Reactor models, applications plug flow

Microreactors proved to be much more eflicient for the phase transfer reactions (23). The two-phase reactions proceed on the phase boundary. As a result of mass transfer coefficient estimation, it can be ascertained that the application of microtechnology for the two-phase liquid reactions promotes instantaneous mixing and intensifies the interfusion of reagents, which is not to be assumed in standard reactors. By slow reactions due to increase in interfacial area, the reaction can be shifted from diffusion to kinetic control. Thus, Dan C 1, which means that there is no mass transfer limitation and the plug flow reactor model can be used to describe such a reaction (see Section 12.2). 

Many wastewater flows in industry can not be treated by standard aerobic or anaerobic treatment methods due to the presence of relatively low concentration of toxic pollutants. Ozone can be used as a pretreatment step for the selective oxidation of these toxic pollutants. Due to the high costs of ozone it is important to minimise the loss of ozone due to reaction of ozone with non-toxic easily biodegradable compounds, ozone decay and discharge of ozone with the effluent from the ozone reactor. By means of a mathematical model, set up for a plug flow reactor and a continuos flow stirred tank reactor, it is possible to calculate more quantitatively the efficiency of the ozone use, independent of reaction kinetics, mass transfer rates of ozone and reactor type. The model predicts that the oxidation process is most efficiently realised by application of a plug flow reactor instead of a continuous flow stirred tank reactor. 

Knowledge of these types of reactors is important because some industrial reactors approach the idealized types or may be simulated by a number of ideal reactors. In this chapter, we will review the above reactors and their applications in the chemical process industries. Additionally, multiphase reactors such as the fixed and fluidized beds are reviewed. In Chapter 5, the numerical method of analysis will be used to model the concentration-time profiles of various reactions in a batch reactor, and provide sizing of the batch, semi-batch, continuous flow stirred tank, and plug flow reactors for both isothermal and adiabatic conditions. 

VL = 1 Wj), partial inversion. In the first case, N = 0 corresponds to a CSTR and N to a plug-flow reactor. It is shown that the best chemical conversion is obtained with complete flow inversion. The RTD in a Kenics mixer comprising 8 elements could be represented by this model with N = 3 and complete mixing. Static mixers could be used as chemical reactors for specific applications (reactants having large viscosity differences, polymerizations) but the published data are still very scarce and additional information is required for assessing these possibilities. 

In the literature many studies on LDPE tubular reactors are found (2-6).All these studies present models of the tubular reactor, able to predict the influence, on monomer conversion and temperature profiles, of selected variables such as initiator concentration and jacket temperature. With the exception of the models of Mullikin, that is an analog computer model of an idealized plug-flow reactor, and of Schoenemann and Thies, for which insufficient details are given, all the other models developed so far appear to have some limitations either in the basic hypotheses or in the fields of application. 

The application of the equations to chemical reactions requires the proper definition of the above quantities as well as correctly defining the transition probabilities pjj and pjk this is established in the following. It should also be noted that the models derived below for numerous chemical reactions, are applicable to chemical reaction occurring in a perfectly-mixed batch reactor or in a single continuous plug-flow reactor. Other flow systems accompanied with a chemical reaction will be considered in next chapters. 

Consequently, we see that Equation (1-11) applies equally well to our model of tubular reactors of variable and constant cross-sectional area, although it is doubtful that one would find a reactor of the shape shown in Figure 1-11 unless it were designed by Pablo Picasso. The conclusion drawn from the application of the design equation to Picasso s reactor is an imponant one the degree of completion of a reaction achieved in an ideal plug-flow reactor tPFR) does not depend on its shape, only on its total volume. 

Where n is the single parameter of the cellular model, equal to the number of cells (devices) in a cascade of perfect mixing reactors. Plug flow mode is achieved at —> o<= [1]. It is assumed [124] that if the number of cells in a reactor n > 8, calculation methods for plug flow reactors can be applied to such a device with accuracy sufficient for industrial application. 

The strategy for predicting the temporal evolution of a complex chemical reaction described in this section is based on the application of mass balances and symmetry relations between concentration dependences, starting from extreme initial values of the concentrations. The results obtained may be very useful for advanced analysis of complex chemical reactions and can be applied to the analysis of linear models of reversible reactions in plug-flow reactors and in the linear vicinity of nonlinear complex reversible reactions both in batch reactors (closed systems) and in plug-flow reactors. They can also be applied to the analysis of pseudomonomolecular models of the Langmuir-Hinshelwood-Hougen-Watson type for reversible reactions. 

The modeling methodology is shown in Figure 6.17.7 for the example of a discontinuous slurry reactor. First, the concentration profiles within the catalyst particles are calculated. This information is then coupled (for each time step) with the change of concentrations in the bulk phase (Cj t)- The link between both procedures, that is, between the bulk phase and the porous catalyst particles, is the concentration gradient of each reactant at the external particle surface. Note that this calculation is also applicable for a continuous plug flow reactor simply by using the residence time t (= x/u) instead of the reaction time, whereby x represents the axial coordinate x in a tubular reactor and u the fluid velocity. 

A successful application of the plug-flow heterogeneous model has been reported by Cappelli and coworkers (1972). Their simulation results show excellent agreement between the model predictions and the data that they obtained from a nonadiabatic industrial reactor for the synthesis of methanol from CO and Hj. The work by Dumez and Froment (1976) is another example of the application of the plug-flow heterogeneous model to an industrial reactor. 

There are numerous applications that depend on chemically reacting flow in a channel, many of which can be represented accurately using boundary-layer approximations. One important set of applications is chemical vapor deposition in a channel reactor (e.g., Figs. 1.5, 5.1, or 5.6), where both gas-phase and surface chemistry are usually important. Fuel cells often have channels that distribute the fuel and air to the electrochemically active surfaces (e.g., Fig. 1.6). While the flow rates and channel dimensions may be sufficiently small to justify plug-flow models, large systems may require boundary-layer models to represent spatial variations across the channel width. A great variety of catalyst systems use... 

An additional and important advantage of the recycle reactor, compared to the differential packed bed reactor, is that here flow uniformity through the bed is not required, so channeling is not a problem and one layer of catalyst or even separate particles can be used in the reactor. For packed bed reactors, flow nonuniformity would inhibit the application of the plug flow model. 

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