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Paul Ashall, 2008 Module 9001 Mass Balance
Paul Ashall, 2008
Module 9001
Mass Balance
Paul Ashall, 2008
The accounting of all mass in a
chemical/pharmaceutical process is referred
to as a mass (or material) balance.
Paul Ashall, 2008
Uses
• ‘day to day’ operation of process for
monitoring operating efficiency
• Making calculations for design and
development of a process i.e. quantities
required, sizing equipment, number of items
of equipment
Paul Ashall, 2008
Simple example – batch mixing
process
200 kg of a 40% w/w methanol/water solution
is mixed with 100 kg of a 70% w/w
methanol/water solution in a batch mixer
unit.
What is the final quantity and composition?
Paul Ashall, 2008
continued
Total initial mass = total final mass = 300 kg
Initial methanol mass = final methanol mass
80 + 70 = final methanol mass = 150 kg
Therefore final composition of batch is
(150/300) x 100 = 50 % by wt.
Paul Ashall, 2008
Exercise
1000 kg of 8% by wt. sodium hydroxide
(NaOH) solution is required. 20% sodium
hydroxide solution in water and pure water
are available. How much of each is
required?
Paul Ashall, 2008
Batch processes
Batch processes operate to a batch cycle and
are non-steady state. Materials are added to
a vessel in one operation and then process is
carried out and batch cycle repeated.
Integral balances are carried out on batch
processes where balances are carried out on
the initial and final states of the system.
Paul Ashall, 2008
Batch cycle
• Sequence of operations/steps repeated
according to a cycle
• Batch cycle time
• Batch size
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Simple batch reaction cycle3 steps
Start cycle t=0 t, finish cycle
Add reactants etc reaction Empty reactor
Next cycle
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Continuous processes
These processes are continuous in nature and
operate in steady state and balances are
carried out over a fixed period of time.
Materials enter and leave process
continuously.
Paul Ashall, 2008
Law of conservation of mass
When there is no net accumulation or
depletion of mass in a system (steady state)
then:
Total mass entering system = total mass
leaving system
or total mass at start = total final mass
Paul Ashall, 2008
General mass balance equation
Input + generation – output – consumption = accumulation
Notes: 1. generation and consumption terms refer only to generation of products and consumption of reactants as a result of chemical reaction. If there is no chemical reaction then these terms are zero.
2. Apply to a system
3. Apply to total mass and component mass
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Definitions
• System – arbritary part or whole of a system
• Steady state/non-steady state
• Accumulation/depletion of mass in system
• Basis for calculation of mass balance (unit
of time, batch etc)
• Component or substance
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Exercise
1000 kg of a 10 % by wt. sodium chloride
solution is concentrated to 50 % in a batch
evaporator. Calculate the product mass and
the mass of water evaporated from the
evaporator.
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Mixing of streams
F1
F2
F3
F4
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Example
Calculate E and x
Fresh feed 1000kg, 15%
by wt sodium hydrogen carbonate
Recycle stream 300 kg, 10% satd. soln.
evaporator feed E, composition x%
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Flowsheets
• Streams
• Operations/equipment sequence
• Standard symbols
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Flowsheets
• Process flow diagram
• PID
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Typical simple flowsheet
arrangement
reactorSeparation &
purificationFresh feed
(reactants, solvents,
reagents, catalysts etc)
product
Recycle of unreacted material
Byproducts/coproductswaste
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Exercise
A 1000 kg batch of a pharmaceutical powder
containing 5 % by wt water is dried in a
double cone drier. After drying 90 % of the
water has been removed. Calculate the final
batch composition and the weight of water
removed.
Paul Ashall, 2008
Exercise – batch distillation
1000 kg of a 20% by wt mixture of acetone in
water is separated by multistage batch
distillation. The top product (distillate)
contains 95% by wt. acetone and the still
contains 2% acetone. Calculate the amount
of distillate.
Paul Ashall, 2008
Use of molar quantities
It is often useful to calculate a mass balance
using molar quantities of materials and to
express composition as mole fractions or
mole %.
Distillation is an example, where equilibrium
data is often expressed in mole fractions.
Paul Ashall, 2008
Molar units• A mole is the molecular weight of a substance
expressed in grams
• To get the molecular weight of a substance you need its molecular formula and you can then add up the atomic weights of all the atoms in the molecule
• To convert from moles of a substance to grams multiply by the molecular weight
• To convert from grams to moles divide by the molecular weight.
• Mole fraction is moles divided by total moles
• Mole % is mole fraction multiplied by 100
Paul Ashall, 2008
Molar units
Benzene is C6H6. The molecular weight is
(6x12) + (6x1) = 78
So 1 mole of benzene is 78 grams
1 kmol is 78 kg
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Exercise – batch distillation
1000 kmol of an equimolar mixture of
benzene and toluene is distilled in a
multistage batch distillation unit. 90 % of
the benzene is in the top product (distillate).
The top product has a benzene mole fraction
of 0.95. Calculate the quantities of top and
bottom products and the composition of the
bottom product.
Paul Ashall, 2008
Mass balance - crystalliser
A crystalliser contains 1000 kg of a saturated solution of potassium
chloride at 80 deg cent. It is required to crystallise 100 kg KCl from
this solution. To what temperature must the solution be cooled?
