Lin S.D. Water and Wastewater Calculations Manual

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A ⫽ C

A, the height H

of the particle–liquid interface at the

underflow desired concentration C

(6.51)

The time t

can be determined as:

Draw a horizontal line through H

and draw a tangent to the subsidence

settling curve at C

. Draw a vertical line from the point of intersection

of the two lines drawn above to the time axis to find the value of t

. With

this value of t

, the area needed for thickening can be calculated using

Eq. (6.50). The area required for clarification is then determined. The

larger of the two calculated areas is the controlling factor for design from

Eqs. (6.49) and (6.50).

Example: The batch-settling curve shown in Fig. 6.10 is obtained for an

activated sludge with an initial solids concentration C

of 3600 mg/L. The ini-

tial height of the interface in the settling column is 900 mm. This continu-

ous inflow to the unit is 380 m

/d (0.10 Mgal/d). Determine the surface area

required to yield a thickened sludge of 1.8 percent by weight. Also determine

solids and hydraulic loading rate.

solution:

Step 1. Calculate H

by Eq. (6.51)

Step 2. Determine t

Using the method described above to find the value of t

⫽ 41 min ⫽ 41 min/1440 min/d

⫽ 0.0285 day

Step 3. Calculate the area required for the thickening, using Eq. (6.50)

5 129

5 12.02 m

A 5

380 m

/d 3 0.0285 day

0.90 m

5 180 mm

3600 mg/L 3 900 mm

18,000 mg/L

5 1.8% 5 18,000 mg/L

Wastewater Engineering 605

Step 4. Calculate the subsidence velocity v

in the hindered settling portion

of the curve

In 10 min

Step 5. Calculate the area required for clarification

Using Eq. (6.49)

A ⫽ Q/v

⫽ 380 m

/d ⫼ 40.6 m/d

⫽ 9.36 m

Step 6. Determine the controlling area

From comparison of areas calculated from Steps 3 and 5, the larger area is

the controlling area. Thus the controlling area is the thickening area of

12.02 m

(129 ft

)

Step 7. Calculate the solids loading

⫽ 3600 mg/L ⫽ 3600 g/m

⫽ 3.6 kg/m

Solids weight ⫽ QC

⫽ 380 m

/d ⫻ 3.6 kg/m

⫽ 1368 kg/d

⫽ 3016 lb/d

Solids loading rate ⫽ 1368 kg/d ⫼ 12.02 m

⫽ 114 kg/(m

⭈ d)

⫽ 23.3 lb/(ft

⭈ d)

Step 8. Determine the hydraulic (overflow) loading rate

Hydraulic loading rate ⫽ 380 m

/d ⫼ 12.02 m

⫽ 31.6 m

/(m

⭈ d) ⫽ 31.6 m/d

or ⫽ 100,000 gal/d ÷ 129 ft

⫽ 776 gal/(ft

⭈ d)

18.6 Compression settling (type 4)

When the concentration of particles is high enough to bring the parti-

cles into physical contact with each other, compression settling will

occur. Consolidation of sediment at the bottom of the clarifier is

5 40.6 m/d

5 0.47 mm/s

s900 2 617d mm

10 min 3 60 s/min

606 Chapter 6

extremely slow. The rate of settlement decreases with time due to

increased resistance to flow of the fluid.

The volume needed for the sludge in the compression region (thick-

ening) can also be estimated by settling tests. The rate of consolidation

in this region has been found to be approximately proportional to the

difference in sludge height H at time t and the final sludge height H

⬁

obtained after a long period of time, perhaps 1 day. It is expressed as

(Coulson and Richardson, 1955)

(6.52)

where H

⫽ sludge height at time t

⫽ constant for a given suspension

⬁

⫽ final sludge height

Integrating Eq. (6.52) between the limits of sludge height H

at time

t and H

at time t

, the resulting expression is

(6.53)

(6.54)

A plot of ln versus (t – t

) is a straight line

having the slope –i. The final sludge height H

⬁

depends on the liquid

surface film which adheres to the particles.

