SOLID Catalyst Particle Porosity Effect upon Flameless Combustion Characteristics

The problem of heat and mass transfer of a porous catalyst particle is considered. On the her surface, including the inner surface of the pores, an irreversibly heterogeneous first-order reaction proceeds. It has been analytically shown that in a heated gas mixture, the catalyst's porosity reduces the minimum impurity's concentration of catalytic spontaneous combustion in the mixture and increases the catalyst particle's corresponding diameter. This concentration corresponds to the external kinetic and internal diffusion reaction's modes.


Introduction
Multiple heterogenous chemical oxidation reactions and flameless combustion of combustible gases admixtures occur on porous catalyst particles staying within gas/air mixture flow. Critical conditions of flameless combustion depend on size of the particle specific surface area and on combustible gases concentration. Platinum-group metals and metallic oxides of variable valence act as catalysts. Platinumgroup metals are applied either in the form of threads, or are speckled into carrier's particles. The majority of active areas are located inside pores in oxidation catalyst [1]. Catalytic reaction occurs after the reagent molecules penetrate through the boundary level surrounding catalyst's particles (external diffusion) and afterwards through the particle's pores (internal diffusion). The resulting interaction between thermal conductivity, reagents diffusion, reaction products and chemical reaction plays an important part in catalyst's efficiency. Ingredients transfer inside the catalyst should be taken into account if the pores' diameter exceeds 50 nm. Such solid catalyst particles with large pores are applied, for instance, in oxidation reactions, membrane reactors and in certain biological applications.
Porosity and nanostructure are the most universal peculiarities of heterogenous solid catalysts capable to determine accessibility of particular active areas, reaction mechanism and selectivity of desirable products [2]. However, thermal radiation losses should be taken into account for large catalyst packs, even with comparatively low radiation factor typical for metallic oxidation catalysts (ε = 0.1 -0.2). Problem of diffusion inside porous catalyst particles is dealt with for a rather long time [3][4][5]. Mostly, attention is focused on simultaneous review of convection processes, diffusion processes and reaction flow inside porous catalyst. However, critical conditions of catalytic reaction's steady running and porosity effect upon reaction characteristics are generally neglected.
This work is aimed to establish the catalyst porosity effect (mean specific surface of pores) upon crucial characteristics of high-temperature heat and mass exchange and kinetic parameters of heterogenous catalytic combustion for minor combustion gases'quantities in heated air. Here the attention is also paid to combustible gases external and internal mass transfer to the particle surface and into the depth of chemical reaction penetration into the particle.  Heterogenous catalytic reaction speed constant in this case is represented by a sum of reaction constants on the external surface and inside pores.
Actual catalytic reaction speed constant on the external surface and on pores surface of catalyst's particle increases as the temperature grows subject to Arrhenius equation: with 0 kpre-exponential multiplier, m/sec; Еactivation energy, J/mole, Runiversal gas constant, J/(mole К). Heat conductivity equation for internal reactions and reaction running on the surface of a porous catalyst particle may be represented, as below: with sparticle shape factor (0plate, 1cylinder, 2sphere), Fvspecific pores' area (total pores' surface area value divided by particle's volume), m -1 ; Qfreaction's thermal effect per 1 kg of combustible gas, J/kg; Ninumber of pores with Si surface area; Vccatalyst's volume, , ch p q heat generation power on pores' surface per particle's volumetric unit, W/m 3 . General heat flow in the particle's center takes a zero value: Boundary condition on catalyst surface may be represented, as below, taking into account reaction running on its surface: The problem may be simplified by means of taking into account correlation between heat conductivity factors for gaseous mixture and solid catalyst and between thermal conductivity factors. In case when the catalyst heat conductivity factor exceeds substantially the respective heat conductivity of gaseous mixture the temperature distribution inside the catalyst may be ignored. Thus dependence of temperature on coordinate may be ignored. It enables to average temperature throughout the entire catalyst volume. Thus, non-steady state heat balance equation for porous catalyst may be written in the format, as follows: Internal diffusion problem should be solved to calculate internal reaction rate and combustible substance concentration profile inside the particle: shows, that it exceeds 1. It means that combustible substance distribution inside the catalyst's particle may not be ignored. On the other side, correlation between combustible's internal diffusion factor to the catalyst's thermal conductivity factor exceeds 1. It enables us to review the internal diffusion problem as a quasi-neutral. Combustible gas surface relative mass concentration may be calculated subject to steady rate of chemical reaction and mass transfer rate to the particle's surface: Solution of the above equation may be represented, as follows: gs g k Se Thus, the more is Lewis' criterion, as is indicated in formula (6), the higher is the thermal diffusion contribution into combustible component general mass transfer process, which is the most substantial in catalytic oxidation of hydrogen.

