Overview of Mass balance
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MASS
BALANCE
CIVL270-Maraqa
Objective
Develop a mass balance expression under different
case scenarios and design a simple system to meet
desired needs
Conservation of Mass
Mass cannot be created nor destroyed.
Implication
Atoms are conserved but molecules may change to
other forms.
CIVL270-Maraqa
Types of Reactors
• Batch Reactors
V
• Completely Stirred Tank Reactors (CSTR)
Q,
Cin
Q,
Cout
V
• Plug-Flow Reactors
Q
Q
Q
CIVL270-Maraqa
Q
to
t1
t2
Q
Q
• Dispersed Plug-Flow Reactors
Q
Q
to
Q
Q
t1
Q
Q
t2
• Packed bed Reactors
• Fluidized Packed bed Reactors
Q,
Cin
Q, Cout
Q,
Cout
CIVL270-Maraqa
Q,
Cin
Completely-Mixed Tank Reactor (CSTR)
Accumulation
Input,
Cin
System boundary
Output,
Cout
Decay
Mass Balance- General Equation
Input
rate
CIVL270-Maraqa
=
Ouput
rate
+
Decay +
rate
Accumulation
rate
Steady-State Conservative System
Steady state
Conservative
Accumulation = 0
Decay = 0
Input = Q C +Q C
s s
w w
rate
Ouput = QmCm
rate
Cs Qs + C w Q w
Cm =
Qm
CIVL270-Maraqa
}
Input =
rate
Stream
Ouput
rate
Mixture
Qs, Cs
CSTR
Waste
Qw, Cw
Qm, Cm
Steady-State with Nononservative Pollutants
Steady state
Accumulation = 0
Nonconservative
Input =
rate
Ouput + Decay
rate
rate
Input
QsCs+QwCw
rate =
Ouput = QmCm
rate
Decay = kCmV
rate
Cs Qs + C w Q w
Cm =
Q m + kV
CIVL270-Maraqa
Decay rate (1st-order) = kCV = kCmV
CSTR
Stream
V
Mixture
Qs, Cs
k
Qm, Cm
Waste
Qw, Cw
Reaction Term
Sedimentation
Radioactive decay
Volatilization
Biodegradation
Bio uptake
Hydrolysis
Photodegradation
CIVL270-Maraqa
Example
Stream
Qs=5 m3/s
Well-mixed lake
Cs =10 mg/L
V=10x106 m3
Waste
k=0.2/day
Qw 0.5 m3/s
Solution
Cw =100mg/L
Qm= Qs+ Qw = 5.5 m3/s
Cm =
Cs Qs + C w Q w
Q m + kV
mg m 3
mg
m3
(10 )(5 ) + (100 )(0.5 )
mg
L
s
L
s
Cm =
=
3
.
5
m3
1
day
L
6 3
(5.5 ) + (0.2
×
)(10 × 10 m )
s
day 24 × 60 × 60s
If there was no reaction in the reactor, Cm will be 18.2 mg/L
CIVL270-Maraqa
Outgoing
Qm=?
Cm=?
Example
Stream
Qs=5 m3/s
V=5x106 m3
V=5x106 m3
Cs =10 mg/L
k=0.2/day
Waste
Cm1
k=0.2/day
Cm2=?
Qw 0.5 m3/s
Solution
Cw =100mg/L
Qm= Qs+ Qw = 5.5 m3/s
Cm =
Cs Qs + C w Q w
Q m + kV
Cm1=5.86 mg/L
Cm1Qm=Cm2Qm+kCmV
Cm2
C m1Q m
=
Q m + kV
Cm2=1.9 mg/L
CIVL270-Maraqa
