Modeling of Stagewise Feeding in Fluidized Bed Reactor of Oxidative

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Modeling of Stagewise Feeding in Fluidized Bed Reactor of Oxidative Coupling of Methane Mahdi Daneshpayeh, Navid Mostoufi,* Abbasali Khodadadi, Rahmat Sotudeh-Gharebagh, and Yadollah Mortazavi Oil and Gas Center of Excellence, School of Chemical Engineering, UniVersity of Tehran, P.O. Box 11155/4563, Tehran, Iran ReceiVed December 5, 2008. ReVised Manuscript ReceiVed May 26, 2009

The influence of distributed reactant injection on the performance of a fluidized bed reactor of oxidative coupling of methane (OCM) was investigated by means of reactor modeling and simulation. A two-phase hydrodynamic model was coupled with a comprehensive kinetic model of OCM over Mn/Na2WO4/SiO2 catalyst to predict the performance of the reactor. In the stagewise feeding, flow of air is divided into few portions. One portion is introduced to the fluidized bed through the distributor at the bottom, and other portions are injected inside the bed. It was shown that at low temperatures C2 yield in the stagewise feeding configuration is higher than the conventional cofeeding, whereas at high temperatures the yield of products in stagewise feeding is lower than cofeeding. Therefore, the optimum operating temperature of the reactor can be decreased from 800 °C in cofeeding to 750 °C with two secondary air injections while keeping the same conversion and yield. Moreover, it was shown that the oxygen distribution along the bed decreases, making the reactor performance less sensitive to changes in temperature. In general, when applying the stagewise feeding configuration, the reactor can operate at lower temperature, effect of temperature change on the performance of the reactor would be less, and removing the heat of reaction becomes more effective when compared to a cofeeding configuration. This results in widening the safe range of operating conditions, providing a more stable process with better temperature control and reducing other problems of high-temperature processes in the OCM fluidized bed reactor.

1. Introduction Natural gas consists mainly of methane and is typically used for heating and power generation in locations far from reservoirs. Natural gas is mostly transported using pipelines, which is expensive and may not be available for all consumption points. Moreover, natural gas reserves are increasing more rapidly than those of petroleum, and it is anticipated that this trend will extend well into the 21st century.1 Therefore, it is important to find a method to convert natural gas into liquid fuels which can be transported easily in vessels.1 Oxidative coupling of methane (OCM) is a promising route for utilization of large reserves of natural gas to higher hydrocarbons as liquid fuels, chemical and petrochemical feedstock. Since 1982, when pioneering work in this area was published by Keller and Bhasin,2 intensive research has been carried out intending to develop new catalysts with higher activity and selectivity toward economical industrialization.3-5 Several researchers have been improving the yields observed by Keller and Bhasin, but even * To whom correspondence should be addressed. Telephone: (9821)6696-7797. Fax: (98-21)6646-1024. E-mail: [email protected]. (1) Lunsford, J. H. Catalytic conversion of methane to more useful chemicals and fuels: a challenge for the 21st century. Catal. Today 2000, 63, 165–174. (2) Keller, G. E.; Bhasin, M. M. Synthesis of ethylene via oxidative coupling of methane. 1. Determination of active catalysts. J. Catal. 1982, 73, 9–19. (3) Mleczko, L.; Baerns, M. Catalytic oxidative coupling of methanereaction engineering aspects and process schemes. Fuel Process. Technol. 1995, 42, 217–248. (4) Kao, Y. K.; Lei, L.; Lin, Y. S. A Comparative Simulation Study on Oxidative Coupling of Methane in Fixed-Bed and Membrane Reactors. Ind. Eng. Chem. Res. 1997, 36, 3583–3593.

