Modeling of Oxidation and Reduction of a Copper-Based Oxygen

Article pubs.acs.org/EF

Modeling of Oxidation and Reduction of a Copper-Based Oxygen Carrier Juan C. Maya and Farid Chejne* School of Chemical and Petroleum, National University of Colombia, Medellín, Crr 80 Number 65-223, Medellín 050001, Colombia ABSTRACT: A mathematical model that describes the conversion and the temperature profile trough time of a copper-based oxygen-carrier particle was developed. The model describes the reaction rate based on an initial distribution of grain, permitting a better adjustment to the experimental data than the classic changing grain size model and it can be used to modeling the chemical looping combustion process at real scale. On other hand, two oxygen carriers were synthesized using wet-impregnation and incipient impregnation techniques, and they were characterized with scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX), BET superficial area, porosimetry, and X-ray diffraction (XRD). Kinetic parameters of the synthesized materials were calculated by thermogravimetry.

1. INTRODUCTION Currently, the generation and use of energy sources is one of the human activities that produces the greatest impact on the environment due to the continuing depletion of the natural resources needed to meet the growing demand of our cities and industries and the need of modern societies in developing countries to have a better lifestyle. The processes of energy transformation from fossil fuels reflect this reality, which release a lot of CO2 into the atmosphere, estimated to represent onethird of the total CO2 emitted by human activity.1 In order to solve this problem, several technologies have been developed, such as precombustion, postcombustion, and oxy-combustion, which require significant energy expenditure, as a consequence reducing process efficiency considerably. However, in recent years, a new technology known as chemical looping combustion (CLC) has emerged, allowing the inherent separation of carbon dioxide at low cost.1 Despite the advantages of CLC with respect to the inherent CO2 capture, this technology still has limitations, mainly due to the problems with oxygen carriers during the cycles. Therefore, the approach that has been given to research is mainly based on the synthesis and characterization of oxygen carriers, leaving the theoretical aspects and modeling behind. Among the investigations addressed the development of oxygen carriers are the by Linderholm et al.2 and to Mattisson et al.,3 where they worked with oxygen carriers based on nickel and iron, which are the most used in the CLC process. In other research, such as Chuang et al.,4 was tested copperbased oxygen carriers that have advantages over conventional materials, such as high reactivity and the exothermicity in the reactions of reduction and oxidation.5 These oxygen carriers agglomeration problems arose because of the low melting point of copper, and only until recently, with works by authors such as Diego et al.6 and Gayan et al.,7 it was possible to optimize the preparation of such transporters, reviving the interest of researchers for these materials. On the other hand, it can be said that has not been carried out extensive research focused on the modeling of oxidation and reduction reactions of particles of a copper-based oxygen carrier.8,9 Therefore, the general objective of this work was to © 2014 American Chemical Society

propose a mathematical model describing the reduction and oxidation reactions of a copper-based oxygen carrier that occur in a CLC process.

2. EXPERIMENTAL SECTION 2.1. Preparation of Oxygen Carriers. For the synthesis of copper-based oxygen carriers have been employed different synthetic methods such as coprecipitation, mechanical mixing, and spray drying impregnation. The most commonly used support is SiO2, which shows a good reactivity with copper and inertia; however, the CuO decomposed to Cu2O.10,11 TiO2 was also tested as support, but showed a strong tendency to form CuTiO4.1 It has been found that the best method of preparation of copper-based oxygen carriers is impregnation of α-alumina, γ-alumina, MgAl2O4, or NiAl2O4−Al2O3 with contents of CuO under 20 wt % to avoid agglomeration.12 In this paper, two methods of impregnation were used, the first was excess wet impregnation based on the work of Celaya13 and the second was the incipient impregnation was used in the work of Jiménez14 for impregnating metals in carbonaceous materials. In both methods, solution Cu(NO3)2·3H2O was used at different concentrations as precursors and γ-alumina Puralox NWa-155 was used as support, and also, a single impregnation to obtain each carrier was made with different concentrations of the precursor solution. This is to find the maximum concentration at which the impregnation was successful without causing blockage of pores, poor dispersion, or excessive reduction of the surface area. Excess Wet Impregnation. In this method, an excess of the precursor solution was used. The steps followed for the preparation of materials by this technique are shown below: I. The alumina powder Puralox NWa-155 was immersed in the solution of Cu(NO3)2·3H2O with stirring for 12 h at room temperature. Received: February 25, 2014 Revised: July 28, 2014 Published: July 28, 2014 5434

