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Mat
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Mass Balance Calculations
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Objectives
At the end of this chapter, you should be able to:
• Apply material balances for simple systems• Formulate and solve material balance
problems
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Mass Balance Calculations
• All material balance problems are variations on a single theme:
• Given values of some input and output stream variables, derive and solve equations for others.
• Deriving the balance equations from a description of a process and a collection of process data may be considerable difficult
• A procedure for reducing a description of a process to a set of equations that can be solved will be outlined in this lecture.
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Flowcharts
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 670oC before it passes into the reactor. The reactor effluent gas, which includes propane, propylene, methane and hydrogen, is cooled from 800oC to 110oC and fed to an absorption 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 absorption tower.
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Flowcharts
• The best way to organize the information convenient for calculations is to draw flowchart of the process
• A flowchart is drawn using boxes or other symbols to represent process units (reactor, mixers, separation units, etc.) and lines with arrows to represent inputs and outputs.
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Flowcharts - Example • Suppose a gas containing N2 and O2 is combined
with propane in a batch combustion chamber in which some of the O2 and C3H8 react to form CO2 and H2O, and the product is then cooled, condensing the water. The flowchart of the two unit process might appear as shown.
COMBUSTION CHAMBER
CONDENSER
1000 mol O2
3760 mol N2
100 mol C3H8
200 mol H2O
50 mol C3H8
750 mol O2
3760 mol N2
150 mol CO2
50 mol C3H8
750 mol O2
3760 mol N2
150 mol CO2
200 mol H2O
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Flowcharts
• A flowchart of a process can help get material balance calculations started and keep them moving
• To do this, the chart must be fully labeled when it is first drawn, with values of known process variables and symbols for unknown variables being written for each input and output stream.
• Several suggestions to get the greatest possible benefit from it in material balance calculations
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Flowcharts
• Suggestions: • Write the values and units of all known stream
variables at the locations of the streams on the chart
• Assign algebraic symbols to unknown stream variables and write these variable names and their associated units on the chart
• As you work the problem, add your findings to the chart
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Example – Flowchart
EXAMPLE: The feed to a continuous still contains 20 mol% C6 and 80 mol% C11 hydrocarbons. The composition of the overhead distillate is essentially pure C6 and the bottoms contain 5 mol % C6 and the balance C11 materials. Sketch the flowchart.
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Flowchart scaling
• Suppose a kilogram of benzene is mixed with a kilogram of toluene. The output of this process is obviously 2 kg of the mixture that is 50% benzene by mass.
• This process shown in the flowchart is said to be balanced.
1 kg C7H8
1 kg C6H6
2 kg
0.5 kg C6H6/kg
0.5 kg C7H8/kg
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Flowchart scaling
• Observe now that the masses (but not mass fractions) of all streams could be multiplied by a common factor and the process would remain balanced.
• The stream masses could also be changed to mass flow rates
• The units of mass of all stream variables could be changed to any other unit
• The process still remain balanced.
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Flowchart scaling
1 kg C6H6
1 kg C7H8
2 kg 0.5 kgC6H6/ kg0.5 kgC7H8/ kg
300 kg C6H6
300kg C7H8
600 kg 0.5 kgC6H6/ kg0.5 kgC7H8/ kg
300 Ibm C6H6/h
300 Ibm C7H8/h
600 Ibm/h0.5 Ibm C6H6/Ibm
0.5 Ibm C7H8/Ibm
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Flowchart scaling
• The procedure of changing values of all stream amounts or flow rates while leaving the stream compositions unchanged is referred to as scaling
• Scaling-up – if the final stream quantities are larger than the original quantities
• Scaling down – if they are smaller
• Since a balanced process can always be scaled, material balance calculations can be performed on the basis of any convenient set of stream amounts or flow rates and the results can afterwards be scaled.
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Choosing a basis
• Early in the solution of most balance problems, you must choose a "basis of calculation."
• The basis is a reference you choose for the calculations you plan to make.
• Your basis is a fixed number -- all other values are determined relative to it.
• If a stream amount or a flow rate is given in the problem statement, it is usually most convenient to use this quantity as a basis
• If no stream amounts or flow rates are known, assume one preferably that of a stream with known composition
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Flowchart scaling
• Exercise
The process shown below was balanced using the indicated basis of calculation.
Basis of calculation: 100 mol C2H6
Scale up to a feed of 1000 kmol C2H6/h.
2000 mol air
0.21 mol O2/mol
0.79 mol N2/mol
100 mol C2H6
2100 mol
0.0476 mol C2H6/mol
0.200 mol O2/mol
0.752 mol N2/mol
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Balancing a process
• Suppose 3.0 kg/min of benzene and 1.0 kg/min of toluene are mixed. The process flowchart might be drawn and labeled as follows:
m• There are two unknowns: and x • Two equations are needed to calculate them
1 kg C7H8/min
3.0 kg C6H6/min kg/min
x (kg C6H6/kg)(1-x) (kg C7H8/kg)
m
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Balancing a process
• Material balance for this nonreactive process has the simple form : input = output
• Three possible balances can be written– Total mass balance– Benzene balance– Toluene balance
• Solve the problem first!!!
