Wastewater Characterization for Evaluation of Biological Phosphorus Removal

Biological Kinetic Parameter Estimation - Required Kinetic Parameters

The important kinetic parameters required for biological phosphorus removal process design include the following.

Y	The cell yield coefficient defined as the mass of activated sludge or biomass produced per unit of substrate removed (mg VSS/mg COD).
kd	The endogenous decay rate or mass of cells lost during endogenous respiration per unit of time (1/day).
max	The maximum specific growth rate. The specific growth rate, , is the rate of growth per unit of time (1/day).
Ks	The half-saturation constant or shape factor of the Monod equation. Ks equals the substrate concentration (mg/L) at which equals 1/2 of max.
qN	The specific nitrification rate, which is measured by rate of NO2-+NO3- formation (mg NO2- + NO3--N/mg VSS/hour).
qD	The specific denitrification rate, which is measured by rate of NO2-+NO3- removed (mg NO2- + NO3-N/mg VSS/hour).

The theories and experimental procedures for determining the biological kinetic parameters defined above are discussed in this section. Also discussed are the measurement methods of phosphorus release and uptake rates. Although phosphorus release and uptake rates are not used in the design equations, the rates can provide insight into the design of BPR systems. Therefore, their measurement techniques are presented here.

Theoretical Base of the Kinetic Equations

The cell yield coefficient, Y, is one of the most important parameters used in biological kinetic models. It represents the mass of biomass produced per substrate removed. The endogenous decay rate, k_d, represents the rate of biomass loss due to endogenous respiration. The cell yield coefficient, Y, and endogenous decay rate, k_d, are critical for the prediction of waste-activated sludge production. In a BPR process, phosphorus is removed in the form of waste activated sludge.

The stoichiometry between the organic substrate consumed and microorganisms produced can be expressed as:

(3)

Where

This equation can be rewritten after dividing Equation 3 by X:

(4)

It can then be rewritten on a finite time and mass basis:

(5)

Where

	=	amount of specific cell mass produced over unit time, (1/day); and
	=	specific substrate utilization rate, U (1/day).

The growth rate of microbial mass () is expressed as the specific growth rate, (i.e., the rate of growth per average unit of biomass during the time interval).

Thus,

(6)

Y and k_d Determination by Batch Test

It is difficult and time consuming to obtain Y and k_d by a conventional method that calls for operating at least four bench-scale, continuous-flow, biological reactors at different sludge ages. These parameters mainly affect activated sludge production and have relatively little effect on predicted effluent quality. However, phosphorus removal in a BPR process occurs through activated sludge wasting; therefore, Y and k_d are important for BPR design.

It is easy to determine Y and k_d by running a batch test, which is similar to the procedure used for T_bOD determination. Therefore, from the same batch test, T_bOD, Y, and k_d can be determined simultaneously. Since there is little difference in Y and k_d values (VSS basis) for conventional and phosphorus-removing treatment plants (McClintock et al. 1992), it may not be necessary to acclimate biomass for phosphorus removal in Y and k_d determination.

Data Analysis:

Some experimental runs may suffer from variability in VSS analyses used to measure biomass growth. If the samples are not carefully taken, the variability in the VSS measurements at each time may be even greater than the net growth of microorganisms, making the kinetic study inaccurate. Thus, the reactor contents must be mixed vigorously to disperse the mixture uniformly before taking samples. Triplicate VSS and duplicate COD samples should be analyzed. It may be desirable to increase the F/M above typical values. In this way, a more noticeable biomass growth may be attained. Idealized cell growth and substrate removal curves are shown in Figure 5. In experimental runs with municipal wastewater, the net growth of microorganisms begins to decrease after several hours and becomes negative after the substrate is consumed. The experimental data are plotted and a smooth "best fit" curve is drawn through the points to average out some of the variability in the test data. These curves can either be drawn by hand or using a computer program to generate a best fit line through the data.

Figure 5. Generalized substrate consumption and biomass growth with time.

