Probabilistic Modeling of Two-Stage Biological Nitrogen Removal Process: Conditions for Enhanced Process Certitude

Abstract

In a conventional two-stage biological nitrogen removal (BNR) process, the extent of uncertainty associated with different operating parameters (e.g., solids retention time, internal recirculation ratio, anoxic hydraulic retention time [HRT], total HRT, and sludge recycle ratio) was evaluated by simulation with Activated Sludge Model no 1. Variability in the values of kinetic parameters was incorporated in performing stochastic simulations by adopting the influent biodegradable chemical oxygen demand–to–total kjeldahl nitrogen (COD:TKN) ratio of 10, an important determinant of BNR performance. Simulation results predicted maximum level of certitude for effective nitrogen removal at 3-h anoxic HRT (and 12-h total HRT). Appreciable rise in process certitude for nitrogen removal was indicated as solids retention time was increased from 5 to 20 days. No noticeable rise in confidence level could be achieved for meeting stipulated treatment targets by increasing internal recycle (for nitrate recirculation) beyond 300%. Process certitude remained virtually unaffected by increase in either sludge recycle ratio or total HRT of the system. Such an approach for reducing treatment uncertainty, related to variability in biokinetic parameters by studying the effect of operating parameters on the system, could be regarded as a valid objective in BNR process design and operation. This would ultimately lead to the development of ranges in operating conditions for enhanced process certitude.

Introduction

Simulation of biological wastewater treatment processes deals with the application of biotreatment models, with appropriate kinetic and stoichiometric parameter values, for analysis and evaluation of design and operating conditions required to meet specific treatment objectives. The selection of biokinetic parameter values intrinsically involves certain amount of uncertainty, as the behavior and performance of any given biological treatment system cannot be entirely known in advance. Also, establishment of detailed kinetic and stoichiometric parameter values might not be justified and would depend on the scale of a project. Therefore, probabilistic analysis of biological system in meeting pre-selected treatment objectives and response of the system to various operating parameters taking into account the variability in biokinetic parameter values become important.

Process simulation tools that have been developed and introduced over the past years have enhanced the design and analysis of biological wastewater treatment systems such as activated sludge and biological nitrogen removal (BNR). Activated Sludge Model no. 1 (ASM1) is normally used for modeling activated sludge process and includes 8 processes, 13 components, 5 stoichiometric coefficients, and 14 kinetic parameters to define carbon and nitrogen removal (Henze et al., 1987a, b). This model has been calibrated and validated by suggesting and including typical values and ranges of these process parameters for simulating treatment of different types of wastewater under various operational conditions. Calibration of the model based on field performance of full-scale installations by Choubert et al. (2008), Muller et al. (2003), Petersen et al. (2003), Kappeler and Gujer (1992), and Siegrist and Tschui (1992) provided a range of parameter estimates. Probability distributions of these kinetic and stoichiometric parameters were later characterized by Cox (2004). These recommended values are by and large accepted in modeling of activated sludge process by ASM1 and other subsequent models incorporated into a number of software packages.

Uncertainty in modeling and analysis of wastewater treatment plant performance has been studied by Sin et al. (2009), Refsgaard et al. (2007), and others. In contrast to the issues discussed in these publications, this study was specifically focused at finding the level of uncertainty associated in the two-stage BNR process by using stochastic modeling that took into account the natural variability of kinetic and stoichiometric parameters without considering variation in either quality or quantity of influent wastewater. Determination of such variability associated with attaining stipulated treatment goals was attempted. Under this present context, process certitude could be defined as the certainty (or statistical probability) of achieving any stipulated treatment target in a two-stage BNR system, as stochastic simulation results were plotted to generate empirical cumulative frequency distributions (CFDs) for the effluent concentrations under defined operating conditions. With the limited literature available on effect of variation in biokinetic parameters on process performance, information collected from this study indicating effective operating conditions could prove to be beneficial to enhance system reliability in meeting treatment targets. The effect of specific operating parameters on process certitude was analyzed to devise guidance on expected process performance, design, and operational strategies to reduce process uncertainty, ultimately leading to safety factors for enhanced process certitude in meeting treatment objectives.

