Dev. Chem. Eng. Mineral Process., 6(3/4),pp. 197-210, 1998. The Utilization of Fluidized Bed Reactors for Oxidative Coupling of Methane S.M. Al-Zahrani"and A.E. Abasaeed Chemical Engineering Department, King Saud University,PO Box 800, Riyadh 11421, SAUDIARABIA A simple mathematical model for the oxidative coupling of methane in a fluidized bed reactor has been developed in order to investigate the possibility of exploiting the advantages of this reactor ConJgurationfor the important exothermic reaction, and also to provide an insight into potential scale-up behaviour. The model is based on the two-phase theory offluidization, and the reaction kinetics are based on triangular kinetics obtained @om the literature. hydrodynamic or Without aausting any of the kinetic parameters, the model predicted fairly well the experimental results obtainedfim the literature under various reaction conditions, and it was then used to investigate the eflect of scale-up on theconversion and selectivity obtained in the methane oxidative coupling process. High C-2 selectivities at reasonably high methane conversions are shown to be possible with large scale fluidized bed reactors. Keywords: Oxidative coupling; methane; modelling;fluidized bed reactors. Introduction Methane conversion to more valuable products is one of the most challenging problems and has been the subject of intensive research in recent years. The work of 'Author for correspondence. 197 S.M. Al-Zahrani and A. E. Abasaeed Keller and Bhasin [l] has drawn worldwide attention to oxidative coupling of methane through catalytic processes to produce ethane and ethylene. Considerable progress has been made in the development of a large number of catalysts; mainly metal oxides such as Li/MgO, F%O/Al2O3, Mn2O3/SiO2, Sr/LaZO3, La2O3/CaO, Zr/La/Sr, etc., for oxidation of methane to ethane and ethylene [2-6]. Fluidized bed reactors are used extensively in the chemical industry, however very few papers have been published regarding the use ( a d o r model) of fluidized bed reactors for methane coupling [4-8]. Compared to fixed bed reactors, the fluidized bed reactors are advantageous. Operation of fixed bed reactors is hampered by the excessive heats which are generated by these highly exothermicreactions. In contrast, fluidized bed reactors can operate under essentially isothexmal conditions due to their high mixing. These reactors also offer the advantages of ease of addition and withdrawal of the catalyst, and relatively low-pressure operations. In this paper a simple yet relatively rigorous model foroxidativecouplingof methane in a fluidized bed reactor is developed. Themodelisbasedonthetwophase theory of fluidization. The hydroaynamc parameters are obtained from the literature, and the kinetic mechanism is based on the triangular kinetics of Gee& et al. [9] which accounts for the conversion of C2 to CO,. This preliminary investigation is intended to serve the twin objectives of providing a relatively rigorous model and a chance to explore the problem of scale-up. A comparison of model predictions with data obtained from the literature is also presented. The results of the numerical simulations (conversion, selectivity, and yield) in a largescale fluidized bed reactor for different operating conditions are also presented. The Model Recognizing the two regions in the fluidized bed reactor, the two-phase theory of fluidization is used to model the oxidative coupling reaction of methane. The bed is considered to be composed of two phases: (I) a bubble phase devoid of catalyst particles and in the plug flow regime; and (2) a completely mixeddensephase consisting of catalyst particles together with interstitial gas. Thedensephaseis considered to be at incipient fluidization conditions. All gas in excess of that 198 Fluidized bed reactorsfor oxidative coupling of methane required for minimum fluidization passes through the bubble phase. Heat and mass are exchanged between the two phases. The relevant hydrodynamic parameters are obtained from the literature and are given in Table 1. The ideal gas law is assumed to apply for the gas in both the bubble and dense phases. The effect of temperature on the gas density, heat capacities of the various components and the heat of reaction has been taken into consideration. Reaction Kinetics The intensive work devoted in recent years to methane coupling Over a wide variety of cataIysts has shown that the detailed reactionpathwaysandthecorresponding kinetic parameters are functions of composition and catalyst type. In this paper, in order to emphasize the reaction engineering aspectsinafluidizedbedractor, we have chosen to keep the kinetic model of