Lin S.D. Water and Wastewater Calculations Manual

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Wastewater Engineering 775

The overall synthesis and oxidation reaction is

⫹ 1.83O

⫹ 1.98HC : 0.021C

⫹ 1.041H

⫹ 0.98N ⫹ 1.88H

(6.184)

Nitrifying bioﬁlm properties. Although the principal genera Nitrosomonas

and Nitrobacter are responsible for biological nitrification, het-

erotrophic nitrification can also occur when nitrite and/or nitrate are

produced from organic or inorganic compounds by heterotrophic organ-

isms (⬎100 species, including fungi). However, the amount of oxida-

tion nitrogen formed by heterotrophic organisms is relatively small

(Painter, 1970).

The growth rate for nitrifying bacteria is much less than of het-

erotrophic bacteria. Nitrifying bacteria have a longer generation time

of at least 10 to 30 h (Painter, 1970, 1975). They are also much more

sensitive to environmental conditions as well as to growth inhibitors.

The growth rate for nitrite oxidizers is much greater than that for the

ammonia oxidizers.

According to Painter (1970), experimental yield values of Nitrosomonas

lay between 0.04 and 0.13 lb volatile suspended solids (VSS) grown per

pound of ammonia nitrogen oxidized; and for Nitrobacter the yield ranged

from 0.02 to 0.07 lb VSS per pound of nitrite nitrogen oxidized. Yield

values based on thermodynamic theory are 0.29 and 0.084, respectively

for Nitrosomonas and Nitrobacter (Haug and McCarty, 1972). The lower

value of the experimental yield is due to the diversion of a portion of the

free energy released by oxidation to microorganism maintenance func-

tions. Based on Eqs. (6.182) and (6.183), the yield for Nitrosomonas and

Nitrobacter should be 0.15 mg cells/mg -N and 0.02 mg cells/mg

-N, respectively.

Kinetics of nitriﬁcation. The kinetics of biological nitrification, using

mathematical expressions for the oxidation of ammonia and nitrite,

have been proposed by many investigators. A variety of environmental

factors, such as ammonia concentration, pH, temperature, and dis-

solved oxygen level, affect the kinetics. For the combined carbon

oxidation–nitrification processes, BOD to TKN ratio is also an important

factor. The reaction is enhanced with higher pH, higher temperature,

and higher DO concentration.

Effect of ammonia concentration on kinetics. Numerous investigators have

developed growth kinetics and substrate utilization equations for nitri-

fiers. However, the most popular method is the Monod model (1949) of

776 Chapter 6

population dynamics. The growth rate of nitrifiers is a function of

ammonia concentration dynamics, as follows:

(6.185)

where ⫽ growth rate of nitrifier, per day

⫽ maximum specific growth rate of nitrifier, per day

X ⫽ concentration of bacteria

S ⫽ concentration of substrate (NH

-N), mg/L

t ⫽ time, days

⫽ half velocity constant, i.e. substrate concentration (mg/L)

at half of the maximum growth rate

Equation (6.185) assumes no mass transfer or oxygen transfer

limitations.

Values of K

for Nitrosomonas and Nitrobacter are generally equal to

or less than 1 mg/L (0.18 to 1.0 mg/L mostly) at liquid temperatures of

20⬚C or less (Haug and McCarty, 1972). The Monod expression for bio-

logical nitrification provides for a continuous transition between first-

and zero-order kinetics based on substrate concentration. Since K

values

for nitrification are much less than ammonia concentrations found in

wastewater, many investigators (Huang and Hopson, 1974, Wild et al.,

1971; Kiff, 1972) found that the growth kinetic model reduces to a zero-

order expression

(6.186)

Equation (6.186) indicates that the nitrification rate is independent of

the initial substrate concentration and the mixing regime. This suggests

that nitrifiers are reproducing at or near their maximum growth rate.

As substrate is removed, and as S approaches the value of K

or less,

further substrate removal will begin to approximate a first-order

reaction.

Estimates of the maximum growth rates ( ) of Nitrosomonas and

Nitrobacter under various environmental conditions, found by other

investigators, are summarized elsewhere (US EPA, 1975c; Brenner

et al., 1984). Both and K

are found to increase with increasing tem-

perature. All nitrification studies were conducted with activated-sludge

processes or river waters. Maximum growth rates might be expected to

approximate those of suspended growth process in which ammonia mass

transfer and DO are not limiting.

m 5

5 m

1 S

Wastewater Engineering 777

The ranges and typical values of kinetic coefficients for suspended

growth nitrification processes using pure cultures are summarized in

Table 6.23. In practice, the values of those coefficients for nitrifiers in

activated-sludge processes will be considerably less than the values

listed in the table.

The reported data indicate that the maximum growth rate of

Nitrobacter is considerably greater than that of Nitrosomonas.

