Lin S.D. Water and Wastewater Calculations Manual

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Wastewater Engineering 685

The absolute temperature may be estimated from the pressure rise

using the following equation

⫽ T

)

0.283

(6.118)

Fittings in an air distribution system may be converted into the equiv-

alent length of straight pipe as below

L ⫽ 55.4 CD

1.2

(SI units) (6.119)

and

L ⫽ 230 CD

1.2

(US customary units) (6.120)

where L ⫽ equivalent length, m or ft

D ⫽ diameter of pipe, m or ft

C ⫽ resistance factor (0.25 to 2.0)

Example: Determine the headloss in 250 m (820 ft) of 0.30-m (12-in) steel

pipeline carrying 42.5 m

/min (1500 ft

/min ⫽ 25 ft

/s ⫽ 0.7 m

/s) of air at a

pressure of 0.66 atm (gauge). The ambient air temperature is 26⬚C (78⬚F).

solution:

Step 1. Estimate the temperature in the pipe using Eq. (6.118)

⫽ 1 atm

⫽ 1 atm ⫹ 0.66 atm ⫽ 1.66 atm

⫽ 26 ⫹ 273 ⫽ 299 (K)

⫽ T

)

0.283

⫽ 299 K (1.66/1)

0.283

⫽ 345 K

Step 2. Estimate the friction factor using Eq. (6.114)

f ⫽ 0.029 D

0.027

0.148

⫽ 0.029 (0.3)

0.027

/(42.5)

0.148

⫽ 0.0161

Step 3. Estimate the head loss using Eq. (6.117)

H ⫽ 9.82 ⫻ 10

( fLTQ

)/(PD

)

⫽ 9.82 ⫻ 10

–8

⫻ 0.0161 ⫻ 250 ⫻ 345 ⫻ 42.5

/(1.66 ⫻ 0.3

)

⫽ 61 (mm of water)

686 Chapter 6

Blower. The blower (compressor) is used to convey air up to 103 kPa

(15 lb/in

). There are two types of blower commonly used for aeration,

i.e. rotary position displacement (PD) and centrifugal units. Centrifugal

blowers are usually used when the air supply is greater than 85 m

/min

(3000 ft

/min or cfm) and are popular in Europe. For pressures up to 50

to 70 kPa (7 to 10 lb/in

) and flows greater than 15 m

/min (530 ft

/min),

centrifugal blowers are preferable. Rotary PD blowers are used prima-

rily in small plants. Air flow is low when pressure is over 40 to 50 kPa

(6 to 7 lb/in

) and plant flows are less than 15 m

/min (530 ft

/min)

(Steel and McGhee, 1979).

As an advantage, PD blowers are capable of operating over a wide

range of discharge pressure, but it is difficult to adjust their air flow rate

(only the speed is adjustable), they require more maintenance, and are

noisy. In contrast, centrifugal blowers are less noisy in operation and

take up less space. Their disadvantages include a limited range of oper-

ating pressure and reduced air flow when there is any increase in back-

pressure because of diffuser clogging. In many plants, single-stage

centrifugal blowers can provide the head requirement (6 m or 20 ft of

water). If higher pressures are needed, multiple units can provide a

pressure of 28 m (90 ft) of water.

The power requirements for a blower may be estimated from the air

flow, inlet and discharge pressures, and air temperature by the follow-

ing equation which is based on the assumption of adiabatic compression

conditions.

(SI units) (6.121)

(British system) (6.122)

where p ⫽ power required, kW or hp

w ⫽ weight of flow of air, kg/s or lb/s

p 5

wRT

155.6 e

0.283

2 1d

p 5

wRT

550 ne

0.283

2 1]

p 5

wRT

8.41 e

0.283

2 1d

p 5

wRT

29.7 ne

0.283

2 1d

Wastewater Engineering 687

R ⫽ gas constant for air

⫽ 8.314 kJ/(kmol ⭈ K) for SI units

⫽ 53.3 ft ⭈ lb/(lb air ⭈ R)

(R ⫽ ⬚F ⫹ 460 for British system)

⫽ inlet absolute temperature, K or R

⫽ inlet absolute pressure, atm or lb/in

⫽ outlet absolute pressure, atm or lb/in

n ⫽ (k ⫺ 1)/k ⫽ 0.283 for air

k ⫽ 1.395 for air

550 ⫽ ft ⭈ lb/(s ⭈ hp)

29.7 ⫽ constant for conversion to SI units

e ⫽ efficiency of the machine (usually 0.7 to 0.9)

As stated above, for higher discharge pressure application (>55 kPa,

>8 lb/in

) and for capacity smaller than 85 m

/min (3000 ft

/min) of free

air per unit, rotary-lobe PD blowers are generally used. PD blowers are

also used when significant water level variations are expected. The units

cannot be throttled. Rugged inlet and discharge silencers are essential

(Metcalf and Eddy, Inc. 1991).

