Countercurrent extraction equilibrium stages

A countercurrent multistage extraction system is shown below, which is to be modelled as a cascade of equilibrium stages. 

FIVE STAGE COUNTERCURRENT EXTRACTION CASCADE EQUILIBRIUM STAGE MODEL... 

Five stage countercurrent extraction cascade with backmixing Equilibrium stage model... 

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... 

Calculations of the relations between the input and output amounts and compositions and the number of extraction stages are based on material balances and equilibrium relations. Knowledge of efficiencies and capacities of the equipment then is applied to find its actual size and configuration. Since extraction processes usually are performed under adiabatic and isothermal conditions, in this respect the design problem is simpler than for thermal separations where enthalpy balances also are involved. On the other hand, the design is complicated by the fact that extraction is feasible only of nonideal liquid mixtures. Consequently, the activity coefficient behaviors of two liquid phases must be taken into account or direct equilibrium data must be available. In countercurrent extraction, critical physical properties such as interfacial tension and viscosities can change dramatically through the extraction system. The variation in physical properties must be evaluated carefully. 

Fora countercurrent extraction column with no discrete stages (or for processes operated within a diffusion-controlled regime far from equilibrium), performance is well modeled by the Colburn equation, where... 

In a chemical processing plant, the acetone concentration in a water-acetone solution stream must be lowered. Acetone extraction using vinyl trichloride (VTC) as the solvent is considered, and the required number of equilibrium stages in a countercurrent liquid-liquid extraction system must be determined. Equilibrium relations were developed based on available data at the expected operating conditions. The extract and raffinate phase and tie-line equations are expressed in terms of the extract component (acetone) and raffinate component (water) weight fractions in each phase. 

A 1000 kg/hr stream of a solution containing 30 wt% acetic acid and 70 wt% water is to be fed to a countercurrent extraction process. The solvent is 99% isopropyl ether and 1% acetic acid, and has an inlet flowrate of 2500 kg/hr. The exiting raflflnate stream should contain 10 wt% acetic acid. The equilibrium data are the same as given in Table 5.1 for the cross-flow Example 5.1. Find the number of equilibrium-limited stages required. 

The calculation of the concentration of extractable components in a countercurrent cascade of equilibrium solvent extraction stages is first developed for the simple countercurrent extraction section of Fig. 4.3. The theory is then extended to the extracting-scrubbing system of Fig. 4.4 for fractional extraction and is illustrated by a numerical calculation for the separation of zirconium from hafnium, using TBP in kerosene as solvent. 

An aqueous acetic acid solution flows at the rate of 1000 kg/hr. The solution is 1.1 wt% acetic acid. It is desired to reduce the concentration of this solution to 0.037 wt% acetic acid by extraction with 3-heptanol at 298 K. For practical purposes, water and 3-heptanol are inmiscible. The inlet 3-heptanol contains 0.02 wt% acetic acid. An extraction column is available which is equivalent to a countercurrent cascade of 35 equilibrium stages. What solvent flow rate is required Calculate the composition of the solvent phase leaving the column. For this system and range of concentrations, equilibrium is given by (Wankat,1988)... 

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. 

Example 10.3. As shown in Fig. 10.22, a countercurrent extraction cascade equipped with a solvent separator to provide extract reflux is used to separate methylcyclopentane A and n-hexane C into a final extract and raffinate containing 95wt% and 5wt% A, respectively. The feed rate is 1000 kg/hr with 55 wt% A, and the mass ratio of aniline, the solvent S, to feed is 4.0. The feed contains no aniline and the fresh solvent is pure. Recycle solvent is also assumed pure. Determine the reflux ratio and number of stages. Equilibrium data at column temperature and pressure are shown in Fig. 10.23. Feed is to enter at the optimum stage. 

One hundred kilogram-moles per hour of an equimolar mixture of benzene B, toluene T, n-hexane C6, and n-heptane C7 is to be extracted at 150°C by 300 kgmole/hr of diethylene glycol (DEG) in a countercurrent liquid-liquid extractor having five equilibrium stages. Estimate the flow rates and compositions of the extract and raffinate streams by the group method. In mole fraction units, the distribution coefficients for the hydrocarbon can be assumed essentially constant at the following values. 

With X = 113 and = 2.4, (1-19) gives Xj = 0.0364, which corresponds to 89.08% overall extraction of p-dioxane. In general, for N countercurrent equilibrium stages, similar combinations of stage equations with X = 0 lead to the equation... 

