneous consumption of each mole of Ce2O3 with the corresponding generation of two moles of Ceria and one mole of CO and H2 respectively. Taking this into account, the reaction rates for each species, in terms of the available solid reactant quantity (molar flow) are listed as per the following equations (3.16-3.21)
2 2
2 2 3
oxdH O oxdCO
oxdCeO Ce O
dα dα
k = 2 n Δt
dt dt
+
(3.16)
2 2
2 3 2 3
oxdH O oxdCO
oxdCe O Ce O
dα dα
k = -1 n Δt
dt dt
+
(3.17)
2
2 2 3
oxdH O
oxdH O Ce O
k = -1 n dα Δt
dt (3.18)
2
2 2 3
oxdH O
oxdH Ce O
k = 1 n dα Δt
dt (3.19)
2
2 2 3
oxdCO
oxdCO Ce O
k = -1 n dα Δt
dt (3.20)
2 2 3
oxdCO
oxdCO Ce O
k = 1 n dα Δt
dt (3.21)
34