Heterogeneous reaction model

As far as the models accounting for these conceptions are concerned, their construction and investigation have just started. The development of these models is sure to be retarded by the absence of data on the detailed reaction mechanism and its parameters. The exception is ref. 147, where the authors construct an unsteady-state homogeneous-heterogeneous reaction model and analyze it with respect to the cyclohexane oxidation on zeolites. The study was aimed at the experimental interpretation of the self-oscillations found. The model constructed is in accordance with the law of mass action. 

Theoretical. In deriving a theoretical expression for k, we have developed a reaction mechanism model for calcite dissolution which expands on the adsorption layer heterogeneous reaction model of Mullin ( ). We assume that a thin (possibly only a few molecules thick) "adsorption layer" (or "surface layer") exists adjacent to the crystal surface, between the crystal surface and the hydrodynamic boundary layer. Species in the adsorption layer are loosely bound to the crystal surface and have relatively low mobility, particularly in comparison with species mobility in the boundary layer. The crystal surface is believed to be sparsely covered by reaction sites at discontinuities in the surface ( 3). To distinguish between species activities in the bulk fluid, at the base of the boundary layer (near the crystal surface), and in the adsorption layer, we use the subscripts (B), (o), and (s), respectively. 

Modelling plasma chemical systems is a complex task, because these system are far from thennodynamical equilibrium. A complete model includes the external electric circuit, the various physical volume and surface reactions, the space charges and the internal electric fields, the electron kinetics, the homogeneous chemical reactions in the plasma volume as well as the heterogeneous reactions at the walls or electrodes. These reactions are initiated primarily by the electrons. In most cases, plasma chemical reactors work with a flowing gas so that the flow conditions, laminar or turbulent, must be taken into account. As discussed before, the electron gas is not in thennodynamic equilibrium... 

E. V. Albano. On the influence of reactant s induced surface transformations in the behavior of a heterogeneously catalyzed dimer-monomer reaction model. J Chem Phys 709 7498-7505, 1998. 

E. V. Albano. Irreversible saturation transitions in dimer-dimer reaction models of heterogeneous catalysis. J Phys A (Math Gen) 25 2557-2568, 1992 Corrigendum. J Phys A (Math Gen) 26.3661, 1993. 

To describe hypergolic heating, Anderson and Brown (A10) proposed a theoretical model based upon spontaneous exothermic heterogeneous reactions between the reactive oxidizer and a condensed phase at the gas-solid interface. In these studies, the least complex case was considered, i.e., the one in which the solid phase is instantaneously exposed to a stagnant (nonflowing) gaseous oxidizer environment. This situation can be achieved experimentally provided the sample to be tested is suddenly injected into the desired environment in a manner designed to minimize gas flow. 

All the rate constants should be positive so the denominator in this expression will always retard the reaction. The same denominator can be used with Equation (7.3) to model reversible heterogeneous reactions ... 

A good model is consistent with physical phenomena (i.e., 01 has a physically plausible form) and reduces crresidual to experimental error using as few adjustable parameters as possible. There is a philosophical principle known as Occam s razor that is particularly appropriate to statistical data analysis when two theories can explain the data, the simpler theory is preferred. In complex reactions, particularly heterogeneous reactions, several models may fit the data equally well. As seen in Section 5.1 on the various forms of Arrhenius temperature dependence, it is usually impossible to distinguish between mechanisms based on goodness of fit. The choice of the simplest form of Arrhenius behavior (m = 0) is based on Occam s razor. 

Assume A, B, C, and D have similar diffusivities so that local stoichiometry is preserved. Under what circumstances will conversion be maximized by (a) complete segregation (b) by maximum mixedness Heterogeneous reactions are often modeled as if they were homogeneous. A frequently encountered rate expression is... 

A variety of models of chemical reactors is discussed in more detail in Section 5.4. Readers who are interested in modelling of chemical reactors are also referred to books of Carberry and Varma (1987), Fogler (1986), Froment and Bischoff (1990), Levenspiel (1999), Smith (1981), Trambouze et al. (1988), Walas (1959), and Westerterp et al. (1990). With respect to heterogeneous reactions athe book of Doraiswamy and Sharma (1984) is also recommended. 

Early studies of ET dynamics at externally biased interfaces were based on conventional cyclic voltammetry employing four-electrode potentiostats [62,67 70,79]. The formal pseudo-first-order electron-transfer rate constants [ket(cms )] were measured on the basis of the Nicholson method [99] and convolution potential sweep voltammetry [79,100] in the presence of an excess of one of the reactant species. The constant composition approximation allows expression of the ET rate constant with the same units as in heterogeneous reaction on solid electrodes. However, any comparison with the expression described in Section II.B requires the transformation to bimolecular units, i.e., M cms . Values of of the order of 1-2 x lO cms (0.05 to O.IM cms ) were reported for Fe(CN)g in the aqueous phase and the redox species Lu(PC)2, Sn(PC)2, TCNQ, and RuTPP(Py)2 in DCE [62,70]. Despite the fact that large potential perturbations across the interface introduce interferences in kinetic analysis [101], these early estimations allowed some preliminary comparisons to established ET models in heterogeneous media. 

Shah, MJ., "Kinetic Models for Consecutive Heterogeneous Reactions", Industrial and Engineering Chemistry, 57, 18-23 (1965). 

The reaction plane model with heterogeneous reactions was discussed at length for acid-base reactions in the previous section. The same modeling technique, of confining the reactions to planes, can be applied to micelle-facilitated dissolution. As with the acid-base model, one starts with a one-dimensional steady-state equation for mass transfer that includes diffusion, convection, and reaction. This equation is then applied to the individual species i, i.e., the solute, s, the micelle, m, and the drug-loaded micelle, sm, to yield... 

Horst C, Chen Y-S, Kunz U, Hoffmann U (1996) Design, modeling and performance of a novel sonochemical reactor for heterogeneous reactions. Chem Eng Sci 51 1837-1846... 

This study was carried out to simulate the 3D temperature field in and around the large steam reforming catalyst particles at the wall of a reformer tube, under various conditions (Dixon et al., 2003). We wanted to use this study with spherical catalyst particles to find an approach to incorporate thermal effects into the pellets, within reasonable constraints of computational effort and realism. This was our first look at the problem of bringing together CFD and heterogeneously catalyzed reactions. To have included species transport in the particles would have required a 3D diffusion-reaction model for each particle to be included in the flow simulation. The computational burden of this approach would have been very large. For the purposes of this first study, therefore, species transport was not incorporated in the model, and diffusion and mass transfer limitations were not directly represented. 

In this chapter we consider the problem of the kinetics of the heterogeneous reactions by which minerals dissolve and precipitate. This topic has received a considerable amount of attention in geochemistry, primarily because of the slow rates at which many minerals react and the resulting tendency of waters, especially at low temperature, to be out of equilibrium with the minerals they contact. We first discuss how rate laws for heterogeneous reactions can be integrated into reaction models and then calculate some simple kinetic reaction paths. In Chapter 26, we explore a number of examples in which we apply heterogeneous kinetics to problems of geochemical interest. 

In this chapter, we first cite examples of catalyzed two-phase reactions. We then consider types of reactors from the point of view of modes of operation and general design considerations. Following introduction of general aspects of reactor models, we focus on the simplest of these for pseudohomogeneous and heterogeneous reactor models, and conclude with a brief discussion of one-dimensional and two-dimensional models. 

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