Characteristics of Oxy-fuel Combustion in an Oxygen Transport Reactor

Jun 21, 2012 - Reactor. R. Ben-Mansour, M. A. Habib,* H. M. Badr, Azharuddin, and M. Nemitallah .... the ITM reactor based on an empirical equation fo...
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Characteristics of Oxy-fuel Combustion in an Oxygen Transport Reactor R. Ben-Mansour, M. A. Habib,* H. M. Badr, Azharuddin, and M. Nemitallah Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia ABSTRACT: This study aims at investigating the characteristics of oxy-fuel combustion in an oxygen transport reactor (OTR). The cylindrical reactor walls are made of dense, nonporous, mixed-conducting ceramic membranes that only allow for oxygen permeation from the outside air into the combustion chamber. The oxygen permeate mixes with a mixture of CO2 and CH4 (sweep gas) that enters the reactor, resulting in combustion products composed of H2O and CO2. The modeling of the flow process considers a numerical solution of the conservation equations of mass, momentum, energy, and species in the axisymmetric flow domain. The oxygen permeation across the membrane depends upon the prevailing temperatures and the oxygen partial pressure at both sides of the membrane. The simulations are performed for different compositions of CH4/CO2 mixtures and different mass flow rates. First, the comparison between the reactive and separation-only OTR units showed that combining reaction and separation increases the O2 permeation rate significantly to about 2.5 times under the assumptions given herein. Second, a mass flow rate of 1.625 × 10−7 kg/s with a CH4/CO2 mass ratio ranging from 0.5:0.5 to 1.0:0 gives an almost uniform axial temperature of about 1250 K in most of the reactor length with a high CH4 conversion of 75 to 35%, respectively. In all of the simulations, the total O2 permeation flux is almost the same, except for 1.625 × 10−7 kg/s with a CH4/CO2 mass ratio less than 0.3:0.7. The results indicate that the heat of reaction is mostly transferred to the air side with a portion used to heat the O2permeating flux. For higher mass flow rates, the OTR operates with a rich mixture, resulting in low CH4 conversion. The combustion process in such cases can be improved by splitting the OTR into a series of units, where the fuel is added at stages along the reactor network.

1. INTRODUCTION Fossil fuels are considered to be the main source of energy. Fossil fuels produce CO2, which is considered as a main contributor of global warming. Oxy-fuel combustion is one of the most promising carbon capture technologies in the world.1 In this technology, oxygen is burnt in a combustion chamber with fuel and the combustion products include only CO2 and H2O, which can be separated easily by the condensation process, leaving behind only CO2 that can be recycled or stored through the sequestration process. For this process, the required pure oxygen is obtained via different methods, such as cryogenic distillation.2 This process of separation of O2 is very costly.3,4 The thermodynamic and economic penalties incurred by the use of a cryogenic air separation unit could easily offset any advantages gained by oxy-fuel combustion, prompting many researchers to investigate the use of alternative air separation systems. One of the alternatives to the separation of oxygen from air is the use of ion transport membranes (ITMs), which are expected to reduce the penalty of air separation units in oxy-combustion. 5 Kvamsdal et al. 6 conducted efficiency analysis for all of the carbon capture technologies, which showed that the efficiency penalty with the membrane separation is 7% with 100% CO2 capture. ITMs are dense nonporous, mixed electronic and ionic conducting in nature. These ITMs have the capability of separating the oxygen from air at elevated temperatures typically above 700 °C. Oxygen permeation through these membranes is the function of the partial pressure of oxygen across the membranes, membrane thickness, and temperature at which these membranes are operating. Many researchers7−12 © 2012 American Chemical Society

conducted experiments based on different ITM materials and found that the Ba0.5Sr0.5Co0.8Fe0.2Ox (BSCF) membrane can only give high oxygen permeation flux. Kim et al.13 developed a semi-empirical correlation for oxygen permeation flux for the BSCF membrane for the surface-reaction-limited mechanism, and it is given as JO = 2