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II. The resulting solution was filtered under vacuum. III. The material was dried for 24 h in an oven. IV. The solid was calcined in air for 10 h at 600 °C to decompose the Cu(NO3)2 to CuO. Incipient Impregnation. In incipient impregnation, the alumina support is contacted with the minimum volume of solution necessary to wet the whole surface. The concentration of the solution should be adjusted depending on the amount of metal to be impregnated. The detailed procedure is described below: I. The alumina was maintained under vacuum at 65 °C for 2 h, to remove air and any adsorbed compounds on the support and facilitate contact of the solution of Cu(NO3)2 supported. II. The solution of Cu(NO3)2 was added to saturation and waited for 20 min. III. The material at 100 °C for 3 h was dried in an oven to achieve complete solvent evaporation. IV. The material was calcined in air for 10 h at 600 °C to decompose the Cu(NO3)2 to CuO. A temperature ramp of 1 K/min was used until it reached the desired temperature. Finally, six oxygen carriers were obtained (see Table 1). The following nomenclature is used: The first letter symbolizes the

the oxygen carrier I21 was not studied further because despite a 1.18 M solution was used, almost the same amount of CuO impregnated was obtained with the carrier I20, which was synthesized with a solution 0.94 M. Therefore, it can be deduced that the impregnation is not satisfactory in concentrations of the precursor that exceed a limit value, probably because a blocking of the pores of the material and poor dispersion occurs, by which, if higher amounts are to be impregnated is it necessary to repeat the impregnation process several times at moderate concentrations of the precursor solution.6,7,15,16 2.2. Oxygen Carriers Characterization. SEM (EDX) Analysis. SEM JEOL JSM 5910 LV equipment with BES and SEI detectors was used, for image generation and EDS and WDS detectors for qualitative and quantitative chemical analysis on conductive and nonconductive samples. Scanning Electron Microscopy (SEM). Initially, it can be seen in the Figure 1a and b micrographs SEI and BES of Al2O3, respectively, which shows that particles have irregular shapes with rounded edges and varying particle sizes. In Figure 2a and b, the oxygen carrier H9 micrographs SEI and BES, respectively, are shown. One can notice that the

Table 1. Composition of Oxygen Carriers sample

concentration Cu(NO3)2 (M)

%w CuO

H9 H10 H12 I20 I23 I21

1.60 2.40 3.60 0.94 1.41 1.18

8.62 9.88 11.76 20.32 22.96 20.66

type of impregnation which was obtained material (H = wet impregnation, I = incipient impregnating) and the number that follows the letter represents the approximate percentage of CuO that has the oxygen carrier. The H9, H10, I20, I23, and I21 are black materials such as CuO, with some small light spots that are probably due to not being fully calcined. The H12 sample kept the light color it had before calcination, indicating that the Cu(NO3)2 did not decompose, so it was discarded from the study. Furthermore,

Figure 2. SEM micrography of oxygen carrier H9.

particles are smaller than the original size alumina, which is due to attrition in the agitation during the synthesis process. In Figure 2c and d, the copper oxide grains are observed in the

Figure 1. SEM micrography of Al2O3. 5435


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Figure 3. SEM micrography of oxygen carrier H10.

