Reactions, noncatalytic diffusion models

TABLE 7-7 Noncatalytic Gas-Solid Reaction-Diffusion Models... 

The first and second integrals have their coordinate systems centered on the catalytic C and noncatalytic N spheres, respectively. The local nonequilibrium average microscopic density field for species a is pa(r) = [Y = 5(r - ( )) The solution of the diffusion equation can be used to estimate this nonequilibrium density, and thus the velocity of the nanodimer can be computed. The simple model yields results in qualitative accord with the MPC dynamics simulations and shows how the nonequilibrium density field produced by reaction, in combination with the different interactions of the B particles with the noncatalytic sphere, leads to directed motion [117],... 

In this chapter, we consider multiphase (noncatalytic) systems in which substances in different phases react. This is a vast field, since the systems may involve two or three (or more) phases gas, liquid, and solid. We restrict our attention here to the case of two-phase systems to illustrate how the various types of possible rate processes (reaction, diffusion, and mass and heat transfer) are taken into account in a reaction model, although for the most part we treat isothermal situations. 

Mathematical modeling is the science or art of transforming any macro-scale or microscale problem to mathematical equations. Mathematical modeling of chemical and biological systems and processes is based on chemistry, biochemistry, microbiology, mass diffusion, heat transfer, chemical, biochemical and biomedical catalytic or biocatalytic reactions, as well as noncatalytic reactions, material and energy balances, etc. 

FIG. 7-14 Concentration profiles with intraparticle diffusion control, = 70. ii absence of gas particle mass-transfer resistance. [From Wen, Noncatalytic Heterogeneous Solid-Fluid Reaction Models, Ind. Eng. Chem. 60(9) 34-54 (1968), Fig. 12.]... 

A similar model that specifically considers the poison deposition in a catalyst pellet was presented by Olson [5] and Carberry and Gorring [6], Here the poison is assumed to deposit in the catalyst as a moving boundary of a poisoned shell surrounding an unpoisoned core, as in an adsorption situation. These types of models are also often used for noncatalytic heterogeneous reactions, which was discussed in detail in Chapter 4. The pseudo-steady-state assumption is made that the boundary moves rather slowly compared to the poison diffusion or reaction rates. Then, steady-state diffusion results can be used for the shell, and the total mass transfer resistance consists of the usual external interfacial, pore diffusion, and boundary chemical reaction steps in series. 

With these we enlist the two fundamental approaches to the noncatalytic gas-solid reaction systems The shrinking core model and volume reaction model. In the volnme reaction model, the solid is porous, the fluid easily diffuses in or ont of the solid, such that the reaction can take place homogeneously everywhere in the solid. On the other hand, with the shrinking core model (SCM), also called the sharp interface model (SIM), there is a sharp interface between the unreacted core and reacted shell of the particles. 

Recall that there are a number of reactions where homogeneous catalysis involves two phases, liquid and gas, for example, hydrogenation, oxidation, carbonylation, and hydroformylation. The role of diffusion becomes important in such cases. In Chapter 6, we considered the role of diffusion in solid catalyzed fluid-phase reactions and gas-liquid reactions. The treatment of gas-liquid reactions makes use of an enhancement factor to express the enhancement in the rate of absorption due to reaction. A catalyst may or may not be present. If there is no catalyst, we have a simple noncatalytic gas-liquid heterogeneous reaction in which the reaction rate is expressed by simple power law kinetics. On the other hand, when a dissolved catalyst is present, as in the case of homogeneous catalysis, the rate equations acquire a hyperbolic form (similar to LHHW models discussed in Chapters 5 and 6). Therefore, the mathematical analysis of such reactions becomes more complex. 

Various reaction models for noncatalytic gas-solid reactions have been proposed and have been summarized by Szekely et al. (70). The effect of diffusion and heat transfer on the chemical reaction rate for a single particle is rather complicated, especially when multiple reactions are occurring simiiltaneously. This subject will be discussed in the following section. 

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