Investigation of Gas-Phase Reactions and Ignition Delay Occurring at

Continuous-flow experiments in an empty aluminum oxide tube for the investigation of the homogeneous gas-phase reactions occurring at conditions typic...
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Ind. Eng. Chem. Res. 1999, 38, 2582-2592

Investigation of Gas-Phase Reactions and Ignition Delay Occurring at Conditions Typical for Partial Oxidation of Methane to Synthesis Gas R. J. Berger* and G. B. Marin† Capaciteitsgroep Reactortechnologie, Schuit Institute of Catalysis, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

Continuous-flow experiments in an empty aluminum oxide tube for the investigation of the homogeneous gas-phase reactions occurring at conditions typical for the partial oxidation of methane to synthesis gas were carried out at pressures from 300 to 800 kPa, temperatures from 1030 to 1300 K, inlet molar ratios of CH4/O2 from 2.1 to 3.1, and residence times from 0.09 to 0.38 s. The oxygen conversion varied from 3% to 43%. A detailed kinetic model based on a free-radical mechanism has been developed, which allows the adequate calculation of the feed conversions and product selectivities. The model includes pressure falloff effects occurring with the unimolecular reactions. The model reveals important features of the complex reaction network with the emphasis on the ignition stage at oxygen conversions between 0% and 5%. The occurrence of both isothermal ignition and thermal ignition can be distinguished in simulations with the model. The model was also used for estimating the ignition delays as a function of the process conditions. Introduction The production of synthesis gas from natural gas by partial oxidation has been extensively investigated as an alternative for the steam-reforming process since it results directly in a H2/CO ratio of 2:1 which is required for methanol and Fischer-Tropsch synthesis. Additionally, the moderate overall exothermicity of partial oxidation allows the use of an adiabatic reactor instead of a more expensive multitubular steam reformer. High temperatures favor high conversion rates and a high product selectivity near thermodynamic equilibrium (Lange et al., 1995; Bharadwaj and Schmidt, 1995). The noncatalytic partial oxidation is applied industrially on a large scale in secondary reforming (Christensen et al., 1995; Twigg, 1996; Farnell, 1994), autothermal reforming, and combined reforming (Farina and Supp, 1992) in which it is combined with steam reforming. As a separate process, the noncatalytic partial oxidation is also applied already on an industrial scale by Shell and Texaco (Pen˜a et al., 1996). Typical features of this noncatalytic route which have to be managed are the hot-spot temperatures amounting to about 15002000 K and the formation of significant amounts of soot in the gas phase. The homogeneous combustion process itself involves a complex chemistry consisting of numerous radical reactions. The catalytic route, which is not industrially applied currently, has recently received increasing attention since it allows the use of lower feed temperatures and since it might eliminate the difficulties with hot spots * To whom correspondence is addressed. Fax: +31-402446653. Present address: Department of Chemical Technology, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands. Phone: +31-15-2784316. Fax: +3115-2784452. E-mail: [email protected]. † Present address: Laboratorium voor Petrochemische Techniek, Universiteit Gent, Krijgslaan 281, 9000 Gent, Belgium. Phone: +32-92644517. Fax: +32-92644999. E-mail: [email protected].

and soot formation. The hot spot could be eliminated if the reaction could be carried out via the direct route (i.e., in one step from methane to synthesis gas) and not via the indirect route (i.e., the combustion to water and carbon dioxide followed by reforming to synthesis gas). Although the possibility of performing the reaction via the direct route has been reported by several researchers (i.e., Hickman and Schmidt, 1993; Hu and Ruckenstein, 1996; Mallens et al., 1997, Au and Wang, 1997) there seems for most catalysts an increasing consensus to the conclusion that the reaction occurs mainly via the indirect route (i.e., Prettre et al., 1946; Vernon et al., 1990; Dissanayake et al., 1993; Van Looij et al., 1994) whereas only at high temperatures the reaction may only partially proceed via the direct route (Boucouvalos et al., 1996; Basini et al., 1996; HeitnesHofstad et al., 1998). The work on the catalytic route has shown that a high temperature is required for achieving high yields to synthesis gas, in particular at high pressure. Typical conditions for the catalytic process are temperatures around 1200-1300 K and pressures of 0.5-4 MPa. Such high temperatures and pressures, however, inevitably enables the possibility of gas-phase combustion reactions to occur. Nevertheless, most papers on the catalytic partial oxidation do not report any influence of gasphase reactions since the laboratory experiments were usually carried out with diluted gas mixtures, at rather low temperatures and at pressures close to atmospheric pressure. However, a significant interplay between catalytic oxidation reactions and gas-phase reactions has been reported experimentally in a gauze reactor by Witt and Schmidt (1996). Additionally, there could be similarities with the catalytic oxidative coupling of methane which has been proven to be a combination of catalytic reactions, gas-phase reactions, and the interaction between both via methyl radicals (Ito et al., 1985; Couwenberg et al., 1996). Therefore, a thorough knowledge about the kinetics of the gas-phase reactions at

10.1021/ie9807304 CCC: $18.00 © 1999 American Chemical Society Published on Web 06/15/1999

Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 2583

the conditions typical for the partial oxidation of methane to synthesis gas is prerequisite for a complete investigation of the process and for the development of a comprehensive reactor simulation at industrial conditions. In the literature, several extensive kinetic models are available which describe the gas-phase reactions via a large number of elementary radical reactions. However, these are optimized for conditions which differ significantly from those typical for the catalytic process. There are several comprehensive models optimized for the combustion of hydrocarbons and other compounds which are valid in a wide range of conditions (i.e., Gardiner and Troe, 1984; Tsang and Hampson, 1986; Tsang, 1988; Baulch et al., 1992; Mallard et al., 1994). The kinetic model developed by the Gas Research Institute can even be obtained from the Internet (Serauskas). As a consequence of the wide range of applicability of these models, however, the accuracy of the kinetic parameters is insufficient for an accurate simulation of the process of interest. There are also kinetic models that focus on a more limited range of conditions which differ, however, too much from those required. Examples are models for the production of methanol from methane in the gas phase (Chun and Anthony, 1993; Lo¨deng et al., 1995) which are valid around 800 K, 5 MPa, and CH4/O2 ratios of 30, models for the homogeneous oxidative coupling of methane (Zanthoff and Baerns, 1990; Andrianova et al., 1993; Chen et al., 1994) which are valid at the right temperature (1100 K) and pressure (0.5 MPa) but for mixtures containing an excess of methane (CH4/O2 ratios around 5), and models for the noncatalyzed partial oxidation of methane to synthesis gas at very high temperatures around 1600 K (Karim and Hanafi, 1992). There is thus an evident need for a kinetic model optimized at the conditions typical for the catalytic partial oxidation of methane to synthesis gas. Such a model also allows simulations of the gas-phase reactions at low oxygen conversion which is essential for an accurate simulation of the homogeneous ignition of gasphase combustion which may cause several undesirable phenomena such as runaways, hot spots, and an irregular reactor performance. This paper focuses on the development of a compact kinetic model optimized for the conditions typical for the partial oxidation of methane to synthesis gas at industrial conditions. The experiments were carried out in a continuous flow empty tube reactor. The work concentrated on experiments with incomplete oxygen conversions. Previous work which concentrated on the oxidative coupling of methane (Chen et al., 1994) has been used as a basis for the work reported in this paper. The resulting kinetic model is used for the simulation of a series of cases of autoignition occurring at conditions which are typical for the catalytic partial oxidation. Experimental Section Equipment. Several series of experiments with undiluted CH4/O2 mixtures were performed in which the temperature, pressure, space time, and CH4/O2 ratio were varied; the range of the conditions covered is shown in Table 1. The experiments were carried out in a continuous flow setup with an empty tubular reactor. All gases are purified by means of columns filled with molecular sieves (MS) to remove water, and all gases except oxygen are purified by a column filled with a BTS

Figure 1. Schematic view of the reactor used. Table 1. Range of Experimental Conditions total pressure T(max) CH4/O2 ratio F(tot) V/F(tot) τ CH4 conversion O2 conversion

kPa K 10-3 mol s-1 10-3 m3 s mol-1 s % %

300-800 1030-1300 2.1-3.1 1.5-7.2 1.0-5.2 0.09-0.38 1-17 3-43

catalyst heated at 323 K to remove oxygen. The gas flows are regulated via mass flow controllers. The reactor pressure is regulated by a manually adjustable back pressure regulator, containing a membrane that is pressurized with nitrogen, and is located downstream of the reactor. The setup contains several safety devices: (i) a spring valve that opens if the system pressure rises above 1 MPa in order to avoid overpressure if the system becomes plugged, for example, as a result of coke formation; (ii) a rupture disk which breaks at ∼3.5 MPa and prevents serious damage in case of explosions; (iii) a flame extinguisher which extinguishes any flames or explosion progressing in an upflow direction; (iv) an emergency valve allowing pressurized nitrogen to flow into the reactor which can be opened manually when runaway starts to occur or if serious malfunctioning of the apparatus takes place. A schematic view of the reactor is shown in Figure 1. The reactor, having a length of 0.65 m and consisting of dense aluminum oxide (alumina), is heated by means of a fluidized quartz sand bed which enables a fast heat exchange with the reactor tube. This is important in order to suppress the axial temperature gradients inside the reactor, thus promoting the isothermicity of the reactor, and also to decrease the chance of runaway. The axial temperature profile was measured by a movable thermocouple placed in an alumina thermowell centered in the reactor tube. Runaway of the reaction downstream of the sand bed was prevented by introduction of a 24 cm long alumina tube in the bottom part of the reactor (o.d. 7.65 mm; i.d. 4.75 mm). A small fraction of the reactor effluent is analyzed

2584 Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 Table 2. Experimental and Simulated Results (Shown within Brackets) of Seven Experiments at Various Pressures, Temperatures, and Space Times p(tot) [kPa]

T(max) [K]a

V/F(tot)inb [m3 s mol-1]

τc [s]

300

1110

0.00239

0.094

500

1110

0.00150

0.099

750

1110

0.00080

0.086

500

1036

0.00158

0.110

500

1300

0.00164

0.106

500

1110

0.00115

0.078

500

1110

0.00425

0.296

X(CH4) [%]

X(O2) [%]

S(H2)d [%]

S(H2O) [%]

S(CO) [%]

S(CO2) [%]

S(C2H6) [%]

S(C2H4) [%]

1.3 (2.0) 3.4 (3.5) 6.4 (6.6) 1.4 (2.6) 14.1 (13.6) 2.9 (2.3) 17.1 (12.7)

3.4 (4.1) 9.5 (7.9) 17.5 (18.1) 4.3 (5.9) 34.4 (34.1) 8.1 (4.8) 43.2 (36.9)

8.5 (16.0) 10.4 (14.7) 19.3 (12.5) 8.7 (13.2) 28.5 (23.0) 11.4 (13.8) 12.1 (16.3)

60.4 (49.8) 65.2 (54.42) 63.2 (67.7) 67.2 (55.5) 53.1 (57.8) 64.6 (52.8) 65.4 (68.2)

37.6 (48.4) 50.8 (49.8) 59.5 (59.7) 50.2 (50.7) 59.4 (58.3) 49.2 (48.9) 59.2 (57.2)

2.5 (1.3) 4.6 (3.2) 7.7 (7.6) 3.1 (2.8) 7.0 (8.5) 4.8 (2.0) 5.9 (16.5)

42.3 (35.2) 22.7 (27.4) 9.3 (10.4) 29.1 (29.6) 9.4 (9.6) 22.7 (33.0) 15.7 (9.0)

15.2 (11.2) 18.3 (15.4) 19.4 (18.2) 12.6 (12.4) 21.7 (21.0) 20.1 (11.6) 16.3 (15.0)

a T(max) refers to the maximum temperatures in the axial temperature profile. b The CH /O ratio was 2.6 in all these experiments. 4 2 τ refers to the residence time in the zone hotter than 750 K. d Additionally, small amounts of formaldehyde (1-5%), propylene (0-1%), and propane (0-2%) were found.

