Mass diffusion with catalytic surface reaction

Steady-state mass diffusion with catalytic surface reaction... 

Diffusion factor y in cylindrical catalyst mass. The case of cylindrical channel filled with catalytic surfaces having one entrance for the reactant leads for a first-order reaction to... 

In the case that the chemical reaction proceeds much faster than the diffusion of educts to the surface and into the pore system a starvation with regard to the mass transport of the educt is the result, diffusion through the surface layer and the pore system then become the rate limiting steps for the catalytic conversion. They generally lead to a different result in the activity compared to the catalytic materials measured under non-diffusion-limited conditions. Before solutions for overcoming this phenomenon are presented, two more additional terms shall be introduced the Thiele modulus and the effectiveness factor. 

There are a number of examples of tube waU reactors, the most important being the automotive catalytic converter (ACC), which was described in the previous section. These reactors are made by coating an extruded ceramic monolith with noble metals supported on a thin wash coat of y-alumina. This reactor is used to oxidize hydrocarbons and CO to CO2 and H2O and also reduce NO to N2. The rates of these reactions are very fast after warmup, and the effectiveness factor within the porous wash coat is therefore very smaU. The reactions are also eternal mass transfer limited within the monohth after warmup. We wUl consider three limiting cases of this reactor, surface reaction limiting, external mass transfer limiting, and wash coat diffusion limiting. In each case we wiU assume a first-order irreversible reaction. 

We have used CO oxidation on Pt to illustrate the evolution of models applied to interpret critical effects in catalytic oxidation reactions. All the above models use concepts concerning the complex detailed mechanism. But, as has been shown previously, critical. effects in oxidation reactions were studied as early as the 1930s. For their interpretation primary attention is paid to the interaction of kinetic dependences with the heat-and-mass transfer law [146], It is likely that in these cases there is still more variety in dynamic behaviour than when we deal with purely kinetic factors. A theory for the non-isothermal continuous stirred tank reactor for first-order reactions was suggested in refs. 152-155. The dynamics of CO oxidation in non-isothermal, in particular adiabatic, reactors has been studied [77-80, 155]. A sufficiently complex dynamic behaviour is also observed in isothermal reactors for CO oxidation by taking into account the diffusion both in pores [71, 147-149] and on the surfaces of catalyst [201, 202]. The simplest model accounting for the combination of kinetic and transport processes is an isothermal continuously stirred tank reactor (CSTR). It was Matsuura and Kato [157] who first showed that if the kinetic curve has a maximum peak (this curve is also obtained for CO oxidation [158]), then the isothermal CSTR can have several steady states (see also ref. 203). Recently several authors [3, 76, 118, 156, 159, 160] have applied CSTR models corresponding to the detailed mechanism of catalytic reactions. 

The most efficacious catalysts to date have been the noble metals, carbons, and some insoluble oxides and salts. As was emphasized in Sect. 1.8, tests should always be carried out to confirm that heterogeneous catalysis is the true reason for any observed rate increase. One of these tests requires the catalytic rate to rise proportionately with the mass or area of the catalyst. While most reaction systems have satisfied this criterion, the rates of several carbon-catalysed reactions in the literature have been reported as increasing either much more or much less than expected when larger amounts of the solid were added. Pore diffusion could account for only some of these results. Since carbons are cheap catalysts with large surface areas, their aberrant behaviour in this respect would be worth serious investigation. 

The observed rate will appear to be first-order with respect to the bulk reactant concentration, regardless of the intrinsic rate expression applicable to the surface reaction. This is a clear example of how external diffusion can mask the intrinsic kinetics of a catalytic reaction. In a catalytic reactor operating under mass transfer limitations, the conversion at the reactor outlet can be calculated by incorporating Equation (6.2.20) into the appropriate reactor model. 

