Modeling Ignition of Catalytic Reactors with Detailed Surface Kinetics

Jul 2, 1997 - Department of Chemical Engineering, University of Massachusetts ... model with detailed gas-phase, surface kinetics and transport using ...
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Ind. Eng. Chem. Res. 1997, 36, 2558-2567

Modeling Ignition of Catalytic Reactors with Detailed Surface Kinetics and Transport: Oxidation of H2/Air Mixtures over Platinum Surfaces P.-A. Bui, D. G. Vlachos,* and P. R. Westmoreland Department of Chemical Engineering, University of Massachusetts Amherst, Amherst, Massachusetts 01003-3110

The catalytic ignition of H2/air mixtures over platinum is modeled using a stagnation-point flow model with detailed gas-phase, surface kinetics and transport using an arc-length continuation technique. Self-inhibition of the catalytic ignition of H2/air mixtures is observed in agreement with experiments. For compositions between ∼0.3 and ∼15% H2 in air at atmospheric pressure, hysteresis is created by site competition, while for mixtures with more than ∼15% H2 in air, thermal feedback is a prerequisite. It is found that the system shifts from a kinetics-limited regime on the extinguished branch to a transport-limited regime on the ignited branch. However, near ignition, the system tends toward a transport- and kinetics-limited regime. Sensitivity analysis on the reaction preexponentials shows that the competitive dissociative adsorption of H2 and O2 and the desorption of H* most affect the catalytic ignition temperature. Reaction path analysis reveals a change in dominant surface reaction paths as a function of feed composition. The effects of strain rate, pressure, and preheating on catalytic ignition are also discussed. Introduction Catalytic oxidation reactors have many important applications ranging from partial to complete oxidation (Trimm, 1983; Prasad et al., 1984; Satterfield, 1991; Warnatz, 1992). Partial catalytic oxidation is widely used for chemical synthesis. Examples include production of ethylene oxide from ethylene over silver catalysts and nitric acid from ammonia over platinum/rhodium catalysts (Satterfield, 1991). Such processes are typically run at low temperatures to optimize yield and to avoid thermal runaway and complete oxidation to CO2 and H2O by creation of flames. The total oxidation of a fuel (consisting of hydrogen and carbon) to CO2 and H2O has applications to catalytic combustors and catalytically assisted combustors for energy generation, such as the Ishikawajima-Harima Heavy Industries power generating unit (Ikeda et al., 1993). Complete combustion is also used for end-of-the-pipe reduction of emissions such as the automotive catalytic converter (Trimm, 1983). Pfefferle and Pfefferle demonstrated that catalytically assisted combustors are efficient for burning fuel-lean mixtures without significant emission of pollutants (Pfefferle and Pfefferle, 1987). In such combustors, catalysts ignite a fuel at low temperatures and stabilize the flames formed. Catalytic ignition is unavoidably a crucial step in the startup of automotive catalytic converters, catalytic combustors and catalytically assisted combustors, and partial oxidation reactors. Understanding the underlying mechanisms affecting catalytic ignition is essential in order to operate safely and to improve the control and design of such inherently nonlinear processes. Here, we study catalytic ignition using detailed gasphase chemistry, surface chemistry, and transport. To provide insight into the mechanisms controlling ignition, numerical bifurcation theory is employed along with sensitivity and reaction path analyses at turning points. To investigate the role of exothermicity of the surface reactions in catalytic ignition, we compare two different * Author to whom correspondence should be addressed. S0888-5885(96)00577-5 CCC: $14.00

cases: the “isothermal surface”, where the temperature is the controlled parameter in an experiment, and the “nonisothermal surface”, where the resistive power input to the surface is the controlled parameter. The effects of composition, strain rate, pressure, and preheating on catalytic ignition are also discussed. Previous Work Many experimental data on catalytic ignition are available. Cho and Law found in experiments over platinum wires that hydrogen, ethylene, propylene, and carbon monoxide inhibit catalytic ignition; i.e., as the composition of the fuel in air increases, the catalytic ignition temperature increases (self-inhibition) (Cho and Law, 1986). On the other hand, paraffins (e.g., ethane, propane, and butane) promote catalytic ignition; i.e., as the composition of the fuel in air increases, the catalytic ignition temperature decreases (Cardoso and Luss, 1969; Rader and Weller, 1974; Cho and Law, 1986; Williams et al., 1991). Cho and Law suggested that the different adsorption strengths of various fuels on platinum cause these different catalytic ignition behaviors (Cho and Law, 1986). More recent experiments on H2/ air catalytic ignition against a platinum foil (a stagnation flow reactor) and over platinum wires have confirmed the self-inhibition of H2 on ignition (Fassihi et al., 1993; Ikeda et al., 1995). Furthermore, the flow rate seems to have a small influence on catalytic ignition of H2/air mixtures (Cho and Law, 1986; Ikeda et al., 1995). Besides experiments, models of different sophistication have been proposed to study catalytic combustion of H2. A criterion for catalytic ignition of H2/O2 was derived by simplifying a surface mechanism and by omitting mass transport (Fassihi et al., 1993) which gave good agreement with experimental data. Flow against a catalytic plate (a stagnation geometry) was modeled with multicomponent transport, a detailed gasphase reaction mechanism, and a global surface reaction mechanism (Schefer, 1982; Ikeda et al., 1993). Theoretical results using a heat balance were in apparent contradiction with experiments (Ikeda et al., 1995). © 1997 American Chemical Society

Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2559

Figure 1. Mole fraction of H2 above the stagnation surface as a function of the surface temperature for 1% H2/air. The extinguished and catalytic ignited branches are represented by a solid line, and the unstable branch is represented by a dashed line. The catalytic ignition and extinction are indicated by a vertical arrow. The inset shows a schematic of the reactor configuration. The parameters are pressure of 1 atm and strain rate of 500 s-1.

