COMPARISON BETWEEN

CONVENTIONAL ACTIVATED SLUDGE

AND WASTE STABILIZATION PONDS

FOR WASTEWATER TREATMENT

Cássia Rocha Pompeu

Promotor: Prof. dr. ir. Peter Goethals

Tutor: Long Tuan Ho

Master’s Dissertation submitted to Ghent University in partial fulfilment of the requirements for the degree of

Master of Science in Environmental Sanitation

Academic year: 2016 - 2017

COPY RIGHT

“The author and promotors give the permission to use this thesis for consultation and to

copy parts of it for personal use. Every other use is subjected to the copyright laws, more

specifically the source must be extensively specified when using results from this thesis.”

“De auteur en promotors geven toelating deze scriptie voor consultatie beschikbaar te

stellen en delen ervan te kopiëren voor persoonlijk gebruik. Elk ander gebruik valt onder

de beperkingen van het auteursrecht, in het bijzonder met betrekking tot de verplichting

uitdrukkelijk de bron te vermelden bij het aanhalen van resultaten uit deze scriptie.”

Ghent, September 2017

The promotor, The tutor,

Prof. dr. ir. Peter Goethals Long Tuan Ho

The author,

Cássia Rocha Pompeu

ACKNOWLEDGEMENTS

First of all, I want to express my gratitude to Gent University for the opportunity and, of course,

Vlaamse Interuniversitaire Raad University Development Cooperation (VLIR UOS) for the

financial support and make it all possible.

I am grateful for my promoter, Prof. Peter Goethals, for accepting me and giving me the chance

to write my master dissertation in his research group. It was a challenging opportunity, but at the

same time, so rewarding.

I would like to especially thank my tutor Long Tuan Ho for all the patience and guidance during

this year. All his advice, suggestions and knowledge were essential to help me overcome the

(many) difficulties of working with models. He was a source of inspiration and support to keep me

motivated to continue and not going crazy during this year filled with so many parameters,

simulations and bacteria.

Studying in Belgium in these two years was indeed a life changing experience. Being away from

home, getting used to the cold and gray days was not that easy. Luckily, I always had friends who

turned it into an amazing time. To all the friends I made in Gent, thank you for being my family

and my support during all the time. Thank you Lígia for making me able to speak Brazilian

Portuguese on a daily basis and for all your help during these 2 years in this rainy country. Thank

you José Luis for the company and making me fluent in Chilean Spanish with 31 Minutos. And

Rodrigo, thank you for all the memes/moments we shared together in Belgium (and Europe),

since day zero. You’re my person, you’ll always be my person.

Thank you to all my friends in Brazil, that even being so far, make me feel so loved. Thaís, thank

you for our conversations, for keeping up with my/your adventures daily and for maintaining our

10+ years of friendship. Being close despite the 5-hour time zone difference during these two

years is not for everyone. Bruno, sorry for bothering you with my activated sludge/slugs

manuscripts, at least you may have learned something from them.

Finally, I want to thank my family back home for the unconditional support and for being whom I

can always count on.

“And once the storm is over you won't remember how you made it through, how you managed to survive.

You won't even be sure, in fact, whether the storm is really over. But one thing is certain. When you come

out of the storm, you won't be the same person who walked in. That's what this storm's all about.”

Haruki Murakami

ABSTRACT

Municipal wastewater treatment is frequently performed by activated sludge (AS) process in a

conventional biological treatment system. However, this system has recently been evaluated as

a low cost-effective technology with high-energy demand and limited recovery potential [1]. From

that perspective, natural systems, such as waste stabilization ponds (WSP), appear as a viable

alternative due to their advantages, i.e. extremely low operation and maintenance costs, simple

operation, and high robustness. In this study, this alternative technique is theoretically evaluated

via a performance comparison regarding the removal efficiency and resilient capacity between

two systems. To this end, two sophisticated mathematical models were developed, based on the

Activated Sludge Model No. 2d (ASM2d) [2] for the activated sludge systems, Anaerobic Digestion

Model (ADM 1) [3], River Water Quality Model 1 (RWQM 1) [4] and Constructed Wetlands Model

1 (CWM 1) [5] for the natural system. Note that, to author’s knowledge, there are no well-

established models describing a conventional WSP system, including an anaerobic pond, a

facultative pond and a maturation pond, due to its complexity.

After development, these models were evaluated and calibrated based on the experimental data

available. The calibration followed a systematic approach proposed by Brun et al. [6], in which

parameters are first individually assessed concerning their local sensitivities. From the

parameters possibly estimated, subsets were formed and evaluated in respect to their

identifiability to, finally, allow the parameter tuning procedure.

The activated sludge model results showed a significant good fit to lab-scale experiments.

Sensitivity analysis was carried out to identify potential parameter subsets in the model. The

importance ranking, constructed based on local sensitivities, demonstrates that the activated

sludge system was strongly influenced by heterotrophic, phosphorous accumulating organisms

(PAO) and influent concentration parameters. From this ranking, a subset of size 7 containing

parameters related to hydrolysis, heterotrophs, autotrophs and PAO was chosen to perform

parameter tuning, improving model fitness to experimental data. This methodology showed to be

a useful tool in the model calibration when handling large quantities of parameters in wastewater

treatment models.

Concerning the WSP model, the simulated organic matter removal presented a reasonable good

fit to experimental data. However, the model could not describe nutrients removal. Biochemical

processes, which contribute largely to nutrients removal such as ammonia volatilization, were not

taken into account due to lack of experimental data, software limitations and model’s complexity

level. These assumptions undermined the model capability of simulating the nutrients removal in

WSP. Since a large number of parameters included in the model were related to nutrient

processes, the sensitivity analysis was not carried out successfully and, consequently, model

calibration was not achieved.

The uncertainties were evaluated in both models by means of Monte Carlo simulations. In this

method, the deterministic model runs with a different series of parameters values, generating the

probability distributions of the results. With samples generated by Latin Hypercube Sampling

(LHS) at the system outlet over time in a uniform distribution considering input uncertainties, the

results, represented by the mean, 10th and 90th percentiles, revealed larger uncertainties at the

influent peaks, especially for BOD and COD. The WSP model presented slighter lower

uncertainties when compared to AS at the reference scenario since nutrients-related parameters

were not taken into account in input uncertainties.

Different scenarios related to wastewater strength were simulated in order to assess the removal

and resilient capacity of the two treatment methods. The evaluation showed that the activated

sludge (AS) can handle high BOD and COD concentrations, presenting a good removal efficiency

(>85%), even at increased wastewater strengths. With regard to nutrients, the removal

efficiencies for TKN ranged from zero (for wastewater strength increased 50 times) up to 67% at

the reference scenario. Total phosphorous reached removal efficiencies up to 50% at the

reference scenario, indicating that the system has more difficulties to handle high nutrients

concentrations. The WSP model presented a similar behavior. The proposed scenarios showed

that the systems could remove organic matter even at increased wastewater strengths, but

nutrients removal (especially phosphorous) were usually low.

The WSP, known as a robust wastewater treatment method, presented a similar behavior to WSP.

It can be an alternative to AS, however, it needs to be improved in relation to system setup to

increase its efficiency. In addition, the model requires further development to be able to describe

the real system.

Keywords: wastewater treatment, activated sludge, waste stabilization ponds; mechanistic

models, identifiability analysis.

TABLE OF CONTENTS

1 Introduction............................................................................................................................. 1

2 Literature Review ................................................................................................................... 2

2.1 Activated sludge systems .............................................................................................. 2

2.1.1 Background ............................................................................................................... 2

2.1.2 Hydraulic flow ............................................................................................................ 2

2.2 Waste Stabilization Ponds ............................................................................................. 4

2.2.1 Background ............................................................................................................... 5

2.2.2 Configurations ........................................................................................................... 5

2.3 Removal processes ....................................................................................................... 6

2.3.1 Organic Matter Removal............................................................................................ 6

2.3.2 Nitrogen Removal ...................................................................................................... 8

2.3.3 Phosphorus removal .................................................................................................. 9

2.4 Models ......................................................................................................................... 11

2.4.1 Types of models ...................................................................................................... 11

2.4.2 Activated Sludge Models ......................................................................................... 12

2.4.3 WSP modeling ......................................................................................................... 13

3 Goals and objectives ............................................................................................................ 14

4 Materials and methods ......................................................................................................... 15

4.1 Case study ................................................................................................................... 15

4.1.1 Experimental setup .................................................................................................. 15

4.1.2 Wastewater composition ......................................................................................... 16

4.2 Model Development..................................................................................................... 16

4.2.1 Activated sludge ...................................................................................................... 16

4.2.2 Waste stabilization ponds ........................................................................................ 18

4.2.3 Model implementation ............................................................................................. 20

4.2.4 Mass balance .......................................................................................................... 21

4.3 Model calibration – parameter identifiability ................................................................ 21

4.3.1 Local sensitivity analysis ......................................................................................... 22

4.3.2 Collinearity and identifiability index ......................................................................... 23

4.3.3 Parameter estimation .............................................................................................. 24

4.4 Model simulations ........................................................................................................ 24

4.4.1 Scenario analysis .................................................................................................... 24

4.4.2 Monte Carlo simulations .......................................................................................... 24

5 Results and Discussions ...................................................................................................... 26

5.1 Model development and evaluation............................................................................. 26

5.1.1 Activated sludge modeling ...................................................................................... 26

5.1.2 Waste stabilization ponds modeling ........................................................................ 30

5.2 Model calibration – parameter identifiability ................................................................ 35

5.2.1 Local sensitivity analysis for AS .............................................................................. 35

5.2.2 Collinearity and identifiability index for AS .............................................................. 37

5.2.3 Parameter estimation for AS ................................................................................... 38

5.2.4 Local sensitivity analysis for WSP ........................................................................... 40

5.3 Model simulations ........................................................................................................ 42

5.3.1 Scenarios evaluation for AS .................................................................................... 42

5.3.2 Scenarios evaluation for WSP ................................................................................. 44

5.3.3 Monte Carlo simulations .......................................................................................... 45

6 Conclusions .......................................................................................................................... 51

7 Future Research .................................................................................................................. 53

8 References ........................................................................................................................... 55

9 Appendices .......................................................................................................................... 60

A. Activated sludge model ....................................................................................................... 60

B. Waste Stabilization Pond Model......................................................................................... 67

LIST OF FIGURES

Figure 1: Completely mixed activated sludge configuration, adapted from Seviour et al. [17] ..... 3

Figure 2: Wuhrmann configuration, adapted from Seviour et al. [17] ........................................... 3

Figure 3: Four stages Bardenpho process, adapted from Barnard [21]........................................ 4

Figure 4: Processes occurring in a facultative pond [45] .............................................................. 8

Figure 5: Simplified biochemical process for PAO occurring in anaerobic and aerobic conditions.