Methodology

Two-stage pre-anoxic denitrification type BNR process for domestic wastewater treatment was simulated with GPS-X (2006) (Hydromantis, Inc., Hamilton, Ontario), a simulation software that incorporated ASM1 modeling. The variability in influent quality and quantity was not included in this work, and influent flow and characteristics (Table 1) were kept the same for all simulations performed. The BNR system comprised two completely mixed stirred tank reactor in series, the anoxic reactor followed by the aerobic one, and a secondary clarifier.

Table 1.

Influent Wastewater Characteristics

Component	ASM1 symbol	Concentration
Particulate inert organic material	X_I	30
Slowly biodegradable substrate^a	X_S	160
Readily biodegradable substrate^a	S_S	240
Active heterotrophic biomass	X_B,H	0
Active autotrophic biomass	X_B,A	0
Debris from biomass death and lysis	X_D	0
Inert soluble organic material	S_I	0
Oxygen	S_O	0
Nitrate nitrogen	S_NO	0
Ammonia nitrogen^a	S_NH	25
Soluble biodegradable organic nitrogen^a	S_ND	6.5
Particulate biodegradable organic nitrogen^a	X_ND	8.5
Alkalinity	S_ALK	5.0

Typical proportions in domestic wastewater (Grady et al., 1999). Concentrations are expressed in mg/L COD for organic components, mg/L N for nitrogenous species, and mM/L for alkalinity.

Cox (2004) put forward the probability density functions (PDFs) of different kinetic and stoichiometric parameters through Bayesian analysis of recommended values and field calibration results (Table 2). These were used in performing stochastic simulations. Out of the 19 coefficients and parameters (Table 2) included in ASM1, 4 were considered to be essentially constant ( f'_D, i_N/XB, i_N/XD, and k_a). Among the rest, 14 model parameters (Y_H, b_H, μ_H, K_S, K_NO, K_O,H, Y_A, μ_A, b_A, K_NH, K_O,A, k_h, K_X, and η_h) were allowed to vary as log-normal PDF Equation 1 and one (η_g) with a uniform PDF Equation 2. \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6} \begin{document} \begin{align*} P ( x ) = \frac{1}{x \sigma \sqrt{2 \pi}} \exp \left[ - \frac{ ( \ln x - \xi) ^2} {2 \sigma^2} \right] \tag{1} \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6} \begin{document} \begin{align*} \\ P ( x ) = \left\{ \begin{array}{ll}\frac{1}{b - a} , & a \le x \le b , \\ 0 , & x < a \ { \rm or} \ x > b , \end{array} \right. \tag{2} \end{align*} \end{document}

Table 2.

Kinetic and Stoichiometric Parameter Values, Ranges, and Distribution at Neutral pH and 20°C for Domestic Wastewater (Cox, 2004)

		Statistical parameters
Symbol	Unit	Mean (ξ)	SD (σ)	Mean
Heterotrophic coefficients
Y_H	mg biomass COD formed/mg COD oxidized	−0.45	0.12	0.64
μ_H	day⁻¹	1.14	0.60	3.13
K_S	mg COD/L	1.44	0.76	4.22
b_H	day⁻¹	−1.06	0.81	0.35
K_NO	mg NO₃^—N/L	−1.55	1.01	0.21
K_O,H	mg O₂/L	−1.46	0.83	0.23
η_g	fraction	^a	0.50
Autotrophic coefficients
Y_A	mg biomass COD formed/mg N oxidized	−1.52	0.55	0.22
μ_A	day⁻¹	−0.51	0.44	0.60
b_A	day⁻¹	−1.97	0.28	0.14
K_NH	mg NH₃-N/L	−0.68	1.00	0.51
K_O,A	mg O₂/L	−0.82	0.96	0.44
Hydrolysis coefficients
k_h	mg slowly biodegradable COD/mg cell COD day	0.83	0.36	2.29
K_X	mg slowly biodegradable COD/mg cell COD	−2.82	1.34	0.06
η_h	fraction	−0.86	0.62	0.42
Other coefficients
f'_D	mg debris COD/mg biomass COD	^b	0.08
i_N/XB	mg N/mg COD in active biomass	^b	0.086
i_N/XD	mg N/mg COD in biomass debris	^b	0.06
k_a	L/mg biomass COD—hour	^b	0.1608

η_g follows a uniform PDF with a minimum of 0.10 and a maximum of 0.90.