Figure 5. SEM micrography of oxygen carrier I23.

surface of the particle. However, they are areas of greatest accumulation of grains. Figure 3a, b, c, and d shows the oxygen carrier H10 micrographs. Particle sizes below that of the alumina particle and stratification was noted. Higher attrition of this transporter compared with H9 was also noted. SEI and BES oxygen carrier I20 micrographs are presented respectively in Figure 4a and b, respectively. In this case, particles

Table 2. Chemical Analysis of Oxygen Carriers sample

O (% W)

Al (% W)

Cu (% W)

Al2O3 H9 H10 I20 I23

37.6 46.2 35.5 39.3 35.6

62.4 46.8 47.6 49.2 37.6

0.0 7.0 16.9 11.5 26.8

carrier I23 presents a high concentration of Cu. However, this high concentration can also cause pore blockage; as observed in SEM images (Figure 5). Surface Area (BET). The specific surface area and porosimetry of oxygen carriers were determined with the ASAP 2020 (Accelerated Surface Area and Porosimetry System) equipment by nitrogen adsorption and desorption. All samples decreased its surface area (see Table 3) with respect to the Table 3. Specific Surface Area of Oxygen Carriers

Figure 4. SEM micrography of oxygen carrier I20.

sample

specific surface area (m2/g)

Al2O3 H9 H10 I20 I23

144 107 96 49 14

original alumina which suggests a blockage of pores as in Cortes work.17 Porosimetry. The mesopore size distribution, pore volume and area distribution were calculated with the BJH method (Barrett, Joyner, and Halenda).18 It was observed that the H9, H10, and I20 carriers conserved pore size distribution similar to the original alumina, whereas I23 carrier porosity decreased sharply (see Figure 6), indicating a block of pores by CuO, which confirms the results obtained by the BET specific surface area analysis. The average pore size (see Table 4) was similar for all oxygen carriers. However, the porosity and, hence, the total pore volume was reduced for each carrier, especially for I23 as mentioned above. The density of the oxygen carriers is presented in Table 5. Note that the real density of I23 is greater than in the other

retained approximately the alumina size, which is because in this method of synthesis is not required agitation. In Figure 4c and d, CuO grains are observed in the surface of the particle, which have a uniform dispersion across the surface with no signs of stratification, contrary to what happened with the wet impregnation. SEI and BES oxygen carrier I23 micrographs are presented in Figure 5a and b, respectively; particles retained approximately the alumina size, which had a particle size similar to the oxygen carrier I20. In Figure 5c and d, a large accumulation of grains is observed uniformly dispersed on the surface of the alumina particle, which can generate blocking of internal pores. Chemical Analysis. From chemical analysis (see Table 2) of carriers which are still being studied, it appears that the oxygen 5436


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Figure 6. Pore size distributions of Al2O3, H9, H10, I20, I23.

Oxidation 1 O2 + Cu → CuO (2) 2 3.1. Determination of Kinetic Parameters. To determine the kinetic parameters of different reactions with oxygen carriers shrinking core model in the grain was used. This model considers the constant size particle formed by nonporous grains initially. The grain reacts, leaving a porous layer of the reaction product that becomes a means of transport of reactants and products (see Scheme 1). However, the shrinking core model

Table 4. Oxygen Carriers Porosimetry sample

total pore volume (cm3/g)

average pore size (Å)

porosity

Al2O3 H9 H10 I20 I23

0.43 0.40 0.37 0.32 0.05

92.20 105.46 103.41 78.51 99.90

0.56 0.53 0.49 0.42 0.07

Table 5. Oxygen Carriers Density sample

bulk density (kg/m3)

real density (kg/m3)

Al2O3 H9 H10 I20 I23

1300.00 1412.07 1428.47 1564.17 1598.53

577.63 669.87 732.55 904.63 1489.87

Scheme 1. Scheme of Shrinking Core Model in the Grain

samples. This indicates that CuO was accumulated on the initial alumina particle. X-ray Diffraction. The technique of X-ray diffraction allows the identification of crystalline phases qualitatively and quantitatively. The equipment used for the XRD analysis was an X-ray diffractometer X’Pert PRO Brand Panalytical reference MPD with Cu anode and Ni filter. In all samples, the presence of CuO, alumina, and copper aluminate was observed; however, quantitative data are inaccurate because the samples are amorphous. For all the features discussed in this chapter, it can be concluded that more oxygen carriers suitable for use in CLC are H9 and I20, and therefore, these two are with those who worked from here.

