Comprehensive Kinetics of Oxidative Coupling of Methane over the

Res. , 1997, 36 (7), pp 2568–2579 ... A comprehensive 10-step kinetic model of the oxidative coupling of methane to C2+ ... reactor covering a wide ...
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Ind. Eng. Chem. Res. 1997, 36, 2568-2579

Comprehensive Kinetics of Oxidative Coupling of Methane over the La2O3/CaO Catalyst Z. Stansch,† L. Mleczko,* and M. Baerns‡ Lehrstuhl fu¨ r Technische Chemie, Ruhr-Universita¨ t Bochum, D-44780 Bochum, Germany

A comprehensive 10-step kinetic model of the oxidative coupling of methane to C2+ hydrocarbons over a La2O3/CaO catalyst was developed on the basis of kinetic measurements in a microcatalytic fixed-bed reactor covering a wide range of reaction conditions (1 < pO2 < 20 kPa, 10 < pCH4 < 95 kPa, 700 < T < 955 °C, 0.76 mCat/V˙ STP e 250 kg‚s/m3). The reaction scheme contains three primary and seven consecutive steps. The conversion of hydrocarbons and of carbon monoxide with oxygen were described by applying Hougen-Watson type rate equations. For the other reactions power-law rate equations were used. From the experimental data kinetic parameters, i.e. frequency factors, apparent activation energies, and adsorption enthalpies, were estimated. With the kinetic model the experimentally determined conversions of methane and oxygen, as well as yields to C2 hydrocarbons and carbon oxides, could be predicted with an average accuracy of (20%. 1. Introduction The catalytic oxidative coupling of methane (OCM) to higher hydrocarbons is considered as a prospective route for the utilization of natural gas as a chemical and petrochemical feedstock. Since 1982, an intensive research has been carried out with the aim to develop new active and selective catalysts. During this time for several catalysts C2+ yields of more than 20% were obtained. However, further improvement of the catalytic performance, by developing more selective catalysts and by reaction engineering means, is necessary in order to make this process commercially viable (Baerns et al., 1994). The results obtained in the last few years in microcatalytic fixed beds indicate, however, that due to the higher reactivity of C2+ hydrocarbons compared to those of methane the internal limit for maximum C2+ yield in fixed-bed reactors has been approached (see, e.g., Anemomiya et al., 1990 and Maitra, 1993). The more promising approach seems to be the improvement of C2+ selectivity and yield by developing new, alternative reactor designs. This conclusion is supported by the results obtained with the countercurrent chromatographic reactor (Tonkovich et al., 1993) and with the electrocatalytic reactor-separator reactor (Jiang et al., 1994). The development and verification of new reactor designs for the oxidative coupling of methane was pursued until now mainly experimentally (for a review see Mleczko and Baerns, 1995). However, due to the complexity of the OCM reaction, this method of approach is time consuming and costly. The more efficient, model-based reactor development has been limited by the inaccuracy and insufficiency of the available kinetics of chemical reactions. The majority of kinetic studies reported for the OCM catalysts are related to investigations of the primary reaction steps (for a review, see Lehmann and Baerns, 1991). On the * To whom correspondence should be addressed. Fax: +0049234/709 4115. † Present address: Procter & Gamble European Service GmbH, Sulzbacher Strasse 40, D-65823 Schwalbach a/Ts, Germany. ‡ Present address: Institut fu ¨ r Angewandte Chemie BerlinAdlershof e.V., Rudower Chaussee 5, Geb. 9.9, D-12484 Berlin, Germany. S0888-5885(96)00562-3 CCC: $14.00

other hand studies performed for several catalysts indicate that consecutive reactions can determine the overall reactor performance (see e.g. Ekstro¨m, 1992; Baerns et al., 1993, and Chen et al., 1994). Although several models which take into account the importance of consecutive reactions were already proposed in the literature (see Table 1), their use for reactor simulation and scale-up is limited due to the narrow range of validity. Against this background the work reported in this paper aimed at the development of comprehensive kinetics for the oxidative coupling of methane that can be used for prediction of reactor performances under a wide range of reaction conditions and for various gassolid contacting modes. The kinetic investigations were performed in a microcatalytic fixed-bed reactor over a La2O3/CaO catalyst. This catalyst was found to be very active and selective toward C2+ hydrocarbons (Becker and Baerns, 1991). On the basis of experimental data the most suitable reaction network, rate equations, and kinetic parameters were determined. In the paper the developed kinetics is presented and discussed with respect to its generic character for other OCM catalysts. 2. Experimental Section Catalyst. The La2O3 (27 at. %)/CaO catalyst, was prepared by wet impregnation of CaCO3 (Rheinische Kalksteinwerke, Wu¨lfrath, Germany) with an aqueous solution of La(NO3)3‚6H2O (Janssen Chimica, Bru¨ggen, Germany). After 12 h of drying at 120 °C, the precursor was calcined at 800 °C for 24 h. Finally, the catalyst was crushed and sieved in order to recover the desired size fractions. In the kinetic measurements, particles with diameters dp ) 0.250-0.355 mm were applied. The particle density and BET surface amounted to 3600 kg/ m3 and 2.2 m2/g, respectively. Reactor and Gas Analysis. A microcatalytic fixedbed reactor (ID ) 6 mm) made of quartz was used (see Figure 1). To suppress homogeneous gas-phase reactions, the precatalytic section was filled with quartz particles of the same diameter as the catalyst. In order to minimize the extent of postcatalytic gas-phase reactions, the gas left the reactor through a capillary (ID ) 2 mm). For minimizing temperature gradients the catalytic bed was diluted with quartz particles having © 1997 American Chemical Society

Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2569 Table 1. Reaction Engineering Kinetics for the OCM Reaction catalyst

reaction scheme

products

T, °C

pO2, kPa

pCH4, kPa

ref

BaCO3/La2On(CO3)3-n Sm2O3 La2O3/BaCO3 model catalyst

5 steps, complex 4 steps 5 steps 3 catalytic and 4 homogeneous steps 4 steps 2 catalytic steps and 1 homogeneous step 3 steps 4 consecutive steps 6 catalytic and 2 homogeneous steps 2 catalytic and 2 homogeneous steps

C2H6, C2H4, COx C2H6, C2H4, COx C2H6, C2H4, COx C2H6, C2H4, CO, CO2

680-720 650-700 720-800 700-850

4.5-6.5 n.n. 4-9 5-20

9-22 n.n. 34-59 60-95

Olsbye et al., 1992 Otsuka et al., 1986 Ding et al., 1991 Dutta and Jazayeri, 1992

C2H6, C2H4, CO2 C2+, COx

650-700 700-820

3-13 5-10

17-65 40-70

Hinsen at al., 1984 Mleczko et al., 1990

C2+, COx C2H6, C2H4, CO, CO2 C2H6, C2H4, CO, Co2

650-750 800 750

n.n. 5-24

n.n. 5-23

Geerts, 1990 Roos et al., 1989 Bartsch, 1991

C2+, COx

700-800

1.4-7

7-21

Santamaria et al., 1991

PbO/Al2O3 PbO/Al2O3 Li/MgO Li/MgO Ce/Li/MgO Na/NiTiO3

were derived as the average value from three to four GC-analyzes. For all experiments, carbon balances were better than 98% and a in majority of experiments were above 99%. The accuracy of oxygen balances was higher than 90% and in most experiments was above 95%. 3. Method of Parameter Estimation

Figure 1. Reactor used for the catalytic experiments.

the same particle size. Dilution ratio varied from 1 to 6. To achieve high external heat exchange coefficients and hence good temperature control, the reactor was immersed in a thermostated fluidized bed of sand. The temperature profiles in the catalytic bed were measured by an axially movable thermocouple, placed in a quartz well. The well was located in the axis of the reactor. Flow rate of all gas components, CH4 (99.95%), O2 (99.95%), C2H6 (99.95%), C2H4 (99.7%), CO2 (99.995%), and N2 (99.99%), were controlled by mass flow controllers. A mass flow controller was also applied for stabilizing the flow of water added to the reaction mixture. Water was vaporized before mixing with other gases. The inlet and outlet gas was analyzed by online gas chromatography, condensing the water before the analysis. Oxygen concentration was additionally monitored by an electrochemical gas analyzer for determining steady-state operation. The details of the experimental equipment are described elsewhere (Stansch, 1995). Experimental Procedure. The reactor was heated before each series of experiments in a stream of nitrogen. At a temperature of approximately 600 °C the reactor was switched to the feed gases. The analysis of the product gas composition was carried out when the hot-spot temperature fluctuations were within a range of (2 °C and the oxygen concentration at the reactor outlet was constant for at least 10 min. All experimental data used for the development of the kinetic model

Parameter Estimation. The catalytic reactor was described by a one-dimensional, pseudo-homogeneous plug-flow model. Furthermore the changes of gas volume during the reaction were taken into account. In case of homogeneous gas-phase reactions the model included also postcatalytic sections, i.e. gas volume in the postcatalytic zone and in the capillary. Since not all experiments could be performed under isothermal conditions, the local reaction rates were calculated by applying experimental profiles of temperature. The parameters of the kinetic model were estimated applying the random search method (Edgar and Himmelblau, 1989). In order to reduce the computation time, a search direction generated by the generator of random numbers had been kept constant until no further improvement of the goal function was achieved. For this one dimensional optimization step, the modified Fibonaci method was applied. In the optimization routine the sum of logarithmic likelihood function (see eq 1) calculated on the basis of experimental data and

n log(Lj) ) - (log(2π) + 1) 2 2 n γn 1 n (xi,j - xˆ i,j) log log(Yi,j) (1) 2 ni)1 2i)1 Yiτ

(

∑

)

∑

model prediction for yields of ethane, ethylene+ (this pseudocomponent includes ethylene, propane, and propene), carbon monoxide, and carbon dioxide was maximized. The optimization procedure was initiated from various starting points in order to achieve a global minimum of the objective function. The starting values for the optimization routine were mostly determined from the analysis of the dedicated experiments aiming at the investigation of the selected reaction steps (see below). On this stage also other optimization routines were applied. The details of the applied routines are given elsewhere (Stansch, 1995). Method of Approach. The complexity of the OCMreaction network led to a large number of reactions and estimated parameters. Consequently, long computation times limited the number of tested alternative models.

2570 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 Table 2. Experimental Range of Reaction Conditions Applied in the Experiments reaction conditions range

