Use of Chemked for Simulation of Gas-Phase Chemical Reactors

Transcription

1 Use of Chemked for Simulatio of Gas-Phase Chemical Reactors Chemked A Program for Chemical Kietics of Gas-Phase Reactios M. Jeleziak ad I. Jeleziak Home page: ifo@chemked.com 18 February 2008, last updated 26 April 2008 Cotets 1. Itroductio 2. Gas Parameters ad Variables 2.1 Mixture-Averaged Gas Parameters 2.2 Species Cocetratio 3 Chemical Reactios 3.1 Reactio Rate 3.2 Heat of Reactio 4. Chemical Reactors 4.1 Plug Flow Reactor Coservatio of Total Mass Coservatio of Mometum Coservatio of Species Coservatio of Eergy Iitial Coditios Reactio Time ad Axial Distace Output Characteristics of Reactor 4.2 Batch Reactor 5. Compariso to Experimets 5.1 Plug Flow Reactor Mixig ad Workig Sectios of Flow Reactor Methaol Oxidatio 5.2 Methaol Oxidatio i Batch Reactor 6 Coclusio Refereces Nomeclature 1

2 1. Itroductio Chemked [1] is a program desiged for creatig ad editig thermodyamic ad chemical kietics databases, for formatio of reactio mechaisms. The program icorporates a solver for solvig the differetial equatios of gas-phase chemical kietics at costat pressure ad at costat volume without mass ad heat trasfer. Such approach is a idealized descriptio of processes that take place i ature ad idustry. Although the approach is very simple, it has bee successfully employed for simulatio of reactio chemistry behid shock waves i gases [2, 3]. I Chemked, the followig differetial equatios for species ad gas temperature are employed for simulatio processes at costat pressure. dy dt m ρ 1 ρcˆ p u w, (1.1), (1.2) where t is time, Y ad m are the mass fractio ad the molecular weight of species, ρ is the mass desity, T is temperature, ĉ p is the mea heat capacity at costat pressure, w is the rate of species productio, u is the rate of heat productio. The summatios are over all reactios. The equatios (1.1, 1.2) i couctio with the equatio of state form the goverig equatios, whose solutio gives the temporal developmet of the chemically reactig system. The obective of this work is to demostrate the capability of Chemked for simulatio of the processes i gas-phase chemical reactors. First we will defie the geeral gas parameters (Sectio 2) ad give the expressios for calculatio of reactio rates ad heat productio rates (Sectio 3). I Sectio 4, the equatios (1.1, 1.2) are derived from a more geeral set of equatios; simple models of the chemical reactors based o these equatios are discussed. I Sectio 5, the computatioal models are validated agaist experimetal data. 2. Gas Parameters ad Variables Here we specify gas parameters that are used as variables i the coservatio equatios or are useful for aalysis of results. 2.1 Mixture-Averaged Gas Parameters The choice of some variables is obvious ad does ot require special commets. These variables are the mixture-averaged gas parameters. Temperature T, [K] Pressure P, [atm] Total gas cocetratio C tot,, [1/cm 3 ] or [mol/cm 3 ]. For give P ad T, the C tot value is foud from the ideal-gas equatio of state. 2

3 where R is the uiversal gas costat. P C tot, (2.1) RT 2.2 Species Cocetratio Species cocetratio is deoted as [X ] ad has the uits of [1/cm 3 ] or [mol/cm 3 ]. The obvious formula relates the [X ] values to the total cocetratio C tot. C tot [ X ], (2.2) where the summatio is over all species of the gas mixture. The species cocetratios ca be expressed also through the mole fractio X. [ X ] The mass fractio Y of the th species is defied as X. (2.3) Ctot [ X ] m Y. (2.4) ρ Here m is the molecular weight of the th species i the uits of (g/mol). The mass desity ρ (g/cm 3 ) ca be calculated by [ ] ρ. (2.5) 3 Chemical Reactios I this sectio, we give oly a short descriptio of chemical reactios; more detailed iformatio o this subect ca be foud i literature, for example, i [4-6]. 3.1 Reactio Rate The stoichiometric equatio of a chemical reactio ca be writte i the followig geeral form: ' v s v '' s, (3.1). where the subscript is the reactio umber, s is the chemical symbol of species, v is the stoichiometric coefficiet. The summatios are over species ivolved i the reactio. The superscript of the stoichiometric coefficiets refers to the reactats, the superscript refers to the products. I this represetatio, the v coefficiets are iteger positive umbers or zeros. The forward, reverse ad et reactio rates are 3

