Feed plate, optimum location

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. 

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. 

In this example, the reflux ratio is to be minimized by finding the optimum feed plate location for a fixed number of total stages N or plates [k2 = N - 2]. This example was included in order to demonstrate the use of the optimization procedure for solving problems involving existing columns. Again the variables listed as usual specifications are fixed. Of the four remaining variables required to completely define the column, three are fixed, namely, bh/dh)Li and... 

Akashah, S., J.H. Erhar, and R.N. Maddox, Optimum feed plate location for multi component distillation separations. Chemical Engineering Communications, 1979, 3 (6) 461 468. 

A distillation column with a total condenser and a partial reboiler is separating an ethanol-water mixture. The feed is 20 mol% ethanol, feed rate is 1000 kmol/h, and feed tenperature is 80°F. A distillate composition of 80 mol% ethanol and a bottoms conposition of 2 mol% ethanol are desired. The external reflux ratio is 5/3. The reflux is returned as a saturated liquid and CMO can be assumed. Find the optimum feed plate location and the total number of equilibrium stages required. Pressure is 1 atm... 

Find the optimum feed plate location and the total number of equilibrium stages. 

A. Define. It helps to draw a schematic diagram of the apparatus, particularly since a new type of distillation is involved. This is shown in Figure 4-15. We wish to find the optimum feed plate location, Np, and the total number of equilibrium stages, N, required for this separatiom We could also calculate Q, D, B, and the steam rate S, but these were not asked for. We assume that the column is adiabatic since it is well insulated. 

When all operating lines have been plotted, step off stages, determine optimum feed plate locations and the total number of stages. If desired, calculate a fractional number of stages. 

The feed flow rate is 2000 kmol/day. Feed is 48 mol% methanol and 52 mol% water and is a subcooled liquid. For every 4 moles of feed, 1 mole of vapor must condense inside the column. Distillate conposition is 92 mol% methanol. Reflux is a saturated liquid, and Lq/D = 1.0. Bottoms conposition is 8 mol% methanol. Boilup ratio is V/B = 0.5. Equilibrium data are given in Table 2-7. Assume that CMO is valid. Find the optimum feed plate location and the total number of equilibrium stages required. 

G3. Write a computer, spreadsheet, or calculator program to find the number of equilibrium stages and the optimum feed plate location for a binary distillation with a constant relative volatility. System will have CMO, saturated liquid reflux, total condenser, and a partial reboiler. The given variables will be F, Zp, q Xg, Xp, a, and Lq/D. Test your program by solving the following... 

The optimum feed plate is defined as the feed plate that gives the fewest total number of stages. To be absolutely sure you have the optimum feed plate location, use this definition. That is, pick a feed plate location and calculate N. Then repeat until you find the minimum total number of stages. Note that often several stages must be stepped off before the feed can be input. The first legal feed stage may be the optimum This procedure sounds laborious, but, as we will see, it is very easy to implement on a spreadsheet (Appendix A of Chapter 51. 

The optimum feed plate location can also be estimated. First, use the Fenske equation to estimate where the feed stage would be at total reflux. This can be done by determining the number of stages required to go from the feed concentrations to the distillate concentrations for the keys. 

Estimate the total number of equilibrium stages and the optimum feed plate location required for the distillation problem presented in Exanples 7-1 and 7=2 if the actual reflux ratio is set at L/D = 2. 

Calculate the optimum feed plate location, product purities, and Qg, and the column diameters at different locations for the base case. Then determine which of the methods in Figure 10-18 will do the best job of balancing the diameters and reducing the column volume with constant product... 

In general the same type of information given by the constant 0/V method can be obtained by the use of the Ponchon and Savarit method. For example, the cases of total reflux, minimum reflux ratio, and optimum feed-plate location can be easily solved. 

Trhe terminal concentrations of the two key components are important because most of the practical equations which have been developed for the minimum number of theoretical plates at total reflux, the optimum feed-plate location, and the minimum reflux ratio have involved these concentrations. However, certain difficulties are involved (1) the design specifications may be such that the key components are not bvious and (2) these design equations often require the concentrations of both key components in the distillate and bottoms as well as the concentration of some of the other components. But as demonstrated in the foregoing analysis, only two of these terminal concentrations are independent and can be arbitrarily fixed as design conditions. 

In using this expression, it is recommended that Ki and Kh be calculated as (ai/aik) and (a /aw), respectively. This expression is similar to that for the intersection ratio, but if Ai is large, will be larger than xik)/ Xhk)% if is large, will be smaller. Using these corrections, the optimum feed-plate location is such that... 

Optimum Feed-plate Location. The use of Eq. (9-12) will be illustrated by the examples already considered. 

Optimum Feed-plate Location, The feed plate was chosen so that the ratio of the key components was approximately the same as in the feed. Equation (9-12) indicates the optimum feed-plate ratio for Cs + /n-Gi should be 1.14 as compared to 0.83 for the ratio in the feed. After rematching, the ratio of the key components for plate 8 in Table 9-3 is 0.803, and for plate 9 (plate T—2) in Table 9-4 the ratio is 1.03. The ratio for these two plates should bracket the value of 1.14. These values indicate that adding the feed to plate 9 would give more effective rectification than the plate that was employed. 

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