Porous particles reactions

Begin by considering a catalyst whose active surface is all on the exterior of non-porous particles. Reaction therefore takes place only on surfaces exposed in the interstices of the packing. What volume should we use for calculating the pertinent time for the measuring the rate of the reaction Neither the volume of the interstices nor that of the solid packing correctly represents the active volume in the reactor. It is the area of the active surface exposed to the reactants that is the best representation of this volume. We are forced to consider a very different measure of space time ... 

The solid may be porous or non-porous. In the first case, the reaction takes place practically only at the internal surface the contribution of the external surface to the overall surface area is mostly negligible as the internal surface area is typically an order of magnitude larger for solid catalysts (up to several 100 m g ), and even for particles of 10 p,m the external surface area is only about 1 m g (Figure 4.5.1). For non-porous particles, reaction can only take place at the shrinking external surface or at the surface of a reactive core if a solid product is formed. However, in most industrially relevant cases, solid reactants are porous or at least a porous structure is formed during the initial phase of the reaction. 

Pore diffusion With porous particles, pore diffusion is likely to limit reaction rates at the internal surface. 

Reaction, diffusion, and catalyst deactivation in a porous catalyst layer are considered. A general model for mass transfer and reaction in a porous particle with an arbitrary geometry can be written as follows ... 

Figure 8.10(b) shows a plot of if/ = cAlcAs as a function of z, the fractional distance into the particle, with the Thiele modulus cj) as parameter. For = 0, characteristic of a very porous particle, the concentration of A remains the same throughout the particle. For (f> = 0.5, characteristic of a relatively porous particle with almost negligible pore-diffusion resistance, cA decreases slightly as z —> 1. At the other extreme, for = 10, characteristic of relatively strong pore-diffusion resistance, cA drops rapidly as z increases, indicating that reaction takes place mostly in the outer part (on the side of the permeable face) of the particle, and the inner part is relatively ineffective. 

The rate is independent of particle size. This is an indication of neghgible pore-diffusion resistance, as might be expected for either very porous particles or sufficiently small particles such that the diffusional path-length is very small. In either case, i -> 1, and ( rA)obs = ( rA)inl for the surface reaction. 

The activity calculated from (7) comprises both film and pore diffusion resistance, but also the positive effect of increased temperature of the catalyst particle due to the exothermic reaction. From the observed reaction rates and mass- and heat transfer coefficients, it is found that the effect of external transport restrictions on the reaction rate is less than 5% in both laboratory and industrial plants. Thus, Table 2 shows that smaller catalyst particles are more active due to less diffusion restriction in the porous particle. For the dilute S02 gas, this effect can be analyzed by an approximate model assuming 1st order reversible and isothermal reaction. In this case, the surface effectiveness factor is calculated from... 

The extent to which a given reactant, such as oxygen, is able to utilize this additional surface area depends on the difficulty in diffusing through the particle to reach the pore surfaces and on the overall balance between diffusion control of the burning rate and kinetic control. To broadly characterize these competing effects, three zones of combustion of porous particles have been identified, as shown in Fig. 9.21. In Zone I the combustion rate is fully controlled by the surface reaction rate (kinetically controlled), because the diffusion... 

Surface area of the reactants For a high-energy reaction to rapidly proceed, the oxidizer must be in intimate contact with the fuel. Decreasing particle size will increase this contact, as will increasing the available surface area of the particles. A smooth sphere will possess the minimum surface area for a given mass of material. An uneven, porous particle will exhibit much more free surface, and consequently will be a much more reactive material. Particle... 

It should be noted that when referring to the reaction rate per unit surface of a porous particle or to the corresponding rate coefficient, it should be clarified whether the rate or the rate coefficient is based on die external or the total surface area. Then, for example, in a sluny reactor where die reaction rate is expressed per unit volume of liquid, the rate could be... 

The oxidation of a VOC to carbon dioxide is conducted over a catalytic bed consisting of porous particles with a diameter of 4 mm. The catalyst particles contain Pt as the active component, which is distributed evenly within each particle. It is suggested to use the same particles but with the Pt placed at the external surface of each particle and at a depth up to 1/10 of its diameter so that the activity of the catalyst is increased. If the reaction is fust order with respect to the VOC, and on the grounds that the active surface of Pt remains the same in the two cases ... 

Current research efforts are concentrating on computationally efficient implementations of the energy equation within the MicroFlowS framework to allow realistic simulations of soot particle reaction in the porous structures. The next section shows a parallel line of development that started in Konstandopoulos and Kostoglou (2004), which tries to extend continuum models of soot oxidation to account for microstructural effects. 

