Crosscurrent Cascades

A theoretical or equihbrium stage is a device or combination of devices that accomplishes the effect of intimately mixing two immiscible liquids until equilibrium concentrations are reached, then physically separating the two phases into clear layers. Crosscurrent extraction (Fig. 15-4) is a cascade, or series of stages, in which the raffinate R from one extraction stage is contacted with additional fresh solvent S in a subsequent stage. 

Crosscurrent contacting, which is intermediate in mass imnsfer efficiency to cocurrent and countereur-met contacting, is shown below for a two-slaga cascade ... 

FIGURE 21.1-10 Schemetic representation of a multistage dialysis process For couiinuous fractionetion of solutes. The process combines a nouseiective solvent stripper (concentrator) with two crosscurrent dialysis cascades (Dt-Du and Di-Da ). (Reprinied by permission of the American Institute of Chemical Engineera.)... 

Consider the extraction process of Problem 7.3. Calculate the total amount of solvent required if the extraction is done in a crosscurrent cascade consisting of 5 ideal stages. Use equation (3-68) from Problem 3.21. 

Alternative The washing can be done in a Podbielniak centrifugal extractor, which is continuous countercurrent extraction. Alternately, the same can be done in a cascade of annular centrifugal extractors configured in the countercurrent mode. It is known that the amount of cold water required and the loss of the API would be far less compared with values for the crosscurrent process [18]. 

Figure 1-64 shows a cascade of three stages operated at steady-state in a crosscurrent flow process where heat and mass transfer occur. 

The single equilibrium stage is the key unit on which the more complex configurations such as the crosscurrent and countercurrent cascades are based. We use it here to introduce the reader to some basic notions of equilibrium stage processes and to make a first presentation of a key tool, the operating diagram. 

Illustration 7.5 Optimum Use of Adsorbent or Solvent in Crosscurrent Cascades... 

It has been shown that this principle applies to any number of stages i.e., the optimum use of adsorbent requires an equal division of that adsorbent among the stages of a crosscurrent cascade. The same principle applies to crosscurrent extraction of systems with mutually insoluble solvents. The solute recovery or removal that results in such cascades is depicted graphically in Figure 7.9. In this plot, m represents the distribution coefficient for extraction or Henry s constant H for adsorption, E is the so-called extraction factor mB/A or HS/L, and Y or x is the effluent concentration from the nth stage of the solution being treated. 

Let us apply this plot to a specific extraction process. We consider 100 kg of a feed of 1% nicotine in water that is to be extracted in a three-stage crosscurrent cascade employing 50 kg kerosene in each stage. The distribution has a slight curvature, with m varying over the range 0.80 to 0.90. We choose a mean value of 0.85 and obtain the extraction factor ... 

Crosscurrent cascades using equal amounts of adsorbent or solvent. 

The optimization problem considered indicates that the best way to operate a crosscurrent cascade is by equal subdivision of solvent or adsorbent. The reader should be aware, however, that the complete optimization of a plant must also consider the cost of the stages, the cost of solvent recovery, and the value of the extracted solute itself. Thus, in addition to optimmn solvent use, we also need to determine the optimum number of stages, and this... 

Illustration 7.6 A Crosscurrent Extraction Cascade in Triangular Coordinates... 

We consider 1000 kg of a feed containing 50% by weight of acetone in water, which is to be reduced to 10% by extraction with 1,1,2-trichloroethane in a crosscurrent cascade 250 kg solvent are to be used in each stage. Representative tie-line data are shown in Figure 7.10. 

The parameter R, which we term the residue factor, is a direct measure of the amount of residual solute leaving the cascade. The smaller the value of R, the lower the effluent concentrations or, and hence the higher the degree of solute recovery. The parameter E, on the other hand, is identical to the extraction ratio we have defined for crosscurrent extraction (Equation 7.11a) and varies directly with the amount of solvent or adsorbent used and its capacity. Large values of E lead to good recoveries and low effluent concentrations, both desirable features. 

This example shows the distinct advantage that tiie countercurrent process holds, not only over the single-stage operation, which was expected, but also over its crosscurrent counterpart Consumption by the latter is higher by a factor of 2.2/0.87 = 2.5. The principal advantage of the crosscurrent cascade is that it is more easily adaptable to batch processing, whereas the counter-current cascade is by necessity continuous. 

Describe what is represented in an operating diagram. What is the meaning of an operating line or curve How many operating lines are required in crosscurrent cascades, and how many in a counter-current operation What are the requirements for fractional distillation ... 

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