Laminar flow over a flat catalytic plate was also modeled with multicomponent transport, a detailed gasphase mechanism, and various simplified surface boundary conditions to study the coupling between the gasphase and surface reactions at high temperatures (Schefer, 1982; Markatou et al., 1991). Recently, the most complex model with detailed homogeneous and heterogeneous reaction mechanisms, and detailed transport has been used to investigate the catalytic ignition of H2/O2 mixtures (Warnatz et al., 1994; Deutschmann et al., 1995). Stationary states were computed from time integration of the corresponding time-dependent differential equations. This solution method is considerably computer-intensive. In addition, ignition and extinction points cannot be determined precisely. As a result, sensitivity and reaction path analyses at critical points are difficult to perform because such analyses involve two-parameter continuation techniques (Bui et al., 1996; Kalamatianos et al., 1997; Vlachos, 1996). We have recently compared the catalytic ignition temperatures for H2/air mixtures obtained from our simulations with experimental data and found good agreement (Vlachos and Bui, 1996). We observed that the platinum surface is blocked by different adsorbates under different conditions and suggested that the selfinhibition of H2 catalytic ignition is due to the surface species H* blocking the surface. We also found that a global one-step chemistry is inadequate for explaining the self-inhibition, indicating the necessity of detailed surface chemistry. Previous theoretical studies focused mainly on reproducing experimental data. As a result, the roles of surface reaction exothermicity, transport, radiation, and pressure in catalytic ignition are not well understood. In addition, the mechanisms underlying catalytic ignition and specifically the self-inhibition have not been sufficiently elucidated. This work examines these issues using a detailed surface and gas-phase reaction model. Model Conservation Equations. A stagnation-point flow geometry is considered, shown schematically in the inset of Figure 1, because it is a widely used experimental configuration (Ablow et al., 1980; Ikeda et al., 1993; Warnatz et al., 1994) and makes mathematical analysis tractable. The ideal-gas law is employed as an equation of state. We consider compressible flow and constant pressure in the reactor. The conservation equations of continuity, momentum, energy, and species for axisymmetric flow are employed.

Using a similarity transformation, the system of partial differential equations is reduced to a set of ordinary differential equations by introducing a stream function f and a dimensionless distance η (Sharma and Sirignano, 1969; Song et al., 1991). Some assumptions are introduced to simplify the equations. These are constant Fµ, constant Prandtl number, constant Schmidt number of each species, and equal specific heats for all species. These assumptions have been discussed elsewhere (Vlachos et al., 1994). The system of differential equations becomes

( ( ))

d2f 1 Fe d3f df + f + 3 2 2 F dη dη dη d2T dη2 d2Wj dη2

+ fPr

+ fScj

Pr

dT + dη

2aFcp

+ dη

2aF

)0

(1)

Ng

(

(-∆Hi)ri) ) 0 ∑ i)1

ScjMj Ng

dWj

2

νijri ) 0 ∑ i)1

(2)

(j ) 1, ..., Mg) (3)

where the continuity and momentum equations are represented by the ordinary differential equation (1). All symbols are listed in the nomenclature. To conserve the overall mass, the inert gas-phase species (N2) is determined from Mg+1

Wj ) 1 ∑ j)1

(4)

Table 1 shows the boundary conditions at the entrance and the surface of the reactor. To derive the dimensionless boundary conditions for energy and species, the following assumptions have been made

x

Te Ts

(5)

Scj ≈ Scej

(6)

ke ≈ ks and

At the inlet, we assume potential flow at a temperature Te and a mixture composition Wej (j ) 1, ..., Mg + 1). At the surface, the no-slip and no-penetration conditions are applied. We consider two cases for the surface energy boundary condition: (1) the isothermal surface, where the surface temperature is the controlled parameter, and (2) the nonisothermal surface, where the resistive power input to the surface is the controlled parameter. In the latter case, the surface temperature becomes a dependent variable determined from the boundary condition. In particular, the conductive heat flux is equal to the sum of the radiation energy loss, the energy loss at the back of the surface (except radiation), the chemical heat release by surface reactions, and the resistive power input Pw to the catalytic surface per unit area. This boundary condition is strongly nonlinear due to the temperature dependence of the surface reaction rates. Thus, comparison of results obtained using these two boundary conditions indicates the role of surface reaction exothermicity in bifurcation behavior. In our study, we assume that

2560 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 Table 1. Dimensionless Boundary Conditions at Ambient and at Surface ambient

surface

ηf∞

η)0

momentum

df )1 dη

f ) 0 and

energy

Θ ) Θe

temperature controlled: Θ ) Θs

df )0 dη

power controlled:

