Numerical model of hydrocarbon oxidation kinetics in a reactor with barrier discharge has been proposed by the example of cyclohexane oxidation reaction. The results of calculations with the use of barrier discharge surface model showed that electron energy and other discharge characteristics in pure oxygen and in the mixture of oxygen with cyclohexane vapors slightly differ that allowed using a simplified model of homogeneous discharge for simulating cyclohexane oxidation reaction. The results of calculation showed good fit with the experimental dat

Kudryashov, S. V.

Ryabov, A. Yu.

Shegoleva, G. S.

Sirotkina, E. E.

Suslov, A. I.

Electronic archive of Tomsk Polytechnic University

IntroductionThe given report continues the series of publishedworks by the results of experiments with steamandgasmixtures of nС5С8 alkanes and cyclohexane with oxygen in barrier electric discharge (BD) in the conditionsof efficient withdrawal of reaction products fromdischarge range. In the previous paper [1] it was shownthat as a result of oxidation of nС5С8 hydrocarbons alcohols, aldehydes and ketones with the same quantity ofcarbon atoms as in the initial hydrocarbon are formed.The main oxidation products of cyclohexane are cyclohexanol, cyclohexanone. Oxidation of hydrocarbonmixtures results in forming the same products of the reaction as for the individual hydrocarbons.The given paper is devoted to simulating cyclohexaneoxidation reaction in BD. BD is understood as a discharge occurred in gas under the influence of stress applied toelectrodes and in this case at least one of electrodesshould be covered with a layer of liquid or solid dielectric.Modern conception of BD physics is reflectedrather completely in scientific literature [2]. A fragmentof discharge cell with BD is showed schematically inFig. 1. Supplying alternating voltage to discharge cellelectrodes electric current flows in a gas gap. If voltageat the gas gap is lower than discharge ignition voltagethen the current flowing through discharge cell has a capacitive character if it is higher then active dischargecurrent is also added to displacement current. Discharge active current has impulsive character.Fig. 1. Fragment of discharge cell with barrier electric discharge: 1, 4) metal electrodes; 2) dielectric barrier; 3) microdischarge; 5) gas gapOscillograms of discharge voltage and current pulsein plasmachemical reactor in which the authors carriedout the oxidation of cyclohexane with oxygen are givenin Fig. 2 [1].Current pulses (Fig. 2) in BD are connected withoccurrence in discharge volume of luminous channels –microdischarges distributed over the area of electrodesin which an active charge transfer initiating chemicalreaction occurs.Typical microdischarge life time is ~25...30 ns [2]and it complicates experimental researches of its characteristics. This is the reason why mathematical simulation is actual when using BD as plasmachemical reactor for carrying out conversions.1. Microdischarge simulation Microdischarge was simulated using surface modeldescribed by the equation system [3, 4]:(1)(2)where ϕ is the potential of electric field, ε0 is the electricconstant, ρ is the total charge density, ni is the concentration of i particle, vi and Di are the drift velocity anddiffusion coefficient, Si is the sum of sources and drainsof i particle.Charge space distribution between dielectric barriersand particle concentrations are determined by joint solving Poisson equation (1) and continuity equations (2)for all plasma components.Electric field and spacetime distribution of particleswere calculated in axially symmetrical geometry of microdischarge in planeparallel gap with two dielectric barriers. The accepted assumption is stipulated by slight influence of electric field irregularity in nonplanar gas space with small gap d (much smaller than cylindrical reactor diameter) on end product output that conforms todirect experimental measurements [5]. Radial derivatives of all magnitudes on the boundary r=rmax (upperboundary of range of integration by radius) and at theaxis of the channel were equal to zero. It was supposeddiv( ) div( grad ) ,i i i i i in n D n Stδ νδ + − ⋅ =0,ρϕ εΔ = −Bulletin of the Томsк Pоlytеchnic University. 