Values represent recommended parameter values.

where P(x) is the probability that a model parameter has a value x; ξ and σ are the mean value and variance, respectively, of the log-transformed parameter values; and a and b are the minimum and maximum, respectively, of the parameter values (Table 2). A set of 1,000 random combinations of parameter values, varying according to their respective PDFs, were generated by using Excel (Microsoft Corp., Redmond, WA). Such a stochastic simulation approach is referred to as Latin hypercube sampling and reported to help ensure uniform distribution of input points in parameter space (Morgan and Henrion, 1990).

Stochastic process simulations were performed for the defined process configuration at selected operating parameter ranges (Table 3) for each of the 1,000 parameter combinations as described above. So, each stochastic simulation comprised 1,000 Monte Carlo runs with the selected operating conditions. Besides, discrete simulations were performed using the mean parameter values (Table 2). Each simulation was allowed to run for 5 times the solids retention time (SRT) value until the state variables stabilized. To maintain the stipulated SRT, sludge wasting was done directly and proportionally from the reactors in line with Garrett configuration (Grady et al., 1999). The dissolved oxygen level in anoxic tank was set at 0 mg/L to maintain anoxic condition and at 2.0 mg/L in aerobic tank to ensure oxygen-independent biokinetics.

Table 3.

Process Configuration and Operating Conditions Used for Stochastic Simulations

Parameter	Parameter range examined ^a	Default parameter value
Anoxic hydraulic retention time (θ₁)	1 to 8-h^b	3-h
Internal recycle ratio (R₁)	1.0 to 5.0	4.0
Total hydraulic retention time (θ)	2 to 24-h^c	12-h
Solids retention time (θ_C)	5 to 30-day	15-day
Sludge recycle ratio (R)	0.25 to 3.0	0.5

System configuration: Complete mix type anoxic and aerobic reactors in series followed by clarifier for biomass separation with sludge wasting and recirculation systems.

Selected ranges typical of a range of pre-anoxic biological nitrogen removal process configuration (Rittmann and McCarty, 2001; Tchobanoglous et al., 2003).

When θ₁ is being varied, total HRT for the system was maintained at 12-h by allocating the balance HRT to aerobic reactor (e.g., if θ₁ is 4-h, HRT for aerobic tank is taken as 8-h for 12-h total HRT).

Default ratio of anoxic and aerobic HRTs was adopted as 1:3.

HRT, hydraulic retention time.

To nullify the influence of physical separation and emphasize on the effect of the biotreatment processes on overall system performance, the secondary clarifier was modeled as an ideal biomass separator with 100% particulate removal efficiency. Consequently, the effluent contained only soluble components, i.e., S_S and S_I (=0) for organic species, and S_NH (NH₄⁺-N), S_NO (NO₃^—N), and total nitrogen (TN). Output of stochastic simulations was used to develop empirical CFDs for the effluent concentrations. These were analyzed for assessment of the certitude of achieving specific treatment targets under given operating conditions.

Results and Discussion

SRT

SRT or sludge age plays a decisive role in design and operation of biological treatment process. The sludge age is adopted to establish a stable microbial population in the system. It is selected based on the minimum SRT required \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6} \begin{document} $$( \theta_C^{\, \min} )$$ \end{document} for the process and by multiplying it with a safety factor (Rittmann and McCarty, 2001): \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6} \begin{document} \begin{align*} \theta_C^ { \min } = \frac { 1 } { ( \hat { \mu } - b ) } \tag { 3 } \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6} \begin{document} \begin{align*} SF = \frac { \theta_C } { \theta_C^ { \min } } \tag { 4 } \end{align*} \end{document}

where SF is the safety factor, θ_C is the adopted SRT, and the model parameters \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\hat{ \mu}$$ \end{document} and b are as defined in Appendix A. Influent substrate concentration is usually included in calculating \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\theta_C^{ \min}$$ \end{document} . However, for a general approach to the concept, a concentration-independent form depicting the limiting value at an infinitely high influent concentration was used to emphasize on the associated biokinetic parameters. Calculated \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\theta_C^{ \min}$$ \end{document} value was about 2.2 days for autotrophic biomass for the mean parameter values and influent characteristics considered in this study. There was marginal increase in these values if influent concentrations were taken. In a situation where no site-specific estimation of process parameters has been determined, SF provides a reasonable amount of certainty that the treatment system would be operating at an expected density of microbial culture. This certitude level was assessed, however, by working out \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\theta_C^{ \min}$$ \end{document} for each of the 1,000 parameter combinations and plotting the empirical cumulative frequency distributions (CFDs) (Fig. 1). The certitude that the associated SRT would either equal or exceed the \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\theta_C^{ \min}$$ \end{document} value in the biological system could be estimated by their cumulative probabilities. As expected, corresponding certitude levels for the \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\theta_C^{ \min}$$ \end{document} values calculated using the mean parameters, were near the midpoint of respective CFDs, around 52% for autotrophs (2.2 days). If a safety factor of 10 is applied to the \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\theta_C^{ \min}$$ \end{document} of each of autotrophic microbial biomass (i.e., 22 days), the certitude level is increased to >99%. Further rise in certitude could be achieved by increasing the SRT, which would also imply a higher safety factor.

