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Control-Based Modeling and Simulation of the Chemical-Looping Combustion Process S. Balaji,† Jovan Ilic,‡ B. Erik Ydstie,*,† and Bruce H. Krogh‡ Departments of Chemical Engineering and of Electrical and Computers Engineering, Carnegie Mellon UniVersity, Pittsburgh, PennsylVania 15213
In this study, we develop a model for the chemical-looping combustion system with a goal of determining the system behavior and the effect of important physical and operating parameters. We propose a model based on system invariants under thermodynamic equilibrium to obtain a computationally inexpensive model that can be utilized for advanced control studies. The system is represented by coupling the mole and energy balances of the system invariants along with the population balance of the particles and the shrinking-core mechanism. The model results are validated based on the experimental data from the literature. The simulated results show that the model is flexible enough to be used for different types of gaseous fuels and metal oxides. In the area of looping combustion, this work is the first in the proposal of a control-oriented model. 1. Introduction
2. Previous Work
Chemical-looping combustion (CLC) is envisioned as a clean coal technology for electrical power plants. Figure 1 illustrates the basic concept of CLC. The system consists of two fluidizedbed reactors connected through loop seals. One reactor acts as a fuel reactor, where the gaseous, liquid, or solid fuel is oxidized by metal oxide particles, producing mainly CO2 and H2O. The fuel reaction can be either endothermic or exothermic based on the types of metal oxide and fuel used. The reduced oxide particles are then transported to the air reactor, where oxygen or air is used to oxidize the solid particles. The reduced metal oxide particles generate heat as they are oxidized or replenished and are ready to be recycled to the fuel reactor. The main advantage of the CLC process is that direct contact between the air and fuel is averted. The formation of harmful NOx gases is thus prevented. The sum of the heat generated or consumed in the reduction stage and the heat generated in the oxidation stage is equal to the heat generated by the direct oxidation of the fuel gas.1 Thus, the heat content of the fuel or the thermal efficiency of the process is unaffected. Moreover, on the basis of thermodynamic equilibrium, it has already been proven that the process produces almost pure CO2 and H2O,2 leading to easy and inexpensive carbon sequestration. In CLCs, when compared with the experimental efforts, dynamic modeling is at the nascent level. A computationally inexpensive model capturing most of the key parameters for the system design and at the same time to be employed for control studies is still missing. In this paper, we propose a new model that can be used for both the design and control of such systems. We believe that our contribution through this work is a step toward the advancement of the computational work in this field. The following section reviews previous experimental and theoretical work on CLC systems. Our model is then presented in section 3, followed by a presentation of the simulation results for a variety of situations in section 4. The concluding section summarizes the contributions of this paper.
The concept of CLC was first proposed by Richter and Knoche.3 After that, for about a decade, there were no significant developments in this area of clean combustion. The exergy analysis of the chemical-looping system by Anheden and Svedberg,4 together with an increasing awareness of the harmful effects of CO2 on the environment, brought attention to the process. Since then, a considerable number of experimental studies have been performed to increase the understanding of the CLC process. Some of this work is reviewed below. The design and operation of a CLC system depends on the nature of the fuel and metal oxide particles used. The fuel can be either in gaseous (e.g., natural gas, syngas, etc.) or in solid form (e.g., coal, charcoal, petcoke, or biomass). Several different combinations of oxide particles along with the inert carriers have been proposed to achieve a required quality of the solid phase. Research groups at Chalmers University of Technology have tested a number of metal oxide particles in an experimental setup consisting of two interconnected fluidized beds.5 Noteworthy studies have been done by Abad et al.6 in determining the rate constants and physical properties of promising metal oxide particles and mapping the range of operating conditions for each oxide particle. An extensive overview of the metal oxide particles used in CLC and their characteristics can be found elsewhere.7,8 There are no large-scale chemical-looping systems in operation yet. However, numerous pilot plants have been built, and more are planned. A 120 kW pilot plant is in operation at Vienna University of Technology,9 and a 50 kW pilot plant is in
* To whom correspondence should be addressed. Tel.: +1-412-2682235. Fax: +1-412-268-7139. E-mail:
[email protected]. † Department of Chemical Engineering. ‡ Department of Electrical and Computers Engineering.