2007. V. 311. № 3106UDC 541:537.523:66.011OXIDATION OF nС5С8 HYDROCARBONS AND CYCLOHEXANE IN A REACTOR WITH BARRIERDISCHARGE. P. 2. SIMULATING CYCLOHEXANE OXIDATION REACTIONS.V. Kudryashov, A.Yu. Ryabov, G.S. Schegoleva, E.E. Sirotkina, A.I. Suslov*Institute of petroleum chemistry of RAS SD, Tomsk*Institute of highcurrent electronics of RAS SD, TomskE mail: ks@ipc.tsc.ruNumerical model of hydrocarbon oxidation kinetics in a reactor with barrier discharge has been proposed by the example of cyclohexaneoxidation reaction. The results of calculations with the use of barrier discharge surface model showed that electron energy and otherdischarge characteristics in pure oxygen and in the mixture of oxygen with cyclohexane vapors slightly differ that allowed using a simplified model of homogeneous discharge for simulating cyclohexane oxidation reaction. The results of calculation showed good fit withthe experimental data.that dielectric absorbs electrons, positive and negativeions on the boundaries gasdielectric therefore respective densities of currents of electron, positive and negativeions, je, j– and j+, were integrated by time for defining surface charges σ(r,t) and respective displacement discontinuity ΔD=σ on both interphase boundaries. Concentrations of ions n+0 and electrons ne0 in gas gap stipulated bynatural radiation background (ne0=n+0~103 cm–3) wereaccepted as their initial values on channel axis with decrease by Gauss law along its radius to periphery. In otherrespects, boundary and initial conditions did not differsignificantly from similar conditions accepted in [4].Complete microdischarge model should also include Boltzmann equations for defining electron energy distribution function (EEDF) and calculating particleformation rates. However, owing to high relaxation rateof electron average energy in molecular gas mixtures atatmospheric pressure the velocity coefficients of electron reactions with plasma particles were estimated byfunctions depending only on reduced electric fieldstrength E/n [2].Numeric calculations of microdischarge surface model were carried out using implicit iteration algorithmwith analytical grid [5]. The calculations were carriedout for plasmachemical reactor used before for oxidationof alkanes nС5С8 and cyclohexane. Sections of electronmolecular processes were taken from papers [6, 7].The results of calculations of electron concentrationdistribution and magnitudes of electric field reducedstrength along microdischarge channel axis at differentmoments of time in mixture of oxygen with cyclohexanevapors are given in Fig. 3.It is seen that electron inhomogeneous distributionalong the axis passes to the uniform one rather rapidly(during ~1,5 ns). Electric field distribution in a gapbetween barriers becomes constant as well (excludingcathode region). The observed picture is typical forglowdischarge plasma and it remains up to microdischarge disappearance (Fig. 3, a).аbFig. 3. Distribution of: а) electron concentration; b) magnitudeof electric field reduced strength along microdischargechannel axis at different moments of time. О2:С6Н12=9:1Сhemistry107Fig. 2. Oscillogram of discharge voltage and current pulseAmplitude, kVDischarge current, AsаbFig. 4. Results of calculation: а) microdischarge current pulse;b) EEDF in pure oxygen (dashed line) and in mixture ofoxygen with cyclohexane vapors (full line). О2:С6Н12=9:1,E/n= 98,8In general the results given in Fig. 3, 4 are typical forbarrier discharge in pure oxygen [2].Comparison of calculation of results of EEDF inpure oxygen and in the mixture of cyclohexane vaporswith oxygen (Fig. 4, b) shows that cyclohexane vaporsinfluence considerably, in general, the highenergy partof EEDF. Function kernel in energy region 0...10 eV,the most important for dissociation processes of oxygenand hydrocarbons, do not undergo great changes.Thus, addition of cyclohexane vapors into oxygen does not result in considerable increase of electron energylosses and change of microdischarge other characteristics. It allows using simpler algorithms in calculations fordetermining concentration of radicals initiating cyclohexane oxidation process and energy consumption for theirformation. Let us give two variants of such calculations:1. The model of homogeneous discharge according towhich the electric field strength in microdischargechannel is considered to be constant. Average particle concentration, electron energy distributionfunction and parameters