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Variation of biomass and kinetic parameters for nitrifying species in the TNCU3 process at different aerobic hydraulic retention times


In this study, the variation of biomass, kinetic parameters, and stoichiometric parameters for ammonia-oxidizing bacteria (AOB) and nitrite-oxidizing bacteria (NOB) in TNCU3 process were explored at different aerobic hydraulic retention time (AHRT). The results indicated that the growth rate constants of AOB were 0.92, 0.88, and 0.95 days−1, respectively, meanwhile, those of NOB were 2.58 1.41, and 1.40 days−1, respectively, when AHRT was 5, 6, and 7 h. The lysis rate constants for AOB and NOB were 0.13 and 0.17 days−1, respectively. When AHRT was 5, 6, and 7 h, the yield coefficients of AOB were 0.20, 0.23, and 0.28 g COD g−1 N, respectively, meanwhile those of NOB were 0.23, 0.19, and 0.22 g COD g−1 N, respectively. The average percentage of AOB was 0.44, 0.61, and 0.64%, respectively, while that of NOB was 0.46, 0.61, and 0.74%, respectively. The relation between the biomass percentage of AOB and AHRT was in a good agreement with first type hyperbolic curve. The relation between the biomass percentage of NOB and AHRT was in a good agreement with seven types of curve including simple exponential curve, power exponential curve, and first type hyperbolic curve etc. When the AHRT increased from 5 to 7 h, the removal efficiency of NH4 +–N increased from 80.2 to 94.8%, or by 14.6%. Meanwhile, the removal efficiency of total nitrogen increased from 63.6 to 70.9%, or by 7.3%.

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Fig. 1
Fig. 2
Fig. 3


bAOB :

Lysis rate constant of ammonia-oxidizing bacteria (1/T)

bNOB :

Lysis rate constant of nitrite-oxidizing bacteria (1/T)


Oxygen uptake rate of ammonia-oxidizing bacteria (M/T L3)


Oxygen uptake rate of heterotrophic bacteria (M/T L3)


Oxygen uptake rate of nitrite-oxidizing bacteria (M/T L3)

\( {\text{S}}_{{{\text{NH}}_{ 4} }} \) :

Concentration of ammonia (M/L3)

\( {\text{S}}_{{{\text{NO}}_{ 2} }} \) :

Concentration of nitrite (M/L3)

\( {\text{S}}_{{{\text{O}}_{ 2} }} \) :

Concentration of oxygen (M/L3)


Concentration of ammonia-oxidizing bacteria (M/L3)


Concentration of nitrite-oxidizing bacteria (M/L3)


Yield coefficient of ammonia-oxidizing bacteria


Yield coefficient of ammonia-oxidizing bacteria

μAOB :

Growth rate constant of ammonia-oxidizing bacteria (1/T)

μNOB :

Growth rate constant of nitrite-oxidizing bacteria (1/T)


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The authors are grateful to the National Science Council of R.O.C. for financial support under the grant number NSC 95-2221-E-324-018.

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Correspondence to Tzu-Yi Pai.



Calculation of growth rate constant, lysis rate constant, yield, and biomass

The process kinetic and stoichiometry shown in Tables 3 and 4 represent the activated sludge behavior which was adopted from Taiwan Extension Activated Sludge model (TWEA; Pai et al. 2009a, b; Pai 2007).According to Tables 3 and 4, oxygen consumed by XAOB with neither substrate nor oxygen limitation is:

$$ {\frac{{{\text{dS}}_{{\text{O}}_{2}} }}{\text{dt}}} = {\text{OUR}}_{\text{AOB}} ({\text{t}}) = \left[ {\left( {{\frac{{3.43 - {\text{Y}}_{\text{AOB}} }}{{{\text{Y}}_{\text{AOB}} }}}} \right) \cdot \mu_{\text{AOB}} \cdot {\text{X}}_{\text{AOB}} ({\text{t}}_{0} )} \right] - {\text{b}}_{\text{AOB}} \cdot {\text{X}}_{\text{AOB}} ({\text{t}}_{0} ). $$

The growth for XAOB with neither substrate nor oxygen limitation can be written as follow:

$$ {\frac{{{\text{dX}}_{\text{AOB}} }}{\text{dt}}} = ({{\upmu}}_{\text{AOB}} - {\text{b}}_{\text{AOB}} ) \cdot {\text{X}}_{\text{AOB}} ({\text{t}}). $$

