Reactor Models General Considerations

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. 

Before discussing in more detail what reaction models (Sect. 2) and reactor models (Sect. 3) are, some general considerations about the classification of models appear convenient. 

The state of mixing in a given reactor can be evaluated by RTD experiments by means of inert tracers, by temperature measurements, by flow visualization and, finally, by studying in the reactor under consideration the kinetics of an otherwise well-known reaction (because its mechanism has been carefully elucidated from experiments carried out in an ideal reactor, the batch reactor being generally chosen as a reference for this purpose). From these experimental results, a reactor model may be deduced. Very often, in the laboratory but also even in industrial practice, the real reactor is not far from ideal or can be modelled successfully by simple combinations of ideal reactors this last approach is of frequent use in chemical reaction engineering. But... 

The equations (19), (20), and (21) are the generalized kinetic equations for the theoretical model under consideration. Note that these equations, because of the related definitions which have been made, bear strong resemblance to the kinetic equations for a bare homogeneous reactor. 

Chapter 3 introduced the basic concepts of scaleup for tubular reactors. The theory developed in this chapter allows scaleup of laminar flow reactors on a more substantive basis. Model-based scaleup supposes that the reactor is reasonably well understood at the pilot scale and that a model of the proposed plant-scale reactor predicts performance that is acceptable, although possibly worse than that achieved in the pilot reactor. So be it. If you trust the model, go for it. The alternative is blind scaleup, where the pilot reactor produces good product and where the scaleup is based on general principles and high hopes. There are situations where blind scaleup is the best choice based on business considerations but given your druthers, go for model-based scaleup. 

Most publications dealing with chromatographic reactors focus on theoretical issues of this very complex system. Models of different complexity were derived and used to predict the behavior of chromatographic reactors. Such models typically take into consideration different types of mass transfer, adsorption isotherms, flow profiles, and reactions. A general scheme of these models, not including the reaction, is presented in Fig. 4. There are also several review papers... 

We have presented a general reaction-diffusion model for porous catalyst particles in stirred semibatch reactors applied to three-phase processes. The model was solved numerically for small and large catalyst particles to elucidate the role of internal and external mass transfer limitations. The case studies (citral and sugar hydrogenation) revealed that both internal and external resistances can considerably affect the rate and selectivity of the process. In order to obtain the best possible performance of industrial reactors, it is necessary to use this kind of simulation approach, which helps to optimize the process parameters, such as temperature, hydrogen pressure, catalyst particle size and the stirring conditions. 

Although this modeling description refers to a general, nonadiabatic packed bed reactor with an axial thermal well, the analysis easily extends to the consideration of adiabatic reactors and those without thermal wells. These are merely subsets of the more general case. 

Chemical vapor deposition (CVD) of thin solid films from gaseous reactants is reviewed. General process considerations such as film thickness, uniformity, and structure are discussed, along with chemical vapor deposition reactor systems. Fundamental issues related to nucleation, thermodynamics, gas-phase chemistry, and surface chemistry are reviewed. Transport phenomena in low-pressure and atmospheric-pressure chemical vapor deposition systems are described and compared with those in other chemically reacting systems. Finally, modeling approaches to the different types of chemical vapor deposition reactors are outlined and illustrated with examples. 

The general equations for chemical reaction in a turbulent medium are easy to write if not to solve (2). In addition to those for velocities (U = U + uJ and concentrations (Cj = Cj + Cj), balance equations for q = A u, the segregation ( , and the dissipations e and eg can be written (3). Whatever the shape of the reactor under consideration (usually a tube or a stirred tank), the solution of these equations poses difficult problems of closure, as u S, 5 cj, cj, and also c cj, c Cj in the reaction terms have to be evaluated. The situation is even more complicated when the temperature and the density of the reacting mixture are also fluctuating. Partial solutions to this problem have been proposed. In the case of instantaneous reactions (t << Tg) the "e-quilibrium assumption" applies the mixed reactants are immediately converted and the apparent rate of reaction is simply that of the decrease of segregation, with Corrsin s time constant xs. For instance, with a stoichiometric proportion of reactants, the extent of reaction X is given by 1 - /T ( 2), a simple result which can also be found by application of the IEM model (see (33)). 

There are many types of chemical reactors which operate under various conditions, such as batch, flow, homogeneous, heterogeneous, steady state, etc. Thus, one general mathematical description which would apply to all types of reactors would be extremely complex. The general approach for reactor design, therefore, is to develop the appropriate mathematical model which will describe the specific reaction system for that particular form of reactor under consideration. For example, if the reaction system is to be evaluated for steady-state... 

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