( ) ∂Θ

-

- Pr

∂η

-Pr species

x

x

Θe Θs

s i

s i

- Pw′)

i)1

Θe [h′(Θs - Θe) + 2σ′(Θs4 - Θe4)] ) 0 Θs

Wj ) Wej

gas-phase species:

j ) 1, ..., Mg+1

h) 1 ∂(WjM M h

Ns

∑∆H ′r

(

( ) ∂η

Ns

) -MjScej

∑ ν r ′, s ij i

j ) 1, ..., Mg

i)1

Mg+1

∑W )1 j

j)1

surface species: Ns

∑ν r ′ ) 0, s ij i

j ) 1, ..., Ms,

j**

i)1 Ms

∑θ ) 1 j

j)1

Table 2. Surface Reaction Mechanism for H2/O2 on Platinum (Units of k0 Are in Moles, Centimeters, Seconds, or Sticking Coefficient) (S1) (S2) (S3) (S4) (S5) (S6) (S7) (S8) (S9) (S10) (S11) (S12) (S13) a

reaction

k0

H* + O* f OH* + * OH* + * f H* + O* H* + OH* f H2O* + * H2O* + * f H* + OH* 2OH* f H2O* + O* H2O* + O* f 2OH* H2 + 2* f 2H* 2H* f H2 + 2* O2 + 2* f 2O* 2O* f O2 + O* H2O + * f H2O* H2O* f H2O + * OH* f OH + *

1.66 × 1.66 × 10-1 1.49 × 108 2.99 × 104 1.66 × 106 106

1.0 1.66 × 104 0.279 1.66 × 104 0.1 1.66 × 104 2.49 × 104

E [cal/mol]

∆H [cal/mol]

2 500 5 000 15 000 37 000 12 300 31 800 0 18 000 0 52 000 0 10 800 48 000

-2 500a 2 500 -22 000a 22 000 -19 500a 19 500 -18 000 18 000b -52 000 52 000b -10 800 10 800b 48 000b

∆Hi ) Ei - Ei+1. b ∆Hi ) Ed.

there is no energy loss at the back of the catalytic foil. Where the radiation loss from the reactive surface is considered, the value of the emissivity is set equal to 0.1 (Warnatz et al., 1994). The factor of 2 in the radiation loss term (see Table 1) takes into account the radiation loss at both the forth and the back of the surface. Concerning the species boundary conditions, the flux of a gas-phase species at the surface is equal to its net rate of consumption due to interfacial reactions. We define as interfacial reactions, these reactions which include at least one surface species. For a surface species, at steady state the net reaction rate is equal to zero. Finally, the coverage of vacancies is computed from an overall balance on catalyst sites. The density of platinum sites is taken to be 1 × 1015 cm-2. Detailed Chemistry. The surface mechanism used (Williams et al., 1992) is of the Langmuir-Hinshelwood type and is shown in Table 2. Interfacial reactions include the competitive dissociative adsorption of H2 and

O2, the competitive adsorption of H2O, the recombinative desorption of H* and O* into H2 and O2, respectively, the desorption of H2O* and OH*, and surface reactions. Second-order adsorption and desorption kinetics for H2 and O2 are used here. The activation energy of the interfacial reaction rate S6 is adjusted to 31.8 kcal/mol in order for the surface mechanism to be thermodynamically consistent. This mechanism has been tested against experimental ignition data, and good agreement was found (Vlachos and Bui, 1996). The rates rsi of interfacial reactions are computed as follows. The rate of a competitive adsorption step i involving species j is

rai ) kai csj θ*ai*

(7)

The adsorption rate constant kai is calculated from the kinetic theory of ideal gases:

Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2561 a

kai

γje-Ei /RT )

RT

x2πMjRT

(8)

The desorption and surface reaction rates are calculated respectively from

rdi ) kdi θaj ij

(9)

and Ms

rsi ) ksi

θaj ∏ j)1

ij

(10)

The detailed gas-phase reaction mechanism of Miller and Bowman (Miller et al., 1990) is employed, including 20 reversible reactions among nine species (H2, O2, OH, H2O, H, O, HO2, H2O2, N2). Even though gas-phase reactions are taken into account, we have shown that catalytic ignition of H2 in air is not affected by gas-phase reactions (Vlachos and Bui, 1996). Thus, gas-phase chemistry is not discussed further here. Solution Methods. The ordinary differential equations (1)-(3) and the boundary conditions are discretized using a second-order finite difference scheme to obtain a set of algebraic equations. An arc-length continuation is used to track solutions and pass around turning points such as ignitions and extinctions. Newton’s method is used to solve the system of nonlinear equations. A bisection method is also employed to obtain more accurate critical solutions. These methods are explained elsewhere (Vlachos et al., 1993; Kalamatianos et al., 1997; Vlachos, 1996). Effect of Composition on Temperature-Controlled Surface Ignition In this section, we study the catalytic ignition of H2 in air when the surface temperature is the controlled parameter. Below, the pressure is 1 atm, the strain rate is 500 s-1, and the temperature at the inlet is 298 K. The effects of these parameters on ignition are discussed later. A mixture of 1% H2 in air is taken as a first example. Figure 1 shows the gas-phase mole fraction of H2 above s the catalytic surface YH versus the surface tempera2 s ture Ts. As Ts increases from low values, YH remains 2 at first constant and then decreases slowly until ∼410 K, where a turning point (called an ignition) is found. These low-conversion solutions correspond to the extinguished branch. At the turning point, there is an onset of catalytic activity and the system is described as jumping to a catalytic ignited branch. As Ts decreases from high values, an extinction is reached at low Ts (below room temperature) indicated by an arrow. The extinguished branch and the catalytic ignited branch are connected with an unstable branch. Between the ignition and extinction temperatures, multiple steady states exist, and hysteresis should be found experimentally as the temperature varies. Even though the surface reaction mechanism shown in Table 2 does not consider the desorption of H* to H and O* to O, thermodynamic consistency calculations suggest that the desorption energies of these interfacial reactions are high. In particular, the absolute values of the estimated heats of adsorption of H* and O* (which are lower bounds of activation energies of desorption) are 60 and 85 kcal/mol, respectively. As a result, these

