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ChE 102 Spring 2011 Project #3 Distillation Column Optimization – Version 3 Background Distillation columns are used throughout the chemical industry to separate and purify products using the difference in volatility of materials to effect the separation. The unit operation of distillation usually involves several pieces of equipment that are shown in Figure 1.

O v e rh e a d C o n d e n s e r

3

4 D is t illa t io n T o w e r o r C o lu m n

cw F IC

L IC

1

R e flu x D r u m R e flu x P u m p

L IC

lp s

2

R e b o ile r Figure 1: Illustration of the main pieces of equipment used in distillation

2 Feed material containing (for our case) two components with different boiling points are introduced into the column in Stream 1. Heat in added to the column through a heat exchanger (the reboiler) located at the bottom of the column, and heat is removed in the exchanger (overhead condenser) located at the top of the column. In order for the column or tower to operate properly, a portion of the top and bottom products must be returned or recycled to the column. We refer to the amount of product (kmol/h) returned to the top of the tower as the reflux and designate this as L. The top product, Stream 2, is usually referred to as D. Other notation used to describe the process at the top of the column is given in Figure 2. D V

L F R = L /D V = L + D = (1 + R )D Figure 2: Illustration of top part of distillation column with stream notation Project Details When designing distillation columns, it is common to optimize the column using the reflux ratio, R, as the “design variable”, where R is defined in Figure 2. The overall cost of building the column and running it must be considered when optimizing the design. The capital investment (cost) for the equipment includes the cost of the column, plus the costs of the reboiler, condenser, reflux drum, and pump. For this project we will consider only the costs of the column and the two heat exchangers (reboiler and condenser). The operating costs include the cost of the cooling medium (water) for the condenser and the heating medium (steam) for the reboiler. Because the equipment costs are one-time purchase costs and the operating costs (steam and water) occur all the time, the time value of money must be taken into consideration when defining an objective function. For this project we want to minimize the equivalent annual operating cost (EAOC) of the column that is defined in Equation 1:

3

EAOC[$ / y ] 

3

2

i 1

i 1

 PCi [$]( A / P, i, n)[1/ y]  UCi [$ / y]

(1)

where PCi are the purchase costs of the column and heat exchangers and UCi are the operating (utility) costs (water and steam). You should assume that the effective annual interest rate, i, is 8% pa and that the length of the project, n, is 10 years. Assignment You are to optimize a distillation column (calculate the value of R that minimizes the EAOC) that is to separate 1000 kmol/h of an equal molar feed of benzene and toluene into a top product containing 99.5 mol% benzene with a recovery of benzene of 98%. The recovery of benzene is the ratio of total amount (kmol) of benzene in the top product to that entering in the feed (DyB/FzB, where zB is the feed mole fraction of benzene). The column is to operate at a pressure of 1 atm. The term yB is the mole fraction of benzene in the top stream and xB is the mole fraction of benzene in the bottom stream. The relationship between the reflux ratio, R, and the number of stages or trays in the column, N, is given by the following relationships:  yB 1  xB    xB 1  yB 

ln  N min 

Y

ln 

(2)

N  N min N 1

(3)

2  1

(4)

R  Rmin R 1

(5)

X 

X 

  1  54.5 X   X  1  Y  1  exp         11  117.2 X   X  

(6)

where  is the relative volatility of the benzene with respect to the toluene, which is equal to 2.3 for this system. Material balances are required to determine xB. If you are not familiar with material balances, you instructor will provide assistance.

4 The costs of utilities for the overhead condenser (cooling water = CW) and reboiler (steam) vary with the cost of energy. Examine the range of costs shown in Table 1. Table 1: Range of Parameters to Use for Utility Costs Utility Equation Low Value High Value -7 UCCW [$/h ]  aVV cooling water a = 0.2510 a = 210-7 UC steam [$/h ]  bUCCW [$/h] steam b = 0.5 b=8 where V is the latent heat of vaporization kJ/kmol) of benzene at its normal boiling point and V (kmol/h) is shown in Figure 2. The purchase cost of the column is given by: 0.85 PCcol  $10, 000Vcol

(7)

where Vcol = d2L/4 is the volume of the column in m3 and d[m] and L[m] are the diameter and height of the column, respectively. The diameter and height of the column are given by:

d [m]  0.15(V [kmol/h] ) 0.5

(8)

L[m]  N

(9)

The purchase costs of the condenser and reboiler may be taken as 10% and 20% of the cost of the column, respectively. You should present your final results as two plots. The first should show how each term in Equation 1 changes with R/Rmin, and the second plot should show the EAOC (y-axis) as a function of R/Rmin (x-axis). Your report should contain a physical explanation of the reason for the trends on these plots.