the most active and selective catalysts4 with a C2 yield of about 20% have not yet achieved the economic targets. Since the OCM reaction comprises a complex reaction network, it is obvious that the reactor configuration and corresponding operating conditions also offer possibilities to improve catalytic performance. Thus, in order to overcome the catalyst yield limitations, considerable attention has been paid to novel reactor configurations. Various reactor types such as multistage fixed beds,6 fixed bed with controlled temperature profile,7 fluidized beds,8,9 membrane reactors,10,11 reactors with molten salts,12,13 and (5) Li, S. J. Reaction Chemistry of W-Mn/SiO2 Catalyst for the Oxidative Coupling of Methane. Nat. Gas Chem. 2003, 12, 1–9. (6) Androulakis, I. P.; Reyes, S. C. Role of Distributed Oxygen Addition and Product Removal in the Oxidative Coupling of Methane. AIChE J. 1999, 45, 860–868. (7) Nouralishahi, A.; Pahlevanzadeh, H.; Towfighi Daryan, J. Determination of optimal temperature profile in an OCM plug flow reactor for the maximizing of ethylene production. Fuel Process. Technol. 2008, 89, 667– 677. (8) Pannek, U.; Mleczko, L. Reaction Engineering Simulations of Oxidative Coupling of Methane in a Circulating Fluidized-Bed Reactor. Chem. Eng. Technol. 1998, 21, 811–821. (9) Pannek, U.; Mleczko, L. Comprehensive model of oxidative coupling of methane in a fluidized bed reactor. Chem. Eng. Sci. 1996, 51, 3575– 3590. (10) Taheri, Z.; Nazari, K.; Safekordi, A. A.; Seyed-Matin, N.; Ahmadi, R.; Esmaeili, N.; Tofigh, A. Oxygen permeation and oxidative coupling of methane in membrane reactor: A new facile synthesis method for selective perovskite catalyst. J. Mol. Catal. A: Chem. 2008, 286, 79–86. (11) Lu, Y.; Dixon, A. G.; Moser, W. R.; Ma, Y. H. Oxygen-permeable dense membrane reactor for the oxidative coupling of methane. Appl. Catal. A: Gen. 1997, 155, L1–L7. (12) Yamazaki, O.; Omata, K.; Fujimoto, K. Selective Oxidation of Methane to C2 Hydrocarbons with Molten Metal Oxide. Stud. Surf. Sci. Catal. 1994, 81, 277–279.

10.1021/ef801060h CCC: $40.75  2009 American Chemical Society Published on Web 06/15/2009

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reverse-flow and counter-current moving bed14,15 have been considered and simulated for this purpose. Some of these approaches have resulted in considerable improvements, reaching C2 yields as high as 85%.16 Despite these extensive studies, there are still many technical problems in commercialization of the OCM reaction. Although one of the obstacles encountered in the commercial application is low catalyst yield, the major engineering challenge is heat management in the reactor to carry out the reaction in a safe manner. Because the OCM reaction is extremely exothermic, hot spots always develop in catalytic fixed beds.17 For such a process, a fluidized bed reactor seems to be the most suitable reactor type which prepares an isothermal catalytic bed with a high heat transfer coefficient and C2 yield comparable to those in fixed bed reactors.18 In the present work, the influence of distributed reactant injection on the OCM reaction in a fluidized bed reactor was investigated by means of reactor modeling and simulation. The reaction model used was based on the two-phase theory of fluidization. This model combines a model for describing the bed hydrodynamics and a kinetics model for the OCM reaction over a Mn/Na2WO4/SiO2 catalyst to predict the reactor performance. The dependence of the flow distribution was considered on the reactor performance in terms of methane conversion, C2 selectivity, product yields, and operating temperature.

