Lin S.D. Water and Wastewater Calculations Manual

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For BOD yields: at Q

ave

A ⫽ 15,900 m

/d ⫻ 1000 L/m

⫻ 55 mg/L/(45 kg/ha ⭈ d ⫻10

mg/kg)

⫽ 19.4 ha

at Q

max

A ⫽ 31,800 ⫻ 1000 ⫻ 38/(45 ⫻ 10

) ⫽ 26.9 ha

For TSS yields: at Q

ave

A ⫽ 15,900 ⫻ 1000 ⫻ 66/(30 ⫻ 10

) ⫽ 35.0 ha

at Q

max

A ⫽ 31,800 ⫻ 1000 ⫻ 32/(30 ⫻ 10

) ⫽ 33.9 ha

The limiting factor is again the TSS loading at average flow conditions where

35.0 ha are required to meet the more stringent effluent standards.

Step 2. Compute the theoretical HRT, t, required for the entire 3-zone FWS

system, assuming an overall average depth, H ⫽ 0.84 m and an average n ⫽

0.82. Using Eq. (6.231)

for Q

ave

t ⫽ V ⫻ n/Q

ave

⫽ A ⫻ H ⫻ n/Q

ave

⫽ 35.0 ha ⫻ 10,000 m

/ha ⫻ 0.84 m ⫻ 0.82/15,900 m

⫽ 15.2 days

for Q

max

t ⫽ 15.2 days/2 ⫽ 7.6 days

Step 3. Determine the area required for each cell (zone)

At maximum monthly flow rate, assuming an equal minimum HRT (t ⫽ 7.6

days/3 ⫽ 2.53 days) in each of 3 cells

for zone 2,

⫽ t Q/nH⫽ 2.53 days ⫻ 31,800 m

/d/(1.0 ⫻ 1.3 m ⫻ 10,000 m

/ha)

⫽ 6.2 ha

Then, area for zone 1 (A

) and zone 3 (A

) would be

⫽ A

⫽ (35.0 ha⫺6.2 ha)/2 ⫽ 14.4 ha

Step 4. Determine the zone dimensions

Say the total area required for the 3 treatment zones is 35 ha (86.5 acres).

By adding in 25% of it, the overall FWS wetland area including inlet/outlet

zones would be 43.8 ha (108 acres).

Wastewater Engineering 875

Again use two parallel trains (17.5 ha each) and aspect ratio of 4 : 1;

then, 4W

⫽ 175,000 m

. We obtain W ⫽ 209 m and L ⫽ 836 m (only for

3 cells). Approximately, the lengths of zones 1, 2, and 3 are 318, 200, and

318 m, respectively. By adding 25% of the length for the inlet and outlet

zones, the total length for the system is 1045 m. The length of the inlet

and outlet zones may be 109 and 100 m, respectively. The depths of the

inlet, 3 treatment, and outlet zones respectively are of 1.0, 0.6, 1.3, 0.6,

and 0.6 m.

Vegetated submerged bed systems. The VSB wetlands are composed of

gravel beds that may be planted with wetland vegetation. Figure 6.64

illustrates a schematic sketch of a VSB wetland system. Typical VSB

components include (1) inlet piping, (2) a clay or synthetic membrane

lined basin, (3) loose media filling the basin, (4) wetland vegetation

planted in the media, and (5) outlet piping with a water-level control

system. The outlet structures are designated for regulation and distri-

bution of wastewater flow. VSB wetlands may contain berms. In addi-

tion to shape and size, other variable factors are choice of treatment

media (gravel shape and size, for example) as an economic factor and

selection of vegetation as an optional feature that affects wetland aes-

thetics more than its performance.

The pollutant removal performance of VSB systems depends on many

factors including influent wastewater quality, hydraulic and pollutant

loading, climate, and physical characteristics of the systems. The main

advantage of a VSB system over a free water surface wetland system is

the isolation of the wastewater from vectors, animals, and humans.

Concerns with mosquitoes and pathogen transmission are greatly

reduced with a VSB system. Properly designed and operated VSB sys-

tems may not need to be fenced off or otherwise isolated from people and

animals. Comparing conventional VSB systems to FWS systems of the

same size, VSB systems typically cost more to construct, primarily

because of the cost of media (Reed et al., 1995).

