Models Considering Detailed Flow Patterns

Models considering detailed flow patterns in multi-phase reactors are similar to those presented in Section 13.7 for fluidized bed reactors. The models are based on the Navier-Stokes equations for each of the moving phases. The different phases are assumed to be fully penetrating each other. Interphase mass, momentum, and energy transfer is accounted for. The methods accounting for the fluctuations in the flow field discussed in Chapter 12 for single phase flow can be extended to multi-phase flow. Application to the simulation of a bubble column reactor is illustrated in Example 14.3.6.A. 

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Fluidized Bed Reactor Models Considering Detailed Flow Patterns Catalytic Cracking of Vacuum Gas Oil... 

FLUIDIZED BED REACTOR MODELS CONSIDERING DETAILED FLOW PATTERNS... 

Example 14.3.6. A Simulation of a Bubble Column Reactor Considering Detailed Flow Patterns and a First-Order Irreversible Reaction. Comparison with Conventional Design Models... 

SIMULATION OF A BUBBLE COLUMN REACTOR CONSIDERING DETAILED FLOW PATTERNS AND A FIRST-ORDER IRREVERSIBLE REACTION. COMPARISON WITH CONVENTIONAL DESIGN MODELS... 

A laminar-flow reactor (LFR) is rarely used for kinetic studies, since it involves a flow pattern that is relatively difficult to attain experimentally. However, the model based on laminar flow, a type of tubular flow, may be useful in certain situations, both in the laboratory and on a large scale, in which flow approaches this extreme (at low Re). Such a situation would involve low fluid flow rate, small tube size, and high fluid viscosity, either separately or in combination, as, for example, in the extrusion of high-molecular-weight polymers. Nevertheless, we consider the general features of an LFR at this stage for comparison with features of the other models introduced above. We defer more detailed discussion, including applications of the material balance, to Chapter 16. 

After introducing some types of moving-particle reactors, their advantages and disadvantages, and examples of reactions conducted in them, we consider particular design features. These relate to fluid-particle interactions (extension of the treatment in Chapter 21) and to the complex flow pattern of fluid and solid particles. The latter requires development of a hydrodynamic model as a precursor to a reactor model. We describe these in detail only for particular types of fluidized-bed reactors. 

At some point in most processes, a detailed model of performance is needed to evaluate the effects of changing feedstocks, added capacity needs, changing costs of materials and operations, etc. For this, we need to solve the complete equations with detailed chemistry and reactor flow patterns. This is a problem of solving the R simultaneous equations for S chemical species, as we have discussed. However, the real process is seldom isothermal, and the flow pattern involves partial mixing. Therefore, in formulating a complete simulation, we need to add many additional complexities to the ideas developed thus far. We will consider each of these complexities in successive chapters temperature variations in Chapters 5 and 6, catalytic processes in Chapter 7, and nonideal flow patterns in Chapter 8. In Chapter 8 we will return to the issue of detailed modeling of chemical reactors, which include all these effects. 

This paper gives a comprehensive review of the up-to-date modeling of reactive separation processes in columns equipped with structured packings and consider in detail two different modeling ways. The first approach is based on the application of CFD, whereas the second one employs the idea of hydrodynamic analogy between complex and simple flow patterns. 

In choosing between these two models, one needs to consider the specific process. The use of mass transfer coefficients represents a lumped, more global view of the many process parameters that contribute to the rate of transfer of a species from one phase to another, while diffusion coefficients are part of a more detailed model. The first gives a macroscopic view, while the latter gives a more microscopic view of a specific part of a process. For this reason, the second flux equation is a more engineering representation of a system. In addition, most separation processes involve complicated flow patterns, limiting the use of Pick s Law. A description of correlations to estimate values of k for various systems is contained in Appendix B. 

The simulation results of the one-dimensional model were found to be in fair agreement with the two-dimensional model considering the chemical conversion of the reactor, as is also utilized by the Kunii-Levenspiel type of modeis [85]. Moreover, with extended conductive fluxes, fair temperature profiles can be predicted with the one-dimensional model. On the other hand, the flow pattern, i.e., the phasic fractions and gas phase velocity, were associated with the largest uncertainty in the current model. However, the internal flow details did not have signiflcant influence on the chemical process performance. Thus, the current one-dimensional model was considered to have good potentials for further CEB model developments in order to study interconnected fluidized bed reactors with a dynamic solid flux transferred between the reactor units. 

With this discussion, we have introduced the basic working characteristics of gas cyclones. In Chaps. 4, 5 and 6 we shall consider the gas flow pattern and the separation in more detail, and also models for predicting them as reported in the research literature. In Chap. 10 we will discuss how cyclone performance can best be determined from laboratory and/or plant measurements. 

The pressure and shear flow factors (

averaged quantities, such as mean pressure (p) and nominal film thickness (h). They are obtained from numerical experiments and full details of the values adopted for calculations carried out as part of the present paper may be found In (4) and (5). Only isotropic surfaces (surface pattern parameter (y) 1) were considered due to the limitation of the asperity interaction model adopted. 

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