Lin S.D. Water and Wastewater Calculations Manual

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Wastewater Engineering 725

Step 2. Compute the required surface area of the RBC

Step 3. Check the design for overall organic loading rate

It is under 2.0 [lbⲐ(1000 ft

⭈ d)], therefore OK.

Step 4. Size the first stage

The size factor for the area required for the first stage is 0.2 ⫻ SBOD load-

ing. For this case, the size factor is 0.346 (0.2 ⫻ 1.73, or 34.6% of total surface

area). This value can be obtained from the manufacturer’s curves.

Surface area for first stage ⫽ 0.346 ⫻ 1,160,000 ft

≅ 400,000 ft

Step 5. Determine configuration

(a) Choice standard media assemblies each having 100,000 ft

for the first

stage

Unit for first stage ⫽ 400,000 ft

/100,000 ft

⫽ 4

Use 4 standard media; each is installed at the first stage of 4 trains.

(b) Choice Hi-Density media assemblies have 150,000 ft

for the following

stages

High-Density media area ⫽ (1,160,000 ⫺ 400,000) ft

⫽ 760, 000 ft

No. of Hi-Density assemblies ⫽ 760,000 ft

/150,000 ft

⫽ 5.1

Alternative 1: Use 4 standard media at stages 2 and 3.

Alternative 2: Use 4 Hi-density media at stages 2 and 4 standard density

media at stage 3

Alternative 1 is less costly.

Alternative 2 has an advantage in preventing shock loadings.

5 1.73 [lb/s1000 ft

dd]

SBOD loading 5

4 Mgal/d 3 60 mg/L 3 8.34 lb/sMgal

mg/Ld

1.160,000 ft

5 1,160,000 ft

Area 5

4,000,000 gal/d

3.44 gal/sd

726 Chapter 6

shown below:

(1) SSSS ⫹ SSSS ⫹ SSSS

(2) SSSS ⫹ HHHH ⫹ SSSS

Note:S ⫽ standard density media; H ⫽ high density media.

Step 6. Determine the required surface area for the secondary settling tank

(a) Compute surface area based on average (design) flow using an overflow

rate of 600 gal/(d ⭈ ft

)

Area ⫽ 4,000,000 (gal/d)/600 (gal/(d ⭈ ft

)

⫽ 6,670 ft

(b) Compute surface area based on peak flow using an overflow rate of

1200 gal/(d ⭈ ft

)

Area ⫽ 10,000,000 (gal/d)/1200 (gal/(d ⭈ ft

))

⫽ 8330 ft

tank is controlled by the maximum hourly flow rate.

24 Dual Biological Treatment

Dual biological treatment processes use a fixed film reactor in series with

a suspended growth reactor. Dual processes include such as activated

biofilter, trickling filter-solids contact, roughing filter-activated sludge,

biofilter-activated sludge, trickling filter-activated sludge, roughing

filter-RBC, roughing filter-aerated lagoon, roughing filter-facultative

lagoon, roughing filter-pure oxygen activated sludge. Descriptions of

these dual processes may be found elsewhere (Metcalf and Eddy, Inc.

1991; WEF and ASCE, 1991a).

25 Stabilization Ponds

The terms stabilization pond, lagoon, oxidation pond have been used syn-

onymously. This is a relatively shallow earthen basin used as second-

ary or tertiary wastewater treatment, especially in rural areas.

Stabilization ponds have been employed for treatment of wastewater for

over 300 years. Ponds have become popular in small communities

because of their low construction and operating costs. They are used to

treat a variety of wastewaters from domestic and industrial wastes and

functions under a wide range of weather conditions. Ponds can be

employed alone or in combination with other treatment processes.

