Feed-plate location

Example 3 Calculation of TG Method The TG method will he demonstrated hy using the same example problem that was used above for the approximate methods. The example column was analyzed previously and found to have C -I- 2N + 9 design variables. The specifications to be used in this example were also hstedat that time and included the total number of stages (N = 10), the feed-plate location (M = 5), the reflux temperature (corresponding to saturated liquid), the distillate rate (D = 48.9), and the top vapor rate (V = 175). As before, the pressure is uniform at 827 kPa (120 psia), but a pressure gradient could be easily handled if desired. 

The feed plate location, for either rectifying or stripping sections ... 

The relation is solved for Sr/Sj. The results are not exact, because the feed tray composition is very seldom the same as the feed which is the assumption in this relation. Actually, the feed point or correct location for the feed may be off by two or three theoretical trays. This will vary with the system. It does mean, however, that when this approach is used for feed plate location, alternate feed nozzles should be installed on the column to allow for experimental location of the best feed point. These extra nozzles are usually placed on alternate trays (or more) both above and below the calculated location. A minimum of three alternate nozzles should be available. 

Continuous binary distillation is illustrated by the simulation example CON-STILL. Here the dynamic simulation example is seen as a valuable adjunct to steady state design calculations, since with MADONNA the most important column design parameters (total column plate number, feed plate location and reflux ratio) come under the direct control of the simulator as facilitated by the use of sliders. Provided that sufficient simulation time is allowed for the column conditions to reach steady state, the resultant steady state profiles of composition versus plate number are easily obtained. In this way, the effects of changes in reflux ratio or choice of the optimum plate location on the resultant steady state profiles become almost immediately apparent. 

Note that the total number of plates, the feed plate location and reflux ratio can all be varied during simulation. The array form of the program also allows graphing the axial steady state tray-by-tray concentration profile. Part of the program is shown below. 

Study the response of the column to changes in the operating variables feed rate, feed composition and reflux ratio, while keeping the number of plates Nplate and feed plate location Fplate constant... 

Effect of Feed Plate Location (Np) - Semi-Continuous Solvent Feeding Mode (Full Charge)... 

Column Specification and Flowsheet. A schematic diagram of the solvent separation scheme and the results of the computer analysis for each column are shown in Figure 4 and Table III, respectively. Feed plate locations are given with respect to the bottom of each column. Plate... 

To determine the optimum feed plate location, draw a line from the feed composition on the y = x line, through the intersection of the top/bottom operating lines, to the equilibrium curve. The step straddling the feed line is the correct feed-plate location. 

Note that the plate numbering in the program is slightly different to that shown in Fig. 1, owing to the use of the vector notation to include both the reflux drum and the column base. In the program, index number 1 is used to denote the reflux drum and product distillate, and index Nplate+1 is used to denote the reboiler and bottoms product. This is convenient in the subsequent plotting of the steady state composition profiles in the column. Both Nplate and the feed plate location Fplate are important parameters in the simulation of the resulting steady state concentration profiles and the resultant column optimisation. 

We desire to use a distillation column to separate an ethanol-water mixture. The column has a total condenser, a partial reboiler, and a saturated liquid reflux. The feed is a saturated liquid of composition 0.10 mole fraction ethanol and a flow rate of 250 mol/hr. A bottoms mole fraction of 0.005 and a distillate mole fraction of 0.75 ethanol is desired. The external reflux ratio is 2.0. Assuming constant molar overflow, find the flowrates, the number of equilibrium stages, optimum feed plate location, and the liquid and vapor compositions leaving the fourth stage from the top of the column. Pressure is 1 atm. 

The same vapor-liquid equilibrium ratio (AT) charts were used for the rigorous solution as for the shortcut, For the rigorous, however, values of K, were combined with total pressure P, and the Kf product was treated as effective vapor pressure" in the Antoine equation. The rigoroas program was nin in a mal-and-error fashion, with constant reflux ratio of 1.722 (from the shortcut) and with iterations of DIF ratio, total plates, and feed plate location. 

For a column whose geometry [the total number of stages, the feed plate locations, and the type of condenser (partial or total)] and feed have been specified, the remaining variables to be specified are as follows ... 

In addition to the specification of the type of condenser, it is also supposed in all of the cases considered that the following variables have been fixed column pressure number of stages N complete definition of the feed (the feed rate F, composition X, and thermal condition) and the feed plate location /. 

Feed plate location / = 6 F j enters on plate 6 F2 enters on plate 21... 

There follows a description of the use of the capital 0 method in the determination of a solution for the system of columns shown in Fig. 7-1 such that the reboiler duty of column 1 is equal to the condenser duty of column 2, that is, such that QRl = QC2. For the system of columns shown in Fig. 7-1, suppose that column 1 has a partial condenser and that the flow rate, composition, and thermal condition of the feed are fixed as well as the pressure, the number of stages, and the feed-plate location. Likewise, suppose that the number of plates, the feed-plate location, and the pressure of column 2 are fixed. Two additional specifications may be made on each column. Since the precise choice of these additional specifications determines the form of the calculational procedures for each column as well as the system, only these additional specifications are listed in the problems considered. In each instance it is supposed, however, that the usual specifications of the type listed above have been made. 

In the formulation of this problem it is supposed that the variables listed as usual specifications are fixed. Of the four remaining variables required to completely define the column, three are fixed, the purity specifications bjdi, bh/dh and the reflux ratio L1/D. Thus, one additional variable remains to be fixed in order to determine the column. Consequently, the problem to be solved consists of finding the feed plate location kx which minimizes the total number of plates k2 (see Fig. 9-1) required to achieve the purity specification at the specified value of the reflux ratio. A concise statement of the problem follows ... 

As shown in Table 9-3, a total of 6 seconds of computer time were required to solve Example 9-1. To solve this same problem when it was uniquely specified (the number of plates, the feed-plate location, the reflux, and distillate rates are fixed) required 0.5 seconds of computer time by the 0 method. Thus, Example 9-1 required about 12 times as much computer time to solve as was required to solve a typical distillation problem in which the plates, configuration, the reflux, and distillate rates are fixed. Since the 0 method is 10 to 20 times faster than Newton-Raphson procedures, the proposed optimization procedure requires about the same amount of computer time as is required to solve a problem involving a fixed column by a Newton-Raphson procedure. 

In the formulation of this problem, it is supposed that in addition to the usual specifications, two purity specifications (bt/dt and bh/dh) are made, and that it is required to find the feed-plate location [plate number (kt + 1)], the total number of plates k2, and the corresponding values of the operating variables Li/D and D that minimize the operating costs and capital costs per mole of the most valuable product (D or B). Since only two of the four additional variables required to define the column are specified, many solutions may be obtained by making different choices for two of the four remaining variables. The best choice for the remaining variables has been made when the objective function is minimized. 

Find the feed-plate location which minimizes the reflux ratio required to effect this separation. Provisions may be made to introduce the feed on any plate between 2 and 28. 

---