Materials and Energy Balance.pdf

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Objectives 2

Explain the concept of mass balance, control volume, steady state condition and uniformly mixed systems ¨  Construct a Mass Balance Diagram ¨  Apply mass balance principles in environmental applications ¨ 

MATERIALS AND ENERGY BALANCE

CE 131

Lecture 5

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In Liquids 4

a) 

HOW TO EXPRESS CONCENTRATIONS OF SUBSTANCES

mass/weight of substance per unit volume of mixture e.g. mg/L , μg/L , g/m3

b) 

mass/weight of substance per unit weight of mixture e.g.

parts per million (ppm) parts per billion (ppb)

Note: Since most pollutants are very small, one liter of mixture weighs essentially 1000 g, 1 mg/L = 1 g/m3 = 1 ppm (by weight) 1 μg/L = 1 mg/m3 = 1 ppb (by weight)

Atomic weights most commonly used in environmental engineering

In Gases 5

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In volumetric terms: 1 ppm (by vol) = 1 vol. of contaminant 106 volumes of air mixture

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In mixed units of mass per unit volume: At 0°C and 1 atm pressure, 1 mole of an ideal gas occupies a volume of 22.4 x10-3 m3 C = ppm x mol. weight (mg/m3) 22.4 For other temperature and pressure: correct the above eqn

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Example 1

Volumetric Flow Rate, Q

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The federal air quality standard for carbon monoxide CO (based on an 8-hr measurement) is 9.0 ppm. Express this standard as a percentage by volume as well as in mg/m3 at 1 atm and 25°C .

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Volume of fluid passing an arbitrary plane per unit of time

Q = V/t = vol/time Q = v*A Q – volumetric flow rate v – velocity A – cross-sectional area

Note: C = ppm x mol. weight 22.4 Ans: 10.3 mg/m3

Mass & Energy Balances 9

provide us with a tool for modeling the production, transport, and fate of pollutants and energy in the environment.

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1. Conservation of Matter 11

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UNIFYING Theories

“Matter can neither be created nor destroyed”.

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2. Conservation of Energy

MATERIALS/ MASS BALANCE 13

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“Energy cannot be created nor destroyed.”

The mass that enters a system must, by conservation of mass, either leave the system or accumulate within the system .

3. Conservation of Matter and Energy 15

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An average-sized adult contains around 7x1018 joules of potential energy- enough to explode with the force of 30 very large hydrogen bombs!

The total amount of energy and matter is constant.

MATERIALS BALANCE 17

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“Mass and energy are two forms of the same thing. Energy is liberated matter, and matter is energy waiting to happen.” -Bill Bryson A Short History of Nearly Everything

INPUTS

There is a huge amount- a really huge amount- of energy bound up in every material thing.

CONTROL Accumulation VOLUME

OUTPUTS

For an ideal system, Accumulation = Input – Output

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Example 3-1(Davis) 19

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Mr. and Mrs. Konzzumer have no children. In an average week they purchase and bring into their house approximately 50 kg of consumer goods (food, magazines, newspapers, appliances, furniture, etc.) . Of this amount, 50% is consumed as food. Half of the food is used for biological maintenance and ultimately released as CO2. The remainder is discharged to the sewer system. The Konzzumers recycle approximately 25% of the solid waste that is generated. Approximately 1 kg accumulates in the house. Estimate the amount of solid waste they place at the curb each week.

Konzzumers’ residence

Konzzumers’ residence

Solution:

Konzzumers’ Residence

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50 kg of consumer goods

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50% (food) 50 % for biological maintenance

CO2

Other 50 % Konzzumers’ residence Waste 1 kg accumulates in the house Sewer system

25 % Solid waste recycled

Food to people

The rest is thrown out

Solid Waste

? Estimate the amount of solid waste they place at the curb each week.

Draw mass balance diagram.

Solution: 23

Konzzumers’ Residence

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INPUT = Accumulation + Output as Food + Output as solid waste

Consumer goods

Accumulation

Consumer goods

Accumulation

Food to people

50% (food) 50 % for biological maintenance

CO2

Solid Waste

Write mass balance equation for the house.

Other 50 % Konzzumers’ residence Waste 1 kg accumulates in the house Sewer system

25 % Solid waste recycled

The rest is thrown out

? Estimate the amount of solid waste they place at the curb each week.

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Time as a factor 25

Example 3-2 (Davis) 26

Modified mass balance equation:

Truly Clearwater 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 Truly shuts off the water when the tub is full and does not flood the house, how much water will be wasted?

Rate of accumulation = rate of input – rate of output

dM d (in) d (out ) = − dt dt dt

Assume density of water is 1,000 kg/m3.

Mixing States 27

Mixing States 28

1. Completely mixed system The output from the system is the same as the contents of the system.

2. Plug flow system Each drop of fluid along direction of flow is unique and has the same concentration and properties as when it had first entered the system.

Steady state condition

MATERIALS BALANCE 29

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Materials balances can be simplified with the assumption of steady state, where the accumulation term is zero.

Materials balances can be simplified with the assumption of steady state, where the accumulation term is zero. The input rate and output rate are constant and equal. There is no accumulation of particles/materials.