Values of S and X are chosen from the initial portion of the curve where the biomass is in the logarithmic growth phase. These data are transformed into estimates of U, the substrate utilization rate, and , the specific growth rate, for each time period (t from i - 1 to i) using the following equations:

	(7)
	(8)

Based on Equation 6, and U can be plotted and a regression line can be drawn as shown in Figure 6. The endogenous decay rate, k_d, is the Y-intercept. Since k_d is extremely sensitive to the variability of the data points, it may be difficult to determine a reasonable value for k_d using this method. However, k_d can be obtained independently from a respirometer experiment that will be described in the section on "k_d Determination by Electrolytic Respirometer." Forcing a regression line to fit through the independently determined k_d makes the resulting slope a more reliable estimate of Y.

Figure 6. Plot of specific growth rate (u) with specific substrate utilization rate (U)

An example illustration of Y and k_d determination from an vs. U plot is provided in Figure 7. The values of Y and k_d are determined to be 0.65 mg VSS/mg COD and 0.0026 ¹/hour (or 0.07 ¹/day), respectively.

Personhours needed: 24 hours + acclimation time (0-30 hours depending on wastewater).

Figure 7. Y and Kd determination from vs. U plot.

_max and k_s Determination by Electrolyic Respirometer

The electrolytic respirometer is a very useful tool for determining the biokinetic growth constants, _max and K_s, used in the Monod equation for non-inhibitory wastewater:

(9)

Where

max =	maximum specific growth rate (1/hour); and
Ks =	half-saturation constant or substrate concentration when = max /2 (mg/L).

If the wastewater shows inhibition, the Haldane equation should be used. Once the relationship between and S is quantified, _max and K_s in the Monod model can be determined graphically or statistically.

Apparatus:

A typical electrolytic respirometer is shown in Figure 8.

Figure 8: Electrolytic respirometer.

Procedure:

The procedures to run an electrolytic respirometer may vary slightly, depending on the manufacturer. Basically, the wastewater concentration is diluted by addition of washed activated sludge and added to each reactor cell. Each cell is prepared at a different F/M ratio, and contains a different initial mixed wastewater concentration (S_o). The activated sludge should be washed using the following procedure to remove any soluble and adsorbed substrate:

1. Settle the mixed liquor suspended solids.
2. Decant the supernatant.
3. Fill remaining volume with BOD₅ nutrient dilution water containing phosphate buffer, MgSO₄, CaCl₂, and FeCl₃ solution (17 mg of KH₂ PO₄, 43.5 mg of K₂HPO₄, 66.8 mg of NaHPO₄.7H₂O, 3.4 mg of NH₄Cl, 45 mg of MgSO₄, 55 mg of CaCl₂, and 0.5 mg of FeCl₃.6H₂O in 2 L of distilled water).
4. Mix gently and settle activated sludge.
5. Repeat step 2 through step 4 three times.

The oxygen uptake rate is automatically recorded by a computer data acquisition system. The initial mixed wastewater COD concentration (S_o) is used to calibrate the Monod equation. The initial mixed liquor VSS concentration (X_o) and the initial mixed wastewater COD concentration in each reactor cell must be analyzed. If an electrolytic respirometer is not available, a series of batch tests (see "Determination of the COD Fractions") for T_bOD determination may be conducted under several different F/M ratios.

Data Analysis:

The electrolytic respirometer's data acquisition system records the accumulated oxygen consumption vs. time, which then can be translated into biomass growth data. A typical plot of O₂ accumulation over time is shown in Figure 9.

Figure 9. Typical O2 accumulated overtime.

Oxygen uptake data can be converted into biomass growth curves using the following equation (Rozich and Gaudy 1992):

(10)

Where

This equation allows the indirect estimation of biomass concentrations over time.

