Ind. Eng. Chem. Res. 1997, 36, 3583-3593
3583
A Comparative Simulation Study on Oxidative Coupling of Methane in Fixed-Bed and Membrane Reactors Y. K. Kao,* L. Lei, and Y. S. Lin Department of Chemical Engineering, University of Cincinnati, Cincinnati, Ohio 45221
Oxidative coupling of methane (OCM) on a conventional fixed-bed reactor (FBR) and a ceramic dense membrane reactor (DMR) packed with Li/MgO catalyst is analyzed using plug-flow reactor models. The validity of OCM kinetic equations employed in the modeling is confirmed by excellent agreement between the simulation and experimental data for OCM on FBR. For FBR, a high methane to oxygen feed ratio favors the OCM reaction, with a low C2 yield because of insufficient oxygen supply. The highest C2 yield achieved with a feed mixture consisting of 70% methane and 30% oxygen is 20.7% at a selectivity of 53% and operating temperature of 750 °C. The C2 yield and selectivity increase slightly at a higher operating temperature. The optimal feed ratio does not change with temperature. DMR is made of a mixed-conducting ceramic membrane tube packed with an OCM catalyst. The membrane tube separates the methane and oxygen feed. The oxygen concentration in the DMR is much lower and more uniform than that in the FBR because of the different reactant feeding mode and logarithemic dependence of oxygen flux on oxygen partial pressures of the dense ceramic membrane. This results in a significantly increased C2 selectivity and yield for the DMR as compared to the FBR. Introduction Oxidative coupling of methane (OCM) to C2 products (mainly ethylene) represents one of the most effective ways to convert natural gas to more useful products (Matherne and Culp, 1992). Due to deep oxidation reactions in the gas phase or on the catalyst surface, it is very difficult to obtain C2 yield higher than 25% in a conventional cofeed fixed-bed reactor. A number of new approaches have been proposed based on the concept of controlling the oxygen concentration or preventing further oxidation of the desirable C2 products. Different oxygen feed methods were examined, resulting in several new types of reactors that can improve the performance of the OCM reaction to achieve higher yield of C2 products. The first new type of reactor is a simulated countercurrent moving-bed chromatographic reactor (Tonkovich et al., 1993, 1994a,b). It consists of several separatorsreactors in series packed respectively with the catalyst and an adsorbent that preferentially adsorbs the desirable products. The desirable products will be separated from the mixture as soon as they are produced. When C2 hydrocarbon reaction products are separated from the reaction mixture, the further oxidation of C2 products will be suppressed. Although the C2 yield per pass remained low, the overall C2 yield and selectivity of this new type of reactor were improved as a result of rapid product separation from reactants. The reported overall C2 yield exceeds 50%. The selectivity is in the range of 80-90% with Sm2O3 catalyst at reaction temperature near 1000 K (Tonkovich et al., 1993). The second reactor type suppresses the further oxidation of C2 products by minimizing the oxygen contact time with methane. The typical design is the fluidizedbed reactor. The fluidized-bed reactor has an additional advantage, as discussed by Edwards et al. (1992), that it can cope with the large amount of heat released by the highly exothermic OCM reaction. The catalyst bed can be maintained at nearly isothermal conditions due * Corresponding author. S0888-5885(96)00669-0 CCC: $14.00
to good solids backmixing and excellent heat-transfer characteristics. It also has the ability to be operated with continuous addition and withdrawal of catalyst from the reaction zone. The best hydrocarbon yield was 19.4% (Do et al., 1995), which is still too low. Another fluidized-bed reactor concept is the Riser simulator reactor. It is an internal recycle fluidizedbed reactor operated under batch conditions. Methane is injected into the reactor tube first, followed by multiple injections of a small amount of oxygen. After a certain reaction time, the process is repeated. In this operation, methane always contacts a very small amount of oxygen both on the catalyst surface and in the gas phase. Methane reacts under “starving oxygen condition” that suppresses the further oxidation of C2 products (Pekediz and de Lasa, 1994). The third reactor type controls the oxygen concentration in a continuous reactor by distributing the oxygen feed during the reaction process to reduce the further oxidation of C2 products. One group of the reactors is fixed-bed reactor with a distributed oxygen feed and the other is