Porous catalyst systems

For gas/porous catalyst systems slow reactions are influenced by alone, in faster reactions intrudes to slow the rate, then and/or enter the picture, unlikely limits the overall rate. In liquid systems the order in which these effects intrude is , , , and rarely and/or . 

Equation (11-13) also reduces to Equation (11-16) for porous catalyst systems in which the pore radii are very small. Diffusion imder these conditions, known as Knudsen diffusion, occurs when the mean free path of the molecule is greater than the diameter of the catalyst pore. Here the reacting molecules eollide more often with pore walls than with each other, and molecules of different speeies do not affect each other. The flux of species A for Knudsen diffusion (where bulk flow is neglected) is... 

A schematic diagram of the unit cell for a vapor-Uquid-porous catalyst system is shown in Fig. 9.9. Each cell is modeled essentially using the NEQ model for heterogeneous systems described above. The bulk fluid phases are assumed to be completely mixed. Mass-transfer resistances are located in films near the vapor-liquid and liquid-solid interfaces, and the Maxwell-Stefan equations are used for calculation of the mass-transfer rates through each film. Thermodynamic equilibrium is assumed only at the vapor-liquid interface. Mass transfer inside the porous catalyst may be described with the dusty fluid model described above. 

To be specific let us have in mind a picture of a porous catalyst pellet as an assembly of powder particles compacted into a rigid structure which is seamed by a system of pores, comprising the spaces between adjacent particles. Such a pore network would be expected to be thoroughly cross-linked on the scale of the powder particles. It is useful to have some quantitative idea of the sizes of various features of the catalyst structur< so let us take the powder particles to be of the order of 50p, in diameter. Then it is unlikely that the macropore effective diameters are much less than 10,000 X, while the mean free path at atmospheric pressure and ambient temperature, even for small molecules such as nitrogen, does not exceed... 

The reaction kinetics approximation is mechanistically correct for systems where the reaction step at pore surfaces or other fluid-solid interfaces is controlling. This may occur in the case of chemisorption on porous catalysts and in affinity adsorbents that involve veiy slow binding steps. In these cases, the mass-transfer parameter k is replaced by a second-order reaction rate constant k. The driving force is written for a constant separation fac tor isotherm (column 4 in Table 16-12). When diffusion steps control the process, it is still possible to describe the system hy its apparent second-order kinetic behavior, since it usually provides a good approximation to a more complex exact form for single transition systems (see Fixed Bed Transitions ). 

Normally when a small change is made in the condition of a reactor, only a comparatively small change in the response occurs. Such a system is uniquely stable. In some cases, a small positive perturbation can result in an abrupt change to one steady state, and a small negative perturbation to a different steady condition. Such multiplicities occur most commonly in variable temperature CSTRs. Also, there are cases where a process occurring in a porous catalyst may have more than one effectiveness at the same Thiele number and thermal balance. Some isothermal systems likewise can have multiplicities, for instance, CSTRs with rate equations that have a maximum, as in Example (d) following. 

A lot of work is currently carried out to extend this idea to fully dispersed two-dimensional (on a YSZ surface) or three-dimensional (in a porous YSZ structure) metal catalysts. The main problems to be overcome is current bypass and internal mass transfer limitations due to the high catalytic activity of such fully dispersed Pt/YSZ catalyst systems. 

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 ratio of the observed reaction rate to the rate in the absence of intraparticle mass and heat transfer resistance is defined as the elFectiveness factor. When the effectiveness factor is ignored, simulation results for catalytic reactors can be inaccurate. Since it is used extensively for simulation of large reaction systems, its fast computation is required to accelerate the simulation time and enhance the simulation accuracy. This problem is to solve the dimensionless equation describing the mass transport of the key component in a porous catalyst[l,2]... 

The reaction kinetics approximation is mechanistically correct for systems where the reaction step at pore surfaces or other fluid-solid interfaces is controlling. This may occur in the case of chemisorption on porous catalysts and in affinity adsorbents that involve very slow binding steps. In these cases, the mass-transfer parameter k is replaced... 

There are three different kinds of octane catalysts in current use. Some are based in part on an active non-zeolite matrix composed of a porous silica/alumina component. Others are based on low cell size (2.425-2.428 nm) ultra stable faujasite (USY), a catalyst composition developed in 1975 (2) for the purpose of octane enhancement. A third catalyst system makes use of a small amount (1-2%) of ZSM-5 as an additive. While the net effect in all cases is an increase in the measured octane number, each of the three catalytic systems have different characteristic effects on the composition and yield of the gasoline. The effects of the ZSM-5 component on cracking is described in other papers of this symposium and will not be discussed here. 