It is not clear if it is desirable to maintain a single plant species, or a

prescribed collection of plant species, for any treatment purpose. Single

plant (monoculture) systems are more susceptible to catastrophic plant

death due to predation or disease (George et al., 2000). It is generally

assumed that multiple plant and native plant systems are less suscep-

tible to catastrophic plant death, although no studies have confirmed

this assumption. Plant invasion and plant dominance further compli-

cate the issue.

It was found that the roots do not fully penetrate to the bottom of the

media and there is substantially more flow under the root zone than

through it (Young et al., 2000). The oxygen supply from the roots is also

likely to be unreliable due to yearly plant senescence, plant die-off due

876 Chapter 6

to disease and pests, and variable plant coverage from year to year.

Considering all of these factors, it is recommended that designers

assume wetland plants provide no significant amounts of oxygen to a

VSB system. The impact of wetland plants on pollutant removal per-

formance appears to be minimal, based on current knowledge; so, the

selection of plants species should be based on aesthetics, impacts on

operation, and long-term plant health and viability in a given geo-

graphical area. Local wetland plants experts should be consulted when

making the selection.

Hydrology. As in all gravity flow systems, the water level in a VSB

system is controlled by the outlet elevation and the hydraulic gradient,

or slope, that is the drop in the water level (head loss) over the length

from the inlet to the outlet. The relationship between the hydraulic gra-

dient and the flow through a porous media is typically described by the

general form of Darcy’s law (Eq. (6.238)). This model assumes laminar

flow through the media finer than coarse gravel. It is recommended

without modification of the general form as sufficient to estimate the

water level within a VSB system. Darcy’s law is a function of the flow,

ALR, water depth, and hydraulic conductivity.

Q ⫽ KA

S ⫽ KWD dh/dL (6.238)

or, for a defined length of the VSB,

dh ⫽ QL/KWD (6.239)

Substitute L ⫽ A /W and rearrange the above equation to solve for min-

imum W:

⫽ QA/KD dh (6.240)

where Q ⫽ flow rate, m

K ⫽ hydraulic conductivity, m

⭈ d, or m/d

⫽ cross-sectional area normal to wastewater flow (⫽ WD), m

W ⫽ width of VSB, m

D ⫽ water depth, m

L ⫽ length of VSB, m

dh ⫽ head loss (change in water level) due to flow resistance, m

S ⫽ dh/dL ⫽ hydraulic gradient, m/m

A ⫽ surface area of zone or of total wetland, m

The water level at the inlet of a VSB will rise to the elevation required

to overcome the head loss in the entire VSB system. It should be

designed to prevent surfacing. K for an operating VSB varies with time

and location within the media and will have a major impact on the head

loss. K is very difficult to determine because it is influenced by factors

Wastewater Engineering 877

that cannot be easily accounted for, including flow patterns (affected by

preferential flow and short-circuiting), and clogging (affected by changes

in root growth/death and solids accumulation/degradation). Therefore,

a value must be assumed for design purposes. Typical clean K values

vary for various sizes of rock and gravel. They are 6200, 21,000, 34,000,

64,000, 100,000, and 120,000 m/d for 5 mm pea gravel, 6 mm pea gravel,

5 to 10 mm gravel, 22 mm coarse gravel, 17 mm creek rock, and 19 mm

rock, respectively. Based on the studies and many observed cases of

surfacing in VSB systems, the following conservative values are rec-

ommend for the long-term operating K values (US EPA, 2000):

Initial 30% of VSB K

⫽ 1% of clean K

Final 70% of VSB K

⫽ 10% of clean K

Design consideration

Media. The media of a VSB system perform several functions: They

(1) are rooting material for vegetation, (2) help to evenly distribute/col-

lect flow at the inlet/outlet, (3) provide surface area for microbial growth,

and (4) filter and trap particles. For successful plant establishment, the

uppermost layer of media should be conducive to root growth. A variety

of media sizes and materials have been tried, but there is no clear evi-

dence that points to a single size or type of media, except that the media

should be large enough that it will not settle into the void spaces of the

underlying layer.

It is recommended (US EPA, 2000) that the planting media would be

5 to 20 mm (1/5 to 4/5 in) in diameter, and the minimum depth should

be 100 mm (4 in). The media in the inlet and outlet zones (Fig. 6.66)

should be between 40 and 80 mm (1.6 and 3.1 in) in diameter to mini-

mize clogging and should extend from the top to the bottom of the

system. All media must be washed clean of fines and debris; more

rounded media will generally have more void spaces; and media should

be resistant to crushing or breakage. The hydraulic conductivity of the

20 to 30 mm diameter clean media is assumed as 100,000 m/d.

