1. Environmental Engineering (Course Note 2_revised)
Joonhong Park
Yonsei CEE Department

2. Extensive and Intensive Properties
Extensive properties: dependent upon the size of the system or the sample.
Intensive properties: independent of the size of the system or the sample.
Question: which are extensive properties among the followings?
Mass, Energy, Heat Capacity, volume, temperature heat capacity, and pressure.

3. Measure of Quantity and Concentration
The quantity of a substance: expressed in terms of mass or weight, volume, or number of moles.
Concentration: the quantity of a substrate (i) in a certain quantity of a particular phase (j)
quantity of a substrate (i)
C(i,j) =
quantity of a particular phase (j)

4. Concentrations and Other Units of Measure
How many molecules in a mole?
Concentration Units
Mass based, mg/L or g/L
Mole based (Molarity), mol/L or M
the concentration of charge associated with ions in water (Normality) eq/L = M X [charge/ion]
Example) 47.8 g of MgCl2 is dissolved in one liter of water. Calculate its mass-based concentration, molarity, and normality.
Ref) Atom mass for Mg = 24.3 g/mole;
Atom mass for Cl = 35.5 g/mole
Concentration units
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5. Other expressions for concentrations
p-notation: negative logarithm of the molar concentration of a substrate, pC = -log [C]
e.g. pH = -log [H+]
Equivalent (eq): the quantity of a substrate equivalent to the quantity of the product in a particular reaction.
e.g. For the sulfuric acid reaction:
H2SO4 + 2H2O = 2H3O+ + SO42-
1 mol H2SO4 equivalent to 2 mol H+
Cf) centi-, milli-, micro-, nano-, pico-,…
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6. Mass Fraction and Mole Fraction
Represent the ratio between the amount of the species and the total amount of the solution (fluid plus species)
% (percent): 1 part species per 100 parts solution
%o (per mil): 1 part species per 1000 parts solution
ppm (part per million): 1 part species per 106 parts solution
ppb (part per billion): 1 part species per 109 parts solution
ppt (part per trillion): 1 part species per 1012 parts solution
cf) molecular fraction, mass fraction, volumetric fraction
By convention (in general):
In air, fractions are generally expressed on a molar or volume basis (ex. 5ppb benzene = 5 x10-9 mole in a mole of air)
In water, fractions are generally expressed on a mass basis (ex. 5ppb benzene = 5 x10-9 gram in a gram of water)
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7. Partial Pressure Ideal gas law Partial pressure
Species amounts in air may be expressed in terms of partial pressure.
Idea gas law: PV = nRT (cf. M = n/V = P/RT)
here P=pressure, V=volume,
R=idea gas constant
(82.05 *10-6 mol-1 m3 atm K-1)
T=absolute temperature (oK)
pi =Pi/Pair = (ni/Vi)/(nair/Vair)
Example) 5ppb benzene in air at Pair = 5 x 10-9 atm
Ideal gas law
Partial pressure
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8. Unit Conversion
Mass Conc. = molecular weight of species i * molarity of i.
Ex) Mass concentration of benzene (C6H6) = 5μg/L
Molecular weight of benzene = 12 x x 6 = 78g/mol
Molarity of benzene = 5 (μg/L) / 78 (g/mol) = μmol/L or μM
Mass concentration = solution density * mass fraction
cf) Solution of density in dilute solution in water = 1g/ml
The molecular fraction of a species: Yi = Ci / Cair
Cair = P/RT When P = 1atm and T=293 oK, Cair = 41.6 mol/m3
[R=82.05 x10-6 atm * m3/(mol * K)]
Ci = 41.6 μmol/m3 corresponds to a mole fraction of 1 ppm.
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9. Some Basic Units and Conversion Factors
Quantity
SI units
SI symbol
Conversion
Factor
USCS
units
Length
Mass
Temperature
Area
Volume
Power
Velocity
Flow rate
Density
Meter
Kilogram
Celsius
Square meter
Cubic meter
Kilojoule
Watt
Meter/sec
Cubic meter/sec
Kilogram/cubic meter M Kg oC M2 M3 kJ W
m/s
m3/s
Kg/m3
3.2808
2.2046
1.8 (oC) + 32
0.9478
3.4121
2.2369 ft Lb oF
ft2
ft3
Btu
Btu/hr
Mi/hr
ft3/s
Lb/ft3

