Ideal Chemical Reactors

Chemical reactions occur almost everywhere in the environment however, a chemical reactor is defined as a device properly designed to let reactions occur under controlled conditions toward specified products. To a visual observation, chemical reactors may strongly differ in dimensions and structure nevertheless, in order to derive a mathematical model for their quantitative description, essentially two major features are to be considered the mode of operation and the quality of mixing. 

Therefore, the analysis of the main object of this book, namely, the batch chemical reactor, can start by considering the different ideal chemical reactors. In fact, ideal reactors are strongly simplified models of real chemical reactors [10], which however capture the two major features mentioned above. These models can be classified according to the mode of operation (i.e., discontinuous vs. continuous) and to the quality of mixing (i.e., perfect mixing vs. no mixing). The three resulting ideal reactors are sketched in Fig. 2.1. 

The discontinuous stirred reactor (Batch Reactor, BR, Fig. 2.1(a)) corresponds to a closed thermodynamic system, whereas the two continuous reactors (Continuous Stirred Tank Reactor, CSTR, Fig. 2.1(b), and Plug Flow Reactor, PFR, Fig. 2.1(c)) 

The two extreme hypotheses on mixing produce lumped models for the fluid dynamic behavior, whereas real reactors show complex mixing patterns and thus gradients of composition and temperature. It is worthwhile to stress that the fluid dynamic behavior of real reactors strongly depends on their physical dimensions. Moreover, in ideal reactors the chemical reactions are supposed to occur in a single phase (gaseous or liquid), whereas real reactors are often multiphase systems. Two simple examples are the gas-liquid reactors, used to oxidize a reactant dissolved in a liquid solvent and the fermenters, where reactions take place within a solid biomass dispersed in a liquid phase. Real batch reactors are briefly discussed in Chap. 7, in the context of suggestions for future research work. 

Those simplified models are often used together with simplified overall reaction rate expressions, in order to obtain analytical solutions for concentrations of reactants and products. However, it is possible to include more complex reaction kinetics if numerical solutions are allowed for. At the same time, it is possible to assume that the temperature is controlled by means of a properly designed device thus, not only adiabatic but isothermal or nonisothermal operations as well can be assumed and analyzed. 

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Figure 3-8 Sketch of ideal chemical reactors in series with Cati, the product Irattt reactor n, which i s also the feed into reactor n +1 ...

As discussed in Sect. 2.1, physical and mathematical models of ideal chemical reactors are based on two very simplified fluid dynamic assumptions, namely perfect mixing (BR and CSTR) and perfect immiscibility (PFR). On the contrary, in real tank reactors the stirring system produces a complex motion field made out of vortices of different dimensions interacting with the reactor walls and the internal baffles, as schematically shown in Fig. 7.2(a). As a consequence, a complex field of composition and temperature is established inside the reactor. 

Fig. 8.1 Types of ideal chemical reactors (Levenspiel, 1996). The batch recirculation reactor system consists of a vessel of total volume V and a reactor of a specified volume Vr, CSTR continuously stirred tank reactor.

This volume describes a methodology to describe the operations ideal chemical reactor. 

Droplet-based two-phase flows offer controlled picoliter or femtoliter volumes of droplets (Fig. 7a) which are almost ideal chemical reactors and therefore have been utilized in emulsification and encapsulation, microreaction, synthesis, mixing, and bioassay [7],... 

Ideal chemical reactors can be linked in many different ways so that the output of one reactor becomes the input of the next so that the reactions occur in stages. Staged reactor models can be adapted to simulate most, if not all, real-world scenarios. This means that the behavior of complex interacting systems can be simplified to combinations of simple reactors, each of which is relatively easy to model. Ideal chemical reactor models can be applied as a first approximation to most natural situations and the concept easily leads to mathematical descriptions of those situations. For example. 

Figure 4.1. The three types of ideal chemical reactors. The ideal batch reactor (BR) is well mixed but closed to mass transfer. The ideal mixed flow reactor (MFR) is well mixed and subject to continuous mass transfer.The fluid in an ideal plug flow reactor (PFR) moves as slugs, which are closed to mass transfer with each other and therefore act as batch reactors moving through space.

Tracer behavior is different in each of the ideal chemical reactors, so the first step in developing a tracer kinetics model is to decide which reactor type best simulates the real situation and which kind of tracer dosing has occurred. If the amount and timing of tracer introduction is known, a forward model can be developed. If the amount and timing of tracer detected is known, an inverse model can be produced. The equations derived in the following section use concentration imits of mg/L because these units are typical of field studies. For laboratory experiments the models would use molal concentration units. The mass (M) variables would be replaced by mole quantities ( ). The volume variables (V) would be replaced by mass of water (M) and the flow rate (0 would have units of kg/sec. 

Rate measurements are best performed with experiments that closely approximate the behavior of ideal chemical reactors. The concept of ideal chemical reactors is well developed (Aris, 1989 Levenspiel, 1972a, 1972b Rimstidt and Newcomb, 1993), so that the methods of extracting rates from the experimental data are relatively simple and reliable. Chemical reactors can have many different design elements, some of which are illustrated in Figure 4.2, but as long as their behavior approximates an ideal chemical reactor the following analysis methods are applicable. 

Before studying nonideal reactors and other generalizations, we will first analyze two types of ideal chemical reactors, the CSTR and the PFR. We will assume that ... 

Set up and solve material balance equations around an ideal chemical reactor. 

There are in general several steps of refinement to model a gasification system. Zero-dimensional models show the lowest complexity, and rely on empirical correlations or thermodynamic equilibrium calculations. The next step is a onedimensional model that usually requires kinetic expressions either to resolve the space or time coordinate using idealized chemical reactor models. Approaching two- or three-dimensional calculations provokes the use of computational fluid dynamics (CFD) that may incorporate either equiUbriiun or kinetics-based turbulence chemistry interactions. Each step of modeling adds significant complexity and calculation time. 

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