Simulation on Operating Conditions of Chemical Looping Combustion

Jan 4, 2012 - Combustion of Methane in a Continuous Bubbling Fluidized-Bed. Process. Djamila .... The model applied to a lab-scale core-annulus bubbl-...
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Simulation on Operating Conditions of Chemical Looping Combustion of Methane in a Continuous Bubbling Fluidized-Bed Process Djamila Brahimi,† Jeong-Hoo Choi,*,† Pil Sang Youn,† Young-Wook Jeon,∥ Sang Done Kim,‡ and Ho-Jung Ryu§ †

Department of Chemical Engineering, Konkuk University, Seoul 143-701, Korea SK Innovation, Daejeon 305-712, Korea ‡ Department of Chemical & Biomolecular Engineering and Energy & Environment Research Center, KAIST, Daejeon 305-701, Korea § Korea Institute of Energy Research, Daejeon 305-343, Korea

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ABSTRACT: In order to simulate the performance of chemical looping combustion (CLC) of pure methane in a continuous bubbling fluidized bed process using a NiO-based oxygen carrier under various operating conditions, this study has developed a mathematical model based on the reaction kinetics and population balance of oxygen carrier (OC) particles in each reactor. Proper operating conditions have been discussed for complete combustion of methane. The minimum OC circulation rate for complete combustion was determined with the variation of temperature and fuel bed mass. The methane combustion efficiency was strongly affected by the distribution of OC between the air reactor (AR) and fuel reactor (FR) at a constant temperature, circulation rate of OC, and total bed mass. The range of OC distribution possible to achieve complete combustion became wider with increasing either the temperature or the circulation rate of OC at a constant total bed mass. In tested conditions of a labscale process, the range on the OC mass ratio of the fuel reactor to the total bed mass extended from 0.527−0.607 to 0.430− 0.705 with an increasing temperature of AR and FR from 850 to 900 °C (circulation rate of OC = 3 g/s, total bed mass = 22.89 kg). It also extended from 0.527−0.607 to 0.491−0.643 with increasing the circulation rate of OC from 3 g/s to 10 g/s (temperature of AR and FR = 850 °C, total bed mass = 22.89 kg). In this range, the amount of elutriated OC particles decreased a little as the FR mass increased because of the higher rates of particle elutriation and attrition in AR than in FR.

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INTRODUCTION The capability to capture a pure carbon dioxide with high potential and without any extra energy makes the chemical looping combustion (CLC) one of the leading technologies for CO2 capture compared to other capture techniques; the compressed carbon dioxide can be injected into oil and natural gas reservoirs for the purpose of simultaneously enhancing oil recovery and reducing the CO2 emissions since it is considered as the main greenhouse gas causing global warming. The chemical looping combustion is an unmixed combustion concept.1−4 It consists of two interconnected fluidized bed reactors, an air reactor (AR) and a fuel reactor (FR), using circulating metal oxide particles to transfer oxygen from AR to FR. Metal oxide oxidizes in AR with air and it is reduced in FR by methane, thus eliminating NOx formation1,5−7 and producing almost pure carbon dioxide. Increasing attention has been paid to the CLC as clean energy technology for CO2 capture,8,9 due to its advantages.10 For this purpose, the investigation of the effects of operational conditions on the performance of the CLC system is required. Unfortunately the study of these effects experimentally is extremely difficult requiring a number of time-consuming experiments. The performance of the CLC system can be easily evaluated, if the CLC system is modeled properly. Different models have been developed,11−19 and effects of some operating conditions have been analyzed to improve the performance of the CLC system. A few computational fluid dynamic models have been developed considering only the FR.11−14 Deng et al.11 studied © 2012 American Chemical Society