membrane reactor. The fixed-bed reactor with a distributed oxygen feed changes the feed method of oxygen from the cofeed method of a conventional fixedbed reactor. The experimental work of this type of reactor has been done by Choudhary et al. (1989) using a tubular reactor with a series of oxygen feed points evenly distributed along the length of the reactor. The result indicated that the distributed oxygen feed can lower the oxygen concentration in the reactor tube and improve the selectivity to 74%. In a simulation study, Santamaria et al. (1992) have shown that this new distributed oxygen feed method can increase yield to 29% and selectivity to 76%. In another modeling study by Reys et al. (1993a,b) using a fixed-bed reactor with 200 distributed oxygen injection points, the theoretical yield can reach 50% under optimal conditions. The membrane reactor is another design which has distinctive characteristics that can closely control the oxygen concentration in the reactor tube. Santamaria and co-workers (Lafarga et al., 1994; Coronas et al., 1994; Santamaria et al., 1994) reported a porous ceramic © 1997 American Chemical Society
3584 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 Table 1. Comparison Simulation Results with Experimental Data run no. feed composition He CH4 O2 experimental product composition CO2 + CO C2H4 + C2H6 simulated product composition CO2 C2H6 experimental selectivity experimental yield simulated selectivity simulated yield
1
2
3
4
5
6
7
8
0.8921 0.0724 0.0355
0.8566 0.1118 0.0316
0.7882 0.1118 0.1000
0.3347 0.3987 0.2066
0.8842 0.0776 0.0382
0.8763 0.0763 0.0474
0.8447 0.1171 0.0382
0.5592 0.2868 0.1540
0.0135 0.0067
0.0110 0.0089
0.0393 0.0108
0.1041 0.0393
0.0149 0.0075
0.0182 0.0076
0.0146 0.0101
0.0693 0.0301
0.0135 0.0062 49.8 18.4 47.8 17.1
0.0112 0.0093 61.8 15.8 62.4 16.6
0.0472 0.0092 35.5 18.3 28.1 16.5
0.0825 0.0287 43.0 16.4 41.1 14.4
0.0146 0.0066 50.3 19.0 47.5 17.0
0.0186 0.0062 45.4 19.4 40.0 16.4
0.0139 0.0098 58.1 16.9 58.5 16.6
0.0643 0.0227 46.5 17.4 41.4 15.7
membrane tube reactor packed with Li/MgO catalyst for OCM. It is reported that this porous membrane reactor allows a more controllable and safer operation for the OCM reaction. The membrane reactor gives a considerably better selectivity than the fixed-bed reactor, especially at low and moderate methane and oxygen conversions. However, the improvement in C2 yield is marginal, probably because the experiments were not performed under optimal conditions. Another group of the membrane reactors is based on the solid oxide fuel cell concept (Nozaki et al., 1992; Eng and Stoukides, 1991; Wang and Lin, 1995). This group of membrane reactors utilizes oxygen semipermeable ionic (or mixed) conducting ceramic membranes to control the feed of oxygen and methane. The membrane surface exposed to methane is catalytically active for OCM in this type of membrane reactor, and the OCM reaction occurs on the membrane surface as well as in the gas phase. Different operation variables in the conventional fixed-bed reactor for the OCM reaction can affect the yield and selectivity of C2 products. There are a lack of detailed investigations of those relationships in order to gain a better insight into the OCM reaction. Such an investigation is useful not only for the optimization of the conventional fixed-bed reactor but also for the development of new reactors for OCM. On the other hand, the catalyst packed membrane reactor, especially with a dense ionic-conducting ceramic membrane, is a new type of reactor for the OCM reaction. The change of oxygen feed mode is designed to control the oxygen concentration in the reactor tube. Hopefully, the yield and selectivity of C2 products could be improved. No studies, however, were found reported on OCM in the tubular dense ceramic membrane reactor packed with an OCM catalyst. The objective of the present paper is to study the performance of the OCM reaction in a conventional fixed-bed reactor and a dense mixedconducting ceramic membrane reactor, both packed with the same OCM catalyst (Li/MgO), by using mathematical models of various reactor configurations. The study is focused on identifying the optimal operation conditions to achieve the highest C2 yield in each respective reactor configuration. Kinetics and Reactor Mathematical Model OCM Kinetic Equations on Li/MgO Catalyst. The kinetics of OCM on Li/MgO are very complicated and involve many species. Wang and Lin (1995) recently reported the following kinetic equations describing the differential formation rates for C2 (r2) and COx
(r1) products in the Li/MgO packed fixed-bed reactor:
r1 )
r2 )
K3PO2
1+
4
K3PO2
[( [(
1.251
K3PO21.251
) ] ) ] 0.5
-1 + Cp 16S0K2 PC2 (1) CT