Adapted from Wentzel et al. [56]. ................................................................................................ 10

Figure 6: Flow chart representing the main steps presented in this work ................................... 14

Figure 7: Model setup for AS in Aquasim .................................................................................... 20

Figure 8: Model setup for WSP in Aquasim ................................................................................ 20

Figure 9: Steps conducted to select a parameter subset and perform model calibration [6] ...... 22

Figure 10: Comparison of BOD and COD concentrations obtained in lab scale experiments

(represented by symbols) and modeling following ASM2d (represented by lines) for influent and

effluent. ........................................................................................................................................ 27

Figure 11: Comparison of total Kjeldahl nitrogen and total phosphorous concentrations obtained

in lab scale experiments (represented by symbols) and modeling following ASM2d (represented

by lines) for influent and effluent. ................................................................................................ 27

Figure 12: Comparison between the concentrations of substrates (SF, SA, SI and XS) in the first

compartment (a) and the second compartment (b). .................................................................... 28

Figure 13: Comparison between concentration of nitrogen-related substrates (SNH, SNO and SN2)

in first compartment (a) and second compartment (b). ............................................................... 28

Figure 14: Comparison between the concentration of SPO4 in the first (a) and the second

compartment (b). ......................................................................................................................... 29

Figure 15: Rates of aerobic (a) and anoxic (b) processes occurring in the system. ................... 29

Figure 16: Hydrolysis rates occurring in the first compartment (a) and the second compartment

(b) ................................................................................................................................................ 30

Figure 17: Comparison of BOD and COD concentrations obtained in lab scale experiments

(represented by symbols) and modeling (represented by lines) for influent and effluent in the WSP

model. .......................................................................................................................................... 31

Figure 18: Comparison of TKN and tP concentrations obtained in lab scale experiments

(represented by symbols) and modeling (represented by lines) for influent and effluent in the WSP

model. .......................................................................................................................................... 31

Figure 19: Algae growth, decay and respiration rates in facultative and maturation ponds ....... 32

Figure 20: Microbiological processes occurring in the anaerobic pond (left), observed at the outlet

of the compartment and substrate concentrations (right) measured at the same point (outlet,

x=4.6dm) ..................................................................................................................................... 33

Figure 21: Biological processes occurring in the facultative pond, showing heterotroph organisms

in aerobic conditions (a) and anoxic conditions (b). .................................................................... 34

Figure 22: Biological processes occurring in the maturation pond, showing heterotroph organisms

in aerobic conditions (a) and anoxic conditions (b). .................................................................... 34

Figure 23: Variations of the components of COD/BOD at the three different WSP compartments

(at outlet) over time ..................................................................................................................... 34

Figure 24: Organic matter concentration profiles (BOD and COD, respectively) after model

calibration .................................................................................................................................... 40

Figure 25: Total Kjeldahl nitrogen and total phosphorous concentrations profiles, respectively,

after model calibration. ................................................................................................................ 40

Figure 26: Scenarios evaluation with changes in the wastewater strength for BOD, COD, TKN

and tP. ......................................................................................................................................... 43

Figure 27: Scenarios evaluation with changes in the wastewater strength for BOD and COD,

evaluated at the system outlet. .................................................................................................... 45

Figure 28: Reference scenario for the activated sludge model and the uncertainties associated

with calibrated model represented by the 10th and 90th percentiles ............................................ 46

Figure 29: Reference scenario for the waste stabilization ponds model and the uncertainties

associated with calibrated model represented by the 10th and 90th percentiles.......................... 46

Figure 30: Scenario 1 (when the wastewater strength was increase twice) for the activated sludge

model and the uncertainties associated to calibrated model represented by the 10th and 90th

percentiles ................................................................................................................................... 47

Figure 31: Scenario 2 (when the wastewater strength was increased five times) for the activated

sludge model and the uncertainties associated with the calibrated model represented by the 10th

and 90th percentiles ..................................................................................................................... 47

Figure 32: Scenario 3 (when the wastewater strength was increased ten times) for the activated

sludge model and the uncertainties associated to calibrated model represented by the 10th and

90th percentiles ............................................................................................................................ 48

Figure 33: Scenario 4 (when the wastewater strength was increased 50 times) for the activated

sludge model and the uncertainties associated with the calibrated model represented by the 10th

and 90th percentiles ..................................................................................................................... 48

Figure 34: Cumulative distribution functions for COD and tP in the AS model, at day 6 in different

scenarios. .................................................................................................................................... 50

LIST OF TABLES

Table 1: Concentration of contaminants in raw artificial wastewater. ......................................... 16

Table 2: COD fractions and corresponding concentrations in the influent (artificial wastewater)

calculated based on Boeije et al. [76] and the experimental measurements. ............................. 16

Table 3: Initial concentrations considered in the activated sludge compartments and influent

concentrations for biomass and PAO related compounds. ......................................................... 17

Table 4: Initial conditions for ponds. ............................................................................................ 19

Table 5: Scenarios evaluated for both wastewater treatment methods in relation to wastewater

strength. ....................................................................................................................................... 24

Table 6: Root mean square errors (RMSE) calculated based on the experimental data and

simulated results for BOD, COD, total nitrogen and total phosphorous (influent and effluent) .. 26

Table 7: Root mean square errors (RMSE) calculated based on the experimental data and

simulated results for BOD, COD, TKN and tP (influent and effluent) in the WSP system .......... 32

Table 8: Parameters analyzed in the AS sensitivity, their respective values and uncertainties. 35

Table 9: Importance ranking at 𝜃𝑖𝑛𝑖 and 𝜃𝑒𝑛𝑑 for the top 30 parameters in activated sludge model

The potentially estimated parameters are indicated with an asterisk. ........................................ 36

Table 10: Selected parameter subsets formed from the potentially identifiable parameters from

the local sensitivity ranking, their collinearity index (𝛾𝐾) and identifiability index (𝜌𝐾) before (𝜃𝑖𝑛𝑖)

and after parameter estimation (𝜃𝑒𝑛𝑑) ........................................................................................ 37

Table 11: Parameters estimated from the subset with size 7. .................................................... 39

Table 12: Chi-squared test and RMSE for initial and end values (after parameter estimation) .. 39

Table 13: Parameters analyzed in the WSP sensitivity, their respective values and uncertainties.

..................................................................................................................................................... 41

Table 14: Importance ranking at 𝜃𝑖𝑛𝑖 for the top 30 parameters in WSP model. The potentially

estimated parameters are indicated with an asterisk. ................................................................. 41

Table 15: Activated sludge matrix, showing stoichiometric coefficients for all processes (first

column) and components (first row) and COD conversion factors (last rows). ........................... 60

Table 16: Processes listed in AS model and respective kinetic rate expressions. ..................... 62

Table 17: Typical values AS for stoichiometric and kinetic coefficients ...................................... 63

Table 18: Mass balance for heterotrophs with respect to COD, nitrogen and phosphorous in the

AS model ..................................................................................................................................... 65

Table 19: Mass balance for autotrophs with respect to COD, nitrogen and phosphorous in the AS

model ........................................................................................................................................... 66

Table 20: Mass balance for PAO with respect to COD, nitrogen and phosphorous in the AS model

..................................................................................................................................................... 66

Table 21: Matrix for the anaerobic pond, first pond composing the WSP system, showing

stoichiometric coefficients for all processes (first column) and components (first row) and COD

conversion factors (last rows). ..................................................................................................... 67

Table 22: Aerobic, anoxic and decay processes occurring in the facultative and maturation ponds

(second and third ponds respectively in the WSP system). ........................................................ 67

Table 23: Phosphorous chemical processes precipitation and redissolution occurring in facultative

and maturation ponds .................................................................................................................. 68

Table 24: Processes listed in WSP model referring to anaerobic, aerobic, anoxic and phosphorous

processes and their kinetic rate expressions .............................................................................. 69

Table 25: Typical values for stoichiometric and kinetic coefficients related to WSPs. ................ 70

Table 26: Mass balance for anaerobic processes occurring in anaerobic ponds ....................... 72

Table 27: Mass balance for aerobic, anoxic and decay processes occurring in the

facultative/maturation ponds ....................................................................................................... 73

Table 28: Mass balance for phosphorous precipitation and redissolution .................................. 75

LIST OF ABBREVIATIONS

AB Autotrophic bacteria

ADM1 Anaerobic Digestion Model No. 1

AMB Acetotrophic methanogenic bacteria

ANO Ammonia oxidizing organisms

AS Activated sludge

ASM Activated Sludge Model

BOD Biochemical oxygen demand

CFD Computational fluid dynamics

C:N:P Carbon:Nitrogen:Phosphorous ratio

COD Chemical oxygen demand

CWM1 Constructed Wetland Model No. 1

DO Dissolved oxygen

EBPR Enhanced biological phosphorus removal

FB Fermenting bacteria

F/M Food to microorganisms ratio

GAO Glycogen accumulating organisms

HB Heterotrophic bacteria

HMB Hydrogenotrophic methanogenic bacteria

HRT Hydraulic retention time

IWA International Water Association

L:D cycle Light:dark cycle

LHS Latin hypercube sampling

L:W:H Length:width:height

MC Monte Carlo

NNO Nitrite oxidizing organisms

OECD Organisation for Economic Co-operation and Development

OM Organic matter

P Phosphorous

PAO Phosphorous accumulating organisms

PHA Poly-ß-hydroxyalkanoates

RMSE Root-mean-square deviation

RWQM1 River Water Quality Model No. 1

SRB Sulfate-reducing bacteria

TKN Total Kjeldahl nitrogen

tP Total phosphorous

TSS Total suspended solids

VFA Volatile fatty acid

WSP Waste stabilization pond

WW Wastewater

WWTP Wastewater treatment plant

LIST OF SYMBOLS

Symbol Name Unit

Soluble compounds (S)

SF Fermentable, readily biodegradable organic substrates

concentration g COD.m-3

SA Fermentation products concentration (considered to be acetate) g COD.m-3

SNH Soluble ammonium plus ammonia nitrogen concentration g N.m-3

SNO Soluble nitrate plus nitrite nitrogen concentration g N.m-3

SN2 Dinitrogen concentration g N.m-3

SO2 Dissolved oxygen concentration g O2.m-3

SPO4 Inorganic soluble phosphorus concentration g P.m-3

SCH4 Methane concentration g COD.m-3

SH2 Hydrogen concentration g COD.m-3

SI Inert soluble organic matter concentration g COD.m-3

SALK Alkalinity concentration mol HCO3.m-3

Particulate compounds (X)

XA Nitrifying organisms (autotrophs) concentration g COD.m-3

XH Heterotrophic organisms concentration g COD.m-3

XI Inert particulate organic material concentration g COD.m-3

XPAO Phosphate-accumulating organisms concentration g COD.m-3

XMeOH Metal-hydroxydes concentration g Ca(OH)2.m-3

XMeP Metal-phosphate (MePO4) concentration g TSS.m-3

XPP Poly-phosphate concentration g P.m-3

XTSS Total suspended solids concentration g TSS.m-3

XS Slowly biodegradable substrate concentration g COD.m-3

XALG Algae concentration g COD.m-3

XFB Fermenting bacteria concentration g COD.m-3

XAMB Acetotrophic methanogenic bacteria concentration g COD.m-3

XHMB Hydrogenotrophic methanogenic bacteria concentration g COD.m-3

η Correction factor for bacteria under anoxic conditions -

ρj Process rates g COD.m-3.d-1

1

1 INTRODUCTION

The demand for high quality water is continuously increasing. In 2015, 884 million people still had

no access to safe water [7] and 2.3 billion lack of basic sanitation [8], which plays a crucial role in

human health. It is estimated that, by 2025, half of the world population will be living in areas with

water scarcity [7]. All these facts contribute accelerating the search for alternative water sources

and treatment methods.

Municipal wastewater treatment is usually performed by activated sludge (AS), a conventional

biological process, capable of removing organic matter and nutrients. Despite its extensive use,

the AS system is not the most sustainable method due to its high energy consumption and low

energy recovery, resulting in high costs and environmental footprint [1].

Natural methods, such as waste stabilization ponds (WSP), are gaining attention due to their

advantages: lower operating costs, good effluent quality and removal of pathogens.

Waste stabilization ponds compose a natural wastewater treatment method, which counts on

biological processes for water purification. Only sunlight is necessary to the operation, avoiding

any need for external energy since the processes happening in ponds would occur in a natural

water body [9]. Their robustness, due to their long retention time, makes them resilient in respect

to both organic and hydraulic shock loads. In addition, simple operation and lower costs make the

WSP an interesting method, applied not only in tropical countries but also in European countries,

such as France and Germany [9].

