Porous catalyst, chemical reaction

Whitaker, S, Transient Diffusion, Adsorption and Reaction in Porous Catalysts The Reaction Controlled, Quasi-Steady Catalytic Surface, Chemical Engineering Science 41, 3015, 1986. 

Our objective here is to study quantitatively how these external physical processes affect the rate. Such processes are designated as external to signify that they are completely separated from, and in series with, the chemical reaction on the catalyst surface. For porous catalysts both reaction and heat and mass transfer occur at the same internal location within the catalyst pellet. The quantitative analysis in this case requires simultaneous treatment of the physical and chemical steps. The effect of these internal physical processes will be considered in Chap, 11. It should be noted that such internal effects significantly affect the global rate only for comparatively large catalyst pellets. Hence they may be important only for fixed-bed catalytic reactors or gas-solid noncatalytic reactors (see Chap. 14), where large solid particles are employed. In contrast, external physical processes may be important for all types of fluid-solid heterogeneous reactions. In this chapter we shall consider first the gas-solid fixed-bed reactor, then the fluidized-bed case, and finally the slurry reactor. 

Magyar E. Exact analytical solution of a nonlinear reaction— diffusion model in porous catalysts. Chemical Engineering Journal 2008 143 167-171. 

Petersen EE. Non-isothermal chemical reaction in porous catalysts. Chemical Engineering Science 1962 17 987-995. 

The general theoretical approach is to develop the mathematical equations for simultaneous mass transfer and chemical reaction, as the reactants and products difHise into and out of the porous catalyst. When reaction occurs simultaneously with mass transfer within a porous structure, a concentration gradient is established. Since interior surfaces are thus exposed to lower reactant concentrations than surfaces near the exterior, the overall reaction rate throughout the catalyst particle under isothermal conditions is less than it would be if there were no mass transfer limitations. As will be shown, the apparent activation energy, the catalyst selectivity, and other important observed characteristics of a reaction are also dependent upon the structure of the catalyst and the effective diffusivity of reactants and products (Charles and Thomas, 1963). 

In catalytic three-phase reactors, a gas phase, a liquid phase, and a solid catalyst phase coexist. Some of the reactants and/or products are in the gas phase under the prevailing conditions (temperature and pressure). The gas components diffuse through the gas-liquid interface, dissolve in the liquid, diffuse through the liquid film to the liquid bulk phase, and diffuse through the liquid film around the catalyst particle to the catalyst surface, where the chemical reaction takes place (Figure 6.1). If catalyst particles are porous, a chemical reaction and diffusion take place simultaneously in the catalyst pores. The product molecules are transported in the opposite direction. 

We have shown that the contribution of the through micropores to diffusion in a porous catalyst may be increased substantially in the presence of a chemical reaction, but it must be emphasized that this is not a consequence of any real modification of the laws of diffusion in the micropores. 

Example The equation governing chemical reaction in a porous catalyst in plane geometry of thickness L is... 

An industrial chemical reacdor is a complex device in which heat transfer, mass transfer, diffusion, and friction may occur along with chemical reaction, and it must be safe and controllable. In large vessels, questions of mixing of reactants, flow distribution, residence time distribution, and efficient utilization of the surface of porous catalysts also arise. A particular process can be dominated by one of these factors or by several of them for example, a reactor may on occasion be predominantly a heat exchanger or a mass-transfer device. A successful commercial unit is an economic balance of all these factors. 

Most of the actual reactions involve a three-phase process gas, liquid, and solid catalysts are present. Internal and external mass transfer limitations in porous catalyst layers play a central role in three-phase processes. The governing phenomena are well known since the days of Thiele [43] and Frank-Kamenetskii [44], but transport phenomena coupled to chemical reactions are not frequently used for complex organic systems, but simple - often too simple - tests based on the use of first-order Thiele modulus and Biot number are used. Instead, complete numerical simulations are preferable to reveal the role of mass and heat transfer at the phase boundaries and inside the porous catalyst particles. 

The reactions are still most often carried out in batch and semi-batch reactors, which implies that time-dependent, dynamic models are required to obtain a realistic description of the process. Diffusion and reaction in porous catalyst layers play a central role. The ultimate goal of the modehng based on the principles of chemical reaction engineering is the intensification of the process by maximizing the yields and selectivities of the desired products and optimizing the conditions for mass transfer. 

P., Detailed characterization of various porous alumina based catalyst coatings within microchannels and their testingfor methanol steam reforming, Chem. Eng. Res. Des., special issue on Chemical Reaction Engineering (2003) submitted for publication. 

From the coverage made thus far, it may be of interest to record in one place the different factors which influence the rate of chemical reactions. The rate of chemical reaction depends essentially on four factors. The nature of reactants and products is one. For example, certain physical properties of the reactants and products govern the rate. As a specific example in this context mention may be of oxidation of metals. The volume ratio of metallic oxide to metal may indicate that a given oxidation reaction will be fast when the oxide is porous, or slow when the oxide is nonporous, thus presenting a diffusion barrier to the metal or to oxygen. The other two factors are concentration and temperature effects, which are detailed in Sections. The fourth factor is the presence of catalysts. 