1.251
16
Cp 8K2 PCH4 CT
1+
Cp 8K2 PCH4 CT K3PO21.251
0.5
2
-1
-
Cp 8S0K2 PC2 (2) CT
where Cp and CT are respectively electron-hole concentration and total concentration of all defects in the catalyst, determined by the partial pressures of reactants and products as
K1PO20.5 Cp ) (3) CT K P 0.5 + K K K + K (P 1 O2 1 2 4 2 CH4 + 8S0PC2) and
S0 )
(
2 K2PCH4
)
1 + 8Z K3PO21.251
Z)
(4)
0.5
+1
K1PO20.5 K1PO20.5 + K1K2K4 + K2PCH4
(5)
Values of the rate parameters appearing in the above equations were obtained by linear regression (Wang and Lin, 1995) of published experimental data of Tung and Lobban (1992), and the results are summarized below:
K1 ) 2.472 × 107e-49.64(kcal/mol)/RT K2 ) 10.10e-23.15(kcal/mol)/RT K3 ) 1.103 × 10-3e-4.548(kcal/mol)/RT K4 ) 2.093 × 10-4e27.94(kcal/mol)/RT
(6)
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3585
The above equations correlate the formation rates (in units of mol/cm3 s) for C2 and COx products to partial pressures (in units of atm) of oxygen, methane, C2 products, and temperature. Details of the above kinetic model were presented elsewhere (Wang, 1994; Wang and Lin, 1995). The validity of these kinetic equations will be demonstrated in the Results and Discussion section. PFR Model for a Conventional Fixed-Bed Reactor. Simulation of the OCM reaction for a fixed-bed reactor (FBR) was carried out on a plug-flow reactor packed with Li/MgO catalyst. Following most work on OCM kinetics, we assume that the C2 product is C2H6 and the side product is CO2. Mass balance on methane and C2 product in the fixed-bed reactor gives
For methane: d(FyCH4) dz
) -A(r1 + 2r2)
(7)
For C2 product: d(FyC2H6) dz
) Ar2
(8)
where F is the total molar flow rate, in mol/s, z is the distance from the reactor inlet, in cm, yi is the mole fraction of component i, and A is the cross-section area of the reactor, in cm2. By considering overall balances of the three elements C, O, and H, the mole fractions and flow rate at any point in the reactor are related to the feed conditions (at a flow rate of F0 and mole fractions y0i ) by the following equations: 0 F(yCH4 + yCO2 + 2yC2H6) ) F0yCH 4
(9)
0 F(yO2 + 2yCO2 + 0.5yH2O) ) F0yO 2
(10)
0 F(yH2O + 3yC2H6 + 2yCH4) ) 2F0yCH 4
(11)
The hydrogen balance can be simplified by substituting eq 9 into the right-hand side of eq 11. Then we have
F(yH2O - 2yCO2 - yC2H6) ) 0
(12)
The molar flow rate changes from the inlet due to the oxidative coupling reaction. The equation that relates the feed molar flow rate to the molar flow rate at any point inside the reactor can be found by the reaction stoichiometry. Each mole of C2H6 produced causes a reduction in the total mole of the gas mixture by 0.5 mol. If the feed rate to the FBR is F0 and, at some point in the reactor, the flow rate is F at a C2H6 mole fraction of yC2H6, then
F ) F0 - 0.5FyC2H6 The boundary conditions, at the entrance of the reactor, z ) 0, are
0 yCH4 ) yCH 4 0 yO2 ) yO 2
yCO2 ) 0 yC2H6 ) 0 yH2O ) 0 Because of the extremely exothermic OCM reaction, many experiments are conducted using methane and oxygen feed diluted with inert gas, such as nitrogen or helium, to control the reactor temperature. Furthermore, it appears that the presence of inert gas in the reactor improves the selectivity. The inert mole fraction can be found by using the following equation in which the total mole fraction including the mole fraction of the inert yin equals unity.
yCH4 + yO2 + yCO2 + yC2H6 + yH2O + yin ) 1 (13) With the introduction of a dimensionless flow rate q ) F/F0, the above equations are rearranged in terms of the dimensionless flow rate and mole fractions as follows:
F0
d(qyCH4) dz
) -A(r1 + 2r2)
d(qyC2H6)
F0
dz
) Ar2
(14) (15)
1 0 yCH4 + yCO2 + 2yC2H6 ) yCH 4 q
(16)
1 0 yO2 + 2yCO2 + 0.5yH2O ) yO q 2
(17)
2yCO2 + yC2H6 ) yH2O
(18)
q)
F 1 ) F0 1 + 0.5yC2H6
(19)
yCH4 + yO2 + yCO2 + yC2H6 + yH2O + yin ) 1 (20) The performance of the reactor is measured by the selectivity and yield of C2. Following the definition of Lane and Wolf (1988), the C2 selectivity is defined to be the fraction of methane consumed which is converted to the desirable C2 product:
SE )
2yC2H6 yCO2 + 2yC2H6
(21)
and the C2 yield is defined to be the fraction of methane in the feed which is converted to C2:
YE )
2qyC2H6
2FyC2H6 0 F0yCH 4
)
0 yCH 4
(22)
The differential equations for the PFR model for the conventional FBR were solved by Gear’s BDF method using DVIPAG routine of the IMSL library (Microsoft). Model for Dense Ceramic Membrane Reactor. The dense membrane reactor (DMR) resembles a tube and shell heat exchanger. The membrane tube is
3586 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997