• Which balances are to use when a choice exists?• What is the order in which the balance equations
are to written?
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Balancing a process
• The maximum number of independent equations that can be derived by writing balances on a non reactive system equals the number of chemical species in the input and output streams
• Write balances first that involve the fewest unknown variables
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Example
An aqueous solution of sodium hydroxide contains 20.0% NaOH by mass. It is desired to produce an 8.0% NaOH solution by diluting a stream of the 20% solution with a stream of pure water. Calculate the ratios (liters of water/kg of feed solution) and (kg product solution/kg feed solution).
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Degrees of Freedom
• One of the analysis used to determine whether you have enough information to solve a given problem: degree-of-freedom analysis.
Uses the equation f = V - E
where f = no. of degrees of freedom
V = independent variables/unknown
E = independent equations• If f = 0, fully specified and can be solved• If f > 0, more unknowns, under specified• If f < 0, more independent equations, over
specified
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Problem Solving Procedure
• The problem-solving approaches discussed earlier are summarised. Take the ideas presented here & use them as a basis for your own approach.
• Almost every engineering problem-solving technique boils down to five broad steps – Describe the problem – Identify pertinent known and unknown facts – Identify the scientific principles needed for
solution – Manipulate the numbers – Evaluate the result
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Problem Solving Procedure
• The steps can be expanded to a detailed solution guide tailored to the solution of balance problems. Notice that the approach has the same basic outline.
1. Read the problem thoroughly. Understand what is required for the answer
2. Make a sketch or flowchart of the problem.
3. Write down the known and label unknown stream variables.
4. Choose a calculation basis.
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Problem Solving Procedure
5. Check the specification of the problem (degrees of freedom). Can it be solved as is, or is more information needed?
6. Determine what additional data, if any, are needed. Find them. • Be sure to indicate the source and
applicability of anything you bring from outside.
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Problem Solving Procedure
7. Write the required equations• Material Balances -- NC +1 can be written,
NC are independent.• Energy Balance• Specifications (additional if any)
– Assigned values of stream variables.– Fractional Recoveries.– Composition Relationships (x1=K*x2).– Flow Ratios.
• Physical Properties• Constraints
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Problem Solving Procedure
8. Keep track of units. They can help tell if an equation is complete. If the problem units are mixed, you may want convert all quantities to a common set of units, but probably should wait until you're sure which numbers you'll need.
9. Solve the equations for the unknowns. • Use a solution strategy. Solve the equations in a
planned order. Often, this allows sequential rather than simultaneous solution.
10. Scale the answer (if necessary).
11. Check the solution. Does it make sense?
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Problem Solving Procedure
– A complete material balance problem, ready for solution, will consist of:
– the system with input and output streams – variables which describe the flow rates and
compositions of all streams – a set of material balance equations – a basis – a set of specifications on the solution.
If you don't have all of these, you probably aren't ready to crunch the numbers.
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Problem Solving Procedure
Example: Dilution of Sulfuric Acid Dilute sulfuric acid has to be added to dry charged batteries at service stations in order to activate the battery. You are asked to prepare a new batch of acid as follows:
A tank of old weak battery acid (H2SO4) solution contains 12.43 mass percent H2SO4 (the remainder is water). If 200 kg of 77.7% acid are added to the tank, and the final solution is 18.63% H2SO4, how many kilograms of battery acid have been made?
Solve!
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Material Balances on Distillation Column
• A liquid mixture of benzene (B) and toluene (T) containing 55% B by mass is fed continuously to a distillation column with a feed rate of 100 kg/h. A product stream leaving the top of the column (overhead product) contains 85% B and a bottom product stream contains 10.6% B by mass.
• Determine the mass flow rate of the overhead product stream and the mass flow rate of the bottom product stream.
• Solve!!!
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Mass balance on a dehumidification process
• Wet air containing 4.0 mole% water vapor is passed through a column of calcium chloride pellets. The pellets adsorb 95.0% of the water and none of the other constituents of the air. The column packing was initially dry and had a mass of 3.40 kg. Following 5.0 hours of operation, the pellets are reweigh and found to have a mass of 3.54 kg.
• Calculate the molar flow rate (mol/h) of the feed gas and mole fraction of water vapor in the product gas.
• Solve!!!
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• You have learnt– To draw flowcharts and indicate the
variables on them– To choose a suitable basis and perform a
mass balance calculations.– Scaling of flowcharts– Perform mass balance calculations on a
single unit systems
Conclusions