Paul Ashall, 2008
T deg cent Solubility
gKCl/100 g water
80 51.1
70 48.3
60 45.5
50 42.6
40 40
30 37
20 34
10 31
0 27.6
Paul Ashall, 2008
At 80 deg cent satd soln contains (51.1/151.1)x100
% KCl i.e. 33.8% by wt
So in 1000 kg there is 338 kg KCl & 662 kg water.
Crystallising 100 kg out of soln leaves a satd soln
containing 238 kg KCl and 662kg water i.e.
238/6.62 g KCl/100g water which is 36 g
KCl/100g. So temperature required is approx 27
deg cent from table.
Paul Ashall, 2008
Mass balance filtration/centrifuge
feed suspension
wash water/solvent
solid
waste waterfiltrate
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Filtration
F1
5000 kg DM water
Impurity 55 kg
Water 2600 kg
API 450 kg
Water 7300 kg
Impurity 50 kg
API 2kg
Water 300 kg
API 448 kg
Impurity 5 kg
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Mass balance - drier
feed product
water/evaporated solvent
Paul Ashall, 2008
Mass balance – extraction/phase
split
A + B
S
A + B
S + B
A – feed solvent; B – solute; S – extracting solvent
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Example (single stage extraction;
immiscible solvents)
E1
feed
solvent
raffinate
extract
Paul Ashall, 2008
F = 195 kg; xf = 0.11 kg API/kgwater
S = 596 kg chloroform
y = 1.72x, where y is kgAPI/kg chloroform in extract and x is kg API/kg water in raffinate.
Total balance 195 + 596 = E + R
API balance 19.5 = 175.5x1 + 596y1
19.5 = 175.5x1 + 596.1.72x1
x1 = 0.0162 and y1 = 0.029
R is 175.5 kg water + 2.84 kg API
and E is 596 kg chloroform + 17.28 kg API
Note: chloroform and water are essentially immiscible
Paul Ashall, 2008
Mass balance – absorption unit
feed gas stream
feed solvent
waste solvent stream
exit gas stream
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Mass balances – multiple units
• Overall balance
• Unit balances
• Component balances
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Multiple units
E – evaporator; C – crystalliser; F – filter unit
F1 – fresh feed; W2 – evaporated water; P3 – solid product; R4 – recycle of saturated solution from filter unit
R4
E C FF1
W2
P3
Paul Ashall, 2008
Mass balance procedures
• Process description
• Flowsheet
• Label
• Assign algebraic symbols to unknowns (compositions, concentrations, quantities)
• Select basis
• Write mass balance equations (overall, total, component, unit)
• Solve equations for unknowns
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Exercise
A mass balance and tracking of usage of a solvent used in an API production process is required for a Pollution Emission Register (PER).
Discuss and outline in general terms how you would do this.
Ref. www.epa.ie
Paul Ashall, 2008
Definitions
• Stoichiometric quantities
• Limiting reactant
• Excess reactant
• Conversion
• Yield
• Selectivity
• Extent of reaction
Paul Ashall, 2008
Stoichiometry
• Refers to quantities of reactants and
products in a balanced chemical reaction.
aA + bB cC + dD
i.e. a moles of A react with bmoles of B to
give c moles of C and d moles of D.
a,b,c,d are stoichiometric quantities
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Reactor mass balances
Paul Ashall, 2008
Example – aspirin synthesis
reaction
Paul Ashall, 2008
Limiting reactant/excess reactant
• In practice a reactant may be used in excess
of the stoichiometric quantity for various
reasons. In this case the other reactant is
limiting i.e. it will limit the yield of
product(s)
Paul Ashall, 2008
continued
A reactant is in excess if it is present in a
quantity greater than its stoichiometric
proportion.
% excess = [(moles supplied – stoichiometric
moles)/stoichiometric moles] x 100
Paul Ashall, 2008
Example – aspirin synthesis
Paul Ashall, 2008
Conversion
• Fractional conversion = amount reactant
consumed/amount reactant supplied
• % conversion = fractional conversion x 100
Note: conversion may apply to single pass reactor
conversion or overall process conversion
Paul Ashall, 2008
Yield
Yield = (moles product/moles limiting
reactant supplied) x s.f. x 100
Where s.f. is the stoichiometric factor =
stoichiometric moles reactant required per
mole product
Paul Ashall, 2008
Example – aspirin synthesis
Paul Ashall, 2008
Selectivity
Selectivity = (moles product/moles reactant
converted) x s.f. x100
OR
Selectivity = moles desired product/moles
byproduct
Paul Ashall, 2008
Extent
Extent of reaction = (moles of component leaving reactor – moles of component entering reactor)/stoichiometric coefficient of component
Note: the stoichiometric coefficient of a component in a chemical reaction is the no. of moles in the balanced chemical equation ( -ve for reactants and +ve for products)
Paul Ashall, 2008
ExamplesA B
i.e. stoichiometric coefficients a = 1; b = 1
100 kmol fresh feed A; 90 % single pass
conversion in reactor; unreacted A is
separated and recycled and therefore overall
process conversion is 100%
reactor separationF
R
P
Paul Ashall, 2008
Discussion - Synthesis of 3,3
dimethylindoline
Paul Ashall, 2008
Discussion - Aspirin synthesis
Paul Ashall, 2008
References
• Elementary Principles of Chemical
Processes, R. M. Felder and R. W.
Rousseau, 3rd edition, John Wiley, 2000