in the grain considers there is no resistance to mass transfer in the film, pores and product layer, whereby the controlling step is the reaction in the grain. Equations required to employ this model are listed below:20 t = 1 − (1 − X̅ )1/3 (3) τ ρmR rg τ= (4) bkC n

3. KINETICS OF COPPER-BASED OXYGEN CARRIERS The kinetic model developed requires input parameters (reaction order, activation energy, and pre-exponential factor) and also requires validation. For this, a thermogravimetric balance LINSEIS STA PT160019 using hydrogen and air as reducing and oxidizing atmospheres were used, respectively. The reactions were taken into account are Reduction H 2 + CuO → H 2O + Cu (1)

rg =

3(%wR ) SR̅ MR ρmR

k = k 0e(−Ea / RT̅ ) 5437

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Figure 7. Calculation complete conversion times at 800 °C (reduction).

To determine the conversion of oxygen carrier from the data provided by the TGA, eqs 7 and 8 are used.

X red =

mox − m mox − mred

Xox = 1 − X red

(7) (8)

where m = instantaneous mass of oxygen carrier mox = mass of fully oxidized oxygen carrier mred = mass fully reduced oxygen carrier To determine the kinetic parameters is necessary to avoid diffusion problems, which was achieved using a very small amount of sample (10.23 mg), and a gas velocity sufficient to overcome the resistance to external mass transfer (200 cm3 STP/min). The H2 passes for 3 min and then purged with He for 5 min to ensure that no explosions were presented. After that, the O2 was allowed to flow for 3 min completing the cycle. 3.2. Determination of Reaction Order (H9). First, it is necessary to determine the time of complete conversion reactions H9 transporter from eq 3. This is achieved by plotting 1 − (1 − X̅ )1/3 vs t. The slope of the line formed will be equal to 1/τ. Figure 7 shows 1 − (1 − X̅ )1/3 vs t at concentrations of 10%, 20%, and 40% of hydrogen. For concentrations of 10%, 20%, and 40% complete conversion times of 22.7, 12.7, and 8.9 s, respectively, were obtained. Now, using eq 4 can calculate the reaction order. If the natural logarithm is applied to each side of the equation ln τ = ln((ρmRrg)/(bk)) −n*ln C is obtained.Therefore, if ln τ vs ln C is plotted, the slope of the line is form is equal to the reaction order. Figure 8 shows the graph of ln τ vs ln CH2 to concentrations of 10%, 20%, and 40% of hydrogen. The data obtained from the above graph shows that the reaction order for the reduction reaction is equal to 0.7. For the oxidation reaction concentrations of 5%, 13%, and 21% were used (the maximum concentration at which the oxygen working is 21% because it is in the air having approximately) and complete conversion time of 63.5, 23.8, and 20.4 s, respectively. From these data, it was concluded that the reaction order for the oxidation of oxygen carrier is equal to 0.8. 3.3. Determination of Pre-Exponential Factor and Activation Energy (H9). To find the values of pre-exponential factor and activation energy of reduction reaction complete

Figure 8. Deduction of reaction order (reduction).

conversion times at 600, 700, and 800 °C are found, as performed above. In Figure 9, the graph shows1 − (1 − X̅ )1/3 vs t to temperatures of 600, 700, and 800 °C at hydrogen concentration of 40%. For temperatures of 600, 700, and 800 °C complete conversion times of 32.3, 19.2, and 8.9 s, respectively, were obtained. Now, it is necessary to calculate the grain radius with eq 5 which has a value of 4.01238 × 10−8 m. k values are subsequently calculated from eq 4 for the temperatures 600, 700, and 800 °C. Now, the natural logarithm is taken on both sides of eq 6 have ln k0 = ln k0 − (Ea/RT). Therefore, if ln k vs 1/T is obtained graph a line with intercept and slope equal to ln k0 and −Ea/R, respectively (see Figure 10). Finally, the activation energy is calculated to be 49705.58 J/mol and the pre-exponential factor is equal to 0.031 mol0.3 m0.1 s−1. To find the values of the pre-exponential factor of the oxidation reaction proceeds as in the reduction reaction, calculating complete conversion times at different temperatures. At oxygen concentration of 21% for temperatures of 600, 700, and 800 °C entire reaction time of 19.6, 18.5, and 15.1 s, respectively, were obtained. From these data, an activation energy of 9927.48 J/mol and a pre-exponential factor of 0.000554 mol0.2 m0.4 s−1 is obtained. Kinetic parameters for all reactions studied are shown in Table 6. The difference between the oxidation reaction order of H9 and I20 (see Table 6) is due the different way of reaction related to the impregnation technique and concentration of CuO. Each impregnation technique produces oxygen carriers with a specific tortuosity. 5438