packed with the Li/MgO catalyst. Methane is fed to the reactor tube packed with the catalyst, and oxygen is fed to the shell side of reactor. The tube wall is made of dense ionic- or mixed-conducting ceramic which allows only oxygen to permeate through it. These ceramics include yttria-stabilized zirconia (YSZ) and many perovskite-type oxides (ABO3) (Lin et al., 1994). A membrane reactor using this type of material as the membrane to feed oxygen into the reactor tube also prevents methane and its products from permeating to the shell side. Since the perovskite-type membranes have the desired oxygen permeation flux, the present simulation study is on a membrane reactor made of a perovskitetype material La1-xSrxCoO3. The oxygen permeation flux through the perovskite-type membrane can be approximately correlated to oxygen partial pressures and temperature by (Itoh et al., 1994)
JO2 ) 7.5 × 10-5
()
Tσi Ph ln tm Pl
(23)
where tm is the thickness of the membrane, in cm, σi is ionic conductivity, 1.21 × 103 exp(-1.08 × 104/T), and Ph and Pl are respectively the oxygen partial pressure on the two sides of the membrane. The reactor model for OCM in DMR is basically the same as the PFR model for the conventional FBR reactor with the exception of the oxygen balance equation. Oxygen mass balance will be different from the PFR model for FBR because of the permeation flux. An oxygen balance equation that includes the oxygen permeation flux J is needed:
d(FyO2) dz
) (πD)J - A(2r1 + 0.5r2)
(24)
This equation, in addition to the differential balance equations for methane and ethane, constitutes the dense membrane reactor (DMR) model. Introducing the dimensionless flow rate q ) F/F0, where F0 is the methane feed rate to the reactor, the model equations are
yCH4 + yO2 + yCO2 + yC2H6 + yH2O ) 1
(25)
1 0 yCH4 + yCO2 + 2yC2H6 ) yCH 4 q
(26)
2yCO2 + yC2H6 ) yH2O
(27)
F0
d(qyCH4) dz F0
F0
d(qyO2) dz
) -A(r1 + 2r2)
d(qyC2H6) dz
) Ar2
) (πD)J - A(2r1 + 0.5r2)
(28) (29) (30)
where the permeation flux J is calculated by eq 23 and A, F0, r1, and r2 are defined in the FBR model (eqs 1 and 2). As for the conventional FBR model, the three differential equations in the model for the DMR model were also solved by Gear’s BDF method for compositions of yCH4, yO2, and yC2H6 in the reactor tube. Two other compositions yCO2 and yH2O and dimensionless variable
Figure 1. Parity plot of simulation results with experimental data.
q were obtained from yCH4, yO2, and yC2H6 with the aid of other algebraic equations in the model. Results and Discussion Simulation was performed for OCM in the conventional fixed-bed and membrane tube of 1 cm internal diameter, packed with the Li/MgO catalyst. The conventional fixed-bed reactor is operated at 1 atm total pressure. In the membrane reactor, pure methane is fed to the reactor tube at 1 atm and oxygen is fed to shell side of the reactor at various pressures. In comparison with experimental data, the actual reactor dimension was used in the simulation. Other conditions are specified in the respective figures or tables to be presented next. OCM in a Conventional Fixed-Bed Reactor. (a) Validity of OCM Kinetics. Validity of the OCM kinetic model used in the present work is critical to the reliability of the simulation results for the fixed-bed and membrane reactors. The kinetic model is verified by comparing the simulation results with the experimental data for OCM in the fixed-bed reactor packed with Li/ MgO reported by Ito et al. (1985). In their experiments, the methane and oxygen were fed with inert gas as the diluent to a conventional FBR tube. The reactor was operated at 720 °C and at a feed flow rate of 0.83 mL/s over 4 g of Li/MgO catalyst. Eight sets of experimental results were reported. The first four runs used 3% Li/ MgO catalyst, and the last four runs used 7% Li/MgO catalyst. The first catalyst had a surface area of 1 m2/ g, and the second catalyst surface area was twice as large. The simulation and the experimental results are compared in Table 1. The tabulated results show that the present FBR model fits the experimental data well for the high methane to oxygen ratio case, such as runs 1, 2, 5, and 7. For the low methane to oxygen feed ratio cases, runs 3, 4, 6, and 8, the simulation results are slightly lower than the experimental data. A better perspective of the comparison is presented in a parity plot given in Figure 1. It shows that the isothermal FBR model with the OCM kinetics equations of Wang and Lin (1995) provides a reasonable prediction of the experimental result. It fits the experimental results of 3% Li/MgO catalyst runs quite well. The
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3587
Figure 2. Yield surface as a function of reactor length and feed composition (T ) 750 °C).