10. Common Prefixes Quantity Prefix Symbol 10^-15 0.000000000001
0.001
0.01
0.1 10
100
1000
10^15
10^18
10^21
10^24
femto
pico
nano
micro
milli
centi
deci
deka
hecto
kilo
mega
giga
tera
peta
exa
zetta
yotta f p n μ m c d da h k M G T P E Z Y

11. Precision and Accuracy
Precise
Imprecise
Accurate
Inaccurate

12. Material Balance Concepts Characteristic times
Contents:
Material Balance Concepts
Characteristic times
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13. Components in Mass/Material Conservation Law (Mass/Material Balance)
Accumulation rate
= Input rate – Output rate + Reaction rate
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14. Material Balance Model containers and flow paths
in environmental system
closed
open
Converging flow paths
Diverging flow paths
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15. Material Balances (MBs)
Different types of MBs
MB1: the amount of a conserved property in a closed container does not change
MB2: the rate of change in the amount of a nonconserved property within a closed container is equal to the net rate of production of that property within the container.
MB3: the rate of change in the amount of a conserved property in an open container is equal to the difference between the rate of flow of that property into the container and the rate of flow out of the container.
MB4: the rate of change in the amount of a nonconserved property in an open container is equal to the rate of flow in, minus the rate of flow out, plus the net rate of production within the container.
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16. Batch (Closed) Systems with Conservative Pollutants (MB1)
V: Control Volume
(Reactor Volume)
C: Cons. Pollutant Conc.
Accumulation rate = Input rate – Output rate + Reaction rate
Input rate = 0, Out rate = 0 since closed system
Accumulate rate = Reaction rate = 0 since cons. material
(assumption: completely mixed; no sink or no source)
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17. In the reactor, what would be concentrations at different locations?
Example for MB1
Reactor Observation
Situation: At t = 0,
add C pollutant
at Co concentration Co
Cons. Poll. Conc.
Completely
Mixed
Batch
Reactor
(CMBR)
Volume (V)
Time (t)
Question:
In the reactor, what would be concentrations
at different locations?
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18. Batch (Closed) Systems with Nonconservative Pollutants (MB2)
V: Control Volume
(Reactor Volume)
C: NC Pollutant Conc.
Accumulation rate = Input rate – Output rate + Reaction rate
In this case, Input rate = Output rate = 0 (since closed system)
Accumulation rate = Reaction rate for NC Pollutant
(assumption: completely mixed; no sink or no source)
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19. Question: What if t = infinitely long?
Example for MB2
Reactor Observation
Situation: At t = 0,
add NC pollutant
at Co concentration Co
NC Poll. Conc.
Completely
Mixed
Batch
Reactor
(CMBR)
Volume (V)
Time (t)
Accumulation rate at t = V * (dC/dt) observed in the reactor at t
(function of reactor configuration and other system factors)
Reaction rate = V * (dC/dt) intrinsic reaction rate
(function of chemical property and transformation process)
At CMBR, V * (dC/dt)reactor = V * (dC/dt)reaction
Question: What if t = infinitely long?
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20. Conservative Pollutants at SS (MB3)
Open Systems with
Conservative Pollutants at SS (MB3)
Completely
Mixed
Continuous
Flow
(V, C)
Cout =C,
Qout = Q
Cin=C
Qin =Q
Terminology:
CSTR: Completely Stirred
Tank Reactor
CMCFR: Completely Mixed
Continuous Flow Reactor
V: Control Volume
(Reactor Volume)
C: Cons. Pollutant Conc.