FIG. 1.

Minimum solids retention time for autotrophic biomass for stochastic and discrete simulation.

To examine the effect of SRT on two-stage BNR system (being operated with θ₁–3-h, R_1-4.0, θ–12-h, and R −0.5), performance of biotreatment was compared at 15 and 30-day SRTs by performing stochastic simulations. The empirical CFDs for steady-state effluent biodegradable COD concentrations for 15-day and 30-day SRTs were almost similar to each other (Fig. 2a). In contrast, CFDs for steady-state effluent TN concentrations showed marginal improvement on raising the SRT from 15 to 30 days (Fig. 2b). The empirical CFDs of the steady state effluent concentrations (Fig. 2) could be construed as the certitude that a certain effluent target would be met under the given operating conditions.

FIG. 2.

Steady-state effluent biodegradable COD and total nitrogen (TN) concentrations for stochastic and discrete simulation.

At 15-day SRT, an effluent TN concentration of 5.67 mg/L was predicted by the discrete simulation, and the certitude of obtaining this effluent TN concentration was 34% as indicated by the corresponding CFD. In other words, a two-stage BNR system operated at 15-day SRT, 3-h anoxic, and 9-h aerobic hydraulic retention times (HRTs), 400% internal recycle, 50% sludge recycle, and designed using the mean parameter values (Table 2) without any site-specific parameter estimates would have a 34% certitude of attaining a TN effluent concentration of 5.67 mg/L or less for treating a typical municipal wastewater (Table 1). Likewise, discrete simulation predicted an effluent COD concentration of about 0.71 mg/L, and the corresponding certitude was about 45%. Increasing the SRT to 30 days had marginal effect on treatment from the viewpoint of TN and organics removal and reduced the effluent TN and COD to 5.83 mg/L (35% certitude) and 0.66 mg/L (46% certitude), respectively.

Effect of sludge age on the certitude of attaining selected treatment goals for various nitrogen species and COD (Fig. 3a–d) was investigated by plotting these against increasing SRT values. Higher certitude could be attained by selecting a less stringent treatment goal or a longer SRT, as anticipated. Two levels of treatment targets were selected for this analysis and these were 5 and 10 mg/L for effluent TN, and 10 and 20 mg/L for effluent biodegradable COD. The same target effluent concentrations were used for other nitrogen species, NH₄⁺-N (S_NH) and NO₃^—N (S_NO), for comparative analysis. Effect of high SRT values on TN and COD removal in the process was found to be different.

FIG. 3.

Effect of solids retention time on certitude of achieving specific target effluent (a) ammonia-nitrogen (S_NH), (b) nitrate nitrogen (S_NO), (c) biodegradable COD, and (d) total nitrogen (S_TN) concentrations.

Adoption of higher SRT value increased the certitude of meeting specified TN treatment targets over a particular range of SRT with higher confidence levels being associated with less stringent treatment goal (Fig. 3c). Field experience in biological wastewater treatment indicated an SRT of 2 to 15 days for nitrification and subsequent denitrification (Tchobanoglous et al., 2003). Also, the certitude of meeting stipulated level of COD removal remained stable over the range examined with a marginal rise over 5 to 15-day SRT range (Fig. 3d). This was probably due to removal of biogenic soluble organic matter at 0.5 to 2-day SRT and particulate organic removal taking place with an SRT of 2 to 4 days (Grady et al., 1999), which would not improve with further increase in SRT. So, the stochastic simulation output was in line with results of field experience.