Figure 2. (a and b) Coverages of surface species as a function of the surface temperature. The inset is a magnification of the surface coverage of H* versus Ts near ignition. Upon ignition, a transition is observed from H* on the extinguished branch to O* on the ignited branch. Upon extinction, a transition occurs from H2O* on the ignited branch to H* on the extinguished branch. The catalytic ignition and extinction are indicated by vertical arrows. The parameters are the same as in Figure 1.

desorption steps are slow at low temperatures and do not affect catalytic ignition. Figure 2 shows the coverages of all surface species versus Ts. The inset in Figure 2a shows a magnification of the coverage of H* versus Ts near ignition. Prior to ignition, H* is the dominant surface species (θH* ∼ 1), and O* is a limiting reactant. As Ts increases on the extinguished branch, θH* decreases until the ignition point is reached. Upon ignition, the system jumps to the catalytic ignited branch, and a transition occurs in the dominant surface species from H* and * on the extinguished branch to O* and * on the catalytic ignited branch. On the extinguished branch, as Ts increases, θO*, θH2O*, θOH*, and θ* increase but their values are low (except for vacancies). As the temperature decreases on the ignited branch, there is a change in the dominant adsorbed species from O* at higher temperatures to OH* and H2O* at lower temperatures. Near extinction (∼275 K), H2O* is the major surface species. At low temperatures, the H2O* formed does not desorb readily, resulting in blocking of adsorption sites on platinum, which, in turn, causes extinction. Catalytic extinction is not discussed further here. The hysteresis discussed above is found for H2/air compositions between ∼0.3% H2 in air and ∼15% H2 in air. For compositions lower than ∼0.3% H2 in air, O* is the dominant surface species at room temperature. As Ts increases, O* desorbs slowly because of the high energy of desorption of O2 (see Table 2). Reactivity occurs at high temperatures (near homogeneous ignition temperature) without hysteresis. For compositions higher than ∼15% H2 in air, H* and * remain the major surface species up to high temperatures where homogeneous ignition occurs (Bui et al., 1995, 1996), and as Ts increases from low values, no catalytic turning point is found in the sense of strict bifurcation. A two-parameter bifurcation diagram is shown as Figure 3, where the solid line shows catalytic ignition temperature versus the inlet composition of H2 in air in the compositional regime where a turning point exists. As the inlet composition of H2 increases, its partial pressure above the surface also increases. Consequently, higher temperatures are needed for H* to desorb, resulting in self-inhibition of catalytic ignition. This self-inhibition is in qualitative agreement with experiments (Cho and Law, 1986; Fassihi et al., 1993; Ikeda et al., 1995; Vlachos and Bui, 1996). The recent

2562 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997

Figure 3. (Solid and dashed lines) Catalytic ignition temperature as a function of H2 composition in air when the surface temperature is the controlled parameter (an isothermal surface) and when the resistive power input is the controlled parameter (a nonisothermal surface), respectively. H2 self-inhibits its catalytic ignition. Very fuel-lean mixtures ignite upon contact with platinum. Ignition of fuel lean mixtures is caused by competition of surface sites. Reaction exothermicity is significant at high compositions. The dominant mechanism and the dominant surface species prior to ignition are also indicated with arrows. The parameters are pressure of 1 atm and strain rate of 500 s-1.

calculations of Behrendt et al. and Fassihi et al. are also in agreement with experiments (Fassihi et al., 1993; Deutschmann et al., 1995). On the other hand, the ignition temperature of the model of Warnatz and coworkers differs from experimental data by ∼250 K (Warnatz et al., 1994). Figure 3 indicates that it should be experimentally easier to ignite fuel-lean mixtures and then to increase the composition to the desired value. Our simulations show that very fuel-lean mixtures can ignite near or below room temperature. When the ignition temperature Tig is below room temperature, an ignition will occur upon contact of the H2/air mixture with platinum. The sharp decrease in ignition temperature with decreasing composition at very fuel-lean mixtures and the transition from H* to O* below ∼0.3% H2/air may explain the poor reproducibility of experimental data of fuel-lean mixtures (Fassihi et al., 1993). Sensitivity Analysis Here, we investigate the role of interfacial reactions in the catalytic ignition temperature by sensitivity analysis through a simple 2-fold decrease in the interfacial preexponential or sticking coefficient and the associated reverse rate constant. Such sensitivity analysis of turning points is a special case of a two-parameter continuation algorithm (Kalamatianos et al., 1997). Figure 4a shows the corresponding change in Tig from its nominal value for various compositions. Note that when a reaction is almost irreversible, this sensitivity analysis captures essentially only the fast step. An example is reactions S9 and S10, where the desorption rate of O* is considerably slower than the adsorption rate of O2. Our results show that three interfacial reactions affect mostly the catalytic ignition temperature: the dissociative adsorption of H2 and O2, reactions S7 and S9, and the recombinative desorption of H*, reaction S8. The rest of the interfacial reactions have a negligible effect on Tig. By examining the sensitivity of Tig on individual reactions (perturbation in only one direction), we have found that the dissociative adsorption of H2 inhibits and the recombinative desorption of H* promotes catalytic ignition, with a net result shown in Figure 4a. When the net flux of H2 decreases, the coverage of H* decreases and that of vacant sites increases. The increase in vacancies allows O2 to adsorb dissociatively on the surface and react with the adsorbed H* to form