2πr1r2LCikio ⎛ P1 ⎜⎜ − A(r1 + r2) ⎝ P0

P2 P0

⎞ ⎟⎟ ⎠

(1)

where L is the effective length of the tube, r1 and r2 are the outer and inner radii of the membrane tube, respectively, A is the effective area of the membrane, Ci is the density of oxygen ions, kio is the surface exchange coefficient, P1 is the global partial pressure of O2 at the feed side, P2 is the global partial pressure of O2 at the permeate side, and P0 is 1 atm oxygen pressure. It can be clearly seen that JO2 is mainly dependent upon the O2 partial pressure differential across the membrane. Because P1 is almost fixed, the only chance to maximize the JO2 is to lower P2, which can be achieved by purging the permeated O2 using an inert gas (such as He) or having O2 consumed by fuel (such as CH4). Balanchandran et al.14 conducted experiments with CH4 as sweeping gas instead of He and found no significant increase in oxygen permeation. Therefore, the use of CH4 for combustion is viable without any efficiency loss from ITMs. Many researchers15−18 tried to simulate the Received: March 30, 2012 Revised: June 20, 2012 Published: June 21, 2012 4599

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separation of species from a mixture of gases. Zhang et al.19 developed a one-dimensional (1D) model developed for O2 permeation through the ITM perovskite membrane [(LaCa)(CoFe)O3−δ] for non-reacting and reacting flow conditions that gives a deviation of 15% between the experimental data. Mancini and Mitsos20,21developed a black box 1D model for the ITM reactor based on an empirical equation for O2 permeation from the experimental data.22 In the present work, a computational fluid dynamics (CFD) model is developed for oxygen separation through ITM and reaction of separated O2 with the fuel. The CFD calculations were carried out using FLUENT 12.1, while the mass transfer of oxygen through the membrane is modeled by a set of userdefined functions.

the sink term and come out on the other side through the source term. Equation 6 represents the source/sink terms based on the partial pressure of O2. ⎧ JO Acell MWO 2 ⎪+ 2 at low partial pressure of O2 Vcell ⎪ Si = ⎨ ⎪ JO2 Acell MWO2 at high partial pressure of O2 ⎪− Vcell ⎩

The source/sink Si term is modeled in such a way that it is 0, unless i = O2 and the computational cell is adjacent to the membrane surface. The diffusion coefficient is determined by specifying the binary mass diffusion coefficient of the component i in the component j. The corresponding diffusion coefficient in the mixture is computed by eq 7.25

2. MATHEMATICAL FORMULATION Problem Statement. The performance of an oxygen transport reactor (OTR) is investigated considering oxygen separation and reaction with the sweep gas. Air (containing 77% N2 and 23% O2) enters at inlet of the feed side, and a sweep gas mixture (CH4 and CO2) enters at inlet of the permeate side of an OTR having a BSCF membrane. The model is assumed as a single ITM tube. The wall of the reactor is assumed to be adiabatic7,23 to ensure similarity with the experimental model for permeation performed by Wang et al.7 Buoyancy and the heat flux by radiation are neglected because of the small diameter of the ITM reactor that leads to high convective heat-transfer coefficients, implying that the differnce of the membrane temperature and free stream is small. The flow considered is laminar and steady in nature. It is also assumed that combustion does not affect the oxygen permeation flux equation. The study focuses on the effect of the reaction of CH4 with the permeated O2 on the O2 permeation rate through the ITM membrane. The validation of the presented model is performed with similar experimental data produced by Wang et al.7 The membrane considered in this work is BSCF with an effective surface area of 12.56 cm2. Hong et al.24 indicated that the membrane temperature strongly influences the O2 permeation rate. Therefore, the present study focuses on the designing of a uniform isothermal OTR with optimization of the consumption of CH4 with a maximum O2 permeation. \ Governing Equations. The steady-state equations for conservation of mass, momentum, energy, and species can be written as ∇(ρU ) = Si

(2)

∇(ρUU ) = −∇p + μ∇2 U

(3)

(ρCp)U ∇T = ∇(λ∇T )

(4)

∇(ρUYi ) − ∇(ρDi ,m∇Yi ) = Si

(5)

(6)

Di ,m =

1 − Xi ⎛X ⎞ ∑j , j ≠ i ⎜ D i ⎟ ⎝ i ,j ⎠

(7)

3. SOLUTION PROCEDURE The numerical simulations were performed using CFD software FLUENT 12.1. In the present simulations, the gas mixture properties were defined before executing the simulation loop. The simulations

