Optimization of Fluidized Bed Reactor of Oxidative Coupling of Methane

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Optimization of process variables in the oxidative coupling of methane (OCM) .... water and dehydrogenation of ethane to ethylene which happens in two ways of.
I NTERNATIONAL J OURNAL OF C HEMICAL R EACTOR E NGINEERING Volume 10

2012

Article A2

Optimization of Fluidized Bed Reactor of Oxidative Coupling of Methane



Mohammad-Hosein Eghbal-Ahmadi∗

Masoud Zaerpour†

Mahdi Daneshpayeh‡

Navid Mostoufi∗∗

University of Tehran, iman [email protected] University of Tehran, [email protected] ‡ University of Tehran, [email protected] ∗∗ University of Tehran, [email protected] ISSN 1542-6580 c Copyright 2012 De Gruyter. All rights reserved. †

Optimization of Fluidized Bed Reactor of Oxidative Coupling of Methane Mohammad-Hosein Eghbal-Ahmadi, Masoud Zaerpour, Mahdi Daneshpayeh, and Navid Mostoufi

Abstract Optimization of process variables in the oxidative coupling of methane (OCM) over Mn/Na2 WO4 /SiO2 catalyst in a fluidized bed reactor was carried out. Effects of operating temperature, distribution pattern of oxygen injected to the reactor and the number of injections on the reactor performance on C2 (ethane + ethylene) yield were investigated. Process variables for one, two and three secondary oxygen injections were investigated to obtain the maximum C2 yield by genetic algorithm optimization method. The maximum C2 selectivity and yield of 47.1% and 22.87%, respectively, were achieved for three secondary oxygen injections at operating temperature of 746.05◦ C. The C2 yield achieved in this study is approximately 4% better than previous works reported in literature while the optimum temperature is lower. KEYWORDS: oxidative coupling of methane, OCM, genetic algorithm, process optimization

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1. Introduction Since the early work of Keller and Bhasin (1982), many investigations have been carried out on production of C2 hydrocarbons, mainly C2H6 and C2H4, by oxidative coupling of methane (OCM). Increasing selectivity and yield of C2 by means of catalyst formulation and/or by reaction engineering has been the focus of these investigations in order to make the process commercially feasible. One of the most effective catalysts for the OCM is believed to be Mn/Na2WO4/SiO2 which was first introduced by Jiang et al. (1993). An 80% C2 selectivity and 33% methane conversion over this catalyst showed that it is one of the most promising catalysts for the OCM reaction, thus, extensively studied by several researchers (Wang et al., 1995; Wu et al., 1995; Kou et al., 1998; Lunsford, 2000; Ji et al., 2002; Wu et al., 2007; Liu et al., 2008; Malekzadeh et al., 2008). It was reported that using this catalyst in the fixed bed reactor, it is possible to reach C2 selectivity up to 80% at a CH4 conversion of about 20% for periods longer than 90 h (Malekzadeh et al., 2007; Pak and Lunsford, 1998). Various type of reactors were proposed for oxidative coupling of methane, such as: counter current moving bed reactor, solid oxide fuel cell reactor, catalytic dense membrane reactor, fixed bed reactor, fluidized bed reactor, membrane reactor and two-zone fluidized bed reactor (Talebizadeh et al., 2009). Heat management and temperature control are key factors for reactor selection and design (Mleczko and Baerns, 1995). Realizing that fluidized beds are ideally suited for efficient heat removal, this type of reactors seems to be one of the most promising one for OCM. Temperature homogeneity may be achieved by applying fluidized bed reactors in which intensive mixing of solids results in a relatively fast dissipation of the heat generated by the catalytic reactor. Some researchers have even claimed that OCM may be carried out isothermally in the fluidized bed reactors (Mleczko et al., 1996; Santos et al., 1995; Andorf et al., 1991). According to Jaso et al. (2010), three types of reactor, including fluidized bed reactor, porous membrane reactor and fixed bed reactor, show the potential to be used industrially. They pointed to the fact that the fluidized bed reactor provides the possibility to operate under isothermal operation under all simulated conditions. Comparable or even higher C2 selectivity and yield were achieved in fluidized beds than in fixed bed reactors (Do et al., 1994; Mleczko et al., 1996; Follmer et al., 1989). It has been shown that geometry and feeding policy of the fluidized bed reactor play an important role in the reactor hydrodynamics and its performance (Jaso et al., 2011). In other words, investigating the best operating conditions of a reactor for increasing the yield of C2 can be as what the kind of catalyst or type of reactor should be. In fact, C2 selectivity and yield were found to be strongly influenced by reaction conditions, i.e., temperature, ratio of methane to oxygen