c

by two on-line HP 5890 series II gas chromatographs, equipped with Chrompack wide-bore molsieve-5A and Poraplot Q columns and a thermal conductivity detector and flame ionization detector using either He or Ar as the carrier gas, which can analyze CH4, O2, CO, CO2, C2H6, C2H4, C3H8, C3H6, H2O, H2, He, and N2. A flow of nitrogen, added to the reactor effluent, was used as the internal standard. The C, H, and O balances were closed within 5% for all the experiments. Conversions, Selectivities, Space Time, and Ignition Delay. The conversions are defined as

Fi Xi ) 1 Fi,0

i ) CH4, O2

(1)

and integral selectivities for the C-containing products (Si,C) and H2 and H2O (Si,H) are defined as

Si,C ) Si,H )

nC,iFi FCH4,0 - FCH4 nH,iFi

4(FCH4,0 - FCH4)

(2)

These are calculated according to the normalization method, that is, assuming 100% C-, H-, and O-balances. In the present work, both space time and residence time are used. The space time is defined as the ratio of the reactor volume and the feed flow rate of methane. For the reactor volume, the part of the reactor tube in which the temperature exceeds the, arbitrarily chosen, limit of 750 K was taken. The residence time is defined as

τ)

p dV

t ) ∫0V FRT

Apt R

dz ∫0lFT

(3)

where pt the total pressure, V the reactor volume, F the local total molar flow rate, A the cross-sectional surface area of the reactor, z the axial coordinate in the reactor, and l the length of the reactor. Since the local molar flow rates are not known at each axial position z and since the temperature profile is measured at 20-30 distinct positions, the residence time is approximated according to

τ)

Apt F0R

∆z

∑T

(4)

The ignition delay is the time interval between the start of the reaction and the ignition. An ignition is characterized by an abrupt increase of the reaction rate, often accompanied by a rapid temperature rise. In this paper, the ignition delay is defined as the residence time required to reach 10% oxygen conversion. Experimental Results The results of seven representative experiments taken from a total of 31 experiments are shown in Table 2. Despite the lower CH4/O2 ratios that were used here, the tendencies found are in line with those found by Chen et al. (1994) for homogeneous reactions occurring during the oxidative coupling of methane. The conversions increase significantly with increasing temperature and pressure. Likewise, the selectivities to H2, CO, and CO2 increase and that to C2H6 decreases. Increasing the space time also increases the conversion and the selectivity to CO at the expense of that to C2H6 and C2H4, which indicates that the C2 products are converted to CO. The selectivity to formaldehyde (CH2O) was always less than 2%, except at temperatures below 1050 K where selectivities up to 5% were found. In all experiments, the selectivity to propane was below 1% and that to propylene below 2%. Variation of the CH4/O2 ratio within the range 2.13.1 has only minor influences on both conversions and selectivities; this is not shown in Table 1. The largest influence is on the selectivity to C2H6 which decreases by approximately 5-10% with decreasing the ratio from 3.1 to 2.1. Because of the large reaction heat of the oxidation reactions, the shape of the axial temperature profiles depends significantly on the experimental conditions. In particular, at pressures above 600 kPa, temperatures above 1200 K, and/or the lowest CH4/O2 ratio used, rather steep temperature profiles were obtained as a result of a close approach to the conditions where runaway starts to occur. With increasing pressure, the temperature of the sand bed had to be decreased in order to keep T(max) constant. Figure 2 shows the effect of the total pressure on the temperature profile; in this figure, the highest temperature of the profile was in all

Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 2585

Dθ0 r2

Figure 2. Axial temperature profiles of three experiments at different pressures (T(max) ) 1110 K; CH4/O2 ) 2.6; τ ) 0.09 s).

cases found near the top of the 24 cm long alumina tube positioned in the bottom part of the reactor. The runaway effect restricted the measurements to the conditions shown in Table 1. The differences in axial temperature profiles also hampered the investigation of the influence of each process parameter independently. To avoid misleading conclusions, no plots of the experimental conversions and selectivities as a function of any variable such as pressure, space time, and so forth are included in this paper; instead of these, an overview of the results of several experiments is included via Table 2. Modeling The experimental results were used to develop a new kinetic model applicable at the conditions typical for high-temperature partial oxidation of methane, using the knowledge from the gas-phase model developed for conditions encountered during the oxidative coupling of methane by Chen et al. (1994). The original model was extended with reactions which may become important at these conditions. Only the Arrhenius parameters of the forward reactions were needed while those for the reverse reactions were calculated from the thermodynamic properties of the components taken from the CHEMKIN thermodynamic database of the Sandia National Laboratory (Kee et al., 1989). Reactor Simulation Model. Previous investigations showed that the heterogeneous termination reactions at the reactor wall could be neglected, and hence, a fortiori at higher pressures (Chen et al., 1994). This was also confirmed by a few additional experiments in which the reactor was filled with dense alumina spheres and an alumina tube which filled up a large part of the reactor volume. In these experiments, carried out at 500 kPa, with a similar axial temperature profile with a maximum temperature of 1060 K, a CH4/O2 ratio of 2, and a similar residence time, both the conversions and the selectivities were similar to those obtained without this filling. The reactor model used consists of a set of continuity equations describing the concentration of each molecule and radical component in the axial direction of the plugflow reactor. The plug-flow assumption was justified using a criterion from Cleland and Wilhelm (1956) who concluded that plug flow can be assumed if

