Porosity reaction rate expressions

The catalyst activity depends not only on the chemical composition but also on the diffusion properties of the catalyst material and on the size and shape of the catalyst pellets because transport limitations through the gas boundary layer around the pellets and through the porous material reduce the overall reaction rate. The influence of gas film restrictions, which depends on the pellet size and gas velocity, is usually low in sulphuric acid converters. The effective diffusivity in the catalyst depends on the porosity, the pore size distribution, and the tortuosity of the pore system. It may be improved in the design of the carrier by e.g. increasing the porosity or the pore size, but usually such improvements will also lead to a reduction of mechanical strength. The effect of transport restrictions is normally expressed as an effectiveness factor q defined as the ratio between observed reaction rate for a catalyst pellet and the intrinsic reaction rate, i.e. the hypothetical reaction rate if bulk or surface conditions (temperature, pressure, concentrations) prevailed throughout the pellet [11], For particles with the same intrinsic reaction rate and the same pore system, the surface effectiveness factor only depends on an equivalent particle diameter given by... 

The specific surface area depends on both the size and shape and is distinctively high for colloidal-sized species. This is important in the catalytic processes used in many industries for which the rates of reactions occurring at the catalyst surface depend not only on the concentrations of the feed stream reactants, but also on the surface area of catalyst available. Since practical catalysts are frequently supported catalysts, some of the surface area is more important than the rest. Also, given that the supporting phase is usually porous, the size and shapes of the pores may influence the reaction rates as well. The final rate expressions for a catalytic process may contain all of these factors surface area, porosity, and permeability. 

Most important, heterogeneous surface-catalyzed chemical reaction rates are written in pseudo-homogeneous (i.e., volumetric) form and they are included in the mass transfer equation instead of the boundary conditions. Details of the porosity and tortuosity of a catalytic pellet are included in the effective diffusion coefficient used to calculate the intrapellet Damkohler number. The parameters (i.e., internal surface area per unit mass of catalyst) and Papp (i.e., apparent pellet density, which includes the internal void volume), whose product has units of inverse length, allow one to express the kinetic rate laws in pseudo-volumetric form, as required by the mass transfer equation. Hence, the mass balance for homogeneous diffusion and multiple pseudo-volumetric chemical reactions in one catalytic pellet is... 

Liquid holdup, which is expressed as the volume of liquid per unit volume of bed, affects the pressure drop, the catalyst wetting efficiency, and the transition from trickle flow to pulsing flow. It can also have a major effect on the reaction rate and selectivity, as will be explained later. The total holdup, h, consists of static holdup, h, liquid that remains in the bed after flow is stopped, and dynamic holdup, h, which is liquid flowing in thin films over part of the surface. The static holdup includes liquid in the pores of the catalyst and stagnant packets of liquid held in crevices between adjacent particles. With most catalysts, the pores are full of liquid because of capillary action, and the internal holdup is the particle porosity times the volume fraction particles in the bed. Thus the internal holdup is typically (0.3 — 0.5)(0.6), or about 0.2-0.3. The external static holdup is about... 

For process modeling proposes the effective chemical reaction rate has to be expressed as a function of the liquid bulk composition x, the local temperature T, and the catalyst properties such as its number of active sites per catalyst volume c, its porosity e, and its tortuosity t. As discussed in Section 5.4.2, the chemical reaction in the catalyst particles can be influenced by internal and external mass transport processes. To separate the influence of these transport resistances from the intrinsic reaction kinetics, a catalyst effectiveness factor p is introduced by... 

The component balance equation is expressed with mass fractions of the individual species, cOt and the density of the reaction mixture, Pg. In Eq. (5.1) Ft is the total volumetric flow rate, = zjL the dimensionless reactor length. The first term on the right-hand side corresponds to sources by chemical reactions the second term quantifies the local mass fluxes, jj(< ), entering through the membrane. In the FBR model the flux term is omitted. The catalyst density is denoted by p t and e is the averaged porosity of the catalyst bed. Vr is the reactor volume. Mi the molecular mass of species i, the surface area of the membrane wall. The reaction rate rj represents the jth rate of the overall Nr reactions taking place. 

Deactivation model is simpler than the random pore and grain models and it involves only the surface reaction and deactivation rate parameters. An expression was also proposed by Dogu (1981) for the prediction of jS from the known values of surface area and porosity. Lee and Georgakis (1981) proposed a similar deactivation model for the overall reaction rate. In the work of Lee et al (1980) and Zeng et al (1982), deactivation model was applied for desulfurization with limestone in a fluidized bed cumbustor. In these studies, pore dif sion was neglected and the decrease of overall rate with respect to time was expressed in exponential form. 

These results indicated that decrease of porosity with conversion agreed well with the prediction of Eq.2.26. Also it was concluded that, first the smallest pores were clogged and the reactivity of the solid decreased with a decrease in active surface area associated with small pores. In the following analysis, experimental structural information was used for the understanding of the controlling mechanism of Ca0-S02 reaction. The rate expression for the deactivation model... 

Remember that the rate equation must be consistent with the measure of the extent of reaction employed if conversion is used, (—r) must be expressed in terms of x if concentration is used, (—r) is in terms of C. If Fis mass flow rate, (—r) and C must be in mass units, and so on. Also, equation (4-45) is often used as a pseudo-homogeneous model for two-phase PER catalytic reactors. In such cases the rate constant contained in (—r) is usually expressed in terms per volume or weight of catalyst. In the former case, V would refer to catalyst volume and a value for bed porosity would be required to obtain reactor volume. In the latter case, catalyst weight would be... 

The transformation (conversion) and carbonation processes are considered to be diffusion controlled first order reactions with rate constants = 0.48 and = 0.007. One unit of conversion results in a 0.57 fold increase in porosity and a corresponding unit of carbonation, 0.18 times decrease in porosity. Therefore, the change in porosity (AZ ) due to these processes can be expressed as follows ... 

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