It has been found that gentle stirring serves to compact sludge in the

compression region by breaking up the floc and permitting water to

escape. The use of mechanical rakes with 4 to 5 revolutions per hour will

serve this purpose. Dick and Ewing (1967) reported that gentle stirring

also helped to improve settling in the hindered settling region.

19 Primary Sedimentation Tanks

Primary treatment has traditionally implied a sedimentation process to

separate the readily settleable and floatable solids from the waste-

water. The treatment unit used to settle raw wastewater is referred to

as the primary sedimentation tank (basin), primary tank (basin), or

primary clarifier. Sedimentation is the oldest and most widely used

process in the effective treatment of wastewater.

After the wastewater passes the preliminary processes, it enters sed-

imentation tanks. The suspended solids that are too light to fall out in

the grit chamber will settle in the tank over a few hours. The settled

[sH

2 H

] 2 lnsH

2 H

ist 2 t

d 5 lnsH

2 H

d 2 lnsH

2 H

5 sH

2 H

2ist2t

5 isH 2 H

Wastewater Engineering 607

sludge is then removed by mechanical scrapers, or pumped. The float-

able substances on the tank surface are removed by a surface skimmer

device. The effluent flows to the secondary treatment units or is dis-

charged off (not in the United States and some countries).

The primary sedimentation tank is where the flow velocity of the

wastewater is reduced by plain sedimentation. The process commonly

removes particles with a settling rate of 0.3 to 0.6 mm/s (0.7 to 1.4 in/min).

In some cases, chemicals may be added. The benefits of primary sedimen-

tation are reduced suspended solids content, equalization of sidestream

flow, and BOD removal. The overflow rate of the primary sedimentation

tanks ranges from 24.5 to 49 m

/(m

⭈ d) (600 to 1200 gal/(d ⭈ ft

)). The

detention time in the tank is usually 1 to 3 h (typically 2 h). Primary

tanks (or primary clarifiers) should remove 90% to 95% of settleable

solids, 50% to 60% of total suspended solids, and 25% to 35% of the

BOD

(NY Department of Health, 1950).

Settling characteristics in the primary clarifier are generally charac-

terized by type 2 flocculant settling. The Stokes formula for settling veloc-

ity cannot be used because the flocculated particles are continuously

changing in shape, size, and specific gravity. Since no mathematical equa-

tion can describe flocculant settling satisfactorily, laboratory analyses of

settling-column tests are commonly used to generate design information.

Some recommended standards for the design of primary clarifiers are

as follows (GLUMRB–Ten States Standards, 1996; Illinois EPA, 1998).

Multiple tanks capable of independent operation are desirable and shall

be provided in all plants where design average flows exceed 380 m

(100,000 gal/d). The minimum length of flow from inlet to outlet should

be 3.0 m (10 ft) unless special provisions are made to prevent short cir-

cuiting. The side depth for primary clarifiers shall be as shallow as

practicable, but not less than 3.0 m (10 ft). Hydraulic surface settling

rates (overflow rates) of the clarifier shall be based on the anticipated

peak hourly flow. For normal domestic wastewater, the overflow rate,

with some indication of BOD removal, can be obtained from Fig. 6.11.

If waste-activated sludge is returned to the primary clarifier, the design

surface settling rate shall not exceed 41 m

/(m

⭈ d) (1000 gal/(d ⭈ ft

)).

The maximum surfaced settling rate for combined sewer overflow and

bypass settling shall not exceed 73.3 m

/(m

⭈ d) (1800 gal/(d ⭈ ft

)), based

on peak hourly flow. Weir loading rate shall not exceed 250 m

/d linear

meter (20,000 gal/(d ⭈ ft)), based on design peak hourly flow for plants

having a design average of 3785 m

/d (1 Mgal/d) or less. Weir loading

rates shall not exceed 373 m

/(d

⭈ m) (30,000 gal/(d ⭈ ft)), based on peak

design hourly flow for plants having a design average flow greater than

3785 m

/d (1.0 Mgal/d). Overflow rates, side water depths, and weir

loading rates recommended by various institutions for primary settling

tanks are listed elsewhere (WEF and ASCE, 1991a).