THS, °C

p°CH4, kPa

p°O2, kPa

p°-CO2, kPa

p°C2H6, kPa

p°H2O, kPa

mCat/V˙ STP, kg‚s/m3

ptot., kPa

V˙ STP, m3/s

700-955

10-95

1-20

1-8

2.5, 6.5

20

7.6 × 10-1-250

100-130

4 × 10-6-13 × 10-6

conversion selectivities range

XO2, %

XCH4, %

SC2+, %

SC2H6, %

SCO, %

SCO2, %

15-100

0.9-32.7

15.7-75.2

1.2-33

4.5-66.7

5.4-46.3

In order to overcome this obstacle, the estimation procedure was decomposed into three stages. In the first stage, kinetics of single reaction steps or submodels containing only a limited number of reaction steps were analyzed on the basis of results from dedicated experiments. Calculations performed at this stage aimed at selection of the most important reaction steps and most suitable rate equations. In the second stage, complete reaction networks were analyzed on the basis of the reduced set of experimental data. At this stage, various alternative kinetic schemes and rate equations were analyzed. Finally, for the selected network and rate equations, kinetic parameters were determined on the basis of the full set of experimental data. At each stage, parameters determined in the previous step were used as starting points for optimization routines. When this strategy was applied, the calculation time was significantly reduced compared to the one-stage parameter estimation. 4. Experimental Results The range of experimental conditions, measured conversions, selectivities, and parameters characterizing catalytic performance are summarized in Table 2. 4.1. General Observations. The La2O3/CaO catalyst exhibited constant catalytic activity and stability during the kinetic measurements. As main products ethane, ethylene, hydrogen, carbon monoxide, carbon dioxide, and water were identified. Selectivity to C3+ hydrocarbons, mainly propane and propylene, was in all experiments below 3%. At low temperatures (T < 700 °C) traces of formaldehyde were detected. Although the catalytic bed was diluted with quartz, isothermal conditions were not always obtained; temperature gradients amounted up to 150 °C. Therefore, the temperatures reported in the following refer to the hot spots. Experiments performed applying a bed of quartz confirmed that at investigated reaction conditions (T < 830 °C, τ < 0.2 s-1) gas-phase reactions of methane could be neglected. 4.2. Effect of Temperature and Contact Time on the Conversion and Yield. The effect of contact time on the conversion of methane and oxygen as well as yield of ethane, ethylene, carbon monoxide, and carbon dioxide is presented for different temperatures (700 and 830 °C) in Figure 2. Conversion of Reactants. At 830 °C almost complete conversion of oxygen (XO2 > 95%) was already achieved for the contact time of 25 kg‚s‚m-3 (see Figure 2a). At 700 °C conversion of oxygen increased slowly with the contact time compared to the dependences measured at 830 °C; i.e., for 50 kg‚s‚m-3, the conversion approached only 50%. The course of the conversion of methane corresponded to that of oxygen. When oxygen conversion was complete, no further increase of methane conversion with contact time was measured. Higher Hydrocarbons. The course of the ethane yield characteristics at short contact times indicates that

this component is formed as a primary product of the OCM reaction (see Figure 2b). At longer contact times the characteristics of the ethane yield depended on temperature. At low temperatures the yield of ethane leveled off although oxygen was still available. At high temperatures (T > 800°C) the ethane yield characteristics passed through a maximum. This part of the characteristics indicates that yield of ethane is strongly influenced by consecutive reactions, especially at high temperatures. The dependence of the yield of ethylene on the contact time at low values of this parameter confirms the generally accepted thesis that ethylene is formed in a consecutive reaction of ethane. However, the leveling off observed at long contact times indicates that ethylene also is an intermediate product of the OCM reaction. The overall yield of C2+ hydrocarbons (not shown) depended on the reaction conditions; at high temperatures and high partial pressures of oxygen, C2+ yield passed through a maximum with respect to the contact time. Also for the C3+ hydrocarbons the yield passed at high temperatures through a maximum (not shown). The drop of the yield of C3+ hydrocarbons is similar to the one observed for ethane, and the leveling off of ethylene occurred at high temperatures in the range of contact times where oxygen was already completely converted. Carbon Oxides and Hydrogen. The steep gradients of the yield to carbon monoxide measured for all temperatures at short contact times indicate that this component is formed as a primary product of the OCM reaction (see Figure 2c). For long contact times (mCat/V˙ > 15 kg‚s‚m-3) and low temperatures (T < 750 °C) the characteristics leveled off. At high temperatures (T > 750°C) the yield of carbon monoxide passed, with respect to contact time, through a maximum; the drop of the yield occurred at high temperatures mainly in the range of contact times for which oxygen was still available. However, when oxygen was completely converted, the yield decreased further with the contact time. The yield of hydrogen (not shown) exhibited a dependence on the contact time that was very similar to the one observed for carbon monoxide. The dependence of yield to carbon dioxide increased for all temperatures with the contact time. As for the other components, two regions can be determined; a fast increase at short contact times, which indicated that carbon dioxide is also formed as primary product, and a significantly slower one at long contact times. The change in CO2 was continued even when oxygen was depleted. 4.3. Conversion of Hydrocarbons in the Absence of Oxygen. The results obtained in the absence of oxygen indicate that further reactions like pyrolysis or steam-reforming of hydrocarbons can proceed in OCM reactors. In order to elucidate the extent of these reactions and their nature, with respect to their heterogeneous catalytic or noncatalytic homogeneous course, dedicated experiments were performed. The extent of gas-phase reactions was analyzed replacing the catalyst

Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2571

Figure 3. Conversion of ethane and yield of ethylene vs temperature in the gas phase and over the La2O3/CaO catalyst. Reaction conditions: mCat/V˙ ) 1 g‚s/mL, coC2H6 ) 5%, coH2O ) 20%, and balance ) nitrogen.

Figure 4. Product distribution vs temperature during the catalytic conversion of ethylene. Reaction conditions: (a) mCat/V˙ ) 500 kg‚s/m-3, (b) mCat/V˙ ) 1000 kg‚s/m-3, coC2H4 ) 6.8%, coH2O ) 25%, coCH4 ) 68.2%, and balance ) nitrogen.

Figure 2. Influence of contact time and temperature on (a) methane- and oxygen conversion, (b) yield of ethane and ethylene+, and (c) yield of carbon monoxide and carbon dioxide (coCH4 ) 70%, coO2 ) 10%, coN2 ) 20%).

by quartz particles of the same diameter. The steamreforming reactions were studied by comparing the conversions and product distributions obtained with dry and water-containing feed. When water and methane are used as reactants, no significant conversion was measured; therefore, steam

reforming of methane can be neglected even when applying high temperatures (T < 880 °C) and long contact times (mCat/V˙ < 250 kg‚s‚m-3). Also steam reforming of ethane can be neglected in this range of reaction conditions since carbon oxides were formed with low selectivity; ethane was converted mainly to ethylene (see Figure 3). Furthermore, when the catalyst particles were replaced by quartz, similar conversions of ethane were obtained in the whole range of temperatures and there was no significant change in the product distribution. From the above measurements, it can be concluded that thermal gas-phase dehydrogenation is the main route in the conversion of ethane when oxygen is no longer available. However, upon replacing ethane by ethylene carbon oxides were the main reaction products as long as water was available in the feed (see Figure 4); this result indicates that at high temperatures (T > 800 °C) and long contact times (mCat/V˙ > 500 kg‚s‚m-3) ethylene is mainly converted by steam reforming. Since high amounts of carbon dioxide were also observed in these experiments (see

2572 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997

Figure 5. Influence of pCH4 on the formation rate of C2hydrocarbons and on the formation rate of COx. Reaction conditions: 700 and 750 °C; poO2 ) 7.5 kPa.

