Heat catalyst effectiveness factors

At this point it is instructive to consider the possible presence of intraparticle and external mass and heat transfer limitations using the methods developed in Chapter 12. In order to evaluate the catalyst effectiveness factor we first need to know the combined diffusivity for use... 

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)]... 

Heterogeneous catalytic reactors are the most important single class of reactors utilized by the chemical industry. Whether their importance is measured by the wholesale value of the goods produced, the processing capacity, or the overall investment in the reactors and associated peripheral equipment, there is no doubt as to the prime economic role that reactors of this type play in modem industry. The focus of this chapter is the design of heterogeneous catalytic reactors. Particular emphasis is placed on the concept of catalyst effectiveness factors and the implications of heat and mass transfer processes for fixed bed reactor design. 

The first step in heterogeneous catalytic processes is the transfer of the reactant from the bulk phase to the external surface of the catalyst pellet. If a nonporous catalyst is used, only external mass and heat transfer can influence the effective rate of reaction. The same situation will occur for very fast reactions, where the reactants are completely exhausted at the external catalyst surface. As no internal mass and heat transfer resistances are considered, the overall catalyst effectiveness factor corresponds to the external effectiveness factor,... 

Fj is the component molar flowrate i = H2O, CO, COj, H2, Inert) rj is the catalyst effectiveness factor e is the catalyst bed porosity (assumed to be equal to 0.5) is the shell tube radius r,i is the membrane tube radius (fco) is the rate of WGS reaction is the reaction temperature (K) n is the number of chemical species cpt is specific heat [J/mol Kj AHreaz is AH of reaction at temperature T [J/molj and U2 is a global heat transport coefficient from catalytic zone to permeation one [J/m -s-K]. 

Tinkler JD, Pigford RL. The influence of heat generation on the catalyst effectiveness factor. Chemical Engineering Science 1961 15 ... 

In indirectly heated reformers operating conditions may vary considerably, but the requirements to the catalyst are similar to those in the tubular reformer. The catalyst activity must be larger for low-temperature adiabatic prereformers, where catalyst effectiveness factors will be outside the strongly diffusion-controlled regime. This implies that a simplified activity expression as in Figure 3.3 is not valid for a prereformer. In an autothermal reformer the requirements to the catalyst includes high temperature stability properties and a good distribution over the catalyst bed of the partly converted gas from the burner. In micro-scale reactors catalyst stability is a major issue. 

The final two-dimensional mathematical model thus consists of one partial parabolic differential mass balance equation (3.12) with boundary and initial conditions in (3.14) for each of the j reactions and one partial parabolic differential heat transfer equation (3.15) with boundary conditions in (3.17), (3.18) and initial conditions in (3.20). Simultaneously the pressure drop ordinary differential equation (3.7) and the differential equations for the temperature and pressure in each of the surrounding channels in (3.22) must be integrated. Catalyst effectiveness factors in the catalyst bed must be available in all axial and radial integration points using the methods in Section 3.4. 

Micro-scale plate-t5q)e reformers and multi-channel reformers are being developed for compact units for small-scale operation [188] [282] [319] [488] — for instance for the use in cars. A better catalyst utilisation (larger catalyst effectiveness factor) can be achieved by catalysing the heat transfer surfaces (catalysed hardware) and by leaving the tubular constraint [166] (refer to Section 1.2.4). Some designs involve a... 

Reactions in porous catalyst pellets are Invariably accompanied by thermal effects associated with the heat of reaction. Particularly In the case of exothermic reactions these may have a marked influence on the solutions, and hence on the effectiveness factor, leading to effectiveness factors greater than unity and, In certain circumstances, multiple steady state solutions with given boundary conditions [78]. These phenomena have attracted a great deal of interest and attention in recent years, and an excellent account of our present state of knowledge has been given by Arls [45]. 

Treatment of thermal conductivity inside the catalyst can be done similarly to that for pore diffusion. The major difference is that while diffusion can occur in the pore volume only, heat can be conducted in both the fluid and solid phases. For strongly exothermic reactions and catalysts with poor heat conductivity, the internal overheating of the catalyst is a possibility. This can result in an effectiveness factor larger than unity. 

Values for the various parameters in these equations can be estimated from published correlations. See Suggestions for Further Reading. It turns out, however, that bubbling fluidized beds do not perform particularly well as chemical reactors. At or near incipient fluidization, the reactor approximates piston flow. The small catalyst particles give effectiveness factors near 1, and the pressure drop—equal to the weight of the catalyst—is moderate. However, the catalyst particles are essentially quiescent so that heat transfer to the vessel walls is poor. At higher flow rates, the bubbles promote mixing in the emulsion phase and enhance heat transfer, but at the cost of increased axial dispersion. 

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]... 

In order for diffusional limitations to be negligible, the effectiveness factor must be close to 1, i.e. nearly complete catalyst utilization, which requires that the Thiele modulus is suffieiently small (< ca. 0.5), see Figure 3.32. Therefore, the surface-over-volume ratio must be as large as possible (particle size as small as possible) from a diffusion (and heat-transfer) point of view. There are many different catalyst shapes that have different SA/V ratios for a given size. 

It is known that high mass velocities are to be employed within the reactor tubes to minimize heat and mass transfer limitations on the catalytic reaction rates. It is also known that the effectiveness factors for the catalysts commonly employed often differ appreciably from unity. 

The activity calculated from (7) comprises both film and pore diffusion resistance, but also the positive effect of increased temperature of the catalyst particle due to the exothermic reaction. From the observed reaction rates and mass- and heat transfer coefficients, it is found that the effect of external transport restrictions on the reaction rate is less than 5% in both laboratory and industrial plants. Thus, Table 2 shows that smaller catalyst particles are more active due to less diffusion restriction in the porous particle. For the dilute S02 gas, this effect can be analyzed by an approximate model assuming 1st order reversible and isothermal reaction. In this case, the surface effectiveness factor is calculated from... 

For a more detailed analysis of measured transport restrictions and reaction kinetics, a more complex reactor simulation tool developed at Haldor Topsoe was used. The model used for sulphuric acid catalyst assumes plug flow and integrates differential mass and heat balances through the reactor length [16], The bulk effectiveness factor for the catalyst pellets is determined by solution of differential equations for catalytic reaction coupled with mass and heat transport through the porous catalyst pellet and with a film model for external transport restrictions. The model was used both for optimization of particle size and development of intrinsic rate expressions. Even more complex models including radial profiles or dynamic terms may also be used when appropriate. 

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