Heat Transfer in Porous Catalysts

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

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. 

A detailed analysis of the radial heat transfer in the catalyst bed /4,5/ shows (see Fig. 3) that e.g. the dispersion parameters in the balance equations for the fluid phase in Fig. 1 are dependent on other parameters characteristic of more fundamental transport mechanisms and, moreover, the heat conduction through the porous particles itself consists again of four basic mechanisms (Fig. 4), each having its own characteristic parameter /6/. 

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. 

The influence which the simultaneous transfer of heat and mass in porous catalysts has on the selectivity of first-order concurrent catalytic reactions has recently been investigated by 0stergaard(27). As shown previously, selectivity is not affected by any limitations due to mass transfer when the process corresponds to two concurrent first-order reactions ... 

Two other crucial factors are mass transfer and heat transfer. In Chapter 3 we assumed that the reactions were homogeneous and well stirred, so that every substrate molecule had an equal chance of getting to the catalytic intermediates. Here the situation is different. When a molecule reaches the macroscopic catalyst particle, there is no guarantee that it will react further. In porous materials, the reactant must first diffuse into the pores. Once adsorbed, the molecule may need to travel on the surface, in order to reach the active site. The same holds for the exit of the product molecule, as well as for the transfer of heat to and from the reaction site. In many gas/solid systems, the product is hot as it leaves the catalyst, and carries the excess energy out with it. This energy must dissipate through the catalyst particles and the reactor wall. Uneven heat transfer can lead to hotspots, sintering, and runaway reactions. 

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]. 

Solve the following problem for reaction and heat transfer in a porous catalyst pellet... 

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

The model presented here is a comprehensive full three-dimensional, non-isothermal, singlephase, steady-state model that resolves coupled transport processes in the membrane, eatalyst layer, gas diffusion eleetrodes and reactant flow channels of a PEM fuel cell. This model accounts for a distributed over potential at the catalyst layer as well as in the membrane and gas diffusion electrodes. The model features an algorithm that allows for a more realistie representation of the loeal activation overpotentials which leads to improved prediction of the local current density distribution. This model also takes into aeeount convection and diffusion of different species in the channels as well as in the porous gas diffusion layer, heat transfer in the solids as well as in the gases, electrochemical reactions and the transport of water through the membrane. 

Dogu, G. Diffusion limitations for reactions in porous catalysts, in Handbook of Heat and Mass Transfer, Volume 2 Mass Transfer and Reactor Design (Ed. Cheremisinoff, N.P.) pp. 433 89, Gulf Publishing Co, Houston, TX, 1989. 

An industrial chemical reacdor is a complex device in which heat transfer, mass transfer, diffusion, and friction may occur along with chemical reaction, and it must be safe and controllable. In large vessels, questions of mixing of reactants, flow distribution, residence time distribution, and efficient utilization of the surface of porous catalysts also arise. A particular process can be dominated by one of these factors or by several of them for example, a reactor may on occasion be predominantly a heat exchanger or a mass-transfer device. A successful commercial unit is an economic balance of all these factors. 

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 chemical micro process technology with porous catalyst layers attached to the channel walls, convection through the porous medium can often be neglected. When the reactor geometry allows the flow to bypass the porous medium it will follow the path of smaller hydrodynamic resistance and will not penetrate the pore space. Thus, in micro reactors with channels coated with a catalyst medium, the flow velocity inside the medium is usually zero and heat and mass transfer occur by diffusion alone. 

Effective Thermal Conductivities of Porous Catalysts. The effective thermal conductivity of a porous catalyst plays a key role in determining whether or not appreciable temperature gradients will exist within a given catalyst pellet. By the term effective thermal conductivity , we imply that it is a parameter characteristic of the porous solid structure that is based on the gross geometric area of the pellet perpendicular to the direction of heat transfer. For example, if one considers the radial heat flux in a spherical pellet one can say that... 

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