Plug flow, mixing model

We must make several modifications to the plug-flow mixing model in order to turn it into the corresponding reactor model. First, since our primary interest will be in the steady-state behavior of the reactor, the time-dependent accumulation term need not be included and the corresponding initial condition disappears. Second, since... 

Here D, the axial dispersion (or diffusion) coefficient, is the parameter used to describe the deviations from ideal flow. If u is taken to be constant in the radial direction, the rightmost terms in equation (5-20) constitute the plug-flow mixing model and D (f Cld ) is a Fickian form of a diflusional correction term. 

The performance of fluidized-bed reactors is not approximated by either the well-stirred or plug-flow idealized models. The solid phase tends to be well-mixed, but the bubbles lead to the gas phase having a poorer performance than well mixed. Overall, the performance of a fluidized-bed reactor often lies somewhere between the well-stirred and plug-flow models. 

A similar spatial mean velocity (bulk mean velocity) is used for the plug flow reactor model. Thus, plug flow with dispersion is a natural match, where the mixing that truly occurs in any reactor or environmental flow is modeled as dispersion. This is the model that will be applied to utilize dispersion as a mixing model. 

DESIGNER also contains different hydrodynamic models (e.g., completely mixed liquid-completely mixed vapor, completely mixed liquid-vapor plug flow, mixed pool model, eddy diffusion model) and a model library of hydrodynamic correlations for the mass transfer coefficients, interfacial area, pressure drop, holdup, weeping, and entrainment that cover a number of different column internals and flow conditions. 

The tank-in-series (TIS) and the dispersion plug flow (DPF) models can be adopted as reactor models once their parameters (e.g., N, Del and NPe) are known. However, these are macromixing models, which are unable to account for non-ideal mixing behavior at the microscopic level. This chapter reviews two micromixing models for evaluating the performance of a reactor— the segregrated flow model and the maximum mixedness model—and considers the effect of micromixing on conversion. 

For a condition between complete mixing and plug flow, diffusional models such as that of Bennett and Grimm (1991) are used. For conservative work, the complete mixing model is appropriate. 

A plug-flow reactor models the conventional plug-flow behavior, assuming radial mixing but no axial dispersion. The reaction kinetics must be specified, and the model has the same limitations as the CSTR model. 

Plug Flow Reactor Model for Mixed-Phase Reactor... 

In practice, the fluid velocity profile is rarely flat, and spatial gradients of concentration and temperature do exist, especially in large-diameter reactors. Hence, the plug-flow reactor model (Fig. 7.1) does not describe exactly the conditions in industrial reactors. However, it provides a convenient mathematical means to estimate the performance of some reactors. As will be discussed below, it also provides a measure of the most efficient flow reactor—one where no mixing takes place in the reactor. The plug-flow model adequately describes the reactor operation when one of the following two conditions is satisfied ... 

Figure 7.8 Models of capillary mixing with a tissue region, (a) Complex patterns of the capillary network in a region of tissue (b) stirred-tank pharmacokinetic model (c) plug-flow pharmacokinetic model.

Figure 10.11 Agent concentrations after bolus delivery. The concentration of agent as a function of time and position within the vaginal tract was determined using a well-stirred (a) or plug-flow (b) model of mixing within the vagina.

Dynamic analysis of TBR by sitimules response technique has been succesfully applied to determine the extent of liquid axial mixing. There are number of learning and predictive models proposed in literature 2. Among them the ones having less number of parameters such as cross-flow model and axially dispersed plug flow ADPF model are the most adequate ones. A more realistic model profound for a TBR can be the one which includes the simultaneous effect of interphase and intraparticle transport rates, and the adequate hydrodynamic model, to minimize the relative importance of liquid mixing on these rates. 

Models can also be used for parameter sensitivity analysis. Due to the complexity of reaction networks and hydrodynamics, the effects of various factors on the reactor performance are complex. Model analysis provides a guiding tool for process development. The effects of PCa on the yield of acrylonitrile are shown in Fig. 30. As shown, when Pe is less than 0.05, the yield of acrylonitrile changes marginally with Pea, and the reactor can be considered well mixed. When Pea is greater than 10, the yield of acrylonitrile is almost the same as that in a plug-flow reactor. Model simulation also reveal the existence of a Pea-sensitive range... 

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). 

Sastri et al. (1983) modeled a three-phase noncatalytic but reactive system to produce industrial concentrations of zinc hydrosulfite (ZnS204) in an SBR. Three different approaches were proposed plug-flow, axial diffusion, and perfect mixing mathematical models. The authors compared the numerical solutions for the three models and noticed that the experimental data are well predicted by the axially dispersed plug-flow (diffusion) model, moderately predicted with the plug-flow model, and poorly predicted with the perfect mixing model. 

Fig. 8. Combined flow reactor models (a) parallel flow reactors with longitudinal diffusion (diffusivities can differ), (b) internal recycle—cross-flow reactor (the recycle can be in either direction), comprising two countercurrent plug-flow reactors with intercormecting distributed flows, (c) plug-flow and weU-mixed reactors in series, and (d) 2ero-interniixing model, in which plug-flow reactors are parallel and a distribution of residence times dupHcates that...

---