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and as well as by the hydrodynamics of the fluidized bed. For instance, in a study by Bhatia et al. (2009) it was shown that selectivity and yield of C2+ were increased with increasing of temperature (700–900 ºC) or the ratio of ethylene to ethane was increased with the reaction temperature in the catalytic membrane reactor. However, there is always a question of what are the optimum operating conditions for the reactor. Due to the complex interaction between kinetics and hydrodynamics, reaction engineering modeling and simulations seems to be the most efficient way for optimization of the reactor design and the reaction conditions. In the present work, C2 yield of OCM was maximized in a fluidized bed reactor with stage wise feeding by optimizing the process variables of reactor, including temperature, oxygen flow rates of each stage (distribution pattern) and length of each stage of the bed. Furthermore, the influences of temperature and distribution pattern of injected oxygen to the reactor performance (yield and selectivity of C2 and conversion of methane) and effect of the number of injections on C2 yield were investigated. Also, the effect of temperature on outlet ethylene to ethane ratio from reactor was studied. 2. Fluidized bed modeling The model used in this work was based on the two-phase theory of fluidization. This model considers the reactor as emulsion and bubble phases. Two types of phenomena, i.e., chemical (kinetics) and physical (hydrodynamics) phenomena, coexist in the fluidized bed reactor. Therefore, the model of the reactor should be obtained by coupling of hydrodynamic and reaction sub-models. Physical (hydrodynamics) and chemical (kinetics) interactions between these phases lead to progress the reaction. In order to simulate the fluidized bed reactor properly, these two sub-models were coupled together and solved. 2.1. Reaction sub-model An OCM kinetic model over Mn/Na2WO4/SiO2 catalyst, presented by Daneshpayeh et al. (2009a) was used as the reaction sub-model. This model considers both catalytic and gas phase as well as primary and consecutive reaction steps. According to this model, methane is converted in three parallel reactions: a) Formation of ethane by oxidative coupling of methane. b) Nonselective total oxidation of methane to carbon dioxide. c) Partial oxidation of methane to carbon monoxide. All these reaction steps and their kinetics are presented in Table 1 and 2.

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The main reactions that lead to change the yield and selectivity of C2 are production of ethane from methane, consumption of ethylene by oxygen and water and dehydrogenation of ethane to ethylene which happens in two ways of thermal decomposition and in presence of oxygen. This means that wherever the oxygen in the bed is finished, the dehydrogenation reaction is only thermal. Step Reaction 1

