MISS. RAHIMAH BINTI OTHMAN (Email: rahimah@unimap.my)

1. ERT 416/3CHAPTER 3: FUNDAMENTALS OF MATERIAL AND ENERGY BALANCES IN BIOPROCESS PLANT MISS. RAHIMAH BINTI OTHMAN (Email: rahimah@unimap.edu.my)

2. COURSE OUTCOMES

3. OUTLINES • Engineering principle for the design process. • The material balances calculations in process design- to study plant operation and troubleshooting. • The energy requirement of the process using energy balances. • Comparison between engineering calculation with suitable process simulators like Aspen HYSYS or Super Pro Design.

4. Quiz 1 (question 1) The general equations for material and energy balances. Material out = Material in + Generation – Consumption - Accumulation Total energy entering the system – Total energy leaving the system = Change in the total energy of the system ∆(Energy of the system) = E in – E out =∆U+∆EK+ ∆EP

5. ASSIGNMENT 1(question 3) Balances on a Batch Mixing Process Two methanol-water mixtures are contained in separate flasks. The first mixture contains 40.0 wt % methanol, and the second contains 70.0 wt % methanol. If 200 g of the first mixture is combined with 150 g of the second, what are the mass and composition of the product? Solution Input = Output

6. assignment 1 (question 4) Yield of a Crystallization Process A salt solution weighing 10000 kg with 30 wt % Na2CO3 is cooled to 293 K (20 °C). The salt crystallizes as the decahydrate. What will be the yield of Na2CO3•10H2O crystals if the solubility is 21.5 kg anhydrous Na2CO3/100 kg of total water? Do this for the following cases: (a) Assume that no water is evaporated. (b) Assume that 3% of the total weight of the solution is lost by evaporation of water in cooling. FIGURE3. Process flow for crystallization

7. Question 4 Solution The molecular weights are 106.0 for Na2CO3, 180.2 for 10H20, and 286.2 for Na2CO3 •10H2O. The process flow diagram is shown in Fig. 3, with W being kg H2O evaporated, S kg solution (mother liquor), and C kg crystals of Na2CO3 •10H2O.Making a material balance around the dashed line box for water for part (a), where W = 0. (13) where (180.2)/(286.2) is wt fraction of water in the crystals.

8. Question 4 (14) Making a balance for Na2CO3, Solving the two equations simultaneously, C = 6370 kg of Na2CO3•10H2O crystals and S = 3630 kg solution. For part (b), W = 0.03(10000) = 300 kg H2O. Equation (13) becomes Equation (14) does not change, since no salt is in the W stream. Solving Eqs. (14) and (15)simultaneously, C = 6630 kg of Na2CO3•10H2O crystals and S = 3070 kg solution. (15)

9. Quiz 1 (question 5) The diagram shows the main steps in a process for producing a polymer. From the following data, calculate the stream flows for a production rate of 10, 000 kg/h. Filter wash water approx. 1 kg/ 1 kg polymer Recovery column yield 98 % (percentage recovered) Dryer feed ~ 5 % water, product specification 0.5 % H2O Polymer losses in filter and dryer ~ 1 %

10. ANSWER Only those flows necessary to illustrate the choice of system boundaries and method of calculation are given in the solution. Basis: 1 h Take the first system boundary round the filter and dryer. Take the next boundary round the reactor system; the feeds to the reactor can then be calculated.

11. ANSWER

12. ANSWER Now consider recovery system; Composition of effluent is 22 kg monomer, 54,461 kg water. Consider reactor monomer feed

13. OUTLINES • Engineering principle for the design process. • The material balances calculations in process design- to study plant operation and troubleshooting. • The energy requirement of the process using energy balances. • Comparison between engineering calculation with suitable process simulators like Aspen HYSYS or Super Pro Design.

14. What is Material Balance? Material balances (mass balances) are based on the fundamental “law of conservation of mass (not volume, not moles)”. In particular, engineers are concerned with doing mass balances around the specific processes. • To describe the chemicals entering a process stream. Now, we must • learn how to: • Specify a process stream • Specify a process unit • Do a mass balance on a process unit • Do a mass balance on a sequence of process units.