The wastewater systems are subject to variations in flow, load and composition of pollutants. This

dynamic behavior, coupled with microbiological activity and interactions, imposes difficulties to

monitor, control and predict the systems. Thereby, mathematical models become powerful tools

to describe, in a simpler way, what happens in the real system.

The objective of this study is, first, develop mathematical models to describe the behavior of these

two different wastewater methods: activated sludge and waste stabilization ponds. They follow

lab-scale experiments carried out previously and are constructed based on the well-established

model ASM2d [2] for AS and different methodologies presented in the literature for WSP.

Therefore, the model fitness to observed data (from experimental phase carried out previously)

is evaluated and improved by means of calibration. The models also allow an overview of systems

behavior in respect to microbial activity and other situations (i.e. different wastewater pollutants

concentrations), comparing both treatment methods.

The basic knowledge to understand both treatment methods and that serves as a theoretical base

for model development, is given in a brief literature review. Materials and methods section

elucidates model development, calibration and evaluation through proposed scenarios. The next

section presents the results obtained in the study and a discussion about systems’ performance,

model evaluation and their efficiency in different wastewater strengths. Finally, conclusions and

recommendations for future research are presented in the last two sections.

2

2 LITERATURE REVIEW

2.1 Activated sludge systems

2.1.1 Background

Activated sludge, a biological method to treat wastewater, was first developed in England by

Lockett and Arden in 1914. The authors noticed that by saving the solid sludge flocs produced

after the aeration of the sewage and then recirculated it into the aerated system, a cleaner effluent

was able to be produced. Since then, this method is continuously being improved to increase its

efficiency. The activated sludge rapidly gained popularity and nowadays is one of the most known

and worldwide used wastewater treatment method [10,11]. At the beginning, only BOD and TSS

removal was achieved, however, in the 1960s, the nitrogen removal was implemented, followed

by phosphorous removal in the 1970s. The most recent developments are focused on reducing

the reactor volume, energy use and site footprint [12].

The conventional activated sludge system is composed of biological sludge containing living

microorganisms mixed with wastewater and aerated in a reactor, forming a mixed liquor. An

association of bacteria, yeast, fungi, protozoa and higher organisms such as rotifiers composes

this microbial population. In addition, dead cells and cell debris are a significant part of the sludge

[13].

A number of factors can affect the activated sludge system performance. Recirculation and sludge

waste rates, temperature, oxygen levels, organic load, pH, aeration time and toxicity are some of

the factors that influence the system [14].

2.1.2 Hydraulic flow

There are several variations for the reactor design regards the wastewater flow. In a complete-

mix reactor, which has usually round or square dimensions, the fluid particles entering the reactor

are uniformly and instantaneously mixed throughout the reactor. The concentrations are the same

in all reactor and there is a higher resistance to overloads and toxic substances. In the plug flow

reactor (predominantly longitudinal), the fluid particles pass through the reactor with little or no

mixing and leave the reactor in the same sequence in which they entered. The demand for oxygen

decreases along the reactor, the sludge produced has better settleability, but is less resistant to

higher loads [15,16] .

However, flow behavior is not always ideal. Some factors such as temperature difference (when

the water entering the reactor is colder or warmer than water already present), inadequate mixing,

poor reactor design, axial dispersion in plug flow reactors, can lead to a non-ideal flow, causing

short circuits and dead zones [16].

3

2.1.2.1 Configurations

2.1.2.2 Conventional Activated Sludge

The standard activated sludge systems are usually composed of an aeration tank and a clarifier

(Figure 1). In the aeration tank, a completely mixed system, compressed air is injected

continuously and distributed by porous diffusers at the bottom of the tank or mechanical aerators

at the surface [4]. The aeration supplies the oxygen to the aerobic organisms, provides mixing

and adequate contact between flocs and incoming wastewater. The microorganisms grow using

the organics as source of food and cling together forming flocs. In the clarifier, the sludge is

allowed to settle, so the microbial flocs produced in the aeration tank are separated from the

treated wastewater. A portion of the sludge is recycled back to the aeration basin and the

remaining is discarded to keep an adequate food to microorganisms (F/M) ratio [5].

Figure 1: Completely mixed activated sludge configuration, adapted from Seviour et al. [17]

2.1.2.3 Wuhrmann Configuration

Referring to nutrients removal, a number of configurations were developed. One of the first single

sludge systems presented, known as Wuhrmann system, is composed of two reactors (Figure 2).

The wastewater enters the aerobic basin, where heterotrophic and nitrifying organisms grow,

promoting organic matter removal and nitrification. Then, in the second reactor (unaerated and

mixed), also called post denitrification reactor, the denitrification occurs. Afterwards, the mixed

liquor goes to the settler and is recirculated to the first aerobic tank [18]. Since most organic matter

is already consumed in the aerobic tank, the energy provided for the denitrification process comes

most from endogenous death and lysis of biomass, causing low denitrification rates [17].

Figure 2: Wuhrmann configuration, adapted from Seviour et al. [17]

4

2.1.2.4 Ludzack-Ettinger Configuration

The pre-denitrification system, proposed by Ludzack and Ettinger [19] is composed of two

reactors. The first one operates in anoxic conditions, and the second one, in aerobic. The mixed

liquor containing nitrate formed in the second reactor in the nitrification process is returned to the

first one. The sludge collected in the settler after the reactors is also recirculated. The main

disadvantage of this system is that a fraction of nitrate is discharged from the settler without

passing through the anoxic reactor.

2.1.2.5 Bardenpho Configuration

In South Africa, the Bardenpho configuration was proposed to achieve lower effluent nitrate

concentrations and phosphorous removal. This process is composed of four reactors, as shown

in Figure 3. The denitrification process occurs in the first basin, an unaerated mixed tank, which

receives nitrified mixed liquor recirculated from the second basin. The third basin removes the

remaining nitrate by endogenous respiration. And in the fourth basin, the dissolved oxygen levels

increase in order to avoid denitrification in the clarifier [20].

Figure 3: Four stages Bardenpho process, adapted from Barnard [21]

Based on the Bardenpho system, a five-stage system (known as Phoredox) was developed. An

anaerobic basin is added before the four reactors, thus it receives the influent flow and the sludge

recycle from the settling tank and allows a reliable phosphorous removal [21]. Most plants today

that have phosphorous biological removal systems are based on this five-stage configuration [22].

2.2 Waste Stabilization Ponds

Waste stabilization pounds (WSP) are simply impoundments into which the wastewater flows and

stay for a relatively long period of time. This treatment method has been used for over 3000 years.

In California, the United States, the value of ponds for this purpose was first accidentally

discovered in 1924, when a gravel bed used for filtering was clogged and it formed an

impoundment [23]. Nowadays, the stabilization ponds serve from small rural communities, such

as in France and Canada, to large urban centers in different countries, including Turkey, Australia,

New Zealand and Latin America [24,25].

5

2.2.1 Background

The waste stabilization ponds are simple for construction and operation with low cost. The natural

processes occurring in the water body need only sunlight as energy source for operation. From

most of previous studies, the treatment efficiency is optimized by selecting the appropriate

parameters, such as retention times, pond depth and organic loading. Additionally, the long

retention times allows fluctuating hydraulic loads without biomass washout. The system is ideally

applied in locations such as summer touristic places, where the higher temperatures allow

increased organic loadings [9]. However, the stabilization ponds are used in temperate climate

countries, like in France (more than 2500 WSP systems) and in Germany (more than 3000) [26].

However, in the pond systems, large areas are required compared to conventional treatment and

the effluent can have high BOD and suspended solids concentration due to the high amount of

algae. Other problems like ground water contamination, mosquito breeding and odor can be

avoided with well-designed and properly maintained waste stabilized ponds [9,25].

2.2.2 Configurations

Typical WSP systems are composed of different types of ponds, classified accordingly to their

biological activity.

2.2.2.1 Anaerobic ponds

The anaerobic ponds are aimed to remove organic matter (with efficiency around 50 to 70%) [27]

and usually receive the effluent for the first biological treatment. The anaerobic environment does

not allow significant algae population. These ponds are usually deeper due to sludge

accumulation. The main function is to remove BOD in a relative short retention time of few days.

Organic matter is removed by the sedimentation of settable solids, and anaerobic digestion in the

sludge layer [28].

Considering the effects on climate change, a disadvantage of anaerobic pond systems is the

emission of greenhouse gases (CH4, CO2 and N2O), which in ponds are normally released to the

atmosphere since the areas are open and need sunlight and wind to operate [29]. The methane

gas is generated by methanogen organisms in the anaerobic decomposition process, in

temperatures above 15°C. In lower temperatures, they are not active and the pond works as a

sedimentation tank. In addition, high organic loads contribute to CH4 generation. Correct sludge

management and aeration can contribute to reduce emissions [30]. However, some covered

anaerobic ponds are being developed with effective wastewater treatment and biogas production

[31].

2.2.2.2 Facultative ponds

Facultative ponds are widely used since their operation is considered simple. They usually receive

settled wastewater from an anaerobic pond and their main purpose is to reduce BOD and

6

suspended solids. The facultative pond is composed at the bottom by an anaerobic sludge layer,

followed upwards by an anoxic zone. The upper layers are oxygenated by algae. To assure an

efficient photosynthesis process, larger surface areas are required, compared to the other pond

types [32,33].

Around 50 cm depth, in the anoxic but illuminated zones, the purple and green sulfur bacteria are

found. In absence of oxygen, they perform anoxygenic photosynthesis and obtain energy by

reducing inorganic compounds, as for example H2S produced by sulfur reducing bacteria [24]. In

the process, the sulfide is oxidized to elemental sulfur and, for green bacteria, it is deposited

outside the cells and, for purple bacteria, inside the cells. Since these bacteria oxidize H2S, they

have an important role in odor filtration and protecting algae from photosynthetic inhibition by

sulfides [34].

2.2.2.3 Maturation ponds

Maturation ponds are well oxygenated and have a mainly function the removal of pathogens. The

biological disinfection mechanisms for most fecal bacteria and viruses are related to light, pH and

oxygen [35]. The photosynthesis performed by algae removes the dissolved CO2 from the water,

more rapidly than it can be replaced. It causes a shift in the carbonate-bicarbonate equilibrium to

produce CO2 and hydroxyl ions, which increase the pH and promotes disinfection [34]. A pH

higher than 8 is considered effective in the disinfection process [36].

In addition, solar radiation contributes significantly to disinfection through different mechanisms

that can simultaneously occur in WSP. The UVB radiation affects bacteria through the photo-

biological DNA damage, as for example E. Coli, causing DNA damage. Bacteria and viruses are

inactivated by the photo-oxidative damage process, where endogenous photosensitizers (DNA

or other cell constituents) absorb short wavelengths and react with oxygen to form highly reactive

photo-oxidizing species, damaging internal structures [37]. Enterococci, for instance, are

inactivated by a wider range of wavelengths in the process of photo-oxidative damage to external

structures (UV and blue-green visible photons are absorbed by humic materials, producing

phototoxic species such as singlet oxygen, which damages the cell membrane). Therefore,

dissolved oxygen levels contribute to the effect of photo-oxidation mechanism [38].

2.3 Removal processes

2.3.1 Organic Matter Removal

The organic matter presenting in domestic wastewater occurs in soluble, colloidal or particulate

forms. The C:N:P ratio is usually around 100:5:1, which is adequate for a wide variety of

organisms. It can be divided in constituents such as carbohydrates, proteins, lipids, organic acids

and other substances and is traditionally described in terms of BOD or COD [39].