>1

(5)

where D is the molecular diffusivity (m2/s), θ0 the residence time of the central streamline in the reactor (s), and r the reactor radius (m). A sufficient high value of 5 follows with a typical diffusivity of 5 × 10-5 m2/s, a residence time of 0.1 s, and an effective reactor radius of 1 mm. The effective reactor radius was taken to equal 1 mm since this equals half the distance between the inside and outside wall of the annular space in the reactor. The reactor model results in a set of stiff first-order differential equations. The method developed by Dente et al. (1979), applying the pseudo-steady-state assumption for the reactive radicals, was used for the integration of the equations. In this method, the reactor is divided into a large number of axial segments in which the reaction rates are calculated using the average concentrations of the molecules in that segment. The measured axial temperature profile was explicitly taken into account during the integration of the equations. The concentrations of the radicals in the beginning of the reactor were estimated by repeating the integration of the first segment 15 times in which each time the resulting radical concentrations were used as the new estimates; with this procedure, the radical concentrations converged to a constant value with all experiments. The size of the axial segments was decreased when the reaction rates increased in order to allow the use of average concentrations in the segments. This resulted in segments having a length varying from 5 mm in the colder zones down to 0.04 mm in the hottest zone of the reactor. The total number of segments varied from 220 in the experiment with the lowest oxygen conversion of 3.4% to 1000 in the experiment with the highest oxygen conversion of 43%. A further increase of the number of segments did not influence the results significantly; that is, an increase by a factor of 5 increased the highest conversion only by 0.8%. Network Construction. The construction of the radical reaction network started from a large set of more than 300 reactions with the Arrhenius parameters taken from the literature on combustion chemistry. The data were taken from the NIST Standard Reference Database (Mallard et al., 1994). From this database, the data from Baulch et al. (1992), or the data from Tsang and Hampson (1986) have been used, as far as it is available. Initially, a large kinetic scheme containing more than 300 reactions with 17 molecules and 16 radicals was investigated. Both sensitivity analyses and contribution analyses were performed in order to identify the important reactions at typical partial oxidation conditions, that is, temperatures ranging from 900 to 1400 K and pressures between 100 and 2000 kPa. The reactions which had a negligible influence at these conditions were removed from the network. Examples are all the reactions involving the radicals CH•, CH2•, C2H•, HCCO•, and CH3CO• and the molecules CH2CO (ketene), CH3CHO (acetaldehyde), and CH3OH (methanol). The compounds propadiene and propyne, of which only traces were found in a few of the experiments, were also removed from the network; the amounts detected were added to the amounts of propylene. Finally, the effects of reactions involving carbon (coke) were not taken into account since carbon formation in methane/oxygen mix-

2586 Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 Table 3. Model for the Partial Oxidation of Methane to Synthesis Gas in the Absence of a Catalyst Covering the Range of Conditions Shown in Table 1 no 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

k0a

reaction •

H•

CH4 + M a CH3 + +M CH4 + O2 a CH3• + HO2• CH4 + H• a CH3• + H2 CH4 + O• a CH3• + OH• CH4 + OH• a CH3• + H2O CH4 + HO2• a CH3• + H2O2 CH3• + O2 a CH2O + OH• CH3• + O2 a CH3O• + O• CH3• + HO2• a CH3O• + OH• 2 CH3• + M a C2H6 + M CH3O• + M a CH2O + H• + M CH2O + O2 a HO2• + CHO• CH2O + OH• a CHO• + H2O CH2O + HO2• a CHO• + H2O2 CH2O + CH3• a CHO• + CH4 CHO• + M a CO + H• + M CHO• + O2 a CO + HO2• CO+ HO2• a CO2 + OH• C2H6 + H• a C2H5• + H2 C2H6 + OH• a C2H5• + H2O C2H6 + CH3• a C2H5• + CH4 C2H5• + M a C2H4 + H• + M C2H5• + O2 a C2H4 + HO2• C2H4 + H• a C2H3• + H2 C2H4 + OH• a C2H3• + H2O C2H4 + CH3• a C2H3• + CH4 C2H3• + M a C2H2 + H• + M C2H3• + O2 a C2H2 + HO2• C2H3• + O2 a CH2O + CHO• C2H5• + CH3• a C3H8 C2H4 + CH3• a C3H7• C3H8+ H• a C3H7• + H2 C3H7• a C3H6 + H• C3H7• + O2 a C3H6 + HO2• O2 + H• a OH• + O• O2 + H• + M a HO2• + M HO2• + HO2• a O2 + H2O2 H2O2 + M a OH• + OH• + M OH• + H2 a H2O + H• HO2• + H• a OH• + OH•

0.240 × 0.398 × 108 0.473 × 108 0.173 × 109 0.659 × 108 0.128 × 108 0.396 × 106 0.102 × 1010 0.255 × 108 0.329 × 107 0.383 × 109 0.282 × 109 0.951 × 109 0.461 × 107 0.266 × 107 0.835 × 108 0.305 × 108 0.474 × 108 0.223 × 109 0.230 × 109 0.874 × 109 0.317 × 1015 0.377 × 105 0.542 × 109 0.205 × 108 0.416 × 107 0.200 × 1015 0.121 × 106 0.542 × 107 0.105 × 109 0.109 × 107 0.238 × 1010 0.433 × 1015 0.119 × 107 0.728 × 109 0.150 × 103 0.121 × 107 0.967 × 1010 0.304 × 108 0.506 × 109 1017

Ea [kJ mol-1]

A/RTb

b r [mol m3 s-1]

438.98 223.03 50.31 49.12 34.54 88.18 54.29 151.30 0.00 -11.34 81.12 184.27 7.74 43.62 13.39 47.07 13.74 73.95 44.10 18.60 97.64 195.98 - 1.56 62.36 24.86 46.56 166.28 0.00 0.00 0.00 35.64 30.44 157.69 11.01 77.91 - 6.98 14.92 159.66 29.08 3.66

-6.3 0.1 2.0 12.0 4.8 5.7 37.8 11.7 23.6 6.9 7.8 8.7 13.5 14.3 8.6 3.8 10.2 33.5 4.5 7.4 2.5 0.8 7.2 4.9 7.8 2.9 0.1 6.5 44.8 3.8 -0.4 4.9 1.0 7.3 14.3 6.4 5.6 14.2 2.9 26.2

0.002 0.64 25.83 8.62 59.70 11.99 20.28 1.38 12.04 18.68 13.46 2.22 11.55 0.40 23.01 30.30 7.77 2.58 1.05 5.15 4.80 1.91 7.80 0.13 0.086 2.17 0.076 0.049 2.18 1.74 1.87 1.28 0.36 0.12 7.27 11.40 0.030 12.38 0.38 0.41

a k is expressed in s-1 or m3 mol-1 s-1 or m6 mol-2 s-1. b Affinity A and the forward reaction rate b r calculated at T(max) in the experiment 0 carried out at the following conditions: p ) 500 kPa, T(max) ) 1110 K, CH4/O2 ratio ) 2.6, and V/F(tot)in ) 0.0015 m3 s mol-1; at the position of T(max) the simulated conversions of methane and oxygen amount to 2.53% and 5.27%, respectively. The relation between the affinity and the forward and backward (r a) reaction rate is ln(r b/r a) ) A/RT.