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Figure 9. Calculation of complete conversion times at different temperatures (reduction).

Scheme 2. Scheme of Changing Grain Size Model

Figure 10. Arrhenius plot for the reduction.

reaction proceeds grain radius r1 is increased or decreased, depending on the molar ratio of densities between the reactant and product (the molar density of the metal copper is 140 kmol/m3 and copper oxide is 80 kmol/m3), whereas the unreacted core radius r decreases.12 The improvement proposed in this paper is to use an initial distribution of radius r0 derived from the analysis of the carrier done porosimetry. Model Assumptions. For the development of this model, the following assumptions were: • A spherical particle made of spherical grains. • The grains are nonporous initially. • The interstices between the grains make the pores of the particle. • The particle maintains its spherical shape and their diameter during the course of the reaction. • At the start of the reaction, the grain sizes are not uniformly distributed. • The reactions to be considered are the following:

Table 6. Kinetic Parameters for H9 and I20 Carriers reaction

n

pre-exponential factor (mol1−n m3n−2 s−1)

activation energy (J/mol)

reduction H9 oxidation H9 reduction I20 oxidation I20

0.7 0.8 0.7 0.9

0.031 0.000554 0.042 0.000727

35879 11345 40512 16789

4. STATEMENT OF MATHEMATICAL MODEL In regard to particle models, the models developed by Szekelly in the 1970s are remarkable.21−27 Of these models, the most used is the variable grain size model, which has been widely used to study gas−solid noncatalytic reactions as calcination28 and carbonation.29 In regard to modeling of the reaction into a particle level for the oxidation and reduction of oxygen carriers is given by CLC process, one can note the work by Garcia et al.,8 in which they evaluated the temperature profiles in a particle of oxygen carrier, and the Noorman et al. work,9 where the redox reactions of a copper-based oxygen carrier using shirking core model were modeled.30 However, these models consider homogeneous the carrier particle and do not take into account the initial characteristics of the material as is its grain size distribution. In this work, it was developed a mathematical model that can describe the oxidation and reduction reactions occurring in the CLC process using a method for determining the grain size distribution within the oxygen carrier particle. Thus, the changing grain size model proposed by Szekelly (see Scheme 2) is used, but given an initial grain size distribution. The classic model considers that the particle consists of a number of nonporous grains with a characteristic length r0 uniform among which pores are formed. As the chemical

Reduction H2 + CuO → H2O + Cu

Oxidation

1 O2 + Cu → CuO 2 • Spatially isothermal particle. • Pseudosteady state is considered. • No sintering occurs. Mass Balance. The gas−solid reaction can be represented according to the following equation: A (g ) + b B(s) → cC(s) + d D(g ) 5439

(9)


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Knowing the conversion, you can find the average particle conversion

The complete model for the oxidation reaction arises (1/2)O2 + Cu → CuO, however, in reducing the equations are similar. The mass balance at pseudo-steady-state for oxygen can be expressed in the following manner, knowing that the phenomenon under study only takes into account the diffusive term, because the flow velocity within the pores of the particle is very low and also is considered a source term for the chemical reaction that occurs in the solid: ∂CO2 ⎞ 1 ∂ ⎛ ⎜De ,O2R2 ⎟ − ( −rȮ 2) 2 ∂R ⎠ R ∂R ⎝

