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Separation Processes: CHE 4M3

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Please note for assignment 4, question 5, you will require making an important correction to the membrane notes: slide 76: $R = 1 - \frac{C_{P}}{C_{F}}$

Some hints and an update for assignment 4, question 5: The $A_{salt}$ and $A_{solv}$ terms are not the area of the membrane: they are the permeances of the salt and solvent respectively. This unfortunate notation is widely used though in most texts. There is a correction, the feed concentration should be 2.5 g NaCl per liter in the feed (not 2.5 wt% NaCl). I apologize for wasting your time for those of you that have been iterating with negative concentrations. And another hint. I found a way to solve question 5 that leads to faster convergence: Specify $C_{F}$ and $θ$ Guess $C_{R}$ instead Calculate $C_{P}$ from equation 5 If your calculated value of $C_{P}$ is negative or exceeds $C_{F}$ , then repeat your guess for $C_{R}$ , until you get a $C_{P}$ that lies between 0 and $C_{F}$ and double check also that the rejection coefficient from this $C_{P}$ is reasonable, around 90 to 99%. This approach to estimate $C_{R}$ and then $C_{P}$ will get you really close to the final answer. Now carry on with the rest of the steps in the notes. It's interesting how simply flipping what you guess first leads to much faster convergence. If you iterate and get a negative value for $C_{P}$ or $C_{R}$ , it simply means that you must decrease your guess for that term, since you obviously can't have a negative concentration. And a final hint: this question is much better to solve on a computer, with goal seek, than by hand. There is tremendous sensitivity to initial guesses, so solving by hand will take too long. For question 2(B), part 3: by definition, optimization implies we have excess degrees of freedom, i.e. more unknowns than equations. You should get a system of 3 unknowns (including $A_{1}$ and $A_{2}$ ) and 2 equations. Set the 3rd unknown to various values (between its lower and upper bound), and solve for $A_{1}$ and $A_{2}$ . Pick the solution that gives the optimum.

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@@ Line 36: / Line 36: @@
 ** This approach to estimate  $C_{R}$  and then  $C_{P}$  will get you really close to the final answer.
 ** Now carry on with the rest of the steps in the notes. It's interesting how simply flipping what you guess first leads to much faster convergence.
-** If you iterative and get a negative value for  $C_{P}$  or  $C_{R}$ , it simply means that you must decrease your guess for that term, since you obviously can't have a negative concentration.
+** If you iterate and get a negative value for  $C_{P}$  or  $C_{R}$ , it simply means that you must decrease your guess for that term, since you obviously can't have a negative concentration.
 * And a final hint: this question is much better to solve on a computer, with goal seek, than by hand. There is tremendous sensitivity to initial guesses, so solving by hand will take too long.
 * For question 2(B), part 3: by definition, optimization implies we have excess degrees of freedom, i.e. more unknowns than equations. You should get a system of 3 unknowns (including  $A_{1}$  and  $A_{2}$ ) and 2 equations. Set the 3rd unknown to various values (between its lower and upper bound), and solve for  $A_{1}$  and  $A_{2}$ . Pick the solution that gives the optimum.

Difference between revisions of "Main Page"

Revision as of 17:20, 5 November 2012

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