Figure 1. Concept of CLC.
10.1021/ie901540m 2010 American Chemical Society Published on Web 04/13/2010
Ind. Eng. Chem. Res., Vol. 49, No. 10, 2010 10
operation at Korea Institute of Energy Research. Chalmers University of Technology in Sweden11,12 and the Institute of Carboquimica in Spain13 operate a 10 kW CLC prototype. At the National Energy Technology Laboratory (Morgantown, WV) and at ALSTOM Power Inc. (Windsor, CT), efforts are underway to develop a large-scale CLC system with an emphasis on the reactor design, sensor location, and possible control methodologies. In this work, we study the CLC system using iron oxide particles. These carrier particles are inexpensive, naturally available, and environmentally safe. Experimental data and required model parameters are available in the literature. Mattisson et al.14 studied the feasibility of using iron oxide as an oxygen carrier in a fixed-bed reactor system. In this work, they assume that hematite (Fe2O3) is reduced to iron (Fe), which is possible only under drastic reducing conditions. With gaseous fuels like methane or syngas, hematite is converted into either magnetite (Fe3O4) or wustite (FeO). Hence, for the types of systems considered, modeling the rate of conversion of Fe2O3 to Fe3O4 and FeO and vice versa would suffice.15 Mattisson et al.16 investigated various iron oxide based oxygen carriers with different inert support and sintering temperatures. They concluded that Fe2O3 with MgAl2O4, ZrO2, and Al2O3 inert particles shows good reactivity. Johansson et al.17 carried out experiments in a fluidized-bed reactor with iron oxide particles on a MgAl2O4 support. The inert particles used to support the oxygen carrier have a significant impact on the overall performance. They concluded that 60% Fe2O3 and 40% MgAl2O4 sintered at 1100 °C is the suitable carrier with optimized particle properties. Son and Kim18 tested the reactivity of NiO and Fe2O3 particles in an annular-shaped circulating fluidized-bed reactor with double loops. They showed that NiO particles are more reactive than Fe2O3 particles. They also suggested that the optimum ratio of NiO to Fe2O3 is 3 based on the price and the attrition test. The effect of the pressure on the behavior of the metal oxide particles has been investigated by Garcia-Labiano et al.19 They showed that an increase in the total pressure has a negative effect on the reaction rates. Thus, in the model equations, it is important to use the appropriate reaction rate constants based on the specified operating pressure. Abad et al.2 examined the iron oxide particles with natural gas or syngas as the fuel. They showed that agglomeration, carbon deposition, and mass loss were not seen after 60 h of operation. They also confirmed that there were only minimal effects in the reactivity and crushing strength of the carrier particles, suitable for the purpose of continuous combustion. One critical step toward commercialization of the CLC process is the development of mathematical models for process evaluation, scale-up, and detailed design. The CLC system is a combination of two interconnected fluidized-bed reactors, making it operationally complex. In addition, the chemical reactions are complex because of the multiphase nature of the reactions. Thus, in order to understand and predict the behavior of such a system and to devise suitable control methodologies, mathematical modeling is essential. Lyngfelt et al.20 developed a steady-state model for conceptual design and feasibility studies. A scaled flow model for the gas-solid contact, heat-transfer, mass-transfer, and chemical reactions proposed by Kronberger et al.21 can be used to determine key operating parameters such as the pressure drop, solid circulation rate, and gas leakage. Garcia-Labiano et al.22 developed a particle reaction model to determine the temperature
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variations along the radial direction of the carrier particles during both reduction and oxidation stages. A detailed two-dimensional heterogeneous model has been developed by Mahalatkar et al.23 and Jung and Gamwo24 to capture the dynamics of fluid-particle and particle-particle interaction. The model equations are solved in ANSYS and are compared with the experimental results. Similarly, Xu et al.25 proposed a population balance model for the bed particle conversion in combination with the two-phase hydrodynamic models, leading to integrodifferential equations. Snider et al.26 propose computational particle fluid dynamic software to accurately model the particle fluid flows in higher dimensions. The models proposed are computationally expensive and are used to predict the overall conversion and fuel efficiency under different operating conditions with required accuracy. 