0=

R

X̅ = 3

∂R

(10)

ρcp

(12)

Chemical Reaction. An equation is necessary to determine the speed of the chemical reaction, which must take into account the resistance to mass transfer in the product layer formed around the grains27

when t = 0

(21)

Scheme 3. Scheme of Oxygen Carrier Particle Formed by Grains

⎛ r ,i2 ⎞ ⎜ ⎟v ⎝ r0,i3 ⎠ i

− rCu ̇ = − 2rȮ 2 = 3k(1 − ∈ )CO2 n ∑ 1+

i

(20)

Pore to Sphere Factor. According to the distribution model of grain raised by Heesink et al.,32 a porous particle is composed of a collection of spherical grains of various sizes, and the pores are in the interstices of these grains as shown in Scheme 3.

The second boundary condition expresses the external mass transfer, that is, the molar flux on the outer surface of the oxygen carrier particle. This condition is shown below in t ≥ 0

∂T = −( −rCu ̇ )ΔHr ,Cu ∂t

T (R , t ) = Tb

(11)

CO2(RP , t ) = CO2,b

(19)

To solve eq 20, an initial condition is necessary to indicate that in the initial state, oxygen temperature inside the particle is equal to the temperature in the bulk and is given by8

when T ≥ 0

=0 R=0

RP 3

Energy Balance. In the energy balance, the transition state is not considered the convective term because it can be assumed that the flow velocity is low in the inside of the pores of the particle, and it also takes into account the diffusive term because for being such a small particle, it can be said that the temperature does not vary radially. It allows for a source term due to the heat produced by the reaction

For the solution of this differential equation, it is necessary to consider two boundary conditions.8 There are typical boundary conditions for this type of problems that have been worked extensively in catalytic31 processes. The first condition indicates that there is symmetry about the center of the particle and is expressed as ∂CO2

∫0 P R2X dR

(1 − )

k r Ds , i

r ,i

r1, i

(13)

where Ds is diffusivity in the product layer which is formed around the grain. However, for very small grain sizes (4.01238 × 10−8 m), Ds → ∞, therefore, the equation is as follows: −rCu ̇ = −2rȮ 2 = 3k(1 − ϵ)CO2

n

⎛r 2⎞ ⎜ ∑ ⎜ ,i 3 ⎟⎟vi r i ⎝ 0, i ⎠

(14)

The unreacted core size variation grain can be calculated with eq 15 dr , i dt

=−

According Frevel and Kressley,33 who studied mercury porosity diagrams of microspheres packages and concluded that the pore size depends only on the size of microspheres. Thus, there is a proportional relationship between the size of the pores and grains that is known as the “pore to sphere” factor F, which can be expressed by eq 22 rpi F= r0i (22)

bkCO2 n ρm ,Cu

(15)

whose initial condition is r,i = r0,i. Grain radius is given by r1, i = [Zr0, i 3 + (1 − Z)r , i 3]1/3

(16)

where Z=

ρm ,Cu /b ρm ,CuO /c

In this paper, the method of Frevel and Kressley33 was used to determine the grain size distribution from the porosity diagrams of oxygen carriers that were studied. The weight fraction occupied by grains of size i can be calculated with eq 23

(17)

Finally, we can obtain an equation for the conversion in the interior of the particle X (R , t ) = 1 −

⎡ r , i(R , t ) ⎤3 ⎥ vi ∑ ⎢⎢ r0, i ⎥⎦ i ⎣

vw , i =

(18) 5440

Vp , i ∑i Vp , i

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Figure 11. Grain size distribution of oxygen carriers.

Figure 12. Grain size distribution of active phase in the sample H9 and I20.