predictions on the 7% catalyst runs are generally low. However, the differences are not significant, in view of the fact that the actual reactor may not have been operated under isothermal conditions. The above comparison verifies the validity of the kinetic model used in the present simulation study. The following presents simulation results on the effects of various parameters on OCM in a fixed-bed reactor packed with Li/MgO based on the confirmed kinetic model. (b) Effects of Feed Composition on OCM in a Fixed-Bed Reactor. Typically, the OCM reactor is operated at a CH4:O2 ratio larger than 2. At a lower methane to oxygen feed ratio, all of the hydrocarbons will be eventually fully oxidized to carbon dioxides. A high methane to oxygen feed ratio must be used in order to suppress the deep oxidation of the feed methane and hydrocarbons produced by the OCM reaction. Higher feed methane mole fractions favor the methyl radical coupling reaction leading to high selectivity. Ideally, one should keep the oxygen concentration as low as possible in order to suppress the deep oxidation of the feed methane and the C2 products produced by the partial oxidative coupling of methane. However, a higher C2 selectivity, achieved with a very low feed oxygen concentration, is accompanied by a reduction in yield because of the insufficient oxygen supply. In the extreme case, when the feed consists of 100% methane, no reaction will take place. The ratio of methane to oxygen is the most important operating parameter to achieve a high C2 yield and selectivity in the conventional FBR model. The performance of FBR as a function of feed composition in the methane feed range greater than 0.333 is subjected to an exhaustive examination with the computer model. These results are presented in two sets of surface and contour plots of the yield and selectivity, respectively, as a function of feed composition and active reactor length, defined as the length where oxygen supply is exhausted. The yield surface is shown in Figure 2. An examination of the surface contour lines shows that, at a feed methane mole fraction of less than 0.42, the yield has a maximum inside the reactor. This indicates that the presence of a large amount of oxygen favors the deep oxidation of C2 products produced by the oxidative methane coupling reaction. The excessive oxygen eventually causes the yield to drop off because of the deep oxidation of C2 products. At a feed methane fraction greater than 0.42, the yield increases along the reactor as long as the oxygen supply lasts. When the feed methane mole fraction is greater than 0.42, the maximum yield always occurs when the reactor is operated at the longest possible residence time depending on the availability of the oxygen supply. These maximal yields are plotted against their respec-
Figure 3. Maximal yield, selectivity, and feed rate at the maximal yield as a function of feed composition.
Figure 4. Selectivity surface as a function of reactor length and feed composition (T ) 750 °C).
tive feed compositions in Figure 3. It shows that the optimal feed composition for a reactor that will achieve the highest yield is at the feed composition of 70% methane and 30% oxygen. Operating the reactor to the point of total exhaustion of the oxygen supply occurs at the feed rate of 2.63 cm3(STP)/s per cm of reactor. The yield is at the maximal value of 20.7% with a selectivity of 52.4%. This observation agrees with experimental observations reported by a number of researchers (Ito and Lunsford, 1985; Itoh et al., 1985; Matsuura et al., 1989). The selectivity surface plot is shown in Figure 4. The selectivity surface shows that the maximal selectivity occurs at the reactor inlet for any feed composition. The selectivity surface has a valley running down the middle of the reactor length when the feed methane mole fraction is greater than 0.44. At lower feed methane mole fractions, the selectivity decreases from the reactor inlet. How the feed composition affects the C2 selectivity and yield in the FBR can be observed by a close examination of the concentration profiles in the reactor. An interesting picture of the competitive reactions taking place inside the reactor can be seen in Figure 5 which shows the concentration profiles inside the reactor at the feed methane mole fraction of 0.4 and the feed rate of 10 cm3(STP)/s. It shows that the C2 product concentration profile has a maximum as well as a minimum. The maximum is reached at approximately 0.7 cm from the reactor inlet. The C2 product concentration decreases from that point on to about 2 cm as the abundant oxygen in the mixture (mole fraction ranging from 0.1 to 0.3) further oxidizes C2 product
3588 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 Table 2. Some Simulation Results of FBR with Diluent 0 yCH 4
0 yO 2
SE (%)
YE (%)
0.7 0.35 0.14 0.07 0.007
0.3 0.15 0.06 0.03 0.003
52.3 54.5 56.7 57.8 59.8
20.7 22.3 24.1 25.1 26.8
Table 3. Effect of Diluent Feed on Kinetics CH4/O2 ) 0.7/0.3 CH4/O2 ) 0.07/0.03 CH4/O2 ) 0.007/0.003
rCO2 (mol/cm3‚s)
rC2H6 (mol/cm3‚s)
2.28 × 10-5 1.87 × 10-6 1.32 × 10-7
1.99 × 10-5 2.39 × 10-6 2.13 × 10-7
Figure 5. FBR concentration profiles for the feed of 40% methane and 60% oxygen.
Figure 7. Effect of feed temperature on selectivity and yield at the optimal feed composition: 70% methane, 30% oxygen. Figure 6. FBR concentration profiles at the optimal feed concentration.