Daneshpayeh et al. Table 1. Stoichiometric Equations of Kinetic Model19 step

reaction 2CH4 + 0.5O2 f C2H6 + H2O

1

rate equation rC2H6 ) m1 k01e-E1/RT(K0O2e-∆Had,O2/RTpO2)n1pCH 4

[1 + (K0O2e-∆Had,O2/RTpO2)n1]2 2

CH4 + 2O2 f CO2 + 2H2O

m2 n2 rCO2 ) k02e-E2/RTpCH p 4 O2

3

CH4 + O2 f CO + H2O + H2

m3 n3 rCO ) k03e-E3/RTpCH p 4 O2

4

CO + 0.5O2 f CO2

m 4 n4 rCO2 ) k04e-E4/RTpCO pO2

5

C2H6 + 0.5O2 f C2H4 + H2O

rC2H4 ) k05e-E5/RTpCm25H6pOn52

6

C2H4 + 2O2 f 2CO + 2H2O

rCO ) k06e-E6/RTpCm26H4pOn62

7

C2H4 + 2H2O f 2CO + 4H2

rCO ) k07e-E7/RTpCm27H4pHn72O

8

C2H6 f C2H4 + H2

rC2H4 ) k08e-E8/RTpCm28H6

9

CO2 + H2 f CO2 + H2O

m9 n9 rCO ) k09e-E9/RTpCO p 2 H2

10

CO + H2O f CO2 + H2

m10 n10 rCO2 ) k010e-E10/RTpCO pH2O

2. Modeling 2.1. Fluidized Bed Modeling. The model used in this work is based on the two-phase theory of fluidization which considers the reactor as bubble and emulsion phases. Due to the bubble and emulsion phases and interaction between them, two types of phenomena, i.e., physical and chemical, coexist in the fluidized bed reactors. According to the physical and chemical phenomena, two submodels are needed to describe the reactor behavior. These two sum models are a hydrodynamic submodel, corresponding to the physical phenomena, and a reaction submodel, corresponding to the chemical phenomena occurring in the reactor. In order to simulate the fluidized bed reactor properly, these two submodels have to be coupled together and solved. 2.1.1. Reaction Submodel. An OCM kinetic model over Mn/ Na2WO4/SiO2 catalyst presented by Daneshpayeh et al.19 is used as a reaction submodel in this work. This model considers both catalytic and gas-phase as well as primary and consecutive reaction steps. The reaction steps of this model and the rate equations are presented in Table 1. According to this model, methane is converted in three parallel reactions: formation of ethane by oxidative coupling (13) Claridge, J. B.; Green, M. L. H.; Lago, R. M.; Tsang, S. C.; York, A. P. E. Investigation of Molten Cobalt Halide/Sodium Metavanadate Mixtures as Redox Catalysts for the Oxidative Coupling of Methane. Stud. Surf. Sci. Catal. 1994, 82, 327–335. (14) Lee, A.; Tonkovich, Y.; Carr, R. W. A simulated countercurrent moving-bed chromatographic reactor for the oxidative coupling of methane: Experimental results. Chem. Eng. Sci. 1994, 49, 4647–4656. (15) Lee, A.; Tonkovich, Y.; Carr, R. W. Modeling of the simulated countercurrent moving-bed chromatographic reactor used for the oxidative coupling of methane. Chem. Eng. Sci. 1994, 49, 4657–4665. (16) Jiang, Y.; Yentekakis, I. V.; Vayenas, C. G. Methane to Ethylene with 85% Yield in a Gas Recycle Electrocatalytic Reactor Separator. Science 1994, 264, 1563–1566. (17) Liu, H.; Wang, X.; Yang, D.; Gao, R.; Wang, Z.; Yang, J. Scale up and stability test for oxidative coupling of methane over Na2WO4-Mn/ SiO2 catalyst in a 200 mL fixed-bed reactor. J. Nat. Gas Chem. 2008, 17, 59–63. (18) Pannek, U.; Mleczko, L. Effect of scale-up on the performance of a fluidized-bed reactor for the oxidative coupling of methane. Chem. Eng. Sci. 1997, 52, 2429–2434. (19) Daneshpayeh, M.; Khodadadi, A.; Mostoufi, N.; Mortazavi, Y.; Sotoudeh-Gharebagh, R.; Talebizadeh, A. Kinetic modeling of oxidative coupling of methane over Mn/Na2WO4/SiO2 catalyst. Fuel Process. Technol. 2009, 90, 403–410.

Table 2. Kinetic Parameters19 k0j ∆Hads,O2 no Ej (kJ/mol) (kmol/s · kg · Pmj+nj) (kJ/mol) 1 2 3 4 5 6 7 8 9 10

212.6 98.54 146.8 114.6 153.5 174.4 394.2 291.9 158.0 131.3 a

2.94 × 101 3.07 × 10-7 6.65 × 10-8 5.26 × 10-4 2.70 × 10-3 1.81 × 10-1 4.61 × 102 1.08 × 107 a 5.77 × 10-3 5.24 × 10-6

-121.9

k0O2 (1/Pa)

mj

4.39 × 10-11 1.00 0.85 0.5 0.50 0.91 0.72 1.62 0.88 1.00 1.00

nj 0.75 0.50 1.57 0.50 0.50 0.40 0.71 0 1.00 1.00

Units are in mol/m3 · s · Pa-m.

of methane, nonselective total oxidation of methane to carbon dioxide, and partial oxidation of methane to carbon monoxide. Carbon monoxide is further oxidized to carbon dioxide. In consecutive steps, the conversion of ethane passes by two parallel routes, i.e., heterogeneous catalytic oxidative dehydrogenation (R5) and thermal gas-phase dehydrogenation of ethane to ethylene (R8). Ethylene converts to carbon monoxide in two parallel ways, i.e., partial oxidation (R6) and steam reforming (R7). Also, the carbon monoxide to carbon dioxide ratio is influenced by the water-gas shift reaction which proceeds in both directions. Kinetic parameters of this model are given in Table 2. 2.1.2. Hydrodynamic Submodel. Various hydrodynamic models are presented in the literature. One-, two-, and three-phase models exist for fluidized bed reactors. Among these three categories of models, the two-phase model is employed more extensively because (20) Jafari, R.; Sotudeh-Gharebagh, R.; Mostoufi, N. Performance of the wide-ranging models for fluidized bed reactors. AdV. Powder Technol. 2004, 0, 1–16.

