Complete liquid phase mixing

In this paper a reasonable classification of BCR models has been given. As criteria for such a classification the mixing behavior of the phases and the absorption-reaction regime has been used. The mathematical efforts to solve the balance equations of the various models differ largely. However, this does not present a serious problem in view of the available numerical solution methods and computational techniques. Versatile analytical solutions for a variety of rate laws could be developed for the fast and slow reaction regime provided complete liquid phase mixing can be presupposed in the last case. 

In slurry reactors, the liquid phase is completely backmixed, whereas backmixing in the gas and solid phases may not be complete. The gas-phase mixing depends on the design of the impeller and the nature of the bubbles, as well as the superficial gas velocity. The presence of gas reduces liquid-phase mixing however, an increase in gas flow increases the mixing. The mixing is also dependent upon the coalescence rate of the bubbles. 

Next, we complete the evaluation of the liquid-phase mixing equation... 

Eor ionic liquids that do not mix completely with water (and which display sufficient hydrolysis stability), there is an easy test for acidic impurities. The ionic liquid is added to water and a pEf test of the aqueous phase is carried out. If the aqueous phase is acidic, the ionic liquid should be washed with water to the point where the washing water becomes neutral. Eor ionic liquids that mix completely with water we recommend a standardized, highly proton-sensitive test reaction to check for protic impurities. 

The most widely encountered biphasic method commences with two immiscible phases, one containing the catalyst, the other the substrate or substrates, and was first recognized by Manassen in 1973 [1], Liquid phases may be immiscible if their polarities are sufficiently different, as explained in Chapter 1. The two phases are vigorously mixed allowing reaction between the catalyst and substrates to take place. When the reaction is complete, the mixing is stopped and the two phases separate. A schematic representation of such a process is illustrated in Figure 2.1. In the ideal system, the catalyst is retained in one phase ready for reuse and the product is contained in the other phase and can be removed without being contaminated by the catalyst. In certain cases, neat substrates may be used as one phase, without additional solvents. 

Intermetallic compound formation may be observed as the result from the diffusion across an interface between the two solids. The transient formation of a liquid phase may aid the synthesis and densification processes. A further aid to the reaction speed and completeness may come from the non-negligible volatility of the component(s). An important factor influencing the feasibility of the reactions between mixed powders is represented by the heat of formation of the desired alloy the reaction will be easier if it is more exothermic. Heat must generally be supplied to start the reaction but then an exothermic reaction can become self-sustaining. Such reactions are also known as combustion synthesis, reactive synthesis, self-propagating high-temperature synthesis. 

The two liquid phases are completely mixed in the agitated sections, but in the last section the two phases are allowed to separate so that the acid can be recycled and the hydrocarbon phase sent off to a distillation column for separation. 

The two films are schematically described in Fig. 5.1, in which the presence of an interfacially absorbed layer of extractant molecules is also shown. 5 and 5 represent the thickness of the organic and aqueous films, respectively. In these layers the liquid phases are considered completely stagnant (i.e., no movement of the fluids takes place in spite of the mechanical energy that is dissipated in the two-phase system to provoke mixing of the aqueous and organic phases). 

Fig. 12. Evaluation of He-Ar and C02-Ar equilibrium conditions. The concentrations are expressed in mmol/ mol on a water-free basis. As an effect of re-injection, the data points, representative of the original fluid before re-injection, move from an almost complete equilibrium in vapour phase towards to a mixed phase, where equilibrium conditions in a pure liquid phase become more and more important. (From Giggenbach Goguel 1989.)...

Figure 2.3 Free energy of mixing curves for solid and liquid phases at various temperatures (a-e) and resulting temperature-composition phase diagram for a completely soluble binary component system (f). From O. F. Devereux, Topics in Metallurgical Thermodynamics. Copyright 1983 by John Wiley Sons, hic. This material is used by permission of John Wiley Sons, Inc.

So, for this binary solution of components A and B, which mix perfectly at all compositions, there is a two-phase region at which both solid and liquid phases can coexist. The uppermost boundary between the liquid and liquid + solid phase regions in Figure 2.3f is known as the liquidus, or the point at which solid first begins to form when a melt of constant composition is cooled under equilibrium conditions. Similarly, the lower phase boundary between the solid and liquid + solid phase regions is known as the solidus, or the point at which solidification is complete upon further equilibrium cooling at a fixed composition. 

For the common case of continuous operation for both phases, where gas flows under plug-flow condition and liquid under complete mixed-flow condition, and for a reaction of the form (nonreacting liquid phase)... 

If the liquid phase is reacting and batch, the system becomes dynamic as the liquid phase concentrations change with time. To simplify the reactor model, we consider the common case of constant gas-phase concentration. Furthermore, the liquid phase is considered to be under complete mixing condition. 

Nonreacting liquid Under the assumption of complete mixing for the liquid phase and at steady-state conditions, mass transfer from gas to the liquid phase is equal to the mass transfer at the liquid-solid interface ... 

In general, the material balances and the corresponding solutions for trickle and bubble bed reactors are the same, under the assumption that the plug-flow condition holds for both phases. Of course, the appropriate correlations should be used for the estimation of mass transfer coefficients. However, in packed bubble bed reactors, the liquid-phase is frequently found in a complete mixed state, and thus some adjustments have to be made to the aforementioned models. Two special cases will be presented here. 

Continuous flow of both phases in upflow and complete mixing of phases For packed bubble columns (upflow of both gas and liquid phases), under the assumption of complete mixed flow, the backmixing model of Ramachandran and Chaudhari (1980) is applicable. The relevant equations are presented in Section 3.5.1 for the continuous flow of gas and slurry phases in complete mixed-flow conditions (slurry CSTR reactor). 

The effectiveness of a fixed-bed operation depends mainly on its hydraulic performance. Even if the physicochemical phenomena are well understood and their application in practice is simple, the operation will probably fail if the hydraulic behavior of the reactor is not adequate. One must be able to recognize the competitive effects of kinetics and fluid dynamics mixing, dead spaces, and bypasses that can completely alter the performance of the reactor when compared to the ideal presentation (Donati and Paludetto, 1997). The main factor of failure in liquid-phase operations is liquid maldistribution, which could be related to low liquid holdup in downflow operation, or other design problems. These effects could be critical not only in full-scale but also in pilot- or even in laboratory-scale reactors. 

As has been analyzed, the basic model for bubble column assumes complete mixed flow for the liquid phase and plug flow for the gas phase. The Deckwer el al. correlation (3.202) for the liquid phase and the Field and Davidson equation (3.206) for the gas phase can be used for the estimation of the dispersion coefficient. The resulting coefficients are Dll = 0.09 m2/s and DLG = 0.49 m2/s. 

In considering the case of maximum release, it is apparent that complete mixing in the liquid phase will lead to a greater release rate than that expected in cases where diffusion operates in two phases. Therefore, consider the case where both the solvent (Na) and the solute (volatile fission product) diffuse through a gas layer of constant thickness. It follows from the solution to Fick s law with appropriate boundary conditions that... 

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