tures only starts to occur after complete consumption of the oxygen whereas the maximum oxygen conversion in the experiments amounts to 43%. The modeling work and the minimization using the experimental results ultimately led to a reaction network containing 40 reversible elementary free-radical reactions with 13 molecules (H2, H2O, H2O2, O2, CH4, C2H6, C2H4, C2H2, C3H8, C3H6, CH2O, CO, and CO2) and 10 radicals (H•, O•, OH•, HO2•, CH3•, C2H5•, C2H3•, C3H7•, CH3O•, and CHO•) which is shown in Table 3. Arrhenius Dependency. Conventional two-parameter Arrhenius relations were used in this study. A third parameter is often used in combustion modeling when the rate equations are intended to cover a broad temperature range. Since the temperature range covered in this study is rather narrow, the three-parameter rate equations from the literature were converted to two-parameter relations over the temperature range of interest, that is, 800-1300 K. Procedure for the Parameter Estimation. A reparametrization of the pre-exponential factor was performed in order to obtain a much faster minimization. This was done by converting the pre-exponential factors from the literature relations to the rate coefficients at 1123 K, a temperature in the middle of the

Table 4. Weighting Factors (wj) Used in the Minimization of the Objective Function O2 CH4 H2 CO H2O CO2 C2H6 C2H4 H2O2 CH2O C3H8 C3H6 10

6

3

15

13

3

5

5

0

0.4

0.2

0.4

range used experimentally, using the activation energies from the literature relations. The parameters were optimized using a minimization routine based on an algorithm from Rosenbrock (Rosenbrock, 1961; Rosenbrock and Story, 1966). The following objective function was minimized: v

S(b) )

n

∑ ∑ j)1 k)1 wj

{ykj - fj(xk,b)}2 {ykjfj(xk,b)}

(6)

with wj the weighting factor for response j, ν the number of responses, ykj the response values observed experimentally for response j in experiment k, n the number of experiments, fj(xk,b) the response value calculated with the model for response j in experiment k, xk the vector of independent variables, and b the parameter vector. The weighting factors wj used are shown in Table 4; the components with the highest concentrations were weighted the heaviest (hydrogen peroxide was not used since it was never detected experimentally). The objec-

Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 2587 Table 5. Falloff Coefficients for Calculation of ku/k∞ or ku/k0 reaction no.

falloff equation

1 19 21 43 53 75

coefficients for calculation of k R2

R1

10-3

-0.4904 3.9690 2.394 × 10-6 1.8920 0.4197 6.003 × 10-5

(7) (7) (8) (7) (7) (8)

-2.3380 × -4.8740 × 10-3 2872.3 -5.0580 × 10-3 -2.7810 × 10-3 2800.1

tive function shown above is derived from a simplified form of the generalized least-squares criterion assuming that the experimental errors associated with different responses are not correlated (Froment and Hosten, 1981). The CH4 and O2 conversions, as well as the selectivity to all components, were taken as responses. However, the selectivities in 4 of the 31 experiments in which the calculated conversion differed significantly from the experimental conversion were not used in the minimization since the selectivities depend significantly on the conversion. Pressure Falloff Equations Used. The effect of “pressure falloff” at unimolecular reactions (see Gardiner and Troe, 1984) was taken into account in the simulations. The collision efficiencies were assumed to be independent of temperature and reaction, and the values of the weight factors required for the calculation of the concentration of third bodies (M) were taken from Warnatz (1984). Many weight factors are equal to unity, except H2O, CH4, CO2, CO, O2, N2, Ar, and He with values of 6.5, 6.5, 1.5, 0.75, 0.4, 0.4, 0.35, and 0.35, respectively, relative to hydrogen. The rate constants of the unimolecular reactions taken from the literature were determined using Ar (or N2) as the bath gas which has a collision efficiency of 0.35 (or 0.4) relative to hydrogen, which was corrected for by multiplying the third body concentration CM by a factor of 1/0.35. For most unimolecular reactions the falloff data were taken from Warnatz (1984); however, for the recombination of two methyl radicals the data from Hessler and Ogren (1994) were applied. The falloff data were accurately fitted by correlations having the shape of eq 7.

CMR4 exp(R1 + R2T + R3T2) ku ) k∞ 1 + C R4 exp(R + R T + R T2) M

1

2

(7)

3

The corresponding falloff coefficients R1-R4 are listed in Table 5. For the unimolecular reactions with numbers 11, 16, 30, 31, 33, 36, and 38 no data concerning the falloff behavior were available. For the pressure range considered in most simulations (0.1-2 MPa), however, the unimolecular reactions 16 and 36 can be assumed to be completely in the low-pressure regime, whereas the unimolecular reactions 30, 31, and 33 may be assumed to be in the high-pressure regime. These latter reactions are therefore represented in Table 3 without the third body M. The two remaining unimolecular reactions, the decomposition of CH3O• (reaction 11) and the decomposition of H2O2 (reaction 38) are also mainly in the lowpressure regime, but these are influenced by pressure falloff to some extent at higher pressures. For these reactions, the literature data concerning the rate equations at both the low-pressure limit and at the highpressure limit were therefore combined, using eq 8:

ku ) k0

CM

( )

R2 1 + CMR1 exp RT

R3

R4 10-7

1.9720 × 3.8020 × 10-7

0.75 0.55

7.2850 × 10-7 3.5420 × 10-7

0.70 0.75

with R1 )

a0 and a∞

R2 ) -Ea,0 + Ea,∞ (8)

