1. Dr. F. Iskanderani Spring 2003/2004 Example C : Component

2. Dr. F. Iskanderani Spring 2003/2004 To find the number of degrees of freedom : 1.Find the min number of unknowns 2.Find the number of equations and given information. 3.Then the number of degrees of freedom, F = number of unknowns –(the number of equations and given information)

3. Dr. F. Iskanderani Spring 2003/2004 Minimum no. of unknownsSTREAM 4F1 3F2 4F3 5F4 16TOTAL To find no. of unknowns:

4. Dr. F. Iskanderani Spring 2003/2004 To find no. of equations and given information available for this problem: No. of equationsType of equations 4MB independent equations 4 Sum of compositions in each stream is = 1 (note 4 streams) 3given information (see next slide) 11Total Therefore F = 16-11 =5 = number of unknown variables to be specified in order to have a unique solution for the problem

5. Dr. F. Iskanderani Spring 2003/2004 C : Component 1 2 3

6. Dr. F. Iskanderani Spring 2003/2004 Elements of Using Flowcharts 1.To prepare the basic flowchart for a process, draw boxes (or other symbols) for all equipment and use arrows to indicate all streams and their directions of flow ( standard practice has major flows from left to right ) 2. All equipment and all streams should be named or numbered

7. Dr. F. Iskanderani Spring 2003/2004 3.Choose a basis for calculation (use an amount or rate of one stream, if one is known. If none are known, assume one for a stream of known composition ) if mole fractions are known, use a molar basis. Write the basis clearly on the flowchart

8. Dr. F. Iskanderani Spring 2003/2004 4.Write in values of all known stream variables (with units) - flow rates - compositions - temperature and pressure 5. Use a common basis (mass or moles -- convert volumes) (all values should be on the calculational basis you chose)

9. Dr. F. Iskanderani Spring 2003/2004 6. Assign symbols to unknown stream variables. Use as few symbols as possible 7. M ake sure mole fractions add to unity 8. Scaling: if needed, change all stream amounts or rates by a proportional amount ( remember that compositions should remain unchanged )

10. Dr. F. Iskanderani Spring 2003/2004 General Material Balance Procedure (no reaction systems) 1.Read the problem clarify what is to be accomplished 2.prepare a flowchart (see Items 1-4 above) 3.do the degree of freedom analysis 4.count the unknowns you wish to calculate 5.count the equations and given information that are available 6.see if the numbers of unknowns and equations and given information are equal

11. Dr. F. Iskanderani Spring 2003/2004 General Material Balance Procedure (no reaction systems) 7.write material balance equations (sometimes you may need to check that these MB equations are all independent) 8. Convert additional relations between variables into equations 9.solve set of equations and write results on the flow chart

12. Dr. F. Iskanderani Spring 2003/2004 General Material Balance Procedure (no reaction systems) 10.Check your answer using any redundant MB equation(s) 11.scale the results if answers are needed on a different basis (see Item 5 above)

13. Dr. F. Iskanderani Spring 2003/2004 Examples on Material Balance for systems with no reactions

14. Dr. F. Iskanderani Spring 2003/2004 Example 1 To be solved in class (in teams) For the distillation column below, Calculate the composition of the bottoms and the mass of the alcohol lost in the bottoms

15. Dr. F. Iskanderani Spring 2003/2004 Example 2. Mixing Dilute sulfuric acid has to be added to dry charged batteries at service stations to activate a battery. Prepare a batch of new 18.63% acid as follows: A tank of old weak battery acid (H 2 SO 4 ) solution contains 12.43% H 2 SO 4 ( the remainder is pure water). If 200 Kg of 77.7% acid is added to the tank and the final solution is to be 18.63% acid, how many Kgs of battery acid have been made? To be solved in class (in teams)

16. Dr. F. Iskanderani Spring 2003/2004 EXAMPLE 3 Drying Fish caught by human beings can be turned into fish meal, and the fish meal can be used as feed to produce meat for human beings or used directly as food. The direct use of fish meal significantly increases the efficiency of the food chain. However, fish­protein concentrate, primarily for aesthetic reasons, is used mainly as a supplementary protein food. As such, it competes with soy and other oilseed proteins. In the processing of the fish, after the oil is extracted, the fish cake is dried in ro­tary drum dryers, finely ground, and packed. The resulting product contains 65% pro­tein. In a given batch of fish cake that contains 80% water (the remainder is dry cake), 100 kg of water is removed, and it is found that the fish cake is then 40% water. Calcu­late the weight of the fish cake originally put into the dryer.

17. Dr. F. Iskanderani Spring 2003/2004 (Textbook)

18. Dr. F. Iskanderani Spring 2003/2004 Example 4 Carbon disulfide CS 2 is to be recovered from a gas containing 15 mole% CS 2, 20% O 2 and 65% N 2. The gas is fed to a continuous absorption tower, where it contacts with pure liquid benzene that enters into the tower and absorbs only CS 2 (not O 2, nor N 2 ). Benzene is fed to the column in a 2:1 mole ratio to the feed gas. The gas leaving the absorber contains 5% CS 2, 3% benzene vapor and the balance is O 2 and N 2. Calculate the mole fraction of CS 2 recovered in the liquid stream. Also, find the analysis of the gas stream leaving the tower.

19. Dr. F. Iskanderani Spring 2003/2004 A saturated solution of Na 2 CO 3 at 25 o C is cooled to 20 o C, What percentage of the dissolved salt crystallizes out? Given: Formula for the crystal is Na 2 CO 3.10H 2 O. The solubility of Na 2 CO 3 at 20 o C is 21.5 g/100 g H 2 O and at 25 o C is 30.1 g/100 g H 2 O. Example 5

20. Dr. F. Iskanderani Spring 2003/2004 Example 6 The Following is a labeled flowchart of an extraction process. Find W, Q and R in Kg/min