To convert O₂ uptake data to biomass data using Equation 10, values for Y and f_cv must be determined. Y can be determined from the kinetic tests described in the section on "Y and k_d Determination by Batch Test." The values of f_cv can be assumed to be 1.42 - 1.48 mg COD/mg VSS. It should be noted that Y and f_cv in Equation 10 are assumed to be constant over time under declining substrate concentration conditions. The growth rate is obtained from the following equation:

(11)

Thus, when plotting the calculated X with time on a semi-logarithmic paper, the specific growth rate () is the slope of the line. The typical plot of lnX vs. time is shown in Figure 9. The slopes in Figure 9 represent values at different substrate concentrations. Table 10 lists the results of specific growth rate () obtained from Figure 9 corresponded with the total substrate concentrations (S), which are predetermined from wastewater in each cell of the electrolytic respirometer. If a lag, stationary, or declining phase is shown in the ln X vs. time plot, the points in these phases should be excluded in the regression analysis. Because of this, only data points up to 10 hours from Figure 9, were used to determine values in Figure 10.

Figure 10. Typical ln X vs. time plot.

Table 10. Results of and S determination.

Cell #	Cell 1	Cell 2	Cell 3	Cell 4	Cell 5
S (mg/L COD)	81	162	244	366	460
(1/hour)	0.0083	0.0151	0.0191	0.0216	0.0230

Assuming a wastewater is not inhibitory, the growth rate data ( vs. S) are fitted to the Monod equation (Equation 9) to determine the values of the biokinetic constants m_max and K_s. An example illustration of a vs. S plot used to determine _max and K_s is provided in Figure 11. Use of statistical computer software is highly recommended for parameter estimation. The curve was obtained from a nonlinear least squares method. The _max and K_s values were 0.034 ¹/hour and 209 mg/L, respectively, with the correlation coefficient of 0.99.

Personhours needed: 6 hours.

Figure 11. vs. S plot to determine max and Ks.

k_d Determination by Respirometer

Theory:
The oxygen consumption rate can be corrected for activated sludge concentration as follows:

(12)

The endogenous decay rate, k_d, is defined as the rate of cell mass decrease per unit of mass:

which can be transformed into

(13)

Where

Substituting Equation 13 into Equation 12 yields

(14)

Taking the natural logarithm, Equation 14 becomes

(15)

In Equation 15, k_d is the slope of the ln (dO/dt) vs. time plot. The dO/dt (rate of oxygen consumption) data can be generated by an electrolytic respirometer.

Apparatus:

Electrolytic respirometer

Procedure

The experimental method to determine k_d by electrolytic respirometer is straight forward. An activated sludge sample is aerated for one day and washed three times with BOD5 nutrient solution to remove any adsorbed and soluble substrate. Oxygen consumption is measured with washed activated sludge in an electrolytic respirometer, and the rate of oxygen consumption (dO/dt) is obtained.

Data Analysis:

Figure 12 shows an example of the results of a k_d determination using an electrolytic respirometer. The results indicated there was still residual substrate left in the first 12 hours. The slope of ln (dO/dt) vs. time plot after 12 hours will indicate the endogenous decay constant, k_d. If the activated sludge is washed well after one day aeration without feed, the sharp oxygen uptake rate at the initial phase will be minimized as shown in another run (Figure 13).

Personhours needed: 6 hours.

Figure 12. Endogenous decay rate, kd, determination without well washed activated sludge.

Figure 13. Endogenous decay rate, kd, determination with well washed activated sludge.

Nitrification and Denitrification Rates Measurement

Nitrification Rate - Theory:

Although the kinetics of nitrification have been modeled by zero-order and first-order reactions, a Monod type equation expressing the effect of substrate concentration on the growth of nitrifying bacteria has been found to fit the data in most nitrification studies (Barnes and Bliss 1983). The effect of individual independent limiting substrates on the specific growth rate can also be expressed. Thus, the effects of NH₄⁺-N and dissolved oxygen on the growth rate of Nitrosomonas are described as follows:

(16)

Where

N	=	specific growth rate of Nitrosomonas (nitrifiers) (1/hour);
Nmax	=	maximum specific growth rate of Nitrosomonas (nitrifiers) (1/hour);
KN	=	half-saturation constant for NH4+- N (mg/L);
DO	=	dissolved oxygen (mg/L); and
Ko	=	half-saturation constant for oxygen (mg/L).

Similar relationships can be written for the oxidation of nitrite to nitrate in terms of Nitrobacter and with NO₂^--N as substrate. Because it is generally the rate-limiting reaction, the nitrifier growth rate can be modeled based on the conversion of ammonium to nitrite by Nitrosomonas.