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it corresponds to the actual phenomena occurring in the fluidized beds more than the other two model categories.20 According to the advantages of the two-phase models,20 the dynamic two-phase model, presented by Mostoufi et al.,21 was used as the hydrodynamic submodel in this work. Previous studies show that predictions of the DTP model have a reasonable fit with the experimental data of the fluidized bed reactors operating in the bubbling regime of fluidization.20 According to this model, the emulsion phase does not stay at the minimum fluidization conditions and bubbles contain various amounts of solid particles. Therefore, the dynamic two-phase model considers the progress of the reaction in both bubble and emulsion phases. Equations of mass balance of species A in bubble and emulsion phases are as follows:

dCAb + Kbeεb(CAb - CAe) + εbrAb ) 0 dz

(1)

dCAe δ - Kbeεb (C - CAe) + εerAe ) 0 dz 1 - δ Ab

(2)

Ub

Ue

The mean concentration of species A at each step i is given by:

j Ai ) C

Ue Ub (1 - δ)CAei + δC U0 U0 Abi

(3)

According to the catalyst properties,19 emulsion and bubble voidage and bubble phase fraction are evaluated by relations given by Cui et al.22 for Geldart A:

εe ) εmf + 0.00061 exp

( (

εb ) 0.784 - 0.139 exp δ ) 1 - exp

(

U0 - Umf 0.262 U0 - Umf -0.272

U0 - Umf -0.62

)

) )

(4)

(5)

(6)

The mean bubble diameter as a function of height and operating conditions was estimated by the semiempirical correlation of Mori and Wen.23 The initial bubble diameter at the distributor was calculated from the correlation of Miwa et al.24 Changes in diffusivities of each component are accounted for as the gas composition varies along the reactor height. The interphase mass transfer coefficient of component A, Kbe, is calculated using the equation given by Sit and Grace25

Kbe )

[

6 Umf +2 db 3

DmAεmfUb πdb

]

(7)

where DmA is the diffusion coefficient of component A in the mixture which can be calculated by the relation given by Wilke and Lee.26 It is worth noting that fluidized bed reactors provide an isothermal catalytic bed with a high heat transfer rate, even in high exothermic (21) Mostoufi, N.; Cui, H.; Chaouki, J. A Comparison of Two- and Single-Phase Models for Fluidized-Bed Reactors. Ind. Eng. Chem. Res. 2001, 40, 5526–5532. (22) Cui, H. P.; Mostoufi, N.; Chaouki, J. Characterization of dynamic gas-solid distribution in fluidized bed. Chem. Eng. J. 2000, 790, 133–143. (23) Mori, S.; Wen, C. Y. Estimation of bubble diameter in gaseous fluidized beds. AIChE J. 1975, 21, 109–115. (24) Miwa, K.; Mori, S.; Kato, T.; Muchi, I. Behavior of bubbles in gaseous fluidized bed. Int. Chem. Eng. 1972, 12, 187–194. (25) Sit, S. P.; Grace, J. R. Effect of bubble interaction on interphase mass transfer in gas fluidized bed. Chem. Eng. Sci. 1981, 36, 327–335. (26) Wilke, C. R.; Lee, C. Y. Estimation of Diffusion Coefficients for Gases and Vapors. Ind. Eng. Chem. 1955, 47, 1253–1257.

Figure 1. Different feeding configurations: (a) cofeeding, (b) stagewise feeding, one secondary injection, and (c) stagewise feeding, two secondary injection.