Example: Estimate the power requirement of a blower providing 890 kg of

oxygen per day through a diffused air system with an oxygen transfer effi-

ciency of 7.2%. Assume the inlet temperature is 27⬚C, the discharge pressure

is 6 m of water, and the efficiency of the blower is 80%

solution:

Step 1. Calculate weight of air flow w

Oxygen required ⫽ (890 kg/d)/0.072

⫽ 12,360 kg/d

In air, 23.2% is oxygen

w ⫽ (12,360 kg/d)/0.232

⫽ 53,280 kg/d

⫽ 0.617 kg/s

Step 2. Determine the power requirement for a blower p

⫽ 27 ⫹ 273 ⫽ 300(K)

⫽ 1 atm

⫽ 1 atm ⫹ 6 m/10.345 m/atm

⫽ 1.58 atm

e ⫽ 0.8

688 Chapter 6

Using Eq. (6.121)

⫽ 31.6 (kW)

Mechanically aerated systems.

Mechanical aerators consist of electrical

motors and propellers mounted on either a floating or a fixed support.

The electrically driven propellers throw the bulk liquid through the air

and oxygen transfer occurs both at the surface of the droplets and at the

surface of the mixed liquor. Mechanical aerators may be mounted on

either a horizontal or a vertical axis. Each group is divided into surface

or submerged, high-speed (900–1800 rev/min) or low-speed (40 to 50

rev/min) (Steel and McGhee, 1979). Low-speed aerators are more expen-

sive than high-speed ones but have fewer mechanical problems and are

more desirable for biological floc formation. Selection of aerators is

based on oxygen transfer efficiency and mixing requirements. Effective

mixing is a function of liquid depth, unit design, and power supply.

Mechanical aerators are rated on the basis of oxygen transfer rate,

expressed as kg of oxygen per kW ⭈ h (or lb/hp ⭈ h) under standard con-

ditions, in which tap water with 0.0 mg/L DO (with sodium sulfite added)

is tested at the temperature of 20⬚C. Commercially available surface

reaerators range from 1.2 to 2.4 kg O

/kW ⭈ h (2 to 4 lb O

/hp ⭈ h) (Metcalf

and Eddy, Inc. 1991).

Mechanical aerator requirements depend on the manufacturer’s

rating, the wastewater quality, the temperature, the altitude, and the

desired DO level. The standard performance data must be adjusted

to the anticipated field conditions, using the following equation

(Eckenfelder, 1966)

(6.123)

where N ⫽ oxygen transfer rate under field conditions,

kg/kW ⭈ h or lb/hp ⭈ h

⫽ oxygen transfer rate provided by manufacturer,

kg/kW ⭈ h or lb/hp ⭈ h

b ⫽ salinity surface tension correction factor

⫽ 1 (usually)

⫽ oxygen saturation concentration for tap water at given

altitude and temperature, mg/L

N 5 N

2 C

s20

b1.024

T220

0.617 3 8.314 3 300

8.41 3 0.8

1.58

0.283

2 1d

p 5

wRT

8.41e

0.283

2 1d

⫽ operating DO concentration (2.0 mg/L)

s20

⫽ oxygen saturation concentration in tap water at

20⬚C, mg/L

⫽ 9.02

T ⫽ temperature, ⬚C

a ⫽ oxygen transfer correction factor for wastewater

⫽ 0.8 to 0.9

Example: An activated-sludge plant is located at an elevation of 210 m.

The desired DO level in the aeration tank is 2.0 mg/L. The range of operat-

ing temperature is from 8 to 32⬚C. The saturated DO values at 8, 20, and 32⬚C

are 11.84, 9.02, and 7.29 mg/L, (from Table 1.2) respectively. The oxygen-

transfer correction factor for the wastewater is 0.85. The manufacturer’s rating

for oxygen-transfer rate of the aerator under standard conditions is 2.0 kg

oxygen/kW ⭈ h. Determine the power requirement for providing 780 kg oxygen

per day to the aeration system.

solution:

Step 1. Determine DO saturation levels at altitude 210 m

For DO, after altitude correction (zero saturation at 9450 m)

