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** This approach to estimate \(C_R\) and then \(C_P\) will get you really close to the final answer.
** 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.
** 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.
* 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.
* 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.

Revision as of 17:20, 5 November 2012

Separation Processes: CHE 4M3


Administrative Class materials
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Announcements (previous ones)

  • Please note for assignment 4, question 5, you will require making an important correction to the membrane notes: slide 76: \(R = 1 - \displaystyle\frac{C_P}{C_F} \)
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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  1. Overview of separation processes
  2. Thickeners and clarifiers (sedimentation), screens, centrifuges and cyclones
  3. Membranes, dialysis, reverse osmosis, filters and bioseparations
  4. Liquid-liquid extraction
  5. Adsorption, ion-exchange and chromatography
  6. Evaporation, drying and overview of crystallization


Assignments, projects, exams Course calendar
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Assignments:

  1. Assignment 1 - 2012 (with solutions)
  2. Assignment 2 - 2012 (with solutions)
  3. Assignment 3 - 2012 (with solutions)
  4. Assignment 4 - 2012
  5. Assignment 5 - 2012

New: How to submit an assignment electronically

Tests, exams and project

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