Catalysts coupled heat/mass transfer

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. 

This chapter is concerned with the mathematical modeling of coupled chemical reaction and heat and mass transfer processes occurring in porous catalysts. It focuses primarily on steady state catalyst operation which is the preferred industrial practice. Stationary operation may be important for the startup and shutdown of an industrial reactor, or with respect to dynamic process control. However, these effects are not discussed here in great detail because of the limited space available. Instead, the interested reader is referred to the various related monographs and articles available in the literature [6, 31, 46-49]. 

In the general case, eqs 4 and 5 constitute a system of nonlinear coupled second-order partial differential equations. To specify the boundary conditions for this problem, it is necessary to include the external (interphase) heat and mass transfer, as both the concentration and the temperature at the external surface of the catalyst pellet may differ from the corresponding values in the bulk of the surrounding fluid phase. 

THERMAL ENERGY BALANCE IN MULTICOMPONENT MIXTURES AND NONISOTHERMAL EFFECTIVENESS FACTORS VIA COUPLED HEAT AND MASS TRANSFER IN POROUS CATALYSTS... 

TABLE 27-3 Numerical Results for Coupled Heat and Mass Transfer with First-Order Irreversible Exothermic Chemical Reaction in Porous Catalysts with Rectangular Symmetry"... 

Explain very briefly the following trends that are predicted for coupled heat and mass transfer in porous catalysts when the chemical reaction is first-order and exothermic. 

In a common industrial heterogeneous catalytic reactor, the data need to include chemical reactions and physical transfer (heat transfer, mass transfer) in varying degrees. It is very difficult to evaluate whether the performance of catalyst is good or not, or to find the way to improve the performance of catalyst according to these combined data. Therefore, it is necessary to dismiss them from the coupling of chemical reactions and physical transfer via appropriate research tools and conditions, to... 

The use of a heterogeneous catalyst not only iaciUtates its reutihzation but also provides certain heat and mass transfer limitations, which are known to modify selectivity and yield. As MSRs offer high spedfic siulaces, the influence of transfer phenomena on the overall reaction can be reduced partially or completely improving the catalytic performance. Some examples reported in the hterature are the Simiki coupling reactions, the Knoevenagel condensation reaction, enzymatic hydrolysis [10], and the esterification reaction [5]. 

Obviously, the manner in which the gas phase is put in contact with the catalyst surface is important as the reactor type influences the catalytic performance through heat and mass transfer (as well as hydrodynamics in special cases). This is true for any catalyst/reaction couple, but alternative designs exploiting the redox mechanism have been proposed in the case of selective oxidation reactions. Redox decoupling... 

A semi-batch reactor is more difficult to analyze mathematically because at least one of the reactant or product species enters or leaves the system boundaries, thus specific applications should be modeled [1,5]. However, the most typical application for a semi-batch reactor is the presence of one reactant initially contained in a stirred tank reactor and a second reactant continuously added to the reactor, with no flow out of the reactor. The addition of a gas to participate in a liquid-phase reaction is one of the more common situations involving a semi-batch reactor, especially because the rate of addition of the gas can be controlled to keep its partial pressure essentially constant as well as providing quantitative information about the rate of reaction. In addition, there is frequently little or no change in the volume of the liquid phase. Well-mixed autoclave reactors coupled with gas pressure controllers, mass flow meters and computers can nicely provide continuous, real-time rate data related to heterogeneous catalysts used in such gas/liquid systems [6-8]. Again, it must be emphasized that experiments must be performed and/or calculations made to verify that no heat or mass transfer limitations exist. 

The existence of radial temperature and concentration gradients means that, in principle, one should include terms to account for these effects in the mass and heat conservation equations describing the reactor. Furthermore, there should be a distinction between the porous catalyst particles (within which reaction occurs) and the bulk gas phase. Thus, conservation equations should be written for the catalyst particles as well as for the bulk gas phase and coupled by boundary condition statements to the effect that the mass and heat fluxes at the periphery of particles are balanced by mass and heat transfer between catalyst particles and bulk gas phase. A full account of these principles may be found in a number of texts [23, 35, 36]. 

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)]... 

For the nonisothermal catalyst pellet with negligible external mass and heat transfer resistances, i.e., with Sh —> 00 and Nu —> 00 and for a first-order reaction, the dimensionless concentration and temperature are governed by the following couple of boundary value differential equations... 

Therefore, the main source of multiplicity in fixed-bed catalytic reactors is through the coupling between the exothermic reaction and the catalyst pellet mass- and heat-transfer resistances. 

In the packed-bed reactor, the molar concentrations and temperature at the exterior of the catalyst particle are coupled to the respective fluid-phase concentrations and temperature through the interfacial fluxes given in Eqs. (3.3-1) and (3.3-2). Overall mass and heat transfer coefficients are often used to describe these interfacial fluxes, similar in structure to Eqs. (3.2-1) and (3.2-2). Complete solution of the packed-bed reactor model... 

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