Continuous equilibrium stage extraction

Here the extraction is carried out continuously in a single, perfectly mixed, extraction stage as shown in Fig. 3.30. It is assumed that the outlet flow concentrations, X and Yj, achieve equilibrium and that density variations are negligible. 

Following an initial transient, the extractor will achieve a steady state operating condition, in which the outlet concentrations remain constant with respect to time. 

At steady state, the quantity of solute entering the extractor is equal to the quantity of solute leaving. A steady-state balance for the combined two-phase system gives 

L and G are the volumetric flow rates of the heavy and the light phases, respectively, Xq and Yq are the respective inlet solute concentrations of the two phases, Xi and Yi are the respective outlet solute concentrations. 

A simple substitution of the value Yj in the balance equation enables the steady-state concentration Xj to be determined, where 

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Figure 1. Continuous equilibrium stage extraction. Solute balances for each phase give ...

While offering a more inherently realistic method of solution, however, the technique may cause some additional problems in the numerical solution, since high values of Kl can lead to increased stiffness in the differential equations. Thus in using this technique, a compromise between the approach to equilibrium and the speed of numerical solution may have to be adopted. Continuous single-stage extraction is treated in the simulation example EQEX. Reaction with integrated extraction is demonstrated in simulation example REXT. 

Figure 3.35. Information flow diagram for the continuous equilibrium extraction stage.

The extraction is represented by a single perfectly mixed constant volume, continuous flow equilibrium stage. This may actually consist of separate mixer-settler units. 

The important question for the designer of a continuous countercurrent extraction process is how many equilibrium stages are needed, given the flow rates and inlet and outlet concentrations A simple graphical procedure is possible for a single-solute extraction when the two... 

Liquid-liquid extraction columns may be designed in three different ways (1) as a collection of equilibrium stages, (2) as a continuous differential contactor with mass transfer, or (3) using purely kinetic models. The first two methods are more commonly used (particularly the first) and, when correctly and carefully performed, they give essentially the same results. The latter method, design... 

Estimate the diameter and height of an RDC to extract acetone from a dilute toluene-acetone solution into water at 293 K. The flow rates for the dispersed organic and continuous aqueous phases are 12,250 and 11,340 kg/h, respectively. The density of the organic phase is 858 kg/m3 and that of the aqueous phase is 998 kg/m3. For the desired degree of separation, 12 equilibrium stages are required. 

Since separations are ubiquitous in chemical plants and petroleum refineries, chemical engineers must be familiar with a variety of separation methods. We will first focus on some of the most common chemical engineering separation methods flash distillation, continuous column distillation, batch distillation, absorption, stripping, and extraction. These separations all contact two phases and can be designed and analyzed as equilibrium stage processes. Several other separation methods that can also be considered equilibrium stage processes will be briefly discussed. Chapters 17 and 18 e5q)lore two inportant separations—membrane separators and adsorption processes— that do not operate as equilibrium stage systems. 

If the distribution equilibrium between the raffinate and extract phase is reached, with continuous and stagewise extraction in each extraction stage, the compositions of the raffinate phases i ], > R and ex-... 

Should the extraction be continued until substantial equilibrium between the phases occurs, then the material balance equation (7) shows that the concentrations in the liquids move along line AB extended until the equilibrium curve is reached at C, giving rise to the ultimate equilibrium concentrations xe and ye. A fractional stage efficiency E may then logically be defined (T3) as the ratio of the number of moles N of solute actually transferred in an extraction to Ne, the moles which would be transferred should equilibrium be reached ... 

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