7

In activated sludge systems and waste stabilization ponds, organic matter oxidation of easily,

soluble biodegradable material is mainly performed by heterotrophic bacteria. First, the organic

matter is transferred from the water to the microorganisms. The soluble particles are directly

absorbed by the cell wall and colloidal and particulate matter are broken down into simpler soluble

forms before absorbed. Then, it is converted to cell matter by following two pathways: oxidation

or synthesis. Oxidation of organic matter provides energy for the microorganisms’ metabolic

processes, producing CO2, which is vented to the atmosphere. Synthesis is the incorporation of

organic matter into the cell mass, contributing to sludge production [13,40]. As the sludge floc

size increases and the oxygen level inside flocs is limited by diffusion, anaerobic bacteria develop

in the inner region [41].

Furthermore, higher organisms, such as protozoa and rotifers, prey on bacteria and consume

larger solid particles and loose suspended material, contributing to a clear effluent [14].

Residual organic matter, which is not easily biodegradable, is usually treated in absence of

oxygen, such as in anaerobic ponds or anaerobic digesters. Hydrolytic bacteria releases enzymes

that contribute to the hydrolysis of complex polymeric molecules [15]. Sugars, carbohydrates,

starches and other complex compounds are converted to volatile acids, carbon dioxide and

hydrogen sulfide. Simpler soluble compounds (short chain fatty acids, glycerol, peptides, mono

and disaccharides) are converted by acidogenic and acetogenic bacteria. Thus, acetate,

hydrogen, carbon dioxide and other intermediate products generated in the previous step serve

as substrate for methanogenesis [42]. Therefore, obligated hydrogen-producing acetogenic

bacteria ferment fatty acids, ethanol and lactate to acetate and methanogenic bacteria consume

carbon dioxide and hydrogen, generating methane [43].

In addition, another type of obligatory anaerobic bacteria is the sulfate-reducing bacteria (SRB).

These bacteria use sulfate as electron donor and reduces a wide range of substrate (volatile fatty

acids, methanol, ethanol, several phenol and aromatic acids) or hydrogen, producing H2S in the

process, which is important in ponds [15]. Their growth is also stimulated by excess sulfate and

organic material. In alkaline or acidic conditions, since methanogenic bacteria are pH-sensitive,

the SRB will proliferate [34].

In facultative ponds, BOD removal is performed by a combination of aerobic, anaerobic and

facultative microorganisms (summarized in Figure 4). In aerobic conditions, a wide range of

aerobic heterotrophic bacteria is found. It is assumed that the organic matter degradation in

pounds occur in a similar way as in other biological sewage treatments, even though the biomass

concentrations are much lower when compared to activated sludge, for example. For this reason,

a longer retention time is required to achieve an effective removal. The aerobic bacteria utilize

the oxygen produced by algal photosynthesis in the organic matter decomposition. The algae also

benefit from the carbon dioxide produced by bacterial respiration, released nutrients and aerobic

metabolism end products to perform photosynthesis and fix carbon for growth, characterizing a

mutualistic relationship [43,44].

8

Figure 4: Processes occurring in a facultative pond [45]

In anoxic conditions, heterotrophic denitrifiers oxidize organic matter and reduce nitrate,

contributing to organic matter removal. This type of bacteria are sensitive and not always present

in ponds due to variations in dissolved oxygen, temperature and pH [46].

2.3.2 Nitrogen Removal

Nitrogen in wastewater usually is present in form of ammonia, ammonium, nitrite and nitrate. The

main sources of nitrogen in fresh wastewater are proteins and urea, organic forms which are

quickly decomposed to ammonia [16].

In wastewater systems, nitrification is one of the most important biological nitrogen removal

processes. It is performed by chemical autotrophic nitrifying organisms, which are slow growers

and use carbon in the form of carbon dioxide to perform cell growth and obtain energy by oxidizing

ammonia and nitrite, using oxygen as an electron acceptor [14,47]. It takes place in two sequential

steps: first, ammonia oxidizing organisms (ANO) convert free and saline ammonia to nitrite

(Equation 1) and then, nitrite oxidizing organisms (NNO) convert nitrite to nitrate (Equation 2).

These oxidizing processes are responsible for obtain energy for biomass synthesis and, for this

reason, they have much lower biomass growth coefficients when compared to ordinary

heterotroph organisms [47].

𝑁𝐻4+ +

3

2𝑂2 (𝐴𝑁𝑂𝑠) → 𝑁𝑂2

− + 𝐻2𝑂 + 2𝐻+ (Equation 1)

𝑁𝑂2 +1

2𝑂2 (𝑁𝑁𝑂𝑠) → 𝑁𝑂3

− (Equation 2)

To perform effective nitrification, the nitrifiers depend on sufficient oxygen and suitable pH. These

organisms require 4.57mg of oxygen, 7.14mg of alkalinity as calcium carbonate for each 1.0mg

of nitrate-nitrogen formed [48].

Denitrification is the reduction of nitrate-nitrogen to nitrogen gas and is performed in anoxic

conditions by a wide range of bacteria. Denitrifiers are facultative heterotrophic organisms and

9

use nitrate as electron acceptor and organic carbon compounds as nutrient source [49]. They

have higher yield and can grow quickly than autotrophic organisms due to lower energy

requirements for synthesis [48]. Alkalinity (as calcium carbonate) produced for each 1.0mg of

nitrate-nitrogen removed is about 3.57mg, so part of the alkalinity consumed in nitrification is

recovered during denitrification [16]. If necessary, the carbon can be supplemented with methanol

or other fermentation products in order to achieve low nitrogen concentrations in effluent [50].

In AS treatments, if the reactor is kept aerobic, the mixed liquor will flow to the settling tank and

denitrification will occur as soon as the oxygen is depleted. As result, nitrogen bubbles will be

formed and rise to the liquid surface, lifting sludge flocs. It may cause high concentrations of

suspended solids and organic matter in effluent. Furthermore, the sludge loss can lead to wash

out of the nitrifiers [18].

In stabilization ponds, nitrogen goes under different transformation processes, such as the

previously mentioned nitrification and denitrification processes, but also volatilization,

sedimentation, uptake by microorganisms and mineralization of organic nitrogen [51]. Ammonia

volatilization or stripping is the most important process, in which ammonium hydroxide ions are

converted to ammonia gas at high pH. In facultative and maturation ponds, the photosynthesis

process consumes CO2, increasing pH and providing conditions for ammonia stripping [32].

Regarding other removal processes, around 10-20% of nitrogen is lost through assimilation by

algae. In this process, the bacteria consumes organic waste, produces biomass and releases

carbon dioxide and organic nutrients. The algae uses the carbon dioxide in the photosynthesis

and assimilates the nutrients into its biomass, releasing oxygen. For the assimilation, nitrate and

nitrite must be first reduced to ammoniacal-N due to greater energy requirements for nitrate

reduction in comparison to ammoniacal-N assimilation [46]. Other nitrogen mechanisms also

occur in the ponds, however, are less significant.

However, accordingly to Lai and Lam [52], the nitrogen removal by nitrification-denitrification

biological process can be important if some conditions are met. When algae presence is high and

retention time is long enough, the oxygen produced during the day allows nitrification. At night,

the oxygen levels have to drop sufficiently low, so the denitrification can occur. The process, like

in the activated sludge systems, is performed by nitrifying bacteria in aerobic zones and then

denitrifying bacteria in anoxic conditions. Although, the nitrifiers are not always easily found in

ponds, which limits the process. They have a slow growth and need attachment surfaces to grow.

When not inhibited by algae, they are present in aerobic surface water; therefore, they may be

easily washed out from the pond and are outcompeted by faster growing heterotrophic bacteria

[53].

2.3.3 Phosphorus removal

Phosphorous is a limiting nutrient to the growth of plants, algae and cyanobacteria, yet a main

cause of eutrophication in water bodies. The nutrient inputs in rivers and lakes substantially

10

increased in the recent years, caused by discharge of domestic waste, detergents containing

phosphate and agricultural fertilizers [54].

To avoid the disturbances caused by high phosphorus levels in waterbodies, the wastewater

should be treated before discharge. In order to do so, chemical and biological treatments, such

as precipitation and enhanced biological phosphorus removal (EBPR), are widely used. When a

high degree of phosphorus removal is required, other processes are necessary. For instance,

chemical treatment with phosphate precipitation in the presence of aluminum (Al3+), calcium

(Ca2+), and iron (Fe3+) ions [55].

To remove phosphorus biologically in the activated sludge system, it is necessary, first, to convert

it to the solid phase in order to remove it from the sludge. In the EBPR, the conversion from

soluble phosphate to particulate form of polyphosphate is performed, basically, through the

growth of the phosphorus accumulating organisms (PAO) using excess phosphate present in

wastewater [56].

Under anaerobic conditions (Figure 5, left side), the PAO can uptake and internally store acetate

and other volatile fatty acids (VFAs). Then, the VFAs are linked together during the synthesis of

poly-ß-hydroxyalkanoates (PHAs), as stored energy source. This degradation process releases

orthophosphate into the bulk liquid. Furthermore, in anaerobic conditions, heterotrophic

organisms (facultative acidogenic fermentation) are stimulated to convert fermentable COD to

VFAs and the PAOs usually do not have to compete for substrate [22,56].

In aerobic conditions (or anoxic, if nitrate is present), the PAOs are able to oxidize the stored PHA

for growth, recover glycogen consumed during the anaerobic phase, uptake phosphorous and

store as polyphosphate (processes summarized in Figure 5, right side). Consequently, the

activated sludge has a high polyphosphate content, then the net phosphorous removal is

performed through the elimination of the sludge [57].

Figure 5: Simplified biochemical process for PAO occurring in anaerobic and aerobic conditions. Adapted from Wentzel et al. [56].

However, the EBPR systems are significantly unreliable and tend to have a deterioration in

performance. The high sensitivity to various system parameters, including hydraulic retention

11

time, sludge retention time, pH, temperature, COD:P ratio and others factors lead to decrease the

process efficiency [58]. The competition of PAO with glycogen accumulating organisms (GAO) is

another factor that decreases the phosphorous removal. These organisms can proliferate in the

same environments as PAO, compete for the same substrate, but do not perform phosphorous

removal [57].

After removing phosphorous from the wastewater, recycling it as a fertilizer in agriculture is an

alternative. In order to do so, phosphorus has to be separated from the other waste components.

Some techniques using struvite (ammonium-magnesium-phosphate) and hydroxyapatite

combined with biological removal allow the recovery from the wastewater [59].

In stabilization ponds, the biological phosphorus removal occurs mainly by microalgae uptake,

thus the organic phosphorus is accumulated in algal biomass. The process depends on amount

of phosphorus that can be accumulated and the algal solids concentration. The temperature also

contributes to the removal, indicating that warmer conditions are favorable. For the phosphorous

removal of the system, the algae need to be harvested from the pond [25]. The phosphorous

present in the non-biodegradable fraction of algal cells stays in the sediments. For this reason, it

is interesting to increase the number of maturation ponds in order to immobilize more

phosphorous in sediments [6].

At high pH levels (higher than 8.2), the phosphates precipitates as inorganic phosphorous, bindind

to cations (Ca2+, Mg2+, Al3+, Fe3+). This process depends on temperature, cations and phosphate

concentration. Ponds with the necessary conditions can have precipitation as the main

phosphorous removal, instead of P assimilation and sedimentation [18].

2.4 Models

In wastewater treatment, models are a powerful tool to evaluate and optimize the performance of

treatment systems under different conditions [60]. Changes in waste load, flow and other

parameters, for example, can be easily evaluated using models, what is important for

development and optimization of wastewater treatment systems. In addition, it is especially useful

for organic matter and nutrients removal, which involves a large number of parameters and

interactions [61].