Figure 4. (a) Change in ignition temperature upon a 2-fold decrease in interfacial reaction preexponentials for various compositions. Only reactions with a strong influence are shown. The adsorption of H2 retards, and the desorption of H* promotes catalytic ignition temperature, with a net result shown in panel a. The adsorption of O2 promotes catalytic ignition. (b) Change in ignition temperature upon a 2-fold decrease in species Schmidt number for various compositions. Near ignition, the diffusion of H2 and O2 affects catalytic ignition. The “-” sign indicates loss of multiplicity for the corresponding change in sticking coefficient. The parameters are pressure of 1 atm and strain rate of 500 s-1.

OH* and subsequently H2O*. At higher compositions, the net catalytic ignition inhibition of S7 and S8 is moderate because the two interfacial reactions approach local equilibrium and their opposing effects cancel each other. The competitive dissociative adsorption of O2, reaction S9, promotes ignition. When the net flux of O2 decreases, O2 does not adsorb as rapidly on the catalytic surface. Therefore, θO* decreases, resulting in less OH* s and H2O*. As a result, θH* and YH are higher, inhib2 iting surface ignition. We have also examined the effect of transport on Tig. A sensitivity analysis on diffusion has first been performed. A 2-fold increase in the Schmidt number Scj of species j is considered which is equivalent to a 2-fold decrease in the species multicomponent diffusion coefficient. Figure 4b shows the resulting changes in catalytic ignition temperature for various compositions indicated. The diffusion of H2 and O2 to the surface has a large influence on Tig. In particular, the diffusion of H2 to the surface inhibits catalytic ignition. A reduced diffusion coefficient for H2 has an effect similar to that of a reduced sticking coefficient for adsorption. On the other hand, the diffusion of O2 to the surface promotes catalytic ignition, in agreement with the sensitivity analysis results shown in Figure 4a. The diffusion of gas-phase radicals has a negligible influence on catalytic ignition due to the small mole fractions of intermediates at low temperatures. A sensitivity analysis on energy conduction was also performed. The effect of Prandtl number on Tig (data not shown) is negligible, indicating that energy transport plays a minor role in catalytic ignition when temperature is the controlled parameter. Thus, the hysteresis shown in Figures 1 and 2 is primarily driven by a surface autocatalytic mechanism and does not require thermal feedback as a prerequisite. Figure 5 shows the corresponding change in the coverage of selected surface species at ignition resulting from a 2-fold decrease in the interfacial preexponential or sticking coefficient and the associated reverse rate constant. The adsorption of H2, the desorption of H*, and the adsorption of O2 influence the coverage of O*, OH*, and *, and to a lesser extent of H2O*. Even though the interfacial reactions S1 and S2, and S3 and S4 have a negligible effect on the catalytic ignition temperature, they strongly affect the surface coverage

Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2563

Figure 5. Relative change in surface coverage at ignition upon a 2-fold decrease in interfacial reaction preexponentials for 1% H2/ air. The surface coverage of H* at ignition is not sensitive to reaction preexponentials. Reactions S1 and S2, and S3 and S4 strongly affect the surface coverages of O* and OH*, respectively, but have no influence on the catalytic ignition temperature. The parameters are pressure of 1 atm and strain rate of 500 s-1.

Figure 6. (a) Dominant surface reaction paths when H* is the dominant surface species. (b) Dominant surface reaction paths when O* is the dominant surface species.

of O* and OH*, respectively. The surface coverage of H* is not sensitive to any interfacial reaction for these conditions (data not shown). These sensitivity analyses indicate that the important reactions which affect each surface species and Tig are different, and thus the minimal reaction scheme affecting ignition is not simply reactions S7, S8, and S9 as Figure 4a indicates. The information of both Figures 4 and 5 is important in reducing kinetic mechanisms and deriving a simplified criterion for ignition. Reduced mechanisms will be presented elsewhere (Bui et al., 1997). Surface Reaction Path Analysis To provide further insight into surface ignition, we have determined the contribution of interfacial reactions to the formation or disappearance rates of surface species at the ignition turning point. The results of the surface reaction path analysis are summarized in Figure 6. First we discuss the case where H* is the dominant surface species. This situation arises (1) before catalytic e ignition for ∼0.03 < YH < ∼0.15 (see Figure 2) and (2) 2 e up to the homogeneous ignition temperature for YH > 2 ∼0.15. H* is produced by the adsorption of H2 through step S7. H* is consumed by its recombinative desorpe tion S8 and the surface reactions S1 and S3. As YH 2 increases, the reactions S1 and S3 of H* with O* and with OH*, respectively, contribute less to the consumption of H*. As an example, this contribution varies from ∼23% of the total consumption of H* for 1% H2/air to below 3% of the total consumption of H* for H2/air e compositions over 10%. Thus, for YH > 0.1, H* is 2 almost in equilibrium with gas-phase H2. O* is primarily produced by the dissociative adsorption of O2 through step S9 and is consumed by H* to