Table (1) - Reaction steps Rate equation

2CH4+0.5O2C2H6+H2O

rC2 H6 

k01e E1 / RT ( K 0O2 e [1  ( K 0O2 e

H ad , O2 / RT

H ad , O2 / RT

2

CH4+2O2CO2+2H2O

rCO2  k 02 e  E2 / RT pCH 4

3

CH4+O2CO+H2O+H2

rCO  k 03 e  E3 / RT pCH 4 3 pOn32

4

CO+0.5O2CO2

rCO2  k 04 e  E4 / RT pCO 4 pOn42

5

C2H6+0.5O2C2H4+H2O

rC2 H 4  k 05 e  E5 / RT pC2 H 6

6

C2H4+2O22CO+2H2O

rCO  k 06 e  E6 / RT pC2 H 4

m6

pOn62

7

C2H4+2H2O2CO+4H2

rCO  k 07 e  E7 / RT pC2 H 4

m7

p Hn72O

8

C2H6C2H4+H2

rC2 H 4  k 08 e  E8 / RT pC2 H 6

m8

9

CO2+H2CO+H2O

rCO  k 09 e  E9 / RT pCO2

p Hn92

10

CO+H2OCO2+H2

rCO2  k 010 e  E10 / RT pCO

m2

m1 pO2 )n1 pCH

4

n1 2

pO2 ) ]

pOn22

m

m

m9

m5

m10

pOn52

p Hn102O

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Table (2) – Kinetic parameters No. 1

a

k0j (kmol/s.kg.Pmj+nj) Ej (kJ/mol) 212.6 2.9410+1

Hads,O2 (kJ/mol) -121.9

k0O2 (1/Pa) 4.3910-11

2 98.54 3.0710-1 3 146.8 6.6510-2 4 114.6 5.2610-4 5 153.5 2.7010-3 6 174.4 1.8110-1 7 394.2 4.6110+2 8 291.9 1.0810+7a 9 158.0 5.7710-3 10 131.3 5.2410-6 Units are in mol/m3.s.Pa-m

mj

nj

1.00

0.75

0.85 0.5 0.50 0.91 0.72 1.62 0.88 1.00 1.00

0.50 1.57 0.50 0.50 0.40 0.71 0 1.00 1.00

2.2. Hydrodynamic sub-model As mentioned above, the hydrodynamic sub-model in this work was based on the two-phase theory of fluidization. Various hydrodynamic models exist in literature. Single-, two- and three-phase models have been proposed for fluidized bed reactors. Among these three categories of models, the two-phase model has been employed more extensively because it corresponds to the actual phenomena occurring in the fluidized beds more than the other two model categories (Jafari et al., 2004). Based on the advantages of the two-phase model, the dynamic twophase (DTP) model, presented by Mostoufi et al. (2001), was used as the hydrodynamic sub-model in this work. Previous studies showed that predictions of the DTP model have a reasonable fit to the experimental data of the fluidized bed reactors operating in bubbling and turbulent regimes of fluidization (Jafari et al., 2004). According to the DTP model, the emulsion phase does not stay at the minimum fluidization conditions and bubbles contain various amounts of solid particles. Therefore, the DTP model considers the progress of the reaction in both bubble and emulsion phases. This is in contrast to the simple two phase model in which the reaction takes place only in the emulsion phase and the products can enter the bubbles only due to mass transfer. According to the catalyst properties (Daneshpayeh et al., 2009a), emulsion and bubble voidage and bubble phase fraction are evaluated by relations given by Cui et al. (2000) for Geldart A particles:

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Eghbal-Ahmadi et al.: Optimization of Fluidized Bed of Oxidative Coupling of Methane

 U o  U mf    0.262   U  U mf   b  0.784  0.139 exp  o   0.272 

 e   mf  0.00061exp 

 U o  U mf    0.62 

  1  exp 

5

(4) (5) (6)

Some other important hydrodynamic parameters such as the mean bubble diameter and initial bubble diameter at the distributor were calculated from the equations of Miwa et al. (1972) and Mori and Wen, (1975). These equations are as follow: d bm  d b z  exp( 0.3 ) d bm  d b 0 dt

 U 0  U mf d b 0  1.38  1  No g 2  A

    

(7)

0.4

  dbm  0.65  dt2 (U 0  U mf )  4 

(8) 0.4

(9)

Changes in diffusivities of each component are accounted for as the gas composition varies along the reactor height. The inter-phase mass transfer coefficient of component A, Kbe, was calculated using the equation given by Sit and Grace (1981).