15. Example 1:Input and Output Diagram Auxiliary materials Water Energy Product (expected) Unit Operation Raw material byproduct (usable) Waste Waste easily assimilated by the environment Inert waste always available toxic/dangerous waste

16. Example 2: Input and Output Raw materials Gaseous emissions Plant, Process or Unit Operación Catalyst Products Air/Water By-products Energy Wastewater Recycle Liquid waste Solid waste Reusable residues in other operation

17. Process Classification Based on how the process varies with time. Steady-state processis one that does not change with time. Every time we take a snapshot, all the variables have the same values as in the first snapshot. Unsteady-state (Transient) processis one that changes with time. Every time we take a snapshot, many of the variables have different values than in the first snapshot. • Based on how the process was built to operate. • A Continuous processis a process that has the feed streams and product streams moving chemicals into and out of the process all the time. At every instant, the process is fed and product is produced. Examples are an oil refinery, a power grid and a steady salaried job. • A Batch processis a process where the feed streams are fed to the process to get it started. The feed material is then processed through various process steps and the finished products are created during one or more of the steps. The process is fed and products result only at specific times. Examples are making a batch of a product, like soup or a specialty chemical. • A Semi-batch process (also called semi-continuous) is a process that has some characteristics continuous and batch processes. Some chemicals in the process are handled batch-wise. Some chemicals are processed continuously.

18. ∆(Energy of the system) + (∆Energy of surroundings) = 0 ∆(Energy of the system) = Q+W ∆(Energy of the system) =∆U+∆EK+ ∆EP

22. Types of Balances Differential Balance is a balance taken at a specific instant in time. It is generally applied to a continuous process. If the process is at steady state, a differential balance applied at any time gives the same result. We will apply differential balances to steady-state continuous processes. Each term in a differential balance represents a process stream and the mass flow rate of the chemical(s) in that stream. Integral balanceis a balance taken at two specific instants in time. It describes what has happened over the time period between the two points. An integral balance is generally applied to the beginning and the end of a batch process. It accounts for what happens to the batch of chemicals. We will apply integral balances to batch processes. Each term in an integral balance represents a process stream and the mass of the chemical(s) in that stream.

23. Example: Integral Balances on Batch Processes Ammonia is produced from nitrogen and hydrogen in a batch reactor. At time t = 0 there are n0 mol of NH3 in the reactor, and at a later time tf the reaction terminates and the contents of the reactor, which include nf mol of ammonia, are withdrawn. Between to and tf no ammonia enters or leaves through the reactor boundaries, so the general balance equation is simply generation = accumulation

24. Example: Integral Balances on Semibatch and Continuoius Processes Air is bubbled through a drum of liquid hexane at a rate of 0.100 kmol/min. The gas stream leaving the drum contains 10.0 mole% hexane vapor. Air may be considered insoluble in liquid hexane. Use an integral balance to estimate the time required to vaporize 10.0 m3 of the liquid. SOLUTION

25. Example: Integral Balances on Semibatch and Continuous Processes – Cont’

26. TEST YOURSELF? Example: A process unit involves 3 chemical components. How many mass balances can be written? Solution: We can write 4 balances. We can write a total balance and 3 component balances.

27. Where am I? Where am I going ? How do I get there? • To answer the first question, you need to • Read, study and understand the problem. • Draw a flow sheet for the process. • Label it with all given information, including symbols for the unknowns • Note any special relationships. • To accomplish this step, you need to learn • The information needed to specify a stream. • How to use symbols to represent the required stream data. • How to determine the mass of each component in a stream (each mass will be a term in a mass balance)

28. EXAMPLE 1 Stream F contains 500 kg of O2 and 700 kg of CH4. Label the stream. Solution: Note that the component masses must add to the total. The total mass in F is 1200 kg. Thus, Stream F F=1200 kg m O2 = 500 kg m CH4 = 700 kg EXAMPLE 2 1200 kg of a mixture of O2 , N2 and CH4 are fed to a process. The stream has 20% O2 by mass. Label the stream. ( Note the Mass of i in the stream is F xi ) Solution: The composition is partially known. Note that the fractional compositions must add to 1.0. Thus, we can write two alternatives Using fractional composition Feed Stream F, F=1200 kg xO2 = 0.2 xN2 = ? xCH4 = 1. – 0.2 - xN2 = 0.8 - xN2

29. or using component masses Feed Stream F, F=1200 kg mO2 = 240 kg mN2 = ? mCH4 = 1200 - 240 - mN2 = 960 - mN2 • Some Suggestions for Component Labeling • If the stream composition is unknown (or if some of the component masses are known) represent the component masses directly and use a lower case letter for each chemical. • Eg. If stream F contains chemicals a, b and c, label the flow rates as; • F, aF, bF and cF=F- aF – Bf • If the stream composition is known from fractional compositions, represent the component masses directly and label as in 2. • If stream composition is partially known with fractional compositions and the total is known, represent the component masses indirectly and use lower case x,y,z for each fractional composition. • Avoid the creation of a product of two unknowns—this will result in a non-linear equation.