3. Modeling Methodology There are different methodologies to obtain a computationally inexpensive model either from the first principles model or from experimental data, such as nonlinear model reduction techniques,27 system identification or data analysis,28 scaling analysis29 etc., or approximating the model based on experience or sensitivity analysis. In contrast to the above-mentioned techniques, we exploit the concept of invariants in the system,30 thereby completely changing the state variables of the system. This reduces the model order suitable for control studies with no further necessity of any model reduction. In addition, momentum balances are not solved explicitly, and the effect of the fluid velocity can be represented by simple mathematical relations based on experimental data. This results in a computationally inexpensive model. For a chemical process, elements or atoms (like carbon, hydrogen, etc.) are said to be invariants because they are neither created nor destroyed by chemical reactions. These elements, together with the total mass and energy, which are also invariant, are considered as state variables in this work. For instance, instead of representing the concentrations of CO, CO2, H2O, H2, CH4, and O2 as six different state variables, we can simply consider the total amounts of C, H, and O and use an appropriate mapping function to calculate the (equilibrium) concentrations of the various gases present in the system. Thermodynamic equilibrium calculations for gases, combined with gas-solid diffusion process dynamics and reaction kinetics as expressed through an extent of the reaction, can be used to calculate the species concentrations. In our study, the equilibrium concentrations for gaseous species at specified operating conditions are calculated by minimizing the Gibbs free energy of the species present in the system.31 The model of the reaction dynamics is based on the shrinking-core dynamics for the solid particles. The overall reaction rates are governed by diffusion through the gas film, product layer (reduced metal oxide formed at the surface), and reaction kinetics. The unreacted shrinking-core model is based on population balances by discretization of the particle size to capture the number of moles in each size interval. The shrinkingcore model is valid as long as the metal oxide particles are nonporous, which is true in the experimental work that we refer to in this study. However, when porous oxide particles are considered, a continuous reaction model rather than the shrinking-core model will be suitable.32 The following sections review the elemental balances, equilibrium calculations, energy balances, gas-solid reaction, and population balance model. 3.1. Concept of Elemental Balance. Consider a reduction chamber where the metal oxide Fe2O3 is reduced to Fe3O4 by
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reaction with methane (CH4). Then, the overall mole balance for CH4 is written as dNCH4
FCH4,in - FCH4,out )
+ rCH4V
dt
(1)
Similarly, we can write the mole balance for other components. Increasing the number of gas molecules and reactions in the system increases the number of equations to be solved. Therefore, the resulting state-space model will be large and complex, making it inappropriate for control studies. To reduce the state-space model, we write the mass balance equations based on invariants: elements and not molecules. This transformation is feasible for gases because when we know the amount of C, H, and O present at a particular temperature and pressure, we can calculate the equilibrium amounts of the molecules present in the system through Gibbs energy minimization. Therefore, writing balance equations for the element C gives number of carbon elements entering the system number of carbon elements leaving the system ) number of carbon elements accumulated Writing this equation in terms of rates gives dNC dt
where s is the stoichiometric coefficient, index i represents the elements C, H, and O, and index j represents the gas molecules CH4, CO2, and H2O. 3.2. Thermodynamic Equilibrium. In CLC systems, in order to increase the percentage conversion of fuel, increased temperature conditions should be maintained. At high temperatures, we can assume that the gas phase is in thermodynamic equilibrium. The thermodynamic equilibrium of a closed reaction mixture assumes constant temperature (T) and pressure (P). For such a system, the minimum Gibbs energy is given as min G(x) s.t. A · x - b ) 0