Integration of Eq. 2 leads to:

$$ {\text{X}}_{\text{AOB}} ( {\text{t}}_{ 0} )= {\text{X}}_{\text{AOB}} ( {\text{t}}_{ 0} )\cdot {\text{e}}^{{ ( {{\upmu}}_{\text{AOB}} - {\text{b}}_{\text{AOB}} )\cdot {\text{t}}}} $$

Equation 3 can be introduced into Eq. 1. Then the oxygen respiration is known at any time without limitations:

$$ {\text{OUR}}_{\text{AOB}} ({\text{t}}) = \left[ {\left( {{\frac{{3.43 - {\text{Y}}_{\text{AOB}} }}{{{\text{Y}}_{\text{AOB}} }}}} \right) \cdot {{\upmu}}_{\text{AOB}} - {\text{b}}_{\text{AOB}} } \right] \cdot {\text{X}}_{\text{AOB}} ({\text{t}}_{0} ) \cdot {\text{e}}^{{ ( {{\upmu}}_{\text{AOB}} - {\text{b}}_{\text{AOB}} ) \cdot {\text{t}}}} $$

The logarithmic configuration of Eq. 4 is:

$$ \ln \left[ {{\text{OUR}}_{\text{AOB}} ({\text{t}})} \right] = \ln \left[ {\left( {{\frac{{3.43 - {\text{Y}}_{\text{AOB}} }}{{{\text{Y}}_{\text{AOB}} }}}} \right) \cdot {{\upmu}}_{\text{AOB}} - {\text{b}}_{\text{AOB}} } \right] + \ln {\text{X}}_{\text{AOB}} ({\text{t}}_{0} ) + ({{\upmu}}_{\text{AOB}} - {\text{b}}_{\text{AOB}} ) \cdot {\text{t}} $$

When time is equal to 0, Eq. 5 becomes:

$$ \ln \left[ {{\text{OUR}}_{\text{AOB}} ( {\text{t}}_{ 0} )} \right] = \ln \left[ {\left( {{\frac{{3.43 - {\text{Y}}_{\text{AOB}} }}{{{\text{Y}}_{\text{AOB}} }}}} \right) \cdot {{\upmu}}_{\text{AOB}} - {\text{b}}_{\text{AOB}} } \right] + \ln {\text{X}}_{\text{AOB}} ( {\text{t}}_{ 0} ) $$

The term \( \ln \left[ {{\text{OUR}}_{\text{AOB}} ( {\text{t}}_{ 0} )} \right] \) in Eq. 6 represents the y-axis intercept of \( \ln \left[ {\text{OUR}} \right]_{\text{AOB}} \) vs. time curve. Then XAOB biomass at initial time in a closed batch chamber can be calculated as follows:

$$ {\text{X}}_{\text{AOB}} ( {\text{t}}_{ 0} )= {\frac{{{\text{e}}^{\text{y - intercept}} \times 24}}{{\left[ {\left( {{\frac{{3.43 - {\text{Y}}_{\text{AOB}} }}{{{\text{Y}}_{\text{AOB}} }}}} \right) \cdot {{\upmu}}_{\text{AOB}} - {\text{b}}_{\text{AOB}} } \right]}}} $$

Since the units of y-axis and x-axis are mg O2 l−1 h−1 and day in the graph of \( \ln \left[ {\text{OUR}} \right]_{\text{AOB}} \) vs. time, a converter of 24 is adopted in Eq. 7. When Eq. 4 is differentiated with respect to time t, the resulting equation is:

$$ {\frac{{{\text{dOUR}}_{\text{AOB}} ( {\text{t)}}}}{\text{dt}}} = ({{\upmu}}_{\text{AOB}} - {\text{b}}_{\text{AOB}} )\left[ {\left( {{\frac{{3.43 - {\text{Y}}_{\text{AOB}} }}{{{\text{Y}}_{\text{AOB}} }}}} \right) \cdot {{\upmu}}_{\text{AOB}} - {\text{b}}_{\text{AOB}} } \right] \cdot {\text{X}}_{\text{AOB}} ({\text{t}}_{ 0} ) \cdot {\text{e}}^{{ ( {{\upmu}}_{\text{AOB}} - {\text{b}}_{\text{AOB}} )\cdot {\text{t}}}} $$