the influence of particle diameter, gas flow rate, and bed temperature on the performance of the (CaSO4 + H2) fuel reactor for a single size of oxygen carrier (OC) particles. Wang et al.12 analyzed the effects of the initial bed height, bed temperature, and operating pressure using a Cu-based oxygen carrier of uniform size and coal gas as the fuel, the decomposition of CuO particles was ignored. Mahalatkar et al.13 studied the influence of superficial gas velocity, metal oxide concentration, and reactor temperature on the CLC system performance using methane as the fuel and nickel or iron particles of uniform size as the oxygen carrier. Jung et al.14 developed a multiphase CFD-based model on the fuel reactor with single size NiO particles as the oxygen carrier and methane as the fuel. KruggelEmden et al.15 developed a multiphase CFD model to describe the transient behavior of a coupled CLC system comprised of both air and fuel reactors in the start-up period for 60 s, using CH4 as the fuel and single size Mn3O4 particles as the oxygen carrier. Abad et al.16,17 developed a mathematical model to simulate the performance of a steady state FR, and the influence of the circulation rate of oxygen carrier (OC) solids, fuel gas load, reactor temperature, and OC particle size were analyzed using single size CuO-based particles as the oxygen carrier and methane as the fuel. Received: October 9, 2011 Revised: January 4, 2012 Published: January 4, 2012 1441

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Kolbitsch et al.18 developed a model to simulate the performance of both FR and AR in a dual circulating fluidized bed, using a uniform size of Ni-based OC particles with natural gas, and effects of reactor temperature, solids circulation rate, air/fuel ratio, and fuel power were determined. Peltola et al.19 developed a model considering both reactors (FR/AR) for steady state conditions, used CH4 as the fuel and NiO as the oxygen carrier, and influences of reactor temperature and static bed height of AR were analyzed. It is unclear what size of OC particles they used in their study. However, few studies have discussed the effect of AR on the FR at different operating conditions for complete combustion of pure methane and therefore preventing CH4 emissions from FR. In addition, no previous studies considered the required carrier makeup to compensate for the attrition loss of OC particles. The objective of this study is to discuss the proper operating conditions in both AR and FR for complete combustion of methane with consideration of the particle attrition and required makeup of fresh OC particles. This mathematical model has been developed, based on the reaction kinetics and population balance of oxygen carrier (OC) particles in each reactor, using NiO-based oxygen carrier particles of a wide size distribution and pure methane as fuel. The model applied to a lab-scale core-annulus bubbling fluidized-beds process under various operating conditions such as temperature, bed weight, solids circulation rate, and methane concentration to predict the CLC system performance.

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Figure 1. Schematic diagram of a bubbling fluidized-bed CLC system.

⎡ F + K *(x)(1 − ψ (x)R ) 1 1 f12 1 αi1(x) = δ1i⎢ ⎢⎣ W1R1(x)

αi2(x) = − δ1i

In this work, the CLC system consists of two interconnected bubbling fluidized beds, an air reactor (AR), and a fuel reactor (FR) using pure methane as the fuel. CH4 gas is introduced to the FR and fluidizes the bed of oxygen carrier (OC) particles; methane burns according to the following endothermic reaction:

+

(1)

The product gas including elutriated particles is sent to the cyclone separator; a certain fraction of particles collected in the cyclone are returned to the fuel reactor; reacted particles are withdrawn from the bottom of the fuel reactor and fed to the air reactor; air is introduced to the AR and fluidizes the bed of OC particles; reduced metal oxide particles (Ni) are oxidized according to the following exothermic reaction:

Ni(s) + 1/2O2 (g) → NiO(s)

αi3(x) = −

dx

constraint:

(2)

(4b)

δ1iF0p0 (x) + R aipai (x) WR i i(x)

(4c)

∫0

x = x max

(4d)

p bi (x) dx = 1

(4e)

for

x max

xmax is the maximum particle diameter. The fresh feed rate of OC particles F0 and the circulation rate of OC particles F10 are controlled to maintain fixed values of F1, W1, and W2 for the given fluidizing condition. Therefore, F0 and F10 are determined to satisfy constraint eq 4e in solving the particle population balances. We used the correlations of Choi et al.22 to calculate the particle elutriation rate, correlations which have been confirmed as providing reasonable accuracy in expressing the effects of temperature and pressure. We used the simple model of Merrick and Highley23 to express the total formation rate of fine particles and size reduction rate of single particle by attrition in the fluidized bed as

