Comprehensive mixing models

In this work, a comprehensive kinetic model, suitable for simulation of inilticomponent aiulsion polymerization reactors, is presented A well-mixed, isothermal, batch reactor is considered with illustrative purposes. Typical model outputs are PSD, monomer conversion, multivariate distritution of the i lymer particles in terms of numtoer and type of contained active Chains, and pwlymer ccmposition. Model predictions are compared with experimental data for the ternary system acrylonitrile-styrene-methyl methacrylate. 

The solid phase of a batch bed can either be fixed, moving or mixed, whereas continuous fuel beds can either be moving or mixed. A successful and comprehensive mathematical model needs to consider these three modes of fuel-bed movement. There is a close analogy between the fluid-solid dynamics, where we have proposed fixed, moving, and mixed, and the fluid dynamics where the corresponding terminology is stagnancy, laminar flow and turbulent flow, respectively. 

Although instrumentation capabilities are continually improving, the limitation of experimental modeling that dynamic similarity can not be obtained is absolute, imposed by the physics of the system. However, computational modeling is continually improving and is indeed the great hope for future comprehensive crystallizer mixing models. 

Coupling CFD with one of the much simpler zone models is potentially particularly valuable. It is difficult and time consuming to add the additional complexity of mixing, heat and mass transfer, and dynamic population balance modeling to the CFD model, plus it makes the CFD model very slow. Sufficient accuracy may be achievable for many applications from applying the population balance modeling to the simpler zone models, although accuracy will be limited because the effects of the particle concentration, distribution and PSD will not be fed back to the transport models. Alternately, comprehensive CFD models can be used to understand the flow and its variation for a limited number of conditions, but simpler zone models may be used for application of the model where speed and convenience are important and detailed accuracy is not, e.g., process control. 

Ah6n VR, Costa JEF, Monteagudo JEP, Fontes CE, Biscaia JEC, Lage PLC. A comprehensive mathematical model for the Fischer-Tropsch synthesis in well-mixed slurry reactors. Chem. Eng. Sci. 2005 60 677-694. 

Before we continue om discussion further, let us cite references to the contributions of Crtrl (1963) and Spiehnan and Levertspiel (1965) to the CD model. In France, the book by Villermaitx (1993) is an authority on the subject matter. A comprehensive review of mixing models is given in the book by Fox, definitely oriented toward their implementation in computatiorral models. 

The models mentioned above were developed under the assumption of isothermal conditions. However, frictional heating is an important factor that has to be taken into account in order to establish a more comprehensive model of mixed lubrication. 

Research into cluster catalysis has been driven by both intrinsic interest and utilitarian potential. Catalysis involving "very mixed -metal clusters is of particular interest as many established heterogeneously catalyzed processes couple mid and late transition metals (e.g., hydrodesulfurization and petroleum reforming). Attempts to model catalytic transformations arc summarized in Section II.F.I., while the use of "very mixed -metal clusters as homogeneous and heterogeneous catalysis precursors are discussed in Sections I1.F.2. and I1.F.3., respectively. The general area of mixed-metal cluster catalysis has been summarized in excellent reviews by Braunstein and Rose while the tabulated results are intended to be comprehensive in scope, the discussion below focuses on the more recent results. 

Several models have been proposed to account for reaction in the freeboard. Yates and Rowe (1977) developed a simple model based upon complete mixing of particles in the freeboard, coupled with either BMF or PF of the freeboard gas. Two model parameters are the rate of particle ejection from the bed, and the fraction of wake particles ejected. Kunii and Levenspiel (1990 1991, pp. 305-307) proposed a model of freeboard reaction which accounts for the contact efficiency of the gas with the solid, and the fraction of solid in the freeboard. A comprehensive freeboard entrainment model is... 

Percolation models differ from the zone-refining model essentially by the absence of mixing in the liquid, giving the liquid position-dependent properties. A simplified account of these models was described in Chapter 8. We will now provide a reasonably comprehensive account which may prove useful to the demanding reader, and then examine some properties of the chromatographic effect in a simple configuration. Let

open volume porosity of the medium, pso, and pliq the density of the solid matrix and melt, respectively, vliq the liquid velocity relative to the matrix, and Cso, and CHq the concentration of element i in the matrix and melt, respectively. Let us rewrite equation (8.3.14) as... 

So far, we have seen that deviation from ideal behavior may affect one or more thermodynamic magnitudes (e.g., enthalpy, entropy, volume). In some cases, we are able to associate macroscopic interactions with real (microscopic) interactions of the various ions in the mixture (for instance, coulombic and repulsive interactions in the quasi-chemical approximation). In practice, it may happen that none of the models discussed above is able to explain, with reasonable approximation, the macroscopic behavior of mixtures, as experimentally observed. In such cases (or whenever the numeric value of the energy term for a given substance is more important than actual comprehension of the mixing process), we adopt general (and more flexible) equations for the excess functions. 

The OZIPR model is described in Appendix III. It is a box model that has comprehensive chemical submodels that lump organics in two different ways. It allows for variation of meteorology through time-dependent mixing heights, temperatures, etc. 

Many correlations for mixing time (see above) have been proposed in the literature (142). One of the most comprehensive treatments of this problem was published by Khang and Levenspiel (143), on the basis of a recycle model 9m is defined as the time constant for the exponential decrease of pseudo-periodic oscillations after a pulse injection of tracer in a batch stirred reactor. 

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