of gasdischarge plasma arecalculated in selfconsistent manner. Such modelallows taking into account the influence of varyingcomposition of gas mixture on rate of molecule electron excitation in gas discharge.2. In the given case when initial hydrocarbon conversionis not high and reaction products are removed efficiently from gas phase change of gas mixture composition may be neglected and homogeneous charge model is significantly simplified. Then initial concentration of particles N–i required for simulating chemicalreaction stage may be calculated by the formula [8]:Here W–ch is the value of specific energy released inmicrodischarge channel, ηi is the value of particle formation efficiency, Ni is the concentration of i particle atthe end of microdischarge pulse, jch is the current density inside the channel, Есh is the value of electric fieldstrength, V is the volume of microdischarge volume.The second variant of calculation may be also usedfor estimating initial concentrations of atoms and radicals formed at one or a series of voltage pulses. Simulating cyclohexane oxidation reaction the latter approachwas used as it is the simplest and reduces significantlycalculation time.2. Simulating cyclohexane oxidation reaction for single voltage pulse Forming possible cyclohexane oxidation mechanismthe following assumptions were accepted: 1) cyclohexane oxidation was considered as chain reaction including events of initiation, continuation and break of chains; 2) only initial compounds undergo BD influence butnot intermediate and end reaction products. 3) under theinfluence of BD gas average temperature rise does notexceed 5 °С [2]; 4) reactions with zero (or almost zero)activation energy are mainly taken into account.The analysis of the papers devoted to plasmachemical methods of air purification from organic contaminators in reactors with BD shows that the main primaryevent initiating oxidation reaction is molecular oxygenexcitation with electron impact forming atomic oxygenin ground О(3Р) and excited О(1D) states [2]:Hydrocarbon molecule excitation with electron impact also occurs and judging by reaction products resultsmainly in forming atomic hydrogen and hydrocarbonradical.Contribution of reaction into oxidation process isless significant as molecular oxygen dissociation occursat lower electron energy magnitudes ~6 eV [2] than it isrequired for breaking СН or ССbond of hydrocarbon molecule (~8...11 eV) [7].Then, the formed particles interact with cyclohexanemolecule by radialchain mechanism suggested in [9].3RH e R H e.k • •+ → + +23 12O e O( P) O( D) e.k+ → + +13 32O e O( P) O( P) e,k+ → + +, .iVi ch ich chN dVN Wj E dVdtη η= =∫∫∫?Bulletin of the Томsк Pоlytеchnic University. 2007. V. 311. № 3108The efficiency values of forming particles ηi werecalculated by [8]. For example, for ηO(3P) the expressionwas obtained(3)where e0 is the electron elementary charge, vdrift is the driftvelocity of electrons, n is the number of particles in cm3,(E/n)eff is the efficient reduced strength of electric field.Similarly to (3) the expressions for ηO(1D), ηC6H11. andηH. are obtained.Calculating ηO(3P) and ηO(1D) the magnitudesvdrift=1,8.107 cm/s, k1,2= 3,9.10–11 cm3/s obtained by datainterpolation for pure oxygen were used [8]. k3 magnitude was not found in scientific literature; it was estimatedby the formula [10]:(4where σ(ε) is the efficient reaction crosssection, fe(ε) isthe EEDF, me is the electron mass, εthresh. is the thresholdreaction energy.Probability of alkanes dissociation from electronexcited states is considered to be close to a unity. Thereforeestimating magnitude k3 the data on sections of excitationof allowed electron transitions in cyclohexane moleculeby electron impact were used [7]. Calculated value k3 amounted to 4,6.10–15 cm3/s that is practically 4 orders lowerthan oxygen dissociation rates by electron impact k1, k2. Itallows ignoring cyclohexane dissociation reaction by electron impact at forming probable oxidation mechanism.The value of efficient reduced strength of electric field (E/n)eff=22 used in calculations corresponds to charge burning voltage and obtained from voltcoulombcharacteristic measured earlier at cycloxehane oxidation [1].Initial concentrations O(3P), O(1D) and values ηicorresponding to them are given in Table. 