Wastewater Engineering 727

Stabilization ponds can be classified as facultative (aerobic-anaerobic),

aerated, aerobic, and anaerobic ponds according to the dominant type

of biological activity or reactions occurring in the pond. Other classifi-

cations can be based on the types of the influent (untreated, screened,

settled effluent, or secondary (activated-sludge) effluent), the duration

of discharge (nonexistent, intermittent, and continuous), and the method

of oxygenation (photosynthesis, atmospheric surface reaeration, and

mechanical aeration). Aerated ponds (aerated lagoons) have been dis-

cussed previously.

25.1 Facultative ponds

The most common type of stabilization pond is the facultative pond. It

is also called the wastewater lagoon. Facultative ponds are usually

1.2 to 2.5 m (4 to 8 ft) in depth, with an aerobic layer overlying an anaer-

obic layer, often containing sludge deposits. The detention time is usually

5 to 30 days (US EPA, 1983b).

The ponds commonly receive no more pretreatment than screening

(few with primary effluent). It can also be used to follow trickling filters,

aerated ponds, or anaerobic ponds. They then store grit and heavy solids

in the first or primary ponds to form an anaerobic layer. The system is

a symbiotic relationship between heterotrophic bacteria and algae.

Bacteria found in an aerobic zone of a stabilization pond are prima-

rily of the same type as those found in an activated-sludge process or in

the zoogleal mass of a trickling filter. The most frequently isolated bac-

teria include Beggiatoa alba, Sphaerotilus natans, Achromobacter,

Alcaligenes, Flavobacterium, Pseudomonas, and Zoogloea spp. (Lynch

and Poole, 1979). These organisms decompose the organic materials

present in the aerobic zone into oxidized end products.

Organic matter in wastewater is decomposed by bacterial activities,

including both aerobic and anaerobic, which release phophorus, nitro-

gen, and carbon dioxide. Oxygen in the aerobic layer is supplied by sur-

face reaeration and algal photosynthesis. Algae consume nutrient and

carbon dioxide produced by bacteria and release oxygen to water. DO is

used by bacteria, thus forming a symbiotic cycle. In the pond bottom,

anaerobic breakdown of the solids in the sludge layer produces dis-

solved organics and gases such as methane, carbon dioxide, and hydro-

gen sulfide. Between the aerobic and anaerobic zones, there is a zone

called the facultative zone. Temperature is a major factor for the bio-

logical symbiotic activities.

Organic loading rates on stabilization ponds are expressed in terms

of kg BOD

applied per hectare of surface area per day (lb BOD/

(acre ⭈ d)), or sometimes as BOD equivalent population per unit area.

Typical organic loading rates are 22 to 67 kg BOD/(ha ⭈ d) (20 to 60 lb

BOD/(a ⭈ d)). Typical detention times range from 25 to 180 days. Typical

728 Chapter 6

TABLE 6.18 Recommended BOD

Loading Rates for Facultative Ponds

Water depth BOD loading rate

Average winter air

temperature, ⬚C m ft kg/(ha ⭈ d) lb/(acre ⭈ d)

<0 1.5–2.1 5–7 11–22 10–20

0–15 (59ºF) 1.2–1.8 4–6 22–45 20–40

>15 1.1 3.6 45–90 40–80

SOURCE: US EPA (1974b)

dimensions are 1.2 to 2.5 m (4 to 8 ft) deep with 4 to 60 ha (10 to 150 acres)

of surface area (US EPA, 1983b).

Facultative ponds are commonly designed to reduce BOD to about

30 mg/L; but, in practice, it ranges from 30 to 40 mg/L or greater due to

algae. Volatile organic removal is between 77% and 96%. Nitrogen

removal achieves 40% to 95%. Less phosphorus removal is observed,

being less than 40%. Effluent TSS levels range from 40 to 100 mg/L,

mainly contributed by algae (WEF and ASCE, 1991b). The presence of

algae in pond effluent is one of the most serious performance problems

associated with facultative ponds. The ponds are effective in removal of

fecal coliform (FC) due to their dying off. In most cases effluent FC den-

sities are less than the limit of 200 FC/100 ml.