R ai = Ka(ui − u mfi)Wi

(5a)

R i(x) = dx /dt = − Ka(ui − u mfi)x /3

(5b)

Ka is the particle attrition rate constant. We assumed that fine particles formed by abrasion were below 5 μm in diameter24 and had a uniform size distribution. In addition, because the rate of size reduction as well as the retention time in the reactor is relatively very small, we assumed that there would be negligible particle attrition on particles below 5 μm in diameter. Minimum fluidizing velocity (umfi) was calculated

+ αik(x)p bk (x) − αi3(x) = 0

(i = 1, 2; k = 1, 2)

1 dR2(x) 3⎤ − ⎥ R2(x) dx x ⎥⎦

B.C.:p bi (x) = 0

Oxidized carrier particles are withdrawn from the bottom of the air reactor and are fed to the fuel reactor. To make up for any loss of OC particles from the process caused by attrition, the fresh OC particles are fed to the FR. In Figure 1, Fj is the solid flow rate of stream j, x is the spherical particle diameter, pj(x) is the probability density function of particles in stream j, pbi(x) probability density function of particles in bed i, Wi weight of bed i, Ri(x) particle attrition rate in bed i, Rai overall formation rate of fine particles by attrition in bed i, Ki*(x) particle elutriation rate from bed i, and ψi(x) fractional particle collection efficiency of cyclone i. The fractional collection efficiency of the cyclone was assumed as that of Lapple.20 We assumed a well-mixed state of bed particles in both reactors (p1(x) = pb1(x), p10(x) = pb2(x)) and a constant apparent particle density. The steady state particle population balance in the fuel (i = 1) and air (i = 2) reactor, considering the elutriation rate and attrition rate, is expressed as follows:21

dp bi (x)

(4a)

F10 W1R1(x) ⎡ F + K *(x)(1 − R ψ (x)) 10 2 f2 2 + δ2i⎢ ⎢⎣ W2R2(x)

MODEL

CH 4(g) + 4NiO(s) → CO2 (g) + 2H2O(g) + 4Ni(s)

F1 1 dR1(x) 3⎤ − ⎥ − δ2i ⎥ R1(x) dx x⎦ W2R2(x)

+

(3) 1442

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from the correlation of Wen and Yu25 as an approximation, based on the bed particle size distribution. We judged the correlation acceptable within the accuracy of the present model. On the basis of experimental results from a thermo-gravimetric analyzer26 and a set of data from a steady state CLC system,27 kinetic equations of reduction reaction (i = 1) and oxidation reaction (i = 2) in reactors could be expressed in a form which incorporates Arrhenius’ law as follows:

6η bikoi e−Ei / RTi(Ci′)ni dX i (1 − Xi)2/3 = i dt γix

Ci′ =

■

oxidation

■

ΔmNiO,1 = 4ΔmCH 4

(10a)

ΔmNiO,2 = 2ΔmO2

(10b)

SIMULATION CONDITIONS

The model applied to predict the CLC system performance under various operating conditions such as temperature, bed weight, and solids circulation rate. The numerical results were validated using experimental measurements obtained from the Korea Advanced Institute of Science and Technology (KAIST)27 in two interconnected bubbling fluidized beds, a high velocity for the AR and a low velocity for the FR. The operating conditions used for the simulation of the CLC process are listed in Table 2. The reducing gas was 100% CH4, and the air was used as an oxidant gas. A NiO oxygen carrier was prepared with 70 wt % NiO and 30 wt % supporter on a dry solid basis, the particle size distribution of a fresh OC is shown in Table 3, the apparent density was 2788 kg/m3, and 20% excess oxygen was supplied to ensure complete oxidation of metal oxide in AR. In order to give safe residence time of particles in the bed, the inlet and the outlet of particles were placed in opposite sides of each reactor without

The fraction of active Ni for oxygen carrier particles is influenced by the CH4 concentration and temperature in the fuel reactor.28 The fraction of active Ni was defined as the fractional conversion of NiO to Ni at which carbon deposition started during fuel combustion. It is represented by the following correlation.

