Three-phase system

Three-phase reactions comprise gas-liquid-solid and gas-liquid-liquid reactions. Gas-liquid reactions using solid catalysts represent a very important class of reactions. Conventionally, they are carried out in slurry reactors, (bubble columns, stirred tanks), fluidized beds, fixed bed reactors (trickle beds with cocurrent downflow or cocurrent upflow, segmented bed, and countercurrent gas-liquid arrangements) and structured (catalytic wall) reactors. 

For gas-liquid-liquid reactions equipment similar to that used for liquid-liquid reactions are employed. The hydrodynamics in these reactors is extremely complex because of the three phases and their convoluted interactions. An example is the grazing behavior of small solid particles enhancing mass transfer at gas-liquid interfaces. The scale-up from laboratory to the production site thus poses numerous problems with respect to the reactant s mixing, temperature control (heat removal), catalyst selectivity, and its deactivation [1]. The performance of such processes can be predicted analytically only to a limited extent for reactors with well-defined flow patterns. 

Ozone is applied in three-phase systems where a selective ozone reaction, oxidation of residual compounds and/or enhancement of biodegradability is required. It can be used to treat drinking water and waste water, as well as gaseous or solid wastes. Especially in drinking water treatment full-scale applications are common, e. g. for particle removal and disinfection, while in waste water treatment sludge ozonation and the use of catalyst in AOP have been applied occasionally. Current research areas for three-phase ozonation include soil treatment and oxidative regeneration of adsorbers. Ozonation in water-solvent systems is seldom studied on the lab-scale and seems favorable only in special cases. In general, potential still exists for new developments and improvements in ozone applications for gas/watcr/solvent and gas/waler/solid systems. 

The principles and goals of ozone application in both types of three-phase systems are discussed in Section B 6.3.1. Since mass transfer may decisively influence the oxidation outcome in these complex systems, their additional resistances and effects on mass transfer is also discussed in detail in this section. In doing so, the gas/water/solvent system is used as an example for both types of system, leaving the reader to adapt the principles to the gas/ waler/solid systems by him- or herself. Examples of ozone application in both types of three-phase systems are then presented (Section B 6.3.2), with emphasis on their goals, as well us technical advantages and disadvantages, while Section B 6.3.3 provides useful advise for experimentation with three-phase systems. 

The two equations obtained by substituting Equation (10.182) for dP/dT in Equations (10.185) and (10.186) then give the dependence of the composition at the maximum or minimum with temperature or pressure, respectively. 

the change of entropy per mole of the triple-primed phase is 

We see by inspection that AS and AV refer to the formation of (x, — x i) moles of the triple-primed phase from (x i — x [) moles of the primed phase and (x i — x i) moles of the double-primed phase. 

The three Gibbs-Duhem equations can also be used to determine the change in the mole fraction of one of the phases with temperature or with pressure. We choose here to determine dx i/dT. We first eliminate dfi2 from the three equations, to obtain 

Substitution of Equation (10.196) into Equations (10.194) and (10.195) with the subsequent elimination of dP yields 

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In three-phase systems the top phase, T, is an oleic phase, the middle phase, Af, is a microemulsion, and the bottom phase, B, is an aqueous phase. Microemulsions that occur ia equiUbrium with oae or two other phases are sometimes called "limiting microemulsions," because they occur at the limits of the siagle-phase regioa. 

Aerosols. Pressurized containers to deHver aerosolized dmg products through appropriate systems of valves and actuators have been available since the 1950s (see Aerosols). Such dosage forms are used as external appHcations of lotions and creams, for oral inhalation, or for treatment of the vaginal cavity, eg, contraceptive foams. Aerosols contain two- or three-phase systems, wherein a volatile Hquid or admixture of Hquids is sealed in a... 

The use of a fluidized-bed reactor is possible only when the reactants are essentiaUy in the gaseous phase. Eluidized-beds are not suitable for middle distiUate synthesis, where a heavy wax is formed. Eor gasoline synthesis processes like the MobU MTG process and the Synthol process, such reactors are especiaUy suitable when frequent or continuous regeneration of the catalyst is required. Slurry reactors and ebuUiating-bed reactors comprising a three-phase system with very fine catalyst are, in principle, suitable for middle distiUate and wax synthesis, but have not been appHed on a commercial scale. 

