Development of a Pressure Dependent Reaction Model for Methane/methanol Mixtures under Pyrolytic and Oxidative Conditions and Comparison with Experiment

Methanol experimental data are obtained under pyrolysis, fuel lean (φ = 0.75) and stoichiometric mixtures with methane in a flow reactor. Methanol pyrolysis experiments are performed under isothermal conditions of 1073K over a pressure range from 1 to 10 atm. Oxidation environments are performed over a temperature range from 873 1073K and a pressure range from 1 5 atm. Oxidation experiments consisting of methane/methanol mixtures are performed under stoichiometric conditions, with varying ratios of the two fuels. A pressure dependent mechanism for methane/methanol oxidation and pyrolysis reaction system is developed and compared with experimental data. Pathways for formation of higher molecular weight species, such as methylethers, are also incorporated in this mechanism. The mechanism consists of about 150 species and 450 elementary reaction steps, with over 200 elementary reactions being pressure dependent. Pressure and temperature dependent rate constants are determined by utilizing quantum RRK (QRRK) analysis on bimolecular (chemical activation) association, addition and insertion reactions and in unimolecular dissociation and isomerization reaction systems, combined with “modified strong collision” treatment for fall-off. Pressure and temperature dependent rate constants are determined by the QRRK code and expressed in the form of an 7 x 3 Chebyshev polynomial formalism over the pressure range of 0.001 to 100 atm and a temperature range of 250 to 2500K. Methane oxidation increased significantly with addition of methanol. INTRODUCTION Oxygenated hydrocarbons play an important role in both industrial and environmental chemistry. Alcohols, such as methanol and ethanol, are in use as alternative motor fuels and as additives to conventional transportation fuels to improve performance. Ethers, such as methyl tert-butyl ether (MTBE), are in use as oxygen additives as anti-knock components in gasoline and other ethers are being considered as additives for diesel fuels. The oxidation and pyrolysis of gas phase methanol has been reported in a number of studies over the past half century by different experimental methods, which range from laser induced fluorescence, diffusion flame, shock-tube and static or flow reactors. Both De Avillez Pereira et. al and Held and Dryer present recent experimental data on this system, as well as a thorough compilation of previous works done on this system.5,10 Three different wide ranges of experimental conditions are performed: methanol pyrolysis, methanol oxidation and methanol/methane oxidation. A reaction mechanism model is also developed, which includes about 200 pressure dependent reaction steps. Pressure and temperature dependent rate constants are represented in Chebyshev polynomial form over a pressure range from 0.001 100 atm and a temperature range of 250 – 2500K. Included in the mechanism are pressure effects on important unimolecular and bimolecular reactions plus negative temperature dependence and pressure effects on hydrocarbon (HC) and oxyhydrocarbon (OHC) species reactions. Pathways for formation and oxidation of higher molecular weight products, such as C2 hydrocarbons and methyl-ethers, which we observe in this study, are also included. EXPERIMENTAL SETUP: The reactor used in the experiment is a 6mm ID (12mm OD) quartz tube, housed in a 75 cm three-zone clamshell 3 cm ID electric tube furnace equipped with three independent digital temperature controllers. A 200 psi back pressure regulator is used to maintain the desired pressure within the reactor. (Refer to Figure 1 for experimental setup). Figure 1. Schematic of experimental flow reactor and analytical system. The feed mixtures are preheated to about 373oK to prevent condensation and improve reactor temperature control. Gas samples are drawn through by a mechanical vacuum pump. An HP-5890 Series II gas chromatograph (GC) with two flame ionization detectors (FID) is used on-line for analysis. A packed column is used for the separation of CO, CO2 and light HC’s and a capillary column is used for heavier HC’s and OHC’s separation. A catalytic converter is used to improve quantitative analysis of CO and CO2 by converting the mixture to methane, which can be detected by the FID. Batch samples of reactor gas drawn from the reactor are collected into evacuated 25 cm stainless steel sample cylinders for verification of products using a GC/MS. Methanol pyrolysis experiments are all performed under isothermal condition at 1073oK, with varying concentrations of CH3OH over a pressure range from 1 to 10 atm. Experimental data on the decomposition of methanol in presence of oxygen and argon were obtained for both fuel lean (φ = 0.75) and stoichiometric (φ = 1.0) conditions over a temperature range from 873 to 1073oK and a pressure range of 1 to 5 atm. All methanol/methane oxidation experiments are carried out under overall stoichiometric conditions. Experimental data for methanol/methane oxidation experiments at two different temperatures and pressure combination conditions are collected: either 873oK and 5 atm or 1073 and 1 atm. Various methanol/methane concentration ratios, ranging from 0:2 to 2:0, were studied for each of the two temperature/pressure conditions. COMPUTATIONAL METHODS Thermodynamic properties. Thermodynamic properties of species are from literature, theoretical and estimation techniques, such Fuel Chemistry Division Preprints 20 02, 47(1), 98 as group additivity2, hydrogen bond increment (HBI)12 and ab initio or density function calculations. The molecular properties