Notable increase in certitude for achieving target effluent TN was indicated when SRT was raised from 5 to 15 days (Fig. 3c). This could be correlated to a notable and almost similar increase in certitude (Fig. 3a) for obtaining effluent S_NH concentrations (5 and 10 mg/L). This indicated occurrence of nitrification that was believed to have been established between 2- and 15-day SRT (Grady et al., 1999). Consequently, a drop in certitude for meeting treatment goals for effluent S_NO implied a rise in possibility of higher effluent S_NO concentration, which in turn confirmed onset of nitrification. In both cases, further increase in SRT from 15 to 20 days slightly improved process certitude for attaining treatment objectives of effluent S_NH and a insignificant decrease in confidence level for target effluent S_NO concentration. Its effect translated into an appreciable rise in certitude for achieving stipulated TN concentrations for rise in SRT from 5 to 15 days due to establishment of nitrification and subsequent denitrification. Adoption of any higher SRT value (e.g., 30 days) was observed to slightly enhance the associated process certitude for less stringent treatment goal (Fig. 3c). Hence, attainment of specific target effluent concentrations at any given SRT and maintenance of a stable microbial population within the two bioreactors in series were intimately connected.

Anoxic HRT

Stochastic simulations were run over a range of HRT for anoxic reactor (1-h to 8-h) keeping total HRT at 12-h (with R_1-4.0, R −0.5, and θ_C–15-day). That is, the ratio of anoxic to total HRT (anoxic HRT fraction) ranged from 0.083 (i.e., 1/12) to 0.67 (i.e., 8/12). Appreciable reduction in certitude of attaining S_NH concentration goals was noted with increase in anoxic HRT (Fig. 4a). With total HRT remaining same, as anoxic HRT was raised, anoxic conditions started to dominate ensuing rise in effluent S_NH concentration. Lesser time was available for S_NH to undergo nitrification as aerobic retention time was correspondingly reduced. A rise in effluent S_NH level was therefore indicated with a consequent drop in certitude of attaining target S_NH concentration. Probability of achieving target effluent S_NO concentration was enhanced as nitrification was subsided for decrease in aerobic HRT (Fig. 4b). Longer anoxic HRT caused S_NH concentration to rise that was incompletely nitrified in the aerobic reactor and returned (with 400% internal recycle) to the anoxic tank. So, denitrification was affected due to low electron acceptor (S_NO) level in the internal recycle. In contrast, for low anoxic HRT, denitrification was suppressed as less time was allowed in anoxic reactor that indicated a greater chance of high effluent TN concentration.

FIG. 4.

Effect of anoxic hydraulic retention time on certitude of achieving specific target effluent (a) ammonia-nitrogen (S_NH), (b) nitrate nitrogen (S_NO), (c) biodegradable COD, and (d) total nitrogen (S_TN) concentrations.

Combining these two scenarios, certitude of achieving target effluent TN concentration was found to be optimum over an anoxic HRT range of 2 to 4-h (i.e., 0.17 to 0.33 anoxic HRT fraction) with the maximum occurring at 3-h (Fig. 4c). Growth of denitrifiers in anoxic tank and nitrification in aerobic tank were presumed to have been balanced over this range of anoxic HRT fraction for most effective performance.

Results indicated that there was >90% certitude that target effluent COD concentration could be attained over 1 to 4-h anoxic HRT (Fig. 4d). However, certitude of achieving such treatment level dropped steadily over 4 to 8-h anoxic HRT range could be attributed to reduced heterotrophic substrate utilization in denitrification as anoxic HRT was gradually increased beyond 3-h.

Internal recycle ratio

A relatively high internal recycle ratio (R₁) needs to be maintained for pre-anoxic BNR process to return sufficient amount of electron acceptor (S_NO) from aerobic to anoxic tank for effective denitrification. It was important to ascertain the effect of internal recycle ratio on certitude of achieving treatment targets, so as not to adopt an unnecessarily high recycle rate having a direct implication on capital cost for recirculation piping and associated energy charges.