the system as simple as possible, while maintaining a reasonably accurate description of the process. For this purpose the 3lump reaction network kinetics obtained by Geerts et al. [9] are used in this investigation. The reaction network differentiatesbetween C1 (CH4) lump, the C2 (C2Hg and C2H.4 at a ratio of2:3) lump, and the COX(C02 and CO at a ratio of I:1) lump. Geerts et al. [9] report that both ratios are realistic with respect to the experimental results. The schematic representation of the kinetic model is shown below: The rate expressions are given by Geerts et al. [9]as: (a) For the conversion of CH,to CZ: --100 rl = 0.016 e P&, 9 0.3 Po2 I99 S.M.Al-Zuhrani and A.E. Abasaeed Table 1. The hydrodynamic,transport and physical parameters. I Theoretical or empirical expression P-eter I Bed voidage atminimumfluidization [I21 Superficial velocity at minimum fluidization [ 131 I x Bubble diameter [141 Bubble rising velocity [151 -0.3yD dB= dM - ( d , - dBo)e d , = 0.652[A(U0 dBo= 0.00376(U0- UM )2 U,= U,- U, + 0.71l(g.d,)’’ Fraction of bubble phase [151 coefficiat for mass transfer [151 I Coefficient for heat trausfer [151 Heat transfer coefficient [161 Binary diffusivity [17 Difhivity in mixture [17] 200 Fluidized bed reactors for oxidative coupling of methane - - 70 (b) For the conversion of cH4 to COX: r2 = 0.02 e (c) For the conversion of C,to COX: r3 = 03 e R T ROT P g , Pdf --150 c, 0 2 Maw and Energy Bolonces The mass and energy balances in the bubble and dense phases of the fluidizedbed reactor at steady-state are given below. 0) The bubble phase At steady-state, the mass balance equation for componentj and the energy balance equation in the bubble phase are given by: dT p C Q b = H A ( T - T ) g p g b h b d b d b (ii) The dense phase The mass balance equation for component j in the dense phase forsteady-state conditionsis given by: and pti is the stochiometriccoefficient of componentj in reaction i. 201 S.M. Al-Zahrani and A.E. Abasaeed The change in volumetric flow rate in the dense phase due to the change in the number of moles due to the reaction is given by: At steady-state, the energy balance for the dense phase is given by: Results and Discussion In order to solve the set of the nonlinear algebraic equations (five mass balance equations) given by Equation (3), an IMSL subroutine called Zspow is used [101. To ensure accuracy of calculation, double precision was used throughout the calculations and also the number of significant digits was set at 12. The solution starts by setting the dense phase temperature at a certain value and giving initial guesses for the distribution of the five components (CHq, 02, C2, COX and H20). The heat capacities and heats of reactions are calculated at the set dense phase temperature. The five mass balance equations given by Equation (3) are solved simultaneouslyfor the chosen value of dense phase temperatureuntil a solution is obtained. During the search for a solution, the density of gas, the diffusivities, and the values of the d o n rates are updated based on the values of the iterative distribution of the five components. The molar values of the five components to which the solution converges are used to calculate the heat function(Equation5). Thisprocedureis repeated by incrementingthe value of the dense phase temperature. This method of solution is employed in order to ensure that all possible steady-state (stable or unstable) solutions are obtained 202 The steady-state values of the dense phase Fluidized bed reactors for oxidative coupling of methane temperature are those values which satisfy Equation (5). The molesofthefive components and the dense phase temperature are usedtocalculatetheexitmolar flow rates of the five components and the exit temperature of the bubble phase. The total number of moles of each component (moles out) is the summation of the moles of that component in the dense phase and at the exit conditions (z = H)of the bubble Phase. Comparison of Simulated and Ejgperimental Reactor Pmformance Santos et al. (81 compared the performance of a fluidized bed with a vibrofluidized bed (viiration is induced in the bed to avoid particle agglomeration at low fluidization velocities). In Figure 1, a comparison between the current model predictions using experimental data for methane oxidative coupling in a fluidized bed reactor obtained from Santos et al. [8] is presented. In order to provide a basis for the comparison, the following parameter values given by Santos et al. [S]are used in the simulation: the reactor height is taken to be 30 cm,bed diameter is 3 cm,particle size is 120 pn (they report a range of 100-250 pm), and a feed methane to oxygen