608 Chapter 6

In cases where a reliable loading–performance relationship is not

available, the primary tank design may be based on the overflow rates

and side water depths listed in Table 6.10. The design surface settling

is selected on the basis of Fig. 6.11 and Table 6.10. The hydraulic

Wastewater Engineering 609

Figure 6.11 BOD

, removal in primary settling tank (source: Illinois EPA 1998).

TABLE 6.10

Typical Design Parameters for Primary Clariﬁers

Surface settling rate,

/(m

⭈ d) (gal/(d ⭈ ft

))

Type of treatment Source Average Peak Depth, m (ft)

Primary settling US EPA, 1975a 33–19 81–122 3–3.7

followed by (800–1200) (2000–3000) (10–12)

secondary

treatment

GLUMEB–Ten States 600 Figure 6.11 minimum 2.1

Standards and Illinois (7)

EPA, 1998

Primary settling US EPA, 1975a 24–33 49–61 3.7–4.6

with waste (600–800) (1200–1500) (12–15)

activated sludge

return

Ten States Standards, ⱕ 41 ⱕ 61 3.0

GLUMRB, 1996

(ⱕ 1000) (ⱕ 1500) (10)

minimum

detention time t in the primary clarifier can be calculated from

Eq. (6.44). The hydraulic detention times for primary clarifier design

range from 1.5 to 2.5 h, typically 2 h. Consideration should be made for

low flow period to ensure that longer detention times will not cause

septic conditions. Septic conditions may cause a potential odor problem,

stabilization and loading to the downstream treatment processes. In the

cold climatic region, a detention time multiplier should be included

when wastewater temperature is below 20⬚C (68⬚F). The multiplier can

be calculated by the following equation (Water Pollution Control

Federation, 1985a)

M ⫽ 1.82e

⫺0.03T

(6.55)

where M ⫽ detention time multiplier

T ⫽ temperature to wastewater, ⬚C

In practice, the linear flow-through velocity (scour velocity) is limited

to 1.2 to 1.5 m/min (4 to 5 ft/min) to avoid resuspension of settled solids

in the sludge zone (Theroux and Betz, 1959). Camp (1946) suggested that

the critical scour velocity can be computed by Eq. (6.39). Scouring veloc-

ity may resuspend settled solids and must be avoided with clarifier

design. Camp (1953) reported that horizontal velocities up to 18 ft/min

(9 cm/s) may not create scouring; but design horizontal velocities should

still be designed substantially below 18 ft/min. As long as scouring veloc-

ities are not approached, solids removal in the clarifier is independent

of the tank depth.

Example 1: Determine the detention time multipliers for wastewater tem-

peratures of 12 and 6⬚C.

solution: Using Eq. (6.55), for T ⫽ 12°C

M ⫽ 1.82e

⫺0.03⫻12

⫽ 1.82 ⫻ 0.70

⫽ 1.27 (6.56)

For T ⫽ 6⬚C

M ⫽ 1.82 ⫻ e

⫺0.03⫻6

⫽ 1.82 ⫻ 0.835

⫽ 1.52

Example 2: Two rectangular settling tanks are each 6 m (20 ft) wide, 24 m

(80 ft) long, and 2.7 m (9 ft) deep. Each is used alternately to treat 1900 m

(0.50 Mgal) in a 12-h period. Compute the surface overflow (settling) rate,

detention time, horizontal velocity, and outlet weir loading rate using H-

shaped weir with three times the width.