Internal reaction area
Having solved the quasi-stationery problem for internal reaction efficient constant (5) kv the following formulae may be obtained: with rsparticle's external surface radius, m; Dvcombustible gas internal diffusion factor inside the pores, m 2 /seс, Sev -Semyonov value number, indentifying relation between chemical reaction running on the pores' surface to combustible substance mass transfer into the particle's pores; hchemical reaction penetration depth into the particle.
Combustible substance internal diffusion factor may be determined by the particle's porosity and combustible substance diffusion factor for gaseous phase [7]: with particle's porosity (volume of pores ratio to entire particle's volume); tr true density of the particle substance. Now let us review two areas where chemical reaction runs. They are internal kinetic and diffusive.
The internal kinetic zone is observed with comparative low temperatures and minor particle diameters, for which Sev < 0.55. In this case: The second expression taken in brackets may be ignored in comparison with 1. The resulting internal reactive constant increases in linear fashion as the particle diameter increases: With Sev = 1 fault of formula (10) amounts to 6 %, and it may be applied for Sev < 1.5. within up to 15 % accuracy.
Further increase in temperature and particle diameter may lead to chemical reaction kinetics shifting to the internal diffusion zone, where 1 Se v  . For Sev > 5 we have cthSev »1. Thus internal reactive constant in this case does not depend on the particle's diameter: For Sev > 2 and Sev < 5 internal reactive constant may be described approximately with relation showing proportional relationship with the particle's diameter:

Stationery stable and critical states
Here all the stationery states (both stable and critical) are reviewed referring to the catalyst temperature. They are determined by combustible component concentration. In this view, relation is subject to review between combustible substance concentration and catalyst temperature obtained from stationary condition (4): Catalytic combustion temperature and lowtemperature oxidation increase as the oxidant concentration grows Fig. 1). The time-independent relation Yа(T), indicates, that maximum point corresponds to critical condition of gases self-ignition (point i), and minimum point corresponds to critical condition of self-fading (point е).
Abnormal drop in catalyst stationary temperature with increasing ammonium concentration Yа is observable within Yаi < Yа < Yаe interval (unstable critical states corresponding to critical initial catalyst temperature Tbi). With catalyst initial temperature exceeding the value corresponding to stationery line Yа(Tbi), the catalyst temperature grows until it achieves stable catalytic combustion temperature. If initial temperature Tb < Tbi, the catalyst temperature will decrease close to low-temperature oxidation value.
Catalyst porosity reduces critical concentration value Fig. 1. Relations between а) stationery temperature and b) reaction penetration depth into pores and combustible substance concentration (line 1) and ignoring the porosity (line 2): particle diameter d* = 1000 μm at Тg = 420 К, Tw= 293 K, Fv =10 3 m -1 ,  = 0.1.  Fig. 1b). Fading concentration critical value does not practically depend on the catalyst porosity. It is rather difficult to apply formula (8) to analytical search for critical states. Referring to Table 1 approximated relations (10), (11) and (12) may be applied to identify critical states depending on particle specific porosity surface area and surrounding gaseous mixture temperatures. Formula (10) with Sevi < 2 may be reasonably applied to calculate internal reactive constant. Formula (11) is applicable for Sevi > 2. As the gaseous mixture temperature decreases, even by 20 К only, the internal Semyonov value number for critical point decreases triple. Fig. 2 represents critical states for ammonium ignition in air on catalyst particle depending on the particle dimensions with various porosity, as a plurality of points being extremum of function (13).
Taking into note thermal losses for radiation leads to formation of diameter limiting value for gases selfignition zone on catalyst particles surface. Applying porous catalyst, even with small specific pores surface area (e.g., 10 3 m -3 ) leads to substantial decrease of minimum critical value of combustible component concentration, which, being exceeded, provokes catalytic ignition on the catalyst surface. Particle diameter increases with porosity increase.
It should be noted, that critical states for self-ignition correspond to external kinetic area where the chemical reaction runs and to internal diffusion area (for d  > 300 μm, Sev > 2). It enables to apply formula (11) to identify location of minimum point to calculate internal reactive constant.
Thus stationary condition may be described, as follows:   Comparing the obtained formulae with similar in which reaction in pores was not taken into account [8], enables to identify a multiplier defining porosity effect on mixture concentration limit value and catalyst particle diameter:  Fig. 3 illustrates time relation of catalyst temperature T and Semyonov value Se during ammonium catalytic oxidation both taking into account and ignoring particles porosity for catalytic ignition case. Apparently, porous particle naturally reduces time of high-temperature oxidation mode gaining (induction period).

Catalyst porosity effect upon induction period
Total time period may be split into three stages. The first represents inert preheating. Semyonov value is extremely small indicating minor chemical heat emission ratio. The second stage represents particle's chemical heating due to chemical heat emission as chemical reaction runs in kinetic zone. The third stage represents particle heating due to chemical heat emission as the chemical reaction runs in diffusion zone.
Porosity effect is shown in Table 3. Decrease of the first stage with increasing porosity is caused by decrease of the upper limit of this stage. Chemical reaction commences earlier due to porosity than with solid particles.
Decrease of the second stage is caused by substantial role played by internal reaction running in kinetic zone. Duration of the third stage does not depend on the particle's porosity. Combustible component does not reach full depth of a particle with chemical reaction running in external diffusion zone.

Conclusions
Combustible gas oxidation reaction inside porous particle of catalyst leads to decrease in combustible gas minimum concentration, which, once exceeded provokes catalytic ignition on catalyst particle surface. The obtained formula enables to analyze porosity effect on critical value and corresponding particle diameter. Increase in catalyst porosity leads to drop of induction period due to reduction in preheating time and chemical heating time with the reaction running in kinetic zone.   3. Time relations а) platinum particle temperature and b) Semyonov value with ammonium concentration Yа = 6.0% for Tg = 420 K, Tw = 293 K, Tb = 293K, d/Nu = 1000 μm. 1solid particle, 2porous particle Fv = 10 3 m -1 ,  = 0.1.