The ammonium oxidation rate can be measured to quantify how fast ammonium is oxidized to nitrate. It should be noted that over 99% of the total ammonia nitrogen (NH₃+NH₄⁺-N) in normal domestic wastewater pH of 7 is in the form of ammonium (NH₄⁺-N). The ammonium oxidation rate (q_N) for activated sludge is often expressed in units of mg NH₄⁺-N removed per hour for each g MLVSS in the aeration tank as follows (Barnes and Bliss 1983):

(17)

The ammonium oxidation rates (q_N) are commonly 1 - 3 mg/g/hour (Barnes and Bliss 1983).

Apparatus:

Procedure:
The procedure to determine the ammonium oxidation rate (q_N) is:

1. Obtain 8 L of wastewater sample.
2. Obtain 8 L of acclimated activated sludge.
3. Place a portion of the wastewater and activated sludge into an 8 L reactor. The dilution ratio used can be the same as the F/M ratio at the treatment plant of interest. For example, the Ashland treatment plant has an F/M = 0.67; thus, 1.3 L of activated sludge with VSS of 1,840 mg/L can be mixed with 6.7 L raw sewage with BOD₅ of 240 mg/L to obtain a F/M ratio of 0.67 in an 8 L reactor.

1. Measure VSS of mixture.
2. Aerate the reactor to reach a DO level of approximately 2 mg/L. If an air pump with a diffuser does not provide sufficient mixing, add a mechanical mixer.
3. Determine concentrations of total ammonia (NH₃+NH₄+-N), nitrite and nitrate (NO₂-+NO₃- -N) over time (at 0, 0.5, 1, 1.5, 2, 2.5, 3, 4, 5 hours) in filtrate passed through 0.45 m membrane filters.

Data Analysis:

Since the organic nitrogen will be transformed by bacteria to form total ammonia nitrogen, it is recommended to measure nitrite and nitrate production rates as the indicator of the ammonium oxidation rate. Table 11 and Figure 14 show an example of an ammonium oxidation rate determination. Even though a single sample is analyzed in this example, duplicated sample analysis is recommended.

Table 11. Example of nitrification determination.

Figure 14. Ammonium oxidation rate determination.

The ammonium oxidation rate is:
(27.6 - 19.8 mg NO₂^-+NO₃^- /L) / 5 hours / 2,454 mg/L = 6.4 x 10^-4 mg/mg/hour

where the initial biomass (MLVSS) in the batch reactor = 2,454 mg/L.

Personhours needed: 5 hours + acclimation time (~30 hours depending on wastewater).

Denitrification Rate

Theory:

Carlson (1971) and Christensen and Harremoes (1977) suggested that the kinetic reaction for denitrification by activated sludge can be expressed by:

(18)

where

This indicates that the denitrification rate is independent of the nitrate concentration and only a function of the volatile suspended solids concentration.

Apparatus:

Procedure

The procedure to determine the specific denitrification rate (q_D) is:

1. Obtain 8 L of wastewater sample.
2. Obtain 8 L of acclimated activated sludge.
3. Place a portion of the wastewater and activated sludge in an 8 L reactor. The dilution ratio used can be the same as the F/M ration at the treatment plant of interest. For example, the Ashland treatment plant has the F/M ratio of 0.67; thus, 1.3 L of activated sludge with VSS of 1,840 mg/L can be mixed with 6.7 L raw sewage with BOD₅ of 240 mg/L to obtain the F/M ratio of 0.1 in an 8 L reactor.

Data Analysis:

Table 12 and Figure 15 show an example of a denitrification rate determination. Even though a single sample is analyzed in this example, duplicated sample analysis are recommended.

From Figure 15, the denitrification rate is estimated to be:

(40.2 - 26.6 mg NO₂^-+NO₃^--N /L) / 5 hours / 2,260 mg/L = 1.2 x 10^-3 mg/mg/hour

Personhours needed: 5 hours + acclimation time (~30 hours depending on wastewater).

Table 12. Example of denitrification determination.