Table 1. List of Model Parameter Values parameter

value

ṁ inlet,permeate (kg/s)

⎧1.625 × 10−7 ⎪ ⎨ 4.625 × 10−7 ⎪ ⎩ 8.625 × 10−7

ṁ inlet,feed (kg/s) Tinlet,permeate (K) Tinlet,feed (K) (YCH4; YCO2;)permeate

5.85 × 10−6 1073 1073 varied

(YO2; YN2;)air

0.23; 0.77

ρmembrane (kg/m3) λmembrane (W m−1 K−1)26

3000 20

were performed using steady flow conditions, as given in Table 1. The discretization of the governing equations was performed using a segregated compressible flow solver, in which each governing equation is solved separately. Figure 1 represents the OTR of the present study. To reduce the numerical errors, structured meshing was performed to divide the flow domain into subdomains (feed side and permeate side) with 12 500 quadrilateral cells. The membrane cell computational geometry consisted of two mass flow inlets, boundaries for introducing the feed and sweep gas mixture, and two pressure outlets for retentate and permeate flows. The membrane in the domain was defined as the shown wall. The computational grid consisted of 40 “mass flow inlet”

In the present computational model, the velocity and pressure fields of the gas mixture are obtained by solving continuity, momentum, and energy equations. The species distribution and the fluxes at the permeate and feed sides are obtained by the convection−diffusion equation. The species transport across the membrane is carried out using a source term. The source/ sink term (Si) accounts for the mass flow of species across the membrane. At the membrane boundary cells, the species are allowed to disappear from one side of the membrane through

Figure 1. Domain for OTR (not to scale). 4600

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edge cells for the air inlet with 50 “pressure outlet” edge cells and 250 cells along the axis of the OTR. Grid refinement was performed to achieve the grid independence by analyzing the mass fractions within the geometrical domain. The grid refinement was concentrated near the walls and in the vicinity of the high-gradient regions. A semi-implicit method for pressure-linked equations (SIMPLE) algorithm27 was used for the pressure−velocity coupling. To ensure a complete converged solution, the continuity and momentum residual values were set to 10−6 and those for species and energy equations were set to 10−9. The gas density is calculated using the ideal gas law, and the gas viscosity, specific heat, and thermal conductivity are calculated as a mass fraction-weighted average of all species. The specific heat of each species is calculated using a piecewise polynomial fit of the temperature. The pressure was set to the pressure-staggered scheme (PRESTO), and momentum, species, and energy were set to the second-order upwind discretization scheme for more accurate results.25 Transport of O2 across the membrane was achieved using a series of user-defined functions (UDFs) that are written in VC++ and compiled and hooked to the FLUENT software. The issue of hydraulic jump across the membrane was resolved by patching the cells from the upper and lower zones with two different values of initial partial pressures of species. The source and sink terms in the UDF were calculated using the following equations:

⎛ P′ 1 − JO = K1K 2(T )⎜⎜ 2 ⎝ P0

K1 =

P″2 P0

2πr1r2L S(r1 + r2)

⎞0.623 ⎟⎟ ⎠

Figure 2. Axisymmetric geometrical view from Wang et al.7 (not to scale).

(8)

(9)

Figure 3. Variation of O2 permation flux with O2 partial pressure in the shell side: (■, □, and ▼) experimental data7 and () present numerical results.

where P′1 and P″2 are the local partial pressures of O2 on the feed and permeate sides, respectively, K1 is a geometric constant, and K2 is a constant that depends upon the temperature. A single-step kinetic reaction mechanism is activated on permeate for combustion of methane with permeated O2. The reaction rate is given by