reactions.27 Hence, it was assumed in the present study that the fluidized bed reactor operates isothermally. Therefore, no heat balance is required to evaluate the temperature of the reactor. 2.2. Stagewise Feeding. As mentioned before, one of the obstacles in commercialization of the OCM process is low selectivity of C2 products (mainly C2H4). The OCM reaction involves consecutive reactions with intermediates being the desired product. In such a process, one possibility to improve the selectivity is to alter the concentration profile of the reactants by distributed feeding. For this purpose, in OCM reactors it has been suggested to keep the oxygen concentration low.28 The effectiveness of this method is still controversial29,30 and seems to depend on the type of catalyst, the reaction conditions applied, and the number of stages for oxygen injection. In addition, to improve the reactor performance with this approach, the heat released in the reaction is more evenly distributed along the bed and provides a better temperature control. On the basis of the above advantages, stagewise feeding was also investigated in the present work. Suggested stagewise feeding configurations considered in this work are shown in Figure 1. In stagewise feeding, the total methane flow is introduced to the bed through the distributor while only part of the oxygen is mixed with methane before the distributor. The rest of the oxygen is divided into equal portions and injected throughout nozzles along the bed. This pattern spreads out the heat of reaction and makes the bed temperature more uniform. Although oxygen concentration in this configuration remains low, still the amount of oxygen required is provided to reach high methane conversions. In this way, both C2 selectivity (ethane and ethylene selectivities) and methane conversion can be improved. Moreover, as shown in Figure 1, heat exchangers can be placed between the sections and the large amount of heat released in each section can be removed by means of these heat exchangers. Therefore, in addition to distributing the heat generated by the reaction along the bed, more heat transfer surface would be provided which leads to better heat management and a more uniform bed temperature. The reactor model described in the previous section is not adequate for a fluidized bed reactor with secondary feed injection. However, it can be applied to each section of the bed, i.e., between one feed injection point and the next one or top of the bed (see Figure 1). Many studies have been carried out considering the hydrodynamics of secondary gas injection in the fluidized bed (27) Marschall, K. J.; Mleczko, L. Experimental Investigations of Catalytic Partial Oxidation of Methane to Synthesis Gas in Various Types of Fluidized-Bed Reactors. Chem. Eng. Technol. 2000, 23, 31–37. (28) Baerns, M.; Hinsen, W. Process for the Production of Ethane and/ or Ethylene from Methane. US Patent 4,608,449, 1986. (29) Reyes, S. C.; Kelkar, C. P.; Iglesia, E. Kinetic-transport models and the design of catalysts and reactors for the oxidative coupling of methane. Catal. Lett. 1993, 19, 167–180. (30) Reyes, S. C.; Iglesia, E.; Kelkar, C. P. Kinetic-transport models of bimodal reaction sequences I. Homogeneous and heterogeneous pathways in the oxidative coupling of methane. Chem. Eng. Sci. 1993, 48, 2643– 2661.

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Daneshpayeh et al. Table 3. Values of Parameters Used in the Simulation parameter

value

particle mean diameter partcle density Umf Archimedes number bed diameter

160 µm 1100 kg/m3 0.028 m/s 4.55 (Geldart A) 1m

feeding configuration 1 section 2 sections lower section upper section 3 sections lower section middle section upper section

height

U0

2m

0.3 m/s

1m 1m

0.2 m/s 0.3 m/s

0.677 m 0.677 m 0.677 m

0.167 m/s 0.234 m/s 0.3 m/s

the Newton method.33 When the solution was reached, concentrations of all components along the reactor in both phases were determined.

3. Results and Discussion

Figure 2. Schematics of phase flows, dispersion, and hold-ups for model in distributed gas injection.

reactors.31,32 These studies show that the injected gas enters the bed mainly as bubbles and mixes rapidly with other bubbles. AlSherehy et al.31 found that within a short distance above the injection point, uniform radial distribution was achieved in the bubble phase. Therefore, it was assumed in the present work that the injected gas immediately is added to the bubble phase in a uniform manner across the bed. This uniformity of concentration at the injection level can be achieved by proper mechanical design of nuzzles. In this way, the reactor with such a configuration can be divided into sections of different feed composition and gas flow rate. In the present work, an equal amount of oxygen was injected into the reactor from either the distributor or the nozzle(s) and the sections were considered to be of equal height (Figure 1). Figure 2 shows the schematics of a two-section bed with secondary feed injection. At the injection level, the superficial gas velocity was changed to include the secondary gas injection. Bubble diameter was adjusted using the correlation of Mori and Wen22 for this change in the superficial gas velocity with the initial bubble size equal to the bubble size obtained at the top of the previous section. Other hydrodynamic parameters above the injection level were then recalculated using this new bubble size. Moreover, at the injection point, bubble phase concentration was changed due to secondary gas added to the bubble phase. The mass balance equations described in section 2.1 were then solved sequentially for each section of the reactor. 2.3. Method of Solution. Writing eqs 1 and 2 for all components leads to a set of first-order differential equations. This initial value problem was solved by the finite difference method.33 In this method, the height of each section was divided into a large number of steps (say 100). The derivatives of differential equations were discretized. Thus, an algebraic equation was obtained at each step for each differential equation for each component which leads to a set of nonlinear equation. This set of equations was solved using (31) Al-Sherehy, F.; Grace, J. R.; Adris, A. E. Gas mixing and modeling of secondary gas distribution in a bench-scale fluidized bed. AIChE J. 2004, 50, 922–936. (32) Sotudeh-Gharebagh, R.; Chaouki, J.; Sauriol, P. An Experimental Study of Non-Premixed Combustion in a Turbulent Fluidized-Bed Reactor. Fuel Process. Technol. 2007, 88, 847–858. (33) Constantinides, A.; Mostoufi, N. Numerical methods for chemical engineering with MATLAB applications; Prentice Hall, Upper Saddle River, NJ, 1999. (34) Schweer, D.; Mleczko, L.; Baerns, M. OCM in a fixed-bed reactor: limits and perspectives. Catal. Today 1994, 21, 357–369.