φ = 0.02629 e0.002463T1(C1′)−0.08465

CALCULATION PROCEDURE

Continue with best guesses for the outlet concentration of CH4 in the fuel reactor and O2 in the air reactor to narrow the differences until relations 10a and 10b are satisfied within tolerance. The fluidizing gas velocity is considered as an arithmetic mean value between the bottom and top of the bed in iteration.

Table 1. Kinetic Parameters of Oxidation−Reduction of Oxygen Carrier 2.312 × 104 0.768 2.625 × 10−2 2 2.586 × 10−3

(9)

Mass flow rates and size distributions of all particle streams can be determined from combining population balances of eqs 3, 4(a−e) by a numerical method, whereby an initial educated guess for the outlet concentration of CH4 in the fuel reactor and O2 in the air reactor is used to determine the consumption rate of each gas (ΔmCH4, ΔmO2) and the average concentration term of each gas as (Ci′)ni in the reactor, in turn. The NiO concentration of particles in each reactor is calculated as follows: (1) Make a best guess for the NiO concentration of particles withdrawn from the air reactor. The particles are fed to the fuel reactor. (2) Evaluate the NiO concentration of the particles when the particles are withdrawn from the fuel reactor after a stay for mean residence time as a reaction time. The particles are returned to the air reactor. (3) Evaluate the NiO concentration of the particles withdrawn from the air reactor after a stay for the mean residence time as a reaction time. (4) See if the difference between the calculated NiO concentration of the particle from the air reactor and the one initially guessed in step 1 is within tolerance. If not, go back to step 1 and make another educated guess from the results. Use the same calculation for all particle sizes. As a result, we can obtain the total mole flow rate of oxygen (O2) removed by CH4 from the solid phase in the fuel reactor (ΔmNiO,1) and the total mole flow rate of oxygen (O2) adsorbed from the gas phase to particles in the air reactor (ΔmNiO,2). The following relations between consumed moles of gaseous reactants (CH4, O2) and reacted moles of NiO (formed and then disappeared) must be satisfied in each reactor

runs the calculation steps of the Calculation Procedure until eqs 10a and 10b with known F10 and combustion efficiency and best guesses for the correction factors. The combustion efficiency gives the outlet concentration of CH4 in the fuel reactor and O2 in the air reactor. Educated guesses for the correction factors continue until eqs 10a and 10b are satisfied within tolerance. The kinetic parameters of oxidation−reduction of the metal oxide are listed in Table 1.

reduction

Ci0′ + Ci f ′ 2

The flow pattern of the bed seemed to change a little with the variation of the operating conditions in the same bubbling fluidization (expected bed voidage21 ≤ 0.60). Therefore, we think that the present reaction rates can be utilized reasonably to model systems of different dimensions and/or some different operating conditions in the same bubbling regime. However, correction in reaction rates should be considered in different fluidization regimes.

Figure 2. Effect of solids circulation rate on performance of CLC at different methane concentrations.

1.859 × 104 0.667 8.224 × 10−3 4 3.866 × 10−4

(8)

The average concentration of the gas reactant in each reactor was simply considered as an arithmetic mean value between the inlet and outlet concentrations.

(6)

parameters

Sij ωij(x)

outflow(j)

The γi is moles of solid reactant per volume of particle in reactor i, the correction factors η1 and η2 were factors compensating the difference in the reaction environment between the TGA26 and the CLC system.27 They were determined by fitting the present model to one of actual process data (F10 = 10.01 g/s) in Figure 2. The fitting procedure

Ei (J/g mol) ni(−) i i koi m3n−2 (kg moln−1 s) bi (−) ηi (−)

∑

τi(x) = Wi ω bi(x)/

(7)

The particle reaction time in each reactor was assumed to be the mean particle residence time written as21 1443

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Table 2. Operating Conditions for the Process Simulation fuel reactor (core bed) air reactor (annulus bed) height (m) diameter (m) feed gas velocity (m/s) pressure (kPa) static bed height (m)

2.1 0.08 0.0372 101.3 0.95

1.6 0.15 0.1867 101.3 0.3

Table 3. Size Distribution of Fresh Oxygen Carrier Particles sieve size (μm)