(7)
where G(x) is the Gibbs energy function and x ∈ Rδ, where δ is the number of possible species (the Appendix provides expressions for the Gibbs energy for our application). A ∈ Ry×x is the atom matrix, and b ∈ Ry is the total number of moles for each atom y. The conditions for the minimization problem can be obtained through the Lagrange function given by L(x, λ) ) G(x) - λT(A · x - b) λ ∈ Ry
(8)
where L is the Langrange operator with respect to species x and chemical potential λ. The sufficient conditions for minimization are
(2)
∂L )0 ∂x
(9)
There is no production or disappearance term because we are writing balance equations for elements that are neither created nor destroyed in the system. Similarly, for H,
∂L )0 ∂λ
(10)
JC,in - JC,out )
JH,in - JH,out
dNH ) dt
(3)
The balance equation for oxygen is a little different because there is a secondary source for O apart from the normal inflow and outflow fluxes. That is, metal oxide particles provide O element to the gas phase, which helps in the oxidation of CH4 gas. Therefore, JO,in - JO,out )
dNO + dt
∑N R
(4)
p p
where Np is the number of particles. Rp is the flow of O from the solid particles to the gas phase due to reaction. For the reaction between Fe2O3 and CH4 (eq 21), by assuming a shrinking-core mechanism, Rp is given by32
Rp )
( )
1 pCH4 SS 3 RTs r e 1 + kdiff
1 r k′′ r0
+
()
2
(
)
1 r0 -1 kp r
(5)
∑s
i,jJi,j
j
∇L(k) + ∇2L(k)∆(x, λ)k+1 ) 0
(11)
The iterative solution is then given by
[
∂2G -AT ∂x ∂xT -A 0
][ k
∆x ∆λ
] [ k+1
)
-µ A·x-b
]
k
(12)
Although the model equations are nonlinear, the proposed approach ensures a global minimum irrespective of the initial guesses.33,34 The equilibrium calculations are also tested by comparing the results with the integrated thermodynamic databank system: FactSage calculations. 3.3. Energy Balance. The energy balance is formulated based on the internal energies of the system. The gas-phase energy balance is written as35 dUg in out ) Jg,flow Hg,in - Jg,flow Hg,out + h(Ts - Tg) + ∆HgRg,rxn dt (13) Similarly, the energy balance in the solid phase can be written as
where the value of the stoichiometric ratio Sr is 12 and Se is the external surface area. There is an extra term (1/3) in the formula to determine the number of O elements produced by Fe2O3. A total of 1 mol of Fe2O3 gives one-third element of O when Fe2O3 is reduced to Fe3O4. The flux of elements J is given by Ji )
Using Newton’s method derived from two terms of the Taylor series
(6)
dUs in out ) Js,flow Hs,in - Js,flow Hs,out + h(Tg - Ts) + ∆HsRs,rxn dt (14) 3.4. Gas-Solid Reaction. The gas-solid reaction is based on the shrinking-core model for spherical particles of unchanging size.36 As mentioned earlier, the shrinking-core model is valid as long as the metal oxide particles are nonporous. However, when porous oxide particles are considered, a
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continuous reaction model rather than a shrinking-core model will be suitable. The total time to reach any stage of conversion is determined by summing the time taken for individual processes such as diffusion through the gas film, diffusion through the product layer, and the chemical reaction. The rate of change of the unreacted core radius can be written as
-
drc ) dt rc2
bCAg FB
(r0 - rc)rc 1 + + 2 r0De k′′ r0 kg
(15)
3.5. Population Balance Model. The population balance model is used to obtain the distribution of moles of the reactants in different reactive core sizes of the solid particles. It is assumed that the entire bed is well mixed with solid particles whose actual size is unchanged and the reactive core size is shrunk with respect to the reaction kinetics. Because the bed is considered to be well mixed, at any given time, there is a distribution for different core sizes, captured by the population balance. It is assumed that the entire bed is divided into m discrete zones characterized by m different core radii.37,38 In other words, the number of moles of Fe2O3 present in each zone is varied by variation of the core radius. The discretization is just for determining the reactive core size distribution, and it does not account for any spatial variation in the reactor. The metal oxide particles are fed to the first zone (m ) 1) with an initial core radius of r0. The particles remain in this zone until the core radius has shrunk to the next core radius value r1 set in the second zone. Once the core radius reaches r1, the particles are shifted to the second zone. Likewise, the calculation