The General Strategy for Solving Material Balance Problems
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- Bernard Sherman
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1 The General Strategy for Solving Material Balance Problems Objectives: o Efficient and effective in solving material balance problems o How similar material balance problems are o How to solve them in the most expeditious manner
2 Problem Solving A problem is a gap between some initial information (the initial state) and the desired information (the final state) Skills in problem solving: formulating specified questions from vaguely specified problems; selecting problem solving strategies; deciding when an estimate will suffice versus an exact answer; using tables, graphs, spreadsheets, calculators, and computers to organize, solve, and interpret the results from solving problems; judging the validity of the work of others; and evaluating answers. Do not allow a problem to become abstract and related to physical behaviour.
3 The Strategy for Solving Problems 1. Read and understand the problem statement. 2. Draw a sketch of the process and specify the system boundary 3. Place labels for unknown variables and values for known variables on the sketch 4. Obtain any missing needed data 5. Choose a basis. 6. Determine the number of unknowns. 7. Determine the number of independent equations, and carry out a degree of freedom analysis. 8. Write down the equations to be solved. 9. Solve the equations and calculate the quantities asked for. 10. Check your answer(s).
4 The Strategy for Solving Problems degrees of freedom = number of unknowns number of independent equations N D = N U N E N U = N S (N sp +1)- N K ; N S = number of streams N sp = number of species N S = number of knowns N E involves independent species/components balances, total mass balance, and in each stream the sums of the mass or mole fractions equals unity (implicit equation)
5 Techniques Used by Experts to Overcome Barriers to Problem Solving Read the problem over several times, but at different limes. Be sure to understand all facets of it. Emphasize the different features each time. Restate the problem in your own worth. List assumptions. Draw a comprehensive diagram of the process and enter all known information on the diagram. Enter symbols for unknown variables and parameters. Formally write down what you are going to solve for: I want to calculate Choose a basis. Relate the problem to similar problems you have encountered before, but note any differences. Plan a strategy for a solution, writing it down if necessary. Consider different strategies.
6 Techniques Used by Experts to Overcome Barriers to Problem Solving Write down all the equations and rules that might apply to the problem. Formally write down everything you know about the problem and what you believe is needed to execute a solution. Talk to yourself as you proceed to solve the problem. Ask yourself questions as you go along concerning the data, procedures, equations involved, etc. Talk to other people about the problem. Break off problem solving for a few minutes and carry out some other activity. Break up the solution of the problem into more manageable parts, and start at a familiar stage. Write down the objective for each subproblem (i.e., convert mole fraction to mass fraction, find the pressure in tank 2, etc.
7 Techniques Used by Experts to Overcome Barriers to Problem Solving Repeat the calculations but in a different order. Work both forward and backward in the solution scheme. Consider if the results you obtained are reasonable. Check both units and order of magnitude of the calculations. Are the boundary conditions satisfied? Use alternative paths to verify your solution. Maintain a positive attitude you know the problem can be solved, just how is the question.
8 <M> Sugar 1000 lb/hr Mill <D> Bagasse 8 <F> Cane 16% sugar 25% water 59% pulp <E> 13% sugar 14% pulp Screen <G> Solids 95% pulp <H> 15% sugar Crystallizer <K> 4 Evaporator <L> Water <J> Water Vapor
9 Step 1 - Step 5 Basis : <M> Sugar 1000 lb/hr <M> Sugar 1000 lb/hr 10 0% water Mill <D> Bagasse a% sugar b% water 8 <F> Cane 16% sugar 25% water 59% pulp <E> 13% sugar 73% water 14% pulp Screen <G> Solids c% sugar d% water 95% pulp <H> 15% sugar 85% water Crystallizer <K> 4 60% water Evaporator <L> Water <J> Water Vapor
10 Step 6 - Step 7 Basis : <M> Sugar 1000 lb/hr <M> Sugar 1000 lb/hr 10 0% water Mill <D> Bagasse a% sugar b% water 8 <F> Cane 16% sugar 25% water 59% pulp <E> 13% sugar 73% water 14% pulp Screen <G> Solids c% sugar d% water 95% pulp <H> 15% sugar 85% water Crystallizer <K> 4 60% water Evaporator <L> Water <J> Water Vapor
11 Step 6 - Step 7 Basis : <M> Sugar 1000 lb/hr <M> Sugar 1000 lb/hr 10 0% water Mill <D> Bagasse a% sugar b% water 8 <F> Cane 16% sugar 25% water 59% pulp <E> 13% sugar 73% water 14% pulp Screen <G> Solids c% sugar d% water 95% pulp <H> 15% sugar 85% water Crystallizer <K> 4 60% water Evaporator <L> Water <J> Water Vapor
12 Step 6 - Step 7 Basis : <M> Sugar 1000 lb/hr N sp = 3; N S = 6 N U = 6(3+1) ( ) = 9 N E = = 5 N D = 9 5 = 4 <F> Cane 16% sugar 25% water 59% pulp <M> Sugar 1000 lb/hr 10 0% water Crystallizer <L> Water Mill <D> Bagasse a% sugar b% water 8 Screen <G> Solids c% sugar d% water 95% pulp Evaporator <J> Water Vapor
13 Step 6 - Step 10 Basis : <M> Sugar 1000 lb/hr N sp = 3; N S = 3 N U = 3(3+1) (3+3+4) = 2 N E = = 2 N D = 2 2 = 0 <K> <L> <M> Species frac. mass frac. mass frac. mass sugar water pulp <M> Sugar 1000 lb/hr 10 0% water Crystallizer <K> 4 60% water <L> Water
14 Step 6 - Step 7 Basis : <M> Sugar 1000 lb/hr N sp = 3; N S = 3 N U = 3(3+1) (3+3+4) = 2 N E = = 2 N D = 2 2 = 0 N sp = 3; N S = 3 N U = 3(3+1) (3+1+4) = 4 N E = = 4 N D = 4 4 = 0 <H> 15% sugar 85% water Screen <E> 13% sugar 73% water 14% pulp <G> Solids c% sugar d% water 95% pulp <K> 2500 lb/hr 4 60% water Evaporator <H> 15% sugar 85% water <J> Water Vapor
15 Step 6 - Step 7 Basis : <M> Sugar 1000 lb/hr N sp = 3; N S = 3 N U = 3(3+1) (3+3+4) = 2 N E = = 2 N D = 2 2 = 0 N sp = 3; N S = 3 N U = 3(3+1) (3+1+4) = 4 N E = = 4 N D = 4 4 = 0 <H> 15% sugar 85% water Screen <E> 13% sugar 73% water 14% pulp <G> Solids c% sugar d% water 95% pulp <K> 2500 lb/hr 4 60% water Evaporator <H> 15% sugar 85% water <J> Water Vapor
16 Step 6 - Step 7 Basis : <M> Sugar 1000 lb/hr N sp = 3; N S = 3 N U = 3(3+1) (3+1+4) = 4 N E = = 4 N D = 4 4 = 0 Mill <D> Bagasse a% sugar b% water 8 <F> Cane 16% sugar 25% water 59% pulp <E> 13% sugar 73% water 14% pulp
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