Two-solute batch extraction

Again, these functional relationships should ideally be available in an explicit form in order to ease the numerical method of solution. Two-solute batch extraction is covered in the simulation example TWOEX. 

TWOEX - Two-Solute Batch Extraction with Interacting Equilibria... 

COMPLEX TWO-SOLUTE BATCH EXTRACTION WITH INTERACTING EQUILIBRIA... 

Batch extraction is the simplest and most useful method, the two phases being shaken together in a separatory funnel until equilibrium is reached and then allowed to separate into two layers. If the distribution ratio is large, a solute may be transferred essentially quantitatively in one extraction, otherwise several may be necessary. The optimum conditions for quantitative extraction have been discussed on p. 57. If several extractions are required, it is advantageous to use a solvent more dense than water, e.g. carbon tetrachloride or chloroform, so that the aqueous phase can be left in the separatory funnel until the procedure is complete. 

In the single-stage batch process illustrated in Figure 13.1, the solvent and solution are mixed together and then allowed to separate into the two phases—the extract E containing the required solute in the added solvent and the raffinate R, the weaker solution with some associated solvent. With this simple arrangement mixing and separation occur in the same vessel. 

Equation 6.2.3 has exactly the same form as Eq. 5.1.3 for binary systems. This means that we may immediately write down the solution to a multicomponent diffusion problem if we know the solution to the corresponding binary diffusion problem simply by replacing the binary diffusivity by the effective diffusivity. We illustrate the use of the effective diffusivity by reexamining the three applications of the linearized theory from Chapter 5 diffusion in the two bulb diffusion cell, in the Loschmidt tube, and in the batch extraction cell. 

A solution of this ester (8.35 g, 21.6 mmol, 1.0 equivalents) in tetrahydrofuran (THF 100 mL) was cooled to 0 °C, and pyridinium p-toluenesulfonate (PPTS, 500 mg, 2.00 mmol, 0.1 equivalents) and then 2,2-dimethoxypropane (20.0 mL, 163 mmol, 5.9 equivalents) were added. The cold bath was removed and the mixture was stirred at room temperature for 48 h, quenched with saturated aqueous NaHCOs solution, and extracted with EtOAc. The combined organic layers were washed with brine, dried (Na2SO4), filtered, and concentrated. Purification by chromatography on SiO2 (3% ethyl acetate and 1% triethylamine in hexanes, and then 100% EtOAc) afforded the acetonide and a small amount of starting diol which was re-subjected and purified as above. The two batches were combined to afford naphthalene-2-carboxylic acid 2-[(4S)-2,2- dimethyl-[l,3]dioxan-4-yl]-2-methylpropyl ester (9.140 g, 97%) as a clear colorless syrup. Reference Wipf, P Graham, T. H.,/. Am. Chem. Soc. 2004,126, 15346-15347. 

Table 7. Solute mass balances for batch extraction through membranes in a two-Uquid phase system (adapted from [99,155,189]). Cy, and C stand for the hulk concentration in the aqueous and organic phases, respectively, A is the area for mass transfer, t is the time of operation, and m is a solute partition coefficient...

For batch extraction between the two liquid phases, and through the membrane, the time course of solute concentration can be calculated by solute mass balances to both aqueous and organic phases, assuming they are perfectly mixed. These are summarized in Table 7. 

D20. The aqueous two-phase system in Example 13-2 will be used in a batch extraction. We have 5.0 kg of PEG solution containing protein at mass fraction Xp. We will use 4.0 kg of pure dextran solution to extract the protein from the solution. Equilibrium data are in Example 13-2. 

In a counter-current batch process, portions of aqueous phase containing the solute are extracted with successive portions of organic solvent phase in such a manner that the fresh solvent always extracts from the weakest aqueous phase, and the most concentrated solvent extracts from the solute-rich aqueous feed. Similarly, the aqueous solutions of intermediate solute concentration are extracted by organic solvent which already has a moderate solute concentration. The situation is illustrated by Fig. 4.4(a). A stream of solvent portions passes from right to left with respect to a stream of initially solute-rich aqueous portions. At each contact of two new portions, it is necessary to mix throughly to allow solute to pass from one phase to the other and then to settle and separate again, into their separate phases. 

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