0−75

75−105

105−125

125−150

150−180

weight fraction (−)

0.075

0.326

0.329

0.213

0.057

any trouble in particle flow, cyclone cut diameter, 0.03 mm; Ka, 4.5 × 10−6 1/m; particles collected by cyclones were not recycled, Rf12 = Rf2 = 0. The attrition coefficient of particles Ka was approximated on the basis of the elutriation loss of particles measured by Jeon.27

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RESULTS AND DISCUSSION Figure 2 shows the effect of solids circulation rate on methane combustion efficiency at different methane concentrations, and lines represent the values predicted by the model while the values measured in the study of KAIST27 are represented by the symbols; the amount of OC in FR and AR were 6.31 and 9.58 kg, respectively, the mean particle diameter is 104.3 μm, the temperature in the two reactors were the same. As expected, the methane combustion efficiency initially increases but levels off with the increase of the solids circulation rate; the initial increase can be explained by the higher amount of oxygen supplied by the circulation solids from AR. However, the mean particle residence time decreases as the solid circulation rate increases. Therefore, the combustion efficiency levels off above a certain solid circulation rate. This is consistent with previous findings.16−18 A significant decrease in methane combustion efficiency was noted when the methane concentration increased, and the combustion of high methane concentration was incomplete under any solids circulation rate due to insufficient bed mass in the fuel reactor. The decrease of combustion efficiency also seemed to be accelerated by a decrease of active Ni of OC as CH4 concentration increased according to eq 7. To fully convert this high methane concentration, the retention time of the methane particles in FR should be increased by increasing the fuel reactor mass. The combustion efficiencies predicted by this model were in good agreement with the experimental measurements for the fuel of 33.3% CH4. Figure 3a illustrates the effect of fuel reactor mass on the performance of CLC of pure methane; at a temperature of 850 °C, there is a considerable increase of the methane combustion efficiency when the FR mass exceeds a value of 9.81 kg, which can be explained by increasing the retention time of OC particles in FR with increasing FR weight according to eq 8. This is consistent with a prior finding.12 To ensure complete conversion of methane and to prevent the CH4 emissions from the FR, the FR weight should be greater or equal than 13.31 kg at this temperature. The minimum solids circulation rate required for complete conversion of methane (F10,min) is shown in Figure 3b and decreases exponentially with increasing FR weight. This indicates the increase of the OC amount and retention time of OC particles in FR. Since the carrier makeup cost is the only significant operation cost of

Figure 3. Effect of fuel reactor mass on the performance of CLC of pure methane. (a) CH4 combustion efficiency (%), (b) minimum F10 (g/s), and (c) solid flow rate of fresh feed (g/s).

this CO2 separation process,13 the required carrier makeup to compensate for the losses of OC weight caused by attrition and entrainment was investigated; Figure 3c shows the dependence of the solid flow rate of fresh feed required to compensate for the total attrition and elutriation loss on FR weight. An increase in FR weight caused an increase in the solid flow rate of fresh feed because of the increase in elutriation rate with increasing the FR weight according to eq 5a and correlation of Choi et al.22 1444

