Lecture 8, 3/9/2012 Chapter 7: A GENERAL Strategy for Solving Material Balance Problems Objectives: Comprehend and execute the 10 elements of effective problem Drive a flow chart and Place labels on the diagram. Choose a proper basis of calculation Understand and apply a degree of freedom analysis 1
Flow Charts and Labels A flowchart, or process flow diagram (PFD), is a convenient way of organizing process information for subsequent calculations. To obtain maximum benefit from the flowchart in material balance calculations, you must: 1. Draw a sketch of the process and specify the system boundary. 2. Place labels (symbols, numbers, and units) on the diagram for all of the known flows, materials, and compositions. For the unknown flows, materials, and compositions insert symbols and units. 2
Choosing a Basis (Chapter 3) Basis: The reference material or time selected to use in making the calculations in a problem. Basis of calculation in material balance: is an amount or flow rate of one of the process streams. If a stream amount or flow rate is given in the problem statement, use this as the basis of calculation (usually) If no stream amounts or flow rates are known, assume one, preferably a stream of known composition if mass fractions are known, choose a total mass or mass flow rate of that stream (e.g., 100 kg or 100 kg/h) as a basis if mole fractions are known, choose a total number of moles or a molar flow rate 3
Degree-of-Freedom Analysis A degree-of-freedom analysis (DFA) is a determination of the number of unknowns in a problem, and the number of independent equations that can be written. The difference between the number of unknowns and the number of independent equations is the number of degrees-of freedom, DF or n df, of the process. n df = n unknowns - n independent equations Possible outcomes of a DFA: n df = 0, there are n independent equations and n unknowns. The problem can be solved. n df > 0, there are more unknowns than independent equations. The problem is underspecified. More independent equations or specifications are needed to solve the problem. n df < 0, there are more independent equations than unknowns. The problem is overspecified with redundant and possibly inconsistent relations. 4
Source of Equations Sources of equations that relate unknown process variables include: 1. Material balances for a nonreactive process, the maximum number of independent equations that can be written equals the number of chemical species in the process 2. Energy balances 2nd half of course 3. Process specifications given in the problem statement such as The ratio of two flow rates is some specific value. The percent conversion in a reaction is given. The value of a concentration, flow rate, temperature, pressure, density, volume, and so on is given. 5. Implicit relations e.g., the sum of the mass or mole fractions must add to 1 6. Stoichiometric relations systems with reaction 5
Problem Solving Procedure 1. READ and UNDERSTAND the problem statement. Ask yourself What information am I given? What am I asked to do? What other info might I need to solve the problem? 2. Select a BASIS. The first two questions in Step 1 should help you pick an amount or a flow rate to use as the BASIS. or assume an amount or flow rate (typically a multiple of 10). 3. DRAW and LABEL a process diagram. boxes (processes) and arrows (input & output). Labels must include units. 6
Problem Solving Procedure 4. ASSIGN ALGEBRAIC SYMBOLS to represent any unknowns using Let x represent... statements. Use as few unknowns symbols as possible. Place symbols with units on process diagram. 5. COLLECT and TABULATE any additional data that may be required. 6. WRITE and BALANCE stoichiometric equations. 7. Create a TABLE OF BALANCES and UNKNOWNS. 7
Problem Solving Procedure 8. WRITE MASS BALANCES. Always start with A = I + G O C and cancel unnecessary terms with justification. Balances must be independent. Write the balances in order, starting with the balance with the fewest unknowns. Number of independent balances should equal the number of unknowns. If not, look for other relationships between unknowns. For non-reactive systems, the max number of independent balances = number of molecular species. 9. SOLVE BALANCES / EQUATIONS. 10. CHECK ANSWER. 11. ANSWER THE FOLLOWING QUESTION: What did I learn? 8
Chapter 8: Solving Material Balance Problem for Single Units without Reaction Objectives: 1. Analyze a problem statement and organize in your mind the solution strategy. 2. Apply the 10-step strategy to solve problems without chemical reactions. 9
Example: A mixing process A continuous mixer mixes NaOH with H 2 O to produce an aqueous solution of NaOH. Determine the composition and flow rate of the product if the flow rate of NaOH is 1000 kg/hr, and the ratio of the flow rate of the H 2 O to the product solution is 0.9. 10
Test yourself: Mass Balance for making strawberry jam Strawberries contain about 15 wt % solids and 85 % water. To make strawberry jam, crushed strawberries and suger are mixed in a 45:55 mass ratio, and the mixture is heated to evaporate water until the residue contains one-third water by mass. Calculate how many pounds of strawberries are needed to make a pound of jam. 11
Example: A condenser 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/hr. Dry air may be taken to contain 21 mol % O 2 and 79 mol % N 2. Calculate the flow rate of the gas stream leaving the condenser and the mole fractions of oxygen, nitrogen, and water in this stream. 12
Test yourself: Mass balance for an evaporator A liquid mixture of benzene and toluene contains 55.0% benzene by mass. The mixture is to be partially evaporated to yield a vapour containing 85.0% benzene and a residual liquid containing 10.6% benzene by mass. Suppose the process is to be carried out continuously and at steady state, with a feed rate of 100.0 kg/h of the 55% benzene. Let m v (kg/h) and m l (kg/h) be the mass flow rates of the vapour and liquid product streams, respectively. Draw and label a process flowchart, then write and solve balances on total mass and on benzene to determine the expected values of and. m v m l 13
Example: Mass Balance for a distillation column A distillation process is shown in the figure. The manufacturer found that too much alcohol is lost in the bottoms ( waste). Calculate the composition of the bottoms and the mass of alcohol lost in the bottoms based on the data shown in the figure that was collected during 1 hour of operation. 14
Example: Mass Balance for a distillation column A liquid mixture containing 45 % benzene (B) and 55 % toluene (T) by mass is fed to a distillation column. A product stream leaving the top of the column contains 95 mole % B, and a bottom product stream contains 8 weight % of the benzene fed to the column. The volumetric flow rate of the feed stream is 2000 L/h and the specific gravity of the feed mixture is 0.872. Determine the mass flow rate of the overhead stream and the mass flow rate and composition (mass fraction) of the bottom product stream. 15
Example: Mass Balance for a separator A solution composed of 50% ethanol (EtOH), 10% methanol (MeOH), and 40% water (H 2 O) is fed at the rate of 100 kg/h into a separator that produces one stream at the rate of 60 kg/h with the composition of 80% EtOH, 15% MeOH, and 5% H 2 O, and a second stream of unknown composition. Calculate the composition (in %) of the three compounds in the unknown stream and its flow rate in kg/h. 16