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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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Accumulation

Control Volume

Food to people

Consumer goods

Solid Waster

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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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Time (d) Waste Concentration (mg/L)

1 280

16 132

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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

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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

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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