Figure 15. Denitrification rate determination.

Phosphorus Release and Update Rates Measurement

In a biological phosphorus removal process, phosphorus will be released by phosphorus-removing microorganisms under anaerobic conditions and taken up under aerobic conditions. The measurement of phosphorus release/uptake rates is meaningful only when phosphorus-removing microorganisms have been selected. An enhanced culture that removes phosphorus can either be obtained from a full scale BPR plant directly or produced in a laboratory reactor by using enrichment culture techniques.

A sequential batch reactor (SBR) can be used to develop the enhanced culture in a laboratory. The operational conditions for SBR to develop the enhanced culture depend on wastewater characteristics. The key feature of a SBR is its flexibility to adjust the anaerobic/aerobic retention time depending on the type of wastewater. Figure 16 shows a typical SBR configuration that controls the anaerobic/aerobic stage by a timer.

Figure 16. A typical SBR configuration.

Operational conditions of the SBR are as follows:

• reactor volume of 6 L; 4 L of fill and withdraw per cycle;
• wastewater feed in 10 minutes at each cycle;
• anaerobic/aerobic retention time = 2 hours/5 hours; 1 hour settling and decanting;
• 8 hours/cycle, 3 cycle/day.

When average COD and phosphorus concentrations in the influent are 200 mg/L and 9 mg-P/L, respectively under the above conditions, the effluent phosphorus concentrations were lower than 0.5 mg/L after 14 days of operation at room temperature. Once activated sludge containing phosphorus-removing microorganisms are obtained, phosphorus release/uptake rates can be measured as follows:

1. For the simulation of the anaerobic conditions, add wastewater and activated sludge to the reactor at a predetermined ratio and mix for a period of time corresponding to the hydraulic retention time of the anaerobic zone of the SBR or full-scale treatment plant. Take samples every 5 to 10 minutes for 0.5-1 hour and analyze for orthophosphate.
2. At the time corresponding to the hydraulic retention time of the anaerobic zone, supply the air using a fine pore diffuser placed at the bottom of the reactor. Take samples every 10 to 20 minute for 3-4 hours and analyze for orthophosphate.

In order to evaluate the effect of denitrification on phosphorus removal, total ammonia, nitrite, and nitrate concentrations are usually monitored. The rates of phosphorus release and uptake are simply expressed by the increase or decrease in phosphorus concentration per unit biomass per unit time (mg-P/g VSS/min).

The Ashland wastewater was used as an example to determine the phosphorus release/uptake rate. An aliquot of 500 ml of activated sludge from the laboratory SBR, where phosphorus-removing microorganisms were developed, was added to 500 ml of the Ashland composite wastewater to simulate a reaction of influent wastewater with 100% sludge recycle. The activated sludge were taken from the aerobic zone of the laboratory SBRs. The F/M ratio was 0.3. The NO₂^-+NO₃^--N concentration in the initial sludge and in the combined solution were 5 and 2 mg-N/L, respectively. The initial MLVSS was 880 mg/L. Samples were taken every 10 minutes during the anaerobic condition and every 20 minutes during the aerobic condition. This experiment was conducted under room temperature condition. The profile of phosphorus release and uptake is shown in Figure 17.

The phosphorus release was slow in the initial 30 minutes and rapid in the following 20 minutes. For the next 10 minutes, the phosphorus released was taken up slightly (approximately 0.2 mg-P/L). The specific phosphorus release rate was 0.064 mg-P/g VSS/min [(4.7 - 1.3)/60/0.880], and the specific phosphorus uptake rate was 0.034 mg-P/g VSS/min [(4.7 - 1.1)/120/0.880]. The total phosphorus released was obtained from the difference between the initial phosphorus concentration and the phosphorus concentration at the end of anaerobic stage. Even though it is uncertain what causes the lag and bump in the phosphorus release and uptake, the phosphorus release rates are comparable with reported values ranging from 0.042 to- 0.056 mg-P/g VSS/min (Kang et al. 1991).

Figure 17. Phosphorus release/uptake profile of Ashland wastewater.

More information on this topic: Gerry Novotny