Thermal conductivity porous catalyst

Here Iq is the thermal conductivity of the system, consisting of the porous solid and the reacting fluid inside the pores. This is the most uncertain value, while everything else is measurable. Two things must be remembered. First, data on thermal conductivity of catalysts are approximate. The solid fraction of the catalyst (1-0) always reduces the possibility for diflhision, while the solid can contribute to the thermal conductivity. Second, the outside temperature difference normal to the surface or Daiv, will become too high, much before the inside gradient can cause a problem. See Hutching and Carberry (19), Carberry (20). 

Temperature gradients within the porous catalyst could not be very large, due to the low concentration of combustibles in the exhaust gas. Assuming a concentration of 5% CO, a diffusion coefficient in the porous structure of 0.01 cms/sec, and a thermal conductivity of 4 X 10-4 caI/sec°C cm, one can calculate a Prater temperature of 1.0°C—the maximum possible temperature gradient in the porous structure (107). The simultaneous heat and mass diffusion is not likely to lead to multiple steady states and instability, since the value of the 0 parameter in the Weisz and Hicks theory would be much less than 0.02 (108). 

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... 

The effective thermal conductivities of common commercial porous catalysts are quite low and fall within a surprisingly narrow range. 

Due to their high electrical and thermal conductivity, materials made out of metal have been considered for fuel cells, especially for components such as current collectors, flow field bipolar plates, and diffusion layers. Only a very small amount of work has been presented on the use of metal materials as diffusion layers in PEM and DLFCs because most of the research has been focused on using metal plates as bipolar plates [24] and current collectors. The diffusion layers have to be thin and porous and have high thermal and electrical conductivity. They also have to be strong enough to be able to support the catalyst layers and the membrane. In addition, the fibers of these metal materials cannot puncture the thin proton electrolyte membrane. Thus, any possible metal materials to be considered for use as DLs must have an advantage over other conventional materials. 

As with thermal conductivity, we see in this section that disorder can greatly affect the mechanism of diffusion and the magnitude of diffusivities, so that crystalline ceramics and oxide glasses will be treated separately. Finally, we will briefly describe an important topic relevant to all material classes, but especially appropriate for ceramics such as catalyst supports—namely, diffusion in porous solids. 

For the detailed study of reaction-transport interactions in the porous catalytic layer, the spatially 3D model computer-reconstructed washcoat section can be employed (Koci et al., 2006, 2007a). The structure of porous catalyst support is controlled in the course of washcoat preparation on two levels (i) the level of macropores, influenced by mixing of wet supporting material particles with different sizes followed by specific thermal treatment and (ii) the level of meso-/ micropores, determined by the internal nanostructure of the used materials (e.g. alumina, zeolites) and sizes of noble metal crystallites. Information about the porous structure (pore size distribution, typical sizes of particles, etc.) on the micro- and nanoscale levels can be obtained from scanning electron microscopy (SEM), transmission electron microscopy ( ), or other high-resolution imaging techniques in combination with mercury porosimetry and BET adsorption isotherm data. This information can be used in computer reconstruction of porous catalytic medium. In the reconstructed catalyst, transport (diffusion, permeation, heat conduction) and combined reaction-transport processes can be simulated on detailed level (Kosek et al., 2005). 

Measurements of A, are scarce. The available data are reviewed by Satterfield [2], The effective thermal conductivity of a porous catalyst can be estimated from the correlation of Russell [30] ... 

Thermal conductivities of porous oxide catalysts, which are of major practical interest, (at atmospheric pressure in air) are within the range 0.2 - 0.5 W nr K 1. The spread of values of the thermal conductivity is remarkably small for the wide range of catalysts studied by several investigators. It does not vary greatly with major differences in void fraction and pore size distribution. 

Dalla Betta et al. first proposed an inert porous layer, or diffusion barrier, to prevent temperature runaway, and loosely interpreted the effect in terms of a reduction in the rate of combustion. A more rigorous interpretation of the effect of an inert porous layer on catalyst temperature was provided by McCarty et al, who also described the desired properties for diffusion layer materials, including a high thermal conductivity and low specific combustion activity. These authors stated that the high washcoat temperatures found in catalytic combustion of natural gas were due to the high diffusivity of methane in air, which causes the diffusion rate to the catalyst surface to match the rate of heat dissipation by conduction to the gas phase. The diffusion barrier decreases the rate of diffusion of methane to the catalyst surface, thus reducing the catalyst temperature. Modeling work by Hayes et al. confirmed those concepts. ... 