Figure 6. Influence of pO2 on the formation rate of C2-hydrocarbons and on the formation rate of COx. Reaction conditions: 700 and 800 °C, poCH4 ) 70 kPa.

Figure 4), it can be concluded that catalytic steam reforming of ethylene is followed by a fast water gas shift reaction. By the nonoxidative conversion of ethylene, propylene was also formed but with significantly lower selectivity than selectivity to carbon oxides. Finally, small amounts of ethane were obtained. Comparative measurements in the catalytic and inert bed indicated that conversion of ethylene in the gas phase was negligible compared to the catalytic route. 4.4. Influence of Reactants and Products on the Reaction Rates. The effect of partial pressures of reactants and products on the reaction rates of the primary steps (conversion of methane) was investigated by means of measurements at low conversions (XO2 < 35%). Formation of C2+ Hydrocarbons. In the investigated range of partial pressures of methane, the rate of C2+ hydrocarbons formation increased linearly with this variable (see Figure 5). This dependence was identified at all temperatures studied. With respect to oxygen, the rate of hydrocarbon formation passed through a maximum (see Figure 6). With increasing temperature the maximum rate increased and the maximum was shifted to higher partial pressures of oxygen. At high temperatures (T > 800 °C) the inhibit-

Figure 7. Influence of pCO2 on the formation rate of C2hydrocarbons and on the formation rate of COx. Reaction conditions: 700 and 800 °C, poCH4 ) 51 kPa, poO2 ) 7.3 kPa, balance ) nitrogen.

ing effect of oxygen on the formation of C2+ hydrocarbons almost diminished. The rate of the primary selective step was influenced not only by oxygen and methane but also by carbon dioxide (see Figure 7). With increasing partial pressure of carbon dioxide the rate of the formation of C2+ hydrocarbons significantly decreased. At low temperatures (T < 750 °C) high partial pressures of carbon dioxide almost blocked the formation of higher hydrocarbons. A similar effect of carbon dioxide was observed for catalytic oxidative conversion of higher hydrocarbons. With increasing partial pressure of carbon dioxide the ethylene-to-ethane ratio decreased. Formation of Carbon Oxides. The rate of carbon oxides formation increased with increasing partial pressure of methane (see Figure 5). The rate was almost a linear function of the partial pressure of methane. The rate of carbon oxides formation increased also with partial pressure of oxygen (see Figure 6). Although formation of carbon oxides was not inhibited by oxygen as observed for the formation of C2 hydrocarbons it was inhibited by carbon dioxide (see Figure 7). Carbon dioxide influenced also the distribution of nonselective primary products; i.e., CO selectivity increased and CO2 selectivity decreased with growing concentration of CO2. 5. Development of the Kinetic Model The database established from the kinetic measurements contained 135 experiments which can be divided into two groups. The first group contained 50 experiments which aimed at the identification of the reaction steps to be considered in the reaction network and at determining the rates of primary reaction steps or single consecutive steps. To this group belonged the measurements of methane coupling that were performed at low conversions (XO2 < 35%) and the investigation of the effect of CO2 on the reaction rates. Furthermore, the conversion of ethane and ethylene under OCM conditions was studied. The second group contained a further 80 experiments that were performed at integral conditions (high oxygen conversions) applying methane and oxygen as reactants. 5.1. Reaction Scheme. Various reaction schemes were analyzed for the description of the network of primary reactions as well as for the consecutive reactions of ethane, ethylene and carbon oxides (Stansch,

Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2573

reaction, competitive adsorption of oxygen and carbon dioxide on the same active site was assumed. With respect to methane, it was shown that the reaction rate is a linear function of its partial pressure. Since for other oxidation reactions, i.e. oxidation of ethane, ethylene, and carbon monoxide, the inhibiting effect of oxygen was not detected, the Hougen-Watson type rate equation (eq 13) was used, which considered only the inhibiting effect of carbon dioxide. In order to determine rates of thermal dehydrogenation, steam reforming of ethylene, and the water gas shift reaction, power-law rate equations (eqs 14-17) were applied.

Figure 8. Reaction scheme.

1995). From these studies the reaction scheme presented in Figure 8 was elucidated. The final model consists of 10 reaction steps. Methane is converted in three parallel reactions. In the selective primary step ethane is formed by oxidative coupling of methane (step 2). Two further primary steps are the nonselective oxidation of methane to carbon dioxide (step 1) and carbon monoxide (step 3). In the direct oxidation of methane to carbon monoxide, two fast steps were lumped, i.e. formation and consecutive decomposition of formaldehyde. In consecutive steps, the conversion of ethane can proceed by two parallel routes, i.e. by heterogeneous catalytic oxidative dehydrogenation of ethane (step 5) or by thermal gas-phase dehydrogenation of ethane (step 7). The direct oxidation of ethane to carbon oxides was neglected. Also ethylene can be further converted in two parallel ways. It can further react with oxygen (step 6) or with water via steam reforming of ethylene (step 8) to carbon monoxide. In the reaction scheme developed, carbon monoxide is an intermediate product; it reacts with oxygen to carbon dioxide (step 4). Moreover, the carbon monoxide-tocarbon dioxide ratio is influenced by the water-gas-shift reaction. This reaction can proceed in both directions (steps 9 and 10). The kinetic model is characterized by the following set of stochiometric equations:

step 1:

