Physical Transport Processes

Diffusion effects can be expected in reactions that are very rapid. A great deal of effort has been made to shorten the diffusion path, which increases the efficiency of the catalysts. Pellets are made with all the active ingredients concentrated on a thin peripheral shell and monoliths are made with very thin washcoats containing the noble metals. In order to convert 90% of the CO from the inlet stream at a residence time of no more than 0.01 sec, one needs a first-order kinetic rate constant of about 230 sec-1. When the catalytic activity is distributed uniformly through a porous pellet of 0.15 cm radius with a diffusion coefficient of 0.01 cm2/sec, one obtains a Thiele modulus y = 22.7. This would yield an effectiveness factor of 0.132 for a spherical geometry, and an apparent kinetic rate constant of 30.3 sec-1 (106). 

If the same quantity of active ingredient is concentrated in an outside shell of thickness 0.015 cm, one obtains y = 2.27. This would yield an effectiveness factor of 0.431 in a slab geometry, and the apparent kinetic constant has risen to 99.2 sec-1. If the active ingredient is further concentrated in a shell of 0.0025 cm, one obtains y = 0.38, an effectiveness factor of 0.957, and an apparent kinetic constant of 220 sec-1. These calculations are comparable to the data given in Fig. 15. This analysis applies just as well to the monolith, where the highly porous alumina washcoat should not be thicker than 0.001 in. 

Oxidation kinetics over platinum proceeds at a negative first order at high concentrations of CO, and reverts to a first-order dependency at very low concentrations. As the CO concentration falls towards the center of a porous catalyst, the rate of reaction increases in a reciprocal fashion, so that the effectiveness factor may be greater than one. This effectiveness factor has been discussed by Roberts and Satterfield (106), and in a paper to be published by Wei and Becker. A reversal of the conventional wisdom is sometimes warranted. When the reaction kinetics has a negative order, and when the catalyst poisons are deposited in a thin layer near the surface, the optimum distribution of active catalytic material is away from the surface to form an egg yolk catalyst. 

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). 

Heat and Mass Transport from the Gases to the Solid Surfaces 

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Turbulent Diffusion FDmes. Laminar diffusion flames become turbulent with increasing Reynolds number (1,2). Some of the parameters that are affected by turbulence include flame speed, minimum ignition energy, flame stabilization, and rates of pollutant formation. Changes in flame stmcture are beHeved to be controlled entirely by fluid mechanics and physical transport processes (1,2,9). 

The rates at which chemical transformations take place are in some circumstances strongly influenced by mass and heat transfer processes (see Sections 12.3 to 12.5). In the design of heterogeneous catalytic reactors, it is essential to utilize a rate expression that takes into account the influence of physical transport processes on the rate at which reactants are converted to products. Smith (93) has popularized the use of the term global reaction rate to characterize the overall rate of transformation of reactants to... 

The classification of wastewater in terms of size distribution is normally done from a practical point of view. Typically, a distinction is made between soluble, colloidal and suspended components (Figure 3.6). While this definition for determining what solids are is rational as far as physical transport processes in sewers are concerned, when dealing with the microbial processes for sewer conditions, an extension of the solids definition is required. Particles larger than about 10-4 pm cannot be transported through the cell wall and are, therefore, from a microbial point of view, considered particles. 

The effects of physical transport processes on the overall adsorption on porous solids are discussed. Quantitative models are presented by which these effects can be taken into account in designing adsorption equipment or in interpreting observed data. Intraparticle processes are often of major importance in adsorption kinetics, particularly for liquid systems. The diffusivities which describe intraparticle transfer are complex, even for gaseous adsorbates. More than a single rate coefficient is commonly necessary to represent correctly the mass transfer in the interior of the adsorbent. 

The Chapman mechanism. The mechanism of ozone formation and destruction in the stratosphere was first formulated by Chapman (205) in 1930. He did not consider the effects of minor constituents and physical transport processes that have since been recognized as important factors to explain the discrepancy between the calculated results and the actual observation. According to his mechanism, ozone is formed by the photolysis... 

To obtain the concentration profiles in an atmosphere, it is important to know the time required to attain the equilibrium concentration. If the equilibrium time scale is more than a year, physical transport processes become appreciable and a large departure from the equilibrium profile is expected. The equilibrium time scale xeq may be obtained from... 

From Table VIII—1B and JQj of Fig. VIII-7, re,(03) is calculated as a function of altitude. This relationship is shown in Fig. VIII—9. The equilibrium time scale near the top of the stratosphere is about a day, while below 15 km Te (Oj) more than a year and downward physical transport processes of 03 become important. 

Physical transport processes and mixing ratio. The concentration profile of a minor constituent in an atmosphere is often expressed as a mixing ratio by volume or a mole fraction rather than the concentration by atmospheric modelers. Physical transport processes involve vertical and horizontal mixing by turbulence and molecular diffusion. The molecular diffusion process can be ignored in the stratosphere since it is important only above about 40 km. 

Deviation from the Chapman mechanism. It was recognized by Nicolet (740) that the observed Oa concentrations were much less than the calculated values even near the stratopause where the physical transport processes are not important (see Fig. VIII 10). He suggested that to explain the observed ozone concentration, the effective value of k44, the rate constant for the destruction of Oj, must be much larger than that given in (VIII-44g) for a pure 02- N2 atmosphere. 

Heterogeneous catalytic reactions, by their nature, involve a separate phase of catalyst, embedded in a phase of reacting species Therefore, the chemical transformation relies on a number of physical transport processes which may have a strong influence on the rate of the overall process and which may introduce an additional dependence on the operating conditions In the industrially important situation that the catalyst is a porous solid and the reactants form either a gaseous or a liquid phase, the following seven steps can be observed (Fig 1)... 

Reactive solute-transport models couple the equations that describe physical transport processes with equations that describe geochemical reactions. These models can be divided into three basic categories (i) equilibrium models, (ii) partial equilibrium models, and (iii) kinetic models. The three are differentiated by the... 

Apart from the inherent efficiency of the reactions leading to the light-induced formation of a ROS as summarized by the relevant apparent quantum yield and action spectrum, the observed rate of production will depend on other factors that affect the photon exposure including water column composition and depth (Chapter 3), time of day (i.e., solar zenith angle), season, latitude (Chapter 2), and physical transport processes (Chapter 4). For more details regarding the fundamental equations used to define the rates of primary and secondary photochemical reactions and their application to aquatic systems, the reader is referred to recent reviews on this topic [41,42]. 

Physical transport processes can play an especially important role in heterogeneous catalysis. Besides film diffusion on the gas/liquid boundary there can also be diffison of the reactants (products) through a boundary layer to (from) the external surface of the solid material and additionally diffusion of them through the porous interior to from the active catalyst sites. Heat and mass transfer processes influence the observed catalytic rates. For instance, as discussed previously the intrinsic rates of catalytic processes follow the Arrhenius... 

Figure 1 Major global reservoirs Involved in active production, exchange and cycling of organic carbon. Reservoir sizes are shown in Gt carbon (1 GtC = 10 g C). Numbers in parentheses are based on 1980s values numbers without parentheses are estimates of the pre-anthropogenic values. Fluxes primarily mediated by biological reactions are shown with dashed arrows physical transport processes are shown with solid arrows. (Modified after Siegenthaler and Sarmiento (1993) and Hedges and Oades (1997).)...

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