An Overview of Mass Exchange Operations Dr. Mario Richard Eden Department of Chemical Engineering Auburn University Lect

1. CHEN 4460 An Overview of Mass Exchange Operations Dr. Mario Richard EdenDepartment of Chemical EngineeringAuburn University Lecture No. 2August 30, 2004

2. What is a Mass Exchanger? • Mass Exchanger • A mass exchanger is any direct-contact mass-transfer unit which employs a Mass Separating Agent (or a lean phase) to selectively remove certain components (e.g. pollutants) from a rich phase (e.g. a waste stream). • Absorption, Adsorption, Extraction, Ion Exchange, ….

3. Equilibrium 1:4 • Generalized Description • The composition of the rich stream (yi) is a function of the composition of the lean phase (xj) • (2.1) • Dilute Systems • For some applications the equilibrium functions may be linearized over the operating range • (2.2)

4. Mole fraction of solute in gas • Vapor pressure of solute at T • Mole fraction of solute in liquid • Total pressure of gas • Mole fraction of solute in gas • Mole fraction of solute in liquid • Henry’s coefficient • Liquid-phase solubility of the pollutant at temperature T Equilibrium 2:4 • Special Cases • Raoult’s law for absorption • (2.3) • Henry’s law for stripping • (2.4) • (2.5)

5. Solute composition in liquid • Solute composition in solvent • Distribution coefficient Equilibrium 3:4 • Special Cases • Distribution function used in solvent extraction • (2.6) • Interphase Mass Transfer • For linear equilibrium the pollutant composition in the lean phase in equilibrium with yi can be calculated as: • (2.7)

6. Overall mass transfer coefficient for rich phase • Overall mass transfer coefficient for lean phase Equilibrium 4:4 • Interphase Mass Transfer (Continued) • For linear equilibrium the pollutant composition in the rich phase in equilibrium with xj can be calculated as: • (2.8) • Rate of Mass Transfer • (2.9) Correlations for estimating overall mass transfer coefficients can be found in McCabe et al. (1993), Perry and Green (1984), King (1980) and Treybal (1980).

7. Mass Exchangers – I 1:2 • Multistage Contactors • Multistage countercurrent tray column

8. Mass Exchangers – I 2:2 • Multistage Contactors (Continued) • Multistage Mixer-Settler System

9. Modeling – I 1:5 • Stagewise Columns • A generic mass exchanger • Schematic of a multistage mass exchanger

10. Modeling – I 2:5 • Stagewise Columns (Continued) • Operating line (material balance • (2.10) • The McCabe-Thiele diagram

11. Modeling – I 3:5 • Stagewise Columns (Continued) • The Kremser equation • Isothermal • Dilute • Linear equilibrium • (2.11)

12. Modeling – I 4:5 • Stagewise Columns (Continued) • Other forms of the Kremser equation • (2.12) • (2.13) • (2.14)

13. Modeling – I 5:5 • Stagewise Columns (Continued) • Number of actual plates • (2.15) • Stage efficiency can be based on either the rich or the lean phase. If based on the rich phase, the Kremser equation can be rewritten as: • (2.16)

14. Mass Exchangers – II 1:3 • Differential (Continuous) Contactors • Countercurrent packed column

15. Mass Exchangers – II 2:3 • Differential (Continuous) Contactors (Continued) • Spray column

16. Mass Exchangers – II 3:3 • Differential (Continuous) Contactors (Continued) • Mechanically agitated mass exchanger

17. Modeling – II • Continuous Mass Exchangers • Height of a differential contactor • (2.17a) (2.17b) • (2.18a) • (2.18b)

18. Crash Course in Economics 1:5 • Which Car is Cheaper? • Fixed cost: The car itself, i.e. body, engine, tires, etc. $500 $21,000

19. Crash Course in Economics 2:5 • Which Car is Cheaper? (Continued) • Annual Operating Cost (AOC): How much to run and maintain the car. $ vs. $/year ??? We need to annualize the fixed cost of the car $4,000/year $700/year

20. Crash Course in Economics 3:5 • Which Car is Cheaper? (Continued) • Annualized Fixed Cost (AFC) • Total Annualized Cost (TAC)

21. Crash Course in Economics 4:5 • Which Car is Cheaper? (Continued) Useful Life: 2 Years Salvage Value: $200 AFC = ($500-$200)/2 yr = $150/yr Useful Life: 20 Years Salvage Value: $1000 AFC = ($21,000-$1,000)/20 yr = $1000/yr

22.   Crash Course in Economics 5:5 • Which Car is Cheaper? (Continued) TAC = $4,000 + $250 = $4,250/yr TAC = $1,000 +$700 = $1,700/yr

23. Minimizing Cost of MENs 1:3 • Total Annualized Cost of Mass Exchange System • Fixed cost: Trays, shell, packing, etc. • Operating cost: solvent makeup, pumping, heating/cooling, etc. • (2.21) • Driving Force • Minimum allowable composition • difference • Must stay to the left of • equilibrium line

24. Minimizing Cost of MENs 2:3 • Driving Force (Continued) • Minimum allowable composition difference at rich end of mass exchanger When the minimum allowable composition difference εj increases, then the ratio of L/G increases. AOC increases, due to higher MSA flow AFC decreases, due to smaller equipment, e.g. fewer stages

25. OPTIMUM Minimizing Cost of MENs 3:3 • Driving Force (Continued) • Trade-off between reducing fixed cost and increasing operating cost • Composition driving force, becomes a optimization variable

26. Homework 1:5 • General Comments • Explain the problem and the solution steps taken. • Explain your train of thought. • Don’t present values at the beginning that you don’t calculate until later. • If you don’t write out the general form of an equation at least give a reference to which equation you are using.

27. Homework 2:5 • General Comments (Continued) • Every value used, which is not given by the problem statement must be explained either by text or a calculation. • All values must be used with the corresponding units in all calculations. This is also an additional check for you. • Always use the general equations. If you use an equation from an example in the book make sure that it can be reused in the problem you’re solving. • Don’t try to put 100 calculations on 1 page! Make it easy to read and get the overview.

28. Homework 3:5 • General Comments (Continued) • Take the time to write up the answers nicely. It gives a bad impression if there are a lot of smudges and/or early calculations, which are now crossed out. • Check your results yourself when possible. If you calculate a value by hand and subsequently you have to redo the calculations for a series of variables, check that your spreadsheet or solver yields the same result as your initial calculation. • When presenting a graph, give some thought to what the purpose of the graph is, i.e. what information is the reader supposed to obtain from this.

29. Homework 4:5 • General Comments (Continued) • Don’t plot series of data with different orders of magnitude in the same diagram. Use a second y-axis or plot the data sets separately. • Use a consistent number of significant figures. • Avoid rounding off intermediate results.

30. Homework 5:5 • Problems 2.1, 2.2 and 2.5 • Turn in at lecture on Monday September 13 • Problem statements are handed out as photocopies • A rough version of Chapter 2 of Dr. El-Halwagi’s book is placed on course webpage as a PDF file in case they have not yet arrived at the bookstore

31. Aspen Lab • Textile 228 and 230 • Computer systems are up and running • Networked with access to internet and H-drive • When starting Aspen, create a working folder on your H-drive • Aspen lab notes available at Engineering Duplicating Services in Ramsay Hall • Labs start this week • Although no lecture, there will be labs next week • Check with Ahmed for schedule if you haven’t yet • Enjoy Labor Day Weekend 