1.Table 1. Initial concentrations O(3P), O(1D) and values ηi(Wimp=5.1016 eV/cm3,(E/n)eff=22, T=298 K, [O2]=2,2.1019,[C6H12]=2,3.1018 cm3) corresponding to themElementary stages of probable oxidation mechanismof cyclohexane and rate constants corresponding tothem are given in Table 2.Reaction product composition obtained by mathematical simulation is shown in Table 3. Satisfactory fitbetween calculated and experimental data allows making conclusion about reliability of suggested reactionmechanism.The simplified cyclohexane oxidation mechanismmay be presented in the following set of reactions:(5)(6)(7)(8)(9)(10)(11)It is seen that the chain reaction is characterized byshort chain – 3 links (reactions 8–10). Chain break occurs by disproportionation reaction of cyclohexil peroxide radicals (11) forming cyclohexanol, cyclohexanone.Table 2. Elementary stages of probable oxidation mechanism ofcyclohexane and rate constants corresponding to themTable 3. Composition of cyclohexane oxidation productsLow temperature in discharge reactor zone andpractically «nonchain» character of reaction makes thetechnique of cyclohexane oxidation in reactor with BDexplosionproof that is certainly an advantage on traditional oxidation techniques where nonexplosivness isone of the main problems.The calculated dependences of cyclohexane oxidation product concentrations in BD are given in Fig. 5.Fig. 5. Calculated dependences of concentration C of cyclohexane oxidation products in BD on time tC. 10–15, molecule.sm–3Substance Experiment [1], wt. % Calculation, wt. %CyclohexanolCyclohexanoneWaterOther49,440,89,50,247,144,58,4–ProcessRate constant,cm3/sLiteratureO(1D)+О2→O(3P)+О2 4,0.10–11 [1]O(3P)+O2+M→O3+M 1,6.10–14 [1]2O(3P)+M→O2+M 2,0.10–14 [1]C6H12+O(3P)→C6H11*+OH* 1,8.10–13 [12]C6H12+O(1D)→C6H11OH 5,0.10–11 Estimationby [11], [13]C6H12+OH*→C6H11*+H2O 3,7.10–12 [14]2OH*+M→H2O2+M 1,5.10–11 [11]C6H11* + O2→C6H11OO* 2,7.10–14 [15]2 C6H11OO*→C6H10O + C6H11OH + O2 1,5.10–14 [15]C6H11OO* + C6H12→C6H11OOH + C6H11* 8,7.10–20 [15]6 11 2 6 11 6 10 22C H O C H OH C H O O .• → + +6 11 2 6 11 2C H O C H O ,• •+ →6 12 6 11 2C H OH C H H O,• •+ → +36 12 6 11O( P) C H C H OH ,• •+ → +1 32 2O( D) O O( P) O ,+ → +3 12O e O( P) O( D) e,+ → + +3 32O e O( P) O( P) e,+ → + +Particle ηi.100, mole/eV Concentration, cm–3О(3Р) 11,8 5,9.1015О(1D) 2,9 1,5.10151 12 2.3 (2 ) ( ) ( ) ,ïîðe ek m f dεε σ ε ε ε∞= ∫321 2 0 . .O( P)[O ](2 ) / ( ) ,drift effk k e E nnη ν= +Сhemistry109It is seen that typical formation time of cyclhexanoland cyclohexanone is ~102 s, water – ~106 s.A good fit between compositions of cyclohexaneoxidation products obtained experimentally and theoretically allows writing down grossequation of this process:(12)As at oxidation of hydrocarbons nС5С8 and cyclohexane the mixture of alcohols and carbonyl compounds with the same number of carbon atoms that is inoriginal hydrocarbon and ratio of alcohols and carbonylcompounds in reaction products ~1:1 is formed, the similar (12) grossequations may be also written down foroxidation process of hydrocarbons nС5С8.On the basis of the obtained results the conclusionmay be made that the studied approach to simulatingcyclohexane oxidation reaction in BD allows describingrather adequately this process. The results of investigations are of interest at developing the processes of plasmachemical conversion of organic substances in charges at atmospheric pressure, for example, in BD.36 12 2 6 11 6 10 22C H +O( P)+O C H OH+C H O+H O.→Bulletin of the Томsк Pоlytеchnic University. 2007. V. 311. № 3110REFERENCES1. Kudryashov S.V., Ryabov A.Yu., Shegoleva G.S., Sirotkina E.E., Suslov A.I. Oxidation of nС5С8 hydrocarbons and cyclohexane in reactor with barrier discharge. P. 1. The results of experimental investigations // Bulletin of the Tomsk Polytechnic University. – 2006. –V. 309. – № 6. – P. 92–96.2. Samoylovitch V.G., Gibalov V.I., Kozlov K.V. Physical chemistry ofbarrier discharge. – Moscow: MSU Press, 1989. – 174 p.3. Eliasson B., Egli W., Kogelschatz U. Modeling of dielectric barrierdischarge chemistry // Pure and Appl. Chem. – 1994. – V. 66. –№ 6. – P. 1279–1286.4. Braun D., Gibalov V., Pietsch G. 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Oxidation of n-С5-С8 hydrocarbons and cyclohexane in a reactor with barrier discharge. P. 2. Simulating cyclohexane oxidation reaction

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