Transport and Reaction

When a catalytic reaction occurs on the surfaces within a catalyst pellet in a packed bed, there are inevitably concentration gradients around and within the pellet. We have thus far considered only the overaU variation in concentrations as a function of distance along the direction of flow J in the reactor. However, in order to account for the variations around and within catalyst peUets, we now need to find Cj x, y, z) rather than just Cj z). Stated 

It is important to note that we need to consider several length scales in attempting to describe catalytic reactors. The reactor is on the order of 1 meter diameter and length, the pellet is typically 1 cm diameter, the pores within the pellet are 0.1 mm m) or smaller in 

In the reactor we are interested in the position in the bed z or height of the bed L, in the pellet we are interested in the position x in the pellet with radius R, in the pore we are interested in distance x down the pore diameter (ipore, nd on the walls of the pore we are interested in reactions on the catalyst particle diameter r/pamcie- 

We are also concerned with gradients in composition throughout the reactor. We have thus far been concerned only with the very small gradient dCj/dz down the reactor from inlet to exit, which we encounter in the species mass balance, which we must ultimately solve. Then there is the gradient in Cj around the catalyst pellet Finally, there is the gradient within the porous catalyst pellet and around the catalytic reaction site within the pellet As we consider 

To summarize the goal of this section, we must start with the microscopic description of the catalytic reaction, then consider diffusion in pores, and then examine the reactant composition around and within the pellet, in order finally to describe the reactor maSS-balance equations in terms of z alone. The student should understand the logic of this procedure as we go from micrscopic to macroscopic, or the following sections will be unintelligible (or even more unintelligible than usual). 

The key to this chapter is the consideration of the kinetics of a heterogeneous elementary step 

In what follows we will be dealing (in contrast to usual cases in semiconductor physics, cf. Section 6.2.2) with comparatively slow transport processes, so that we 

Physical Chemistry of Ionic Materials leans and Electrrjns in Solids. 

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Catalyst design is in a primitive stage. There are hardly any examples of tme design of catalysts (42). However, development of improved catalysts has been guided successfully in instances when the central issues were the interplay of mass transport and reaction. An example is catalysts used for hydroprocessing of heavy fossil fuels. 

Whitaker, S, Transport Processes with Heterogeneous Reaction. In Concepts and Design of Chemical Reactors Whitaker, S Cassano, AE, eds. Gordon and Breach Newark, NJ 1986 1. Whitaker, S, Mass Transport and Reaction in Catalyst Pellets, Transport in Porous Media 2, 269, 1987. 

OS 92[ [R 32] [P 72] A mathematical model based on transport and reaction was able to reproduce the experimental findings described above [145]. 

N. Y. Chen, T. F. Degnan, C. M. Smith 1994, Molecular Transport and Reaction in Zeolites, VCH Publishers, New York. 

MZ Southard, DW Green, VJ Stella, KJ Himmelstein. Dissolution of ionizable drugs into unbuffered solution A comprehensive model for mass transport and reaction in the rotating disk geometry. Pharm Res 9 58-69, 1992. 

WASP/TOXIWASP/WASTOX. The Water Quality Analysis Simulation Program (WASP, 3)is a generalized finite-difference code designed to accept user-specified kinetic models as subroutines. It can be applied to one, two, and three-dimensional descriptions of water bodies, and process models can be structured to include linear and non-linear kinetics. Two versions of WASP designed specifically for synthetic organic chemicals exist at this time. TOXIWASP (54) was developed at the Athens Environmental Research Laboratory of U.S. E.P.A. WASTOX (55) was developed at HydroQual, with participation from the group responsible for WASP. Both codes include process models for hydrolysis, biolysis, oxidations, volatilization, and photolysis. Both treat sorption/desorption as local equilibria. These codes allow the user to specify either constant or time-variable transport and reaction processes. 

Applications of packed tube CFD to improve transport and reaction understanding and models are still in early stages. A number of studies have focused on addressing the technical issues of using CFD for packed tubes, and have presented qualitative results that have yielded insight into the phenomena. Other studies have tried to use CFD simulations to extend experimental data, and provide estimates of familiar transport parameters. 

Van Cappellen, P. Wang Y. 1996. Cycling of iron and manganese in surface sediments a general theory for the coupled transport and reaction of carbon, oxygen, nitrogen, sulfur, iron and manganese. American Journal Sciences, 296, 197-243. 

Little is known about the mechanisms that cause the three other current extrema ]2 to J4. The kinetic and diffusional contributions of the characteristic currents Ji to J4 show a different concentration dependence. While the diffusion current is found to be roughly proportional to Cp, the kinetic current shows an exponent of 2 < <2.5 [Ha3]. No dependence of the characteristic currents to ]4 on doping kind and density is observed. This indicates again that to ]4 depend on mass transport and reaction kinetics rather than on charge supply. For n-type electrodes, of course, strong illumination is necessary in order to generate a sufficient number of minority carriers to support the currents. 

At the mesoscopic scale, interactions between molecular components in membranes and catalyst layers control the self-organization into nanophase-segregated media, structural correlations, and adhesion properties of phase domains. Such complex processes can be studied by various theoretical tools and simulation techniques (e.g., by coarse-grained molecular dynamics simulations). Complex morphologies of the emerging media can be related to effective physicochemical properties that characterize transport and reaction at the macroscopic scale, using concepts from the theory of random heterogeneous media and percolation theory. 

In general. Equations (6.59) and (6.61) highlight the importance of adjusting thickness and effective properties of transport and reaction in CLs in such a way that 6cl 3 Lcl- If we replace dcL by rjg, using Equation (6.59), we obtain an explicit expression for rcL as a function of the catalyst layer voltage loss ... 

Nourbakhsh, N., A. Champagnie, T. T. Tsotsis and 1. A. Webster. 1989. Transport and reaction studies using ceramic membranes. In A.I.Ch.E. Symp. Scr. Membrane Reactor Technology, eds. R. Govind and N. Itoh, pp. 75-84. New York Am. Institute of Chem. Engr. 

Rachhpal-Singh and Kirk (1993a,b) developed a model of these processes based on equations for the transport and reaction of urea, ammoniacal species (NH4+, NH3, NH4OH), carbonate species (H2CO3, HCOs", COs ) and mobile acid-base pairs (H2C03-HC03, HCOs -COs , NH4+-NH3, NH4+-NH4OH, H20-OH ). The equations are of the form of Equation (2.6)... 

Neiburger, M., J. G. Edinger, and H. C. Chin. Meteorological Aspects of Air Pollution and Simulation Models of Diffusion, Transport and Reactions of Air Pollution. Task Force No. 4. In Project Clean Air. Task Force Assessments. Vol 4. Riverside University of CalifomU, 1970. [60 pp.]... 

Although a good deal is known about the permeability of the pleura to proteins, the transport and reactions of the tissue to particulates such as fi-... 

Taken together, the transport and reaction considerations have two broad implications for dark reactions in well-designed CSTR-recycle systems ... 

Ionization of atoms or molecules is the main primary event induced by the interaction of radiations with condensed matter. The charged species produced by ionization, if not removed from the irradiated system, will naturally tend to recombine. The conventional theories of recombination treat the transport and reactions of charged species only after the electrons ejected from atoms or molecules become thermalized by dissipating their initially high kinetic energies to the surrounding medium and form a spatial distribution around their parent cations. The thermalization in condensed phases is fast and is usually... 

In Eqs. (3.58) and (3.59), the kt are the reaction rate constants. We will see in Chapter 4 that many solid-state ceramic processes involve simultaneous mass transport (diffusion), thermal transport, and reaction. 

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