## 51 Introduction

Modeling and analysis of reactive flow processes is the most important task carried out by chemical reactor engineers. A brief introduction to the classical reaction engineering approach to this task is given in Chapter 1. The concepts of residence time distribution and mixedness have been used extensively in the past to gain an insight into the interaction of flow, mixing and chemical reactions. Classical analysis based on these concepts, treats the chemical reactions in a rigorous way but makes some drastic assumptions about the underlying fluid dynamics. When the characteristic time scale of chemical reactions is comparable to or lower than the characteristic time scale for mixing, effective reaction rate is a complex function of mixing (and fluid dynamics) and chemical kinetics. Several idealized models, the so-called micromixing models, have been developed to treat such situations (some of which are discussed later in this chapter). These micromixing models require information about local turbulent kinetic energy and energy dissipation rates. It is, therefore, necessary to develop fluid dynamics based models of reactive mixing to enable better understanding and control over reactive flow processes. In many practical situations, even when reaction time scales are not smaller than mixing time scales globally, local hot spots may make reaction time scales smaller than local mixing time scales. Detailed CFD-based models need to be developed to understand the formation of such local hot spots and their effect on reactive flow processes. Even for slow reactive processes, CFD-based models are needed to establish relationships between several hardware-related issues (location, orientation and design of feed nozzles, distributors, internals and so on) and reactor performance. This chapter discusses various issues concerned with modeling approaches to reactive flow processes.

In any reactive flow process, molecular diffusion, which brings molecules of different species together, is essential for chemical reactions to occur. Mixing or some form of interspecies contact is essential for mutual molecular diffusion. Reactive flow processes are therefore controlled by fluid mechanics, mixing, diffusion and chemical reactions. Any useful mathematical model of reactive flow processes should give emphasis to all contributions in proportion to the importance of their effects. The interaction of these processes may lead to different reactor performances for the same chemical reaction. The same reaction rate (kinetics) may be classified as 'slow' or 'fast' depending on the relative rates of reactions and mixing. In principle, it is possible to represent all details of the reactive flow processes by the governing equations discussed in Chapter 2. These governing equations may be solved to get all the information, from the largest macroscopic space scale to the point where the fluid assumption itself breaks down, provided all the necessary data and boundary conditions are available.

The real question is how, in practice, this information can be obtained from the governing equations considering the severe constraints imposed by finite computer memory, storage and processing speeds. Even in the case of slow reactions, solutions to reactive flow processes require special techniques because of the presence of nonlinear reaction sources. When reactions are fast, obtaining accurate solutions of even laminar reactive flow processes is extremely difficult (Oran and Boris, 1982). The presence of turbulence complicates the task of modeling reactive flow processes by an order of magnitude. The existence of widely different and interacting scales makes the task of formulating governing equations much more difficult than with laminar flow processes. It is necessary to understand the different steps occurring in turbulent reactive flow processes in order to examine the possibility of developing models suited to specific classes of flow processes. Though such models may lack universal applicability, they will still be valuable tools in modeling particular classes of reactive flow processes. The presence of more than one phase further complicates the modeling of reactive flow processes. It is necessary to judiciously combine conventional reaction engineering models developed for multiphase reactors with rigorous CFD-based models to achieve the relevant reactor engineering objectives.

In this chapter, modeling turbulent reactive flow processes and multiphase reactive processes is discussed. First, the following section discusses general aspects of mixing and defines various characteristic time scales for turbulent reactive flow processes. Different approaches to modeling single-phase reactive processes are briefly reviewed. More emphasis is given to modeling reactive flow processes in the liquid phase than in the gas phase. RANS-based phenomenological models and probability density function based models to simulate single-phase flows are then discussed in detail. In Section 5.3, modeling multiphase reactive processes is briefly discussed. Applications of these models to simulate different industrial reactors are discussed in Part III and Part IV.

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