Therefore the oxidation of ammonia to nitrite is the rate-limiting reac-

tion in nitrification. For this reason, nitrite does not accumulate in

large amounts in mature nitrification systems for municipal waste-

waters.

Oxidation rate. The ammonia oxidation rate is related to the Nitrosomonas

growth rate. Its maximum oxidation rate can be expressed as

(6.187)

where r

⫽ ammonia oxidation rate, lb -N oxidized/(lb VSS ⭈ d)

⫽ Nitrosomonas growth rate, day

⫺1

⫽ organism yield coefficient, lb Nitrosomonas

grown(VSS)/lb -N removed

⫽ /Y

⫽ peak ammonia oxidation rate,

lb -oxidized/(lb VSS ⭈ d)

⫽ peak Nitrosomonas growth rate, day

⫺1

N ⫽ -N concentration, mg/L

⫽ half saturation constant, mg/L -N, mg/L

5 r

1 N

TABLE 6.23 Values of Kinetic Coefﬁcients for the Suspended Growth Nitriﬁcation

Process (Pure Culture Values)

Value (20°C)

Kinetic coefficient Unit Range Typical

Nitrosomonas

per day 0.3–2.0 0.7

-N, mg/L 0.2–2.0 0.6

Nitrobacter

per day 0.4–3.0 1.0

-N, mg/L 0.2–5.0 1.4

Overall

per day 0.3–3.0 1.0

-N, mg/L 0.2–5.0 1.4

Y mg VSS/mg -N 0.1–0.3 0.2

per day 0.03–0.06 0.05

SOURCES: US EPA, 1975b and 1975c; Schroeder, 1977

Loading rate. Referring to Eqs. (6.185) and (6.187), the growth rate of

nitrifier is proportional to substrate (NH

-N) concentration. The ammo-

nia loading rates applied to the biological nitrification unit (aeration

tank) are 160 to 320 g/(m

⭈ d) (10 to 20 lb/(1000 ft

⭈ d)) with corre-

sponding wastewater temperature of 10 to 20⬚C, respectively. The aer-

ation periods are 4 to 6 h for an average wastewater secondary effluent

(Hammer, 1986).

BOD concentration. The combined process oxidizes a high proportion of

the influent organics (SBOD

) relative to the NH

-N concentration,

while less nitrifiers are present in the biofilm. Separate nitrification

processes have relatively low SBOD

values, relative to the NH

-N con-

tent, when a high level of SBOD

removal is provided prior to the nitri-

fication stages. High populations of nitrifiers occur in the separate-stage

nitrification process.

In combined carbon oxidation–nitrification processes the ratio of BOD

to TKN is greater than 5, whereas in separate processes the BOD to TKN

ratio in the second stage is greater than 1 and less than 3. Reducing the

ratio to 3 does not require a high degree of treatment in the first stage

(US EPA, 1975b; McGhee, 1991).

Biological nitrification is sensitive to organic loading, depending on

the carbon removal sections, because of the nitrifiers having a much

slower growth rate. Nitrification will take place when organic content

is reduced to a certain level. There are discrepancies about what is the

critical concentration for organic matter. The values cited in the litera-

ture are as follows: TBOD

approaching 30 mg/L (Antonie, 1978; Khan

and Raman, 1980); TBOD

reaching 20 mg/L (Banerji, 1980); SBOD

less

than 20 mg/L (Autotrol Corp, 1979); SBOD

reduced to 15 mg/L; SBOD

around 10 mg/L (Miller et al., 1980).

Temperature. The optimum range for nitrification is 30 to 36⬚C (Haug

and McCarty, 1972; Ford et al., 1980). Nitrifiers have been found not to

grow at temperatures below 4⬚C or above 45⬚C (Ford et al., 1980).

In a suspended-growth activated-sludge system, Downing and Hopwood

(1964) found that the maximum growth and the half-velocity constant

for both Nitrosomonas and Nitrobacter were markedly influenced by

temperature. The relationships developed for Nitrosomonas are as follows:

per day (6.188)

and

⫽ 10

0.051T–1.158

, mg/L as N (6.189)

where T is the wastewater temperature, ⬚C.

5 0.47e

0.098sT215d

778 Chapter 6

For attached-growth systems, different temperature effects have been

reported. Attached-growth systems have an advantage in withstanding

low temperature (⬍15⬚C) without as severe a loss of nitrification rates

as suspended-growth systems.

The following equation describes temperature effects on nitrification

rate at a temperature T, ⬚C

(6.190)

where T is wastewater temperature, ⬚C and u is a temperature correc-

tion coefficient. From laboratory and pilot RBC studies, the value of u

is found to be 1.10 (Mueller et al., 1980).

