Countercurrent Multistage Calculations

The method assumes equilibrimn stages the stage efficiency data would be required to represent an actual coliunn in terms of equilibrium stages. The stage efficiency depends on the physical properties of the liquids and the type of equipment used. It is usually estimated on the basis of experimental data or previous experience with similar columns. 

An inherent limitation in using triangular diagrams for solving liquid-liquid 

FIGURE 11.3 Equilibrium. stages in a liquid-liquid extractor. 

FIGURE 11.4 Graphical construction of extractor equilibrium stages. 

Rearranging Equation 11.3 defines the difference point A for streams and and streams and Lq. 

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Related Calculations. This basic calculation procedure can be extended to the case of countercurrent multistage extraction with reflux. A schematic of the basic extractor is shown in Fig. 9.5. For this extractor there are N stages in the extracting section, 1E to NE, and there are M stages in the stripping section, 15 to MS. 

In some cases, especially with multiple solutes and complex phase equilibria, it may be useful to perform laboratory batch experiments to simulate a continuous, countercurrent, multistage process. These experiments can be used to test/verify calculation results and determine the correct distribution of components. For additional information, see Treybal, Chap. 9 in Liquid Extraction, 2d ed. (McGraw-Hill, 1963), pp. 359-393, and Baird and Lo, Chap. 17.1 in Handbook of Solvent E raction (Wiley, 1983 Krieger, 1991). 

EXAMPLE 12.7-1. Material Balance for Countercurrent Stage Process Pure solvent isopropyl ether at the rate of, = 600 kg/h is being used to extract an aqueous solution of Lq = 200 kg/h containing 30 wt % acetic acid (/4) by countercurrent multistage extraction. The desired exit acetic acid concentration in the aqueous phase is 4%. Calculate the compositions and amounts of the ether extract and the aqueous raffinate L. Use equilibrium data from Appendix A.3. 

Although the most useful extraction process is with countercurrent flow in a multistage battery, other modes have some application. Calculations may be performed analytically or graphically. On flowsketches like those of Example 14.1 and elsewhere, a single box represents an extraction stage that may be made up of an individual mixer and separator. The performance of differential contactors such as packed or spray towers is commonly described as the height equivalent to a theoretical stage (HETS) in ft or m. 

We wish to remove acetic acid from water using pure isopropyl ether as solvent. The operation is at 293 K and 1 atm (see Table 7.2). The feed is 45 wt% acetic acid and 55 wt% water. The feed flow rate is 2000 kg/h. A multistage countercurrent extraction cascade is used to produce a final extract that is 20 wt% acetic acid and a final raffinate that is also 20 wt% acetic acid. Calculate how much solvent and how many equilibrium stages are required. 

The principle of distillation is the use of differences in volatiHties of the components to be separated. Distillation processes are usually carried out in countercurrent mode in multistage units. The differences that can be obtained in concentrations of the components in the vapor and liquid phases are determined by the vapor-liquid equihbrium (VLE). Until the 1970s reliable data for vapor-liquid equilibria could only be obtained by measurement, which, for a mixture containing more than two components, required a large number of time-consuming measurements. Advances in chemical thermodynamics have resulted in methods activity coefficient models (g models or equations of state) for the calculation of the phase-equihbrium behavior of multicomponent mixtures on the basis of binary subsystems. In the case that no information about the binary subsystems is available, predictive methods (group contribution methods) are available to allow estimation of the required phase equilibria. 

With multistage countercurrent adsorption, the receiving adsorbent phase passes from top to bottom in an adsorption column, while the carrier phase flows in the reverse direction toward the adsorbent phase (Fig. 4-16), i. e., upward. If only one adsorbate component is removed from the carrier phase, the determination of the number of theoretical separation stages A, of the adsorber and the calculation of the active adsorber height for mass transfer Z are analogous to countercurrent absorption. 

One of the most complicated systems for mass balance calculations is a multistage countercurrent washing system. Figure 16.27 shows an example of a nine-stage system, with an additional separator on the system overflow as is used to minimize product losses in washing of wheat starch. The most suitable separator in this specific application is a 10 mm hydrocyclone operated at a... 

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