30. FLOWCHARTS CASE STUDY: The catalytic dehydrogenation of propane is carried out in a continuous packed-bed reactor. One thousand kilograms per hour of pure propane is preheated to a temperature of 670 oC before it passes into the reactor. The reactor effluent gas, which includes propane, methane, and hydrogen, is cooled from 800 oC to 110 oC and fed to an adsorption tower, where the propane and propylene are dissolved in oil. The oil then goes to a stripping tower in which it is heated, releasing the dissolved gases; these gases are recompressed and sent to a distillation column in which the propane and propylene are separated. The propane stream is recycled back to join the feed to the reactor preheater.The product stream from the distillation column contains 98 % propylene, and the recycle stream is 97 % propane. The stripped oil is recycled to the adsorption tower. Draw the flowchart for this system.

31. SOLUTION: Write the values and units of all known stream variables at the locations of the streams on the chart. For example; A stream containing 21 mole % O2, and 79 % N2 at 320 oC and 1.4 atm flowing at a rate of 400 mol/h might be labeled.

32. Assign algebraic symbols to unknown stream variables [such as (kg solution/min), x (lbm N2/lbm), and n (kmol C3H8)] and write these variable names and their associated units on the chart. For example; If you did not know the flow rate of the stream described in the first illustration of step 1, you might label the stream.

34. EXAMPLE

35. SOLUTION

36. SOLUTION

37. FLOWCHART SCALING AND BASIS OF CALCULATION EXAMPLE

38. SOLUTION

39. DEGREE-OF-FREEDOM ANALYSIS ndf (= nunknowns – nindep eqns) Equation: Three possibilities: If ndf = 0, there are n independent equations in n unknowns and the problem can in principle be solved. If ndf > 0, there are more unknowns than independent equations relating them, and at least ndf additional variable values must be specified before the remaining variable values can be determined. Either relations have been overlooked or the problem is underspecified and has infinitely many solutions; in either case, plugging into calculations is likely to be a waste of time. If ndf < 0, there are more independent equations than unknowns. Either the flowchart is incompletely labeled or the problem is overspecified with rebundant and possibly inconsistent relations. Again there is little point wasting time trying to solve it until the equations and unknowns are brought into balance.

40. DEGREE-OF-FREEDOM ANALYSIS 2. Energy Balances 1. Material Balances 3. Process Specifications Source Of Equations Relating Unknown Process Stream Variables 4. Physical Properties and Laws 6. Stoichiometric Relations 5. Physical Constrains

41. DEGREE-OF-FREEDOM ANALYSIS EXAMPLE Degree-of-Freedom Analysis A stream of humid air enters a condenser in which 95 % of the water vapor in the air is condensed. The flow rate of the condensate (the liquid leaving the condenser) is measured and found to be 225 L/h. Dry air may be taken to contain 21 mole% oxygen, with the balance nitrogen. Calculate the flow rate of the gas stream leaving the condenser and the mole fractions of oxygen, nitrogen and water in this stream. SOLUTION

42. DEGREE-OF-FREEDOM ANALYSIS Suppose we had given an additional piece of information- for example, that the entering air contains 10.0 mole% water. The flowchart would then appear as follows;

43. GENERAL PROCEDURE FOR SINGLE-UNIT PROCESS MATERIAL BALANCE CALCULATIONS Choose as a basis of calculation an amount or flow rate of one of the process streams. Draw flowchart and fill in all known variable values, including the basis of calculation. Then label unknown stream variables on the chart. Express what the problem statement asks you to determine in terms of the labeled variables. If you are given mixed mass and mole units for a stream (such as a total mass flow rate and component mole fractions or vice versa), convert all quantities to one basis. Do the degree-of-freedom analysis. If the number of unknowns equals the number of equations relating them (i.e: ndf =0), write the equations in an efficient order (minimizing simultaneous equations) and circle the variables for which you will solve. Solve the equations. Calculate the quantities requested in the problem statement if they have not already been calculated. If the stream quantity or flow rate ngwas given in the problem statement and another value nc was either chosen as a basis or calculated for this stream, scale the balanced process by the ratio ng/nc to obtain the final result.

44. EXAMPLE Material Balances on a Distillation Column A liquid mixture containing 45.0% benzene (B) and 55.0% toluene (T) by mass is fed to a distillation column. A product stream leaving the top of the column (the overhead product) contains 95.0 mole % B, and a bottom product stream contains 8.0 % of the benzene fed to the column (meaning that 92 % of the benzene leaves with the overhead product). The volumetric flow rate of the feed 2000 L/h and the specific gravity of the fed mixture is 0.872. Determine the mass flow rate of the overhead product stream and the mass flow rate and composition (mass fractions) of the bottom product stream. SOLUTION We will explicitly illustrate the implementation of the steps of the procedure just outlined. Choose a basis. Having no reason to do otherwise, we choose the given feed stream flow rate (2000 L/h) as the basis of calculation. Draw and label the flowchart.

45. NOTIFICATION:

49. BALANCES ON MULTIPLE-UNIT PROCESSES

50. BALANCES ON MULTIPLE-UNIT PROCESSES EXAMPLE