CH4 + 2O2 f CO2 + 2H2O

(2)

step 2:

2CH4 + 0.5O2 f C2H6 + H2O

(3)

step 3:

CH4 + O2 f CO + H2O + H2

(4)

step 4:

CO + 0.5O2 f CO2

(5)

step 5:

C2H6 + 0.5O2 f C2H4 + H2O

(6)

step 6:

C2H4 + 2O2 f 2CO + 2H2O

(7)

step 7:

C2H6 f C2H4 + H2

(8)

step 8:

C2H4 + 2H2O f 2CO + 4H2

(9)

step 9:

CO + H2O f CO2 + H2

(10)

step 10:

CO2 + H2 f CO + H2O

(11)

5.2. Rate Equations and Kinetic Parameters. In order to describe the inhibiting effect of oxygen and carbon dioxide on the formation of ethane a HougenWatson type rate equation (eq 12) was applied. For this

r2 ) k0,2e-Ea,2/RT(K0O2e-∆Had,O2/RTpO2)n2pCH4 [1 + (K0,O2e-∆Had,O2/RTpO2)n + Kj,CO2e-∆Had,O2,j /RTpO2]2 (12)

rj )

k0je-Ea/RTpCmjpO2nj (1 + Kj,CO2e-∆Had,CO2,j /RTpCO2)n

j ) 1, 3-6 (13)

r7 ) k0,7e-Ea,7/RTpC2H6

(14)

r8 ) k0,8e-Ea,8/RTpC2H4m8pH2On8

(15)

r9 ) k0,9e-Ea,9/RTpCOm9pH2On9

(16)

r10 ) k0,10e-Ea,10/RTpCO2m10pH2n10

(17)

The kinetic parameters estimated for the reaction scheme presented above and respective rate equations are summarized in Table 3. In order to obtain the high accuracy under a wide range of reaction conditions, in which a change of the mechanism of surface reactions can occur (see Discussion) no constraints were set on the exponents in the hyperbolic rate equations. Furthermore, the enthalpy of carbon dioxide adsorption was estimated separately for each reaction step since the IR investigations (Stansch 1995) showed, that different CO2 species (lanthanum and calcium carbonates and oxycarbonates) were formed on the surface of the catalyst. 5.3. Model Validation. The kinetic model was verified by comparing model predictions with experimental data for all 135 experiments. In Figure 9, parity plots are presented which illustrate the accuracy of the model for predicting conversions of oxygen and methane as well as the yields of ethane, ethylene, carbon oxide, and carbon dioxide. Almost a symmetrical distribution of the data points on both sides of the diagonal was obtained for all variables. The average relative prediction error for oxygen and methane conversion amounted to 17 and 15%, respectively. The average error of the yield of ethane amounted to 16%. When integral and differential data were split, accuracies of 12% and 21%, respectively, were reached. The prediction of the ethylene yield was for the majority of experimental data within the 20% limit. Better accuracy was obtained for the yield of carbon dioxide; the relative average error amounted to 14%. Only the yield of carbon monoxide was predicted with lower accuracy, i.e. experimental yields determined under differential and integral conditions were calculated with an average error of 25 and 14%, respectively. 6. Discussion The kinetic model developed in this work will be compared with the kinetics proposed in the literature in order to elucidate the possibility of using the kinetics developed in this work as a generic one, applicable after adjusting kinetic parameters also for catalysts of similar properties (basic support, nonreducible catalytic com-

2574 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 Table 3. Kinetic Parameters step 1 2 3 4 5 6 7 8 9 10

k0j, mol‚g-1‚s-1‚Pa-(m+n) 0.20 × 10-5 23.2 0.52 × 10-6 0.11 × 10-3 0.17 0.06 1.2 × 107 a 9.3 × 103 0.19 × 10-3 0.26 × 10-1

Ea,j, kJ/mol

Kj,CO2, Pa-1

∆Had,CO2, kJ/mol

48 182 68 104 157 166 226 300 173 220

0.25 × 10-12 0.83 × 10-13 0.36 × 10-13 0.40 × 10-12 0.45 × 10-12 0.16 × 10-12

-175 -186 -187 -168 -166 -211

K O 2, Pa-1 0.23 × 10-11

∆Had,O2, kJ/mol -124

mj

nj

0.24 1.0b 0.57 1.0c 0.95 1.0

0.76 0.40 0.85 0.55 0.37 0.96

0.97 1.0 1.0

0 1.0 1.0

a Units are mol‚s-1‚m-3‚Pa-1. b First order was determined in the differential measurements. c Molecular adsorption for CO was set according to Martin et al., 1989.