In many industrial reactions, the overall rate of reaction is limited by the rate of mass transfer of reactants and products between the bulk fluid and the catalytic surface. In the rate laws and cztalytic reaction steps (i.e., dilfusion, adsorption, surface reaction, desorption, and diffusion) presented in Chapter 10, we neglected the effects of mass transfer on the overall rate of reaction. In this chapter and the next we discuss the effects of diffusion (mass transfer) resistance on the overall reaction rate in processes that include both chemical reaction and mass transfer. The two types of diffusion resistance on which we focus attention are (1) external resistance diffusion of the reactants or products between the bulk fluid and the external smface of the catalyst, and (2) internal resistance diffusion of the reactants or products from the external pellet sm-face (pore mouth) to the interior of the pellet. In this chapter we focus on external resistance and in Chapter 12 we describe models for internal diffusional resistance with chemical reaction. After a brief presentation of the fundamentals of diffusion, including Pick s first law, we discuss representative correlations of mass transfer rates in terms of mass transfer coefficients for catalyst beds in which the external resistance is limiting. Qualitative observations will bd made about the effects of fluid flow rate, pellet size, and pressure drop on reactor performance. 

In a heterogeneous reaction sequence, mass transfer of reactants first takes place from the bulk fluid to the external surface of the pellet. The reactants then diffuse from the external surface into and through the pores within the pellet, with reaction taking place only on the catalytic surface of the pores. A schematic representation of this two-step diffusion process is shown in Figures 10-3 and 12-1. 

With this introduction, we are ready to treat individually the steps involved in catalytic reactions. In this chapter only the steps of adsorption, surface reaction, and desorption will be considered [i.e., it is assumed that the diffusion steps (1, 2. 6, and 7) arc very fast, such that the overall reaction rate is not affected by mass transfer in any fashion]. Further treatment of the effects involving diffusion limitations is provided in Chapters II and 12. 

This is a mathematical expression for the steady-state mass balance of component i at the boundary of the control volume (i.e., the catalytic surface) which states that the net rate of mass transfer away from the catalytic surface via diffusion (i.e., in the direction of n) is balanced by the net rate of production of component i due to multiple heterogeneous surface-catalyzed chemical reactions. The kinetic rate laws are typically written in terms of Hougen-Watson models based on Langmuir-Hinshelwood mechanisms. Hence, iR ,Hw is the Hougen-Watson rate law for the jth chemical reaction on the catalytic surface. Examples of Hougen-Watson models are discussed in Chapter 14. Both rate processes in the boundary conditions represent surface-related phenomena with units of moles per area per time. The dimensional scaling factor for diffusion in the boundary conditions is... 

Unlike porous pellets, it is mathematically feasible to account for chemical reaction on the well-defined catalytic surfaces that bound the flow regime in regular polygon duct reactors. A qualitative description of the boundary conditions is based on a steady-state mass balance over a differential surface element. Since convective transport vanishes on the stationary catalytic surface, the following contributions from diffusion and chemical reaction are equated, with units of moI/(areatime) ... 

A to products by considering mass transfer across the external surface of the catalyst. In the presence of multiple chemical reactions, where each iRy depends only on Ca, stoichiometry is not required. Furthermore, the thermal energy balance is not required when = 0 for each chemical reaction. In the presence of multiple chemical reactions where thermal energy effects must be considered becanse each AH j is not insignificant, methodologies beyond those discussed in this chapter must be employed to generate temperature and molar density profiles within catalytic pellets (see Aris, 1975, Chap. 5). In the absence of any complications associated with 0, one manipulates the steady-state mass transfer equation for reactant A with pseudo-homogeneous one-dimensional diffusion and multiple chemical reactions under isothermal conditions (see equation 27-14) ... 

The immobilized-catalysts are confined to a region in space defined by the dimensions of the polymer particle. Reactant(s) must diffuse ftom the external surface to the catalytic sites within the particle before any chemical reaction can occur. This sequential process, mass transfer with reaction, has been treated extensively for catalytic reactions in porous solids (13,14,15). A limited number of studies have shown that the mathematical formalism which is applied to heterogeneously-catalyzed reactions can be used to interpret mass transfer with reaction in immobilized catalysts which employ polymers as supports (11,16,17). 

The latter is a well-known quantity in the reaction-diffusion analysis in catalytic media (see Section 8.2.3) and can be written as the ratio between the average reaction rate over the washcoat cross-sectional area at a given axial position and its value at the surface. The former compares the driving force for mass transfer toward the coating, with the total potential for concentration decay (due to mass transfer and surface reaction). For a first-order reaction, 0 reduces to the Carberry number (see Chapter 3), and >/ is a concentration ratio between the averaged value inside the washcoat and the one at the surface. 

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