R CH4 = − k[CH4]nCH4 [O2 ]nO2 where

high temperatures. It is also useful to note that the rise in the temperature of the membrane results in higher oxygen fluxes, as also indicated by eq 8. General Features. In the present investigation, a concentric tubular configuration geometry is selected, in which the inner cylinder is made of ITM. Air (77% N2 + 23% O2 by weight) is feed in the shell side, and a mixture of CH4 and CO2 is feed in the core side of the reactor. The study focuses on the effect of the reaction of CH4 with the permeated O2 on the O2 permeation rate through the ITM membrane. The present study focuses on designing a uniform isothermal OTR with optimization of the consumption of CH4 with a maximum O2 permeation. To study the ITM characteristics and combustion characteristics, the numerical simulations are carried out with the conditions shown in Table 1. Thermal conductivity of perovskite membranes, such as La0.6Sr0.4Co0.2Fe0.8O3−δ (LSCF), BaCeO3, and BaZrO3, ranges from 5 to 12 W m−1 K−1 for temperature operation in the range of 500−1000 °C.28−30 The thermal conductivity is still unknown for BSCF, and the analysis26 suggested that, for the ceramic membrane, the thermal conductivity is very low and varies from 3 to 100 W m−1 K−1. In the present simulation, the thermal conductivity of BSCF is assumed as 20 W m−1 K−1. To investigate the influence of the reactivity on the oxygen permeation, the results of the two cases of separation and reaction were compared, as shown in Figure 4. It is evident from the figure that the O2 permeation flux for the case of the reaction mode is very high compared to the separation-only mode. This is attributed to the high partial pressure difference of O2 created across the membrane by the chemical reaction. It gives a conclusive remark that, with the chemical reaction for a particular membrane surface, the amount of O2 permeated is higher compared to the separation-only mode, thereby the

(10)

21

⎛ −E ⎞ k = AT β exp⎜ a ⎟ ⎝ RT ⎠ where A = 2.119 × 1011, Ea = 2.027 × 108 J kg−1 mol−1, β = 0, nCH4 = 0.2, nO2 = 1.3, and k is the Arrhenius reaction rate. Now, using both the membrane permeation model and combustion together will be a challenging part to model the ITM reactor.

4. RESULTS AND DISCUSSION Model Validation. The computational scheme developed for the membrane permeation model was validated through comparison to the experimental data.7 Comparisons are limited to the case of non-reactive applications because the experimental data for the reactive case is not available. The dimensions of the computational domain for validation were identical to that of the experimental membrane cell (Figure 2) by Wang et al.7 In this experiment, the test section was surrounded by a tubular furnace that maintains a constant surface temperature. The inlet conditions are taken from the experiments with an increasing order of partial pressure on the shell side for different operating temperatures and O 2 permeation fluxes. A comparison is made between the model prediction and the measured values of the total O2 permation flux (Figure 3), showing good accuracy, especially at high oxygen partial pressure in the feed side. The largest deviation was about 15%, occurring at 900 °C and 0.19 atm. This deviation may be attributed to experimental uncertaninties at 4601

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Figure 4. Oxygen permeation flux for the reactive and separation-only cases.

length of the ITM reactor can be greatly reduced. The profile for the reaction case exhibits a minimum value at around 0.01 m. As shown, the permeation rate decreases for the case of the non-reactive case. As reactivity is considered, oxygen is consumed, causing the partial pressure in the permeate side to increase. Thus, two contradicting effects are initiated. As a result, a minimum value of the flux appears. Temperature Characteristics. Figure 5 presents the axial temperature profiles within the reactor for different sweep gas mixture compositions. For the low mass flow rate of 1.625 × 10−7 kg/s, the temperature rises quickly to 1250 K at 1/5th of the length from the inlet of the reactor and then decreases in the downstream sections. This drop is due to the cooling of the flue gases by permeating O2 from the membrane. When the mixture composition of CH4/CO2 (mass ratio mR) increases beyond 0.4:0.6, the exit temperature of the reactor becomes almost constant at about 1222 K. Figure 5b shows the temperature profile for the mass flow rate of 4.625 × 10−7 kg/s. From the figure, it is evident that the maximum temperature reaches 1310 K for almost all of the mass ratios mR and the exit temperature is about 1220 K, except for the first two cases with mass ratios mR of 0.1:0.9 and 0.12:0.88. This is mainly because the fuel is completely consumed within the reactor and the incoming O2 lowers the exit temperature to 1142 K for the case with the mass ratio mR of 0.12:0.88. Figure 5c shows the temperature profile for the mass flow rate of 8.625 × 10−7 kg/s, where the maximum temperature drops from 1411 to 1334 K for the composition CH4/CO2 mass ratio from 0.06:0.94 to 1.0:0. Unlike the cases of the mass flow rate of 1.625 × 10−7 and 4.625 × 10−7 kg/s, the exit temperature in the present case varies from 1214 to 1297 K with the composition mass ratio mR from 0.1:0.9 to 1.0:0, except for 0.06:0.94 with 1149 K, and this is due to the complete combustion before the exit of the reactor and can be clearly explained by the rate of reaction profiles. To explain the temperature profiles, the rate of reaction profiles for the aforementioned mass flow rates of 1.625 × 10−7, 4.625 × 10−7, and 8.625 × 10−7 kg/s are presented in Figure 6. In Figure 6a, it is shown that the rate of reaction reaches nearly 0.0062 kg mol m−3 s−1 and drops along the length of the reactor. For the composition CH4/CO2 mass ratio mR from 0.1:0.9 to 0.3:0.7, the rate of the reaction becomes 0 within the