⫽ 0.98C

At 8⬚C

⫽ 0.98 ⫻ 11.84 mg/L (from Table 1.2)

⫽ 11.6 mg/L

At 32⬚ C

⫽ 0.98 ⫻ 7.29 mg/L [calculated by Eq. (1.4)]

⫽ 7.14 mg/L

Step 2. Calculate oxygen transfer under field conditions

At 8⬚C, by Eq. (6.123)

⫽ 2.0 kg oxygen/kW ⭈ h

b ⫽ 1

⫽ 11.6 mg/L

⫽ 2.0 mg/L

s20

⫽ 9.02 mg/L

T ⫽ 8⬚C

a ⫽ 0.85

5 C a1 2

altitude, m

9450 m

b 5 C a1 2

210 m

9450 m

Wastewater Engineering 689

690 Chapter 6

⫽ 1.36 kg/kW ⭈ h

At 32⬚C

⫽ 1.29 (kg/kW ⭈ h)

⫽ 31 kg/kW ⭈ d

Step 3. Calculate the power required per day, p

At 32⬚C

p ⫽ (780 kg/d)/(31 kg/kW ⭈ d)

⫽ 25 kW

Note: Transfer rate is lower with higher temperature.

Aerated lagoon. An aerated lagoon (pond) is a complete-mix flow-

through system with or without solids recycle. Most systems operate

without solids recycle. If the solids are returned to the lagoon, the system

becomes a modified activated-sludge process.

The lagoons are 3 to 4 m (10 to 13 ft) deep. Solids in the complete-mix

aerated pond are kept suspended at all times by aerators. Oxygen is usu-

ally supplied by means of surface aerators or diffused air devices.

Depending on the hydraulic retention time, the effluent from an aerated

pond will contain from one-third to one-half the concentration of the

influent BOD in the form of cell tissue (Metcalf and Eddy, Inc. 1991).

These solids must be removed by settling before the effluent is dis-

charged. Settling can take place at a part of the aerated pond system

separated with baffles or in a sedimentation basin.

The design factors for the process include BOD removal, temperature

effects, oxygen requirements, mixing requirements, solids separation,

and effluent characteristics. BOD removal and the effluent character-

istics are generally estimated using a complete-mix hydraulic model

and first-order reaction kinetics. The mathematical relationship for

BOD removal in a complete-mix aerated lagoon is derived from the fol-

lowing equation

– QS – kSV ⫽ 0 (6.124)

N 5 2a

7.14 2 2

9.02

bs1.024

32220

d 0.85

5 s2 kg/kW

hda

1 3 11.6 mg/L 2 2.0 mg/L

9.02 mg/L

bs1.024

8220

d 0.85

N 5 N

2 C

s20

b1.024

T220

Wastewater Engineering 691

Rearranging

(6.125)

(6.126)

where S ⫽ effluent BOD

concentration, mg/L

⫽ influent BOD

concentration, mg/L

k ⫽ overall first-order BOD

removal rate, per day

⫽ 0.25 to 1.0, based on e

Q ⫽ wastewater flow, m

/d or Mgal/d

u ⫽ total hydraulic retention time, day

Typical design values of u for aerated ponds used for treating domestic

wastewater vary from 3 to 6 days. The amounts of oxygen required for

aerated lagoons range from 0.7 to 1.4 times the amount of BOD

removed

(Metcalf and Eddy, Inc. 1991).

Mancini and Barnhart (1968) developed the resulting temperature in

the aerated lagoon from the influent wastewater temperature, air tem-

perature, surface area, and flow. The equation is

(6.127)

where T

⫽ influent wastewater temperature, ⬚C or ⬚F

⫽ lagoon water temperature, ⬚C or ⬚F

⫽ ambient air temperature, ⬚C or ⬚F

f ⫽ proportionality factor

⫽ 12 ⫻ 10

⫺6

(for British system)

⫽ 0.5 (for SI units)

A ⫽ surface area of lagoon, m

or ft

Q ⫽ wastewater flow, m

/d or Mgal/d

Rearranging Eq. (6.127), the lagoon water temperature is

(6.128)

Aerated lagoons, usually followed by facultative lagoons, are used for

first-stage treatment of high-strength domestic wastewaters and for

pretreatment of industrial wastewaters. Their BOD removal efficiencies

range from 60% to 70%. Low efficiency and foul odors may occur for

AfT

1 QT

Af 1 Q

2 T

dfA

1 1 ku

1 1 ksV/Qd

effluent BOD

influent BOD

692 Chapter 6

improperly designed or poorly operated plants, especially if the aeration

devices are inadequate. Wet weather flow, infiltration, and icing may

cause the process to be upset.