Certitude associated with achieving pre-set effluent S_NH and COD concentrations remained unaffected by any increase in internal recycle ratio (Fig. 5b). The certitude profile for response of the process in achieving target effluent S_NO concentration to varying internal recycle ratio was very similar to that for TN (Fig. 5a). Probability of attaining more stringent target effluent S_NO concentration (5 mg/L) went up steadily as the recycle ratio was increased. However, for less stringent target (10 mg/L), such rise in process certitude was found to level off beyond 200%, after rising initially. Simulation results predicted that over the R₁ range of 300% to 500%, there was practically no improvement in process for meeting 10 mg/L effluent S_NO concentration. The same was indicated for attaining effluent TN goals (Fig. 5a). Rate of return of S_NO from aerobic to anoxic tank improved the overall nitrogen removal by supplying sufficient amount of electron acceptor (S_NO) to the anoxic reactor for denitrification. Yet, certitude for achieving a treatment target of 10 mg/L for effluent TN was found to stabilize after R₁ was adequately increased, and beyond this value no further improvement was recorded. However, for meeting stricter discharge criteria of 5 mg/L TN, increase in internal recycle ratio indicated better process certitude. A certitude profile was also worked out for an intermediate effluent TN concentration of 8 mg/L, indicating that probability of attaining this target flattened out beyond R₁ of 300%. So, it could be concluded that over the range of less stringent treatment goal (8 to 10 mg/L S_TN), adoption of 400% internal recycle was adequate for optimum process certitude.

FIG. 5.

Effect of internal recycle ratio on certitude of achieving specific target effluent (a) total nitrogen (S_TN) and (b) biodegradable COD concentrations.

Sludge recycle ratio

The certitude of attaining specific treatment targets was plotted as a function of R to examine the effect of sludge recycle ratio on system performance (with θ₁–3-h, R₁-4.0, θ–12-h, and θ_C–15-day) over a range of sludge recycle ratios (0.25 to 3.0). The response of the system was found to be consistent signifying marginal effect on the levels of certitude associated with TN and COD removal.

Total HRT

Stochastic simulations of the system (with θ_C–15-day, R₁-4.0, R −0.5, and anoxic HRT fraction 1:4) indicated that there was virtually no effect of HRT on the certitude of meeting TN and COD treatment goals. For TN and COD removals, the certitude level remained at 62% and 92%, respectively, for less stringent treatment goals.

Summary and Conclusion

Probabilistic modeling provided a platform for quantitative assessment of the certitude levels associated with two-stage pre-anoxic BNR process. Estimated values and PDFs for biokinetic parameters suggested by Cox (2004) were used to evaluate the extent of uncertainty associated with operating parameters. In the absence of sufficient information on site-specific estimate of kinetic and stoichiometric parameter values, these results could provide process designers with useful guidance on the levels of certitude related to specific treatment targets. Output from simulations, in principle, agreed with prevailing practice and field experience in BNR process, and provided background for process certitude.

Results of the analysis can be summarized as follows:

Use of a safety factor for heterotrophic biomass, more importantly, autotrophic biomass, in the two-stage BNR system as a multiplier of minimum SRT was validated from the standpoint of increasing process certitude.

Process certitude of attaining treatment targets for effluent TN increased significantly as SRT was raised from 5 to 20 days and stabilized thereafter. The certitude of meeting stipulated level of biodegradable COD removal remained stable over the range examined with a marginal rise between 5- and 15-day SRT.

Over the range of 2 to 4-h anoxic HRT (i.e., 0.17 to 0.33 anoxic HRT fraction), maximum treatment certitude for target TN removal could be obtained and the maximum occurred at 3-h. Process certitude dropped consistently for targeted COD levels beyond 3-h anoxic HRT.

Process certitude was improved over 100% to 300% internal recycle (R₁) for less stringent TN target and did not vary much beyond 400%. Internal recycle had marginal effect on certitude of COD removal being >90% for the range studied.

Treatment performance and certitude of the BNR system remained unaffected by increase in either sludge recycle ratio (R) or total HRT for nitrogen and COD removal.

The results predicted and analyzed in this study might vary depending on variation in quality and quantity of influent wastewater. However, operational strategies could be formulated from the above analysis, indicating that the pre-anoxic BNR process would have the highest probability of attaining the selected treatment goals for TN and biodegradable COD removal if operated at 15- to 20-day SRT, 2- to 4-h anoxic HRT, 300% internal recycle, 12-h total HRT, and 50% sludge recycle to counter the natural variation in biokinetic parameter values.

Footnotes

Acknowledgments

This material is based upon work supported in part by the National Science Foundation under Grant No. BES-0348161, and by the Mississippi Department of Environmental Quality under Work Order No. 05-0001MSU-006. The authors would also like to thank the reviewers for their critical and constructive comments.

Author Disclosure Statement

No competing financial interests exist.