610 Chapter 6

solution:

Step 1. Determine the design flow Q

Step 2. Compute surface overflow rate v

⫽ Q/A ⫽ 3800 m

/d ⫼ (6 m ⫻ 24 m)

⫽ 26.4 m

/(m

⭈ d)

⫽ 650 gal/(d ⭈ ft

)

Step 3. Compute detention time t

Tank volume V ⫽ 6 m ⫻ 24 m ⫻ 2.1m ⫻ 2

⫽ 604.8 m

t ⫽ V/Q ⫽ 604.8 m

/(3800 m

/d)

⫽ 0.159 day

⫽ 3.8 h

Step 4. Compute horizontal velocity v

Step 5. Compute outlet weir loading, wl

19.1 Rectangular basin design

Multiple units with common walls shall be designed for independent

operation. A bypass to the aeration basin shall be provided for emergency

conditions. Basin dimensions are to be designed on the basis of surface

5 17,000 gal/sd

ftd

5 211 m

/sd

wl 5

3800 m

6 m 3 3

5 0.686 ft/min

5 0.209 m/min

5 301 m/d

3800 m

6 m 3 2.1 m

5 3800 m

Q 5

1900 m

12 h

24 h

1 day

Wastewater Engineering 611

overflow (settling) rate to determine the required basin surface area. The

area required is the flow divided by the selected overflow rate. An over-

flow rate of 36 m

/(m

⭈ d) (884 gal/(ft

⭈ d)) at average design flow is gen-

erally acceptable.

Basin surface dimensions, the length (l ) to width (w) ratio (l/w), can

be increased or decreased without changing the volume of the basin. The

greater the l/w ratio, the better the basin conforms to plug flow condi-

tions. Also, for greater l/w ratio, the basin has a proportionally larger

effective settling zone and smaller percent inlet and outlet zones.

Increased basin length allows the development of a more stable flow.

Best conformance to the plug flow model has been reported by a basin

with l/w ratio of 3:1 or greater (Aqua-Aerobic Systems, 1976).

Basin design should be cross-checked for detention time for confor-

mance with recommended standards by the regulatory agencies.

For bean bridge (cross the basin) design, a commercially available eco-

nomical basin width can be used, such as 1.5 m (5 ft), 3.0 m (10 ft), 5.5 m

(18 ft), 8.5 m (28 ft) or 11.6 m (38 ft).

The inlet structures in rectangular clarifiers are placed at one end and

are designed to dissipate the inlet velocity to diffuse the flow equally

across the entire cross section of the basin and to prevent short circuit-

ing. Typical inlets consist of small pipes with upward ells, perforated baf-

fles, multiple ports discharging against baffles, a single pipe turned

back to discharge against the headwall, simple weirs, submerged weirs

sloping upward to a horizontal baffle, etc. (Steel and McGhee, 1979;

McGhee, 1991). The inlet structure should be designed not to trap scum

or settling solids. The inlet channel should have a velocity of 0.3 m/s

(1 ft/s) at one half design flow (Ten States Standards, GLUMRB, 1996).

Baffles are installed 0.6 to 0.9 m (2 to 3 ft) in front of inlets to assist

in diffusing the flow and submerged 0.45 to 0.60 m (1.5 to 2 ft) with 5 cm

(2 in) water depth above the baffle to permit floating material to pass.

Scum baffles are placed ahead of outlet weirs to hold back floating mate-

rial from the basin effluent and extend 15 to 30 cm (6 to 12 in) below the

water surface (Ten States Standards, GLUMRB, 1971). Outlets in a rec-

tangular basin consist of weirs located toward the discharge end of the

basin. Weir loading rates range from 250 to 373 m

/(d ⭈ m) (20,000 to

30,000 gal/(d ⭈ ft)) (Ten State Standards, GLUMRB, 1996).

Walls of settling tanks should extend at least 150 mm (6 in) above

the surrounding ground surface and shall provide not less than 300 mm

(12 in) freeboard (GLUMRB, 1996).

Mechanical sludge collection and withdrawal facilities are usually

designed to assure rapid removal of the settled solids. The minimum

slope of the side wall of the sludge hopper is 1.7 vertical to 1 horizon-

tal. The hopper bottom dimension should not exceed 600 mm (2 ft). The

sludge withdrawal line is at least 150 mm (6 in) in diameter and has a

612 Chapter 6

static head of 760 mm (30 in) or greater with a velocity of 0.9 m/s (3 ft/s)

(Ten States Standards, GLUMRB, 1996).