Example: Design a complete-mix aerated lagoon system using the conditions

given below.

solution:

Step 1. Determine the surface area of the lagoon with a depth of 3 m

Volume V ⫽ Qu ⫽ 3000 m

/d ⫻ 5 days

⫽ 15,000 m

Area A ⫽ V/(3 m) ⫽ 15,000 m

/3 m

⫽ 5000 m

⫽ 1.23 acres

Step 2. Estimate lagoon wastewater temperature in summer and winter

Using Eq. (6.128), in summer (T

⫽ 26.5⬚C)

AfT

1 QT

Af 1 Q

Wastewater flow 3000 m

/d (0.8 Mgal/d)

Influent soluble BOD

180 mg/L

Effluent soluble BOD

20 mg/L

Soluble BOD

first-order k

2.4 per day

Influent TSS (not biodegraded) 190 mg/L

Final effluent TSS 22 mg/L

MLVSS/MLSS 0.8

Kinetic coefficients:

k 5 per day

60 mg/L BOD

Y 0.6 mg/mg

0.06 per day

Design depth of lagoon 3 m (10 ft)

Design HRT, u 5 days

Detention time at settling basin 2 days

Temperature coefficient 1.07

Wastewater temperature 15°C (59°F)

Summer mean air temperature 26.5°C (78°F)

Winter mean air temperature 9°C (48°F)

Summer mean wastewater temperature 20.2°C (68°F)

Winter mean wastewater temperature 12.3°C (54°F)

Aeration constant a 0.86

Aeration constant b 1.0

Plant site elevation 210 m (640 ft)

Wastewater Engineering 693

In winter (T

⫽ 9⬚C)

Step 3. Calculate the soluble BOD

during the summer

Using Eq. (6.80)

Step 4. Calculate first-order BOD removal rate constant for temperature

effects

In summer at the mean wastewater temperature 20.2⬚C

⫽ k

(1.07)

T–20

20.2

⫽ 2.4/day (1.07)

20.2–20

⫽ 2.43/day

In winter mean wastewater temperature at 12.3⬚C

12.3

⫽ 2.4/day (1.07)

12.3–20

⫽ 1.43/day

Step 5. Calculate the effluent BOD

using Eq. (6.126)

In summer mean wastewater temperature at 20.2⬚C

S 5 13.7 mg/L

180 mg/L

1 1 2.43 3 5

1 1 ku

5 5.7 mg/L

mg/Ls1 1 5 days 3 0.06/daysd

5 days s0.6 3 5/day 2 0.06/dayd 2 1

S 5

s1 1 uk

usYk 2 k

d 2 1

5 54.18F

5 12.3s8Cd

5000 3 0.5 3 9 1 3000 3 15

5000 3 0.5 1 3000

5 68.48F

5 20.2s8Cd

5000 3 0.5 3 26.5 1 3000 3 15

5000 3 0.5 1 3000

694 Chapter 6

In winter at 12.3⬚C

Ratio of winter to summer ⫽ 22.1 : 13.7 ⫽ 1.6 : 1

Step 6. Estimate the biological solids produced using Eq. (6.78), Q ⫽ Q

Step 7. Calculate TSS in the lagoon effluent before settling

TSS ⫽ 190 mg/L ⫹ 100 mg/L

⫽ 290 mg/L

Note: With low overflow rate and a long detention time of 2 days, the final

effluent can achieve 22 mg/L of TSS.

Step 8. Calculate the amount of biological solids wasted per day

Since X ⫽ 80 mg/L ⫽ 80 g/m

⫽ 0.08 kg/m

(from Step 6)

⫽ 3000 m

/d ⫻ 0.08 kg/m

⫽ 240 kg/d

Step 9. Calculate the oxygen required using Eq. (6.94a)

Using the conversion factor f for BOD

to BOD

, f ⫽ 0.67

5 970 lb/d

5 400 kg/d

3000 m

3 s180 2 5.7d g/m

1000 g/kg 3 0.67

2 1.42 3 240 kg/d

Oxygen 5

QsS

2 Sd

s1000 g/kgd f

2 1.42 p

5 100 mg/L

TSS 5 80 mg/L 4 0.8

5 80 mg/Lsof VSSd

X 5

YsS

2 Sd

1 1 k

0.6s180 2 5.7d mg/L

1 1 0.06 3 5

5 22.1 mg/L

S 5

180 mg/L

1 1 1.43 3 5