Kbe 

DmA mf U b 6  U mf 2  db  3  db

   

(10)

It is well known that the rate of heat transfer in fluidized bed is very high due to high mixing rate of solids. In fact, the rate of heat generated by the reaction is considerably lower than the rate of heat removed by solids movement. Therefore, the emulsion can be practically considered to be isothermal during the reaction. Of course, there is always a temperature difference between emulsion and incoming gas. However, due to high rate of heat transfer between bubble and emulsion, the incoming gas reaches the reactor temperature shortly after entering

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the reactor. Therefore, it was assumed that the fluidized bed reactor operates isothermally and it was not required to consider the heat balance in the reactor. 3. Stage wise feeding In the OCM process, one possibility to improve the selectivity is to alter the concentration profile of the reactants by stage wise feeding. For this purpose, it was suggested to keep the oxygen concentration low (Daneshpayeh et al., 2009b). In addition, by this method the heat released in the reaction is more distributed along the bed which provides a better temperature control. It was assumed that all the methane is introduced to the bed at the entrance of the reactor but the oxygen is injected throughout separate grids into the bed in a stage wise manner. Many studies have shown that secondary gas injections into the reactor enter the bed mainly as bubbles and mixes rapidly with other bubbles (Al-Sherehy et al., 2004; Sotudeh-Gharebagh et al., 2007). Therefore, it was assumed that the injected gas in each stage immediately is added to the bubble phase in a uniform manner across the bed. Figure (1) shows different feeding configurations considered in this work.

Section 4

Section 3

Section 2

Section 3

Section 2

Section 2

Section 1

Air Methan

1- (a)

Air Methan

1- (b)

Section 1

Section 1

Air Methan

Air Methan

1- (c)

1- (d)

Figure 1. Schematics of different feeding configurations 1-a: co-feeding. 1-b: stage wise feeding- one secondary injection. 1-c: stage wise feeding- two secondary injections. 1-d: stage wise feeding- three secondary injections.

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4. Optimization In the present work, it was desired to reach the maximum yield by considering that the selectivity should not decrease significantly. The fluidized bed reactor was modeled, solved and C2 yield was optimized for 2, 3 and 4 stages of oxygen injection which are shown in Figure 1. Each case was divided in two subproblems: a) Constant height of the reactor (6 m) in which the amount of catalyst is determined based on the voidage at the operating conditions. b) Constant amount of catalyst with no limitation on the height of the reactor. Therefore, the problems considered in this work include total 6 sub-problems which are listed in Table 3. Case-1 Case-2 Case-3 Case-4 Case-5 Case-6

Table (3)- The cases considered in this work Bed with a limited length of 6 m and 2 stages of injection No limitation for length of the bed and 2 stages of injection Bed with a limited length of 6 m and 3 stages of injection No limitation for length of the bed and 3 stages of injection Bed with a limited length of 6 m and 4 stages of injection No limitation for length of the bed and 4 stages of injection

The yield of C2 was considered as the objective function, defined by the following equation: YC2  S C2 

[ N CH 4  i  N CH 4  e ] [ N CH 4  i ]

 100

(8)

where SC2 that is the selectivity of C2 defined as: S C2 

[2  N C2 ] [ N CH 4  i  N CH 4  e ]

(9)

Decision variables and the constraints are listed in Table 4.

