Stage Requirements

These equations should plot linearly on log-log coordinates they are tested in Example 14.1. 

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. 

This nomenclature is shown with Example 14.3. On the triangular diagram, the proportions of feed and solvent locate the mix point 

The extract E and raffinate R are located on opposite ends of the tieline that goes through M. 

In this process the feed and subsequently the rafiinate are treated in successive stages with fresh solvent. The sketch is with Example 14.3. With a fixed overall amount of solvent the most efficient process is with equal solvent flow to each stage. The solution of Example 14.3 shows that crosscurrent two stage operation is superior to one stage with the same total amount of solvent. 

---

If the feed, solvent, and extract compositions are specified, and the ratio of solvent to feed is gradually reduced, the number of ideal stages required increases. In economic terms, the effect of reducing the solvent-to-feed ratio is to reduce the operating cost, but the capital cost is increased because of the increased number of stages required. At the minimum solvent-to-feed ratio, the number of ideal stages approaches infinity and the specified separation is impossible at any lower solvent-to-feed ratio. In practice the economically optimum solvent-to-feed ratio is usually 1.5 to 2 times the minimum value. 

This quantity is minimised when the stage is operated at a pressure ratio across the barrier corresponding to r = 0.285. Furthermore, if power were the only economic consideration, the stage would be operated at this pressure ratio. However, as the value of ris decreased from this optimum, although the cost of power is increased, the number of stages required and hence the capital cost of the plant is decreased. Thus, ia practice a compromise between these factors is made. 

The variable that has the most significant impact on the economics of an extractive distillation is the solvent-to-feed (S/F) ratio. For closeboiling or pinched nonazeotropic mixtures, no minimum-solvent flow rate is required to effect the separation, as the separation is always theoretically possible (if not economical) in the absence of the solvent. However, the extent of enhancement of the relative volatihty is largely determined by the solvent concentration and hence the S/F ratio. The relative volatility tends to increase as the S/F ratio increases. Thus, a given separation can be accomplished in fewer equihbrium stages. As an illustration, the total number of theoretical stages required as a function of S/F ratio is plotted in Fig. 13-75 7 for the separation of the nonazeotropic mixture of vinyl acetate and ethyl acetate using phenol as the solvent. 

For the system water-acetic acid-MIBK in Fig. 15-11 the raffinate (water) layer is the solubility curve with low concentrations of MIBK, and the extract (MIBK) layer is the solubihty curve with high concentrations of MIBK. The dashed lines are tie lines which connect the two layers in equihbrium as given in Table 15-1. Example 2 describes the right-triangular method of calculating the number of theoretical stages required. 

For certain simplified cases it is possible to calculate directly the number of stages required to attain a desired product composition for a given set of feed conditions. For example, if equilibrium is attained in all stages and if the underflow mass rate is constant, both the equilibrium and operating lines on a modified McCabe-Thiele diagram are straight, and it is possible to calculate direc tly the number of ideal stages required to accommodate arw rational set of terminal flows and compositions (McCabe, Smith, and Harriott, op. cit.) ... 

Figure 14.1 The McCabe-Thiele diagram for the calculation of the number of theoretical stages required to separate two liquids to yield relatively pure products...

To detemiine number of stages required, assume 7 1 compression ratio maximum per stage. 

Step 8. Determine the number of stages required using the modified rule of thumb on head per stage, Hjtg. 

Divide the total head per section by the allowable head per stage to develop the number of stages required in each section. 

The risk inventory or risk evaluation is die ne. t part of die hazard survey. It is not practical to expect the plan to cover every potential accident. When die hazards liave been evaluated, die plan should be focused on die most significant ones. This risk assessment stage requires die technical expertise of many people to compare die pieces of data and detennine die relevance of each. Among die important factors to be considered in performing die risk evaluation are die following ... 

The enantiomeric purity that can be obtained as a function of a for one, two, and three stages is given in Table 8-1. It is apparent that the higher the a value, the fewer the number of separations stages required to reach 99 % enantiomeric purity. For an a value of 5, the use of three stages allows one to obtain > 99 % purity. The required purity of the end-product defines the minimum performance requirement of the resin. 

B = parameter in correlating equation In = natural logarithm log = logarithm to the base 10 N = actual theoretical stages required for a given separation... 

The combined Fenske-Underwood-Gillilland method developed by Frank [100] is shown in Figure 8-47. This relates product purity, actual reflux ratio, and relative volatility (average) for the column to the number of equilibrium stages required. Note that this does not consider tray efficiency, as discussed elsewhere. It is perhaps more convenient for designing new columns than reworking existing columns, and should be used only on at acent-key systems. 

Determine the number of casing stages required. Using Table 12-9B, determine nominal speed. Calculate Q/N. 

---