zerihun alemayehu (aait-ced) alemayehu (aait-ced) ... the simplest form of a materials balance or...
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Zerihun Alemayehu (AAiT-CED)
Tools for quantitative understanding of the behavior of environmental systems.
For accounting of the flow of energy and materials into and out of the environmental systems.
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Material Balance Energy Balance
production, transport, and fate
modeling
Pollutant Energy
The law of conservation of matter states that (without nuclear reaction) matter can neither be created nor destroyed.
We ought to be able to account for the “matter” at any point in time.
The mathematical representation of this accounting system is called a materials balance or mass balance.
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The law of conservation of energy states that energy cannot be created or destroyed.
Meaning that we should be able to account for the “energy” at any point in time.
The mathematical representation of this accounting system we use to trace energy is called an energy balance.
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The simplest form of a materials balance or mass balance
Accumulation = input – output
Accumulation
input
output
Environmental System (Natural or Device)
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Mass rate of accumulation = Mass rate of input – Mass rate of output
Selam is filling her bathtub but she forgot to put the plug in. if the volume of water for a bath is 0.350 m3 and the tap is flowing at 1.32 L/min and the drain is running at 0.32 L/min, how long will it take to fill the tub to bath level? Assuming Selam shuts off the water when the tub is full and does not flood the house, how much water will be wasted? Assume the density of water is 1,000 kg/m3
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Vaccumulation Qin = 1.32 L/min Qout = 0.32 L/min
We must convert volumes to masses. Mass = (volume)(density) Volume = (flow rate)(time) = (Q)(t)
From mass balance we have Accumulation = mass in –mass out (Vacc)() = (Qin)()(t) - (Qin)()(t) Vacc = (Qin)(t) – (Qin)(t) Vacc = 1.32t – 0.32t 350L = (1.00 L/min)(t) t= 350 min The amount of wasted water is
Waste water = (0.32)(350) = 112 L
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rate)tion)(flow(concentratime
MassMass flow rate =
outoutinin QcQcdt
dMMass balance
inin
outoutinin
outin QC
QCQC
QC
dtdM Efficiency of a system
inmass
outmassinmass OR
The air pollution control equipment on a municipal waste incinerator includes a fabric filter particle collector (known as a baghouse). The baghouse contains 424 cloth bags arranged in parallel, that is 1/424 of the flow goes through each bag. The gas flow rate into and out of the baghouse is 47 m3/s, and the concentration of particles entering the baghouse is 15 g/m3. In normal operation the baghouse particulate discharge meets the regulatory limit of 24 mg/m3.
Calculate the fraction of particulate matter removed and the efficiency of particulate removal when all 424 bags are in place and the emissions comply with the regulatory requirements. Estimate the mass emission rate when one of the bags is missing and recalculate the efficiency of the baghouse. Assume the efficiency for each individual bag is the same as the overall efficiency for the baghouse.
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Accumulation = particle removal
Hopper
Cout = 24 mg/m3
Qout = 47 m3/s
Cin = 15 g/m3
Qin = 47 m3/s
Baghouse
kinetic reactions : reactions that are time dependent.
Reaction kinetics: the study of the effects of temperature, pressure, and concentration on the rate of a chemical reaction.
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The rate of reaction, ri, the rate of formation or disappearance of a substance.
Homogenous reactions. single phase reactions Heterogeneous reactions : multiphase reactions (between
phases surface)
ri = kf1(T,P);f2([A],[B], …)
Rate constant Concentration of reactant
Assuming that the pressure and temperature are constant
aA + bB cC
Rate of reaction rA = - k[A]α[b]β = k[C]γ
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Rate of reaction rA = - k[A]α[b]β = k[C]γ
order of reaction = α + β,
the order with respect to reactant A is α, to B is β, and to product C is γ.
rA = -k zero-order reaction
rA = -k[A] first-order reaction
rA = -k[A2] second-order reaction
rA = -k[A][B] second-order reaction
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batch reactors and flow reactors.
fill-and-draw
Unsteady state
material flows into, through, and out of the reactor
IDEAL REACTORS REAL REACTOR
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Conserved system: where no chemical or biological reaction takes place and no radioactive decay occurs for the substance in the mass balance.
Steady-state: Input rate = Output rate Accumulation =0
Mixture
Wastes
Stream Qm
Cm
Qw
Cw
Qs
Cs
Decay rate = 0
Accumulation rate = 0
Q = flow rate C = concentration
CsQs + QwCw = QmCm
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For non-conservative substances Accumulation rate = input rate – output rare ±
transformation rate
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With first-order reactions Total mass of substance = concentration x volume
when V is a constant, the mass rate of decay of the substance is
first-order reactions can be described by r = -kC=dC/dt,
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Sewage Lagoon
Decay
Accumulation=input rate – output rate – decay rate
Assuming steady-state condition, accumulation = 0
input rate = output rate + decay rate
CinQin = CeffQeff + (K)(Clagoon)(V)
Control volume
0)()(
dt
outd
dt
ind
kCVdt
dM
kCdt
dCV
dt
dC
dt
dM
dM/dt = ?
