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: \(R = 1 - \displaystyle\frac{C_P}{C_F} \)
- Important: parts of assignment 4 will be covered in class on Tuesday. Assignments must be submitted by the start of class on 6 November.
Some hints and an update for assignment 4, question 5:
- The \(A_\text{salt}\) and \(A_\text{solv}\) 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 \(\theta\)
- 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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