produced upstream. From that point onward, the oxygen concentration is low (less than 0.1 mole fraction), which favors the oxidative coupling reaction. Consequently, the C2 product concentration increases. The concentration profiles at the optimal feed condition consisting of 70% methane and 30% oxygen are shown in Figure 6. It shows that, unlike the previous example of a feed containing 40% methane, the C2 product concentration increases from the inlet to the outlet of the reactor at approximately a constant rate. The carbon dioxide concentration increases at first at a steady rate and then levels off near the exit of reactor where the oxygen concentration is very low. Consequently, this mixture composition is most favorable for the OCM reaction. Most reported experiments were carried out with diluted reactant gas. We also examined the FBR performance for OCM with a diluted feed mixture. The optimal feed composition was found at the methane to oxygen ratio of 7:3. The simulation results for FBR operated to the point of total exhaustion of the oxygen supply are presented in Table 2. There is a noticeable increase in selectivity and yield under isothermal conditions when the diluent concentration increases. This improvement, however, was obtained at the expense of an increase in the size of the reactor for the same production rate. The improvement in selectivity, and hence also the yield, is due to the
dependency of the formation rates of C2H6 and CO2 on the diluent concentration. The formation rate of C2H6 can be greater than that of CO2 when the reactant mixture is diluted with an inert gas. This can be seen in Table 3, which lists the results of comparison of formation rates of C2H6 and CO2. So the selectivity and yield will be improved as a result of increasing formation rate of C2H6. In conclusion, when the oxygen to methane feed ratio is greater than 2, given enough reaction time all methane as well as the C2 products will be totally oxidized into CO2. The only way to improve the selectivity and yield is to increase the feed methane fraction. The overall conversion is, however, low because of insufficient oxygen supply in the feed. The yield will be low. The opposite dependencies of the overall conversion and yield with the methane fraction in the feed lead to the existence of an optimal feed composition. (c) Effects of Temperature on OCM in a FixedBed Reactor. The OCM reaction takes place at the temperature ranging from 700 to 900 °C. It was found that the optimal methane to oxygen feed ratio within that temperature range did not change to any significant extent. The effect of temperature on the performance of isothermal FBR at optimal feed ratio (70% methane, 30% oxygen) is presented in Figure 7. The highest yield is achieved when the oxygen is completely exhausted by the reactions. Both yield and selectivity increase with increasing temperature. This
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3589
result is not surprising for the following reasons. The methyl radical concentration increases with increasing temperature. The rate of methyl radical oxidation reaction is linearly dependent on the methyl radical concentration, and the rate of methyl coupling reaction is proportional to the square of methyl radical concentration. Higher temperature, therefore, favors the formation of C2 products to CO2. However, the OCM reaction, and more so for the deep oxidation reactions, is very exothermic. The reactor temperature will increase with the accumulation of reaction heat. Most experimental work was carried out under isothermal conditions. The isothermal conditions are maintained by operating under differential reactor condition or using a very diluted reactant mixture. In actual operation, heat generated should be removed. How to remove the reaction heat is a very challenging task in the design of industrial OCM reactors. The OCM reaction in a nonisothermal FBR was also analyzed (Luo, 1996). The results will not be presented here as it is beyond the scope of the present paper which is focused on comparison of OCM in fixed-bed reactors and membrane reactors. OCM in a Dense Membrane Reactor. The dense membrane reactor (DMR) has a significant advantage over the FBR since the oxygen concentration can be controlled by adjusting the feed pressure of oxygen at the shell side. It is possible to maintain the oxygen concentration at a uniform low value. Therefore, one can avoid the high oxygen concentration in the entrance region of the tubular reactor. One needs not to feed more methane than what can be reacted for the purpose of inhibiting further deep oxidation reaction. All of the feed methane will undergo reaction with the oxygen supplied through the membrane wall. The C2 yield can be as high as C2 selectivity would allow. The selectivity can be as high as the reactor oxygen concentration which will be controlled by the oxygen pressure on the shell side. The two operating parameters of DMR are the oxygen feed side pressure and the methane feed rate to the reactor. The effects of these two factors are examined in the following sections. From the FBR study, it was found that temperature does not have a significant effect on the selectivity. In the following discussion, the reactor is assumed to be operated under isothermal conditions. (a) Effect of Oxygen Feed Pressure. According to the permeation flux equation, the membrane thickness, temperature, and feed pressure all can affect the permeation flux. The membrane thickness is fixed by the equipment design. Temperature is determined by the reaction condition. The permeation flux across the membrane is controlled by the feed oxygen partial pressure on the shell side. Different feed pressures will lead to different permeation fluxes, which finally control the oxygen concentration in the reactor tube. The selectivity and the yield were examined with a reactor of 10 cm length and 1 cm i.d. The methane feed is kept at 10 cm3(STP)/s. The effect of oxygen pressure on yield and selectivity of C2 products is shown in Figure 8. It shows that the yield is considerably higher than the FBR maximum of 20.7%. In the range of feed oxygen pressure of 0.5-10 atm, the yield is greater than 34%. The yield increases with oxygen feed pressure and levels off at around 37% when the feed pressure reaches 5 atm and beyond. The increase in yield is obviously the result of more oxygen available for reaction at higher feed pressure.
Figure 8. Effect of oxygen feed pressure on selectivity and yield at the methane feed rate of 10 cm3(STP)/s.