Figure 5. Temperature profiles for the different sweep gas mixtures for three different mass flow rates.

reactor, and for mR = 0.33:0.67, the rate of reaction becomes 0 at the exit of the reactor, which is due to the fact that the fuel is totally consumed. It is noted that temperatures and rates of reaction profiles for the mR ranging from 0.5:0.5 to 1.0:0 are almost the same, leaving some unburned fuel at the exit with high temperatures. If the reactor is designed to follow a uniform temperature combustion process more closely, then the temperature-related problems could be significantly mitigated. Therefore, the composition mR from 0.5:0.5 to 1.0:0 could be used, and the ITM reactor could be split into a series of units, where the exhaust of the first reactor unit is feed to second, etc., until the fuel is totally consumed. With the increase of the mass flow rate from 1.625 × 10−7 to 4.625 × 10−7 kg/s, the maximum value of the rate of the reaction increased to 0.001 08 kg mol m−3 s−1 and the reaction started earlier at the left side of the reactor. This is due to the fact that the rate of O2 permeation is the same but the velocity of fuel is increased; hence, it takes time to start the reaction kinetics. It may be indicated here that the incomplete combustion at the exit of the reactor should be avoided. Another section should be added at the end of the reactor with no extra fuel to ensure complete combustion of the fuel and to avoid losses in efficiency in real combustion furnaces. Figure 6c shows the reaction rate profiles for the mass flow rate of 8.625 × 10−7 kg/s. It can be seen that the magnitude of 4602

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the inlet, high maximum temperatures can be achieved with an increasing mass flow rate. This is accompanied by a reduction in the conversion percentage of CH4. With the split ITM reactor design, the problem of fuel conversion can be overcome with a uniform temperature along the reactor. Combustion Characteristics. Figure 8 shows the CH4 mass fraction profiles for different CH4/CO2 mR compositions

Figure 6. Kinetic rate of reaction profiles for different sweep gas mixtures for three different mass flow rates.

the maximum reaction rate decreases as we increase mR and the start of the reaction shifts to almost the middle of the reactor. This is attributed to the fact that the O2/CH4 value decreases along the length of the reactor, as seen in Figure 7. It is clear from the figure that, for a high mass flow rate, the increase of the CH4 content reduces the reaction kinetics and the CH4 conversion percentage becomes reduced. From the above discussion, it can be concluded that, with less diluent CO2 at

Figure 8. CH4 mass fraction profiles for different sweep gas compositions.

with increasing mass flow rates. It is evident that the conversion of CH4 to combustible products decreases with the increase of the CH4 percentage at the inlet. For the optimal design of the ITM reactor, which combines O2 separation and fuel oxidation, the amount of CH4 conversion is an important parameter that is affected by the diluent CO2 concentration and O2 permeation flux. For a more dilute CO2 at higher mass flow rates at the inlet, the maximum temperature is reached but the exit temperature for all of the simulations ranges from 1148 to 1297 K. To increase the O2 permeation flux from ITM, there must be sufficient methane input, so that the chemical reaction does not stop at the first part of the reactor. For mR in the range from 0.1:0.9 to 0.3:0.7 with a mass flow rate of 1.625 × 10−7 kg/s, all CH4 is consumed and the permeating O2 downstream cools the flue gases, resulting in a decrease in the temperature. For the case of mR of 0.33:0.67, the reaction ends near the exit of the