Process design. Several design formulas with operational data were

presented in the design manual (US EPA, 1974b). Calculations of the size

of a facultative pond are also illustrated for the areal loading rate pro-

cedure, Gloyna equation, Marais–Shaw equation, plug-flow model, and

Wehner–Wilhelm equation. The design for partial-mix aerated lagoon is

given elsewhere (WPCF, 1990). In this section, design methods of the

areal loading rate method and the Wehner and Wilhelm model are

discussed.

Areal loading rate method. The design procedure is usually based on

organic loading rate and hydraulic residence time. Several empirical

and rational models for the design of facultative ponds have been pro-

posed. Several proposed design methods have been discussed elsewhere

(US EPA, 1983b). The areal loading rate is the most conservative design

method and can be adapted to specific standards. The recommended

BOD loading rates based on average winter air temperature are given

in Table 6.18 (US EPA , 1974b).

The surface area required for the facultative pond is determined by

dividing the organic (BOD) load by the appropriate BOD loading rate

listed in Table 6.18 or from the specific state standards. It can be

Wastewater Engineering 729

expressed as the following equation (as used for other processes):

(6.147)

(6.148)

where A ⫽ area required for facultative pond, ha or acre

BOD ⫽ BOD concentration in influent, mg/L

Q ⫽ flow of influent, m

/d or Mgal/d

LR ⫽ BOD loading rate for average winter air temperature,

kg/(ha ⭈ d) or lb/(acre ⭈ d)

1000 ⫽ conversion factor, 1000 g ⫽ l kg

8.34 ⫽ conversion factor, 1 Mgal ⭈ mg/L ⫽ 8.34 lb

The BOD loading rate at the first cell in a series of cells (ponds) should

not exceed 100 kg/(ha ⭈ d) (90 lb/(acre ⭈ d)) for warm climates, average

winter air temperature greater than 15⬚C (59⬚F), and 40 kg/(ha ⭈ d)

(36 lb/(acre ⭈ d)) for average winter air temperature less than 0⬚C (32⬚F).

Example 1: The design flow of facultative ponds for a small town is 1100 m

(0.29 Mgal/d). The expected influent BOD is 210 mg/L. The average winter tem-

perature is 10⬚C (50⬚F). Design a three-cell system with organic loading less than

80 kg/(ha ⭈ d) (72 lb/(acre ⭈ d)) in the primary cell. Also estimate the hydraulic deten-

tion time when average sludge depth is 0.5 m and there are seepage and evapo-

ration losses of 2.0 mm of water per day.

solution:

Step 1. Determine area required for the total ponds

From Table 6.18, choose BOD loading rate LR ⫽ 38 kg/(ha ⭈ d) (33.9 lb/(acre ⭈ d)),

because mean air temperature is 10⬚C. Using Eq. (6.147)

Step 2. Determine the area required for the primary cell (use LR ⫽ 80 kg/

(ha ⭈ d))

5 2.80 shad

Area 5

1100 3 210

80 3 1000

5 60,800 m

5 6.08 ha s16.6 areasd

A 5

QsBODd

sLRds1000d

1100 m

/d 3 210 g/m

38 kg/sha

dd 3 1000 g/kg

A 5

QsBODds8.34d

sLRd

 s British unitsd

A 5

QsBODd

sLRds1000d

 sSI unitsd

730 Chapter 6

Step 3. Sizing for 3 cells

Referring to Table 6.18, choose water depth of 1.5 m (5 ft) for all cells.

(a) Primary cell:

Area ⫽ 2.88 ha ⫽ 28,800 m

Use 100-m (328-ft) wide, 288-m (945-ft) long and 1.5-m (5-ft) deep pond.

(b) Two other cells:

Area for each ⫽ (60,800 ⫺ 28,800) m

⫽ 16,000 m

Choose 144 m in length, then the width ⫽ 111 m

The pond arrangements are as shown below.