is continued until the core radius is decreased to rm. For the CLC system, in order to simulate the continuous process, we assume that a certain percentage (in the present study, 5%) of the solid particles (inclusive of all reactive core sizes r0 to rm) leaves the reduction chamber. The core radius of the metal oxide particles in a given discrete zone is constant. With m discrete zones, the core radius is varied to represent the shrinking-core mechanism. In the current study, we assume that the core radius decreases linearly. However, on the basis of the experimental data, the change in the core radius along the column can be modeled accurately by increasing the number of zones and specifying the appropriate value in each zone. On the basis of the population balance, the change in the number of particles in each discrete zone is calculated as RFe2O3Np RFe2O3Np dNp ) dt 4 4 F π(rm-13 - rm3) F π(rm3 - rm+13) 3 3
(16)
where F is the density of the particles, Np is the number of particles, RFe2O3 is the moles of Fe2O3 reacted, rm is the radius of the reactive core at the end of the mth discrete zone. 3.6. Elemental Invariants to Molecular Concentrations. To calculate the number of moles of a particular gas component AxBy based on Gibbs energy minimization: mole(AxBy) ) NAxBy )
(
xλA + yλB - ∆GAxBy PV exp RT RT
)
(17)
where λA and λB are the Lagrange multipliers for elements A and B. P is the standard pressure, V is the volume of gas, R is
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Table 1. Model Parameters Used in the Simulations parameters
experimental values
model values
temperature, K particle size, mm feed composition CH4 flow rate, mL/s (mol/s) porosity amount of bed material, g reduction period, s
1223 0.18-0.25 CH4 (100%) 5 (2.2 × 10-4) 0.3 15-90 180-720
1223 0.2 CH4 (100%) (2.24 × 10-4) 0.3 90 400
the gas constant, T is the temperature, and ∆G is the Gibbs energy of the compound AxBy. The number of moles of species A in the gas phase calculated using Lagrange multipliers must be equal to the total number of moles of A in the gas phase calculated using the overall elemental balance. Therefore, the values of the Lagrange multipliers λA and λB have to be computed based on the elemental balance calculations. For example, in a system with CH4, H2O, and CO2, the following constraints can be implemented to compute the Lagrange multipliers and, in turn, the number of moles present in the system. NCO2 + NCH4 - TC ) 0 (based on C elements)
(18)
4NCH4 + 2NH2O - TH ) 0 (based on H elements) (19) 2NCO2 + NH2O - TO ) 0 (based on O elements) (20) where Nx is the number of moles of x (calculated from eq 17) and Ty is the total number of elements y in the gas phase calculated by elemental balance. 4. Simulation Results The model equations discussed above are the balance equations for the entire system and do not carry any information on the spatial variations. Hence, a given reactor system should be divided into n number of zones and, in each zone, the proposed equations should be solved to capture the spatial variations in the reactor. The number of zones can be determined based on the process conditions. The experimental setup discussed in Mattisson et al.14 is considered in this study to verify the proposed model. The reduction chamber is a fixedbed reactor, initially loaded with a specified amount (Table 1) of metal oxide particles. The fuel (CH4 or syngas) is fed to the system until all of the metal oxide particles are reduced significantly, leading to a decrease in the percentage conversion of the fuel to less than 40%. Then, the bed is rejuvenated by supplying air-oxygen (oxidation stage). Thus, only one fixedbed reactor is used to perform both reduction and oxidation of the metal oxide particles. We first simulate only the reduction chamber for model validation. For simulation of the CLC system (section 4.4), we need to model two circulating fluidized-bed reactors. The same model equations can still be used with appropriate changes in the number of zones to represent the spatial distribution of the porosity in the fluidized bed and inlet and outlet conditions to capture the exchange of mass and energy between the reduction and oxidation chambers. On the basis of the extent of fluidization, the number of zones can be determined. In this case, for simplicity, we assume that the chambers are in complete fluidization, which can be represented by a single zone with fixed porosity. For these systems, it has been believed that the chambers can be modeled with less than three zones to appropriately represent the spatial characteristics.