Figure 7. O2/CH4 profiles for the different sweep gas compositions. 4603

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flow rate of 1.625 × 10−7 kg/s, the CH4 conversion is 100%. The O2 conversion increases until 40% CH4 and becomes constant with 93% conversion. The figure also represents the O2 permeation rate, which becomes constant above 33% CH4 at the inlet to a value of 9.33 × 10−6 mol/s. A similar profile for the O2 permeation rate and conversions of CH4 and O2 is obtained by Tan et al.31 for the LSCF ITM membrane. The O2/CH4 value is an important parameter to decide the region of the flammability limit for combustion. Figure 11

reactor and ΔT is not much less compared to the lower percentage of CH4 at the inlet. For mR > 0.33:0.67 in the feed with a mass flow rate of 1.625 × 10−7 kg/s, the CH4 conversion reduced to 36.8% for mR = 1.0:0, as seen in Figure 9. For the

Figure 9. Percentage of CH4 conversion for different mass flow rates.

mass flow rate of 4.625 × 10−7 kg/s, 100% CH4 conversion is obtained for mR = 0.12:0.88 or less, and CH4 conversion is greatly reduced to 13.5% for mR = 1.0:0. The mass flow rate of 8.625 × 10−7 kg/s yields 7.5% CH4 conversion for mR = 1.0:0 and 100% CH4 conversion at very low mR = 0.06:0.94 or less. On the whole, the amount of CH4 burned does not vary much because it depends upon the O2 available for combustion. To burn a greater amount of CH4, the surface area of the membrane must be increased in such a way that the surface/ volume ratio of the reactor must be high. Panels b and c of Figure 8 depict that the consumption of CH4 is delayed because of the increase of the flow velocity; hence, the length to attain O2−CH4 in the flammability limit is increased. To maintain a uniform temperature within the reactor, the maximum methane percentage is required from the three mass flow rates presented, 1.625 × 10−7, 4.625 × 10−7, and 8.625 × 10−7 kg/s, with the lowest giving the uniform temperature with the composition of mR above 0.5:0.5. Figure 10 shows the percentage of CH4 and O2 conversions with an increasing percentage of CH4 at the inlet. It is evident from the figure that, with up to 33% of CH4 at the inlet with the

Figure 11. O2/CH4 versus the percentage of CH4 at the inlet for different mass flow rates.

shows the representation of all three mass flow rates with different CH4 percentages at the inlet. It can be seen that the only low mass flow rate of 1.625 × 10−7 kg/s comes under a lean region with 100% conversion of CH4 with an O2/CH4 value of 5.178. This is because the combustion of CH4 in the ITM reactor is non-premixed and is highly dependent upon mixing of species. The oxygen mass fractions are important because the mass fraction is related to the mole fraction. Because the ITM reactor is operating at atmospheric pressure, the mole fraction is nothing but the O2 partial pressure, and the permeation rate is highly dependent upon that O2 partial pressure. Figure 12 shows the O2 mass fraction with an increasing CH4 percent concentration at the inlet for three different mass flow rates. Figures 12 and 13 are related because the O2 permeation flux JO2 is dependent upon the O2 partial pressure across the membrane. Because the O2 partial pressure at the feed is fixed (0.21 atm) as per eq 8, the variation of JO2 is more governed by the O2 partial pressure at the permeate side than the temperature because the temperature rise within the reactor is nearly on the order of 200 K. The lesser the O2 partial pressure at the permeate side, the higher the O2 permeation flux. Figure 12a shows that the O2 partial pressure is 0 at the inlet of the permeate side, hence, the maximum O2 permeation flux. Along the length of the reactor, the O2 mass fraction increases until O2 is sufficient to burn CH4 and then decreases until the reaction rate becomes maximum. For mR of 0.1:0.9, the reaction is ended at X/L of 0.25 because the total CH4 is consumed and the O2 mass fraction increases downstream, while O2 permeation decreases until the exit of the reactor. For mR ranging from 0.2:0.8 to 0.33:0.67, the trend of the O2 mass fraction follows that of the previous ratio, except that the magnitude increases and the reaction zone increases. For a

Figure 10. Percentage of O2 and CH4 conversions and O2 permeation rate with a mass flow rate of 1.625 × 10−7 kg/s. 4604

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Figure 13. O2 permeation flux for different sweep gas compositions.