Steady state does not imply equilibrium.

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Conservative Pollutants 31

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the pollutant does not change form over time ¨  no radioactive decay ¨  no bacterial decomposition ¨  no chemical reaction ¨  vs non-conservative pollutants ¨ 

Mass of contaminant per unit time:

Mass = (Concentration)(Flow rate) Time

mg s

mg m3

m3 s

MASS FLOW RATE

Recall: 33

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Mass Balance ¨  Control Volume and Mass Balance Diagram ¨  Mixing States ¨  Steady-State Condition ¨  Conservative vs Non-conservative pollutants

dM = CinQin − Cout Qout dt

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Where: C = concentration of contaminant Q= flow rate

dM / dt CinQin − Cout Qout = CinQin CinQin

Example: Completely mixed, Steady-state system with conservative pollutant

Efficiency 35

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mass in − mass out η= x 100% mass in

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Two streams enter a lake. The main stream has a flow of 10 m3/s, and a chloride concentration of 20 mg/L. The tributary stream has a flow of 5 m3/s and a chloride concentration of 40 mg/L. What is the chloride concentration leaving the lake system?

If flow rate in and flow rate out are the same,

η=

concentration in − concentration out x 100% concentration in

Ans: 26.67 mg/L

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Example 3-4 (Davis)

Baghouse

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The air pollution control equipment on a municipal waste incinerator includes a fabric filter particle collector (known as baghouse). The baghouse contains 424 cloth bags arranged in parallel, that is, 1/424 of the flow goes through each bag. Qin= Qout=47 m3/s Cin,particles= 15 g/m3 For normal operation, Cout=24 mg/m3 (regulatory limit) During maintenance, one bag is inadvertently not replaced, so only 423 bags are in place.

Calculate: 1.  Fraction of particulate matter removed 2.  efficiency of the baghouse when all bags are in place and emissions comply with the regulatory requirements. Draw the MBD.

Non-conservative pollutants 39

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dM d (in) d (out ) = − +r dt dt dt

r = −kC n =1 =

dC dt

In first-order reactions, the rate of loss of a substance is proportional to the amount of substance present at any time t.

Accumulation

C

dC = ∫ k dt C Co 0

∫

OUTPUTS

INPUTS

t

Transformation

C = Co e − kt

Where: C = pollutant concentration t = time k = reaction rate coefficient [T-1] n = reaction order V = volume

Accumulation = Input – Output ± Transformation rate

Decay Rate for the mass balance equation is kCV.

Example: 41

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Mass balance equation for non-conservative pollutant w/ first-order reactions: dM d (in) d (out ) = − − kCV dt dt dt

Raw sewage

Cin= 180 mg/L Qin= 430 m3/day

Decay

Sewage Lagoon

Surface Area of lagoon= 10 hectares Depth = 1.0 m k= 0.70 /day Ceff= ? Qeff= 430 m3/day

Assuming no other water losses or gains and that the lagoon is completely mixed, find the steady-state concentration of the pollutant in the lagoon effluent. Note: The organic matter in the sewage decays in the lagoon. Ans: 1100 mg/m3

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Example

Seatwork

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a) 

b) 

There are 50 smokers in a room and each smoker smokes 2 cigarettes per hour. An individual cigarette emits, among other things, 1.4 mg of formaldehyde (CH2O). Formaldehyde converts to CO2 with a reaction rate coefficient k = 0.4/hr. Fresh air enters the room at 1000 m3/hr and stale air leaves at the same rate. The volume of the room is 500 m3. Estimate the steady-state concentration of formaldehyde in the air, assuming complete mixing. At 25 °C and 1 atm of pressure, how does the result compare with the threshold for eye irritation of about 0.05 ppm?

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A sewage lagoon that has a surface area of 10ha and a depth of 1m is receiving 8640 m3/day of sewage containing 100 mg/L of biodegradable contaminant. At steady state, the effluent from the lagoon must not exceed 20 mg/L of biodegradable contaminant. Assuming the lagoon is well-mixed and that there are no losses or gains of water in the lagoon other than the sewage input, what biodegradation reaction rate coefficient (d-1) must be achieved for a first-order reaction?

References: 46

THANK YOU!

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Davis. Principles of Environmental Engineering and Science.

Masters. Introduction to Environmental Engineering and Science.

Ma. Brida Lea Diola Environmental and Energy Engineering Group Institute of Civil Engineering

CE 131 Reporting 47

§  Discuss a low-cost, innovative and local (if applicable) applications of the following topics. §  By pair §  5-10 min presentation

Date   28-Jan   30-Jan   4-Feb   6-Feb   11-Feb   13-Feb   18-Feb   20-Feb   25-Feb   27-Feb   4-Mar   6-Mar   11-Mar   13-Mar   18-Mar   20-Mar  

Topic   SWM   SWM   SWM 1 & 2   Geo-engg   Exam  

Examples  

WQM   WQM   WQM   WQM-Eco-san   MASDAR City   Soil & GW   Geo-engg   Noise   AQM   AQM  

filtration  

Recycling,  Zero   Baht  Shop   Ocean  Fert,  SRM  

waterless toilet   Sust dev   FPIC   optional topics   Egg  trays   EDSA  

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