Figure 7. (a) Mole fraction of H2 above the surface as a function of the surface temperature for 1% H2/air at 1 atm and various strain rates. (b) At various strain rates the corresponding rate of adsorption of O2 versus surface temperature. As the temperature increases from low values, the system shifts from a kinetics-limited regime on the extinguished branch at low surface temperatures, to a transport- and kinetics-limited regime near ignition, and finally to a transport-limited regime on the ignited branch. The desorption of H* controls the rate of oxidation prior to ignition.

form OH* through reaction S1. Once OH* forms, it is consumed with the abundant H* to form H2O* through reaction S3. As a result, θOH* is low, as shown in Figure 2. The recombination of two OH* radicals through reaction S5 and the desorption steps of O* and OH* is negligible under these conditions. The desorption of H2O* (step S12) is the primary path e consuming H2O*. As YH increases, the adsorption of 2 H2O (step S11) becomes the dominant step, forming H2O* at the expense of the reaction of H* with OH* (step S3). Thus, as the inlet composition increases, H2O* tends to be in equilibrium with H2O in the gas phase. When H* is the dominant surface species, the main surface reaction path for formation of H2O* is ads O* H* 1 H 798 H* 98 OH* 98 H2O* 2 2

(G1)

The results of the reaction path analysis indicate that, under certain conditions, some of the surface species may be in local equilibrium with the corresponding gasphase species. Furthermore, the compositional regime where such equilibrium assumptions employed before (e.g., Schefer, 1982; Markatou et al., 1991) are valid changes with parameters in a nonlinear way. Next we discuss the case where O* is the dominant surface species. This situation arises (1) upon ignition of mixtures with composition between ∼0.3% and ∼15% of H2 in air and (2) for mixtures with less than 0.3% H2 in air. The dominant surface reaction pathways are shown in Figure 6b. Upon adsorption of H2, H* is consumed by O* (an excess surface reactant). As a result, θH* is very low. Since OH* desorbs very slowly, OH* recombines with another OH* to form H2O*. The main surface reaction path for formation of H2O* is ads

2H*

O2 98 2O* 98 2OH* f H2O* + O*

(G2)

Effect of Strain Rate on Catalytic Ignition We next study the role of strain rate in catalytic ignition. Figure 7a shows the mole fraction of H2 above the surface versus Ts for 1% H2 in air at different strain rates. Tig increases as the strain rate increases. The strain rate has a negligible effect on the extinguished and ignited branches of YH2 (flat portions) except near ignition where the strain rate affects the turning point of the system. On the other hand, most of the interfacial

2564 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997

Figure 8. Catalytic ignition temperature as a function of strain rate for 1% H2/air at atmospheric pressure for the isothermal surface and the nonisothermal surface. The catalytic ignition temperature increases logarithmically with increasing strain rate.

rates are affected by the strain rate near ignition and on the ignited branch. On the extinguished branch, at low Ts, the interfacial rates are independent of strain rate. Figure 7b shows as an example the adsorption rate of O2 versus Ts for 1% H2 in air at different strain rates. The rate of adsorption of O2 depends strongly on Ts on the extinguished branch but is a weak function of temperature on the ignited branch. An Arrhenius plot prior to ignition gives an activation energy of 18 kcal/mol which is in agreement with the fact that the desorption of H* controls oxidation prior to ignition (see also Table 2). Thus, for these conditions, the system shifts from a kinetics-limited regime (extinguished branch at low Ts) to a transport-limited regime (catalytic ignited branch). Near ignition, the system is in a combined transport- and kinetics-limited regime. The sensitivity of Tig to transport is also independently illustrated from the diffusion sensitivity analysis in Figure 4b. The solid line in Figure 8 summarizes the effect of strain rate on the catalytic ignition temperature for 1% H2 in air. We observe that the catalytic ignition temperature depends logarithmically on the strain rate. The influence of convection on surface ignition is rationalized by the species surface boundary condition shown in Table 1 through the dependence of the dimensionless reaction rate on the strain rate. As the strain rate increases, the transport of species to the surface is facilitated. An increase in strain rate can be thought of as an effective increase in the sticking coefficient of all gas-phase species adsorbing to the catalytic surface, in particular that of H2. As a result, H* blocks the surface more effectively, increasing Tig. This bifurcation behavior is in contradiction with the simple thermal ignition model where the blocking of platinum sites by H* was not considered (Ikeda et al., 1995). Our results on the ignition temperature regarding the effect of flow velocity are in agreement with experimental data (Cho and Law, 1986; Ikeda et al., 1993). Effect of Pressure on Catalytic Ignition Here, the effect of pressure on catalytic ignition is studied. The solid line in Figure 9 shows the catalytic ignition temperature versus the pressure in the reactor for 1% H2 in air. As the pressure increases, the catalytic ignition temperature increases. As with the strain rate, the catalytic ignition temperature depends logarithmically on pressure. A pressure increase results in higher partial pressure of H2 and O2 above the surface and thus in a more effective blocking of the surface by H*. This inhibition can again be rationalized through the surface species boundary condition shown in Table 1 and, in particular, the dependence of the dimensionless inter-

Figure 9. Catalytic ignition temperature as a function of pressure for 1% H2/air at 500 s-1 for the isothermal surface and the nonisothermal surface. The catalytic ignition temperature increases logarithmically with increasing pressure.