4 q ' v, for k, for [ X ], q rev k, rev [ X ] v,, q, et q, for q, rev, (3.2). where k,for ad k,rev are the forward ad reverse rate costats of the th reactio, [X ] is the cocetratio of species. The Arheius form is used most frequetly for calculatio of the reactio rate costat: a E, for, for k A T, for, for exp, (3.3) RT where A,for, a,for ad E,for are the parameters that ate available i chemical kietics databases, for example [7]. The reverse rate costat is related to the forward rate costat by k k, for, rev, (3.4) K '' where K is the equilibrium costat of the th reactio. Remark The Arheius form is oe of the simplest expressios of the rate costat; i may cases the more sophisticated expressios are required. Descriptio of other reactio types ca be foud i 4-6] Each evet of the Jth reactio yields the umber ( ) '' v ' species i the th reactio is give by v of species. The productio rate of '' ' ( v v ) q et w,. (3.5) The sig of w shows the actual situatio. If w > 0, the the species are produced; if w < 0, the the species are cosumed. The reactio rates (Eq. 3.2) ad the species productio rate (Eq. 3.5) have the uits of (1/cm 3 sec) or (mol/cm 3 sec). 3.2 Heat of Reactio The fial products of a chemical reactio are ot oly ew chemical compouds, but releasig (cosumig) of heat as well. The last processes are described by the reactio thermochemistry. The basic thermochemical quatity is the heat of reactio H, which closes the eergy balace of the reactio. The heat of reactio H is the differece i the ethalpies of the products ad reactats at costat pressure ad at a defiite temperature. This value is calculated from the molar ethalpies H of species ivolved i the reactio. '' ' H ( v v ) H The rate of heat productio i the Jth reactio is give by. (3.6) 4

5 u H q, et. (3.7) The sig of u shows the actual situatio. If u < 0, the the heat is cosumed; if u > 0, the the heat is released. The heat of reactio H has the uits of eergy per mole, (J/mol) or (cal/mol). Correspodigly, the reactio et rate q,et must have the uits of molar productio, (mol/cm 3 sec). The the u values describe the rate of heat productio i the th reactio per uit volume, (J/cm 3 sec) or (cal/cm 3 sec). 4. Chemical Reactors I this sectio, a simplified descriptio of chemical processes i plug flow ad batch reactors are preseted. We will cosider reactors of costat pressure ad without surface reactios. I additio we will eglect diffusio processes ad heat trasfer i the reactor volume. The equatios obtaied here are the coservatio equatios for total mass, species ad ethalpy. These are a simplified versio of the more geeral equatios from [4, 5]. The more detailed iformatio o chemical reactors ca be foud i [5, 8, 9]. 4.1 Plug Flow Reactor Let a tube with a variable cross-sectioal area A(x) be a workig sectio of a plug flow reactor, Fig.4.1. A stirred gas mixture of reagets eters the sectio at x 0. The iitial gas parameters (mass desity ρ 0, temperature T 0, velocity U 0 ad chemical compositio X 0 ) are kow. The chemical reactios proceed whe the gas mixture moves through the workig sectio. The products of the chemical reactios are removed from the exit of the sectio (x L). Below we will discuss the equatios that describe the processes i such reactor. A(x) U 0 U L ρ 0 T 0 X k,0 ρ L T L X k,l x L Fig Schematic diagram of plug-flow reactor Whe describig the reactor the followig assumptios will be used. All the processes are steady state Gas flow is subsoic (low Mach umber) The reactor walls are well isulated 5

6 There are o surface reactios There is o upstream or dowstream mixig There is perfect mixig i the trasversal directio Coservatio of Total Mass The steady-state equatio of total mass coservatio is dq dx 0, Q A ρ U, (4.1) where U is axial flow velocity, Q is mass flux across a surface A (the total mass of molecules which move across A per uit time, the Q uits are g/sec). Eq. (4.1) correspods to a gas flow without mass accumulatio i the reactor volume Coservatio of Mometum The steady-state mometum equatio without surface reactios is writte as dp dx + du 1 df ρ U + 0, (4.2) dx A dx where F is the drag forces exerted o the gas by the tube wall (viscous term), the secod term is resposible for the chage of mometum of the gas. I subsoic gas flows (low Mach umber), whe the flow velocity U is much less tha the mea thermal gas velocity, it is ofte possible to eglect the pressure chages due to both the drag forces ad chagig the flow velocity. The dp/dx 0 ad the assumptio of the costat pressure ca be applicable Coservatio of Species Similar to Eq.(4.1), we ca write the cotiuity equatio for each species. 1 A d dx ( QY ) m w. (4.3) Here QY is the mass flux of species across a surface A, the uits are (g/sec). The right-had side of Eq.(4.3) is the mass productio rate of the th species by gas-phase reactios (Eq. 3.5). Differetiatig the left-had side leads to Y A d dx Q A d dx ( Q ) + ( Y ) m w. (4.4) 6