The Effectiveness Factor Analysis in Terms of Effective Diffusivities First-Order Reactions on Spherical Pellets. Useful expressions for catalyst effectiveness factors may also be developed in terms of the concept of effective diffusivities. This approach permits one to write an expression for the mass transfer within the pellet in terms of a form of Fick s first law based on the superficial cross-sectional area of a porous medium. We thereby circumvent the necessity of developing a detailed mathematical model of the pore geometry and size distribution. This subsection is devoted to an analysis of simultaneous mass transfer and chemical reaction in porous catalyst pellets in terms of the effective diffusivity. In order to use the analysis with confidence, the effective diffusivity should be determined experimentally, since it is difficult to obtain accurate estimates of this parameter on an a priori basis. 

The analysis of simultaneous diffusion and chemical reaction in porous catalysts in terms of effective diffusivities is readily extended to geometries other than a sphere. Consider a flat plate of porous catalyst in contact with a reactant on one side, but sealed with an impermeable material along the edges and on the side opposite the reactant. If we assume simple power law kinetics, a reaction in which there is no change in the number of moles on reaction, and an isothermal flat plate, a simple material balance on a differential thickness of the plate leads to the following differential equation... 

The only instances in which external mass transfer processes can influence observed conversion rates are those in which the intrinsic rate of the chemical reaction is so rapid that an appreciable concentration gradient is established between the external surface of the catalyst and the bulk fluid. The rate at which mass transfer to the external catalyst surface takes place is greater than the rate of molecular diffusion for a given concentration or partial pressure driving force, since turbulent mixing or eddy diffusion processes will supplement ordinary molecular diffusion. Consequently, for porous catalysts one... 

Internal diffusion ofreactants. This step depends on the porosity of the catalyst and the size and shape of the catalyst particles, and occurs together with the surface reaction. The active catalyst component is usually highly dispersed within the three-dimensional porous support. The reactant molecules have to diffuse through the network of pores toward the active sites. The activation energy for pore diffusion li2 may represent a substantial share of the activation energy of the chemical reaction itself. 

The porous structure of either a catalyst or a solid reactant may have a considerable influence on the measured reaction rate, especially if a large proportion of the available surface area is only accessible through narrow pores. The problem of chemical reaction within porous solids was first considered quantitatively by Thiele [1] who developed mathematical models describing chemical reaction and intraparticle diffusion. Wheeler [2] later extended Thiele s work and identified model parameters which could be measured experimentally and used to predict reaction rates in... 

In practice, of course, it is rare that the catalytic reactor employed for a particular process operates isothermally. More often than not, heat is generated by exothermic reactions (or absorbed by endothermic reactions) within the reactor. Consequently, it is necessary to consider what effect non-isothermal conditions have on catalytic selectivity. The influence which the simultaneous transfer of heat and mass has on the selectivity of catalytic reactions can be assessed from a mathematical model in which diffusion and chemical reactions of each component within the porous catalyst are represented by differential equations and in which heat released or absorbed by reaction is described by a heat balance equation. The boundary conditions ascribed to the problem depend on whether interparticle heat and mass transfer are considered important. To illustrate how the model is constructed, the case of two concurrent first-order reactions is considered. As pointed out in the last section, if conditions were isothermal, selectivity would not be affected by any change in diffusivity within the catalyst pellet. However, non-isothermal conditions do affect selectivity even when both competing reactions are of the same kinetic order. The conservation equations for each component are described by... 

The first example cited is one in which the solid is totally consumed, whereas the second and third examples involve the formation of a new solid product which might be either a desired product, as in the second case, or a waste product (the gangue) as in the third example. Despite such fundamental differences from catalytic reactions, there are many similarities. In each case, chemisorption, surface chemical reaction emd diffusion through porous media occurs which is in common with heterogeneous chemical reactions. Hence, models representing the dynamics of these non-catalytic gas—solid processess incoporate the same principles of chemical reaction concomitant with diffusion and reaction in heterogeneous catalysts. 

Internal and external mass transfer limitations in porous catalyst layers play a central role in three-phase processes. The governing phenomena are well-known since the days of Thiele (1) and Frank-Kamenetskii (2). Transport phenomena coupled to chemical reactions is not frequently used for complex organic systems. A systematic approach to the problem is presented. 

In general, experimental conditions are such that mass transport of reactants and products is not rate-limiting and the observed rate expressions refer to the true chemical processes in steps (ii)—(iv). The diffusion limitation is likely to be important in liquid phase hydrogenation reactions, particularly when hydrogen has a limited solubility in the liquid phase, and in gas phase hydrogenation where the catalyst is porous and the reaction occurs within the catalyst pores. 

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