for the explicit CH3OH dissociation system, including methanol, transition states (TS) and products, are determined by the high level composite CBS-APNO ab initio calculations. The ab initio calculations are performed using Gaussian94.6 The CBS-APNO calculations are performed in accordance to the method outlined by Montgomery et al15. Vibrational frequencies, ZPVE and thermal correction contributions are calculated at the HF/6-311G(d,p) level of theory, with scaling factors consistent with the recommended values by Scott and Radom.18 The optimized geometry is calculated at the QCISD/6-311G(d,p) level of theory. Figure 2 illustrates the potential energy diagram of the CH3OH subsystem. The enthalpies of the two biradicals in the system are determined by use of isodesmic working reactions9 with group balance. Figure 2. Potential energy diagram of the methanol subsystem calculated at CBS-APNO level of theory. Conventional statistical mechanics analysis was employed to determine the vibrational, external rotational and translational contributions to entropy and Cp(T). Unpaired electrons are also included in the S and Cp(T) calculations accordingly. Contributions of internal rotation to S and Cp(T) are incorporated based on the Pitzer-Gwinn formalism.17 Calculation of High-Pressure Rate Constants. Abstraction reaction rate constants are not pressure dependent and are usually taken from evaluated literature when available. Evans-Polanyi analysis is used on the reaction in the exothermic direction to estimate the energy of activation (Ea) for rate constant. The high-pressure forward rate constants in the CH3OH subsystem are determined by application of macrocanonical transition state theory (CTST) for temperatures from 300 – 2500 K. Forward rate constants from 300 – 2500 K are calculated and fitted by a nonlinear least squares method to the form of a modified Arrhenius rate expression. The rate constants for the three combination and dissociation reaction in the CH3OH system are calculated by variational transistion state theory (VTST), with thermochemical properties determine at the CBS-Q//B3LYP/631G(d,p) level of theory.16,1,13 The combination reaction rate constant is determined by satisfying the microscopic reversibility criteria. Kinetic Analysis. Pressure and temperature dependent rate constants are determined by a modified quantum RRK (QRRK) formalism for k(E). Two methods to analyze the collisional deactivation of the energized adduct are used: master equation analysis and the modified strong collision model. Chang et al described a modified QRRK analysis that is used in this paper.4 Master equation analysis is used for fall-off in this analysis as described by Sheng et al19 and follows Gilbert and Smith7. Pressure Dependent CHEMKIN Mechanism.: Both the modified strong collision and master equation codes incorporate a temperature and pressure dependent output formalism for the rate constants, in the form of an N x M Chebyshev polynomial expression. The temperature-pressure dependent rate coefficients in Chebyshev format for the current system of interest are derived from application of the methodology described by Venkatesh et al21,20. The CHEMKIN interpreter is modified to accept the N x M Chebyshev polynomial formalism of rate constant.11 RESULTS AND DISCUSSION Enthalpies of CH3OH Subsystem. The sum of enthalpies for the respective product sets are compared with data from the study of Walch22 and Harding et al8. Harding et al’s data are calculated at the RMP4/6-31G(d,p) level of theory and Walch’s data are derived using complete-active-space self-consistent-field (CASSCF) / internally contracted configuration-interaction (CCI), ab initio calculations. Table 1. Comparison of Product Enthalpies in the Methanol System with Literature Data. CBS-APNO Walch22 Harding et al.8 CH3OH 0 0.0 0.0 CH3O + H 104.1 CH2OH + H 95.1 CH2 + H2O 91.8 88.8 94.9 CH2 CH2 -8.99 -9.0 CH3 + OH 90.5 HCOH + H2 72.8 71.1 71.1 CH2O + H2 20.1 18.1 16.4 [H2CO···H2] 90.7 91.9 96.5 [HCOH···H2] 86.5 85.0 91.0 [CH2···H2O] 83.6 82.3 84.6 The enthalpy for the transition state of CH2 + H2O channel, as reported also by Walch and Harding et al, is lower than the enthalpy of CH2 + H2O. The CH3OH dissociation barrier, through the CH2 + H2O channel is calculated form canonical transition state theory, based on an excited state of TS that has the same enthalpy as the enthalpy of CH2 + H2O with a corresponding entropy at the same energy level as the “excited” TS. The high-pressure limit rate constants are shown in Table 2. Table 2. High-Pressure Limit Rate Coefficient for the CH3OH System. Reaction A n Ea (kcal/mol) CH3 + OH CH3OH 3.3133E6 2.0765 -1.7551 a CH3OH CH3 + OH 3.2591E10 2.05451 90.347 b CH3OH CH2OH + H 1.6369E7 2.54513 91.951 b CH3OH CH3O + H 1.1908E7 2.38792 99.614 b CH3OH CH2O + H2 1.1004E9 1.28149 90.233 c CH3OH HCOH + H2 2.0299E10 1.22342 86.411 c CH3OH CH2 + H2O 2.8735E11 1.60030 92.538 d (a) Microscopic reversibility (b) Variational transition state theory calculation, based on CBS-Q//B3LYP/6-31G(d,p) (c) Canonical transition state theory calculation, based on CBS-APNO (d) Adjusted canonical Fuel Chemistry Division Preprints 20 02, 47(1), 99 Comparisons with Experimental Results. Methanol pyrolysis comparisons between the model with experimental results at 1 atm is illustrated in Figure 3. Comparisons of the methanol oxidation model and the experimental results at 5 atm at an equivalence ratio of φ = 1 is shown in Figures 4. These show reasonable agreement for reactant decay and main product formation. transition state theory calculation – thermochemical properties of the transition state taken at the corresponding energy level of the sum of the