The selectivity is higher when the oxygen feed pressure is lower. At the feed pressure of 1 atm, the selectivity is greater than 83%. At a lower feed pressure, the permeation flux of oxygen is smaller, resulting in lower oxygen concentrations in the reactor tube. Such a reaction mixture favors the OCM reaction. Consequently, the selectivity is higher. The selectivity decreases as the feed pressure increases. The selectivity drops to around 76% when the feed pressure is 10 atm. The pressure dependency of both yield and selectivity curves is logarithmic, reflecting the fact that the permeation flux is logarithmic with respect to the feed side pressure. (b) Effect of Methane Feed Rate. When the oxygen feed pressure is fixed, the methane feed flow rate, which is related to the residence time for the OCM reaction, will affect the performance of the OCM reaction. DMR is different from FBR in the way it controls the oxygen concentration profile in the reactor tube. In FBR, the oxygen concentration, with the maximum at the entrance, decreases to zero along the reactor length. The amount of methane that can react is limited by the oxygen supplied in the feed mixture. But in DMR, the oxygen is fed to the entire reactor length by permeation. The methane feed can always react as long as there is enough oxygen available. The effect of feed flow rate on DMR performance is examined with a reactor of the same dimension operating at an oxygen feed pressure of 5 atm. The results are shown in Figure 9. It shows that the selectivity increases sharply at first with increasing methane feed rate. It reaches asymptotically the value beyond 85%. Since the oxygen supply across the membrane is practically constant, the reaction rate is controlled by the oxygen supply. A higher methane feed rate will maintain the methane concentration at a higher value. Therefore, the selectivity will increase with the methane feed rate. The yield increases at first with increasing methane feed rate. The yield reaches a maximum close to 50% at the feed rate of about 5 cm3(STP)/s. As the feed rate is further increased, the yield drops. This behavior is due to the competitive nature of the OCM and the deep oxidation reaction. A larger methane feed flow rate means a smaller resident time. The methane concentration will be higher because a smaller fraction of the methane will be reacted. The selectivity is high, but
3590 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997
Figure 9. Effect of methane feed rate on selectivity and yield at the oxygen feed pressure of 5 atm.
Figure 11. Contour plot of the yield surface and the line of maximal yield.
Figure 10. Surface plot of yield as a function of methane feed rate and oxygen feed pressure.
the yield is low. When the methane feed flow rate is reduced, more methane will be converted to C2 products by the OCM reaction. In the meantime, more deep oxidation reactions will also take place. However, the amount of C2 products produced is greater than the deep oxidation reaction. So, the yield will increase when the feed rate is reduced with some decrease in selectivity. If the flow rate keeps on decreasing, the oxygen supply will eventually exceed what is needed for the OCM reaction. Further oxidation of C2 products will finally exceed the amount of C2H6 produced. Then the yield begins to drop after a certain feed rate accompanied by a sharp drop in the selectivity. In extreme conditions of very low methane feed rate, oxygen can oxidize nearly all of the C2 products. (c) Combined Effect of the Oxygen Pressure and the Methane Feed Rate. The combined effect of the oxygen feed pressure and the methane feed rate on the performance of DMR was examined by an exhaustive study with the computer model. These results are summarized in two sets of surface and contour plots of yield and selectivity. Figures 10 and 11 show the surface plot and its contour plot of yield as a function of the methane feed rate and oxygen feed pressure. The range of oxygen feed pressure examined was from 0.5 to 10 atm, and the feed
Figure 12. Yield profiles at oxygen feed pressure of 1, 5, and 10 atm, respectively.
rate varies from 2 to 15 cm3(STP)/s. The yield surface has a ridge oriented in the direction of varying feed pressure. This means that, at each feed pressure, there is an optimal methane feed rate when the yield is at a maximum. The ridge’s height increases in the direction of decreasing feed pressure. The maximum yield is higher when the oxygen feed pressure is lower. The yield as a function of methane feed rate at oxygen feed pressures of 1, 5, and 10 atm is shown in Figure 12. The maximum yield is high when the oxygen feed pressure is low. At 1 atm oxygen feed pressure, the maximal yield is greater than 50%. The maximum yield reduces to about 47% when the feed pressure is 5 atm. The optimal methane feed rate is smaller at a lower oxygen feed pressure. The decrease in yield from the maximum as the methane feed rate decreases is due to the longer residence time that allows further oxidation reaction to take place. The decrease in yield as the methane feed rate increases is due to the fact that there is not enough residence time for the reaction to take
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3591 Table 4. Comparison of DMR with FBR feed temperature (°C) feed flow rate (cm3(STP)/s) reactor length (cm) feed ratio (CH4/O2) C2 yield (%) C2 selectivity (%)
FBR
DMR
750 45 20 0.7/0.3 20.6 52.3
750 45 20 (Pf ) 5 atm) 21.0 87.1
Figure 13. Surface plot of selectivity as a function of methane feed rate and oxygen feed pressure.
Figure 15. Concentration profiles of DMR at the methane feed rate of 45 cm3(STP)/s and the oxygen feed pressure of 5 atm.
Figure 14. Selectivity profiles at oxygen feed pressure of 1, 5, and 10 atm, respectively.