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4.1. Nonisothermal Simulation of the Fuel Reactor with Fe2O3 and CH4. To start with, we simulate the reduction chamber with Fe2O3 metal oxide and CH4 as the fuel. The simulation conditions are given in Table 1. As per the experimental data, CH4 reduces Fe2O3 particles into the following forms: Fe3O4, FeO, and Fe. In the modeling work, because of the unavailability of complete experimental data on the reaction kinetics, we assume that Fe2O3 is reduced to Fe3O4 only. In other words, the reactions considered are 12Fe2O3 + CH4 f 8Fe3O4 + CO2 + 2H2O
(21)
3Fe2O3 + CO f 2Fe3O4 + CO2
(22)
3Fe2O3 + H2 f 2Fe3O4 + H2O
(23)
The reactions are assumed to be of nth order,6 and the rate equation is generally represented as -rA ) krcAgn
Figure 2. Percentage concentration of various gases in the reduction chamber with Fe2O3 particles and CH4 as the feed.
(24)
where kr is the reaction rate constant, cAg is the concentration of the gas, and n is the reaction order. The rate constants for the three reactions are
(
krCO ) 0.062 exp -
20000 RT
)
(25)
(
24000 RT
)
(26)
(
49000 RT
(27)
krH2 ) 0.23 exp -
krCH4 ) 0.08 exp -
)
The values are taken based on the experimental results for ironbased metal oxide particles called Fe45Al-FG.6 The rate constants are calculated by assuming that the reaction is the rate-controlling mechanism, thereby ignoring the film and product layer diffusion. The operating and physical parameters shown in Table 1 are based on the experimental data given by Mattisson et al.14 The model equations are solved in MATLAB/Simulink. The differential algebraic equation system is solved by sequentially solving of the ordinary differential equations (ODEs) using the MATLAB function ODE15s and the algebraic equations using fsolve. The termination tolerance on the function value is taken as 1 × 10-12 to ensure convergence. The computation time was 159 s for simulating 400 s of the process in a 1GB, 1.99 GHz computer. The simulation results are shown in Figure 2. The figure shows that more than 70% of CH4 is converted to CO2 initially. With time, the metal oxide is reduced and the number of O atoms given out by the metal oxide decreases gradually. Initially, there is ample supply of O, leading to the production of more CO2 than CO. As the metal oxide deteriorates with time (>250 s), there is less O present and the Bodouard reaction shifts equilibrium toward the production of CO rather than CO2 (around 300-400 s). The same explanation holds for the production of H2. Initially, more H2O is produced (not shown), and with time, only H2 is produced. The production of CO and H2 continues until all of the O from the oxygen carrier (metal oxide) is used up, after which only pure CH4 is seen at the outlet. Figure 3 shows the number of moles of Fe2O3 present in the particles of different reactive core radii. In Figure 3, each line is for a different particle, with a decreasing core radius in the direction of the arrow. From Figure 3, it is inferred that most
Figure 3. Moles of Fe2O3 present in various particles of different reactive core radii (with CH4 as the feed).
Figure 4. Experimental validation of the percentage concentration of various gases in the reduction chamber with Fe2O3 particles and CH4 as the feed.
of the metal oxide is reacted around 360 s, which is in accordance with the results shown in Figure 2. 4.2. Model Validation. Figure 4 shows the percentage concentration of various gases in the reduction chamber through both simulations and experimental results. The model results are similar to the experimental results. The discrepancy between the plant and model may be due to the fact that we simulate a fixed-bed reactor system with the assumptions that are valid
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Figure 5. Temperature of the gas and metal oxide particles.