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. 

Gas adsorption is the most commonly used method for characterizing the surface area of catalysts. Both physical adsorption and chemisorption may be used. Furthermore, EM can provide supplementary information. A large surface area is desirable since activity is defined as the rate per unit active surface area ((per metre) ), and this necessitates porous catalysts. Eor an idealized porous system. 

The computer-reconstructed catalyst is represented by a discrete volume phase function in the form of 3D matrix containing information about the phase in each volume element. Another 3D matrix defines the distribution of active catalytic sites. Macroporosity, sizes of supporting articles and the correlation function describing the macropore size distribution are evaluated from the SEM images of porous catalyst (Koci et al., 2006 Kosek et al., 2005). Spatially 3D reaction-diffusion system with low concentrations of reactants and products can be described by mass balances in the form of the following partial differential equations (Koci et al., 2006, 2007a). For gaseous components ... 

The kinetic and thermodynamic selectivity factors are quantities which are functions of the chemistry of the system. When an active catalyst has been selected for a particular reaction (often by a judicious combination of theory and experiment) we ensure that the kinetic and thermodynamic factors are such that they favour the formation of desired product. Many commercial processes, however, employ porous catalysts since this is the best means of increasing the extent of surface at which the reaction occurs. Chemical engineers are therefore interested in the effect which the porous nature of the catalyst has on the selectivity of the chemical process. 

The starting point of a number of theoretical studies of packed catalytic reactors, where an exothermic reaction is carried out, is an analysis of heat and mass transfer in a single porous catalyst since such system is obviously more conductive to reasonable, analytical or numerical treatment. As can be expected the mutual interaction of transport effects and chemical kinetics may give rise to multiple steady states and oscillatory behavior as well. Research on multiplicity in catalysis has been strongly influenced by the classic paper by Weisz and Hicks (5) predicting occurrence of multiple steady states caused by intrapellet heat and mass intrusions alone. The literature abounds with theoretical analysis of various aspects of this phenomenon however, there is a dearth of reported experiments in this area. Later the possiblity of oscillatory activity has been reported (6). 

The significance of the key parameters which govern concentration and temperature distribution in a single porous catalyst may be illustrated most effectively by presentation and manipulation of the differential equations which are supposed to describe the system. 

Rate-determining step. In immobilized (bio)catalyst systems, especially in porous particles, the catalytic step is only one of several rate processes in sequence ... 

Using 324 measuring points taken at temperatures between 35 and 75 °C, hydrogen concentrations between 1.6 10-3 and 11.0 10-3 mol NdnT3 and oxygen concentrations between 1.7 10 3 and 7.3 10 3 mol Ndm-3, a kinetic expression for the reaction was determined on the basis of a Langmuir-Hinshelwood model (Figure 2.30). The Mears criterion was applied to verify that no mass transfer limitation was to be expected for the system from the gas phase to the non-porous catalyst ... 

An important problem in catalysis is to predict diffusion and reaction rates in porous catalysts when the reaction rate can depend on concentration in a non-linear way.6 The heterogeneous system is modeled as a solid material with pores through which the reactants and products diffuse. We assume for diffusion that all the microscopic details of the porous medium are lumped together into the effective diffusion coefficient De for reactant. 

Figure 2 shows a schematic of a porous catalyst slab that is supplied by reactant from the outer surface and in which reaction takes place at the internal catalytic surface. It is known in such systems that, when diffusion of species internally in the structure is slow in comparison to the rate of reaction, a variation in reactant concentration will occur in the catalyst. This variation in concentration changes the rate locally in the electrode. 

The standard k-e model simulates the turbulence in the reactor. For flow within the porous catalyst bed, however, we suppress the turbulence. We enter the appropriate physical properties of the system, and employ standard boundary conditions at the impermeable walls and the reactor outlet. To represent the turbulence of the feed stream at the inlet, we treat it as pipe-flow turbulence. These model equations can then be solved for instance, via the well-known Simple algorithm [3]. To facilitate fast convergence, it is useful to make a reasonable initial guess of the pressure drop across the catalyst bed. 

The region over which this balance is invoked is the heterogeneous porous catalyst pellet which, for the sake of simplicity, is described as a pscudohomoge-ncous substitute system with regular pore structure. This virtual replacement of the heterogeneous catalyst pellet by a fictitious continuous phase allows a convenient representation of the mass and enthalpy conservation laws in the form of differential equations. Moreover, the three-dimensional shape of the catalyst pellet is replaced by assuming a one-dimensional model... 

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