Staged columns

A more physically consistent way to describe a column stage is known as the rate-based approach (57,85,86). This approach implies that actual rates of multi-component mass and heat transfer and chemical reactions are taken into account directly. 

Eckert [9] showed that a relative height equivalent to a theoretical stage (HETS) vs. the dispersed-phase velocity revealed the packed-column efficiency, or simply the required height, to make one theoretical stage. (See Fig. 7.10). Eckert and others [6, 8] have shown that normally the theoretical packed-column stage requires 2.5 ft of column packed height. All this of course refers strictly to liquid-liquid extraction processing. Also, the continuous-phase velocity Vc (ft/h) and the dispersed-phase velocity VD (ft/h) are referenced to the liquid-phase... 

Assuming that the relative volatilities of the components are constant and that the vapor and liquid phases on the column stages are at equilibrium, we... 

Dynamic simulations were aimed at capturing the multiple-time-scale behavior revealed by the theoretical developments presented above. Figures 7.5 and 7.6 show the evolution of the mole fraction of n-butane and of the temperature on selected column stages for a small step change in the reboiler duty. Visual inspection of the plots indicates that the temperatures exhibit a fast transient,... 

Figure 7.5 Mole fractions of n-butane on representative column stages for a 0.1% increase in column reboiler duty at time t = 1 h.

Figures 7.9 and 7.10 show the evolution of the compositions and temperatures on representative column stages for a small step change in the feed flow rate. According to our theory, this disturbance influences the slow material-balance dynamics and has very little impact on the fast energy dynamics of the column. Indeed, while there are significant (albeit slow) changes in the stage compositions,...

Figure 7.10 Temperatures of representative column stages for a rise of the feed flow rate from 360.0 kmol/h to 366.0 kmol/h.

CpUj Heat capacity of the liquid holdup in tbe column, stage j, Sec. 4,2.11,... 

As stated earlier in Section 5.1.1, if the external feeds to a column stage or section and its pressure are defined, the stage or section performance is defined. Equations 5.11 and 5.12 are now examined from this perspective. Consider first a single stage. If the external feeds are defined, then L, V, Xy i, and are known. This leaves two unknowns, Xj and T, between Equations 5.11 and 5.12 hence the problem is completely specified. 

Going up the column, the vapor is at equilibrium with leaner oil (dodecane with lower concentrations of propane and other dissolved gases). Hence, the propane concentration in the vapor is lower in the upper column stages. The /(-values of propane are higher in the lower column stages because the temperature is... 

Beer feed (wt. %) Reflux ratio Rectifying column stages Stripping column stages Energy use (BTU/lb.) Column diameter (in.) Energy ratio in/out... 

Solution, (a) For this case, Eq. (5.5-13) is used, with N = 6 (column stages plus stillpot) ... 

The dimension of the state is 2 x NC + 6 states per column stage, where NC stands for the number of components ... 

It is interesting to compare this rigorous number with the approximate prediction of the Fenske equation for the same system. The first issue is to find an appropriate value for the relative volatility for the propane/isobutane system at the operating pressure of the column (16.8 atm). The usual approach is to find the relative volatility at the temperature in the top of the column (Stage 2 temperature is 325.6 K) and at the temperature in the reboiler (Stage 32 temperature is 366.1 K). 

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