for a fluidized-bed reactor system (e.g., well-mixed reactor system). Also, there might be some mismatch in the physical parameters. However, it is seen that the percentage conversion of CH4 is in good agreement with the data available in the literature.14 The gas and solid temperatures shown in Figure 5 show that there is a decrease in the gas temperature due to the reaction, and it then heats up because of the gas-solid heattransfer mechanism. On the basis of the heat-transfer mechanism between the gas and solid phases, the actual gas and solid temperatures should equilibrate after a prolonged time. If the heat-transfer coefficient is high, the difference between the gas and solid temperatures will soon be negligible. Because of the high heat capacity, the solid particles act as a large heat sink in the system. Also, there might be heat losses due to radiation. In the current study, we assume that the system is perfectly insulated and there are no radiation losses. The characteristics of the metal oxide vary significantly with and without inert carriers. The experimental results using iron oxide particles14 are quite different from those using iron oxide on an inert SiO2 carrier.39 We assume that Fe2O3 is reduced to Fe3O4. However, there is a possibility that Fe2O3 can be reduced to FeO in addition to Fe3O4. The reaction model in the population balance can be updated if the kinetics for such reactions are determined. The operating parameters used are based on Fe45Al-FG particles. Other model parameters are based on the Fe2O3 particles. This might cause a discrepancy in the simulated results. However, the current model and the simulation results are satisfactory for use in control studies. 4.3. Nonisothermal Simulation of the Fuel Reactor with Fe2O3 and Syngas. The proposed Simulink model is flexible enough to allow us to experiment with different numbers of particle size intervals, particle sizes, fuel composition, etc. We have also simulated the fuel reactor for the Fe2O3 particles with a syngas feed for the same operating conditions as those given in Table 1. Again, we assume that Fe2O3 is reduced to Fe3O4 only. The following reactions are considered in the simulation: 3Fe2O3 + CO f 2Fe3O4 + CO2 3Fe2O3 + H2 f 2Fe3O4 + H2O The percentage concentrations of CH4, CO2, CO, and H2 in the reactor are shown in Figure 6. With the presence of metal oxide in the system, CO is converted into CO2 and H2 is converted into H2O. After 900 s, almost all of the metal oxide is used up,
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Figure 6. Percentage concentration of various gases in the reduction chamber with Fe2O3 particles and syngas as the feed.
leading to only CO and H2 at the exit. The same mass of metal oxide persists up to 900 s with the syngas feed; it persists around 400 s with a CH4 feed. This is because 2 mol of O is needed to oxidize 1 mol of CH4 (eq 21), whereas only 1 mol of O (eqs 22 and 23) is needed to oxidize 1 mol of the syngas mixture (CO and H2). It is relatively simple to change the types of gaseous fuel and metal oxides, making the model flexible enough to be extended for different process conditions. 4.4. Nonisothermal Simulation of the CLC System. The proposed idea of simulating the reduction chamber can be implemented in a similar way for the oxidation chamber. We have simulated the entire CLC unit under nonisothermal conditions by combining the air and fuel reactors with simple relations for the cyclone separators. A particle size of 0.2 mm is used, and the reduction chamber is initially heated to 1223 K. The inlet temperature of both the fuel and the air stream in the reduction and oxidation chamber, respectively, is assumed to be at room temperature. The amount of Fe2O3 particles getting into the oxidation chamber is based on the loop seal settings.18 We assume that 5% of particles of each size are fed to the oxidation chamber. Because the oxidation chamber is considered more as a riser, we assume that particles of all sizes are replenished and sent back to the reduction chamber with a time delay. On the basis of the moles of Fe2O3 and Fe3O4 transferred between the two chambers, the corresponding heat exchanges are calculated and included in the model. In this study, we have fixed the solid circulation rate as 5% of the total particles present in the reduction chamber. However, on the basis of the experimental conditions, a simple mathematical relation can be employed for the solid circulation rate. It has been proven experimentally that the oxidation stage is much faster than the reduction stage and almost complete conversion takes place in the oxidation chamber.17 We assume that Fe2O3 molecules leaving the fuel reactor along with Fe3O4 are returned to the fuel reactor without any loss. Thus, we have accounted for only Fe3O4 as the feed to the air reactor. Numerous experiments conducted in the literature confirm that the loss of solid particles is negligible.11,40 Figures 7 and 8 show the number of moles of Fe2O3 and Fe3O4 present in different reactive particle core sizes in the fuel and air reactor, respectively, with time. The transient behavior of the CLC system due to the cyclic movement of the solid particles prevails for about 250 s, after which both reactors reach steady state. The total number of moles of the reactants in the respective reactor is also plotted. From the simulation results, it can be seen that proper interlinking between the two reactors
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Figure 7. Number of moles of Fe2O3 present in (10) different particle sizes (0.2, 0.183, 0.165, 0.148, 0.130, 0.113, 0.095, 0.078, 0.061, and 0.043) and the total number of moles of Fe2O3 in the reduction chamber.