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Table (4)- Decision variables and their constraints Decision variables The constraints Methane flow rate (Uc) 0.03 to 0.5 m3/s Oxygen flow rate at each injection part (Ui) 0.03 to 0.5 m3/s (×0.21)* Operating temperature (T) 700 to 850 ̊C Length of each section of reactor (Lj) 0.5 to 4 m *Note that actually it is the air which entered to bed 4.1. Optimization method A genetic algorithm (GA) optimization method that operates in a continuous variable space was used for solving the optimization problem in this work. Continuous genetic algorithm is computationally fast and stable in converging to the global optimum, as it avoids plenty of bit operations and the imposition of boundaries on the variables, associated with binary code because a single floatingpoint number represents the variable instead of Nbits integers. The main GA parameters are presented in Table - 5. Table (5) - The GA parameters Parameters Value Population size, N 50 Generations 10000 Survival probability 0.5 Linear crossover probability 0.5 Mutation probability 0.167 5. Results and Discussion The C2 yield was maximized using the GA method. The optimum values of decision variables at maximum C2 yield in all 6 cases (listed in Table 3) are presented in Table 6. Dependence of the reactor length to C2 concentration at the optimum condition for the 6 cases mentioned above is shown in Figures 2 to 7. In each figure, abrupt alteration in the concentration profiles of C2 along the bed can be observed which correspond to the oxygen injection positions. These figures demonstrate that at the injection points of oxygen, the yield of C2 increases due to the fact that the reactions which consume oxygen and produce C2 products (especially the first reaction in Table 1) progress again. In case 1which oxygen is injected to 0.5 m above the inlet of the reactor, it is clear that the oxygen required for reactions finishes soon and new oxygen should be injected to avoid side reaction. After 1 m from the reactor feed point, there is no significant

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variation in C2 concentration. This conclusion is confirmed in case 2 in which the length of reactor is not fixed, thus, length of each section was calculated to be 0.501 m and 0.504 m, respectively. Therefore, increasing the length of reactor is not justifiable when large amount of oxygen is injected. This is important from the economic point of view. Almost the same conclusion can be made in the rest of cases 3 to 6. Table (6) - Optimum values of decision variables at maximum yield 2 sections L=6 m Oxygen flow at beginning of the reactor (m3/s) Oxygen flow at 2nd section of the reactor (m3/s) Oxygen flow at 3rd section of the reactor (m3/s) Oxygen flow at 4th section of the reactor (m3/s) Methane flow at beginning of the reactor (m3/s) Length of first section (m) Length of 2nd section (m) Length of 3rd section (m) Length of 4th section (m) Temperature (°C) Yield Selectivity

3 sections L=6 m

0.0840

2 sections No length limit 0.0420

4 sections L=6 m

0.0821

3 sections No length limit 0.0836

0.0825

4 sections No length limit 0.0833

0.0544

0.0222

0.0697

0.0525

0.0427

0.0500

-----------

----------

0.0833

0.0729

0.0531

0.0536

----------

----------

---------

----------

0.0834

0.0755

0.2442

0.1167

0.3844

0.3367

0.3960

0.3998

0.5002

0.5001

2.7371

0.5509

1.3580

0.6345

5.5000

0.5041

2.6448

3.3602

1.9840

3.9389

---------

----------

0.6182

0.6916

1.8347

0.5882

----------

---------

----------

----------

0.8233

1.0116

769.0625

780.6602

765.6748

756.0151

752.1580

746.0531

21.8231 47.8825

21.4691 48.1046

22.4093 48.6948

22.5179 48.3427

22.6512 46.9420

22.8685 47.1032

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Figure 2. C2 (ethane + ethylene) concentration profile. Case 1: A FBR with 2 sections, Length of reactor=6m.  

 

Figure 3. C2 (ethane + ethylene) concentration profile. Case 2: A FBR with 2 sections, no limitation for length.  

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Figure 4. C2 (ethane + ethylene) and methane concentration profiles. Case 3: A FBR with 3 sections, length of reactor=6m,  

 

Figure 5. C2 (ethane + ethylene) concentration profile. Case 4: A FBR with 3 sections, no limitation for length.  