2.4.1 Types of models

Empirical models, which are usually expressed by statistically fitting equations, are based on

relationships originated from observational data (e.g. an algebraic equation representing the

chlorophyll and phosphorous concentrations in a lake) [62]. The simplicity and minimal data

requirement are the main advantages. Although, they may have a limited use, since the

application outside boundaries in which the models were developed can result in large standard

errors for prediction [62]. In wastewater treatment context, this approach is focused only on the

12

influent and effluent characteristics which does not take into account the processes occurring

inside reactors [63].

On the other hand, process-driven models are based on mathematical formulation to describe

system dynamics (e.g. chemistry, mass and conservation laws) [64]. They are more reliable and

can be applied outside the boundaries in which the model was developed. Their complexity

depends on the degree of process understanding. The calibration is necessary and needs data

to be performed, what can be time and cost consuming. In addition, the correct model selection

and operation are not always simple and may be a disadvantage in mechanistic models [61].

2.4.2 Activated Sludge Models

Activated Sludge Models (ASM) were first developed by the University of Cape Town in the 1970s,

incorporating oxygen consumption, carbon degradation, nitrification and denitrification reactions

for a steady state. Additionally, the fractionation of substrate was already incorporated in the

model as readily biodegradable and slowly biodegradable substrate, which is still present in the

current used models [65].

The ASMs established a common language in wastewater modeling. The presentation format

allowed further research and development, also for operational matters [2,66]. The matrix

notation, known as Gujer Matrix, is used to show all the interactions in a comprehensive way and

allows seeing the impact of all listed conversion processes on all components. This notation and

symbols commonly adopted were first described by Grau et al. [67] and standardized by IWA [60].

In the matrix, an index “i” is assigned to the components, listed at the top row (e.g. dissolved

oxygen concentration, heterotrophs concentration) and “j” is assigned to the processes listed at

the leftmost column (e.g. autotrophs growth, denitrification). The process rates are denoted as

“ρj” and are described using Monod based expressions for biomass growth or first order equations

for decay [2]. The stoichiometric coefficients (νij) within the matrix describe the mass relationship

between components in each process. All the organic compounds are expressed as equivalent

chemical oxygen demand (COD) [2].

The International Water Association (IWA) created a task group in 1982 in order to establish a

common framework and guidelines to future activated sludge models containing nitrogen removal

processes. In 1987, the Activated Sludge Model No. 1 (ASM1) was presented. It was based on

previous works and was focused on organic matter and nitrogen removal for municipal

wastewater treatment, containing 42 parameters [61]. The chemical and biological phosphorus

removal was introduced in the ASM2, published in 1995, increasing the AS models complexity

and summing up 127 parameters [65].

Both ASM models consider the wastewater divided in fractions (for instance, fractions of organic

matter, biomass, nutrients). Other models, like the Activated Sludge Model No. 3 and the TU Delft

EBPR, have a higher complexity level and a more detailed approach, including metabolic

processes and routes [63].

13

The relevant kinetics and stoichiometric processes involved in the activated sludge models are

characterized through equations and mass balance for each process. However, simplifications

assumed in the models may lead to errors. In the ASM1, for example, pH, temperature and

coefficient for nitrification are assumed to be constant, the nutrient limitation is not taken into

account and the biomass is considered homogeneous [61].

2.4.3 WSP modeling

WSP modeling started in the early 1990s, with simple models focused on water quality, followed

by more complex approaches, including also hydraulics, biological, physical and chemical

processes [68].

At first, waste stabilization ponds were designed and operated based on rules of thumb. According

to Shilton and Mara [69], first order reaction rate coefficients (k) were implemented to WSP as

first forms of modeling, which represent the effect of many physical, chemical and biological

processes. For instance, a model developed by Fritz et al. [70] used twelve mass balance

equations of biomass and biochemical variables in a non-steady-state mechanistic model for a

facultative pond [69]. Typically, pathogen and BOD removals are assumed to follow the first order

kinetics and within a large number of equations to estimate the “k” coefficient for these

parameters.

Later, hydraulic behavior was incorporated in WSP models. Computer development allowed

software application such as computational fluid dynamics (CFD). In 1995, Wood et al. [71]

published a study using modeling using CFD but limited to a two-dimensional flow. Some following

works included three-dimensional CFD models and turbulence. In recent years, integrated models

including hydraulics and first order kinetics were developed. It allowed a better understanding and

optimization, for instance, of coliforms decay in different hydraulic configurations [69].

Despite the simplicity of WSP operation and the ongoing research about the method, the

processes occurring in ponds are still not fully understood. Hence, the models developed so far

do not completely describe the complex interactions and processes occurring in the ponds.

Additionally, the simplification of some parameters and processes that deviate from the reality

may cause inconsistencies in WSP modeling. Dead zones, short circuiting, wind mixing and the

effect on temperature and dissolved oxygen concentrations are some factors not considered in

steady-state models, however, can have significant effects [68].

The ASM approach is also being incorporated into the new WSP models due to its advantages

[68]. As an example, the model proposed by Sah et al. [72] for a facultative pond is based on the

ASM concept, giving a more realistic view of the process and performance when compared to

first-order models.

14

3 GOALS AND OBJECTIVES

As the first goal of this study, two mathematical models were constructed to evaluate the resiliency

capacity and removal efficiency of conventional and natural wastewater treatment systems. They

were based on well-stablished models from literature: including the Activated Sludge Model No.

2d (ASM2d) and the River Water Quality Model No. 1 (RWQM1). These models were designed

to fit lab-scale experiments carried out previously. The full description of these models can be

found in Section 4 (Materials and Methods).

Some specific objectives are outlined for an enhanced understanding and application of these

models:

Calibrate the models based on identifiability of the parameters that compose the model

and using experimental data;

Making use of the calibrated models, assess proposed scenarios for the different

wastewater strengths;

Evaluate the prior uncertainties in each proposed scenario by applying a probabilistic

Monte Carlo engine associated with the deterministic models.

In summary, the main steps that compose this work can be represented in a flow chart (Figure 6).

Figure 6: Flow chart representing the main steps presented in this work

15

4 MATERIALS AND METHODS

This section describes two mechanistic models, which were built to simulate two systems,

conventional activated sludge and waste stabilization ponds. The activated sludge model was

based on the well-established ASM2d [2] and the latter, constructed based on parts from different

methodologies found in the literature.

The full description of the experimental part, which was the base for the model development, is

described in Section 4.1. The description of developed models, which were built using the

AQUASIM software [73], are given in Section 4.2. Model calibration procedures, performed after

model development, are shown in Section 4.3 and, finally, simulations and proposed scenarios

are described in Section 4.4.

4.1 Case study

4.1.1 Experimental setup

A set of experiments were carried out previously by Panayiotis [74] in order to obtain data and

allow the models calibration. The OECD artificial wastewater was treated in the AS and WSP

systems during a stabilization period (considered as reference conditions) and, after that, a

disturbance was applied.

For the activated sludge system, two different compartments (volume of three liters each,

dimension 24.5 cm x 14.5 cm x 8.5 cm (L:W:H)) were installed using the Wuhrmann configuration:

an aerobic tank followed by an anoxic tank. Oxygen was provided only into the first tank to keep

dissolved oxygen (DO) concentration constant (4 mg O2.L-1). Both tanks were mixed by magnetic

stirrers in order to keep sludge in suspension. A settling tank allowed collecting the treated

wastewater and settled sludge. The influent was supplied with a flow of 3.4 L.d-1, resulting in a

hydraulic retention time of around 1 day for each tank. The sludge was recirculated twice per day

to the aerobic tank.

The waste stabilization pond experimental setup was composed of three compartments in series:

an anaerobic, a facultative and a maturation pond. The anaerobic pond was set in a cylindrical

container (base diameter 0.2 m and a total height of 1 m) and inoculated with anaerobic sludge.

The following ponds (facultative and maturation) were installed in plastic aquaria (dimension 37

cm x 20 cm x 20 cm (L:W:H)), and inoculated with a consortium of microalgae. The system was

also fed with an average flow of 3.4 L.d-1, resulting in an HRT of around 12 days in total.

Both systems were set up in triplicates at a constant temperature of 21 (±2)oC. The disturbances

were evaluated during a month. For eight days, the system was initially exposed to the standard

OECD wastewater. It was followed by a five-day period of a high strength artificial wastewater

(concentration was tripled), then for 17 days fed with regular wastewater. However, the first 6

days were not taken into account due to the initial instability of the system. The different

16

wastewater strengths allowed the evaluation of system resiliency, buffering capacity and

treatment efficiency with regard to BOD5, COD, total Kjeldahl nitrogen (TKN) and total

phosphorous (tP).

4.1.2 Wastewater composition

The wastewater used in the experimental phase was based on the OECD guidelines [75].

Concentrations of contaminants present in influent (obtained experimentally [74]) are shown in

Table 1.

Table 1: Concentration of contaminants in raw artificial wastewater.

Contaminant Concentration

BOD5 150 g BOD m-3

COD 275 g COD m-3

Total Kjeldahl nitrogen 40 g N m-3

Total phosphorous 7 g P m-3

According to Boeije et al. [76], due to the OECD artificial wastewater recipe, the main part is

composed of particulate components XS, which accounts for the easily accessible colloidal

peptone and meat extract used in the wastewater preparation. The remaining part is composed

of soluble fermentation substrate (SF). Following this definition, Table 2 summarizes the

wastewater composition expressed in ASM components. As the biodegradable percentage

corresponds to 55% of total COD, it results in concentrations of 150 gCOD.m-3 for SF and 125

gCOD.m-3 for XS. No biomass was assumed to be present in the artificial wastewater.

Table 2: COD fractions and corresponding concentrations in the influent (artificial wastewater) calculated based on Boeije et al. [76] and the experimental measurements.

Symbol Component Fraction in Total COD (%) Concentration (g COD m-3)

SF Soluble fermentable substrate 54.5 150.00

SA Fermentation products (acetate) 0 0

SI Inert, non-biodegradable organics (soluble) 0 0

XS Slowly biodegradable substrate 45.5 125.00

XI Inert, non-biodegradable organics 0 0

4.2 Model Development

4.2.1 Activated sludge

The activated sludge model was built based on the model ASM2d and the experimental setup

described in section 4.1.1.

Nineteen processes were considered in the activated sludge, following the ASM2d [2] model,

which involved different microorganisms and transformations. Among these process, one of the

most important are the heterotrophic bacteria performing organic matter oxidation and

participating in the denitrification process. Hydrolysis processes are also dependent on this

bacterial group and are divided in aerobic, anoxic and anaerobic hydrolysis, whereby the slowly

biodegradable substrate (XS) is degraded to fermentable substrate (SF). Autotrophic biomass

17

performed nitrification and phosphorous uptake is performed biologically by PAO, which can grow

in aerobic and anoxic environments using internal storage products (XPHA), obtained from poly-

phosphate (XPP) hydrolysis.

The biomass decay process, which includes mechanisms such as death, predation, endogenous

metabolisms and lysis in ASM2d, is addressed as a conversion of bacterial biomass into slowly

biodegradable substrate and inert particulate products [2].

In the kinetic equations, the consumption of components was described by a limitation function

(Monod term), in order to assure that the reaction would stop in case of limiting concentrations or

inhibition [66]. Biomass decay was expressed based on first order equations.

With regard to nutrients removal, only biological nitrogen and phosphorous removal were taken

into account, while chemical and physical transformations were neglected.

In biomass growth processes, ammonium and phosphate are assumed as nitrogen (iNXB) and

phosphorous (iPXB) source for all bacteria.