In a countercurrent multistage section, the phases to be contacted enter a series of ideal or equilibrium stages from opposite ends. A contactor of this type is diagramatically represented by Fig. 8.1, which could be a series of stages in an absorption, a distillation, or an extraction column. Here L and V are the molal (or mass) flow rates of the heavier and lighter phases, and x,- and y,- the corresponding mole (or mass) fractions of component /, respectively. This chapter focuses on binary or pseudobinary systems so the subscript / is seldom required. Unless specifically stated, y and x will refer to mole (or mass) fractions of the lighter component in a binary mixture, or the species that is transferred between phases in three-component systems. 

Example 15.5. The separation of benzene B from n-heptane H by ordinary distillation is difficult. At atmospheric pressure, the boiling points differ by 18.3°C. However, because of liquid-phase nonideality, the relative volatility decreases to a value less than 1.15 at high benzene concentrations. An alternative method of separation is liquid-liquid extraction with a mixture of dimethylformamide (DMF) and water. The solvent is much more selective for benzene than for n-heptane at 20°C. For two different solvent compositions, calculate interstage flow rates and compositions by the rigorous ISR method for the countercurrent liquid-liquid extraction cascade, which contains five equilibrium stages and is shown schematically in Fig. 15.22. 

The holdups of the two phases are very small, which is advantageous in certain applications. As the phases are in the co-current flow, they can attain equilibrium. Therefore, the extractor is at best one equilibrium stage. However, multiple units can be configured to form a multi-stage countercurrent extraction unit. There is a need to evaluate the relative merits of the multiple units configuration vis vis the Podbielniak extractor, which offers 4 to 6 stages in a single unit. 

The most effective mode of operation of extraction processes is depicted in Fig. 6.2-5. The raffinate R and the extract. E are in countercurrent contact in a cascade of n (here 4) equilibrium stages. The concentration of the feed decreases from Xp to x (n = 4). The transfer component B eruiches from to yj. An overall mass balance delivers the mixing point of the system ... 

Processes of solvent extraction are mostly performed in countercurrent operation mode. Due to restrictions set by the equipment the number of equilibrium stages should be lower than 10. If more equilibrium stages are required to meet the product specifications, extraction is unfavorable and has to be replaced, if possible, by any other separation process. 

The most common type of extraction cascade is the countercurrent system shown schematically in Figure 13-3. In this cascade the two phases flow in opposite directions. Each stage is assumed to be an equilibrium stage so that the two phases leaving the stage are in equilibrium. 

A countercurrent cascade allows for more complete removal of the solute, and the solvent is reused so less is needed. A schematic diagram of a countercurrent cascade is shown in Figure 13-20. All calculations will assume that the column is isothermal and isobaric and is operating at steady state, hi the usual design problem, the column tenperature and pressure, the flow rates and conpositions of streams F and S, and the desired composition (or percent removal) of solute in the raffinate product are specified. The designer is required to determine the number of equilibrium stages needed for the specified separation and the flow rates and conpositions of the oudet raffinate and extract streams. Thus, the known... 

D12. We plan to recover acetic acid from water using 1-butanol as the solvent. Operation is at 26.7°C. The feed flow rate is 10.0 kmol/h of an aqueous solution that contains 0.0046 mole frac acetic acid. The entering solvent is pure and flows at 5.0 kmol/h. This operation will be done with three mixer-settlers arranged as a countercurrent cascade. Each mixer-settler can be assumed to be an equilibrium stage. Equilibrium data are available in Table 13-3. Find the exiting raffinate and extract mole fractions. 

D19. Many extraction systems are partially miscible at high concentrations of solute, but close to immiscible at low solute concentrations. At relatively low solute concentrations both the McCabe-Thiele and trianglar diagram analyses are applicable. This problem explores this. We wish to use chloroform to extract acetone from water. Equilibrium data are given in Table 13-4. Find the number of equilibrium stages required for a countercurrent cascade if we have a feed of 1000.0 kg/h of a 10.0 wt % acetone, 90.0 wt % water mixture. The solvent used is chloroform saturated with water (no acetone). Flow rate of stream Eq = 1371 k. We desire an outlet raffinate concentration of 0.50 wt % acetone. Assume immiscibility and use a weight ratio units graphical analysis. Conpare results with Problem 13.D43. 

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