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tivity of OC at high temperature according to eqs 6 and 7; on the other hand, the increase of temperature is accompanied by an increase of elutriation rate as illustrated in Figure 4c. The fresh feed rate of OC particles required to replace the elutriated amount of OC particles slightly increases with increasing temperature according to the correlation of Choi et al.22 at the minimum OC particles circulation rates. The simulation results showed that the combustion efficiency of methane was strongly affected by the distribution of OC solids between AR and FR, and Figure 5a,b shows the relationship between methane combustion efficiency, mass fraction of OC in the FR, and solids circulation rates at a fixed total mass of OC particles in the FR and AR at 850 °C. In Figure 5a, the methane combustion efficiency increases as the mass of FR increases, and this is related to the increase of particle retention times in FR and therefore increases the reduction rate of the OC particles. After that, the increase in FR mass reflected negatively on the oxidation reaction of OC in AR causing a decrease of the OC particle retention time in AR, a decrease in methane combustion efficiency, and an increase of the minimum solids circulation rate (F10,min) as shown in Figure 5b. This effect is related to the retention time necessary for enough reduction and oxidation reactions of OC in FR and AR, respectively. A possible range of solids distribution was determined where the complete combustion of methane could be achieved at constant temperature and total mass of OC particles. Any combustion outside this interval is incomplete; these are consistent with prior results of Kolbitsch et al.18 Figure 5c shows the parabolic relationship between the minimum solids circulation rates required for a complete methane combustion (F10,min) and mass fraction of OC in FR at different temperatures. The left-handside of the parabolic curve shows a decrease in the minimum solids circulation rate (F10,min) and an increase of efficiency with an increasing of FR mass, as shown in Figure 5a for 850 °C. The right-hand-side of the curve shows the increase of the minimum solids circulation rate (F10,min) with increasing FR mass due to a decrease in particle retention time in AR. In addition, it is observed that the axis of symmetry is at xOC,FR > 0.5, which means that the bed mass needed for complete methane combustion in FR must be greater than that in AR, because the rate of the OC oxidation is relatively faster than that of the reduction, and it agrees with the result of Kolbitsch et al.18 in the case of complete combustion. Moreover, it is very important to note that the possible range can be extended by increasing temperature as shown in Figure 5c. Figure 5d indicates that the required fresh particles feed rate decreases a little as FR mass increases because of the gas velocity in the AR is higher than that in the FR as in the most common design of a CLC plant.16−19 However, it increases as temperature increases because the elutriation rate increases with temperature.22 Figure 6 represents the methane combustion efficiency as a function of the mass fraction of OC in the FR at different solids circulation rates and different temperatures, and the increase in the solids circulation rates produces an increase in the combustion efficiency of methane. The methane is never completely burned at a low solids circulation rates, and the range of OC solids fraction in FR where the complete combustion of methane takes place extends very slowly when the solid circulation rate exceeds the minimum solid circulation rate for complete combustion of methane (F10,min). However, a noticeable extension occurs with an increase of temperature as discussed in Figure 5c.

Figure 4. Effect of temperature on performance of the CLC process. (a) CH4 combustion efficiency (%), (b) minimum F10 (g/s), and (c) solid flow rate of fresh feed (g/s).

The effect of temperature and solids circulation rate on the methane combustion efficiency are illustrated in Figure 4a, and an increase in temperature or solids circulation rate produces an increase in the methane combustion efficiency because of the increase of the reaction rate due to the higher reactivity and fraction of active Ni of OC with the temperature, but at a low temperature of 800 °C the methane combustion was incomplete. These are consistent with prior results.11−13,16−19 The minimum OC particles circulation rates required for complete conversion of methane (F10,min) were determined at different temperatures. It decreases exponentially with increasing temperature as shown in Figure 4b because of the high reac1445

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Figure 5. Influence of distribution of OC solids between FR and AR. (a,b) CH4 combustion efficiency (%), (c) minimum F10 (g/s), and (d) solid flow rate of fresh feed (g/s).

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CONCLUSIONS The influence of the main operating parameters on the CLC performance of pure methane in a continuous bubbling bed process was mathematically simulated, based on the reaction kinetics and population balance of OC in each reactor (AR/ FR) and taking into consideration the complete combustion of fuel and the required carrier makeup to compensate for the OC loss. The simulation results showed that the bed temperature and fuel bed mass could enhance the performance of the CLC process by increasing the OC reactivity and retention time of the gas phase in FR, respectively. High FR mass was required to fully burn the high concentration methane. The methane combustion efficiency was strongly affected by the distribution of OC between AR and FR at constant temperature, circulation rate of OC, and total bed mass. The possible range of OC distribution was determined

where the complete combustion could be achieved, and any combustion outside this range was incomplete. The range became wider with increasing either temperature or the circulation rate of OC. In tested process conditions, the range on the OC mass ratio of the fuel reactor to the total bed mass xOC,FR extended from 0.527−0.607 to 0.430−0.705 with increasing the temperature of AR and FR from 850 to 900 °C (circulation rate of OC = 3 g/s, total bed mass = 22.89 kg). It also extended a little from 0.527−0.607 to 0.491−0.643 with increasing the circulation rate of OC from 3 to 10 g/s (temperature of AR and FR = 850 °C, total bed mass = 22.89 kg). The amount of elutriated OC particles and thus the feed rate of fresh OC particles increased as little as AR mass increased because the gas velocity in AR was higher than that in FR. 1446