In these equations a0 and Ea,0 are the pre-exponential factor and the activation energy for the rate equation at the low-pressure limit and a∞ and Ea,∞ those for the high-pressure limit. With eq 8, ku becomes equal to 1/2k∞ if CM has such a value that the reaction rate according to the equation for the low-pressure limit is equal to that for the high-pressure limit. The p1/2 values of all unimolecular reactions studied are shown as a function of temperature in Table 6; a collision efficiency of 4, which is typical for methanerich mixtures, was used for the calculation of the p1/2 values. Parameter Estimation. Using the literature values for parameters as the first estimate and including the pressure falloff effect, the calculated conversions were in the right order of magnitude; however, the conversions were too high at high temperatures and too low at low temperatures. With the literature values for the parameters also too high selectivities to C2H6 and too low selectivities to C2H4, H2, and CO were simulated. To obtain the best fit, it appeared to be very useful to start with minimization of the O2 conversion only. Initially, only the most sensitive parameters were optimized to obtain a better description of the experimental results. The rates of reactions that most strongly influence the conversions are 8, 9, 10, and 36 while at higher conversions also the rates of reactions 3, 6, 7, and 17 become sensitive. Subsequently, varying also the other, less sensitive parameters further optimized the fit. Since the Rosenbrock routine showed that there exist many local minima of the objective function, many series of minimizations were done in which the most sensitive parameters were also varied by means of a randomizer. In all minimizations, however, the parameters were allowed to change only within a fixed window having a width approximately equal to the uncertainties given with the literature data. To obtain a good fit, about 60% of the parameters had to be adapted. To increase the C2H4 selectivity at the expense of the C2H6 selectivity, the rate of reaction 20 had to be increased by a factor of 5 in comparison to the literature value. The rate of reaction 32 had to be increased by a factor of 25 in order to fit the C3H6/C3H8 ratio observed. Ultimately, also the k0 value of reaction 13 had to be increased strongly by a factor of 25, while the k0 values of reactions 2, 6, 1416, 18, 30, 31, 33, 34, 38, and 40 were increased by a factor varying from 2 to 7. The k0 values of reactions 3, 8, 17, 22, 23, 36, and 37, however, were decreased by a factor varying from 2 to 7. Additionally, the Ea values of reactions 7, 12, 21, and 22 were increased significantly by values ranging from 10 to 20 kJ/mol, whereas the Ea values of reactions 2, 3, 6, 14-16, 18, 23, 32, 34,

2588 Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 Table 6. P1/2 Values of the Unimolecular Reactions in the Kinetic Model Calculated for a Gas Mixture Having an Average Collision Efficiency of 4 Relative to That of H2 p1/2/100 kPaa no.

reaction

900 K

1100 K

1300 K

source

1 10 11 16 22 27 30 31 33 36 38

CH4 + M a CH3• + H• + M 2 CH3• + M a C2H6 + M CH3O• + M a CH2O + H• + M CHO• + M a CO + H• + M C2H5• + M a C2H4 + H• + M C2H3• + M a C2H2 + H• + M C2H5• + CH3• a C3H8 C2H4 + CH3• a C3H7• C3H7• a C3H6 + H• O2 + H• + M a HO2• + M H2O2 + M a OH• + OH• + M

0.35 0.0073 112

1.36 0.027 250 very high 0.33 0.15 very low very low very low very high 10.4

3.62 0.090 434

b c d e b b f f f e d

0.10 0.072

4.83

0.94 0.3

18.2

The pressure at which the ratio ku/k∞ ) 1/2 is referred to as p1/2. b Falloff bahavior according to Warnatz (1984). c Falloff bahavior according to Hessler and Ogren (1996). d Estimated from the kinetic equations for the unimolecular and bimolecular rate expression taken from NIST. e The p1/2 value is probably very high and no kinetic data were available for the high-pressure regime. f The p1/2 value is probably very low and no kinetic data were available for the low-pressure regime. a

Figure 3. Parity plots for the simulated and the observed CH4 and O2 conversions and the CO, CO2, C2H6, and C2H4 selectivities.

and 38 were decreased significantly by values ranging from 10 to 25 kJ/mol. The other parameters were not or only slightly modified. The rate parameters of the final model are shown in Table 3, together with the corresponding affinities and reaction rates at typical conditions. Modeling Results. Figure 3 shows the parity plots obtained for the conversions and selectivities; the parity plots for the other selectivities are comparable. Most results are close to the diagonal line that indicates that a good fit has been obtained. From the whole set of 31 experiments only the conversions and the CO2 selectivity as a function of the space time could not be described well. An impression of the fit obtained with the model

can also be obtained from the data in Table 2, which shows for 7 of the 31 experiments the conversions and selectivities obtained with the model together with those observed. The collision efficiencies used for the description of the falloff effect significantly influence the simulation results. Since the values of these collision efficiencies are rather uncertain, it was necessary to perform a sensitivity analysis on this factor. This was done by using a weight factor of unity instead of 6.5 for the most abundant molecular species, methane. This factor directly influences the reaction rates of many unimolecular reactions almost proportionally, and therefore another parameter optimization was required. After

Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 2589 Table 7. Local Conversions and Selectivities of the Experiment Carried Out at p ) 500 kPa, T(max) ) 1110 K, CH4/O2 ) 2.6, and V/F(tot)in ) 0.00150 m3 s mol-1 Obtained from the Simulation axial position local [s] local T [K] conversion [%] CH4 O2 selectivity [%] H2O2 H2 H2O CH2O CO CO2 C2H6 C2H4 C2H2 C3H8 C3H6 τb

0.084 m 0.191 m 0.0342 0.0842 902.5 1107.0 0.35 2.5 0.84 5.3 0.28 0.00 0.54 14.4 48.3 51.6 79.9 2.8 5.8 47.5 0.01 1.9 14.3 33.6 0.7 12.3 0.00 0.06 0.00 1.3 0.00 0.6

0.226 ma 0.0990 686.0 3.5 7.9 0.33 14.7 54.4 2.1 49.8 3.2 27.3 15.4 0.02 0.7 1.4

a The axial position of 0.226 m refers to the end of the reactor. The local τ refers to the residence time in the zone hotter than 750 K.