Figure 10. (a and b) Surface temperature and mole fraction of H2 above the surface, respectively, as a function of the resistive power input per surface area for 1% H2/air, at 1 atm and 500 s-1. The dotted and dashed lines in panel a indicate the conductive and reaction contributions to Pw. At low temperatures, conduction dominates, but near ignition, the interfacial reactions exothermicity becomes important.

facial reaction rate rsi ′ (see Nomenclature) on mixture density. Figure 9 indicates that when a fuel fragment blocks the catalyst, higher pressure makes it more difficult to ignite the catalyst in partial oxidation reactors and catalytic gas turbines. However, this effect is relatively weak. Effect of Preheating on Catalytic Ignition Simulations have been performed to examine the effect of preheating on catalytic ignition. Preheating is often done to improve the selectivity of industrial reactors (Hickman and Schmidt, 1993). We have found that, as the inlet temperature increases, Tig decreases slightly. As an example, the relative change in Tig is smaller than ∼1.5% for mixtures of 1% and 10% H2 in air as the inlet temperature increases from 25 to 300 °C. Overall, the effect of preheating on ignition is very small, in agreement with the negligible effect of the Prandtl number on the catalytic ignition temperature. Effect of Surface Reaction Exothermicity on Catalytic Ignition In this section, we investigate the role of the interfacial reactions exothermicity in catalytic ignition of H2 in air. To achieve that, the resistive power input to the surface per surface area Pw is taken as the controlled parameter. The 1% H2/air mixture is chosen to compare the results to the ones when Ts is the controlled parameter (Figures 1 and 2). The solid line in Figure 10a shows Ts versus Pw. As Pw increases, Ts increases almost linearly until a turning point (an ignition) where the system jumps to an ignited branch. Tig is now lower than the one found when Ts is the controlled parameter, indicating that the exothermicity of the interfacial reactions promotes ignition.

Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2565

Figure 10b shows the mole fraction of H2 above the surface versus Pw. H2 above the surface behaves similarly to the isothermal surface case. However, the reactivity of the system at ignition is lower compared to Figure 1, resulting in almost flat profiles of major species versus the distance from the catalyst. Upon ignition, a transition in the dominant surface species from H* to O* occurs similarly to the isothermal surface case shown in Figure 2. Similarly to the isothermal surface, as Pw increases, the system shifts from a kinetics-limited regime (extinguished branch at low Pw), to a combined transport- and kinetics-limited regime (near ignition), and then to a transport-limited regime (catalytic ignited branch). However, when power is the controlled parameter, other situations arise as well. For example, for 20% H2 in air, upon catalytic ignition the system jumps directly to the homogeneous ignited branch which is transportlimited. These interactions of the catalyst with the gasphase chemistry at high temperatures will be discussed elsewhere. At each temperature, the contributions of the important energy terms to Pw (see also the surface boundary condition in Table 1) are also plotted in Figure 10a. The loss by conduction toward the cold incoming gases is almost a linear function of Ts. On the other hand, the power generated by the interfacial reactions is almost zero at low Ts. Thus, at low Ts, the conduction loss determines the energetics of the system. As the power input increases, the exothermicity of the interfacial reactions increases considerably due to the Arrhenius temperature dependence of the interfacial rates. The results shown in Figure 10 include radiation loss. To study the influence of the radiation loss, we set artificially the value of the emissivity to zero. We found that the radiation loss has a small effect on both Pw and Tig almost in the entire compositional regime. As examples, when the radiation loss is omitted, Tig decreases by ∼0.4% for mixtures of 1% H2/air and 20% H2/air. However, when H2 and O2 are sufficiently diluted in N2 (a case not presented here), the radiation loss affects Pw and Tig because it is of the same order of magnitude as Pw required for ignition. The dashed line in Figure 3 shows Tig versus the inlet composition of H2 for the power-controlled case. The compositional regime over which ignition occurs is extended compared to the isothermal surface. We observe that the catalytic ignition temperature increases as the inlet composition of H2 in air increases. This selfinhibition is again due to platinum blocked by H*. It is shown that, as the composition of H2/air decreases toward ∼0.3%, the nonisothermal Tig coincides with the isothermal Tig, demonstrating that the interfacial reactions exothermicity is negligible for very fuel-lean mixtures. Figure 3 indicates also that thermal exothermicity is a prerequisite for hysteresis of mixtures with more than ∼15% H2 in air. The effects of strain rate, pressure, and preheating on catalytic ignition are similar to the isothermal surface. Examples are shown with dashed lines in Figures 8 and 9. To examine the effect of heat of reactions, an additional sensitivity analysis on the heat of each reaction (one at a time) has been carried out (data not shown). The heats of reactions S3, S7, S9, S11, and, to a lesser extent, S1 promote catalytic ignition. On the other hand, the endothermic reactions S8 and S12 inhibit catalytic ignition. Even though the interfacial reactions S11 and S12 play a minor role in Tig for the isothermal