kt
oeCC
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dt
CdV
dt
outd
dt
ind
dt
dM )()()(
Mass balance for each plug element
No mass exchange occurs across the plug boundaries, d(in) and d(out) = 0
kCdt
dCV
dt
dC
dt
dM
kt
inout eCC
The residence time for each plug:
koutin eCC
Residence time
L=length
Q
V
Au
AL
)()(
)()(
Q
Vk
u
Lkk
C
C
in
out )(
)(ln
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Using the 1st and 16th day, the time interval t= 16-1 = 15 d
kt
o
t eC
C )15(
/280
/132 dkeLmg
Lmg
Solving for k, we have k = 0.0501 d-1
To achieve 99 % reduction the concentration at Time t must be 1 – 0.99 of the original concentration
)(05.001.0 t
o
t eC
C t = 92 days
0 Time
Step increase
0 Time
Step decrease
0 Time
pulse/spike increase
Co
nce
ntr
atio
n, C
in
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Co
nce
ntr
atio
n, C
in
0 Time
1/k Time
Decay
1/k Time
Formation
kt
o
t eC
C
Co
nce
ntr
atio
n, C
in
0 Time
Influent concentration
Co
nce
ntr
atio
n, C
in
C1
C0
Time Effluent concentration
0 t=
C1
C0
-0.37C0 + 0.63C1
C0
Co
nce
ntr
atio
n, C
in
Co
nce
ntr
atio
n, C
in
C0
0.37C0
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For balanced flow (Qin = Qout) and no reaction, the mass balance becomes
outoutinin QcQcdt
dM
Where M = CV. The solution is
tC
tCCt exp1exp 10
Where = V/Q
Flushing of nonreactive contaminant from a CMFR by a contaminant-free fluid
Which means Cin = 0 and the mass balance becomes
outoutQcdt
dM
Where M = CV. The initial concentration is C0=M/V
tCCt exp0For time t 0 we obtain
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For balanced flow (Qin = Qout) and first-order reaction the mass balance becomes
VkCQCQCdt
dMoutoutoutinin
Where M = CV. By dividing with Q and V we have
outoutin kCCCdt
dC
1
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0 Time
0 Time
Co
nce
ntr
atio
n, C
in
Co Co
For stead-state conditions dC/dt=0
k
CC o
out
1 k
CC o
out
1OR
Decay Formation
VkCQCdt
dMoutoutout 0
A step decrease in influent concentration (Cin=O) for non-steady-state conditions with first-order decay
Where M = CV. By dividing with Q and V we have
outCkdt
dC
1
t
k
CCC o
oout1
exp
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0 Time
Influent concentration
0 Time
Effluent concentration
C0
Co
nce
ntr
atio
n, C
in
Co
nce
ntr
atio
n, C
in
C0
A chemical degrades in a flow-balanced, steady-
state CMFR according to first-order reaction kinetics. The upstream concentration of the chemical is 10 mg/L and the downstream concentration is 2 mg/L. Water is being treated at a rate of 29 m3/min. The volume of the tank is 590 m3. What is the rate of decay? What is the rate constant?
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For a first-order reaction, the rate of decay, r =-kC, thus we have to solve for kC from
VkCQCQCdt
dMoutoutoutinin
For steady-state, dM/dt = 0 and for balanced flow, Qin = Qout
3
3
580
min)/29)(/2/10(
m
mLmgLmg
V
QCQCkCr outoutinin
r=kC=0.4
For a first-order reaction in a CMFR
k
CC o
out
1
The mean hydraulic detention time is
min20min/29
5803
3
m
m
Q
V
Solving for the rate constant we get
1min20.0min20
1)/2//10(1)/(
LmgLmgCC
k outo
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Topics Presentation Date
Ground water pollution and remediation
April 11 Global warming and greenhouse gas effect
Recent climate change and its impact
Noise Pollution and Control
Hazardous and Radioactive wastes
April 18 Automobiles and the environment
Product life cycle assessment
A case study of a green building
Topics Presentation Date
Recycling, reuse and resource recovery
April 25 Investigate a renewable source of energy
Environmental Impact of Mining
Effect of Climate change on Water Resource
and its mitigate measures
Water Quality and Treatment technologies
May 2 Wastewater treatment and reuse
Nanotechnology and the environment
How to save our Environment
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Topics Presentation Date
Industrial Ecology and sustainable
Development
May 9 Urbanization and its Environmental
Impacts
Environmental Effects of Natural Hazards
visit aaucivil.wordpress.com/enveng
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R epo rt fo r m at
2 0 t o 3 0 pa g e s
C o v e r pa g e : T i t l e a n d G r o u p m e m b e r n a m e s
Ta b l e o f c o n t e n t
R e f e r e n c e s
L a s t D at e o f S u b m i s s i o n : J u n e 1 7 , 2 0 1 1
Ground water pollution and remediation Hazardous and Radioactive wastes Noise Pollution and Control Explore some approaches to reduce the environmental
impacts of construction What can be done to make buildings more energy efficient? Product life cycle assessment (choose specific product, e.g.,
cars, computers, etc) Global warming and greenhouse gas effect A case study of a green building: what is green and what are
the interesting design approaches (consider materials, energy efficiency, lighting, water use, etc.)?
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Recent climate change and its impact Risk assessment and decision analysis Recycling, reuse and resource recovery Investigate a renewable source of energy (such as wind,
solar, geothermal), or a new technology that will reduce greenhouse gas emissions due to energy consumption (such as fuel cells or hydrogen fuel).
Indoor air quality and models Automobiles and the environment Ecological Foot prints Air quality measurement and analysis