b

Table 8. Predominating Reactions in the Ignition Stage at X(O2) ) 0.84% where T ) 902.5 K, in the Experiment Carried Out at p ) 500 kPa, T(max) ) 1107 K, CH4/O2 ) 2.6, and V/F(tot)in ) 0.00150 m3 s mol-1 no. 5 6 7 10 15 16 36 38

reaction OH•

•

CH4 + a CH3 + H2O CH4 + HO2• a CH3• + H2O2 CH3• + O2 a CH2O + OH• 2 CH3• + M a C2H6 + M CH2O + CH3• a CHO• + CH4 CHO• + M a CO + H• + M O2 + H• + M a HO2• + M H2O2 + M a OH• + OH• + M

A/RT

local r [mol m3 s-1]

11.7 5.4 48.1 16.4 10.1 11.9 8.6 16.2

0.246 0.018 0.210 0.024 0.023 0.014 0.010 0.016

performing this optimization, however, the description of the experiments was almost unchanged. This indicates that the uncertainty in the collision efficiency has a limited influence on the results obtained with the model within the range of conditions investigated. Model Analysis Reaction Path Analysis. The kinetic model determined in this study allows an analysis of the most important reaction paths with a particular interest for the branching reactions. The reaction paths determine the course of the acceleration of the conversion rate during and after ignition and also the selectivity as a function of the conversion. Such a contribution analysis was carried out for one typical experiment (p ) 500 kPa, T(max) ) 1110 K, CH4/ O2 ) 2.6, V/F ) 0.00150 m3 s mol-1) at two different axial positions, near the reactor entrance at z ) 0.084 m where the process is in the ignition stage and at z ) 0.191 m where the maximum temperature was observed. The local conversions and selectivities are shown in Table 7. At the ignition stage with an oxygen conversion of 0.84% and a temperature of 902.5 K, the model simulates a very high selectivity of 80% to formaldehyde, while also ethane and water are primary products. In this stage, reactions 5 and 7 are clearly the predominating reactions as shown in Table 8 that explains the high formaldehyde selectivity. The process proceeds through a degenerate branched-chain mechanism, similar to the oxidative coupling of methane (Chen et al. 1994), with the decomposition of hydrogen peroxide (reaction 38)

Table 9. Concentrations of the Radicals According to the Model at the Axial Positions z ) 0.084 m and z ) 0.191 m (Experiment Carried Out at p ) 500 kPa, T(max) ) 1107 K, CH4/O2 ) 2.6, and V/F(tot)in ) 0.00150 m3 s mol-1) radical

concentration at z ) 0.084 m [mol %]

concentration at z ) 0.191 m [mol %]

H• O• OH• HO2• CH3• CHO• CH3O• C2H3• C2H5• C3H7•

0.24 × 10-8 0.22 × 10-9 0.12 × 10-7 0.56 × 10-5 0.61 × 10-4 0.15 × 10-9 0.10 × 10-8 0.61 × 10-12 0.77 × 10-7 0.32 × 10-9

0.62 × 10-5 0.50 × 10-6 0.19 × 10-5 0.65 × 10-3 0.24 × 10-2 0.15 × 10-6 0.59 × 10-6 0.55 × 10-3 0.12 × 10+0 0.80 × 10-2

being the most important branching step. The degeneration of the branched chain is caused by the disappearance of radicals in the dominant termination reaction 10: the combination of two methyl radicals toward ethane. This reaction thus suppresses the acceleration of the conversion rate with increasing conversion. It is also the only source of the product ethane. At a later stage where the oxygen conversion has increased to 5.3% and the temperature amounts to 1107 K, the selectivity to formaldehyde has decreased strongly to only 2.8% while that to its sequential product carbon monoxide has increased from 5.8% to 47.5%. Also, the selectivities to ethane and its sequential products ethylene and hydrogen have increased. In this stage of the ignition, also the branching reactions 4, 35, and to a lesser extent 8 have become important branching steps besides reaction 38, as can be seen from the rates shown in the last column of Table 3. Reaction 10 is still the most important termination reaction; additional termination occurs in reaction 30: the coupling of a methyl radical with an ethyl radical to propane. Reaction 5 in which methane reacts with a hydroxyl radical, OH•, toward CH3• is the most frequent occurring reaction at both stages. Most Abundant Radicals. In the reaction scheme of Table 3 two major reaction routes can be distinguished: the route via formaldehyde, CH2O, and formyl radicals, CHO•, to carbon monoxide and carbon dioxide and the route to C2+ products. The rates of the individual reactions of these routes, however, influence each other via the radicals in a rather complex way. The concentrations of the radicals at the two axial positions where the contribution analysis was carried out are shown in Table 9. At the ignition stage at X(O2) ) 0.84% and T ) 902.5 K, the methyl, CH3•, and the hydrogen peroxy, HO2•, radicals are the most abundant radicals with concentrations in the order of 10-5 mol %. At the stage where X(O2) ) 5.3% and T ) 1107 K, the concentration of the radicals has increased significantly and the thermodynamically more stable C2H5• has become clearly the most abundant radical with a concentration of 0.115 mol %. Simulation of Ignition Simulation of Isothermal Ignition. The kinetic model is suitable for simulation of the ignition of methane/oxygen mixtures since the chemical process occurring during the ignition delay at the conditions simulated is the same as that during the experiments. This implies that the model that describes the process occurring during the experiments can also describe the

2590 Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999

Figure 4. Ignition at isothermal conditions in a plug-flow reactor at p ) 500 kPa, CH4/O2 ) 2.0, and T ) 1000 K, simulated using the kinetic model of Table 3. The residence time is calculated according to eq 4.