surface, their exothermicity is significant for the nonisothermal surface. Because of the slight reactivity at ignition (see Figure 10), diffusion is less important when the power is the experimentally controlled parameter. On the other hand, sensitivity analysis on the Prandtl number shows that conduction has a strong effect on Tig. The thermal conductivity of H2 is about an order of magnitude larger than those of O2, H2O, and N2. Consequently, as the inlet H2 composition increases, the thermal conductivity of the mixture increases as well. The increased heat loss by conduction is then balanced by a higher reaction energy generated at a higher Tig. Conclusions We have studied the catalytic ignition of H2/air mixtures over platinum surfaces using a detailed surface reaction mechanism and numerical bifurcation theory. When an isothermal surface is considered, a catalytic ignition occurs between ∼0.3 and ∼15% H2 in air at atmospheric pressure. The main points can be summarized as follows: (1) As the composition of H2 in air increases, the catalytic ignition increases due to blocking of platinum sites by H*. (2) Upon ignition, a transition occurs from a H*blocked surface to an O*-blocked surface. This transition causes a change in the dominant surface reaction path of formation of H2O* from

(extinguished branch) ads O* H* 1 H 798 H* 98 OH* 98 H2O* 2 2

to

(ignited branch) ads

2H*

O2 98 2O* 98 2OH* f H2O* + O* (3) The system shifts from a kinetics-limited regime on the extinguished branch at low surface temperatures to a transport-limited regime on the ignited branch. Near ignition, the system tends toward a transport- and kinetics-limited regime. (4) Sensitivity analysis indicates that the competitive dissociative adsorption of H2 and O2, the desorption of H*, and the diffusion of H2 and O2 most affect catalytic ignition. (5) The strain rate and pressure have a weak inhibiting effect on catalytic ignition. (6) The exothermicity of the interfacial reactions promotes catalytic ignition and is a prerequisite for hysteresis of mixtures with more than ∼15% H2 in air. (7) Sensitivity analysis shows that conduction plays also an important role in catalytic ignition of a nonisothermal surface. Our simulations presented here have elucidated the role of surface reaction mechanisms, transport, and reaction exothermicity in catalytic ignition. Work on hydrocarbons is in progress. Acknowledgment This work was supported in part by the Office of Naval Research with Dr. G. D. Roy through a Young Investigator Award under Contract No. N00014-96-10786 (P.-A.B. and D.G.V.) and by the Department of

2566 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997

Energy Grant No. DE-FG02-91ER14192 (P.-A.B. and P.R.W.). Nomenclature a ) strain rate, s-1 aij ) order of reaction i with respect to surface species j cj ) molar concentration of species j, mol cm-3 csj ) molar concentration of species j above the surface, mol cm-3 cp ) constant pressure specific heat of mixture, cal g-1 K-1 Dj ) multicomponent diffusion coefficient of species j in the mixture, cm2 s-1 E ) activation energy, cal mol-1 f ) stream function h ) heat-transfer coefficient in energy loss term, cal cm-2 s-1 K-1 hTr

1 ) dimensionless heat-transfer c Fx2aνe pTr coefficient in energy loss k ) thermal conductivity of mixture, cal cm-1 K-1 s-1 ki ) rate constant of ith interfacial reaction, mol, cm, s-1 kai ) adsorption reaction rate constant, cm s-1 k0 ) reaction preexponential, mol, cm, s-1 M h ) average molecular weight of the mixture, g mol-1 Mj ) molecular weight of species j, g mol-1 Mg ) number of gas-phase species not including the carrier gas Ms ) number of surface species Ng ) number of gas-phase reactions Ns ) number of surface reactions Pr ) Prandtl number Pw ) resistive power input per unit area, cal cm-2 s-1 h′ )

Pw

1 ) dimensionless resistive power input c p Fx2aνe Tr ri ) molar rate of the ith gas-phase reaction, mol cm-3 s-1 rsi ) rate of the ith interfacial reaction, mol cm-2 s-1 P w′ )

rsi ′ )

rsi

) dimensionless rate of the ith interfacial reaction R ) ideal gas constant, cal mol-1 K-1 Scj ) Schmidt number of species j T ) temperature, K Te ) temperature at the inlet, K Tr ) reference temperature, K Wj ) weight fraction of species j Yj ) mole fraction of species j

x2aµeFe

Greek Symbols γj ) sticking coefficient of species j δj ) thickness of boundary layer of species j, cm ∆Hsi ) heat of the ith interfacial reaction, cal mol-1 ∆Hsi 1 ) dimensionless heat of the ith cpTrF 2aν x e interfacial reaction  ) emissivity of the surface η ) dimensionless distance from the surface θj ) surface coverage of the jth surface species Θ ) T/Tr dimensionless temperature ν ) kinematic viscosity, cm2 s-1 νij ) stoichiometric coefficient of the jth species in the ith reaction F ) density of mixture, g cm-3 σ ) Boltzmann factor, cal s-1 cm-2 K-4 ∆Hsi ′ )

σ′ )

σTr4

1 ) dimensionless product of the c Fx2aνe pTr Boltzmann factor and the emissivity of the surface

Superscripts and Subscripts a ) adsorption d ) desorption e ) entrance of the reactor g ) gas i ) reaction ig ) ignition j ) species 0 ) nominal value s ) surface * ) vacancies or adsorbed species

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Received for review September 23, 1996 Revised manuscript received April 7, 1997 Accepted April 7, 1997X IE960577I

X Abstract published in Advance ACS Abstracts, June 1, 1997.