The influent composition was based on the OECD artificial wastewater and adapted following the

ASM2 raw wastewater composition, as listed in Table 2. The initial pollutants concentrations in

reactors were based on the initial values described in the experimental phase, as well as

concentrated sludge was used as inoculating material for the initial microbial biomass. Sludge

recirculation was also occurring in the system, so a biomass concentration was accounted in

influent representing sludge recirculation. The biomass and PAO related components for initial

reactor conditions and influent concentrations are shown in Table 3. These values are based on

the proposed fractions of municipal wastewater [2] and some were used to reach numerical

stability in the model.

Table 3: Initial concentrations considered in the activated sludge compartments and influent concentrations for biomass and PAO related compounds.

Initial conditions Concentration

(g COD m-3)

XH Heterotrophic biomass 10

XAUT Autotrophic biomass 5

XPAO Phosphorous accumulating organisms 2.75

XPHA Stored poly-hydroxy-alkanoate 2.75

XPP Poly-phosphate 0.01

Influent

XH Heterotrophic biomass 15

XAUT Autotrophic biomass 2.75

XPAO Phosphorous accumulating organisms 2.75

XPHA Stored poly-hydroxy-alkanoate 15

XPP Poly-phosphate 2.75

Some elements from the ASM2d original model [2] were not included in the present model to

avoid variables not taken into account in the experimental phase.

The stoichiometric factors, kinetic expressions and parameter related to the microbial community

and processes considered in the model were mainly collected from the literature [2]. In Appendix

18

A, with the AS Gujer matrix (representing all the processes, state variables and stoichiometry)

listed in Table 15, kinetics rate expressions in Table 16; and typical stoichiometric coefficients

related to the activated sludge in Table 17.

4.2.2 Waste stabilization ponds

The present waste stabilization pond model was constructed based on the experimental setup for

WSP, as outlined in section 4.1.1. The three different compartments (anaerobic, facultative and

maturation ponds) were presented in the model, each one containing different microorganisms,

processes and variables, increasing significantly the complexity when compared to the AS model.

In contrast to the AS, the WSP model was not entirely built based on one well-established model.

Different methodologies from the literature were combined and adapted since no mathematical

model for three compartments of a conventional WSP was found in literature.

The processes in the first compartment, an anaerobic pond that receives raw wastewater, include

hydrolysis of slowly biodegradable COD and activity of anaerobic bacteria. The anaerobic pond

included fermenting bacteria (FB), which for their growth consume SF and release SA and SH2 as

by-products; acetotrophic methanogenic bacteria (AMB), which consume SA, releasing SCH4; and

hydrogenotrophic methanogenic bacteria (HMB), which consume SH2 and produce SCH4.

Nevertheless, acetotrophic sulfate reducing bacteria and other sulfur-related processes (often

part of models based on Anaerobic Digestion Model No 1 [3]) were not included in the parameters.

The influent wastewater used in the experimental phase did not contain any sulfur, so sulfate

related processes were not taken into account.

In the facultative pond, the oxygen gradient varies along the pond depth. At the upper layers,

algal growth on ammonium and nitrate provide oxygen, depending on light intensity [33,72].

During the 16 hours per day when algae receive light (16:8h L:D cycle using fluorescent lamps

with a light intensity of 100 μE.m-2.s-1 [77]), oxygen is provided to the system through

photosynthesis, enabling aerobic processes. Light incidence and its attenuation through the pond

depth (described by the Lambert Beer law) were simplified using the mean compartment depth

due to the Aquasim software limitations. Outside the light hours, the oxygen levels drop quickly,

enhancing anoxic and anaerobic processes. However, only aerobic and anoxic processes were

considered in the model for facultative and maturation ponds, since these types of bacteria and

algae characterize the most important occurring processes.

The maturation (or polishing) pond is the last compartment. The same processes and bacteria

listed in the facultative pond were also considered in the maturation pond.

Given the facultative and maturation ponds characteristics, such as higher pH due to algae

growth, aerobic conditions and also significant calcium concentrations in the influent water [78],

phosphorous removal was mainly occurring through chemical precipitation [43], so biological

phosphorous removal processes were not taken into account. Ammonia volatilization, which is

enhanced by the high pH as well, was not considered in this model due to lack of experimental

19

data, software limitations and model structure. For the same reason, reactions and processes

occurring in the pond’s sediments were also not taken into account.

Although the model was built intended to describe the concentrations of BOD, COD and nutrients

(total Kjeldahl nitrogen and total phosphorous), only organic matter removal was taken into

account for the model results. The complexity of the ponds ecosystem and a combination of many

processes contributing to nutrient removal in WSPs are yet not fully understood [46]. These

factors, coupled with the limitations of the software, experimental data available and model

structure lead to unreliable model predictions regarding nutrients removal.

The influent characteristics adopted for the WSP were the same as in the activated sludge system

(Table 2). There was no sludge recirculation nor biomass present in the influent, therefore only

the ponds’ initial conditions (due to inoculation of sludge or algae) contributed to the bacteria and

algae amount. These biomass concentrations (listed in Table 4) were based on the concentrations

proposed in literature [72] or adapted in order to reach numerical stability. The initial

concentrations for anaerobic pond were composed only by anaerobic biomass (XFB, XAMB and

XHMB) and for facultative and maturation ponds composed of aerobic/anoxic biomass (XH, XA,

XALG).

Table 4: Initial conditions for ponds.

Symbol Biomass Concentration

(g COD m-3)

XFB Fermenting bacteria 14

XAMB Acetotrophic methanogenic bacteria 14

XHMB Hydrogenotrophic methanogenic bacteria 14

XH Heterotrophic biomass 2.8

XA Autotrophic biomass 2.8

XALG Algae 5

In addition, the influent alkalinity was incorporated in the WSP model due to its influence in

phosphorous precipitation and redissolution processes. The water alkalinity in influent (SALK =

0.013 mol HCO3/l [78]), calcium and magnesium present in water (represented by XMeOH, in this

case Ca(OH)2 with influent concentration of 330mg/l [78]) contribute to the phosphorous

precipitation (metal-phosphate MePO4 formation (XMeP)) and redissolution processes, following

the equilibrium [2] shown in Equation 3:

𝑋𝑀𝑒𝑂𝐻 + 𝑆𝑃𝑂4 ↔ 𝑋𝑀𝑒𝑃 (Equation 3)

The stoichiometric factors, kinetic expressions, parameters related to the microbial community

and processes considered in the model were mainly collected from the literature [2,4,72]. The

Appendix B contains waste stabilization pond matrices (Table 21, Table 22 and Table 23), kinetic

expressions for each process (Table 24) and stoichiometric and kinetic values listed in Table 25.

20

4.2.3 Model implementation

The software Aquasim [73] was used to construct the models. For the activated sludge, the

developed model was composed of two compartments with volume of 3 liters each. They are

mixed rectors with a fixed volume and connected by an advective link. The aerated compartment

was set to keep a constant DO concentration of 4 gO2.m-3. Figure 7 illustrates the model setup

built in Aquasim.

Figure 7: Model setup for AS in Aquasim

Twelve processes were listed in the aerated compartment: aerobic growth of heterotrophs (on SF

and on SA), autotrophs and PAO; aerobic storage of polyphosphate and PHA; aerobic hydrolysis

and decay of biomass and PAO-related processes. For the anoxic compartment, also twelve

processes are active: anoxic growth of heterotrophs (on SF and on SA) and PAO; anoxic storage

of polyphosphate and PHA; fermentation; anoxic and anaerobic hydrolysis and decay of biomass

and PAO-related processes.

The present waste stabilization pond model was constructed based on the experimental setup for

WSP discussed in section 4.1.1. The three different compartments (anaerobic, facultative and

maturation ponds) were described on the model using advective-diffusive compartments,

connected by advective links (as shown in Figure 8). This type of reactor allows one-dimensional,

advective-diffusive transport of substances with a plug flow [79]. For each compartment, the cross

section, start, and end coordinates were specified. Each pond contains different microorganisms,

processes and variables, increasing significantly the complexity when compared to the AS model.

Figure 8: Model setup for WSP in Aquasim

The processes taking place in the anaerobic pond include the anaerobic growth of AMB, HMB

and FB, anaerobic hydrolysis, phosphorous precipitation and redissolution and biomass decay.

21

For facultative and maturation ponds, the following processes are set: algal growth on SNH and

SNO; aerobic and anoxic growth of heterotrophs (both on SF and on SA); growth of autotrophs;

phosphorous precipitation and redissolution; decay of biomass and algal respiration.

In both models, the initial pollutants concentration in each tank was set based on the experimental

data (effluent at time zero) and adjusted to reach numerical stability in the model. Since there was

no data related to the first tanks’ initial condition, it was set to zero in the aerobic tank (AS model)

and anaerobic tank (WSP model).

4.2.4 Mass balance

The mass balance is based on the mass conservation and allows evaluating the mass flow within

a system. It is an essential tool to detect inconsistencies in the model [66]. It is usually performed

for nitrogen, carbon and phosphorous and allows the flux estimation for these substances and

lead to conclusions of validity [80]. The basic principle is described by Equation 4 [2]:

𝐼𝑛𝑝𝑢𝑡 + 𝑅𝑒𝑎𝑐𝑡𝑖𝑜𝑛 = 𝑂𝑢𝑡𝑝𝑢𝑡 + 𝐴𝑐𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 (Equation 4)

The input and output terms are related to transport occurring in the system. The reactions are

described as products of the stoichiometric coefficients vij and the process rate expressions pj for

each component (Equation 5) [2], or in this case, for a specific component (columns in Gujer

matrix - Table 17) summing the products of the process rate expressions (Table 18) multiplied by

the correspondent stoichiometric coefficients found in the matrix [81].

𝑟𝑗 = ∑ 𝑣𝑖𝑗𝑗 𝜌𝑗 (Equation 5)

For example, the rate of reaction for autotrophic biomass formation (XA), with regard to COD, is

given by Equation 6:

𝑟𝑋𝐴= (1) ∗ 𝜇𝐴.

𝑆𝑂2

𝐾𝑂2𝐴 +𝑆𝑂2

.𝑆𝑁𝐻

𝐾𝑁𝐻𝐴 +𝑆𝑁𝐻

.𝑆𝑃𝑂4

𝐾𝑃𝐴+𝑆𝑃𝑂4

. 𝑋𝐴 + (−1) ∗ 𝑏𝐴. 𝑋𝐴 (Equation 6)

The mass balances correspondent to the activated sludge model processes are listed in Appendix A (from Table 18 to Table 20) and referring to WSP, in Appendix B (from Table 26 to 28).

4.3 Model calibration – parameter identifiability

The model calibration process is aimed to find an optimal fit of the model outcomes to

experimental data through the adjustments of model parameters. Therefore, a series of steps

(summarized in Figure 9, following the methodology outlined by Brun et al [6]) were performed to

reach calibration. From the built models, first, local sensitivity analysis allowed to identify the most

important parameters, listed on a ranking. After that, subsets consisting of the most relevant

parameters were analyzed in relation to its identifiability to detect the most relevant ones to be

changed and, finally, parameters were tuned. After that, the results were analyzed to identify

potential bias problems.

22

Figure 9: Steps conducted to select a parameter subset and perform model calibration [6]

4.3.1 Local sensitivity analysis

The sensitivity analysis followed the methodology proposed by Brun et al [6,82]. The first steps

are based on the sensitivity matrix 𝑆 = {𝑠𝑖𝑗}, in which sij is calculated using Equation 7. 𝜕𝜂𝑖 𝜕𝜃𝑗⁄

represents the derivative of the output 𝜂𝑖 in relation to the parameter θj, evaluated at the point θ0.

The range of a parameter θ is defined by ∆𝜃𝑗 and the scale factor or weighting factor is

represented by 𝑠𝑐𝑖. The scale factor has the same dimensions as the model variable and makes

the influence on the contribution of different model variables similar and nondimensional [83].