The term of \( \left[ {\left( {{\frac{{3.43 - {\text{Y}}_{\text{AOB}} }}{{{\text{Y}}_{\text{AOB}} }}}} \right) \cdot {{\upmu}}_{\text{AOB}} - {\text{b}}_{\text{AOB}} } \right] \cdot {\text{X}}_{\text{AOB}} ( {\text{t}}_{ 0} ) \cdot {\text{e}}^{{ ( {{\upmu}}_{\text{AOB}} - {\text{b}}_{\text{AOB}} ) \cdot {\text{t}}}} \) equals \( {\text{OUR}}_{\text{AOB}} ( {\text{t)}} \) again, so Eq. 8 can be rearranged as:

$$ {\frac{{{\text{dOUR}}_{\text{AOB}} ( {\text{t)}}}}{\text{dt}}} = ({{\upmu}}_{\text{AOB}} - {\text{b}}_{\text{AOB}} ) \cdot {\text{OUR}}_{\text{AOB}} ( {\text{t)}} $$

Rearranging Eq. 9, the following expression can be obtained:

$$ {\frac{ 1}{{{\text{OUR}}_{\text{AOB}} ( {\text{t)}}}}}{\frac{{{\text{dOUR}}_{\text{AOB}} ( {\text{t)}}}}{\text{dt}}} = ({{\upmu}}_{\text{AOB}} - {\text{b}}_{\text{AOB}} ) $$

Integrating Eq. 10, the resulting equation is:

$$ \ln [{\text{OUR}}_{\text{AOB}} ( {\text{t)]}} = ({{\upmu}}_{\text{AOB}} - {\text{b}}_{\text{AOB}} ) \cdot {\text{t}} + {\text{C}} $$

When time equals 0, Eq. 11 becomes:

$$ \ln [{\text{OUR}}_{\text{AOB}} ( {\text{t}}_{ 0} )] = {\text{C}} $$

Substituting Eq. 12 into Eq. 11, the resulting equation is:

$$ \ln [{\text{OUR}}_{\text{AOB}} ( {\text{t}})] = ({{\upmu}}_{\text{AOB}} - {\text{b}}_{\text{AOB}} ) \cdot {\text{t}} + \ln [{\text{OUR}}_{\text{AOB}} ( {\text{t}}_{ 0} )] $$

This equation represents a straight line with (μAOB − bAOB) as slope in a diagram of natural logarithm of OUR vs. time. If bAOB value can be determined, μAOB can be approximately calculated:

$$ {{\upmu}}_{\text{AOB}} = {\text{slope}} + {\text{b}}_{\text{AOB}} $$

The bAOB value was determined by the following steps. First, a fixed amount of sludge was placed into a non-fed aerated batch reactor for 10 days. Second, a certain amount of sludge was taken from the above batch reactor each time and transferred into the OUR chamber to measure the OURAOB. By plotting the OURAOB vs. time, the lysis rate constant, bAOB could be estimated by exponential curve fitting. The XNOB biomass can be calculated according to analogous derivation and expressed as:

$$ {\text{X}}_{\text{NOB}} ( {\text{t}}_{ 0} )= {\frac{{{\text{e}}^{\text{y - intercept}} \times 2 4}}{{\left[ {\left( {{\frac{{1.14 - {\text{Y}}_{\text{NOB}} }}{{{\text{Y}}_{\text{NOB}} }}}} \right) \cdot {{\upmu}}_{\text{NOB}} - {\text{b}}_{\text{NOB}} } \right]}}} $$

According to our previous work (Tsai et al. 2006), the yield coefficient for XAOB can be determined using respirometer and calculated by the following equation:

$$ {\text{Y}}_{\text{AOB}} = 3.43 - {\frac{{\int {\text{OUR(t)dt}} }}{{\left( {{\text{S}}_{{{\text{NH}}_{{4,{\text{i}}}} }} - {\text{S}}_{{{\text{NH}}_{{4,{\text{f}}}} }} } \right)}}} $$

The yield coefficients for XNOB are calculated according to

$$ {\text{Y}}_{\text{NOB}} = 1.14 - {\frac{{\int {\text{OUR(t)dt}} }}{{\left( {{\text{S}}_{{{\text{NO}}_{{ 2 , {\text{i}}}} }} - {\text{S}}_{{{\text{NO}}_{{ 2 , {\text{f}}}} }} } \right)}}} $$
Table 3 Stoichiometric matrix (Pai 2007; Pai et al. 2009b)
Table 4 Process rate equations (Pai 2007; Pai et al. 2009b)

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Pai, T., Chiou, R., Tzeng, C. et al. Variation of biomass and kinetic parameters for nitrifying species in the TNCU3 process at different aerobic hydraulic retention times. World J Microbiol Biotechnol 26, 589–597 (2010).

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  • Ammonia-oxidizing bacteria (AOB)
  • Growth rate constant
  • Hydraulic retention time (HRT)
  • Lysis rate constant
  • Nitrite-oxidizing bacteria (NOB)
  • Yield coefficient