1. An Overview of Mass Exchange Operations Dr. Mario Richard Eden Department of Chemical Engineering Auburn University Lecture No. 2 August 30, 2004 CHEN 4460

2. What is a Mass Exchanger? Mass ExchangerMass 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. Generalized DescriptionGeneralized Description –The composition of the rich stream (y i ) is a function of the composition of the lean phase (x j ) (2.1) Dilute SystemsDilute Systems –For some applications the equilibrium functions may be linearized over the operating range (2.2) Equilibrium 1:4

4. Special CasesSpecial Cases –Raoult’s law for absorption (2.3) –Henry’s law for stripping (2.4)(2.5) Equilibrium 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

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

6. Interphase Mass Transfer (Continued)Interphase Mass Transfer (Continued) –For linear equilibrium the pollutant composition in the rich phase in equilibrium with x j can be calculated as: (2.8) Rate of Mass TransferRate of Mass Transfer(2.9) Equilibrium 4:4 Overall mass transfer coefficient for rich phase Overall mass transfer coefficient for lean phase 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. Multistage ContactorsMultistage Contactors –Multistage countercurrent tray column Mass Exchangers – I 1:2

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

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

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

11. Stagewise Columns (Continued)Stagewise Columns (Continued) –The Kremser equation IsothermalIsothermal DiluteDilute Linear equilibriumLinear equilibrium(2.11) Modeling – I 3:5

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

13. Stagewise Columns (Continued)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) Modeling – I 5:5

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

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

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

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

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

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

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

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

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

24. Driving Force (Continued)Driving Force (Continued) –Minimum allowable composition difference at rich end of mass exchanger Minimizing Cost of MENs 2:3 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. Driving Force (Continued)Driving Force (Continued) Minimizing Cost of MENs 3:3 Trade-off between reducing fixed cost and increasing operating cost Composition driving force, becomes a optimization variable OPTIMUM

26. General CommentsGeneral 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. Homework 1:5

27. General Comments (Continued)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. Homework 2:5

28. General Comments (Continued)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. Homework 3:5

29. General Comments (Continued)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. Homework 4:5

30. Problems 2.1, 2.2 and 2.5Problems 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 Homework 5:5

31. Textile 228 and 230Textile 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 Enjoy Labor Day Weekend Aspen Lab