𝑠𝑖𝑗 =∆𝜃𝑗

𝑠𝑐𝑖

𝜕𝜂𝑖

𝜕𝜃𝑗 (Equation 7)

Then individual sensitivity 𝛿𝑗𝑚𝑠𝑞𝑟

is calculated by Equation 8. It describes the mean sensitivity of

the model output to a change in parameter 𝜃𝑗 and can be used to rank the parameters’ individual

sensitivity.

𝛿𝑗𝑚𝑠𝑞𝑟

= √1

𝑛∑ 𝑠𝑖𝑗

2𝑛𝑖=1 (Equation 8)

The uncertainties of all parameters were based on the classification provided by Brun et al. [6].

Accurately known parameters (stoichiometric parameters and 𝑖𝑁𝑋𝐵, which are known more

accurately) have an uncertainty of 5% and classified as class 1. Moderately known parameters

were classified as class 2, with 20% uncertainty (parameters which lie between the interval of 0

and 1 and some kinetic parameters, such as 𝜇𝐴𝑈𝑇, 𝑏ℎ, 𝐾𝑂2𝐴 , 𝐾𝑁𝑂

𝐻 , which are known more accurately

from other experiments and influent composition parameters related to known data). Poorly

23

known parameters (some influent composition and other kinetic parameters) classified with 50%

uncertainty and as class 3, as for example SA, SF, SI and XS in influent, since COD fractioning is

not accurately known.

The parameter sensitivities were calculated using the program package Uncsim [84] coupled with

Aquasim software [73]. Based on the model output for all parameters, uncertainties, standard

initial values (𝜃𝑖𝑛𝑖) and scale factors (average results for each state variable evaluated over time),

a ranking listing the parameters in a decreasing importance order was built. It must be noted that

the sensitivity is a local measurement for each parameter, so each adjustment made in the model

leads to different sensitivity values. For this reason, after the identifiability analysis and parameter

estimation, the local sensitivity values should be recalculated for 𝜃𝑒𝑛𝑑.

Some parameters were disregarded from the parameters estimation process and kept fix since

they are unrelated to the available data or not a necessary have to be changed. However, all the

parameters were previously evaluated with respect to their individual sensitivity in order to show

their influence on the model and possible bias problems. From the importance ranking, the

collinearity and identifiability analysis was limited to the 30 most important parameters, following

the methodology presented by Brun et al. [6].

4.3.2 Collinearity and identifiability index

Groups of parameters are evaluated in order to avoid that changes in model output caused by

alterations in one parameter may be canceled by changes in another parameter contained in the

same subset K, which is addressed by the collinearity index 𝛾𝐾 (Equation 9). The eigenvalue of

the matrix �̃�𝐾𝑇�̃�𝐾 is represented by �̃�𝑘. �̃�𝐾 is a submatrix of 𝑆 containing the parameters in K.

According to Brun et al. [6], a high value of 𝛾𝑘 (empirical threshold around 10-15) indicates that

the subset K is poorly identifiable even if it is composed of important parameters indicated

previously by 𝛿𝑗𝑚𝑠𝑞𝑟

.

𝛾𝑘 =1

√𝜆𝑘

(Equation 9)

The identifiability index (or determinant measure) 𝜌𝐾 (Equation 10) combines sensitivity measures

and collinearity to assess the identifiability of a subset of k parameters using a determinant

function “det ()” of the matrix �̃�𝐾𝑇�̃�𝐾. A higher 𝜌𝐾 indicates a highly identifiable subset and a low

degree of collinearity between these parameters.

𝜌𝑘 = det (𝑆𝐾𝑇𝑆𝐾)1/2𝑘 (Equation 10)

From the 30 most important parameters defined in the sensitivity ranking, subsets were formed

combining the different types of parameters (related to heterotrophs, autotrophs, PAO and

hydrolysis). Then, the collinearity index threshold of 10 was applied. It means that only parameter

subsets with 𝛾𝑘 <10 and high 𝜌𝑘 are considered potentially identifiable [6].

24

4.3.3 Parameter estimation

The estimation of parameters is aimed to find an optimal value for a specific parameter based on

the experimental data. This procedure was performed using the software Aquasim in order to

minimize the sum of squares of the weighted deviations between the model calculated results

and real measurements (Equation 11). This test, which is known as chi-squared test, is also used

to evaluate the goodness of fit between experimental and simulated data [79].

χ2(𝑝) = ∑ (𝑦𝑚𝑒𝑎𝑠,𝑖−𝑦𝑖(𝑝)

𝜎𝑚𝑒𝑎𝑠,𝑖)

2𝑛𝑖=1 (Equation 11)

In the chi-squared test (Equation 11), n is the number of data points, 𝑦𝑚𝑒𝑎𝑠,𝑖 and 𝜎𝑚𝑒𝑎𝑠,𝑖 refer

respectively to the experimental measurements and its standard deviation, 𝑦𝑖(𝑝) relates to the

values calculated in the model constant variable, evaluated at a specific point of time [79].

4.4 Model simulations

4.4.1 Scenario analysis

The robustness and resilient capacity of the two systems were evaluated via five scenarios of

different wastewater strengths. The reference scenario was set based on the experimental data:

standard OECD wastewater concentrations with a peak (as described in Section 4.1.2).

For scenarios 1 to 4, the wastewater strength was increased from two to 50 times the standard

concentration (Table 5) for both treatment methods.

Table 5: Scenarios evaluated for both wastewater treatment methods in relation to wastewater strength.

Scenario Wastewater strength

(times increased)

Reference 1

1 2

2 5

3 10

4 50

The proposed scenarios were used to evaluate the system efficiencies and compare both

wastewater methods with regard to BOD, COD, total Kjeldahl nitrogen and total phosphorous

removal. Uncertainties associated with the scenarios were also evaluated using Monte Carlo

simulations in each scenario, as elucidated in the following section (section 4.4.2).

4.4.2 Monte Carlo simulations

In environmental sciences, parameter uncertainties, lack of experimental data, assumptions and

many factors contribute to parameter uncertainties. More precisely, uncertainties may be related

to lack of knowledge about model inputs (inputs uncertainty), mathematical structure of the model

(structural uncertainty) and stochastic uncertainties (e.g. failure events) [85].These models are

usually evaluated using a linear error propagation approach, although nonlinear error propagation

25

can be useful when models involve many uncertainties [86]. One of the most used methods for

the latter approach is the Monte Carlo simulation, a probabilistic framework, in which a set of

model inputs (randomly generated) from probability distributions are evaluated. It shows how a

random sample (including errors, lack of knowledge, variations in the population) affects the

model performance and reliability [87] and gives a comprehensive view of how likely an outcome

is. However, since a huge number of simulations are performed to evaluate the parameter

combinations, large computational costs are demanded [88].

Among the sampling techniques, the Latin Hypercube Sampling (LHS) is one the most used

methods. It provides an effective coverage of the parameter space by choosing at random a

selection that has not yet been selected [87]. It is especially efficient and stable in comparison

with random sampling for models with a small number of parameters [88,89].

The Monte Carlo simulations were calculated using the Uncsim package [84] for AS and WSP

models. The following steps compose this process and were applied to the models [86]:

1. The parameters that compose each model are assumed to have uniform probability

distributions and follow the same uncertainties based on classes as outlined in Brun et

al. [6]: uncertainties of 5, 20 and 50% around parameters default values (for the AS, the

calibrated parameter values were used);

2. 500 sets of samples are generated using Latin Hypercube Sampling (LHS) (for WSP, 250

sets were used due to the high computational costs), which provides a better coverage

of the parameter space [87], resulting in a matrix with LHS samples (rows) and

parameters (columns);

3. The model is solved for each shot (set of samples), storing each model output;

4. The results generate a probability density function and are evaluated representing the

90th percentile,10th percentile and mean;

The results were evaluated in combination with the different evaluated scenarios for activated

sludge and waste stabilization ponds.

26

5 RESULTS AND DISCUSSIONS

In this section, the simulation of activated sludge and waste stabilization pond systems are

introduced and discussed. At first, the model’s results are presented following the experimental

configuration in order to compare the real data and simulations results (Section 5.1.1 for activated

sludge and Section 5.1.2 for waste stabilization ponds). The calibration procedure results are

shown in Section 5.2 and scenarios evaluation for each model, in Section 5.3.

5.1 Model development and evaluation

5.1.1 Activated sludge modeling

The model fitness to the measurements was evaluated visually through graphs and numerically

using the root mean square error (RMSE). The RMSE test was performed for the available

experimental data (influent and effluent COD, BOD, total Kjeldahl nitrogen and total phosphorous)

and the correspondent influent and effluent results generated by the model. The RMSE values

obtained are listed in Table 6. The graphical comparisons between the simulations and

experimental data for influent and effluent are shown in Figure 10 and Figure 11.

Table 6: Root mean square errors (RMSE) calculated based on the experimental data and simulated

results for BOD, COD, total nitrogen and total phosphorous (influent and effluent)

Influent Effluent

BOD 28.43 g BOD.m-3 15.64 g BOD.m-3

COD 43.61 g COD.m-3 27.93 g COD.m-3

TKN 6.37 g N.m-3 5.33 g N.m-3

tP 3.15 g P.m-3 2.22 g P.m-3

As observed in Figure 10 and Figure 11, the model results are close to the experimental data,

representing a reasonably good model fitness. Although, some points can be highlighted. For

BOD (first graph), the experimental influent concentrations differ from the modeled ones,

indicating an underestimation of wastewater concentration during the peak. The same happens

with the effluent, in which the peak is not well described by the model. COD and TKN fit better

the experimental data for both influent and effluent. For tP, the influent concentrations were

overestimated by the model, as well as the effluent peak.

27

Figure 10: Comparison of BOD and COD concentrations obtained in lab scale experiments (represented by symbols) and modeling following ASM2d (represented by lines) for influent and effluent.

Figure 11: Comparison of total Kjeldahl nitrogen and total phosphorous concentrations obtained in lab scale experiments (represented by symbols) and modeling following ASM2d (represented by lines) for

influent and effluent.

The substrate concentrations vary with time, compartment and influent peaks. As seen in Figure

12, the soluble readily available substrate (SF) quickly decrease as it is consumed by heterotrophs

and PAO in both compartments. The hydrolysis process is responsible for the transformation of

slowly biodegradable particulate COD (XS) into readily available fermentable substrate (SF). It is

enhanced by the higher concentration of heterotrophic biomass in the aerated compartment and

contributes to a quickly decrease in XS concentration. In the second compartment, the

heterotrophic biomass concentrations are lower and, due to the anoxic limitations (𝜂𝑁𝑂), the

28

hydrolysis rates are slower. It causes an accumulation of XS and consequently, higher

concentrations in the anoxic tank when compared to the aerated one.

Figure 12: Comparison between the concentrations of substrates (SF, SA, SI and XS) in the first

compartment (a) and the second compartment (b).

With respect to nutrients, nitrogen (in form of ammonium) enters the system with the influent

wastewater and the concentration profile follows the influent peak (Figure 13). It is consumed by

autotrophs in the first tank, in the nitrification process. In addition, biomass formation contributes

to a decrease in TKN concentrations. In the second compartment, denitrification takes place,

decreasing nitrate concentrations and producing nitrogen gas. Lower substrate concentrations

(SF and SA), as well as anoxic correction factors decrease significantly the heterotrophic activity

in this compartment; consequently, keeping low denitrification rates. However, from the graphs,

one can notice that the SNH concentrations increase in the second compartment. It happens

because none of the anoxic bacteria are consuming SNH at this tank and processes such as

biomass decay, fermentation and hydrolysis contribute to ammonium concentration increase.