7 If we take ito accout Eq.(4.1) ad use the relatio dx/u, the the differetial equatios for mass fractio of species may be writte as dy m ρ w. (4.5) This equatio is fully coicidet with Eq.(1.1) used i Chemked Coservatio of Eergy The eergy equatio will be obtaied uder the assumptios discussed i the begiig of this sectio. The steady-state eergy equatio for a gas flow i a tube with chemically o-reactive ad isulated walls without heat trasfer ad diffusio may be writte as where h is mea specific ethalpy, d 1 Q h + U A dx , (4.6) h Y h. (4.7) Here h is the specific ethalpy of the th species i the uits of (J/g) or (cal/g); the summatio is over all species of the gas mixture. This equatio (4.6) represets the coservatio of the total gas eergy that is the sum of ethalpy ad kietic eergy. Agai, as i Sectio 4.1.2, we will cosider subsoic gas flows at low Mach umbers, where h>>u 2 /2. Uder these coditios the kietic eergy term ca be omitted. Differetiatig out the products gives h A dq dx + Q A dh dx 0. (4.8) The first term is equal to zero (Eq. 4.1), the Eq.(4.8) ca be writte i the form d ρ Y h 0. (4.9) Here, as i Sectio 4.1.3, we use the relatio dx/u. The ideal-gas specific ethalpy h is fuctio of the gas temperature oly. The the h derivative ca be writte as 7

8 dh c p dt, c dh dt p, (4.10) where c p is the specific heat capacity of the th species at costat pressure; the uits are (J/g K) or (cal/g K). After differetiatig the sum i Eq.(4.9), we obtai the fial equatio for the gas temperature. dt 1 ρcˆ p u, (4.11) where the rates of heat productio i reactios u are defied by Eq.(3.7); the summatio is over all reactios. Mea specific heat capacity at costat pressure ĉ p is Eq.(4.11) is fully coicidet with Eq.(1.2) used i Chemked. ĉ Y c. (4.12) p p Iitial Coditios Coservatio equatios (4.1, 4.5, 4.11) ad the equatio of state (2.1) describe the temporal developmet of chemically reactig gas mixture i a plug flow reactor. These equatios must be accompaied by iitial coditios; values U, P, T, ρ ad Y must be kow at t 0, that is, at x 0, Fig Reactio Time ad Axial Distace The solutio of Eqs.(2.1, 4.5, 4.11) with iitial coditios at t 0 gives the gas parameters T, ρ, Y versus time t We deote the time t as reactio time. The reactio time is a time required for reagets to pass from the ilet of the workig sectio to a positio x. The fuctio x(t) is importat for reactor egieerig ad is defied by the differetial equatio: dx U. (4.13) The desirable fuctio x(t) is a simultaeous solutio of the equatios (4.1) ad (4.13). I Eq.(4.1), the cross-sectioal aria A(x) is specified as a parameter of the problem ad the fuctio ρ(t) must be take from the umeric solutio. The simplest solutio of Eq.(4.13) ca be obtaied for reactors with a costat cross-sectioal aria. x () t t d t ρ 0U 0, (4.14) ρ 0 ( t ) 8