Simulation of Reduction (H9). To validate the data provided by the model developed in this work, a comparison with experimental data obtained in the thermobalance was performed. In addition, we also compared our data with the data provided by the classical model using a average initial grain size. In Figure 13, H9 average conversion is plotted over time for the reduction reaction with hydrogen under conditions of kinetic control to the experimental data, the new model, and the classical model of Szekelly explained above. The concentration of H2 is 20% to 800 °C and with a gas flow of 200 cm3 STP/min. One can observe that the experimental graph tends to be linear with a very slight curvature, which fails to describe the classical model; however, the model proposed here achieves considerably closer to the actual behavior of the phenomenon because the reaction considered each type of grain. In Figure 14, the temperature profile predicted by the classical model and the new model is presented. Both models show similar trends, but there is no experimental data to compare these results. 8 ́ the temperature must reach a According to Garcia-Labiano, maximum and then go down to the temperature of the bulk phase; however, because the model of this study does not take into account the diffusive and convective terms in equation 20, energy can not observe this behavior, and the maximum temperature is reached when the conversion is too.

The specific surface area can be calculated with eq 24 v 3 S= ∑ w,i ρCu i r0i (24) Thus, knowing the specific surface area of the sample, it is possible to derive the pore to sphere that is shown in eq 25 v 3 F= ∑ w,i SρCu i rpi (25) Grain Size Distributions. To determine the grain size distributions of oxygen carriers studied, eqs 23−25 were used. The grain size distributions of alumina and oxygen carriers can be seen in Figure 11. However, in the calculation of the grain size distribution of the oxygen carrier, no difference between the alumina grains and the grains of the active phase is made. Therefore, it can be assumed that the grains of the support do not change the distribution with the impregnation, as in so small grains attrition is unlikely. Then, the distributions of the oxygen carrier are subtracted with the grain distribution of the alumina to obtain the grain distribution of active phase. In Figure 12, the grain size distribution of active phase of H9 and I20 are observed. 5441


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Figure 15. Conversion vs time for the reduction (H9).

Figure 13. Conversion vs time for the reduction in kinetic control (H9).

Figure 14. Temperature profile of the reduction (H9). Figure 16. Conversion vs time for the oxidation in kinetic control (I20).

To check the operation of the new model in different conditions of kinetic control, experimental tests in which the diffusion resistance is not negligible were performed. These measurements were performed at a temperature of 800 °C, 20% H2, and a flow of 50 cm3 STP/min and are shown in Figure 15. It may be noted that as in the conditions of kinetic control, the proposed model shows good fit to the experimental results better than the classical model, which demonstrates once again the importance of an initial distribution of grain. Many gas−solid reactions show concave curves of conversion vs time,34 so the classics grain model has been widely used, but for the reactions of oxygen carriers based on copper, results do not fit the experimental data, which is better to use other models as proposed in this work. Simulation of the Oxidation (I20). Similar to what happened with the oxygen carrier H9, the results of the new model is better adjusted to this type of quasilinear kinetic. Figure 16 shows the graph of the average conversion time for the oxidation reaction of I20 under conditions of kinetic control. O2 concentration is 21% at 800 °C and with a gas flow of 200 cm3 STP/min. The temperature profile vs time (see Figure 17) needs to be validated again, although it is remarkable to note that both

Figure 17. Temperature profile of the oxidation (I20). 5442


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prepared by incipient impregnation require less precursor solution to achieve a given composition, but a notable drop in the surface area occurs. Oxygen carriers were characterized by scanning electron microscopy (SEM), energy-dispersive spectroscopy X-ray (EDX), surface area (BET) porosimetry, and X-ray diffraction (XRD). The carriers synthesized by incipient impregnation from a certain concentration (1.41 M) are at an almost complete blockage of pores of the surface. Additionally, all showed the formation of copper aluminate in the calcination process. Finally, H9 and I20 carriers for validation of the model were chosen.

models reach the same maximum temperature of particles, which is probably due to the were not taken into account the diffusive and convective terms in the energy equation, which is a considerable simplification. Finally, Figure 18 shows the graph of average conversion vs time for conditions in which the system is not in kinetic

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AUTHOR INFORMATION

Corresponding Author

*[email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors wish to thank the “Departamento Administrativo de Ciencia Tecnologiá e Innovación”COLCIENCIAS (Administrative Department of Science, Technology and Innovation from Colombia) through the project “Research on advanced combustion innovation in Industrial use”, code no. 1115-543-31906 contract no. 0852-2012 and the Universidad Nacional de Colombia.

