Degrees of Freedom in Material Balance Problems

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

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

3. To find no. of unknowns: Dr. F. Iskanderani Spring 2003/2004

4. To find no. of equations and given information available for this problem: Therefore F = 16-11 =5 = number of unknown variables to be specified in order to have a unique solution for the problem Dr. F. Iskanderani Spring 2003/2004

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

6. Elements of Using Flowcharts • 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 ) • All equipment and all streams should be named or numbered Dr. F. Iskanderani Spring 2003/2004

7. 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 Dr. F. Iskanderani Spring 2003/2004

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

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

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

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

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

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

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

15. 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 (H2SO4) solution contains 12.43% H2SO4( 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) Dr. F. Iskanderani Spring 2003/2004

16. 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. Dr. F. Iskanderani Spring 2003/2004

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

18. Example 4 Carbon disulfide CS2 is to be recovered from a gas containing 15 mole% CS2, 20% O2 and 65% N2. The gas is fed to a continuous absorption tower, where it contacts with pure liquid benzene that enters into the tower and absorbs only CS2 (not O2 , nor N2). Benzene is fed to the column in a 2:1 mole ratio to the feed gas. The gas leaving the absorber contains 5% CS2, 3% benzene vapor and the balance is O2 and N2 . Calculate the mole fraction of CS2 recovered in the liquid stream. Also, find the analysis of the gas stream leaving the tower. Dr. F. Iskanderani Spring 2003/2004

19. Example 5 A saturated solution of Na2CO3 at 25oC is cooled to 20oC, What percentage of the dissolved salt crystallizes out? Given: Formula for the crystal is Na2CO3.10H2O. The solubility of Na2CO3 at 20oC is 21.5 g/100 g H2O and at 25oC is 30.1 g/100 g H2O. Dr. F. Iskanderani Spring 2003/2004

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