Step 4. Estimate the hydraulic retention time

(a) Calculate the storage volume V (when average sludge depth ⫽ 0.5 m)

V ⫽ (1.5 m ⫺ 0.5 m) ⫻ 60,800 m

⫽ 60,800 m

(b) Calculate the water loss V ⬘

V⬘⫽0.002 m/d ⫻ 60,800 m

⫽ 122 m

5 62 days

HRT 5

Q 2 V r

60,800 m

1100 m

/d 2 122 m

Wastewater Engineering 731

Example 2: A lagoon system contains two cells in series. Each cell is 110 m ⫻

220 m (360 ft ⫻ 720 ft) in size with a maximum operating depth of 1.64 m

(5.4 ft) and a minimum operating depth of 0.55 m. (1.8 ft). The wastewater

flow is 950 m

/d (0.25 MGD) with an average BOD

of 105 mg/L. Determine

the organic loading rate and the detention time of the lagoon. The tempera-

ture ranges 10 to 15⬚C.

solution:

Step 1. Calculate the BOD

loading rate

BOD

mass ⫽ 950 m

/d ⫻ 105 mg/L ⫻ 1000 L/m

⫻ 10

⫺6

kg/mg

⫽ 99.75 kg/d

Area of the primary cell ⫽ 110 m ⫻ 220 m

⫽ 24,200 m

⫻ 10

⫺4

ha/m

⫽ 2.42 ha

BOD

loading rate ⫽ (99.75 kg/d)/(2.42 ha)

⫽ 41.2 kg/(ha ⭈ d)

This loading rate is acceptable by checking with Table 6.18, at temperature

⬎15⬚C, the recommended BOD

loading rate ranges 22 to 45 kg/(ha ⭈ d).

Step 2. Calculate the detention time

The detention time ⫽ 24,000 m

/cell ⫻ (1.64 m ⫺ 0.55 m) ⫻ 2 cells ⫼ 950 m

⫽ 55.5 days

Wehner and Wilhelm equation. Wehner and Wilhelm (1958) used the first-

order substrate removal rate equation for a reactor with an arbitrary

flow-through pattern, which is between a plug-flow pattern and a

complete-mix pattern. Their proposed equation is

(6.149)

where C ⫽ effluent substrate concentration, mg/L

⫽ influent substrate concentration, mg/L

a ⫽

k ⫽ first-order reaction constant, 1/h

t ⫽ detention time, h

D ⫽ dispersion factor⫽H/uL

H ⫽ axial dispersion coefficient, m

/h or ft

u ⫽ fluid velocity, m/h or ft/h

L ⫽ length of travel path of a typical particle, m or ft

21 1 4ktD

4a exp s1/2Dd

s1 1 ad

expsa/2Dd 2 s1 2 ad

exps 2 a/2D d

732 Chapter 6

Figure 6.34 Relationship between kt values and percent BOD remaining

for various dispersions factors, by the Wehner-Wilhelm equation.

The Wehner-Wilhelm equation for arbitrary flow was proposed by

Thirumurthi (1969) as a method of designing facultative pond systems.

Thirumurthi developed a graph, shown in Fig. 6.34, to facilitate the use

of the equation. In Fig. 6.34, the term kt is plotted against the percent

BOD

remaining (C/C

) in the effluent for dispersion factors varying

from zero for an ideal plug-flow reactor to infinity for a complete-mix

reactor. Dispersion factors for stabilization ponds range from 0.1 to 2.0,

with most values not exceeding 1.0 due to the mixing requirement. Typical

values for the overall first-order BOD

removal rate constant k vary from

0.05 to 1.0 per day, depending on the operating and hydraulic character-

istics of the pond. The use of the arbitrary flow equation is complicated

in selecting k and D values. A value of 0.15 per day is recommended for

(US EPA, 1984). Temperature adjustment for k can be determined by

⫽ k

(1.09)

T ⫺ 20

(6.150)

where k

⫽ reaction rate at minimum operating water

temperature T, per day

⫽ reaction rate at 20⬚C, per day

T ⫽ minimum operating temperature, ⬚C

Wastewater Engineering 733

Example: Design a facultative pond system using the Wehner-Wilhelm

model and Thirumurthi application with the following given data.