In this section, the results of the described reactor model are presented for cofeed and stagewise feeding of the fluidized bed of OCM and the performances of different feeding structure are compared. The reactor design parameters as well as catalyst properties used in the simulations are listed in Table 3. 3.1. Cofeeding. Model predictions for a conventional cofeed fluidized bed reactor are shown in Figure 3. In this case, methane and air are chosen as feed with CH4/O2 ) 2.5 and the reactor operated at 1 atm and 800 °C (optimum operating temperature for cofeed structure) at a superficial gas velocity of 0.3 m/s. Consistent with the expected behavior of the OCM reaction over an active catalyst, the concentration of feed components (i.e., methane and oxygen) decreases sharply above the distributor. It can be seen in Figure 3 that the oxygen in the emulsion phase is completely converted shortly above the gas distributor (∼5 cm) while the oxygen in the bubble phase is consumed more slowly up to a height of 0.25 m. The results indicate that methane is converted into ethane via selective reaction (step 1). Parallel to the ethane production, oxidative and thermal dehydrogenation of ethane to ethylene promote the ethylene concentration along the bed. As a result, the ethane concentration profile has a maximum. In the upper part of the bed, where oxygen is depleted, only thermal dehydrogenation and slow steam reforming of ethane take place. These reactions are a result for changes in selectivity of products in the oxygen free part of the bed. According to Figure 3, a bed with a height of 25 cm is sufficient for complete oxygen conversion due to the high activity of the catalyst. However, this height is not adequate for removing the heat released in the OCM reaction by means of an immersed heat exchanger. In such operating conditions (CH4/O2 ) 2.5 and U0 ) 0.3 m/s) the heat of reaction amounts to 0.31 MW per unit of reactor cross-section area. Carrying out this reaction adiabatically, this amount of energy can increase the bed temperature up to 1680 °C. In order to remove this huge amount of energy and control the bed temperature at around 800 °C, at least a height of 0.2 m is needed if using a heat exchanger of vertical tubes with a coil cross section of 10% of the bed area which produces steam at 4.1 MPa at 672 K. In addition, in order to avoid catalyst attrition and tube erosion, this heat exchanger should not be placed very close to the distributor. With such a configuration in a commercial largescale fluidized bed, a sharp temperature gradient may occur between the reaction zone (right above the distributor) and the



Figure 3. Concentration of methane, oxygen, ethane, and ethylene in cofeed fluidized bed. T ) 800 °C, CH4/O2 ) 2.5.

heat exchanging zone. This temperature gradient affects the product selectivity and oxidizes the hydrocarbon products. Another problem of this configuration is the high optimum operating temperature (see Figure 10). To further operating problems, catalyst agglomeration is observed for many selective catalysts at high temperatures.2 Therefore, operating the reactor at a thermally optimal temperature can cause catalyst cohesiveness which results in defluidization. 3.2. Stagewise Feeding. A possible solution to overcome the heat management problem in a fluidized bed reactor of OCM is distributed feeding. In order to study the effects of distributed feeding on the performance of the reactor, this type of reactor was simulated with one injection point using the same operating conditions as the cofeeding example. In this case, the total methane flow is introduced to the bed through the distributor and the air is distributed equally between the distributor and a sparger located 1 m above the distributor. Reactor design parameters of each section are given in Table 3. The simulation results for this reactor are presented in Figure 4 in terms of concentrations of methane, oxygen, and C2 products in bubble phase, emulsion phase, and the bed. Similar to the cofeeding example, below the injection point, the methane concentration of both phases decreases via selective and nonselective oxidations to produce ethane, ethylene, and COx. As shown in this figure, a step change can be observed in methane, oxygen, and C2 product concentrations which correspond to secondary air injection. According to the model assumptions, the injected air is totally mixed immediately with bubble phase at the injection level. Therefore, the injected air changes the components concentration of the bubble phase which in turn increases the concentration gradient between the phases. Above the air injection, oxidation reactions continue by consumption of all oxygen and methane in the bubble phase. Moreover, due to a concentration gradient, mass transfer of methane from emulsion to bubble phase and oxygen from bubble to emulsion phase decreases the methane content of emulsion.