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Rf2 = recycle fraction of solid collected by air reactor’s cyclone to air reactor Ri(x) = particle attrition rate in bed i (m/s) Sij = mass flow rate of total particle in outflow stream j from bed i (kg/s) t = time (s) Ti = temperature of reactor i (K) ui = fluidizing velocity in reactor i (m/s) umfi = minimum fluidizing velocity in reactor i (m/s) Wi = weight of bed i (kg) x = spherical particle diameter (m) Xi = conversion of solid reactant (NiO or Ni) for reaction i xmax = maximum particle diameter (m) xOC,FR = mass fraction of OC solids in fuel reactor per total bed mass (−) YCH4 = mole fraction of methane in fuel gas (−) Greek Letters

αik = functions defined as in eqs 4a and 4b (1/m) αi3 = function defined as in eq 4c (1/m2) γi = mole of solid reactant per volume of particle in reactor i (kg mol/m3) δij = Kronecker delta, one at i = j and zero at i ≠ j ηi = correction factor for reaction i ρB = mole Ni per mass of fresh particle (kg/m3) ρp = particle density (kg/m3) τi(x) = mean particle residence time in reactor i (s) φ = fraction of active Ni for oxygen carrier particle (−) ψi(x) = fractional particle collection efficiency of cyclone i (−) ϕbi(x) = mass fraction of particle in bed i (−) ϕij(x) = mass fraction of particle in outflow stream j from bed i (−)

Figure 6. Influence of distribution of OC solids between FR and AR at different temperature and solids circulation rate (YCH4 = 1).

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AUTHOR INFORMATION

Corresponding Author

*Phone: 82-2-450-3073. Fax: 82-2-458-3504. E-mail: [email protected].

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ACKNOWLEDGMENTS This work was supported by the Power Generation & Electricity Delivery of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) Grant funded by the Korea Government Ministry of Knowledge Economy (Grant 2009101010010A).

Subscripts

■

NOMENCLATURE bi = stoichiometric factor for reaction i Ci′ = average concentration of gaseous reactant in reactor i (kg mol/m3) Cio′ = feed gas concentration (kg mol/m3) Cif′ = gas concentration (kg mol/m3) Ei = activation energy of reaction i (J/kg mol) Fj = solid flow rate of stream j (kg/s) Ka = particle attrition rate constant (1/m) koi = frequency factor of reaction i (m3ni−2/(kg molni−1 s)) Ki*(x) = particle elutriation rate from bed i (kg/s) mNiO,i = formed (i = 2) or disappeared (i = 1) NiO in reactor i (kg mol/s) mi = consumption of gaseous reactant (CH4 or O2) in reaction i (kg mol/s) ni = order of reaction i pai(x) = probability density function of particles formed by attrition in bed i (1/m) pbi(x) = probability density function of particles in bed i (1/m) pj(x) = probability density function of particles in stream j (1/m) p0(x) = probability density function of fresh feed particles (1/m) R = gas constant, 8.314 (kPa m3/kg mol K) Rai = overall formation rate of fine particles by attrition in bed i (kg/s) Rf12 = recycle fraction of solid collected by fuel reactor’s cyclone to fuel reactor

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AR = air reactor FR = fuel reactor i = free index, 1 for fuel reactor or reduction of NiO or CH4; 2 for air reactor or oxidation of Ni or O2 j, k = dummy indices min = minimum value required for complete combustion of fuel OC = oxygen carrier particles total = total bed of air and fuel reactors

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dx.doi.org/10.1021/ef2015233 | Energy Fuels 2012, 26, 1441−1448