Effectiveness factors catalyst design

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 concentration and temperature Tg will, for example, be conditions of reactant concentration and temperature in the bulk gas at some point within a catalytic reactor. Because both c g and Tg will vary with position in a reactor in which there is significant conversion, eqns. (1) and (15) have to be coupled with equations describing the reactor environment (see Sect. 6) for the purpose of commerical reactor design. Because of the nonlinearity of the equations, the problem can only be solved in this form by numerical techniques [5, 6]. However, an approximation may be made which gives an asymptotically exact solution [7] or, alternatively, the exponential function of temperature may be expanded to give equations which can be solved analytically [8, 9]. A convenient solution to the problem may be presented in the form of families of curves for the effectiveness factor as a function of the Thiele modulus. Figure 3 shows these curves for the case of a first-order irreversible reaction occurring in spherical catalyst particles. Two additional independent dimensionless paramters are introduced into the problem and these are defined as... 

The equations describing the concentration and temperature within the catalyst particles and the reactor are usually non-linear coupled ordinary differential equations and have to be solved numerically. However, it is unusual for experimental data to be of sufficient precision and extent to justify the application of such sophisticated reactor models. Uncertainties in the knowledge of effective thermal conductivities and heat transfer between gas and solid make the calculation of temperature distribution in the catalyst bed susceptible to inaccuracies, particularly in view of the pronounced effect of temperature on reaction rate. A useful approach to the preliminary design of a non-isothermal fixed bed catalytic reactor is to assume that all the resistance to heat transfer is in a thin layer of gas near the tube wall. This is a fair approximation because radial temperature profiles in packed beds are parabolic with most of the resistance to heat transfer near the tube wall. With this assumption, a one-dimensional model, which becomes quite accurate for small diameter tubes, is satisfactory for the preliminary design of reactors. Provided the ratio of the catlayst particle radius to tube length is small, dispersion of mass in the longitudinal direction may also be neglected. Finally, if heat transfer between solid cmd gas phases is accounted for implicitly by the catalyst effectiveness factor, the mass and heat conservation equations for the reactor reduce to [eqn. (62)]... 

Recall that for a heterogeneous catalytic reactor we had to consider the microscopic concentration profiles around and within a catalyst particle and then elirninate them in terms of the macroscopic position variable z in the reactor design ecpaations (mass transfer limits and effectiveness factors). 

To sum up, special attention should be given to the effect of temperature on the process during the design and control of commercial catalytic reactors. Moreover, the same size of catalyst particles should be used at any scale so that the catalyst effectiveness factor also remains the same. The available catalytic surface per reactor volume and the space velocity (when the rate is not controlled by mass transfer phenomena) should also be left unchanged at any scale. 

In this section we have presented and solved the BVPs associated with the diffusion and reaction that take place in the pores of a porous catalyst pellet. The results were expressed graphically in terms of the effectiveness factor rj versus the Thiele modulus d> for two cases One with negligible external mass and heat transfer resistances, i.e., when Sh and Nu —> oo, and another with finite Sh and Nu values. This problem is very important in the design of fixed-bed catalytic reactors. The sample results presented here have shown that for exothermal reactions multiple steady states may occur over a range of Thiele moduli d>. Efficient numerical techniques have been presented as MATLAB programs that solve singular two-point boundary value problems. 

Derive the material and energy-balance design equations, including the equations of the catalyst pellets to calculate the effectiveness factor rj. 

For the particle sizes used in industrial reactors (> 1.5 mm), intraparticle transport of the reactants and ammonia to and from the active inner catalyst surface may be slower than the intrinsic reaction rate and therefore cannot be neglected. The overall reaction can in this way be considerably limited by ammonia diffusion through the pores within the catalysts [211]. The ratio of the actual reaction rate to the intrinsic reaction rate (absence of mass transport restriction) has been termed as pore effectiveness factor E. This is often used as a correction factor for the rate equation constants in the engineering design of ammonia converters. 

Since most practical problems do not have analytical expressions for the effectiveness factor, the use of Equations (10.2.6) and (10.2.7) are more generally applicable. If Equations (10.2.6) and (10.2.7) are to be solved numerous times (e.g., when performing a reactor design/optimization), then an alternative approach may be applicable. The catalyst particle problem can first be solved for a variety of Cab, Tg, (p, Bi , Bi, that may be expected to be realized in the reactor design. Second, the values can be fit to a function with Cab, Bi ... 

As seen from Fig. 13, which gives a model unit of the laboratory cell reactor, this cell contains specially designed nets, to provide turbulence of the liquid flow. From the experimental result it was shown that the effectiveness factor was very high (up to 0.84) in experiments with plates with a very thin catalytic layer located close to the liquid side. In experiments with plates with a thick catalytic layer located in the middle of the plate, the effectiveness factor was very low (down to 0.02), and only a small part of the catalyst layer was utilized, since p-nitrobenzoic acid vanished in the plate after only 10% of the thickness of the catalytic layer had been passed in this particular run. 

Catalyst deactivation in large-pore slab catalysts, where intrapaiticle convection, diffusion and first order reaction are the competing processes, is analyzed by uniform and shell-progressive models. Analytical solutions arc provid as well as plots of effectiveness factors as a function of model parameters as a basis for steady-state reactor design. 

Advanced design Control of the catalyst layer thickness and composition provide the means to optimize catalyst utilization and performance issues. Taking together all factors listed above, only 10-20% of the catalyst is effectively... 

As illustrated in Scheme 12, the metallocene-mediated copolymerization of a-olefin and reactive comonomer forms a copolymer containing several pendent reactive groups, and then serves as an intermediate for the transformation to functional polyolefins by various reaction mechanisms. In addition to the metallocene catalyst for effective copolymerization, the key factor in this approach is the design of a comonomer containing a reactive group that can simultaneously fulfill the following requirements. First, the reactive group must be stable to metallocene catalysts and soluble in hydrocarbon polymerization media. 

CHAPTER 36, FIGURE 16 Proteinase inactivation by SERPINS. Proteinase inactivation occurs by reaction between proteinase and inhibitor, e.g., antithrombin. The proteinase is a stoichiometric reactant in this instance but is not a catalyst. This reaction results in the formation of a covalent bond between the reactive site residue of the inhibitor (Arg in antithrombin) and the active site residue (Ser in the proteinase). This complex formation prevents the proteinase from hydrolyzing any other peptide bond. Proteinases, thrombin, factor Xa, factor IXa, and, less effectively, factor Vila and factor XIa are all inactivated by the plasma protein inhibitor antithrombin (previously designated antithrombin III). The product AT is the cleaved form of antithrombin. It is formed in both the absence and presence of heparin, but more so in the presence. The proteinase is indicated is indicated by green, the inhibitor by red, and the inactivated proteinase by gray. Stripes on the inhibitor represent the helices (Figure 36-7). 

The objective of Chaps. 10 and 11 is to combine intrinsic rate equations with intrapellet and fluid-to-pellet transport rates in order to obtain global rate equations useful for design. It is at this point that models of porous catalyst pellets and effectiveness factors are introduced. Slurry reactors offer an excellent example of the interrelation between chemical and physical processes, and such systems are used to illustrate the formulation of global rates of reaction. 

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