The viscosity of most gases at atmospheric pressure is of the order of 10"7 Ns/m2, so for pores of about 1 /mi radius DP is approximately 10"5 m2/s. Molecular diffusion coefficients are of similar magnitude so that in small pores forced flow will compete with molecular diffusion. For fast reactions accompanied by an increase in the number of moles an excess pressure is developed in the interior recesses of the porous particle which results in the forced flow of excess product and reactant molecules to the particle exterior. Conversely, for pores greater than about 100/im radius, DP is as high as 10"3 m2/s and the coefficient of diffusion which will determine the rate of intraparticle transport will be the coefficient of molecular diffusion. 

Since is proportional to VF we may conclude that for competing simultaneous reactions strongly influenced by diffusion effects (where is large and tanh — 1) the selectivity depends on Vs (where S = kjk2), the square root of the ratio of the respective rate constants. The corollary is that, for such reactions, maximum selectivity is displayed by small sized particles and, in the limit, if the particle size is sufficiently small (small so that tanh - )the selectivity is the same as for a non-porous particle, i.e. S itself. 

In general, CTL intensity depends on the catalytic reaction rate, so that a catalyst with a large surface-to-volume ratio is preferable. In this sense, the catalyst powder or a sintered layer of porous particles is used as the sensor material. As the CTL catalyst should be heated to a working temperature, the catalyst powder is pressed in a ceramic pot with a heating wire, or the sintered catalyst layer is formed on a substrate with an electric heater. 

The catalysts used for cracking before the 1960s were amorphous [Si-Al] catalysts. The replacement of these catalysts by faujasite zeolites was a big step forward in the oil refining industry, which led to an increase in the production of gasoline [20], The acid catalyst, currently used in FCC units, is generally composed of 5-40 wt % of 1-5 pm crystals of the H-Y zeolite included in a porous particle composed of an active matrix, which in turn is composed of amorphous alumina, silica, or [Si-Al] and a binder. The porous particle allows the diffusion of the reactants and products of the cracking reaction to and from the micropores of the zeolite [10]. 

Figure 6. Concentration profiles for mass transfer into a slurry with catalytic particles, with no enhancement at the gas-liquid interface (above) mass transfer and reaction at the interface (below) mass transfer and reaction in the porous particles.

For a first-order reaction in porous particles, R4 should be replaced by... 

Although inside the porous particle, mass transport and reaction are in parallel, the overall process can still be described by resistances in series. From these resistances, R2 might be influenced by the presence of the catalyst particles in two ways ... 

Because coal chars are highly microporous, most of the gasification reactions take place inside the char particles. Therefore, diffusion of gas into, and products out of, porous particles is required. The overall diffusion process can be described by the following steps (1) diffusion of the reactant from the bulk gas to the solid surface (film diffusion) (2) diffusion of the reactant from the particle s surface to its interior (internal diffusion) (3) diffusion of the product from the interior to the particle s surface (internal diffusion) and (4) diffusion of the product from the surface to the bulk gas (film diffusion). 

The intraparticle transport effects, both isothermal and nonisothermal, have been analyzed for a multitude of kinetic rate equations and particle geometries. It has been shown that the concentration gradients within the porous particle are usually much more serious than the temperature gradients. Hudgins [17] points out that intraparticle heat effects may not always be negligible in hydrogen-rich reaction systems. The classical experimental test to check for internal resistances in a porous particle is to measure the dependence of the reaction rate on the particle size. Intraparticle effects are absent if no dependence exists. In most cases a porous particle can be considered isothermal, but the absence of internal concentration gradients has to be proven experimentally or by calculation (Chapter 6). 

At present two models are available for description of pore-transport of multicomponent gas mixtures the Mean Transport-Pore Model (MTPM)[4,5] and the Dusty Gas Model (DGM)[6,7]. Both models permit combination of multicomponent transport steps with other rate processes, which proceed simultaneously (catalytic reaction, gas-solid reaction, adsorption, etc). These models are based on the modified Maxwell-Stefan constitutive equation for multicomponent diffusion in pores. One of the experimentally performed transport processes, which can be used for evaluation of transport parameters, is diffusion of simple gases through porous particles packed in a chromatographic column. 

In order that a reactant in the main fluid phase may be converted catalytically to a product in the main fluid phase, it is necessary that the reactant be transferred from its position in the fluid to the catalytic interface. be activatedly adsorbed on the surface, and undergo reaction to form the adsorbed product. The product must then be desorbed and transferred from the interface to a position in the fluid phase. The rate at which each of these steps occurs influences the distribution of concentrations in the system and plays a part in determining the over-all rate. Because of the differences in the mechanisms involved, it is convenient to classify these steps as follows when dealing with catalysts in the form of porous particles ... 

---