Stage requirements, equilibrium

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. 

A column is to be designed to separate a mixture of ethylbenzene and styrene. The feed will contain 0.5 mol fraction styrene, and a styrene purity of 99.5 per cent is required, with a recovery of 85 per cent. Estimate the number of equilibrium stages required at a reflux ratio of 8. Maximum column bottom pressure 0.20 bar. 

Equilibrium stage requirements for the separation of water and n-butanol. 

Solvent Loading. The solvent circulation rate is a function of the reflux ratio in the primary tower and the liquid-phase concentration of the solvent. For a given solvent selectivity, as the solvent concentration rises, the propane-propylene relative volatility increases and hence the required reflux rate falls. The increased relative volatility results in a decreased number of equilibrium stages required for the desired separation. Figure 4 shows the effect of solvent concentration on the number... 

Selectivity and Activity Coefficients. The solvent selectivity determines the relative volatility of the propane-propylene system, with a higher selectivity yielding a higher relative volatility of propane to propylene. An increasing selectivity therefore results in a smaller reflux ratio and fewer equilibrium stages required for the separation. The lower reflux rate corresponds to a lower vapor-flow rate in the tower and hence to a thinner tower. The lower reflux rate also results in a smaller solvent-flow rate with a consequent decrease in the solvent-cooler size and duty and in the reboiler duties. 

Changes in relative volatility and activity coefficients with changing selectivity act against each other in affecting the equilibrium-stage requirements of the main column. The net result is shown in Figure 6 where the total number of equilibrium stages in the main column is... 

Equilibrium stage requirements fer the separatien ef water and n-butanel. 

This type of calculation does not have to be carried out for a plate column because the two phases are well mixed on each plate. This means that on each individual plate a state of equilibrium can be presumed. Therefore a volume element is identical to an equilibrium stage, and the height of the column can be obtained from the number of equilibrium stages required for a particular separation. This is a thermodynamic rather then mass transfer problem. This explains why a mass transfer device, such as a distillation column can be sized without any knowledge of the laws of mass transfer. 

J.B. Chemicals, Inc., has hired Theodore Distillation Consultants (TDC) to assist in the separation of 500 kmol/h of a saturated vapor feed (quality, = 0) consisting of 40 mol % benzene (C), 30 mol % toluene (A), and 30 mol % cumene (B). It has been suggested that the distillation column include a partial reboiler and a total condenser. J.B. Chemicals requires 99% recovery of the toluene in the distillate (FRA)dist and 95% recovery of the cumene in the bottoms (FRg)(,o,. As an engineer for TDC you need to determine the actual number of equilibrium stages required for the... 

In the next section, we will see how these two curves can be used to determine the number of equilibrium stages required to achieve some desired degree of separation. 

The number of theoretical equilibrium stages required for a given separation at a given reflux ratio is often determined by empirical correlations [38,39]. The abscissa, X, represents a reflux function as ... 

Designing a column usually starts with heat and material balance calculations, preferably using a computer simulation program. These calculations determine the liquid and vapor flow rates and the number of equilibrium stages required to meet the design performance specifications (separation, recovery, etc.). Fluid properties, such as densities and viscosities, may also be generated by the computer program. 

For the absorption column in Problem 3.12, estimate the number of equilibrium stages required for equilibrium relationships ofy = 1.2xandy = 3.8x, respectively. How does increasing the Henry s Law relationship affect the number of required stages ... 

Figure 5.24 is a schematic of a water purification system. A 20 wt% mixture of acetic acid in water is to be extracted with 1-butanol. The outlet concentrations of acetic acid should be 5 wt% in the water phase and 10 wt% in the 1-butanol phase. Pure solvent is used. Find the number, N, of equilibrium stages required and the ratio, F /Fs, of water to 1-butanol. The distribution coefficient, Kd, for this system is 1.6. 

The variable h shifts the coordinate system to the intersection of the operating and stripping curves. One special case is that of total reflux. In this case D = 0 as no product is being withdrawn and the reflux ratio Ry= becomes 1. This also corresponds to the minimum number of equilibrium stages required for a separation when this is the case,... 

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