9 Equatios (4.13) ad (4.14) also relate the two importat reactor parameters: reactor legth L ad residece time t r. The residece time is a time required for reagets to pass from the ilet (x 0) to exit of the workig sectio (x L) Output Characteristics of Reactor Whe desigig a reactor, the basic problem is to achieve the largest reaget coversio i miimal reactor volume. Solutio of the problem requires optimizatio of the reactor parameters; this problem is t discussed here. We believe that all the reactor characteristics are specified. The the solutio of Eqs.(2.1, 4.5, 4.11) gives directly parameters of the reactor product, amely, the species mass fractios Y (t r ) at the exit of the workig sectio (x L). If the yield must be expressed i cocetratios [X ], the the Y (L) values must be reduced to [X ] through Eq.(2.4). A essetial characteristic of the reactor is the productio rate of the th species Q (t r ). This value has the uits of (g/sec) ad ca be calculated as 4.2 Batch Reactor Q ( t ) Q 0 ) Y ( t ) r (. (4.15) A batch reactor cosists of a vessel with a meas to stir the gas mixture (Fig. 4.2). After charge of reagets, the vessel is closed ad the chemical processes are iitiated. Whe the chemical coversio of reagets is completed, the vessel is opeed ad the products are removed. I cotrast to the plug flow reactor (Sectio 4.1), which ca work i steady-state mode, the batch reactor works oly trasietly. Nevertheless, the chemical processes i the batch ad plug flow reactors are very similar; i particular, the courses of chemical reactios i time are idetical. Here we will cosider a batch reactor that is held at costat pressure P 0. I order to sustai the costat pressure a special tool is required; this tool is depicted schematically as bellows i Fig I additio we believe that the stirrig time of the gas is much less tha the times of chemical coversio of reagets. Agai, as is doe for plug flow reactor (Sectio 4.1), we will cosider reactor with isulated walls ad without surface reactios. Therefore, the batch reactor processes take place i wellstirred gas at costat pressure ad at uchaged total mass ad ethalpy of the gas. r 9

10 P 0 Bellows Reactor Volume Fa Fig Schematic diagram of batch reactor If the total gas mass i the reactor volume is deoted as Q, the the coservatio of the total mass ca be writte as dq 0, Q V ρ, (4.16) where V is the reactor volume ad ρ is the mass desity; these values ca chage i order to keep the costat pressure. Usig the coservatio equatio (4.16), we ca directly obtai equatios for species mass fractios (4.5) ad temperature (4.11). Thus Eqs. (2.1, 4.16, 4.5, 4.11) with correspodig iitial coditios for V, P, T, ρ, Y at t 0 describe the temporal chage of the gas parameters i the batch reactor. The solutio of these equatios gives specific gas parameters (per uit of mass), which ca be used as source data for calculatio of reactor parameters. I particular, the yield of the th species Q (t r ) ca be calculated, as before, by Eq.(4.15); the yield has the uits of (g). The ethalpy equatio Eq.(4.11) was obtaied for isulated walls. However i batch reactor, a mode of costat gas temperature ca be realized as well. Thus mode takes place, if there is a strog thermal iteractio betwee gas ad vessel walls, ad if wall temperature is kept costat. I this case Eq.(4.11) may be omitted ad the reactor performace is described by Eqs. (2.1, 4.16 ad 4.5). Remark Whe describig the batch reactor, a stirrig meas (fa) is usually itroduced. Actually the fa is t required, if the iitial distributio of the gas parameters is uiform ad the effect of the reactor walls is egligible. The the gas will stay uiform durig the course of chemical coversio. For this reaso, the batch reactor equatios ca be employed for descriptio of a uiform reactig area i the atmosphere. This approach is valid, if the reactig area is a result of a short discharge of pollutats ad if the area size is much larger tha the mixig layer with surroudig air

11 5. Compariso to Experimets I this sectio, the coservatio equatios (4.1, 4.5, 4.11), which are derived previously, are validated agaist experimetal data for plug flow ad batch reactors. 5.1 Plug Flow Reactor Here the umerical calculatios compare with experimets [11]. I [11], the methaol oxidatio has bee examied at wide rages of temperatures ad pressures. We do ot discuss the full set of the data [11] ad will cosider oly a experimet matchig a plug flow coditios Mixig ad Workig Sectios of Flow Reactor I sectio 4.1, a idealized descriptio of a plug flow reactor is give. Actually the gas flow i the reactor has much more complex structure; a sketch of the flow is show i Fig The reactor duct cosists at least of two mai parts: mixig sectio ad workig sectio. The mixig sectio icludes iectors for itroductio of reactats ito carrier gas. Well-desiged mixig sectio provides a wellstirred ad uiform gas mixture at the ilet of the workig sectio. The mai experimetal study of the chemical processes is carried out i the workig sectio. Mixig Sectio Workig Sectio U L Carrier Gas x L ρ L T L X k,l Reactats Iitial Coditios U 0 ρ 0 T 0 X k,0 Fig 5.1 Sketch of plug flow reactor Experimetal data must be referred to a coordiate system. Normally the axial distace x from the ilet of the workig sectio is used as a coordiate (Fig. 5.1). The reactio time t, coected with a gas elemet, has the origi at the istat, whe this elemet goes ito the workig sectio (t 0 at x 0). Here, at t0, we must kow the gas parameters that are the iitial coditios for Eqs. (4.1, 4.5, 4.11). But i may cases the exact determiatio of these parameters is t achievable due to very sophisticated arragemet of the mixig flow ad possible chemical reactios durig the mixig process. As a cosequece, special approaches must be used; a approach for compariso betwee experimetal ad calculated data will be discussed below. 11