Appendix A. List of Nomenclature

b_A	Decay coefficient for autotrophic biomass
b_H	Decay coefficient for heterotrophic biomass
f'_D	Fraction of biomass leading to debris
i_N/XB	Mass of nitrogen per mass of COD in biomass
i_N/XD	Mass of nitrogen per mass of COD in products from biomass
k_h	Maximum specific hydrolysis rate
K_NH	Ammonia half-saturation coefficient for autotrophic biomass
K_NO	Nitrate half-saturation coefficient for denitrifying heterotrophic biomass
K_O,A	Oxygen half-saturation coefficient for autotrophic biomass
K_O,H	Oxygen half-saturation coefficient for heterotrophic biomass
K_S	S_S half-saturation coefficient for heterotrophic biomass
K_X	Half-saturation coefficient for hydrolysis of slowly biodegradable substrate
k_a	Ammonification rate
μ_A	Maximum specific growth rate for autotrophic biomass
μ_H	Maximum specific growth rate for heterotrophic biomass
η_g	Correction factor for μ_H under anoxic conditions
η_h	Correction factor for hydrolysis under anoxic conditions
Y_A	Yield factor for autotrophic biomass
Y_H	Yield factor for heterotrophic biomass

References

Choubert

J.M.

, Marquot

, Stricker

A.E.

, Gillot

, Racault

, Héduit

2008. Maximum growth and decay rates of autotrophic biomass to simulate nitrogen removal at 10°C with municipal activated sludge plants. Water SA, 34:71.

Cox

C.D.

2004. Statistical distribution of uncertainty and variability in activated sludge model parameters. Water Environ. Res., 76:2672.

GPS-X. 2006. Software for Modeling and Simulation of Municipal and Industrial Wastewater Treatment Processes Manual. Ontario, Canada: Hydromantis Inc.

Grady

C.P.L.

Jr. , Daigger

G.T.

, Lim

H.C.

1999. Biological Wastewater Treatment, 2nd. New York: Marcel Dekker, Inc.

Henze

, Grady

C.P.L.

Jr. , Gujer

, Marais

G.V.R.

, Matsuo

1987a. Activated sludge model no. 1. IAWPRC Scientific and Technical Report, No. 1. London: International Association on Water Pollution Research and Control.

Henze

, Grady

C.P.L.

Jr. , Gujer

, Marais

G.V.R.

, Matsuo

. 1987b. A general model for single-sludge wastewater systems. Water Res., 21:505.

Kappeler

, Gujer

1992. Estimation of kinetic parameters of heterotrophic biomass under aerobic conditions and characterization of wastewater for activated sludge modeling. Wat. Sci. Technol., 25:125.

Morgan

M.G.

, Henrion

1990. Uncertainty: A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis. Cambridge: Cambridge University Press.

Muller

, Wentzel

M.C.

, Loewenthal

R.E.

, Ekama

G.A.

2003. Heterotroph anoxic yield in anoxic aerobic activated sludge systems treating municipal wastewater. Water Res., 37:2435.

10.

Petersen

, Garnaey

, Henze

, Vanrolleghem

P.A.

2003. Calibration of activated sludge models: A critical review of experimental designs. Agathos

S.N.

, Reineke

Biotechnology for the Environment: Wastewater Treatment and Modeling, Waste Gas Handling. Dordrecht: Kluwer Academic Publishers.

11.

Refsgaard

J.C.

, van der Sluijs

J.P.

, Hojberg

A.L.

, Vanrolleghem

P.A.

2007. Uncertainty in the environmental modelling process—a framework and guidance. Environ. Model. Softw., 22:1543.

12.

Rittmann

B.E.

, McCarty

P.L.

2001. Environmental Biotechnology: Principles and Applications, 1st. New York: Mc-Graw Hill.

13.

Siegrist

, Tschui

1992. Interpretation of experimental data with regard to the activated sludge model No. 1 and calibration of the model for municipal waterwater treatment plants. Wat. Sci. Technol., 25:167.

14.

Sin

, Gernaey

K.V.

, Neumann

M.B.

, van Loosdrecht

M.C.M.

, Gujer

2009. Uncertainty analysis in WWTP model applications: a critical discussion using an example from design. Water Res., 43:2894.

15.

Tchobanoglous

, Burton

F.L

, Stensel

H.D.

2003. Wastewater Engineering: Treatment and Reuse, Metcalf and Eddy, 4th. Boston: McGraw-Hill.