Shortcut Calculation, Case

Example 3 Shortcut Calculation Case A Let us solve the problem in Example 2 by using the shortcut calculation method assuming immiscible solvents, case A. 

Example 4 Shortcut Calculation Case B Let iis solve the problem in Example 2 hy assuming case B. The solute (acetic acid) concentration is low enough in the extract so that we may assume that the mutual solubilities of the solvents remain nearly constant. The material balance can be calculated by an iterative method. 

Example 1 Shortcut Calculation, Case A Consider a 100-kg/h feed stream containing 20 wt % acetic acid in water that is to be extracted with 200 kg/h of recycle MIBK that contains 0.1 wt % acetic acid and 0.01 wt % water. The aqueous raffinate is to be extracted down to 1% acetic acid. How many theoretical stages will be required and what will the extract composition be The equilibrium data for this system are listed in Table 15-8 (in units of weight percent). The corresponding Hand plot is shown in Fig. 15-20. The Hand correlation (in mass ratio units) can be expressed as Y = 0.930(X ) °, for X between 0.03 and 0.25. 

With the superior accuracy and capabilities of modern rigorous methods, a column should not be designed without them. A shortcut calculation is inferior in accuracy, and in some cases may give mis-... 

In many cases, shortcut calculations can fill in the gaps. An example used in Kenney s book (Kenny, 1984) gives good illustration for how to do it Consider the tower in Figure 13.2. As for many plants, cooling water rates are not measured and overhead product comes off on level control. However, since feed rate and composition and overhead product composition are known, much of the missing data can be derived by energy and mass balances. 

Shortcut calculation methods. In the remainder of this chapter, shortcut calculation methods for the approximate solution of multicomponent distillation are considered. These methods are quite useful to study a large number of cases rapidly to help orient the designer, to determine approximate optimum conditions, or to provide information for a cost estimate. Before discussing these methods, equilibrium relationships and calculation methods of bubble point, dew point, and flash vaporization for multicomponent systems are covered. 

The reference stripping factor, S, is calculated from effective component stripping factors only the first time in each base case calculation in order to determine parameters /I,. In subsequent shortcut calculations of deviations from the base case, 5, is calculated from the reduced model equations. 

For these parameters, the equations predict a much higher vacuum (24.5 in Hg or 230 percent of the shortcut method) than the gravity-discharge case. Of course, different tank dimensions and pump characteristics coiild give different comparisons between cases. If conditions are such that the pump can completely empty the tank before backflow occurs, the vacuum is Rest calculated from Eq. (26-57). 

We note that, at its simplest, the optimization will be on an epoch by epoch basis (the so-called greedy or myopic approach). In this case, the mode is chosen just to optimize for the next epoch and defer consideration of future behavior. A more sophisticated system would look several epochs ahead in applying the measure of effectiveness, though it would also update the scheduling policy on an epoch by epoch basis. Such an approach is, a priori, very computer intensive, and much work is needed to develop shortcuts to calculation of the optimal policy. Sometimes it may be appropriate to choose to measure the effectiveness of a policy only at the last epoch of application of that policy. 

The latter equation is easier for repetitive computations because the term at the bottom needs to be calculated only once, and such shortcuts were helpful prior to the computer age. However, using modem packages, it is not difficult to use the first equation, which will be employed in this text. It is important, though, always to understand and check different methods. In most cases there is little difference between the two calculations. 

In the present case, hand calculation and shortcut procedures are adequate because the benzene-toluene-xylene system is close to ideal. 

In a first case study, the zeotropic mixture of pentane, hexane, heptane and octane is supposed to be separated into the pure components. Five different sequences are possible (Fig. 1), which have ten individual separation tasks. They are referenced as sequence one to five according to the labeling in the figure. Assuming a pressure of 1.013 bar, an equimolar feed and a total flowrate of 10 mol/s, the energy and exergy demands are calculated for the ten tasks using the RBM shortcut. Sequence five, which corresponds to the direct sequence, is foimd to be optimal. Obviously, the optimal sequence depends on... 

---