ratio ranging from 9:l to 2:1. Figure 1 shows excellent agreement between the model predictions (none of the model hydrodynamic or kinetic parameters have been adjusted) and the experimental values in the conversion range of 10-35%; the deviation between model predictions and experimental data tends to increase with the decrease of methane conversion. However, in the promising and most practical range of methane conversion, the model showed excellent performance. The madel performance has also been compared to the experimentaldataof Edwards et al. [I.In this simulation, the reactor diameter is taken to be 2.5 cm and the ratio of superficial velocity to the velocity at minimum fluidization conditions is equal to 13 as reportedby Edwards et al. [7]. Figure 2 shows the match between the model predictions (shown as lines) and the experimental data (shown as symbols) for the variation of % methane conversion and for % C2 selectivity with % oxygen in the feed. Figure 2 shows excellent agreement betweenthemodelpredictionsandthe experimental data for both methane conversion and C2 selectivity. The percentage deviations between model predictions and experimental data for 02 loadings of 5.6% 203 S.M.Al-Zahrani and A.E. Abasaeed and 10.7% respectively are: for methane conversion -2.0 % and 0.00/4 and for C2 selectivity +7.3% and 4.1%. 6 16 10 26 20 40 36 30 CH4 conversion (%) F w e 1. Comparison between experimental data of Spntos et al. f8J and model predictions CC, selectivity vs. methane conversion). 2s 100 - t Moddpndktbn. 0 l . . . l . . . , . . . ~ . . . l . . . l . . . ~ . . . 4 S 6 7 8 9 10 11 12 0 2 in hod (%v/v) F i e 2. Comparison between model predictions and experimental data of Edwards et al. [7] for methane conversion and C2 selectivity vs % oxygen in the feed These two comparisons demonstrate that this model in itspresentformatcan provide an adequate tool for studying the large scale applications of fluidized bed reactors for oxidative coupling of methane. No industrial (large-scale) data is 204 Fluidized bed reactorsfor oxidative coupling of methane available at the present time. However, based on the success in predicting experimental data, the potential for using large-scale fluidized bed reactors for methane oxidative coupling is investigated. Large-Sca&muidizedBed Recrctors The effects of methane to oxygen feed ratio and reactor height on the performance of a large-scale fluidized bed reactor are discussed below. The reactor has a diameter of 460 cm and height of 230 cm, catalyst particle diameter is 75 pm, the super&icial velocity is 7.5 times the minimumfluidizationvelocity, and the pressure is 1 am. II am an mm mK 1= qoo F i r e 3. The variation of the (a) heatfunction curve, (b) methane and oxygen conversion and (c) C2 selectivity and yield with the reactor dense phase temperature fir CHq:O2=6:1 and 9:l. 0) Eflect of methane to o m e nfeed ratio Figure 3 shows the variation of the heat function (given by Equation 5), methane and oxygen conversion, C2 selectivity and yield for reactor dense phase temperature (Td) 205 S.M.Al-Zuhrani andA.E. Abasaeed variations for two methane to oxygen feed ratios (CH4:Oz = 6:1 and 9: 1). It is clear from Figure 3a that in the range of operating temperatures of practical importance there is a single stable steady-state (the stability of this state has been confirmed by other simulation techniques). The steady-state dense phase temperatures which correspond to a heat function value of zero in Figure 2%are about 1056 and 1033K for methane to oxygen feed ratios of 6: 1 and 9:l mpectively. As shown in Figure 3b, the steady-state methane conversions are found to be 31.8% and 24.1% for feed ratios of 6: 1 and 9:l respectively with the corresponding oxygen conversionsof 96.2% and 96.5%. Higher selectivitiesof C2 (90.1%) but lower yields (21.7%) are obtained at the higher feed ratio (CHq:O2 =9:1) compared to values of 84.5% for selectivity and 26.0%for yield for CH4:O2 = 6:l as shown in Figure 3c. (ii) Efect of reactor length Figures 4(ad) show the variation of the bubble phase temperature, oxygen conversion, methane conversion and C2 yield over the height of the fluidized bed reactor, for a W o n temperature of 1056K and methane to oxygen ratio of 6:l in the feed. From Figure 4%the bubble phase temperature reaches a steady-state value (same as the dense phase temperature) after a relatively short distance above the distributor (about 8% ofthe total bed height). This important result is indicative of the effectiveness of a fluidized bed configurationin uniformly distributing the large amounts of hirated heat due to the exothermic reactions in the bed(av0iding m w a y temperatures