Concentration difference, bulk fluid-catalyst surface

No matter how active a catalyst particle is, it can be effective only if the reactants can reach the catalytic surface. The transfer of reactant from the bulk fluid to the outer surface of the catalyst particle requires a driving force, the concentration difference. Whether this difference in concentration between bulk fluid and particle surface is significant or negligible depends on the velocity pattern in the fluid near the surface, on the physical properties of the fluid, and on the intrinsic rate of the chemical reaction at the catalyst that is, it depends on the mass-transfer coefficient between fluid and surface and the rate constant for the catalytic reaction In every case the concentration of reactant is less at the surface than in the bulk fluid. Hence the observed rate, the global rate, is less than that corresponding to the concentration of reactants in the bulk fluid. 

Concentration or Partial Pressure and Temperature Differences Between Bulk Fluid and Surface of a Catalyst Particle ... 

CONCENTRATION OR PARTIAL PRESSURE AND TEMPERATURE DIFFERENCES 163 BETWEEN BULK FLUID AND SURFACE OF A CATALYST PARTICLE... 

When a solid acts as a catalyst for a reaction, reactant molecules are converted into product molecules at the fluid-solid interface. To use the catalyst efficiently, we must ensure that fresh reactant molecules are supplied and product molecules removed continuously. Otherwise, chemical equilibrium would be established in the fluid adjacent to the surface, and the desired reaction would proceed no further. Ordinarily, supply and removal of the species in question depend on two physical rate processes in series. These processes involve mass transfer between the bulk fluid and the external surface of the catalyst and transport from the external surface to the internal surfaces of the solid. The concept of effectiveness factors developed in Section 12.3 permits one to average the reaction rate over the pore structure to obtain an expression for the rate in terms of the reactant concentrations and temperatures prevailing at the exterior surface of the catalyst. In some instances, the external surface concentrations do not differ appreciably from those prevailing in the bulk fluid. In other cases, a significant concentration difference arises as a consequence of physical limitations on the rate at which reactant molecules can be transported from the bulk fluid to the exterior surface of the catalyst particle. Here, we discuss... 

In Illustration 12.5, we considered the problem of estimating the concentration differences that exist between the bulk fluid and a catalyst used for the oxidation of sulfur dioxide. If the reported temperature is that of the bulk fluid, determine the external surface temperature corresponding to the conditions cited. Additional useful data are ... 

At steady state, the rates of each of the individual steps will be the same, and this equality is used to develop an expression for the global reaction rate in terms of bulk-fluid properties. Actually, we have already employed a relation of this sort in the development of equation 12.4.28 where we examined the influence of external mass transfer limitations on observed reaction rates. Generally, we must worry not only about concentration differences between the bulk fluid and the external surface of the catalyst, but also about temperature differences between these points and intraparticle gradients in temperature and composition. 

Since our calculations indicate that intraparticle mass transfer limitations are significant, we must now consider the possibility that temperature and concentration differences will exist between the bulk fluid and the external surface of the catalyst. Appropriate mass and heat transfer coefficients must therefore be determined. 

The Schmidt and Prandtl numbers must be evaluated in order to be able to determine concentration and temperature differences between the bulk fluid and the external surface of the catalyst. The Schmidt number for naphthalene in the mixture may be evaluated using the ordinary molecular diffusivity employed earlier, the viscosity of the mixture, and the fluid density. 

Now let us consider the possibility that there will be a significant temperature difference between the bulk fluid and the external surface of the catalyst pellet. Equation 12.5.6 indicates that the temperature and concentration gradients external to the particle are related as follows ... 

Under adiabatic conditions with external diffusion, temperature and concentration differences will develop between the bulk of the fluid and the surface of the catalyst. The rate of reaction is the rate of diffusion, r = kga(Cg-Cs) and the heat balance is... 

When external gradients correspond to substantial differences in concentration or temperature between the bulk of the fluid and the external surface of the catalyst particle, the rate of reaction at the surface is significantly different from that which would prevail if the concentration or temperature at the surface were equal to that in the bulk of the fluid. The catalytic reaction is then said to be influenced by external mass or heat transfer, respectively, and, when this influence is the dominant one, the rate corresponds to a regime of external mass or heat transfer. 

Under some circumstances there will be a resistance to the transport of material from the bulk fluid stream to the exterior surface of a catalyst particle. When such a resistance to mass transfer exists, the concentration CA of a reactant in the bulk fluid will differ from its concentration CAi at the solid-gas interface. Because CAi is usually unknown it is necessary to eliminate it from the rate equation describing the external mass transfer process. Since, in the steady state, the rates of all of the steps in the process are equal, it is possible to obtain an overall rate expression in which CM does not appear explicitly. 

Another classification involves the number of phases in the reaction system. This classification influences the number and importance of mass and energy transfer processes in the design. Consider a stirred mixture of two liquid reactants A and B, and a catalyst consisting of small particles of a solid added to increase the reaction rate. A mass transfer resistance occurs between the bulk liquid and the surface of the catalyst particles. This is because the small particles tend to move with the liquid. Consequently, there is a layer of stagnant fluid that surrounds each particle. This results in reactants A and B transferring through this layer by diffusion in order to reach the catalyst surface. The diffusion resistance gives a difference in concentration between... 

For positive reaction orders the existence of significant concentration differences between the bulk of the fluid phase and the external surface of the catalyst pellet leads to lower reaction rates. This can be expressed by the external effectiveness factor, r e ... 