The Power Factor is obtained by tbe ratio of the algebraic sum of wattmeter rettdings to voh-atnpere readings. For a three-phase system ... 

The instant (sub-transient) fault current, /jjgf, through a generator in a symmetrical three-phase system, irrespective of the condition of neutral as defined in Table 13.9 will be... 

Figure 21.7 Phaser sum of a balanced three-phase system is zero...

The reactance thus obtained can be doubled for singlephase systems. For a three-phase system the configuration of the three phases with respect to each other will play a significant role and the linear centre spacing S has to be modified to an effective or geometric mean spacing S, where... 

Figure 28.19(b) Reactance of tubular busbars for singlephase or three-phase systems at 50 Hz... 

These should normally be used in a box form for better mounting, uniformity and metal utilization. The method of determining the reactance for single- and three-phase systems is the same as for rectangular sections (Figure 28.20(a)). 

A three-phase system has three current-carrying conductors in close proximity. While the conductors of phases R and B will have an almost identical impedance, with the same skin and the proximity effects, the conductor of phase Kis under the cumulative effect of electric fields... 

Figure 28.23 Balancing of phase currents in a large three-phase system by introducing a reactor in the middle phase...

Calculation of long-term interference voltages is involved with a multiconductor problem which, in contrast to the short-term interference that derives from a one-pole grounding short circuit, in this case is related to the superposition of alternating magnetic fields of all the conductors of one or several three-phase systems as well as the ground wire. 

Electrical power systems are normally three-phase systems connected using wye or delta connections. In wye connections the three phases are connected to form a letter Y with a neutral point at the intersection of the three phases. In delta connections the three phases are connected to form a Greek letter delta (A). Delta systems do not have a neutral hence delta systems are 3-wire systems. A Y connection has a neutral and thus it is a 4-wire system. 

The more complicated separation for a three phase system is discussed by Harrison [134]. 

It should be noted once more that filled polymers may be treated as three-phase systems only nominally, since thermodynamically the interphase cannot be regarded as a phase in its own right. 

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. 

Bubble-column slurries have much in common with two-phase bubble columns containing no solid particles, which have also been studied in great detail. Reference will be made in the following to a number of those studies considered to be of relevance with respect to the analysis and design of corresponding three-phase systems containing suspended solids. 

Table 11.4 lists reactors used for systems with two fluid phases. The gas-liquid case is typical, but most of these reactors can be used for liquid-liquid systems as well. Stirred tanks and packed columns are also used for three-phase systems where the third phase is a catal5hic solid. The equipment listed in Table 11.4 is also used for separation processes, but our interest is on reactions and on steady-state, continuous flow. 

These reactors contain suspended solid particles. A discontinuous gas phase is sparged into the reactor. Coal liquefaction is an example where the solid is consumed by the reaction. The three phases are hydrogen, a hydrocarbon-solvent/ product mixture, and solid coal. Microbial cells immobilized on a particulate substrate are an example of a three-phase system where the slurried phase is catalytic. The liquid phase is water that contains the organic substrate. The gas phase supplies oxygen and removes carbon dioxide. The solid phase consists of microbial cells grown on the surface of a nonconsumable solid such as activated carbon. 

Either a negative deviation or a positive deviation is regularly observed. In any phase diagram, composition is plotted against temperature. In this way, we can see how the interactions between phases change as the temperature changes and the behavior as each solid phase then melts. Either two-phase or three phase systems can be illustrated. This is shown in the following ... 

The melting temperature of A is higher them that of B. Therefore, the melting temperature of a drops as the composition becomes richer in B. At specific temperatures on the diagram (see 1. 2.), a two-phase system appears, that of a Uquid plus that of a. Finally, as the temperature rises, the melt is homogenous and the solid, a, has melted. In the three-phase system, only the relationship between A, B and C can be illustrated on a two-dimensioncil drawing. A three-dimensional diagram would be required to show the effect of temperature as well. 

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