ponents), e.g. alkaline, alkaline earth, or rare earth metal oxides. 6.1. Reaction Network and Reaction Rates. Reaction Network. The proposed reaction scheme differs from the networks proposed for other catalysts (see Table 1) in the primary reaction step as well as in consecutive reaction steps. Although primary formation of ethane from methane (step 2) was proposed in all models, the respective reaction schemes differ significantly in the routes for the formation of nonselective products. Carbon oxides are often lumped to a pseudocomponent COx which is generated parallel to ethane. The latter approach was previously applied in the kinetics developed for catalysts consisting of NaOH/CaO (Lehmann and Baerns, 1992), Sm2O3 (Otsuka et al., 1986), PbO/MgO (Asami et al., 1987), Li/MgO (Mirodatos and Martin, 1988), PbO/Al2O3 (Mleczko et al., 1994), and NaNiTiO3 (Santamaria et al., 1991). Alternatively, formation of CO2 as the only nonselective, primary product of methane oxidation was proposed, e.g. for Ce/ Li/MgO (Bartsch, 1990), PbO/MgO, PbO/Al2O3, Ce/Li/ MgO (Dutta and Jazayeri, 1992), and La2O3 (Lacombe et al., 1995). The parallel formation of CO and CO2 as proposed in this work (steps 1 and 3) was postulated only for La/B2O3 (Wada et al. 1989) and BaCO3/La2On(CO3)3-n (Olsbye et al., 1992). However, results of the model discrimination showed that for La2O3/CaO, even under differential conditions, significant improvement in data fitting was achieved upon assuming parallel formation of CO and CO2 as well further oxidation of CO to CO2. With respect to the consecutive steps there is a common agreement in the literature, that ethane is converted mainly by oxidative dehydrogenation to ethylene (Figure 8, step 5). An accurate estimation of the rate of this reaction step is of special importance when modeling distributed feed of oxygen or a fluidized-bed reactor. When the oxygen feed is staged (Baerns and Hinsen, 1986) or when oxygen is supplied by means of mass transport from bubbles to the emulsion phase of a fluidized-bed (Mleczko et al., 1994), it enters reactor zones rich in C2+ hydrocarbons. The kinetic parameters of this step should be determined from dedicated experiments since during OCM in a fixed-bed reactor the oxygen concentration profile is complementary to that of C2+ hydrocarbons. In several kinetic models, direct oxidation of ethane to carbon oxides was also considered (Ali Emesh and Amenomiya, 1986; Olsbye et al., 1992; Ding et al., 1991; Bartsch, 1990; Otsuka et al., 1986; Dutta and Jazayeri, 1992; Lacombe et al., 1995). Latest experiments performed in the polytropic fixed-bed reactor indicate that at very high temperatures (T > 820 °C) and high concentrations of oxygen (pO2 > 20 kPa) a

deep oxidation of ethane can also take place (Schweer, 1997). In the previous study (Mleczko et al., 1992) conversion of ethane by steam reforming was also postulated; however, the kinetic measurements of this reaction (Stansch, 1995) indicated that this route can be neglected compared to the oxidative and thermal dehydrogenation of ethane. In the kinetic schemes proposed for other catalysts, thermal dehydrogenation of ethane (step 7) has not been considered in spite of the fact that there is experimental evidence that in the oxygen free zones of a reactor this reaction is the main route for ethylene generation. Although this reaction is much slower than the parallel total oxidation, it has to be considered either when the performance of a studied reactor is characterized by a wide residence time distribution, e.g. fluidized-bed reactors, or when the oxygen free part of the bed is used for improving the ethylene-to-ethane ratio. When an ethane feed is introduced into the oxygen free reactor zones as reported for fixed-bed (Raimbault and Cameron, 1991; Taniewski et al., 1994) and fluidized-bed (Edwards et al., 1992) reactors, a high selectivity of the pyrolysis of ethane to ethylene is achieved. Reactions of ethane and ethylene to higher hydrocarbons (C3+) are in most cases neglected since experimentally determined C3+ selectivities were generally lower than 5%. At oxidative conditions formation of coke is negligible; however under oxygen lean conditions carbon deposition may occur and then result in catalyst deactivation (Pereira et al., 1992; Taniewski et al., 1994). Catalytic oxidation of ethylene to carbon monoxide, as proposed in this work (step 6), was also considered in the network for La2O3 (Lacombe et al., 1995). In the reaction scheme for Ce/Li/MgO, Bartsch (1990) assumed that this reaction step takes place in the gas phase. Oxidation of ethylene to COx was postulated for lanthanum-supported catalysts (Olsbye et al., 1992; Ding et al., 1991). Steam reforming of ethylene (step 8) was not considered in the schemes proposed for other catalysts. The reactions of C2+ hydrocarbons with water are much slower than the ones with oxygen. Therefore, in microcatalytic fixed-bed reactors, in which contact time is determined by complete conversion of oxygen, their extent is mostly negligible. Moreover, the majority of the kinetics (see Table 1) were determined for temperatures below 800 °C. Steam reforming reactions were not found at temperatures below 800 °C for CaO/ CeO2 (Zhang and Baerns, 1991), MgO (Hargreaves et al., 1991), and PbO/SiO2 (Lugo et al., 1993). However, at temperatures above 800 °C, steam reforming of ethylene was observed not only for La2O3/CaO but also for CaO/CeO2 (Zhang and Baerns, 1991). Since the highest C2+ selectivities and yields measured in fixed

Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2575

Figure 9. Parity plots of experimental and calculated (a) conversion of methane, (b) conversion of oxygen, (c) yield of ethane, (d) yield of ethylene+, (e) yield of carbon dioxide, and (f) yield of carbon monoxide.

and fluidized-bed reactors were obtained at temperatures above 800 °C, this reaction has to be taken into

account. Moreover, it has to be considered in reactors characterized by a wide distribution of residence times,

