Transcript Lecture 3

Lecture 3 – Materials
Balances
Introduction to Environmental Engineering
Lecture3
Dr. Jawad Al-rifai
The accounting of all mass in a
chemical/Environmental process is
referred to as a mass (or material)
balance.
 ‘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
Conservation of Mass – mass is neither
created nor destroyed
 Mass Flow – therefore mass flowing into a
box will equal the flow coming out of a
box

0
X0
1
X1
◦ Black box – schematic representation
M.B. with a Single Material

One or more effluent
X0

0
1
2
X1
X2
One or more Feed Source / influent
X1
X2
X0
[Accumulation]= [In]– [Out] +[Produced] –
[Consumed]
M.B. with a Splitting Single
Material
Steady state
 The rate of input= rate of out put, mass
rate of accumulation is Zero
[In]= [Out]
1.
◦ Conservation: In many problems conservation
is assumed
 Material of concern is not consumed or
produced
 No chemical, biological or radioactive decay
◦ Ex. Salt in Sewer & stream
 M.B. equation
 0 = [In] – [Out] + 0 - 0
State of Mixing-Steady State
2. Reactions/ loss process
[Accumulation]= [In]– [Out] + [Produced] –
[Consumed]
dM/dt = [d(in)/dt – d(out)/dt]+ r
◦
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r=-KVCn
K; reaction rate constant; S-1 or d-1
C: Concentration of substances
n: reaction order
V: volume
- Indicate disappearance of substances
The reaction rate is often complex function of T, P
State of Mixing- Reactions/ loss
process

General Rules for solving M.B. Problems
1. Draw the system as a diagram
2. Add the available information
3. Draw a dotted line around the component
being balanced
4. Decide material to be balanced
5. Write the basic M.B. equation
6. If only one missing variable, solve
7. If more that one unknown, repeat the
procedure
Complex Processes with a Single
Material
A completely mixed lake receives two inflows:
natural stream flow 0.1 m3/s, wastewater discharge 0.054
m3/s and has a constant volume of 2 x 106 m3.
Given:
◦ 1) the wastewater has 20 mg/L NH3-N
◦ 2) stream has 1 mg/L NH3-N
bacteria in the lake convert NH3 to NO3- by a process
called nitrification.
-rN = k*CN
where k = a first-order rate constant = 0.03 day-1 and CN
= concentration of ammonia-nitrogen mg/L
FIND:
lake and outflow NH3-N
Assume steady-state, non-conservative mass balance:
Ammonia is very toxic to fish, 1 mg/L NH4-N. Does the
amount of natural nitrification in the lake allow
wastewater discharge of 20 mg/L ammonia-N?
Example
◦
◦
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◦
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◦
◦
◦
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QW*CNW + QN*CNN - QTCN - V*k*CN = 0
where QW = wastewater flow, = 0.054 m3/s
CNW = wastewater ammonia-N = 20 mg/L
QN = stream flow = 0.1 m3/s
CNN =stream ammonia-N = 1 mg/L
QT = lake outflow = QW +QN = 0.154 m3/s
CN = lake and outflow ammonia-N = ?
V = lake volume = 2 x 106 m3
t = 150 days
Complex Processes with a Single
Material
find CN: by rearranging mass balance:
QTCN + V*k*CN = QW*CNW + QN*CNN
CN (QT + V*k) = QW*CNW + QN*CNN
Divide everything by QT;
CN (1 + V/ QT *k) = (QW*CNW + QN*CNN)/ QT
CN =[ 1 / (1+ (V/QT)*k)]*[(QWCNW +
QN*CNN)/QT]
CN = [ 1/(1+ (t)*k)]*[(QW*CNW + QN*CNN)/QT]
CN = [1 /(l +(150d * 0.03d-1))]*[(0.054m3/s*20
mg/L + 0.1 m3/s*1 mg/l)/0.154m3/s]
CN = 1.4 mg/L ammonia-nitrogen
1.4 mg/L ammonia-N > 1 mg/L standard.
Complex Processes with a Single
Material
Aside:What is the detention time of water in the lake
(Hydraulic Residence Time)?
◦ Define detention time, t in the book:
t = V/Q = volume/flow rate = time
2 x 106 m3/(0.1 m3/s + 0.054 m3/s)*(1
day/86,400 s) = 150 days
Complex Processes with a Single
Material
Sequence of operations/steps repeated
according to a cycle
 Batch cycle time
 Batch size

Batch cycle
Paul Ashall, 2008
Typical simple flowsheet
arrangement
Recycle of unreacted material
reactor
Fresh feed
(reactants, solvents,
reagents, catalysts etc)
Separation &
purification
waste
product
Byproducts/coproducts
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Mass balance filtration/centrifuge
wash water/solvent
solid
feed
suspension
waste
water
filtrate
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5000 kg DM water
F1
Impurity 55 kg
Water 2600 kg
API 450 kg
Filtration
Water 300 kg
API 448 kg
Impurity 5 kg
Water 7300 kg
Impurity 50 kg
API 2kg
Paul Ashall, 2008
water/evaporated solvent
feed
product
Mass balance - drier
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A+B
A+B
S
S+B
Mass balance – extraction/phase
split
A – feed solvent; B – solute; S – extracting so
Paul Ashall, 2008
Example (single stage extraction;
immiscible solvents)
feed
raffinate
E1
solvent
extract
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Mass balance – absorption unit
exit gas stream
feed solvent
feed gas
stream
waste solvent stream
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Multiple units
W2
F1
E
C
F
P3
R4
E – evaporator; C – crystalliser; F – filter unit
F1 – fresh feed; W2 – evaporated water; P3 – solid product;
R4 – recycle of saturated solution from filter unit
Paul Ashall, 2008