Accumulation rate = Input rate – Output rate + Reaction rate
At Steady-State (Water & Pollutant), Accumulation = 0
Since the pollutant is a conservative material, intrinsic reaction rate = 0
Input rate = Output rate
Question: By the way, what is steady state??
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21. Steady-State Conservative Systems at SS
Steady State: Accumulation rate = 0
Conservative Pollutant: No transformation rate
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22. Example: Steady-State Conservative Systems
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23. Steady-State Conservative Systems
Step 1: Make simplified the situations (Sketch) Qs
Assumptions: conserved properties
converging flow paths
steady state Cs Qm Cm
What materials?
What Processes? (Transformation? Transport?) Qw Cw
Cw: contaminant concentration in wastewater
Qw: volumetric flow rate of wastewater
Cs: contaminant concentration in upstream river
Qs: volumetric flow rate in upstream river
Cm: contaminant concentration in downstream river
Qm: volumetric flow rate in downstream river
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24. Steady-State Conservative Systems
Step 2: Set the material balances
Accumulation Rate = Input Rate – Out Rate
+ Reaction Rate
Steady-State means Accumulation Rate = 0
Conservative Materials means Reaction Rate = 0
Therefore, Input Rate = Out Rate Qs Cs Qm
Water Balance: Water Density *Qm =
Water Density * (QS + QW)
Contaminant Balance: CmQm = QSCS +QWCW
Qm = Qs + Qw = 10.0 m3/s m3/s = 15.0 m3/s
Cm = (CsQs +CwQw)/Qm
= (20.0* *5.0) (mg/L * m3/s) / (15.0 m3/s)
= 26.7 mg/L Cm Qw Cw
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25. Steady-State Systems with Nonconservative Pollutants (MB4)
Completely
Mixed
Continuous
Flow
(V, C)
Cout =C,
Qout = Qin =Q
Cin
Qin =Q
V: Control Volume
(Reactor Volume)
C: NC Pollutant Conc.
Accumulation rate = Input rate – Output rate + Reaction rate
At Steady-State (Water & Pollutant), Accumulation = 0
Reaction rate = - V * (dC/dt)
0 = Input rate - Output rate + Reaction rate
0 = Cin * Q - C * Q - V * (dC/dt)
=> C*Q = Cin*Q - V*(dC/dt) => C = Cin – V/Q * (dC/dt)
here V/Q = hydraulic retention time
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26. Characteristic times Characteristic time (τ)
Def: magnitude estimates of the time required for a process to approach completion.
When t >> τ (fast process); When t << τ (slow process)
When t ~ τ (intermediate cases)
Characteristic residence time (τr)
Def: a magnitude estimate of the average time that a molecule of a specific matter(or material) will remain in the system before being removed by flow out of the system.
S (stock):
the amount of
the materials
in a system
Fin (flow in)
Assume Fin = Fout= F
τr = S/F
Fout (flow out)
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27. Example: Characteristic residence time
Given) In Nanji Wastewater Treatment Plant (Seoul, Korea), wastewater flows into its treatment reactor at a steady flow rate (Q) of 1,000 m3/day, and flows out of the treatment reactor at the sample steady flow rate. The volume of treatment reactor (V) was 50 m3.
Mission) Calculate the characteristic residence time of a water molecule
Step 1: Identify S
☞ NOTE: What assumptions may be needed?
Step 2: Identify F
☞ NOTE: Any assumptions to be made?
Step 3: Calculate residence time by S/F in hours
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28. Reading Assignment and HW#2
Reading Assignment: EES (Environmental Engineering Science, Nazaroff & Alvarez-Cohen) pp. 1-25
H.W.#2
In EES, solve some problems in Chapter 1 (p.26-29)
-1.1, 1.2, 1.3, 1.8, 1.9, 1.12, 1.14
-Due(제출마감일시): March 23 (6pm) at C218
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