Due to dividing oxygen in this configuration, the heat of reaction in each section is approximately one-half the heat released in the cofeeding case. Also, as can be seen in Figure 4, oxygen exists in the longer part of the bed which alters the length of the reaction zone. Therefore, the heat of reaction in the second section of the bed (above the secondary gas injection) can be removed by means of a heat exchanger of both sections (see Figure 1b) and a more uniform bed temperature profile can be achieved in this configuration. 3.3. Comparison of Cofeeding and Stagewise Feeding. In order to investigate the effect of stagewise feeding on reactor performance, C2 production, methane conversion, C2 selectivity, and C2 yield profiles of these two types of reactors were compared. For this purpose, both configurations were run at 750 °C, U0 of 0.3 m/s, and using air and methane as feed (CH4/ O2 ) 2.5). More reactor parameters for simulation are presented in Table 3. Figure 5 shows the methane conversion vs height of the bed for cofeeding and stagewise feeding. As shown in this figure, methane conversion increases in two steps and a marginally higher methane conversion was reached at the exit of the stagewise feeding reactor. Figure 6 demonstrates the selectivity of C2 products for both reactor configurations. It can be seen in this figure that the C2 selectivity of stagewise feeding is more than that of cofeeding. This can be explained by the fact that the C2 selectivity is enhanced at higher methane to oxygen ratios for all catalysts. Since stagewise feeding lowers the oxygen concentration, this configuration increases the C2 selectivity. The methane to oxygen ratio in the stagewise feeding increases in two ways. The first way is the secondary feeding of oxygen inside the bed instead of the main distributor which increases the methane to oxygen ratio in each section. The second way is feeding the oxygen to emulsion through the mass transfer from bubble to emulsion. As mentioned earlier, the secondary gas enters the bed as bubbles and then the oxygen diffuses into the emulsion. Slow mass transfer of oxygen from bubble to emulsion keeps the emulsion oxygen content at low

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Figure 4. Concentration of methane, oxygen, ethane, and ethylene in a stagewise feeding fluidized bed with one secondary injection. T ) 800 °C, CH4/O2 ) 2.5.

Figure 5. Methane conversion vs bed height in a fluidized bed with stagewise feeding and cofeeding configurations. T ) 750 °C, CH4/O2 ) 2.5.

level. Product yields for both configurations are shown in Figure 7. As could be seen in this figure, the C2 yield for the cofeeding is slightly lower than that of the stagewise feeding at reactor exit. It is obvious from Figures 5-7 that stagewise feeding improves the reactor performance in presented operating conditions. In order to elucidate the effect of stagewise feeding on reactor performance, the effects of distribution percent (number of injection points) and operating temperature are discussed next. In all cases, methane and air volumetric flow rates were the same and methane was fed completely from the distributor while air was equally divided between the distributor and injection points. Because of the construction limitations in internal equipments (i.e., nozzles and heat exchangers), only reactors with one, two, and three sections were considered for comparison. Figure 8 illustrates the C2 selectivity versus temperature

Figure 6. C2 selectivity vs bed height in a fluidized bed for stagewise feeding and cofeeding configurations. T ) 750 °C, CH4/O2 ) 2.5.

for different feed injection configurations of the fluidized bed reactor. As shown in this figure, at low temperatures, stagewise feeding improves the C2 selectivity whereas at higher temperatures selectivity drops for this configuration. This could be explained by the fact that distributed feeding maintains the oxygen concentration of the bed at a low level which causes increasing the C2 selectivity. However, low C2 selectivity at high temperatures is due to an increase in the rate of consecutive oxidation reactions. Figure 8 illustrates that C2 selectivity passes through a maximum in all feeding configurations. According to this figure, the temperature at which the maximum selectivity is reached shifts toward low temperature with increasing number of injection points. In addition, increasing the number of air injection points extends the C2 yield maxima in a wider temperature range. Therefore, it can be concluded that distributed feeding allows the fluidized reactor to operate at lower tem-



Figure 7. C2 yield vs bed height in a fluidized bed for stagewise feeding and cofeeding configurations. T ) 750 °C and CH4/O2 ) 2.5.