Tn the remainder of the text the term effective is used to indicate that a transport coefScient applies to a porous material, as distinguished from a homogeneous region. Effective diffusivities Dg and thermal conductivities kg are based on a unit of total area (void plus nonvoid) perpendicular to the direction of transport. For example, for diffusion in a spherical catalyst pellet at radius r, Dg is based on the area Anr. ... 

Strongly exothermic or endothermic reactions may cause a temperature profile within the catalyst layer, and reaction rates and thus selectivity may be altered. The importance of the temperature profile depends on the reaction rate, the layer thickness, the reaction enthalpy, AHR, the activation energy, E, and the thermal conductivity of the porous catalyst, le. To achieve what is considered quasi-isothermal behavior, the observed rate, reff, must not differ from the rate at uniform temperature by more than about 5%. The following criterion, designed for a catalyst layer in a microchannel, can be formulated ... 

Various simplified models can be used with varying degrees of accuracy for the simulation of the transient behaviour of non-porous catalyst pellets. The most suitable unsteady state model for this problem is that with infinite thermal conductivity. This simplified model is quite accurate for metal and metal oxide catalysts. In this model, equation (5.45) disappears and the model becomes strictly lumped parameter described only by ordinary initial value differential equations. 

In the general case where the active material is dispersed through the pellet and the catalyst is porous, internal diffusion of the species within the pores of the pellet must be included. In fact, for many cases diffusion through catalyst pores represents the main resistance to mass transfer. Therefore, the concentration and temperature profiles inside the catalyst particles are usually not flat and the reaction rates in the solid phase are not constant. As there is a continuous variation in concentration and temperature inside the pellet, differential conservation equations are required to describe the concentration and temperature profiles. These profiles are used with intrinsic rate equations to integrate through the pellet and to obtain the overall rate of reaction for the pellet. The differential equations for the catalyst pellet are two point boundary value differential equations and besides the intrinsic kinetics they require the effective diffusivity and thermal conductivity of the porous pellet. 

It is obvious that catalytic distillation requires a reactor dedicated to one specific type of catalytic reaction. It can be questioned whether the fine-chemical industry performs many reactions needing a dedicated reactor. Application of the catalyst as a thin porous layer on the surface of a metal or ceramic material, however, affords interesting possibilities in the fine-chemical industry. With liquid-phase reactions, the catalyst is still almost completely involved in the reaction when the layer in which the catalyst is present is not much thicker than ca 100 pm. Separation of the catalyst from the reaction product, removal of the catalyst from the reactor, and collection and storage of the catalyst is no longer required this greatly facilitates operation. The catalyst can, furthermore, be treated thermally in a gas flow, because the pressure drop depends on the structure of the solid on which the catalyst has been applied. This structure can easily be selected thus that the pressure drop is low. When, finally, the catalyst is applied to a metal surface with appreciable thermal conductivity the temperature of the reaction can be maintained accurately at the value desired. 

The effective bed conductivity has a static or zero-flow term, which is usually about 5k when the particles are a porous inorganic material such as alumina, silica gel, or an impregnated catalyst, and kg is the thermal conductivity of the gas. The turbulent flow contribution to the conductivity is proportional to the mass flow rate and particle diameter, and the factor 0.1 in the following equation agrees with the theory for turbulent diffusion in packed beds ... 

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)]. 

Table 7.5 Thermal Conductivities of Some Porous Catalysts...

The effective thermal conductivities of common commercial porous catalysts are quite low and fall within a surprisingly narrow range. The heat transfer path through the solid phase offers considerable thermal resistance for many porous materials, particularly if the pellet is formed by tableting of microporous particles. Such pellets may be regarded as an assembly of particles that contact one another at only a relatively small number of points that act as regions of high thermal resistance. 

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