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Figure 6. C2 (ethane + ethylene) concentration profile. Case 5: A FBR with 4 sections, length of reactor=6m,  

 

Figure 7. C2 (ethane + ethylene) concentration profile. Case 6: A FBR with 4 sections, no limitation for length. The optimum values of oxygen and methane flow rates, length of each section and operating temperature are shown in Table 6 for each case. The maximum C2 selectivity and yield of 47.1% and 22.87 %, respectively, were

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achieved for three secondary oxygen injections at operating temperature of 746.05 ºC. The C2 yield obtained in this work is approximately 4% higher than reported by Daneshpayeh et al. (2009b) while the optimum temperature is lower. Also, the results in Table 6 show positive effect of increasing the sections on the C2 yield in the OCM reactor. When the number of oxygen injections to the bed is increased, it leads to more uniform distribution of oxygen in the bed. In other words, further injections of oxygen predispose an appropriate amount of oxygen in all the bed. Therefore, this prohibits those undesirable reactions which progress due to high or low amount of oxygen in the bed and lead to decreasing the yield of C2. Figure 8 shows this positive effect of increasing the sections on the C2 yield in the OCM process.

Figure 8. Effect of number of sections on C2 yield. 5.1. Analyzing the effect of variables at optimum condition 5.1.1. Effect of temperature 5.1.1.1. Effect on yield and selectivity Figures 9 and 10 show the variations of C2 yield and selectivity respectively at different operating temperatures while other variables remained constant in their optimum values.

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Figure 9. Effect of temperature on C2 yield.

Figure 10. Effect of temperature on C2 selectivity. Initially, both C2 yield and selectivity increase by increasing the temperature. However, further increase in temperature results in decreasing yield and selectivity. This trend can be explained by the influence of temperature on progress of the reactions. At low temperatures, the reactions which cause increasing the yield and selectivity (such as the first reaction in Table 1) are faster

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than the others while at higher temperatures they become slower than others reactions. This happens due to the fact that the reactions with higher activation energy accelerate more than those reactions with lower activation energy. In the reaction network shown in Table 1, reaction 7 has the highest activation energy. This reaction consumes ethylene and causes a decrease in the yield or selectivity. Moreover, an appropriate range of temperature for high C2 yield and selectivity can be obtained in lower range of temperature in contrast with previous work done by Daneshpayeh et al. (2009b). Finally, it was found that the applicable range of temperature to gain the optimum range of yield of C2 explained as follows: For the reactor with 2, 3 and 4 sections, the optimum ranges are 730-830 ⁰C, 720-820 ⁰C and 710-810 ⁰C, respectively. Therefore, it is possible to operate in a lower band of temperature to obtain higher yields by increasing the number of oxygen injections and cause less side effect of high temperature. 5.1.1.2. Effect on ethylene/ethane molar ratio Ethylene is the most important product in the OCM process. Therefore, it is useful to determine the fraction of ethylene in the C2 product. Figure 11 shows the molar ratio of ethylene/ethane produced in reactors with various sections. It can be seen in this figure, the ratio of ethylene to ethane increases by increasing temperature. In fact, by increasing the temperature, the reactions which produce ethylene and consume the ethane overcome to others that prevent from increasing this ratio.

Figure 11. Influence of operating temperature on C2H4/C2H6 molar ratio

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5.1.2. Effect of distribution of oxygen In the cases of 2, 3 and 4 sections, for which there is no limitation on the length of the reactor, Tables 7, 8 and 9 show the influence of oxygen flow distribution on selectivity and yield of C2, C2H6 and C2H4 and conversion of methane. Similar to previous section the other variables remained constant in theirs optimum value. As you observed in two sections case, by increasing the ratio of second injected oxygen to first injected oxygen, C2 yield was increased until it reaches in its maximum value. However, in exceeded ratio, the C2 yield will decrease. It can be seen in Tables 8 and 9 that in cases of 3 and 4 sections, the effect of several kinds of oxygen distribution flow pattern similar to 2 sections can be observed. Table (7) - 2-sections YC2H6

YC2H4

YC2

SC2H6

SC2H4

SC2

XCH4

Distribution *** Increasing 0.2/0.8 3.8 14.9 18.8 9.1 Increasing 0.4/0.6 3.9 16.5 20.4 8.9 Equal 0.5/0.5 4.0 17.1 21.1 9.1 Decreasing 0.6/0.4 4.1 17.3 21.4 9.2 Decreasing 0.8/0.2 4.2 17.1 21.3 9.4 ***: The second column of table-7 indicates the ratio of:

35.9 37.7 38.5 38.8 38.5

45.1 46.6 47.5 47.9 47.9

41.7 43.8 44.3 44.6 44.5

SC2

XCH4

Distribution *** Equal 0.33/0.33/0.33 4.6 17.7 22.2 9.8 38.0 47.8 Decreasing 0.5/0.33/0.17 4.4 17.5 21.9 9.2 36.5 45.7 increasing 0.17/0.33/0.5 4.5 16.7 21.2 10.4 38.8 49.2 ***The second column of table - 8 indicates the ratio of:

46.5 47.9 43.1

Oxygen flow at beginning the reactor / oxygen flow at second section

Table (8) - 3-sections YC2H6

YC2H4

YC2

SC2H6

SC2H4

oxygen flow at beginning the reactor/ oxygen flow at second section/ oxygen flow at third section

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Table (9) - 4 sections YC2H6

YC2H4

YC2

SC2H6

*** 0.25/0.25/0.25/0.25 4.5 18.1 22.6 9.3 0.4/0.3/0.2/0.1 4.4 17.8 22.3 8.9 0.1/0.2/0.3/0.4 4.4 17.1 21.5 9.7 *** The second column of table - 9 indicates the ratio of: Distribution Equal Decreasing Increasing

SC2H4

SC2

XCH4

37.4 46.7 48.5 35.8 44.7 49.8 38.1 47.9 45.0

oxygen flow at beginning the reactor/ oxygen flow at second section/oxygen flow at third section/ oxygen flow at forth section.

6. Conclusion Optimization of process variables and effects of operating temperature, oxygen distribution flow pattern and the number of injection on reactor performance in the OCM process in a fluidized bed reactor with stage-wise feeding was investigated. The optimized values of process variables, including methane flow rate, oxygen flow rate at each injection part, operating temperature and length of each section of the reactor, were obtained to obtain maximum yield of C2. The maximum C2 selectivity and yield of 47.1 % and 22.87 %, respectively, were achieved for three secondary oxygen injections at operating temperature of 746.05 ºC. This yield is approximately 4% higher than the previous work reported by Daneshpayeh et al. (2009b). Results from studying the effect of temperature and distribution pattern of injected oxygen to the reactor performance and the effect of the number of injections on C2 yield were presented. Moreover, it was found that C2 yield increases by increasing the number of injections. Notation A CA CAb CAe Conv db db0 dbm dt DmA ∆H ad ,O

area of the bed, m2 CA average concentration of component A , kmol/m3 concentration of component A in bubble phase, kmol/m3 concentration of component A in emulsion phase, kmol/m3 conversion mean bubble diameter , m initial bubble size formed above the distributor orifices, m maximum bubble size of the bed, m bed diameter, m diffusion coefficient of A in mixture (m2/s) adsorption enthalpy for O2 , kJ/mol

Ej g

activation energy in the reaction step j , kJ/mol gravity constant, m/s2

2

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i -

H C

e -

4

H C

Kbe Lj No N N N

4

2

C

2

C

P rAb rAe S T Ub Ue Umf U0 Y z

Vol. 10 [2012], Article A2

2

C

bubble to emulsion mass transfer coefficient , 1/s length of each section, m number of the orifice in the distributor moles of CH4 at feed moles of CH4 at the end of reactor produced moles of C2 (ethane + ethylene) partial pressure, Pa reaction rate based on component A in bubble phase, kmol/m3 · s reaction rate based on component A in emulsion phase, kmol/m3.s selectivity of C2 reactor operating temperature, K bubble velocity, m/s emulsion gas velocity, m/s minimum fluidization velocity, m/s superficial gas velocity, m/s yield of C2 axial position above the distributor, m

Greek Letters



b e  mf

bubble phase fraction bubble phase porosity emulsion phase porosity bed porosity at minimum fluidization velocity

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