Slopes. The top surface of the media should be leveled or nearly

leveled for easier planting and routine maintenance. Theoretically, the

bottom slope should match the slope of the water level to maintain a uni-

form water depth throughout the VSB. However, because the hydraulic

conductivity of the media varies with time and location, it is not prac-

tical to determine the bottom slope this way; the bottom slope should

be designed only for draining the system, and not to supplement the

hydraulic conductivity of the VSB. A practical approach is to uniformly

slope the bottom along the direction of flow from inlet to outlet to allow

for easy draining when maintenance is required. No research has been

878 Chapter 6

done to determine an optimum slope, but Chalk and Wheale (1989)

recommended a slope of to 1% is for ease of construction and proper

draining.

System size. The surface area required is calculated based upon

desired effluent quality and areal loading rate. The ALRs for BOD are

6 g/m

⭈ d (53.5 lb/acre ⭈ d) and 1.6 g/m

⭈ d (14.3 lb/acre ⭈ d) to attain 30

and 20 mg/L effluents, respectively. The ALR for TSS is 20 g/m

⭈ d

(178 lb/acre ⭈ d) to attain 30 mg/L effluent. VSB system is not designed

for nutrients (N and P) removal.

There is no optimum depth for a VSB system. But the media depth

should be set equal to the maximum root depth of the wetland species

to be used in the VSB. Typical average media depths in VSB systems

have ranged from 0.3 to 0.7 m (12 to 28 in), and various researchers have

recommended depths from 0.4 to 0.6 m (16 to 24 in). It is recommended

to use a design with maximum water depth (at the inlet of the VSB) of

0.50 m (20 in). The depth of the media will be defined by the level of the

wastewater at the inlet and should be about 0.1 m (4 in) higher than the

water.

The width of an individual VSB is set by the ability of the inlet and

outlet structures to uniformly distribute and collect the flow without

inducing short-circuiting. The width can be determined using Darcy’s

law (Eq. (6.238)). The recommended maximum width in a TVA design

manual is 61 m (200 ft). If the design produces a larger value, it should

divide the VSB into several cells that do not exceed 61 m in width—use

at least 2 VSBs in parallel; use an adjustable inlet device with capabil-

ity to balance flows; and use an adjustable outlet control device with

capability to flood and drain system.

Wastewater Engineering 879

Figure 6.66 Proposed zones in a VSB.

Several researchers have noted that most BOD and TSS are removed

in the first few meters of VSB, but some recommend minimum lengths

ranging from 12 to 30 m (39 to 98 ft) to prevent short-circuiting. The min-

imum length recommended by the US EPA (2000) is 15 m (50 ft).

Therefore, the aspect ratio is not a factor in the overall size design.

However, the recommended values for maximum width and minimum

length tend to result in individual VSB cells with a length-width ratio

between 1 : 1 and 1 : 2.

Example: Design a VSB constructed wetland system with some assumptions

or given conditions:

■

The total VSB has four zones as shown in Fig. 6.65.

■

The initial treatment zone 1 occupies about 30% of the total area, performs

most of the treatment, and has a big decrease in hydraulic conductivity (use

K ⫽ 1% of clean K).

■

The final treatment zone 2 will occupy the remaining 70% of the area and

has little change in hydraulic conductivity (use K ⫽ 10% of clean K).

■

Darcy’s law, while not exact, is good enough for design purposes.

■

The sizing of the initial and final treatment zones follows these steps:

■

Determine the surface area, using recommended ALR

■

Determine the width, using Darcy’s Law

■

Determine the length and head loss of the initial treatment zone, using

Darcy’s law

■

Determine the length and head loss of the final treatment zone, using

Darcy’s law

■

Determine bottom elevations, using bottom slope

■

Determine water elevations throughout the VSB, using head loss

■

Determine water depths, according for bottom slope and head loss

■

Determine required media depth

■

Determine the number of VSB cells

■

Maximum monthly flow Q ⫽ 380 m

/d ⫽ 0.1 MGD

■

Maximum monthly influent C

BOD ⫽ 80 mg/L ⫽ 80 g/m

■

Maximum monthly influent C

TSS ⫽ 90 mg/L ⫽ 90 g/m

■

Required discharge limits ⫽ 30 mg/L for both BOD and TSS

■

Recommended values for VSBs are:

■

ALR for BOD ⫽ 6 g/m

⭈ d

■

ALR for TSS ⫽ 20 g/m

⭈ d

■

Use washed, rounded media 20 to 30 mm in diameter, clean K ⫽ 100,000 m/d

■

Hydraulic conductivity of initial treatment zone 1: K

⫽ 1% of 100,000 m/d ⫽

1,000 m/d

880 Chapter 6

■

Hydraulic conductivity of final treatment zone 2: K

⫽10% of 100,000 m/d ⫽

10,000 m/d

■

Bottom slope: s ⫽ 0.5% ⫽ 0.005

■

Design water depth at inlet: D

⫽ 0.44 m

■

Design water depth at beginning of final treatment zone: D

⫽ 0.44 m

■

Design media depth: D

⫽ 0.6 m

■

Maximum allowable head loss through initial treatment zone dh

⫽ 10%

of D

⫽ 0.06 m

solution:

Step1. Determine the surface area for both BOD and TSS, using Eq. (6.234)

For BOD removal:

A ⫽ QC

/ALR ⫽ (380 m

/d ⫻ 84 g/m

)/6 g/m

⭈ d

⫽ 5320 m

For TSS removal:

A ⫽ (380 m

/d ⫻ 96 g/m

)/20 g/m

⭈ d

⫽ 1824 m

Use the large area required, i.e. 5320 m

. The surface area for the initial

treatment zone 1 is A

⫽ 5320 m

⫻ 0.3 ⫽ 1600 m

. The surface area for the

final treatment zone 2 is A

⫽ 5320 m

⫻ 0.7 ⫽ 3720 m

Step 2. Determine the minimum width needed to keep the flow below the

surface, using Eq. (6.240) and recommended values (K

⫽ 1000 m/d, D ⫽ 0.44

m, dh ⫽ 0.06 m) for the initial treatment zone 1

⫽ QA/KD dh (A ⫽ A

⫽ 1600 m

)

⫽ 380 m

/d ⫻1600 m

/(1000 m/d ⫻ 0.44 m ⫻ 0.06 m)

⫽ 23,030 m

W ⫽ 152 m

Note: This width of 152 m is needed to have a head loss of 0.06 m under all

given parameters.

Step 3. Compute the length L

and check the head loss of zone 1; K

⫽1,000 m/d

⫽ A

/W ⫽ 1600 m

/152 m ⫽ 10.5 m

Using Eq. (6.239)

⫽ QL

WD ⫽ 380 m

/d ⫻10.5 m/(1000 m/d ⫻ 152 m ⫻ 0.44 m)

⫽ 0.06 m

Wastewater Engineering 881

Step 4. Compute the length L

and check the head loss of zone 2; K

⫽

10,000 m/d

⫽ A

/W ⫽ 3720 m

/152 m ⫽ 24.5 m (is a minimum)

⫽ QL

/ K

WD ⫽ 380 m

/d ⫻ 24.5 m/(10,000 m/d ⫻ 152 m ⫻ 0.44 m)

⫽ 0.014 m

Step. 5. Calculate bottom elevations

Let bottom elevation at the outlet, E

⫽ 0 as reference point for all elevations.

s ⫽ 0.005. The elevation at the beginning of zone 2, E

, is:

⫽ L

⫻ s ⫽ 24.5 m ⫻ 0.005 ⫽ 0.12 m

The elevation at the inlet (the beginning of zone 1), E

, is:

⫽ (10.5 m ⫹ 24.5 m) ⫻ 0.005 ⫽ 0.18 m

Step 6. Determine the water surface elevations

The water surface elevation at the beginning of zone 2, E

, is:

⫽ E

⫹ D

⫽ 0.12 m ⫹ 0.44 m ⫽ 0.56 m

The water surface elevation at the outlet, E

, is:

⫽ E

⫺ dh

⫽ 0.56 m⫺0.01 m (use 0.01 instead 0.014 from Step 4)

⫽ 0.55 m

The water surface elevation at the inlet, E

, is:

⫽ E

⫹ dh

⫽ 0.56 m ⫹ 0.06 m ⫽ 0.62 m

Step 7. Compute water depth

The depth of water at the inlet, D

, is:

⫽ E

⫺ E

⫽ 0.62 m ⫺ 0.18 m ⫽ 0.44 m (as designed)

The depth of water at the beginning of zone 2, D

, is:

⫽ E

⫺ E

⫽ 0.56 m ⫺ 0.12 m ⫽ 0.44 m (as designed)

The depth of water at the outlet, D

, is:

⫽ E

⫺ E

⫽ 0.55 m ⫺ 0 m ⫽ 0.55 m

Step 8. Determine the media depth

The media depth can be designed based on two concepts: (a) level the media

surface and (b) a minimum depth to water throughout the VSB system.