Example: Design a primary clarification system for a design average waste-

water flow of 7570 m

/d (2.0 Mgal/d) with a peak hourly flow of 18,900 m

(5.0 Mgal/d) and a minimum flow of 4540 m

/d (1.2 Mgal/d). Design a multi-

ple units system using Ten States Standards for an estimated 35% BOD

removal at the design flow.

solution:

Step 1. List Ten States Standards

Referring to Fig. 6.11, for 35% BOD removal:

Surface settling rate v ⫽ 28.5 m

/(m

⭈ d) or (700 gal/(d ⭈ ft

))

Minimum depth ⫽ 3.0 m (10 ft)

Maximum weir loading ⫽ 124 m

/(d ⭈ m) or (10,000 gal/(d ⭈ ft))

for average daily flow

Step 2. Determine tank dimensions

1. Surface area needed

Use two settling tanks, each with design flow of 3785 m

(1.0 Mgal/d)

Surface area A ⫽ Q/v ⫽ 3785 m

/d ⫼ 28.5 m

/(m

⭈ d)

⫽ 132.8 m

2. Determine length l and width w using l/w ratio of 4/1

(w)(4w) ⫽ 132.8

⫽ 33.2

w ⫽ 5.76 (m)

Standard economic widths of bean bridge are: 1.52 m (5 ft), 3.05 m

(10 ft), 5.49 m (18 ft), 8.53 m (28 ft), and 11.58 m (38 ft).

Select standard 5.49 m (18 ft width); w ⫽ 5.49 m

5.49l ⫽ 132.8

l ⫽ 24.19 (m)

⫽ 79.34 ft

Say area is 5.5 m ⫻ 24 m (18 ft ⫻ 79 ft)

Compute tank surface area A

A ⫽ 132 m

⫽ 1422 ft

Wastewater Engineering 613

3. Compute volume V with a depth of 3 m

V ⫽ 132 m

⫻ 3 m

⫽ 396 m

⫽ 14,000 ft

Step 3. Check detention time t

At average design flow

t ⫽ V/Q ⫽ 396 m

/(3785 m

/d)

⫽ 0.105 day ⫻ 24 h/d

⫽ 2.5 h

At peak flow

t ⫽ 2.5 h ⫻ (2/5)

⫽ 1.0 h

Step 4. Check overflow rate at peak flow

v ⫽ 28.5 m

/(m

⭈ d) ⫻ (5/2)

⫽ 71.25 m

/(m

⭈ d)

Step 5. Determine the length of outlet weir

Length ⫽ flow ⫼ weir loading rate

⫽ 3785 m

/d ⫼ 124 m

/(d ⭈ m)

⫽ 30.5 m

It is 5.5 times the width of the tank.

19.2 Circular basin design

Inlets in circular or square basins are typically at the center and the

flow is directed upward through a baffle that channels the wastewater

(influent) toward the periphery of the tank. Inlet baffles are 10% to 20%

of the basin diameter and extend 0.9 to 1.8 m (3 to 6 ft) below the

wastewater surface (McGhee, 1991).

Circular basins have a higher degree of turbulence than rectangular

basins. Thus circular basins are more efficient as flocculators.

A typical depth of sidewall of a circular tank is 3 m (10 ft). As shown

in Fig. 6.12, the floor slope of the tank is typically 300 mm (12 in) hor-

izontal to 25 mm (1 in) vertical (Aqua-Aerobic Systems, 1976).

Outlet weirs extend around the periphery of the tank with baffles

extending 200 to 300 mm (8 to 12 in) below the wastewater surface to

retain floating material (McGhee, 1991). Overflow weirs shall be located

to optimum actual hydraulic detention time and minimize short circuiting.

614 Chapter 6