Modeling three-phase systems

One goal of our experimental program with the bench-scale unit was to develop the necessary correlations for use in the ultimate design of large commercial plants. Because of the complexity inherent in the three-phase gas-liquid-solid reaction systems, many models can be postulated. In order to provide a background for the final selection of the reaction model, we shall first review briefly the three-phase system. 

It seems probable that a fruitful approach to a simplified, general description of gas-liquid-particle operation can be based upon the film (or boundary-resistance) theory of transport processes in combination with theories of backmixing or axial diffusion. Most previously described models of gas-liquid-particle operation are of this type, and practically all experimental data reported in the literature are correlated in terms of such conventional chemical engineering concepts. In view of the so far rather limited success of more advanced concepts (such as those based on turbulence theory) for even the description of single-phase and two-phase chemical engineering systems, it appears unlikely that they should, in the near future, become of great practical importance in the description of the considerably more complex three-phase systems that are the subject of the present review. 

Thus a quantitative model of the structure would probably require to consider a third phase (three-phase system). 

Indirectly related to the cell models of this section is the work of Davis and Brenner (1981) on the rheological and shear stability properties of three-phase systems, which consist of an emulsion formed from two immiscible liquid phases (one, a discrete phase wholly dispersed in the other continuous phase) together with a third, solid, particulate phase dispersed within the interior of the discontinuous liquid phase. An elementary analysis of droplet breakup modes that arise during the shear of such three-phase systems reveals that the destabilizing presence of the solid particles may allow the technological production of smaller size emulsion droplets than could otherwise be produced (at the same shear rate). 

In our discussion of surface reactions in Chapter 11 we assumed that each point in the interior of the entire catalyst surface was accessible to the same reactant concentration. However, where the reactants diffuse into the pores within the catalyst pellet, the concentration at the pore mouth will be higher than that inside the pore, and we see that the entire catalytic surface is not accessible to the same concentration. To account for variations in concentration throughout the pellet, we introduce a parameter known as the effectiveness factor. In this chapter we will develop models for diffusion and reaction in two-phase systems, which include catalyst pellets and CVD reactors. The types of reactors discussed in this chapter will include packed beds, bubbling fluidized beds, slurry reactors, and trickle beds. After studying this chapter you will be able to describe diffusion and reaction in two- and three-phase systems, determine when internal pore diffusion limits the overall rate of reaction, describe how to go about eliminating this limitation, and develop models for systems in which both diffusion and reaction play a role (e.g., CVD). 

Rigorous distillation models can be used to model absorber columns, stripper columns, refluxed absorbers, three-phase systems such as extractive distillation columns, many possible complex column conflgurations, and columns that include... 

The theory for BOHLM is developed for flat thin uncharged symmetric membranes without variation in porosity and pore sizes across the membrane thickness. To develop a three-phase system model [1,2], the transport model simpUfication analysis, developed by Hu [68] for the two-phase system, is used. Titanium(IV) was chosen, as an example for transport model verification, because of the extensive experimental data available on Uquid-Uquid extraction and membrane separation [1, 2, 64, 65] and for its extraction double-maximum acidity dependence phenomenon [63]. The last was observed for most extractant famUies basic (anion exchangers), neutral (complexants), and acidic (cation exchangers). So, it is possible to... 

The application of mercury is widespread in agriculture, for example, as insecticide in seed treatment, and different types of industry [60]. A promising method for the removal and preconcentration of mercury from wastewater has been the application of liquid membranes containing calixarenes as carriers [61]. A three-phase system for the extraction of Hg from industrial wastewater has been reviewed by Ersoz [62]. Models and implication of theoretical conclusions are presented. 

A different design for three-phase systems was proposed by Kobayashi et al. [120]. The authors immobilized a palladium catalyst on the glass wall of a capillary and operated the microchannel reactor such that an annular flow pattern was obtained, which is characterized by a liquid film on the wall (Figure 16). The hydrogenation of benzalacetone was used as a model reaction to demonstrate the general applicability of this concept. The authors could achieve an effective interaction between H2, substrate, and the palladium catalyst as a result of the large interfacial area and the short diffusion path in the narrow space. 

When carried out in a kerosene medium, the carbonation occurs in a three-phase system in which CO2 first dissolves in the liquid and then diffuses to the solid naphthenate as a particulate suspension in the liquid. Because the solid is insoluble in kerosene, reaction occurs only in the solid phase. Using the data of Phadtare and Doraiswamy (1965, 1969), reproduced in Table 17.11, formulate a model to predict the conversion of sodium naphthenate to BON acid as a function of time. 

The selectivity displayed for F-relative to other halide anions encouraged Sessler and coworkers to investigate whether sapphyrin would act as a fluoride anion carrier in a model three-phase H2O-CH2CI2-H2O bulk liquid membrane transport system.When two aqueous solutions with different fluoride anions concentrations, were separated by a dichloromethane solution, slow transfer of fluoride anions from the more concentrated... 

The composition of the liquid phase co-existing with the solid, as it has been mentioned above, is of special importance in the hydration process. This system is far from the equilibrium and at the usual water content on the level 33 % approximately (w/c=0.5), there are the micro-areas of different composition. Simultaneously, the diffusion becomes more and more difficult as the hydrates are formed. The gradients of concentrations appear, as well as the differences of temperature between the particular micro-areas. Therefore the image of the process becomes more sophisticated. To simplify this, we take into account the model, three-component systems CaO-Si02-H20 or Ca0-Al203-H20 which correspond to the calcium silicate or calcium aluminate hydration. However, the processes occurring in these simplified systems are complex, as one could conclude from the aforementioned considerations. 

Monomer extraction from latex products involves mass transfer in a heterogeneous system. Three phases have to be considered the polymer particles, the aqueous phase, and the CO2 phase (see Fig. 14.3). In this work, the film model has been used to describe the diffusion of MMA in this three-phase system, for which the following assumptions have been made ... 

In order to design an extraction unit, the rate-limiting step in the extraction process has to be determined. As explained in Section 14.4 and Fig. 14.3, the film model can be used to describe extraction in the three-phase system. The overall mass transfer flux of monomer in this extraction process is given by Eq. (14)... 

For bulk materials, all techniques based on structure-insensitive properties, as described in this section and elsewhere, yield closely similar data. The crystallinity model is thus a valid defect concept to describe structure-insensitive properties of semicrystalline polymers. It breaks down for three-phase systems, consisting, for example, of a crystalline phase, a mobile amorphous phase, and a rigid-amorphous fraction (see Chap. 6). In addition, one does not expect valid answers for structure-sensitive properties. 

Three phase systems have been the main focus of activities in chemical reaction engineering, and the many novel aspects of them are too numerous to cover here, hence only a few examples will be referenced. In the case of gas-1iquid-sparingly soluble solid, it has been demonstrated that particles substantially smaller than the diffusion film thickness of film model can enhance the specific rates of mass transfer if the reaction is sufficiently fast (45). Work in this area has been persistently pursued by Sada and coworkers (46,47). Recently Alper et al. (24) has pointed out and demonstrated that in catalytic slurry reactors similar enhancement can be observed if the catalyst particles are sufficiently small. There is however some dispute on the order of magnitude of the enhancement (48,49). Another aspect is complex reactions and in the case of slurry reactors the product distribution may well depend on the degree of diffusional resistance (50). Dynamic methods have been ingeniously employed to obtain physicochemical parameters in slurry reactors (51). 

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