12 5.1.2 Methaol Oxidatio Now we tur to a close examiatio of the chemical processes i a flow reactor uder coditios of the works [11]. I this work, the methaol oxidatio uder wide rages of temperatures ad pressures is ivestigated. O the bases of the experimetal data a detailed reactio mechaism has bee developed ad tested. I order to validate Eqs. (2.1, 4.1, 4.5, 4.11) for plug flow coditios, a experimet from [11] has bee chose. The chose data are show i Fig.5.2; the coditios are preseted i the figure captio (φ is the equivalece ratio). For simulatio of the chemical processes, the reactio mechaism [11] cosistig of 22 species ad 97 reactios is used. The reactios from the mechaism are used to calculate the reactio rates that are formed right-had sides of the differetial equatios of species ad eergy. These equatios must be accompaied by iitial coditios for T ad Y at the reactor ilet (t 0). Nevertheless, as metioed above, there are difficulties with defiitio of the iitial coditios (Sectio 5.1.1). I this coectio the authors [11] recommed the followig procedure for comparig calculatios with experimets. The iitial coditios for the differetial equatios are defied i accordace to the flow rates of the carrier gas ad reagets at ilets of the mixig sectios (for the cosidered experimet, these coditios are show i the captio of Fig. 5.2). The set of chemical kietics equatios are solved with these iitial coditios. The calculated species profiles are traslated alog the time axis to achieve miimum distictios betwee calculated ad experimetal data. This procedure has bee carried out i the work [11]; the results are show i Fig. 5.1a. It must be emphasized that i Fig. 5.2a the poit t 0 correspods to the ilet of the workig sectio (x 0). I order to brig the calculatio ad experimet ito agreemet, the calculated profiles have bee shifted by t sh 0.05 sec towards the origi. I the work [11], the calculatios have bee made with the stadard CHEMKIN package [5]. Now we will compare calculatios performed with Chemked [1] to the results [11]. The flow reactor [11] has operated uder a costat pressure ad the effect of walls of the workig sectio was egligible. These are ust the coditios, uder which Eqs. (2.1, 4.1, 4.5, 4.11) icorporated i Chemked ca be used. I our calculatio, the reactio mechaism [11] is employed as well. As previously, the iitial coditios are stated accordig to the flow rates of the carrier gas ad reagets at ilets of the mixig sectios. The species profiles obtaied with Chemked are preseted i Fig. 5.2b. To compare the calculatios with the experimet [11], we will follow the recommedatios [11] discussed above. As may be see, the Chemked profiles will coicide with calculatio ad experimet [11], if they are shifted by t sh 0.05 sec. The agreemet testifies that Chemked ca be used for simplified descriptio of plug flow reactors. 12

13 Fig 5.2. Species profiles of methaol oxidatio products i plug flow reactor Gas mixture: CH3OH/N2/O2, P 1atm, T K, X CH3OH,0 3.44E-03, φ 0.86 a - experimet [11] (symbols), calculatios [11] (lies), b this calculatio It should be oted that the discussed method for validatio of reactio mechaism is t fully substatiated due to the lack of exact iitial values at the etrace of the workig sectio. However, this method has bee successfully employed i other works, for example, i [12] where the ethaol oxidatio reactio mechaism was developed. The agreemet betwee experimets ad calculatios is excellet. 5.2 Methaol Oxidatio i Batch Reactor Here, as i Sectio 5.1, we cosider the kietics of methaol oxidatio usig results of the work [11]. I [11], a proposed reactio mechaism was validated agaist experimets [13] obtaied i a laboratory batch reactor. The experimets were carried out i a costat reactor volume. I additio, due to strog thermal iteractio the temperatures of the gas ad vessel walls were idetical, ad this commo temperature was kept costat. Experimetal [13] ad calculated [11] species profiles are show i Fig.5.3; the coditios are preseted i the figure captio (φ is the equivalece ratio). 13

