Interstage flow rates

Feed for each stage consists of heads from the next lower stage and tails from the next higher stage. These interstage flow rates and compositions will be called the internal variables of the cascade. 

Equation (12.72) gives the minimuni number of stages for a particular overall separation. The minimum nutiiber of stages requires that the ratio of interstage flow rate to product be infinite. 

The large interstage flow rate at the feed point (M iolP— 58,229) and its rapid decrease as the product and tails ends of the plant are approached are characteristic of an ideal cascade. 

The total interstage flow rate of heads or tails is a measure of the size of the separation plant. In a distillation plant, for example, the total volume of column internals is proportional to the total interplate vapor flow rate. In a gaseous diffusion plant, the total amount of power expended in pumping gas from one stage to the next is proportional to the total heads flow rate. 

Because of the first assumption, the total inventory is proportional to the total interstage flow rate, given by (12.181), so that... 

In some isotope separation plants, notably those using distillation or exchange processes, it is more economic to use a constant interstage flow rate over a considerable composition interval rather than a flow rate that decreases steadily from the feed point to the product ends, as is characteristic of an ideal cascade. Cohen [C3] has called such cascades squared-off cascades and has derived equations for their separation performance. This section summarizes the derivation for a close-separation, squared-off cascade. 

The development next to be given of equations for the number of stages, interstage flow rates, and fraction on each stage does depend on the process used. In subsequent numerical examples, the gaseous diffusion process with a U/ U stage separation factor of 1.00429 is assumed. 

Equations for interstage flow rates and compositions in the enriching section are obtained by applying to the section of the cascade from the product end through stage / + 1 shown in Fig. 12.28 a development similar to the one used earlier for the complete cascade. 

A mixture of cyclohexane and cyclopentane is to be separated by liquid-liquid extraction at 25°C with methanol. Phase equilibria for this system may be predicted by the van Laar equation with constants given in Example 5.11. Calculate, by the ISR method, product rates and compositions and interstage flow rates and compositions for the conditions below with ... 

Use the Naphtali-Sandholm SC method with the Chao-Seader correlation for thermodynamic properties to calculate product compositions, stage temperatures, interstage flow rates and compositions, reboiler duty, and condenser duty for the following distillation specifications. 

Toluene and n-heptane are to be separated by extractive distillation with phenol. One proposed specification for the operation is shown below. Use the Naphtali-Sandholm SC method, with the Wilson equation for activity coefficients, to calculate the product compositions, stage temperatures, interstage flow rates and compositions, and condenser and reboiler duties. Constants for the Wilson equation can be determined readily for the van Laar constants An developed in Example 5.5 by computing from these constants the infinite-dilution activity... 

Associated with each general theoretical stage are the following indexed equations expressed in terms of the variable set in Fig. 15.1. However, variables other than those shown in Fig. 15.1 can be used. For example, component flow rates can replace mole fractions, and side-stream flow rates can be expressed as fractions of interstage flow rates. The equations are similar to those of Section... 

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 interstage flow rate L,- that must be maintained in order that there be any enrichm t in the ideal cascade at the point, where the concentraticm Xj occurs, is giv by... 

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