Homogeneous Ideal Reactors

Under ideal conditions similar to homogeneous batch reactor case. 

In this chapter, we develop some guidelines regarding choice of reactor and operating conditions for reaction networks of the types introduced in Chapter 5. These involve features of reversible, parallel, and series reactions. We first consider these features separately in turn, and then in some combinations. The necessary aspects of reaction kinetics for these systems are developed in Chapter 5, together with stoichiometric analysis and variables, such as yield and fractional yield or selectivity, describing product distribution. We continue to consider only ideal reactor models and homogeneous or pseudohomogeneous systems. 

Chapter 1 reviews the concepts necessary for treating the problems associated with the design of industrial reactions. These include the essentials of kinetics, thermodynamics, and basic mass, heat and momentum transfer. Ideal reactor types are treated in Chapter 2 and the most important of these are the batch reactor, the tubular reactor and the continuous stirred tank. Reactor stability is considered. Chapter 3 describes the effect of complex homogeneous kinetics on reactor performance. The special case of gas—solid reactions is discussed in Chapter 4 and Chapter 5 deals with other heterogeneous systems namely those involving gas—liquid, liquid—solid and liquid—liquid interfaces. Finally, Chapter 6 considers how real reactors may differ from the ideal reactors considered in earlier chapters. 

In this chapter we develop the performance equations for a single fluid reacting in the three ideal reactors shown in Fig. 5.1. We call these homogeneous reactions. Applications and extensions of these equations to various isothermal and noniso-thermal operations are considered in the following four chapters. 

So far we have concentrated on homogeneous reactions in ideal reactors. The reason is two-fold because this is the simplest of systems to analyze and is the easiest to understand and master also because the rules for good reactor behavior for homogeneous systems can often be applied directly to heterogeneous systems. 

Idealized Reactor with Instantaneous Mixing. For a reactor of the second type, a homogeneous system, where the composition, temperature, and pressure is everywhere the same, Equation 11 is immediately intcgrable to... 

For p — /Pe — 0, this model reduces to the ideal PFR model, for p — 0, it reduces to the Danckwerts model, for l/Pe — 0, it reduces to the two-mode plug-flow model while for Pe — 0, it reduces to the two-mode CSTR model (discussed below). Thus, we have shown that the hyperbolic two-mode model given by Eqs. (130)—(134) has a much larger region of validity than the traditional homogeneous tubular reactor models. 

In each case of Section 4.3 the reactor models obtained on the basis of the mixing models were left in general form, with specific results for concentration or conversion versus reactor size depending on the type of rate law to be used. In the following we shall derive a number of expressions for particular rate laws which relate conversion, reactor size, and residence time for the particular case of homogeneous, isothermal ideal reactors. 

This partial differential equation is deterministic by nature. In practice, however, many hydrodynamic phenomena (e.g., transition from laminar to turbulent flow) have chaotic features (deterministic chaos [Stewart 1993]). The reason for this is that the Navier-Stokes equation assumes a homogeneous ideal fluid, whereas a real fluid consists of atoms and molecules. Today highly developed numerical flow simulators (computational fluid dynamics, CFD) are available for solving the Navier-Stokes equation under certain boundary conditions (e.g.. Fluent Deutschland GmbH). These even allow complex flow conditions, including particle, droplet, bubble, plug, and free surface flow, as well as multiphase flow such as that foundin fluidized-bed reactors and bubble columns, to be treated numerically [Fluent 1998]. 

The simplest fixed bed reactor model formulation is the pseudo-homogeneous ideal model, by which ... 

The Reynolds and Peclet numbers indicate a pseudo-homogeneous reactor behavior, close to an ideal reactor. In such a condition, one can calculate the catalyst mass using the equations of an ideal PFR. 

The work is organized in two parts in the first part kinetics is presented focusing on the reaction rates, the influence of different variables and the determination of specific rate parameters for different reactions both homogeneous and heterogeneous. This section is complemented with the classical kinetic theory and in particular with many examples and exercises. The second part introduces students to the distinction between ideal and non-ideal reactors and presents the basic equations of batch and continuous ideal reactors, as well as specih c isothermal and non-isothermal systems. The main emphasis however is on both qualitative and quantitative interpretation by comparing and combining reactors with and without diffusion and mass transfer effects, complemented with several examples and exercises. Finally, non-ideal and multiphase systems are presented, as well as specific topics of biomass thermal processes and heterogeneous reactor analyses. The work closes with a unique section on the application of theory in laboratory practice with kinetic and reactor experiments. 

First, let us analyze ideal reactors of constant reaction volume in which a stoichiometrically single reaction takes place without explicitly taking into account the presence of a solid catalyst, that is, we are assuming the reaction is not catalyzed or is homogeneously catalyzed. 

Critical Experiments for the Preliminary Design of the Argonne High Flux Reactor, Part B, J. O. Juliano, C. N. Kelber, and K, E, Plumlee (ANL), Theoretical neutron flux-dls-trlbutlon of a homogenized idealization of the Argonne High Flux Critical (AHFCR) core C-1 was made and com pared with the experimental measurements. 

Homogeneous Non-Ideal Reactors 3.2.1 Non-Ideal Reactors versus Ideal Reactors... 

Non-ideality in a homogeneous reactor refers to any kind of deviation from the fluid mixing pattern defined for ideal reactors (ideal CSTR and ideal PFR). In reality, all the reactors are non-ideal. In order to evaluate the performance of any reactor (i.e. extent of conversion achieved in a reactor), it is necessary to diagnose the non-ideality in the reactor. 

Equations (19) and (22) are theoretically pleasing but their practical utility is limited. In a troubleshooting problem eq. (22) would allow us to recover E(s) of the system but we rarely deal with a homogeneous system of linear reactions I In a design problem we often do not know the actual RTD and are trying to design an ideal reactor. If the RTD can be predicted based on a nonideal reactor model, then species concentrations can also be calculated based on that model. Then eq. (22) represents at best only a mathematical short-cut I... 

Experiments in open stirred reactors have become common place these days for the study of time-dependent phenomena. By dint of the usual hypothesis of ideality, i.e. that the medium is instantaneously of homogeneous composition ( ), the concentrations are space-independent functions, whence a considerable simplification of the equations describing the behaviour. The time variations of the concentrations within an ideal reactor (as in the scheme of fig. 1), can thus be expressed simply with the set of autonomous differential equations (8) ... 

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