14 Some problems arise from the use of Chemked for descriptio of the experimets [13]. I the costat volume batch reactor, the pressure ca chage due to chemical reactios, eve though the gas temperature is costat. Chemked is t meat for problems with variable pressure. Nevertheless, a approximate approach ca be formulated. I the [13], the gas mixture cosists of a iert gas (N 2 ) with small-admixed reagets (CH 3 OH ad O 2 ). The, the chemical reactios do t cause great chages of the pressure, ad umeric simulatio ca be made at a mea costat pressure. Besides, there is a chemical iteractio betwee the vessel walls ad the gas; this iteractio ca substatially cotrol the chemical processes. I particular, the surface reactio of hydroge peroxide decompositio was foud to be importat uder coditios of Fig. 5.3 [11]. (R) H2O2 (+ wall) > H2O O2 k 0.35 s This is t a elemetary reactio. I order to iclude the reactio (R) i the reactio mechaism of the methaol oxidatio we replace this with two elemetary reactios. (R1) H2O2 > H2O + OW k s (R2) OW + OW > O2 k 2 1E+18 mol/cm 3 s where the symbol OW deotes atomic oxyge absorbed o the walls. I Chemked there are o tools for processig the surface reactios, ad we will cosider the reactios (R1, R2) as gas-phase oes. I this case the reactio (R2) must be very fast, for example, must have the reactio rate costat k 2 1E+18 mol/cm 3 s. The the cocetratio OW will be always small ad the actio of the reactios (R1, R2) will be equal to the actio of the reactio (R). Fig 5.3. Methaol oxidatio i batch reactor Gas mixture: CH3OH/N2/O2, X CH3OH,0 0.06, φ 2, T 823K Calculated [11] (black lies) ad measured [13] (symbols) species profiles, P torr Costat pressure calculatio, this work (blue lies), P 205 torr 14

15 Thus, the simulatio of the methaol oxidatio i the batch reactor [13] is made uder costat pressure (P 205 toor) ad costat temperature (823 K) with usig the reactio mechaism [11] ad the reactios (R1, R2). Geerally the full set of equatios Eqs. (2.1, 4.1, 4.5, 4.11) is required for descriptio of the reactor performace. However, uder discussed isothermal coditios the ethalpy equatio (4.11) ca be omitted ad oly equatios (2.1, 4.1, 4.5) may be used. These equatios are solved with Chemked [1]. Some calculated profiles of species mole fractios are preseted i Fig.5.3 (blue lies). These results are i reasoable agreemet with the experimets [13] ad calculatios [11], which are made with the stadard CHEMKIN package [5]. This agreemet testifies that Chemked ca be used for simulatio of costat pressure batch flow reactors. Remark Whe usig the reactio (R), we implicitly suppose that the umber of oxyge atoms absorbed o the wall is much less tha the umber of the atoms i the gas-phase oxyge molecules. I this calculatio, this requiremet is always met; the mole fractio of the OW species is less tha Coclusio We have demostrated the capability of Chemked for solvig the complex problems of gas-phase chemical kietics. This study focuses o the applicatio of the coservatio equatios of species ad ethalpy (1.1, 1.2) for descriptio of gas-phase chemical reactors. Simplified computatioal models of the reactors are preseted ad validated agaist experimetal data. Besides, the previous works [2, 3] showed that Eqs. (1.1, 1.2) also describe the reactio kietics behid shock waves, if the shocked gas mixture cosists of a iert gas with a small amout of chemically reactive substaces. Thus, the equatios (1.1, 1.2) ca adequately simulate a wide class of reactig systems. O the basis of this ad previous studies we ca summarize the requiremets for the use of Eqs. (1.1, 1.2). Let us cosider a gas-phase reactig system. We select a uiform area iside the system. The selected area ca be at rest or ca move with a gas flow; the volume ad the form of the area ca chage due to chemical processes ad gas movemet. The equatios (1.1, 1.2) describe the temporal behavior of the selected area, if the followig coditios are satisfied. There are o mass fluxes through the boudary of the area; the gas mass i the area is costat. There are o ethalpy fluxes through the boudary of the area; the gas ethalpy i the area is costat. There are o temperature ad species gradiets withi the area; the gas i the area is always uiform. Total gas pressure i the area is costat. If the gas temperature i the area is costat, the oly the equatio (1.1) must be used for calculatio of gas compositio. 15