place. In the range when the methane feed rate is greater than a certain value, the yield is higher when the DMR is operated at a higher oxygen feed pressure. This is a direct result of the higher oxygen supply, leading to a higher reaction rate. More methane will be converted and thus the yield is higher. The slight decrease in the maximum yield is due to the variation in the oxygen concentration in the reactor as oxygen feed pressure changes. For the same oxygen flux across the membrane as demanded by the reaction, the oxygen concentration in the reactor is lower. The lower oxygen concentration favors the OCM reaction. Consequently, more of the methane can be converted to C2 products by the OCM reaction and the yield will be higher. It is obvious based on the above discussion that selectivity has a strong influence on the yield. The influence of these two operating parameters on the selectivity is shown in the surface plot in Figure 13. The selectivity surface shows that the selectivity increases monotonically with increasing methane feed rate and with decreasing oxygen feed pressure. The selectivity is greater than 60% for most of the region. The selectivity of DMR operating under oxygen feed pressure of 1, 5, and 10 atm is shown in Figure 14. The selectivity of DMR is higher when the reactor is oper-
ated at lower oxygen feed pressure over any methane feed rate. A lower oxygen concentration is needed to maintain the oxygen flux across the membrane when the feed pressure is lower. The oxygen-deficient condition favors the OCM reactor and inhibits the deep oxidation reactions. Therefore, the selectivity is higher when the oxygen feed pressure is lower. Comparison of Two Reactors. The conventional FBR achieves only around 20% in C2 yield. The main reason for this low yield is due to the fact that methane and oxygen are fed together to the reactor tube. One must maintain a certain level of oxygen feed in order to achieve reasonable conversion. On the other hand, higher oxygen in the feed mixture will also promote the deep oxidation of methane and the OCM reaction products. In DMR, the oxygen concentration is at almost a uniform low level. The DMR appears to be able to achieve far better selectivity at the same yield. A comparison of these two reactors at comparable yield is summarized in Table 4. The concentration profiles in FBR operating at the optimal condition were shown in Figure 6. The oxygen concentration starts at the inlet at 0.3 mole fraction. It is consumed at approximately the same rate in the first two-thirds of the reactor length. The rate of oxygen usage decreases when its concentration is reduced to a rather low level. The reduced oxygen consumption reflects the fact that coupling reaction becomes dominant at a low oxygen concentration environment. In the dense membrane reactor oxygen is introduced across the oxygen-permeating reactor tube. Oxygen concentration in the reactor can be controlled to a very low level. The concentration profiles of the DMR is shown in Figure 15. The oxygen mole fraction in the reactor is less than 1/100. Deep oxidation reactions are suppressed in the low oxygen concentration environment. The formation of C2 products is preferred over the formation of CO2. The concentration of C2 products is higher than that of
3592 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997
carbon dioxide. The DMR achieves a much higher selectivity at comparable yield of a FBR. The simulation results reveal the possibility of achieving higher C2 yield of OCM in catalyst-packed DMR than in FBR. However, there are no experimental data reported on OCM in a dense perovskite-type ceramic tube packed with Li/MgO catalyst, which was examined in this simulation study. Thus, at this stage the simulation results cannot be verified by the experimental data. The higher C2 yield and selectivity obtained in DMR is in part due to the logarithmic dependency of the oxygen permeation flux on the oxygen partial pressure ratio. In reality, such a dependency could be more complicated and may not be logarithmic. The catalytic properties of Li/MgO when packed in DMR where oxygen and methane are fed separately are assumed to be the same as those measured in the FBR. It is likely that the radius of dense membrane reactor has a strong influence on its performances. The overall performance for OCM in DMR considering the radial oxygen distribution may not be as good as that in the ideal DMR assuming a uniform oxygen concentration in the radial direction. Therefore, the simulated results of the much higher C2 yield for OCM in DMR reported here should be considered indicative of feasibility, rather than reality. Conclusions The PFR model was used to examine the performance of OCM in a conventional fixed-bed reactor packed with Li/MgO as a function of the feed composition and reactor length. The global picture was presented in the form of C2 selectivity and yield surfaces. The results indicate that the maximum yield is obtained with the complete exhaustion of the oxygen supply to the reactor. The maximum C2 yield at 750 °C is about 20.7% at an optimal feed of 70% methane and 30% oxygen. The selectivity is about 52.4%. A higher yield and selectivity can be obtained with higher operating temperature. However, due to the way the reactant mixture is fed to the reactor, it is unlikely that the yield will be greater than 30%. A dense ceramic membrane reactor exhibits the possiblility of achieving yield and selectivity beyond the limit of 20.7% yield and 52.4% selectivity at 750 °C of the conventional fixed-bed reactor. The improvement is obtained by limiting the oxygen concentration in the reactor to a very low level. The deep oxidation reaction of the C2 product is significantly reduced. Consequently, the selectivity is higher and the yield is also greater. Acknowledgment Y.S.L. acknowledges partial support from the NSF (Career Award: CTS-9502437) on this project. Nomenclature A: cross-sectional area of reactor C1: carbon oxides concentration C2: ethane and ethylene concentration D: reactor i.d. F: molar flow rate Ki’s: reaction kinetics parameters JO2: permeation flux of oxygen P: reactor pressure Ph: DMR oxygen feed side pressure Pi: partial pressure of component i Pl: DMR methane feed side pressure
SE: selectivity of C2 products YE: yield of C2 products q: dimensionless flow rate r1: formation rate of carbon dioxide r2: formation rate of C2 products S0: fraction of radials that undergoes deep oxidation reaction tm: thickness of dense membrane yi: moler fraction of component i yi0: initial mole fraction of component i z: distance from the reactor inlet
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Received for review October 21, 1996 Revised manuscript received April 22, 1997 Accepted May 4, 1997X IE9606698
X Abstract published in Advance ACS Abstracts, July 15, 1997.