Design flow rate Q ⫽ 1100 m

/d (0.29 Mgal/d)

Influent TSS ⫽ 220 mg/L

Influent BOD

⫽ 210 mg/L

Effluent BOD

⫽ 30 mg/L

Overall first-order k at 20⬚C ⫽ 0.22 per day

Pond dispersion factor D ⫽ 0.5

Water temperature at critical period ⫽ 1⬚C

Pond depth ⫽ 2 m (6.6 ft)

Effective depth ⫽ 1.5 m (5 ft)

solution:

Step 1. Calculate the percentage of BOD remaining in the effluent

C/C

⫽ 30 mg/L ⫻ 100%/(210 mg/L)

⫽ 14.3%

Step 2. Calculate the temperature adjustment for k

using Eq. (6.150)

⫽ k

(1.09)

T⫺20

⫽ 0.22 (1.09)

1⫺20

⫽ 0.043 (per day)

Step 3. Determine the value of k

t from Fig. 6.34

At C/C

⫽ 14.3% and D ⫽ 0.5

t ⫽ 3.1

Step 4. Calculate the detention time for the critical period of year

t ⫽ 3.1/(0.043 d

⫺1

)

⫽ 72 days

Step 5. Determine the pond volume and surface area requirements

Volume ⫽ Qt ⫽ 1100 m

/d ⫻ 72 days

⫽ 79,200 m

Area ⫽ volume/effective depth ⫽ 79,200 m

/1.5 m

⫽ 52,800 m

⫽ 5.28 ha

⫽ 13.0 acres

734 Chapter 6

Step 6. Check BOD

loading rate

Step 7. Determine the power requirement for the surface aerators

Assume that the oxygen transfer capacity of the aerators is twice the value

of the BOD applied per day and that a typical aerator has a transfer capacity

of 22 kg O

/(hp ⭈ d)

required ⫽ 2 ⫻ 1100 m

/d ⫻ 210(g/m

)/(1000 g/kg)

⫽ 462 kg/d

Power ⫽ (462 kg/d)/(22 kg/hp ⭈ d)

⫽ 21.0 hp

⫽ 15.7 kW

Use seven 3-hp units

Step 8. Check the power input to determine the degree of mixing

Power input ⫽ 15.7 kW/79.2 ⫻ 1000 m

⫽ 0.20 kW/1000 m

⫽ 0.0076 hp/1000 ft

Note: In practice, the minimum power input is about 28 to 54 kW/1000 m

(1.06 to 2.05 hp/1000 ft

) for mixing (Metcalf and Eddy, Inc. 1991).

Tertiary ponds. Tertiary ponds, also called polishing or maturation ponds,

serve as the third-stage process for effluent from activated-sludge or

trickling filter secondary clarifier effluent. They are also used as a second

stage following facultative ponds and are aerobic throughout their depth.

The water depth of the tertiary pond is usually 1 to1.5 m (3 to 4.5 ft).

BOD loading rates are less than 17 kg/(ha ⭈ d) (15 lb/(acre ⭈ d)). Detention

times are relatively short and vary from 4 to 15 days.

25.2 Aerobic ponds

Aerobic ponds, also referred to as high-rate aerobic ponds, are relatively

shallow with usual depths ranging from 0.3 to 0.6 m (1 to 2 ft), allowing

light to penetrate the full depth. The ponds maintain DO throughout their

entire depth. Mixing is often provided to expose all algae to sunlight and

to prevent deposition and subsequent anaerobic conditions. DO is supplied

by algal photosynthesis and surface reaeration. Aerobic bacteria utilize and

stabilize the organic waste. The HRT in the ponds is short—3 to 5 days.

5 40.0 lbsacre

5 43.8 kg/sha

Loading 5

1100 m

/d 3 210 g/m

5.28 ha 3 1000 g/kg