In the case of a solid catalyst operating in a liquid phase reaction system the problems of diffusion and concentration gradients can be particularly severe. Substrate diffusion can be further broken down into two steps, external diffusion and internal diffusion. The former is controlled by the flow of substrate molecules through the layer of molecules surrounding catalyst particles and is proportional to the concentration gradient in the bulk liquid, i.e. the difference in the concentrations of the substrate in the bulk medium and at the catalyst surface. The thickness of the external layer in a liquid medium is dependent on the flowing fluid and on the agitation within the reaction system typically it is 0.1-0.01 mm thick. Internal diffusion of substrate molecules is a complex process determined not only by the resistance to flow due to the... 

To this point we have dealt only with transport effects within the porous catalyst matrix (intraphase), and the mathematics have been worked out for boundary conditions that specify concentration and temperature at the catalyst surface. In actual fact, external boundaries often exist that offer resistance to heat and mass transport, as shown in Figure 7.1, and the surface conditions of temperature and concentration may differ substantially from those measured in the bulk fluid. Indeed, if internal gradients of temperature exist, interphase gradients in the boundary layer must also exist because of the relative values of the pertinent thermal conductivities [J.J. Carberry, Ind. Eng. Chem., 55(10), 40 (1966)]. 

When studying the kinetics of heterogeneous reactions or when designing a large catalytic reactor, there are more factors to consider than when dealing with homogeneous reactions. For a solid-catalyzed reaction, the rate depends on the reactant concentrations at the catalyst surface, but these are not the same as the bulk concentrations, because some driving force is needed for mass transfer to the surface. If the catalyst is porous, as is usually the case, there are further differences in the concentration between the fluid at the external surface and the fluid in the catalyst pores. Models must be developed to predict the surface concentrations as functions of the partial pressures or concentration in the gas or liquid, and the rate expression can then be written in terms of the fluid concentrations. 

Diffusion of reactants to the external surface is the first step in a solid-catalyzed reaction, and this is followed by simultaneous diffusion and reaction in the pores, as discussed in Chapter 4. In developing the solutions for pore diffusion plus reaction, the surface concentrations of reactants and products are assumed to be known, and in many cases these concentrations are essentially the same as in the bulk fluid. However, for fast reactions, the concentration driving force for external mass transfer may become an appreciable fraction of the bulk concentration, and both external and internal diffusion must be allowed for. There may also be temperature differences to consider these will be discussed later. Typical concentration profiles near and in a catalyst particle are depicted in Figure 5.6. As a simplification, a linear concentration gradient is shown in the boundary layer, though the actual concentration profile is generally curved. 

The above discussion indicates an approach that may be used in deriving an expression for the reaction rate in terms of the physical and chemical parameters of the system. However, for most practical catalyst systems, it will not be possible to arrive at closed-form expressions for the reaction rate per unit mass of catalyst. Consequently, this approach is of extremely limited utility for reactor design purposes. The most common approach to the analysis of external mass transfer limitations in heterogeneous catalytic reactors is usually couched in terms of calculations of the difference in reactant concentrations between the bulk fluid and the exterior surface. Illustration 12.5 indicates the manner in which one can calculate such differences. 

Heterogeneous catalytic reactions involve by their nature a combination of reaction and transport processes, as the reactant must be first transferred from the bulk of the fluid phase to the catalyst surface. In Figure 11.2, the combined reaction and transport processes are shown schematically for a fast exothermic chemical reaction within a porous catalyst. If the rate of the intrinsic reaction is comparable to the rate of transport processes, significant concentration profiles of the reactants and products will develop. In addition, the temperature of the catalyst particle will be different from that of the bulk fluid. With increasing temperature, the influence of transport phenomena becomes more important and finally limits the overall reaction rate. This has detrimental influences on product yield and selectivity, and may lead to high overtemperatures of the catalyst and its fast deactivation [6]. The influence of transport phenomena is commonly characterized by an effectiveness factor as defined in Eq. (11.2). 

Consider the hydrogenation of benzene, which is exothermic with a heat of reaction 50 kcal/mol. For a catalyst pellet containing 58% Ni on Kieselguhr (Harshaw A1-0104T), the effective thermal conductivity and diffusivity are 3.6 lO cal/(cm s K) and 0.052 cm /s, respectively. The fluid bulk concentration of benzene is 5.655 x 10 mol/cm, and the fluid bulk temperature is 412 K. The characteristic length of the pellet is 0.296 cm. The observed rate for the reaction is 2.258 10 mol/(gcats) and the density of the catalyst is 1.88 g/cm. The modified Sherwood and Nusselt numbers are 215 and 10.8, respectively. Estimate the internal and external temperature differences. (Note The experimental values of the internal and external temperatures are 35 and 40 K, respectively. The difference between the surface and bulk fluid temperature is 6-7 K, Froment and Bischoff, 1979)... 

Equation 3.39 expresses an averaged reaction rate evaluated with the actual concentration and temperature profiles that are observed inside the pellet, in the presence of reaction superposed with the eventual presence of significant limitations from diffusion through the catalyst pores. If transport to the catalyst surface is also limited, conditions on the interface may differ significantly from those in the bulk fluid. In this case, it maybe more useful to refer the observed average rate of reactant consumption to the conditions in the interparticular bulk fluid, defining a global effectiveness factor fj, which is related to (3.39) by... 

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