Figure 18. Conversion vs time for the oxidation (I20).

■

control. O2 concentration is 21% at 800 °C and with a gas flow of 50 cm3 STP/min. It is important to mention that the experimental data is not so well accommodated in the oxidation as in reduction with the new model, although the trend remained.

ABBREVIATIONS

Symbols with Latin Letters Symbol Term Unit SI

b = Stoichiometric coefficient of the reactant c = Stoichiometric coefficient of the product cp = Average specific heat at constant pressure of the particle, J kg−1 K−1 C = Concentration, mol m−3 De = Effective diffusion coefficient, m2 s−1 Dg = Diffusion coefficient of the gas, m2 s−1 DK = Knudsen diffusion coefficient, m2 s−1 Dm = Molecular diffusioncoefficient, m2 s−1 Ds = Diffusion coefficient in the product layer, m2 s−1 Ea = Activation energy, J mol−1 F = Pore to sphere factor k = Reaction rate constant, mol1−n m3n−2 s−1 k0 = Pre-exponential factor, mol1−n m3n−2 s−1 m = Mass of the carrier, kg m0 = Mass of the oxidized carrier, kg mr = Mass of the reduced carrier, kg M = Molecular weight, kg mol−1 n = Reaction order N = Number of Avogadro, particles mol−1 ṙ = Reaction rate, mol m−3 s−1 r0 = Initial grain radius, m r0 = Initial average grain radius, m r1 = Grain radius, m r = Unreacted core radius, m rg = Average grain radius, m rp = Pore radius, m R = Radial coordinate in the particle, m R̅ = Universal ideal gas constant, J mol−1 K−1 RP = Particle radius, m S = Specific surface area per unit mass, m2 kg−1 SR̅ = Specific surface area per unit volume, m−1

5. CONCLUSIONS A mathematical model, which was derived from the changing grain size model, based on the definition of a “pore to sphere” factor and the prediction of an initial grain size distribution was developed. The use of this distribution is the main contribution of this work, as in the classic changing grain size model is assumed that the grains are uniform at the start of the reaction, which is a significant simplification. The model describes the reaction rate based on an initial distribution of grain. Results that predict conversion over time consistent with the experimental data, both the oxidation reaction and the reduction is obtained. The results were considerably better than those obtained with the classical model. The model was tested for the case of kinetic control and for the case in which the system was not in this regime, showing highly approximate results in the two situations, and better adjusted than the classical model, which is the contribution of this paper. This model can be used to modeling the chemical looping combustion process at real. Six copper-based oxygen carriers by incipient impregnation and wet impregnation were synthesized. Wet impregnation involves immersing the support in a precursor solution, and then filtering, drying, and calcining. It was found that the transporters prepared by wet impregnation retain almost all of the initial surface area, although a greater amount of precursor solution is needed. Synthesis by incipient impregnation consists of filling the total pore volume of the support with an exact amount of the precursor solution and then drying and calcining. The carriers 5443


Energy & Fuels

Article

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t = Time, s T = Temperature, K vi = Volume fraction of grains, i vw,i = Weight fraction of grains, i Vp = Specific pore volume, m3 kg−1 %w = Weight percent X = Conversion X̅ = Average conversion Z = Ratio of molar density between reactant and product

Symbols with Greek Letters

ΔHr = Heat of reaction, J mol−1 ∈ = Porosity ρ = True density, kg/m3 ρ̅ = Average particle density, kg/m3 ρm = Molar density, mol m−3 τ = Time of complete conversion, s Subscript

b = Bulk phase Cu = Relating to copper CuO = Relating to copper oxide He = Relating to helium ox = Oxidation O2 = Relating to oxygen R = Relating to reactive phase

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REFERENCES

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Modeling of Oxidation and Reduction of a Copper-Based Oxygen

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