Figure 9. Methane conversion vs temperature for different feeding configurations. CH4/O2 ) 2.5.

Figure 8. C2 selectivity vs temperature for different feeding configurations. CH4/O2 ) 2.5.

Figure 10. C2 yield vs temperature for different feeding configurations. CH4/O2 ) 2.5.

peratures while its performance is the same compared to the cofeeding configuration. Decreasing the temperature leads to a more stable process and better process control. It is worth mentioning that this maximum temperature shifting is similar to what was reported by Scheweer et al.34 for distributed feeding of a fix bed of La2O3/CaO catalyst. Nevertheless, distributed feeding slightly decreases the product selectivity in fixed beds. Figure 9 shows methane conversion vs bed temperature for different oxygen distribution configurations. It can be seen in this figure that methane conversion is higher at low temperature but decreases at high temperatures. As explained before, at high temperatures, the rate of reaction for partial oxidation of ethylene (step 6) and oxidation of carbon monoxide (step 4) is high. Thus, these reactions consume the oxygen faster than C2 production reactions. Consequently, a decrease in oxygen content causes the methane conversion to drop. It is worth noting that decreasing the methane conversions in a fluidized bed at high temperatures is in agreement with fixed bed experiments reported by Scheweer et al.34 The C2 yields of different feeding configurations vs temperature are presented in Figure 10. This figure demonstrates that the maximum C2 yield decreases slightly with increasing injection points. The maximum yield for stagewise feeding with two injection points is 19.9%, which is very close to that of cofeeding, which is 20.1%. However, this can be achieved at a

temperature 50 °C, lower than cofeeding (from 800 °C in cofeeding to 750 °C with two injection points). 4. Conclusion The performance of a stagewise feeding fluidized bed reactor was compared with the conventional cofeed fluidized bed reactor of OCM. A comprehensive kinetic model and a two-phase hydrodynamic model were coupled to predict concentration profiles of the reactants and products for different feeding configurations. The simulation results showed that in the cofeeding configuration the heat of reaction would be released over a short height of the bed which makes temperature control of the bed difficult due to technical problems. Due to the high optimum temperature and a large amount of heat released in this configuration, problems such as the temperature gradient in the bed, catalyst agglomeration, and difficulty in bed temperature control may occur. In order to overcome these problems, stagewise feeding was proposed in which the oxygen would be introduced to the bed at different heights. The simulations showed that the distributed feed injection has significant effects on the performance of the reactor, such as distributing the heat of reaction, lowering the optimum bed temperature, and reducing the temperature dependency of the reactor in terms of products yield, when compared to those in the cofeed configuration. A lower operating temperature and better distribution of heat generation through the bed also

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prevent catalyst agglomeration, increase process safety, provide a more stable process, and allow better temperature control. Acknowledgment. The authors appreciate financial support from National Petrochemical Co. under contract no. 84132.

Nomenclature

j A ) average concentration of component A (kmol/m3) C CAb ) concentration of component A in bubble phase (kmol/m3) CAe ) concentration of component A in emulsion phase (kmol/m3) DmA ) diffusion coefficient of A in mixture (m2/s) db ) bubble diameter (m) ∆Had,O2 ) adsorption enthalpy for O2 (J/mol) Ej ) activation energy in the reaction step j (J/mol) k0j ) pre-exponential factor Kbe ) bubble to emulsion mass transfer coefficient (1/s) mj ) reaction order nj ) reaction order p ) partial pressure, Pa

Daneshpayeh et al. rAb ) reaction rate based on component A in bubble phase (kmol/ m3 · s) rAe ) reaction rate based on component A in emulsion phase (kmol/ m3 · s) T ) reactor operating temperature (K) Ub ) bubble velocity (m/s) Ue ) emulsion gas velocity (m/s) Umf ) minimum fluidization velocity (m/s) U0 ) superficial gas velocity (m/s) z ) axial position above the distributor (m) Greek Letters ∆ ) bubble phase fraction εb ) bubble phase porosity εe ) emulsion phase porosity εmf ) bed porosity at minimum fluidization velocity EF801060H

Modeling of Stagewise Feeding in Fluidized Bed Reactor of Oxidative

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