Dissolved oxygen. When dissolved oxygen concentration is a limiting

factor, the growth rate of nitrifiers can be expressed as following the

Monod-type relationships as follows:

(6.191)

where is the half-saturation constant for oxygen in mg/L. Values of

have been reported to vary from 0.15 mg/L at 15⬚C to 2.0 mg/L at

20⬚C (US EPA, 1975b).

Alkalinity and pH. From stoichiometry (Eq. (6.181)), 7.14 mg/L of alka-

linity as CaCO

will be destroyed for every one mg/L of NH

-N oxi-

dized. However, Sherrard (1976) claimed this value to be in error and

suggested that it should be less for biological nitrification, because

ammonia is incorporated into the biomass resulting in a lesser quan-

tity of NH

-N available for oxidation to nitrate. The alkalinity destruc-

tion in a nitrifying activated sludge process is a function of solids

retention time and influent wastewater BOD

:N:P ratio. Alleman and

Irving (1980) observed a considerably low value (2.73 mg/L of alkalinity

as CaCO

per mg/L of NH

-N oxidized) for nitrification in a sequential

batch reactor.

With the RBC system at Cadillac, Michigan, alkalinity declined 8.1

mg/L for each mg/L of NH

-N oxidized (Singhal, 1980; Chou et al., 1980).

At Princeton, Illinois, the alkalinity reduction ratios were respectively

6.8 and 9.1 for stages 3 and 4 in a combined BOD

-nitrification 5-stage

RBC system (Lin et al., 1982). Therefore it is important to have suffi-

cient alkalinity buffering capacity for nitrifiers to maintain the accept-

able pH range.

Reported data show a wide range of optimum pH of 7.0 to 9.5 with

maximum activity at approximately pH 8.5 (Painter, 1970, 1975; Haug

5 m

1 DO

5 m

T220

Wastewater Engineering 779

and McCarty, 1972; Antonie, 1978). Below pH 7.0, adverse effects on

ammonia oxidation become pronounced.

Full-scale kinetic studies conducted at the Autotrol Corporation (1979)

showed that the nitrification rate declined from 0.31 lb NH

-N/(d ⭈ 1000 ft

)

(1.52 g NH

-N/(m

⭈ d)) at pH 7.0 to 0.17 lb/(d ⭈ 1000 ft

) (0.83 g/(m

⭈ d))

at pH 6.5.

Downing and Hopwood (1964) proposed the following relationship for

the growth rate for nitrifiers and pH values up to 7.2 in a combined

carbon oxidation and nitrification system.

[1 – 0.833(6.2 – pH)] (6.192)

It is assumed that the growth rate is constant for pH levels between 7.2

and 8.0. Eq. (6.192), when applied to separate-stage nitrification systems,

is probably conservative.

Combined kinetics expression. As previously presented, the major factors

which affect the nitrification rate are ammonia nitrogen concentration,

temperature, DO, and pH. In the absence of toxic or inhibitory sub-

stance in the wastewater, US EPA (1975b) applied Chen’s model (1970)

which combined Monod’s expression for ammonia-N concentration

(Eq. (6.185)), DO (Eq. (6.191)), and pH (Eq. (6.192)) effects on nitrifier

growth as follows:

(6.193a)

Substituting the effects of temperature (Eq. (6.188)), Eq. (6.189) for K

1.3 mg/L for , the following equation is valid for Nitrosomonas for pH

⬍ 7.2 and wastewater temperature between 8 and 30⬚C

(6.193b)

[1 – 0.833(6.2 – pH)]

The terms in the first bracket represent the effect of temperature. The

second bracket terms are the Monod expression for the effect of NH

N concentration. The terms in the third bracket take into account

the effect of DO. The terms in the last bracket account for the effect

of pH: it will be unity for pH ⱖ 7.2. From Eq. (6.193) it can be seen

that if any one factor becomes limiting, even if all the others are non-

limiting, the nitrification rate will be much lower, perhaps even

approaching zero.

5 0.47

[

0.098sT215d

]

s0.051T21.158d

1 N

1.3 1 DO

5 m

1 N

1 DO

b[1 2 0.833s6.2 2 pHd]

5 m

780 Chapter 6

Example: Design an activated-sludge process for carbon oxidation–nitrification

using the following given data. Determine the volume of the aeration tank,

daily oxygen requirement, and the mass of organisms removed daily from the

system.