Figure 9. Percentage concentration of various gases after reduction with Fe2O3 particles and CH4 as the feed (CLC system).
Figure 8. Number of moles of Fe3O4 present in (10) different particle sizes (0.2, 0.183, 0.165, 0.148, 0.130, 0.113, 0.095, 0.078, 0.061, and 0.043) and the total number of moles of Fe3O4 in the oxidation chamber.
Figure 10. Amount of Fe2O3 produced in the oxidation chamber and the amount of Fe3O4 produced in the reduction chamber.
is significant for sustained operation. This, in turn, is dependent on the amount of fuel (CH4) and oxygen/air at the feed. In other words, for a given concentration and flow of the fuel, the amount of metal oxide to be used should be determined, and on the basis of the reduction rate, the amount of oxygen-air to be fed to the air reactor should be determined. Any imbalance in the amount of metal oxide used or variations in the air reactor feed might induce unstable operation with smaller conversion and, hence, less power generation (explained further in the subsequent discussion in Figures 14 and 15). We believe that, with the proposed model and a simple control strategy, efficient and sustainable operation can be achieved. Figure 9 shows the percentage concentration of various gases at the exit of the fuel reactor. More than 99% of CH4 is converted into CO2 and CO. About 80% of CO2 is produced. Other parameters, like temperature, reactivity of the metal oxide, and flow characteristics can be tuned appropriately to increase the CO2 purity (more than 99%) in order to substantiate the purpose of using a CLC system toward CO2 sequestration. Elevated temperatures or other highly active metal oxides such as NiO can lead to almost complete conversion of CH4 to CO2. Figure 10 shows the number of moles of Fe3O4 produced in the reduction chamber and the number of moles of Fe2O3 produced in the oxidation chamber. At steady state, the moles of Fe2O3 produced in the air reactor stoichiometrically equal the moles of Fe3O4 produced in the fuel reactor, confirming the
Figure 11. Temperature of the gas and solid phases in the reduction chamber.
mass balance constraints over the entire system. The Fe inventory in the system is balanced and reaches a steady state. The gas and solid temperatures in the reduction stage are shown in Figure 11, and the temperatures in the oxidation stage are shown in Figure 12. In Figures 5, 11, and 12, the gas temperature is less than the solid temperature. This is because of the fact that we assume that the gas is fed into the reactor at room temperature and the solid particles are initially heated to
Ind. Eng. Chem. Res., Vol. 49, No. 10, 2010
Figure 12. Temperature of the gas and solid phases in the oxidation chamber.
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Figure 14. Effect of changes in the operating parameters on the percentage conversion and metal oxide inventory in the fuel reactor.
Figure 15. Effect of changes in the operating parameters on the metal oxide inventory and power generation in the air reactor. Figure 13. Energy that can be utilized for power production from the CLC unit (with 80% heat efficiency).
1223 K. Also, the difference in temperature may be due to the difference in the heat capacities of gas and solid particles. The figures confirm that a mild endothermic reaction takes place in the reduction chamber and exothermic reaction in the oxidation chamber. In the simulations, the energy produced in the air reactor is utilized to heat up the solid particles to the required temperature and then fed into the fuel reactor. The air fed to the oxidation chamber is assumed to be at room temperature, and there are no Fe3O4 molecules to begin with. Hence, initially (