2576 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997

e.g. fixed-bed reactors influenced by intra- or interparticle mass transport limitation or fluidized-bed reactors. Carbon oxides are often lumped into one pseudocomponent. However, for design of the separation units of an OCM plant for ethylene or gasoline production on an industrial scale, a correct prediction of the composition of the product gas is very important also with respect to the byproducts. Moreover, the composition of the nonselective products also influences the economics of the OCM process; e.g., higher selectivities to CO and H2 at constant selectivity to C2+ hydrocarbons result in lower consumption of oxygen and therefore a lower amount of heat which is released in the OCM reactor. In the proposed kinetics the CO-to-CO2 ratio is influenced by several primary as well as consecutive reaction steps. Oxidation of CO to CO2 (step 4) was postulated for various OCM catalysts (see e.g. Bartsch, 1990; Lacombe et al., 1995; Geerts et al., 1989). The water gas shift reaction (steps 9 and 10), which can influence the CO-to-CO2 ratio, was mostly neglected in published kinetics. However, this reaction was experimentally confirmed for many catalysts in the temperature range between 700 and 800 °C, e.g., for Sr/La2O3 (Deboy and Hicks, 1988) Li/ZnO (Zhang et al., 1988), Li/MgO (Roos et al., 1987), NaOH/CaO (Lehmann and Baerns, 1992), PbO/SiO2 (Lugo et al., 1993), Sm2O3 (Ekstrom, 1992), and CaO/CeO2 (Zhang and Baerns, 1991). Reaction Rates. When rates of different reaction steps are compared, the elaborated kinetics confirms that ethane and ethylene can be converted much easier (dehydrogenated and oxidized) than methane. The ratio of the reaction rates calculated at selected conditions (T ) 800 °C, pCH4 ) 63 kPa, pO2 ) 4.2 kPa, pC2H6 ) 1.9 kPa, pC2H4 ) 0.6 kPa, pH2O ) 7.4 kPa, and pCO2 ) 1.5 kPa) for oxidative dehydrogenation of ethane and its primary selective formation amounted to r5/r2 ) 5. Also when oxidation of ethylene and the primary formation of ethane under the above conditions are compared, the high ratio of r6/r2 ) 42 indicated that oxidation of ethylene proceeds much faster than coupling of methane. Similar results were also reported for other catalysts. Van Kasteren et al. (1991) reported for a Li/ MgO catalyst that at low pressure (p ) 66 Pa) and 800 °C ethane and ethylene were converted faster than methane by a factor 4 and 2.6 respectively. For Sm2O3 (T ) 700 °C) Ekstrom (1992) reported that if the disappearance of hydrocarbons obeys pseudo-first-order kinetics, the difference in the overall rate constants for the conversion of CH4 and C2H6 to COx is a factor of 6.5. With respect to the rates of conversion of higher hydrocarbons, the oxidation reactions (steps 5 and 6) are much faster than thermal dehydrogenation and steam reforming (steps 7 and 8); e.g., under the abovedefined conditions, the ratio of the reaction rates of oxidative to thermal dehydrogenation of ethane amounted to r5/r7 ) 1121. A similar high ratio was obtained when comparing the rates of oxidation with steam reforming of ethylene; i.e., r6/r8 ) 230. The ratio of the reaction rates calculated for the oxidation of carbon monoxide to carbon dioxide and for the water gas shift reaction, which amounted to 15, indicates that the last reaction contributes to the formation of carbon dioxide even in the presence of oxygen. 6.2. Rate Equations and Kinetic Parameters. Rate Equations. The maximum in the rate of hydrocarbon formation with respect to oxygen partial pressure measured over the La2O3/CaO catalyst was also re-

ported for Sm2O3 (Otsuka et al., 1986) and NaOH/CaO (Lehmann and Baerns, 1992). For the La2O3/CaO catalyst this effect was explained by competitive adsorption of oxygen, methane, and carbon dioxide. A similar explanation was proposed by Lehmann and Baerns (1992) for the NaOH/CaO catalyst. In the equation used for calculation of the rate of ethane formation (eq 12) an absorption term for methane was neglected. This was possible due to the linear dependency of hydrocarbon formation on methane partial pressure (see Figure 5), which jusitfied the assumption of low surface coverage of methane. The measured maximum in the dependency could not be described by the Eley-Rideal reaction mechanism considering interaction of methane and oxygen molecules as well as adsorption of methane and oxygen on different active sites, although the EleyRideal mechanism was proposed for (CaO)x(CeO2)1-x catalysts (Wolf, 1994). The estimated power exponent of 0.4 in eq 12 for the adsorption term indicates a dissociative adsorption of oxygen. However, when this parameter was estimated from the differential measurements separately for various temperatures, the exponent for the oxygen adsorption increased with decreasing temperature; e.g., it increased from 0.65 at 750 °C to 1.0 at 700 °C (Stansch, 1995). This result indicates that the type of adsorption changes from a molecular one to dissociative adsorption with increasing temperature. The value of 0.4 results from the high number of experiments at temperatures above 800 °C in the whole data set. IR measurements (Stansch, 1995) indicated that the inhibitory effect of carbon dioxide observed in the kinetic measurements is due to formation of the lanthanum and calcium carbonate species on the catalytic surface. Formation of carbonates affecting oxidative reaction steps was also identified for a Li/MgO catalyst (Galuszka, 1994). The inhibiting effect of CO2 on the rate of the methane coupling was also reported for other catalysts, e.g. Li/MgO (Roos, 1989; Al-Zahrani et al., 1994), Li/Pb/CaO (Smith and Galuszka, 1994), MgO and Sm2O3 with and without promoters, CaO, and SrO (Suzuki et al., 1990). In order to describe the inhibitory effect of various components on the rate of oxidation of hydrocarbons and the maximum in the dependence of the rate of ethane formation on partial pressure of oxygen Hougen-Watson type rate equation have been applied. These effects cannot be described by the often applied power-law rate equations (see Table 1). Kinetic Parameters. The estimated apparent activation energy of the primary selective step, which amounts to 182 kJ/mol, is similar to the ones reported for other La-supported catalysts; e.g., activation energies of 172 and 168 kJ/mol were determined for La2O3/ BaCO3 (Ding et al., 1991) and for BaCO3/La2On(CO3)3-n (Olsbye et al., 1992), respectively. The activation energies for the formation of carbon monoxide and carbon dioxide, which amounted to 48 and 68 kJ/mol, respectively, are significantly lower than the activation energy of the formation of ethane. The higher activation energies for the primary, selective step, i.e. formation of ethane from methane, compared to the one(s) of the nonselective primary step(s) are a common feature of the OCM reaction observed for various catalysts, e.g. for PbO/MgO (Asami et al., 1987), Na/CaO (Follmer et al., 1989), Li/MgO (Mirodatos and Martin, 1989; Geerts, 1990), Na/NiTiO3 (Santamaria et al., 1991), La2O3/