which could be experienced with a fixed bed configuration). The oxygen conversion curve along the reactor is shown in Figure 4b, and almost all of the oxygen is depleted at about 35% of the total bed height. This agrees well with the experimentalfindings of Edwards et al. [111 in a small reactor which showed that oxygen has been depleted after a relatively short distance above the distributor leaving an essentially oxygen-& environment above that distance. Since no oxygen is available for the reaction, the methane conversion curye reaches a plateau as shown in Figure 4c. The variation of C2 yield along the fluidized bed reactor height is shown in Figure 4d. 206 Fluidized bed reactors for oxidative coupling of methane 5 'E e 76 #) 0 0 40 80 120 160 200 240 Height (cm) 0 40 80 120 180 #K) 240 Height (cm) F i r e 4. The variation of (a)bubble phase rmpmtut-e,(b) oxygen conversion, (c) m e t h e ememion. and (4 CZyieUalong the length of the mctorfor CH402 = 6:l. It is an important assumption that only 35% of the total bed height (80 cm of the 230 cm bed) appearsto be needed to achieve the desired conversion, selectivity and However,for a total bed of 80 cm,the mass and heat transfer area (important factors in a fluidized bed configuration)will be smaller which could result in lower yield. conversion, selectivity and yield. Numeric simulationwith a total bed height of only 80 cm (all other parameter values are fixed) confirmed this hypothesisas the methane conversion dropped to 20% at a selectivity of 59% (i.e. only 12% C2 yield is possible for H = 80 cm). Conclusions In this paper a relatively rigorous yet mathematidy simple model has been prtsented for oxidative coupling of methane in a fluidized bed reactor. The model is based on the two-phase theory of fluidization and uses a 3-lump kineticmodel obtained from the literature. Comparison of model predictions with experimental data obtained from the literature is excellent. The model results confirm the applicability of fluidized bed reactors for the methane oxidative coupling reaction. 207 S.M. Al-Zuhrani and A.E. Abasaeed The results also show that higher selectivities are obtained athighermetbaneto oxygen feed ratios. Nomenclature A Ab Ad dB 43M 430 2ij cdj Coj CTef Crn’CPI D Ei g H b, HW KW Kbc Kcd %j Nbjo Ndj Ndjo NQ pcH4 Qf ‘i Remf R Tb Tbo Td 208 cross sectional area ofthe fluidized bed (cm2) Cross sectional area of the bubble phase (an2) cross sectional area ofthe dense phase (cm2) Bubble diameter (cm) Maximum bubble diameter (cm) Initial bubble diameter (cm) Catalyst particle diameter (cm) Concentration of component j (i=1,2,3,4,5) in bubble phase (m0~~m3) Concentration of componentj in dense phase m0v~m3) Initial concentration of componentj moVCm ) Reference gas concentration (moVcm ) Molar heat capacity of gas and solid respectively (J/mol K) Bed diameter (cm) Activation energy for reaction i i=1,2,3) (kJ/mol) Gravitational acceleration (cm/s ) Bed height (cm) Wall heat transfer coefficient (J/cm2 s K) Interphase heat transfer coefficient between bubble anddense phase based on bubble phase volume (J/cm3 s K) Interphase mass transfer coefficient between bubbleanddense phase based on bubble phase volume (s-l) Interphase mass transfer coefficient between bubbleandcloud phase based on bubble phase volume (s-1) Interphase mass transfer coefficient between cloud anddense phase based on bubble phase volume (s-l) Average thermal conductivityof the gas (J/cm s K) Molar flow rate of componentj in bubble phase (moVs) Initial molar flow rate of componentj in bubble phase (moVs) Molar flow rate of componentj in dense phase (moVs) Initial molar flow rate of componentj in dense phase (moVs) Molar flow rate of componentj in feed phase (moVs) Partial pressure of methane (atm Volumetric flow of the feed (cm /s) Rate for reaction i (i=1,2,3) (moVkt s) Reynold number at minimum fluidization Gasconstant Bubble phase temperature (K) Bubble phase temperature @ z = 0 (K) Dense phase temperature (K) I $ 4 4 Fluidized bed reactors for oxidative coupling of methane Dense phase temperature @ z = 0 (K) Feed gas t e m p e m (K) Reference temperature (K) WaU temperature (K) Bubble velocity ( d s ) Velocity of gas through emulsion phase ( d s ) Inlet gas velocity ( d s ) Minimum fluidizationvelocity (cm/s) Mole fiaction of component j Distance along the reactor length (cm) Tdo Tf Tref Tw vb Ue UO unlf yj z Greek letters s %f P p* PS 4s Fraction of bed consistingof bubbles Void fiaction at minimumfluidization viscosity s) Density of gas wcm3) Density solids (g/cm3) Sphericity (=1) References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 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