Mixing Models Reactors with Ideal Flows

In this chapter the most important operation modes of reactors are considered. Models are developed by combining simple reaction kinetics for single-phase reactions with mass balances for five ideal model reactors the ideal batch reactor the semi-batch reactor the plug flow reactor the perfectly mixed continuous reactor and the cascade of perfectly mixed reactors. For isothermal conditions, conversions can be calculated on the basis of chemical kinetics only. 

Reactor design usually begins in the laboratory with a kinetic study. Data are taken in small-scale, specially designed equipment that hopefully (but not inevitably) approximates an ideal, isothermal reactor batch, perfectly mixed stirred tank, or piston flow. The laboratory data are fit to a kinetic model using the methods of Chapter 7. The kinetic model is then combined with a transport model to give the overall design. 

Ideal flow is studied and represented using the classic dispersion or dispersed plug-flow model of Levenspiel (1962). Recall the material balance of a fixed-bed reactor with perfect radial mixing (eq. (3.285)) ... 

The perfectly stirred reactor (PSR) or continuously stirred tank reactor (CSTR) is an idealization that proves useful in describing laboratory experiments and can often be used in the modeling of practical situations. As illustrated in Fig. 16.4, gases enter the reactor with a mass-flow rate of m, a temperature of T, and a mass-fraction composition of Y . Once inside the reactor, the gases are presumed to mix instantaneously and perfectly with the gases already resident in the reactor. Thus the temperature and composition within the reactor are perfectly uniform. 

On the basis of the considered macroscopic flow pattern, the dominant circulation flows (/ c and Fc/2) subdivide the reactor into three parallel levels, where each level is then divided into Nc/3 equally sized compartments of equal volume Vc = Vr/Nc. Every compartment is modeled as a nonstationary ideal continuous stirred tank reactor, with a main inlet and outlet flow, which connects the given compartment with adjacent compartments on the same level, and secondary exchange flow rates accounting for the turbulent mixing with adjacent compartments laying on the upper and/or lower level (Fig. 7.3). 

Reaction Engineering with Idealized Models Liquid / slurry phase- complete mixing Gas phase- complete mixing or plug flow No heal transfer limitations Reactor volume for different degrees of mixing and for different values of malts transfer coctTicient Heat transfer area for different values of overall heal transfer coeflicients... 

Another model, which will not be analyzed, is the plug-flow reactor with recycle shown in Fig. 6-1. The reactor itself behaves as an ideal tubular type, but mixing is introduced by the recycle stream. When the recycle rate becomes very large, ideal stirred-tank performance is obtained, and when the recycle is zero, plug-flow operation, results. The response data on the actual reactor are used to evaluate the recycle rate and then the conversion is estimated for a plug-flow reactor with this recycle rate. 

When dispersion is complete and uniform, the contents of the vessel are perfectly mixed with respect to both phases. In that case, the concentration of the solute in each of the two phases in the vessel is uniform and equal to the concentrations in the two-phase emulsion leaving the mixing tank. This is called the ideal CFSTR (continuous-flow-stirred-tank-reactor) model, sometimes called the perfectly mixed model. Next we develop an equation to estimate the Murphree-stage efficiency for liquid-liquid extraction in a perfectly mixed vessel. 

Compartment model. A real reactor may be approximated by the combination of zones with ideal mixing patterns, as perfect mixing or plug flow, connected by streams (Figure 8.9). The volume of different zones and the corresponding flows can be optimised to fulfil some criteria of productivity or selectivity. The idea has been developed in the recent years in a much more sophisticated manner. Ideal models may be assembled in a superstructure , from which the final configuration are determined by means of optimisation techniques. This topic will be discussed later in this chapter. 

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