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BaCO3 (Ding et al., 1991), and Sm2O3 (Otsuka et al., 1986). This difference of the activation energy explains the increase of C2 selectivity with temperature, which is a common feature of OCM catalysts (Mleczko and Baerns, 1995). The activation energies of the primary formation of ethane determined for different materials varied in a wide range, e.g. for the above-listed catalysts between 66 and 156 for the selective step and from 100 to 210 kJ/mol for the formation of the nonselective products. The adsorption enthalpy of carbon dioxide derived for the primary selective step (step 2) with -182 kJ/mol indicates that carbon dioxide more strongly adsorbed than oxygen, for which an adsorption enthalpy of -124 kJ/mol was estimated. The adsorption enthalpies of carbon dioxide for steps 1-5 are similar; they vary in the range from -166 to -186 kJ/mol. Only the value determined for this parameter for the oxidation of ethylene to carbon monoxide (-211 kJ/mol) is significantly higher. The reason for such a strong inhibition of this step by CO2 could not be clarified as yet. Also the kinetic parameters estimated for other reaction steps agree well with the values reported in the literature. The activation energy of 157 kJ/mol determined for the oxidative dehydrogenation of ethane is higher that those for La2O3/BaCO3 (Ding et al., 1991) and BaCO3/La2On(CO3)3-n (Olsbye et al., 1992) which amounted to 131 and 132 kJ/mol, respectively, but lower than the one for Sm2O3 (Otsuka et al., 1986), which amounted to 173 kJ/mol. Only the activation energy of oxidation of ethylene to carbon monoxide of 166 kJ/mol obtained in this work is significantly higher than the data reported in literature, which vary between 40 kJ/ mol for BaCO3/La2On(CO3)3-n (Olsbye et al., 1992) to 94 kJ/mol for Sm2O3 (Otsuka et al., 1986). 6.3. Range of Validity and Accuracy of the Kinetics. The developed model appears to be superior to previous kinetics with respect to its range of validity. The wide range of validity and the achieved accuracy allow its application for reaction engineering simulations. The main drawback of the proposed kinetics lies in the neglecting of gas-phase reactions. These may lead to significant errors in analysis of reactors characterized by a large gas volume, e.g. industrial-scale bubbling-bed or circulating fluidized-bed reactors. In order to account for the interaction between heterogeneous and gas-phase reactions, a model that combines the description of elementary catalytic steps with the complex kinetics of gas-phase reactions (see, e.g., Chen et al., 1994, Zanthoff, 1994, and Reyes et al., 1993) should be applied. However, kinetic models of this type have not found until now a wide application due to extremely long computation times when using them for predictions of reactor performance (see, e.g., Couvenberg et al., 1994). The effect of gas-phase reactions can be, however, estimated by superposition of the proposed heterogeneous model with separate kinetics of the relevant gas-phase reactions. This approach was successfully applied when modeling a laboratory-scale bubbling-bed reactor (Pannek and Mleczko, 1996) and distributed feed of oxygen in a fixed-bed reactor (Schweer, 1997). 7. Conclusions A comprehensive kinetic model of the oxidative coupling of methane to C2+ hydrocarbons over a La2O3/CaO catalyst was developed on the basis of experimental studies performed in a microcatalytic fixed-bed reactor under a wide range of experimental conditions (1 < pO2

< 20 kPa, 10 < pCH4 < 95 kPa, 700 < T < 955 °C, 0.76 e mCat/V˙ STP e 250 kg‚s/m3). This model is suitable for reliable reaction engineering simulations of catalytic reactor performance. The developed reaction scheme contains 10 reaction steps. In three primary steps, each parallel to one another, methane is converted catalytically to ethane as well as carbon monoxide and carbon dioxide. The network of consecutive reactions consists of oxidative and thermal dehydrogenation of ethane, oxidation and steam reforming of ethylene, oxidation of carbon oxide, and the water gas shift reaction. The kinetics of oxidative reactions of hydrocarbons were described by Hougen-Watson type rate equations. For the oxidation reactions an inhibiting effect of carbon oxide had to be taken into account. For the primary selective reaction step of ethane formation additionally an inhibiting effect of oxygen had to be considered. The other reactions were described by applying power-law rate equations. The kinetic parameters estimated appear reasonable from a more fundamental point of view. The developed kinetics was evaluated by comparing calculated and experimental data. The measured conversions of methane and oxygen, as well as yields to C2 hydrocarbons and carbon oxides were predicted with an average relative error of less then 22% for integral data. The model contains almost all reaction steps proposed in the literature for other catalysts; from this point of view, it may be used as a generic one for OCM catalysts with similar properties (basic carrier, nonreducible catalytic components). Its application is, however, limited to operating conditions at which gas-phase reactions can be neglected in the first approximation, e.g. short contact time and low gas volume in the reactor. Nomenclature Symbols c°j: concentration of the component j at inlet of the reactor, vol. % EA,L: activation energy in the reaction step L, J/mol ∆Had,CO2: adsorption enthalpy for CO2, J/mol ∆Had,O2: adsorption enthalpy for O2, J/mol ID: inner diameter of the reactor, m k0L: pre-exponential factor KL: adsorption constant, Pa-1 mj: reaction order n: number of experiments mCat: mass of the catalyst, kg nj: reaction order p: partial pressure, Pa PT: average pressure in the reactor, bar R: gas constant, J/(mol‚K) rL: reaction rate (catalytic), mol/(g‚s) rLG: reaction rate (gas phase), mol/(m3‚s) S: selectivity, % T: temperature, K TN: standard-temperature, K THS: hot-spot temperature, K V˙ STP: volumetric gas flow rate under STP conditions, m3/s xi,j: measured and estimated variable j in experiment i X: conversion, % Y: yield, % γ: heteroscedasticity parameter (0 < τ < 2)

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Received for review September 9, 1996 Revised manuscript received March 31, 1997 Accepted April 12, 1997X IE960562K X Abstract published in Advance ACS Abstracts, June 1, 1997.