process during the ignition delay. Figure 4 shows the results obtained for a stoichiometric methane/oxygen mixture at typical partial oxidation conditions with the assumption of isothermal operation. The S-shaped conversion plots for methane and oxygen show initially a very low reaction rate which increases until an oxygen conversion of about 1% is reached. During this period, the concentrations of radical species and the concentrations of molecular species that are more reactive than methane (i.e., formaldehyde and ethane) build up. After ignition, the amount of formaldehyde quickly decreases as a result of reaction toward carbon monoxide and ethane starts to react further to ethylene. In parallel, carbon monoxide reacts further to carbon dioxide. At this temperature of 1000 K, very little acetylene is formed. Simulation of Adiabatic Ignition. Since the gasphase combustion reactions produce a large amount of heat, the ignition normally involves a significant and rapid temperature rise. The simulation of the ignition was therefore also carried out with the assumption of adiabatic operation, which is much closer to the practical situation. For these simulations, the one-dimensional plug-flow reactor was used as well. The results of such a simulation for a stoichiometric methane/ oxygen mixture at 500 kPa and a feed temperature of 1000 K is shown in Figure 5. During the first 0.02 s, the plots are almost identical to those in Figure 4 because the effect of the heat up of the gas by the reactions is still small. The isothermal ignition that occurs during the first 0.03 s is followed by a thermal ignition and runaway after 0.037 s, where the oxygen conversion amounts to approximately 20%. After this thermal ignition, all the oxygen is consumed instantaneously and the temperature rises steeply, reaches a maximum of 2078 K, and then decreases again because of the endothermic cracking of CH4, C2H6, and C2H4 to

Figure 5. Ignition at adiabatic conditions in a plug-flow reactor at p ) 500 kPa, CH4/O2 ) 2.0, and T ) 1000 K, simulated using the kinetic model of Table 3. The residence time is calculated according to eq 4.

Figure 6. Ignition delay (residence time to achieve 10% O2 conversion) at adiabatic conditions as a function of pressure, inlet temperature, and inert dilution (CH4/O2 ) 2.0), simulated using the kinetic model of Table 3. (The ignition delay is calculated analogous to the residence time in eq 4.)

C2H2 and H2. The major products formed after the ignition are H2O, H2, and CO. It is likely that soot will be formed from the acetylene after the runaway, but such reactions are not included in the model. The assumption of plug flow in the simulation implies that the effect of axial dispersion is neglected. Once runaway has occurred, however, very steep axial gradients arise which enormously enhance the effect of axial dispersion. This implies that the simulation results obtained with the plug-flow model after ignition should only be interpreted in a qualitative way. However, the adiabatic plug-flow simulations are still useful for estimating the ignition delay and also for investigation of the influence of temperature, pressure, and gas composition on this ignition delay. Figure 6 shows the influence of the reaction conditions on the ignition delay at adiabatic conditions. The results at pressures below 2 bar and above 8 bar are shown dashed since these fall outside the range covered experimentally. The plot shows that the ignition delay

Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 2591

is approximately inversely proportional to the pressure, an increase of the temperature by 100 K decreases the ignition delay approximately 3-fold, and dilution of the feed with 50% nitrogen increases the ignition delay about 3-fold. It should be noted that the effect of dilution with nitrogen was not verified experimentally. Applicability of the Model The kinetic model developed in this study can accurately describe the observed results within the range of conditions covered (Table 1). Since it is based on first principles, simulations carried out at conditions not too far outside the conditions covered seem also reliable. Since the rates of the individual reactions influence each other via the radicals in a rather complex way, however, further simplification or modification of the model is not recommended. For example, even the reactions with relatively very low reaction rates are important at different conditions. The model does not include any carbon-forming reactions, which implies that the model cannot describe accurately the cracking reactions after complete consumption of the oxygen. The model is useful for simulation of the gas-phase reactions occurring parallel to the catalytic reactions in a partial-oxidation reactor containing a catalyst bed. In particular, at high temperatures and high partial pressures of the reactants, the contribution of the gas-phase reactions may be larger than expected. The model can also be used for estimating the ignition delay with mixtures containing methane and oxygen which can be used for the design of a safe partial-oxidation reactor and the choice of the process conditions herein. In relation to this, the dead volumes in the preheater zone and the precatalytic zone should be kept sufficiently small to avoid thermal ignition. However, one should be careful with using the model for simulations at conditions outside those covered experimentally. Conclusions Continuous-flow experiments in an empty aluminum oxide tube could be carried out successfully, although some difficulties due to runaway tendencies caused by the large reaction heat of the oxidation reactions limited the maximum attainable temperature to 1300 K and the pressure to 800 kPa. When the study was started from literature data and by regression using the experimental data obtained, a detailed kinetic model based on a freeradical mechanism could be developed, which adequately described the observed conversions and product selectivities over the complete range of the experimental conditions investigated. The model includes pressure falloff effects of the unimolecular reactions. The model developed in this study is suitable for revealing the essential features of the complex reaction network with the emphasis on the ignition stage at oxygen conversions between 0% and 5%. The occurrence of both isothermal and thermal ignition can be distinguished in simulations with the model. Isothermal ignition occurs at an oxygen conversion of approximately 1%, and thermal ignition at an oxygen conversion of approximately 20%. The ignition delays occurring with typical partial oxidation gas mixtures could be calculated as a function of the process conditions. The model is also suitable for simulation of the gasphase reactions occurring parallel to the catalytic reactions in a partial-oxidation reactor containing a catalyst

bed, in particular, for experiments carried out at high temperatures and high partial pressures of the reactants. Acknowledgment The financial support by the Commission of the European Union in the framework of the Joule Program, Contract No. JOU2-CT92-0073 and JOU3-CT95-0026, is gratefully acknowledged. Notation a ) pre-exponential factor A ) cross-sectional area of the reactor, m2 b ) parameter vector CM ) concentration of “third bodies”, mol m-3 D ) molecular diffusivity, m2 s-1 Ea ) activation energy, J mol-1 Fi ) molar flow of component i, mol s-1 fj(xk,b) ) calculated response value for response j in experiment k k0 ) rate coefficient for unimolecular reactions at a lowpressure limit ku ) rate coefficient for unimolecular reactions k∞ ) rate coefficient for unimolecular reactions at a highpressure limit pt ) total pressure, Pa r ) reactor radius, m Sij ) selectivity of i with respect to element j Sb ) objective function T ) temperature, K V ) reactor volume, m3 wj ) weighting factor for response or component j xk ) vector of independent variables Xi ) conversion of component i ykj ) experimentally observed response value of response j in experiment k z ) axial reactor length, m R ) falloff coefficient θ0 ) residence time of the central streamline in the reactor, s τ ) residence time (calculated using eq 4), s

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Received for review November 18, 1998 Revised manuscript received March 4, 1999 Accepted March 17, 1999 IE9807304