16 Refereces [1] M. Jeleziak, I. Jeleziak. Chemked A Program for Chemical Kietics of Gas-Phase Reactios. [2] M. Jeleziak, I. Jeleziak. Reactio Kietics Simulatio [3] M. Jeleziak, I.Jeleziak. Reduced Reactio Kietics [4] Gas-Phase Combustio Chemistry. W.C. Gardier, Jr. (Editor). Spriger-Verlag, New York (2000) [5] R.J. Kee, F.M. Rupley, J.A. Miller, M.E. Coltri, J.F. Grcar, E. Meeks, H.K. Moffat, A.E. Lutz, G. Dixo-Lewis, M.D. Smooke, J. Waratz, G.H. Evas, R.S. Larso, R.E. Mitchell, L.R. Petzold, W.C. Reyolds, M. Caracotsios, W.E. Stewart, P. Glarborg, C. Wag, ad O. Adigu. CHEMKIN Collectio, Release 3.6, Reactio Desig, Ic., Sa Diego, CA (2000). [6] M. Jeleziak, I. Jeleziak. Gas-Phase Chemical Reactios [7] Chemical Kietics Database o the Web (NIST). A Compilatio of Kietics Data o Gas-Phase Reactios. [8] H. S. Fogler. Elemets of Chemical Reactio Egieerig (Pretice Hall Iteratioal Series i the Physical ad Chemical Egieerig Scieces). Pretice Hall PTR (2005) [9] R. Aris. Elemetary Chemical Reactor Aalysis. Dover Pub., Mieola, New York (1989) [10] A. Burcat. Ideal Gas Thermodyamic Data i Polyomial Form for Combustio ad Air Pollutio Use (the THERM.DAT file). [11] T. J. Held, F. L. Dryer. A comprehesive mechaism for methaol oxidatio. It. Joural of Chemical Kietics, V. 30, p (1998) See also the publicatio list of Fuels ad Combustio Research Laboratory, Priceto Uiversity [12] J. Li, A. Kazakov, M. Chaos, F.L. Dryer. Chemical Kietics of Ethaol Oxidatio. 5th US Combustio Meetig, Sa Diego, March (2007) [13] M. Cathoet, J. C. Boetter, H. James. J. Chim. Phys., 79, 475 (1982). 16

17 Nomeclature A cross-sectioal area cm 2 c p specific heat capacity at costat pressure of the th species (cal / g K), (J / g K) ĉ p mea specific heat capacity at costat pressure (cal / g K), (J / g K) C p molar heat capacity at costat pressure of the th species (cal / mol K), (J / mol K) Ĉ p mea molar heat capacity at costat pressure (cal / mol K), (J / mol K) C tot total gas cocetratio (1/cm 3 ), (mol/cm 3 ) h mea specific ethalpy of the th species (cal / g), (J / g) h mea specific ethalpy of a mixture (cal / g), (J / g) H molar ethalpy of the th species (cal / mol), (J / mol) L reactor legth cm k,for forward rate costat of the th reactio depeds o reactio k,rev reverse rate costats of the th reactio depeds o reactio K equilibrium costat for the th reactio depeds o reactio m molecular weight of the th species g / mol M mea molecular weight of a gas mixture g / mol P pressure atm q,for, forward rate of the th reactio (1/ cm 3 sec), (mol / cm 3 sec) q rev, reverse rate of the th reactio (1/ cm 3 sec), (mol / cm 3 sec) q et rate of the th reactio (1/ cm 3 sec), (mol / cm 3 sec) Q mass flux across a surface (for plug flow reactor) g / sec total gas mass i the reactor volume (for batch reactor) g R uiversal gas costat (cal / mol K), (J / mol K) s chemical symbol of the th species t time sec t r reactor residece time sec T temperature K u rate of heat productio i the th reactio (cal / cm 3 sec), (J / cm 3 sec) U axial gas velocity i a plug flow reactor cm / sec V volume of a batch reactor cm 3 w productio rate of species i the th reactio (1/ cm 3 sec), (mol / cm 3 sec) x axial distace cm X mole fractio of the th species [X ] molar cocetratio of the th species (1/ cm 3 ), (mol / cm 3 ) Y mass fractio the th species v stoichiometric coefficiet of the th species i the th reactio ρ mass desity g / cm 3 φ equivalece ratio 17