Design average flow 3785 m

/d (1 Mgal/d)

BOD of influent (primary effluent) 160 mg/L

TKN of influent (primary effluent) 30 mg/L

-N of influent (primary effluent) 15 mg/L

Minimum DO in aeration tank 2.0 mg/L

Temperature (minimum) 16⬚C

Maximum growth rate, 1.0 per day

Minimum pH 7.2

Assume a safety factor, SF 2.5

(required due to transient loading conditions)

MLSS 2500 mg/L

Maximum effluent SS or BOD 15 mg/L

Total alkalinity, as CaCO

190 mg/L

solution:

Step 1. Compute the maximum growth rate of nitrifiers under the stated

operating conditions

T ⫽ 16⬚C

DO ⫽ 2 mg/L

pH ⱖ 7.2

Additional required data for Eqs. (6.193a) and (6.193b)

⫽ 0.47 d

⫺1

⫽ 1.3 mg/L

⫽ 10

0.051T–1.158

⫽ 10

0.051⫻16–1.158

⫽ 0.455 mg/L as N

N ⫽ 15 mg/L as N

Temperature correction factor ⫽ e

0.098(16–15)

⫽ 1.10

pH correction factor ⫽ 1 for pH ⱖ 7.2

Eqs. (6.193a) and (6.193b)

5 0.30 d

5 s0.47 d

ds1.1ds0.97ds0.61ds1d

5 0.47d

[

0.098sT215d

]

0.455 1 15

1.3 1 2

bs1d

5 m

1 N

1 DO

b[1 2 0.833s6.2 2 pHd]

Wastewater Engineering 781

Step 2. Compute the maximum ammonia oxidation rate under the envi-

ronmental conditions of temperature, pH, and DO

Using Eq. (6.187)

Referring to Table 6.23

⫽ 0.2 mg VSS/mg -N

Step 3. Compute the minimum cell residence time

Using Eq. (6.76)

Note: Another rough estimate of u

(solids retention time) can be determined by

Step 4. Compute the design cell residence time

Step 5. Compute the design specific substrate utilization rate U for ammo-

nia oxidation

Using Eq. (6.84)

5 YU 2 k

5 10 days

Design u

c2d

5 SF 3 min. u

c2min

5 2.5 3 4 days

5 1/m

5 1/0.30 d

5 3.33 days

5 4 days

Minimum u

c2min

5 1/0.25 d

5 0.25 d

1/u

5 0.2s1.5 d

d 2 0.05 d

5 0.05 sfrom Table 6.23d

kr 5 r

5 1.5 d

sfrom Step 2d

Y 5 Y

5 0.2 sfrom Table 6.23d

1/u

< Ykr 2 k

5 1.5 d

Max. r

5 s0.30 d

d/0.2

782 Chapter 6

Applying

Note: U ⫽ r

for Eq. (6.187).

Step 6. Compute the steady state ammonia concentration of the effluent, N

Using Eq. (6.187)

where U ⫽ 0.75 d

–1

(Step 5)

⫽ 0.455 mg/L for -N (Step 1)

⫽ 1.50 d

–1

⫽ maximum growth rate (Step 2)

Step 7. Compute organic (BOD) removal rate U

The design cell residence time applies to both the nitrifiers and hetero-

trophic bacteria.

Referring to Table 6.12, for heterotrophic kinetics

Y ⫽ 0.6 kg VSS/kg BOD

⫽ 0.06 day

–1

Then

U 5 0.27 kg BOD

removed/skg MLVSS

10 d

5 0.6U 2 s0.06 day

c2d

5 10 days

c2d

5 YU 2 k

c2d

N 5 0.455 mg/L

0.75 d

s1.50 d

s0.455 mg/Ld 1 N

5 r

1 N

5 0.75 d

0.2

10 days

1 0.05 d

c2d

as u

U 5

1 k

Wastewater Engineering 783

assuming there is 90% BOD

removal efficiency.

The food to microorganism ratio is

F/M ⫽ 0.27/0.9

⫽ 0.30 kg BOD

applied/(kg MLVSS ⭈ d)

Step 8. Compute the hydraulic retention time u required for organic and

ammonia oxidations

Using Eq. (6.83)

(a) For organic oxidation

⫽ 160 mg/L (given)

S ⫽ 15 mg/L (regulated)

U ⫽ 0.27 day

–1

(Step 7)

X ⫽ MLVSS ⫽ 0.8 MLSS ⫽ 0.8 ⫻ 2500 mg/L

⫽ 2000 mg/L

Therefore

⫽ 0.269 day

⫽ 6.4 h

(b) For nitrification

⫽ TKN ⫽ 30 mg/L (given)

N ⫽ 0.45 mg/L (Step 6)

U ⫽ 0.75 d

–1

(Step 5)

X ⫽ 2000 mg/L ⫻ 0.08 (assuming 8% of VSS is nitrifiers)

⫽ 160 mg/L

⫽ 0.246 days

⫽ 5.9 h

Note: Organic oxidation controls HRT; u ⫽ 6.4 h

u 5

s30 2 0.45d mg/L

s0.75 d

ds160 mg/Ld

u 5

s160 2 15d mg/L

s0.27 day

ds2000 mg/Ld

U 5

2 S

oru 5

2 S

784 Chapter 6