882 Chapter 6

a. Determine the media depth based on level surface

The elevation of media top must be greater than the highest water ele-

vation, i.e. at the inlet, E

⫽ 0.62 m. Let us set the media top elevation

at 0.68 m.

Then, the depth of media at the inlet,

⫽ 0.68 m ⫺ E

⫽ 0.68 m ⫺ 0.18 m ⫽ 0.50 m

The depth of media at the beginning of zone 2,

⫽ 0.68 m ⫺ E

⫽ 0.68 m ⫺ 0.12 m ⫽ 0.56 m

The depth of media at the outlet,

⫽ 0.68 m ⫺ E

⫽ 0.68 m ⫺ 0 m ⫽ 0.68 m

The media depth-to-water at the inlet,

twi

⫽ 0.68 m ⫺ E

⫽ 0.68 m ⫺ 0.62 m ⫽ 0.06 m

The media depth-to-water at the beginning of zone 2,

twf

⫽ 0.68 m ⫺ E

⫽ 0.68 m ⫺ 0.56 m ⫽ 0.12 m

The media depth-to-water at the outlet,

two

⫽ 0.68 m ⫺ E

⫽ 0.68 m ⫺ 0.55 m ⫽ 0.13 m

Note: The media depth-to-water is small at the inlet (0.06 m). However, the

designer may want to add an additional layer of media in the first few meters

of the initial treatment zone 1 as an added precaution against surfacing,

even though the design ALR and K values are very conservative. The result-

ing D

two

in the final treatment zone 2 would be 0.12 to 0.13 m, which should

not inhibit the growth of aquatic species.

b. Determine the media depth based on a constant depth-to-water (use 0.1 m)

The elevation of media surface at the inlet,

⫽ E

⫹ 0.1 m ⫽ 0.62 m ⫹ 0.1 m ⫽ 0.72 m

The elevation of media surface at the beginning of zone 2,

⫽ E

⫹ 0.1 m ⫽ 0.56 m ⫹ 0.1 m ⫽ 0.66 m

The elevation of media surface at the outlet,

⫽ E

⫹ 0.1 m ⫽ 0.55 m ⫹ 0.1 m ⫽ 0.65 m

The depth of media at the inlet,

⫽ E

⫺ E

⫽ 0.72 m ⫺ 0.18 m ⫽ 0.54 m

Wastewater Engineering 883

The depth of media at the beginning of zone 2,

⫽ E

⫺ E

⫽ 0.66 m ⫺ 0.12 m ⫽ 0.54 m

The depth of media at the outlet,

⫽ E

⫺ E

⫽ 0.65m ⫺ 0 m ⫽ 0.65 m

Note: This approach would result in a drop in the media surface of (E

⫺ D

⫽

0.72 m ⫺ 0.54 m) 0.18 m over the 10.5-m length of the initial treatment zone

(slope ⫽ 1.7%), which would probably not impair operation and maintenance

activities.

Step 9. Determine the number of cells

It is recommended that at least two VSBs be used in parallel in all but the

smallest systems, so that one of the VSBs can be taken out of service for main-

tenance or repairs without causing serious water quality violations. In this

example, the total size of the treatment zones is 152 m wide and 35 (10.5 ⫹

24.5) m long. Therefore, four VSB trains, each 38 m wide and 35 m long, could

be used. Other combinations of length and width that have the required sur-

face area will also work as long as the hydraulics conditions are met. Also

remember that inlet (2 m in length) and outlet zones (1 m) will add to the over-

all length of the VSB. Thus the total length of a VSB system will also be 38 m.

In summary, to treat the 380 m

/d (0.1 MGD) of wastewater flow and to

meet the 30-30 standards, a VSB constructed wetland system that consists

four trains is designed. Each train is 38 m wide and 38 m long (2, 10.5, 24.5,

and 1 m in length, respectively, for the inlet zone, zone 1, zone 2, and outlet

zone). The depths and media sizes are close to the values recommended by

the US EPA (2000), as shown in Fig. 6.65.

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884 Chapter 6