HW11sol_KS_v4_9dec05

HW11sol_KS_v4_9dec05 - Chemical Engineering 150B Fall 2005...

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Page 1 of 17 Chemical Engineering 150B- Fall 2005 Problem Set #11 Solutions (165 point assignment) Problem 1. (40 Points) A distillation operating will separate a mixture of 8 components with the following feed rates at 700 kPa: Compound f i (kmol /hr) C 3 2500 iC 4 400 nC 4 600 iC 5 100 nC 5 200 nC 6 40 nC 7 50 nC 8 40 It is known that the heavy key is iC 5 , which will have a distillate rate of 15 kmol/hr, and the light key is nC 4 , which will have a bottoms rate of 6 kmol/hr. Furthermore, assume for all parts of this problem that only the light key and heavy key distribute; all other components do not distribute. Determine the following: (a) the minimum number of equilibrium stages and the distribution of nonkey components by the Fenske equation. (b) what class of separation is this? (c) the minimum external reflux rate and distribution of nonkey components at minimum reflux by the appropriate Underwood equation (see class notes from Wed, November 23 for handling distributing keys and non-distributing other components) if the feed is a bubble-point liquid at column pressure. Hint: You may find the following equation useful: 3 12 61 2 ln ln P TT TP a aa Ka a P P =+++ + , where P is in psia, T is in o R, and the constants are the following: Compound a T1 a T2 a T6 a P1 a P3 C 3 -970,688.5626 0 7.15059 -0.76984 6.90224 iC 4 -1,166,846 0 7.72668 -0.92213 0 nC 4 -1,280,557 0 7.94986 -0.96455 0 iC 5 -1,481,583 0 7.58071 -0.93159 0 nC 5 -1,524,891 0 7.33129 -0.89143 0 nC 6 -1,778,901 0 6.96783 -0.84634 0 nC 7 -2,018,803 0 6.52914 -0.79543 0 nC 8 0 -7,646.81641 12.48457 -0.73152 0 In addition, you might find MathCAD useful to find the bubble-point temperature of the feed, bottoms, and distillate streams, so that you can determine the K-value of each component in each stream. This will
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Page 2 of 17 allow the calculation of volatility of each stream for various components to help you use the Fenske and Underwood equations. Part a: To use the Fenske equation, we need the geometric mean of the relative volatilities of the distillate and bottoms stream. In order to get a rough estimate of these values, we will use an extremely crude estimate for the separation. We will assume that anything lighter than nC 4 (which is iC 4 and C 3 ) only appears in the distillate, while anything heavier than iC 5 (which include nC 5 , nC 6 , nC 7 , and nC 8 ) only appear in of the bottoms stream. nC4 and iC5 will have the flow rates specified in the problem statement. Therefore, the distillate stream will have the following flow rates: Compound d i (kmol /hr) z i (kmol /hr) C 3 2500 0.712 iC 4 400 0.114 nC 4 594 0.169 iC 5 15 0.005 nC 5 0 0 nC 6 0 0 nC 7 0 0 nC 8 0 0 and the bottoms flow rates are the following: Compound b i (kmol /hr) z i (kmol /hr) C 3 0 0 iC 4 0 0 nC 4 6 0.014 iC 5 85 0.202 nC 5 200 0.475 nC 6 40 0.095 nC 7 50 0.119 nC 8 40 0.095 Using these flow rates, we can calculate the mole fraction of each stream, which is shown to the right on the tables. These numbers will be useful in order to estimate the relative volatility between species in the distillate and bottoms streams. First of all, we must calculate the temperature of the above streams by doing a bubble point temperature calculation at a given pressure, which we know is 700 kPa (101.5 psia).
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HW11sol_KS_v4_9dec05 - Chemical Engineering 150B Fall 2005...

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