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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

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A flowchart, or process flow diagram (PFD), is a convenient way of organizing processinformation 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 insertsymbols and units.

Flow Charts and Labels

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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 massflow 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

Choosing a Basis (Chapter 3)

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A degree-of-freedom analysis (DFA) is a determination of the number ofunknowns in a problem, and the number of independent equations that can bewritten. The difference between the number of unknowns and the number ofindependent equations is the number of degrees-of freedom, DF or ndf, of theprocess.

ndf = n unknowns - nindependent equations

Possible outcomes of a DFA:

– ndf = 0, there are n independent equations and n unknowns. The problem can besolved.

– ndf > 0, there are more unknowns than independent equations. The problem isunderspecified. More independent equations or specifications are needed tosolve the problem.

– ndf < 0, there are more independent equations than unknowns. The problem isoverspecified with redundant and possibly inconsistent relations.

Degree-of-Freedom Analysis

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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 –

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

Source of Equations

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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 pickan 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.

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.

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6. WRITE and BALANCE stoichiometric equations.

7. Create a TABLE OF BALANCES and UNKNOWNS.

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?

Problem Solving Procedure

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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.

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Example: A mixing process

A continuous mixer mixes NaOH with H2O 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 H2O to the product solution is 0.9.

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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.

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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 (kg/h) and (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 .

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vm

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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.