Figure 12. O2 mass fraction profiles for different sweep gas compositions.

5. CONCLUSION The analysis presented in this work is used to predict the temperature and combustion characteristics for the different sweep gas mixture. The scope of the model is of utmost importance in predicting the amount of CH4 required for a given membrane area to design the uniform isothermal reactor of tubular configuration. The results of the comparison between reactive and separation-only OTR units showed that combining reaction and separation significantly increases the O 2 permeation rate to about 2.5 times under the assumptions given herein. In all of the simulations, the total O2 permeation flux is almost the same, except for 1.625 × 10−7 kg/s with CH4/ CO2 less than 0.3:0.7. Because the thermal resistance of these membranes is low, the heat of reaction is mostly transferred to the air side with a portion used to heat the O2-permeating flux. For higher mass flow rates, the OTR operates with a rich mixture, resulting in low CH4 conversion. The combustion process in such cases can be improved by splitting the OTR into a series of units, where the fuel is added at stages along the reactor network.

higher mR > 0.33:0.67, the O2 mass fraction is almost constant, leading to an almost constant O2 permeation flux, as shown in Figure 13a. For the increased mass flow rates at the inlet of 4.625 × 10−7 and 8.625 × 10−7 kg/s, the maximum value of the O2 mass fraction is almost the same but the peak is shifted from X/L of 0.25 to 0.6. This is attributed to the shift in the rate of the reaction, as seen in Figure 13. At the higher mass flow rate of 8.625 × 10−7 kg/s, the O2 permeation flux decreases until X/ L of 0.7 for mR = 1.0:0. From the above discussion, it is depicted that, for an ideal ITM reactor, the mass flow rate of 1.625 × 10−7 kg/s with composition mR from above 0.5:0.5 to 1.0:0 is suitable for uniform temperature operations. This results in a maximum O2 permeation flux with 75% CH4 conversion for mR = 0.5:0.5 to 37% for mR = 1.0:0. For the case without reaction (separation-only), oxygen permeate does not react with the sweep gases (CH4 + CO2). Therefore, the O2 partial pressure at the permeate side (P2) is much larger in the case of the non-reacting medium. As a result, the driving force ((P′1/P0)1/2 − (P″2/P0)1/2)0.623 will be lower than that in the case of combustion.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 4605

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Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the support received from King Abdulaziz City for Science and Technology (KACST) through the Science and Technology Unit at King Fahd University of Petroleum and Minerals (KFUPM) for funding this work through Project 09-ENE755-04 as part of the National Science, Technology, and Innovation Plan.

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NOMENCLATURE A = effective area of the membrane tube (m2) Acell = area of the cell (m2) Ci = density of oxygen ions (mol/m3) Cp = heat capacity (J kg−1 K−1) Di,m = diffusion coefficient of the mixture of species i (m2/s) JO2 = oxygen permeation flux (mol m−2 s−1) kio = surface exchange coefficient (m/s) K1 = geometric constant K2 = constant depending upon the temperature (mol m−2 s−1) L = effective length of the tube (m) mR = ratio of CH4/CO2 MWO2 = molecular weight of oxygen (kg/kmol) p = pressure (Pa) P1 = global partial pressure of oxygen at the feed side (atm) P2 = global partial pressure of oxygen at the permeate side (atm) P′1 = local partial pressure of oxygen at the feed side (atm) P″2 = local partial pressure of oxygen at the permeate side (atm) P0 = 1 atm oxygen pressure r1 = outer radius of the membrane tube (m) r2 = inner radius of the membrane tube (m) Si = source/sink term (kg m−3 s−1) T = temperature (K) U = velocity vector (m2/s) Vcell = volume of the cell (m3) Xi = mole fraction of species i Yi = mass fraction of species i

Greek Symbols

λi = thermal conductivity of species i (W m−1 K−1) μ = viscosity (kg m−1 s−1) ρ = density (kg/m3)

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REFERENCES

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dx.doi.org/10.1021/ef300539c | Energy Fuels 2012, 26, 4599−4606