Figure 13: Comparison between concentration of nitrogen-related substrates (SNH, SNO and SN2) in first

compartment (a) and second compartment (b).

29

The total phosphorous concentration (Figure 14) follows the influent peaks and depends on PAO-

related processes. PAO growth and accumulation of polyphosphate have higher rates in the

aerobic tank, since they are not limited by the anoxic correction factors. However, the lower

concentrations of SA make the aerobic storage of polyphosphate rates decrease and the

complexity and dependency on anoxic and aerobic processes limit the phosphorous uptake in the

system. The SPO4 concentration in the second tank is higher than the first one due to processes

contributing to SPO4 increase: hydrolysis, fermentation and biomass decay.

Figure 14: Comparison between the concentration of SPO4 in the first (a) and the second compartment (b).

The rates of kinetic processes occurring in each compartment are observed in Figure 15. It is

clear that the heterotrophs growth rate is influenced by substrate availability and follows the

influent concentration pattern. The availability of fermentable substrate (SF) allows the high rates

of heterotrophic growth. The kinetic rates are much lower in the anoxic compartment due to the

limited available substrate and correction factors for bacterial growth in anoxic conditions (η).

Figure 15: Rates of aerobic (a) and anoxic (b) processes occurring in the system.

30

The hydrolysis processes (Figure 16), which occurs in both tanks, have an important role in the

compartments since they are responsible for SF availability and, consequently, enhance biomass

growth.

Figure 16: Hydrolysis rates occurring in the first compartment (a) and the second compartment (b)

5.1.2 Waste stabilization ponds modeling

The model fitness to lab-scale measurements was evaluated at the first moment, visually by

means of graphs generated by Aquasim. For organic matter removal, the results fit reasonably

the experimental data, as can be seen in Figure 17. Although, the effluent model output for

nutrients clearly do not fit the experimental data (Figure 18), revealing that the model does not

reflect the real system behavior.

Many factors contribute to this divergence between the experimental data and model results. The

different conditions (anaerobic, anoxic and aerobic) present in the WSP system affect directly the

nutrients. For instance, an increase in pH due to algae activity leads to ammonia volatilization in

the facultative and maturation ponds, which contributes significantly to nutrients removal. This

mechanism was not considered in the present model.

The model constructed for the WSP predicts only biological removal of nitrogen. This assumption,

which is adopted in many other similar models (for instance in CWM1 [5], RWQM1 [4], Sah (2011)

[72]), limits the nitrogen removal to the activity of autotrophs. The inclusion of ammonia

volatilization and nutrients accumulation in bottom sediments, for example, would require a

broader range of parameters and processes, increasing the model complexity. In respect to

phosphorous, the precipitation-redissolution process is included in the present model, but only

described by a first-order equation, dependent on phosphate and metal-hydroxides (Ca(OH)2)

concentrations in the influent wastewater. Furthermore, the software limitations do not allow

describing some of the physical and chemical processes. Diffusion of each specific substance,

transport of substances in y and z-axes, exchanges between water column and air are some of

the factors not taken into account due to the Aquasim compartment (advective-diffusive)

configurations. Moreover, the experimental phase results show that the WSP presented an

31

average removal of nitrogen of 55% [74], lower than values reported in literature for the same

treatment method [32], indicating problems with the experimental setup or measurements. For

these reasons, the nutrients modeling for waste stabilization ponds were disregarded from the

model results.

Figure 17: Comparison of BOD and COD concentrations obtained in lab scale experiments (represented by symbols) and modeling (represented by lines) for influent and effluent in the WSP model.

Figure 18: Comparison of TKN and tP concentrations obtained in lab scale experiments (represented by symbols) and modeling (represented by lines) for influent and effluent in the WSP model.

The RMSE (Table 7) was calculated for organic matter and nutrients (influent and effluent) with

respect to experimental data and model output. Comparing to the AS modeling RMSE (Table 6),

one can notice that there is an increase in the RMSE values. It means that there is a larger

difference between the observed and predicted data for BOD, TKN and tP in the WSP model,

32

except for COD. In addition, visually, the COD and BOD have a reasonably good fit, showing that

the model could be capable of describing organic matter removal. For these reasons, the model

built to describe the waste stabilization pond system, although not fully reliable, is assumed to

describe organic matter removal only.

Table 7: Root mean square errors (RMSE) calculated based on the experimental data and simulated results for BOD, COD, TKN and tP (influent and effluent) in the WSP system

Influent Effluent

BOD 28.43 g BOD.m-3 27.98 g BOD.m-3

COD 43.61 g COD.m-3 20.28 g COD.m-3

TKN 6.37 g N.m-3 36.56 g N.m-3

tP 3.15 g P.m-3 7.21 g P.m-3

In respect to algal and microbiological processes happening in the compartments, some points

can be highlighted. Although the nutrients-related processes are not considered reliable, the algal

photosynthetic process is important to be observed since it influences the heterotrophs behavior.

As seen in Figure 19, the algae present in facultative and maturation ponds have activities based

on light availability. The light cycle (16:8h L:D cycle) determines the photosynthesis-respiration

activity and, consequently, the SNH and SNO algal consume. At the first days, the activity of algae

consuming nitrate prevail, which happens due to the inhibition of this group of algae by the

presence of ammonium. Therefore, in the first days, before the influent containing high

concentrations of ammonium reach the facultative pond, the nitrate-consuming algae are active.

When the SNH concentrations are high enough to stop the SNO-algae, the SNH algae activity starts.

The nitrate is a product of the autotrophic organisms, which activity is enhanced by the oxygen

produced by algae and in the first days, consume the initial concentrations of nitrogen present in

the compartment. Then, SNO is freely available for the algal uptake. In addition, the competition

for SNH between organisms that, at the same time that algae are growing, are consuming SNH for

biomass formation, decreases the NH-algae activity.

Figure 19: Algae growth, decay and respiration rates in facultative and maturation ponds

33

In the first pond, the anaerobic conditions allow only specific organisms to develop (Figure 20,

left). The wastewater influent containing SF allow the fermentating bacteria (FB) development

since the beginning, which consume SF and produce SA and SH2. The acetate (SA) is used by

AMB, increasing its growth rate after day 2 (after the influent peak and growth of FB). The

hydrogen (SH2) produced by FB allows the HMB growth. Both HMB and AMB, in their growth

processes, produce methane (SCH4) as a metabolic by-product. The graph on the left shows the

concentrations of substrates. SF is zero at this point (outlet) because of its consume through the

length of the compartment. The fermenting bacteria have a high maximum growth rate (when

compared to AMB and HMB) and, coupled with the abundant substrate SF, produces high

quantities of SA and SH2, at same proportions. The slightly smaller SH2 concentration (when

compared to SA in Figure 20, right side) is due the HMB consuming H2 around day 5.

Figure 20: Microbiological processes occurring in the anaerobic pond (left), observed at the outlet of the compartment and substrate concentrations (right) measured at the same point (outlet, x=4.6dm)

The second pond (facultative) is characterized by aerobic conditions at the surface (algal

photosynthesis) and, at deeper levels, anoxic and anaerobic conditions. Since the advective-

diffusive compartments in Aquasim only vary along the x-axis, the different conditions cannot be

well portrayed. With respect to aerobic processes (Figure 21, “a”), heterotrophic bacteria

consuming organic matter follow the oxygen availability pattern (dependent on algal activity). The

higher availability of fermentable substrate at the first days benefits the heterotrophs consuming

SF and then, later, there is some activity of SA-consuming heterotrophs, following the algae activity

pattern. When the oxygen levels are low, the anoxic processes take place (Figure 21, “b”).

Heterotrophs consuming SF and SA and doing denitrification are present in this compartment.

Their activity depends on the algal photosynthesis-respiration cycle and on the availability of

substrate.

At the last compartment, the maturation pond, a small quantity of organic matter is available,

favoring nutrient removal processes. Aerobic (Figure 22 “a”) and anoxic processes (Figure 22

“b”), as in the facultative pond follow the oxygen availability, imposed by the algae. As it is the last

pond, the rate peaks take more time to happen when compared to the previous compartment.

34

Figure 21: Biological processes occurring in the facultative pond, showing heterotroph organisms in

aerobic conditions (a) and anoxic conditions (b).

Figure 22: Biological processes occurring in the maturation pond, showing heterotroph organisms in aerobic conditions (a) and anoxic conditions (b).

Figure 23: Variations of the components of COD/BOD at the three different WSP compartments (at outlet)

over time

The BOD/COD concentration varies in the compartments along the length and time. Figure 23

shows the concentrations of SF, SA, XS and SI into the three compartments at the outlet. In the

35

anaerobic one (a), the hydrolysis process converts XS into SF, which is quickly consumed and

transformed into SA by the fermenting bacteria. Since the hydrolysis considered in the WSP model

is a first order process and is based on the ADM1 [3,90], it depends on fermenting bacteria and

occurs only in anaerobic conditions. The inert soluble organic material (SI), which is produced

from hydrolysis of XS, has a very low concentration due to the low conversion factor fSI (production

of SI in hydrolysis).

5.2 Model calibration – parameter identifiability

The model calibration procedure was divided into two stages: sensitivity analysis and parameter

estimation, as described Materials and Methods. Since each model has its own characteristics,

variables and processes, they were calibrated separately but following the same methodology,

specified in Section 4.3.

5.2.1 Local sensitivity analysis for AS

The sensitivity analysis was performed for all parameters listed in the activated sludge model in

respect to the state variables linked to the available data: SA, SF, SI, XS, SNH and SPO4. The

parameter values specified in literature (from Henze et al. [2]), classes and uncertainties taken

into account during the sensitivity analysis are listed in Table 8.

Table 8: Parameters analyzed in the AS sensitivity, their respective values and uncertainties.

Parameter Value Class Δθ

Parameter Value Class Δθ

𝜇𝐻 6 3 3 𝐾𝑁𝐻𝐴 1 3 0.5

𝑞𝑓𝑒 3 3 1.5 𝐾𝑃𝐴 0.01 3 0.005

𝜂𝐻 0.8 2 0.16

𝑏𝐻 0.4 2 0.08 𝑘𝐻𝑌𝐷 3 3 1.5

𝐾𝑂2𝐻 0.2 3 0.1 𝐾𝑂2

𝐻𝑌𝐷 0.2 3 0.1

𝐾𝐹𝐻 4.00 3 2 𝐾𝑋

𝐻𝑌𝐷 0.1 3 0.05

𝐾𝐴𝐻 4.00 3 2 𝐾𝑁𝑂

𝐻𝑌𝐷 0.5 3 0.25

𝐾𝑓𝑒 4.00 3 2 𝜂𝑁𝑂𝐻𝑌𝐷 0.6 3 0.3

𝐾𝑁𝑂𝐻 0.5 2 0.1 𝜂𝑓𝑒

𝐻𝑌𝐷 0.4 3 0.2

𝐾𝑁𝐻𝐻 0.05 3 0.025

𝐾𝑃𝐻 0.01 3 0.005 iNSF 0.03 2 0.006

iNXB 0.07 1 0.0035

𝑞𝑃𝐻𝐴 3 3 1.5 iNXI 0.02 2 0.004

𝑞𝑃𝑃 1.5 3 0.75 iNXS 0.04 2 0.008

𝜇𝑃𝐴𝑂 1 3 0.5 iPSF 0.01 3 0.005

𝜂𝑃 0.6 2 0.12 iPXB 0.02 2 0.004

𝑏𝑃𝐴𝑂 0.2 3 0.1 iPXI 0.01 3 0.005

𝑏𝑃𝑃 0.2 3 0.1 iPXS 0.01 3 0.005

𝑏𝑃𝐻𝐴 0.2 3 0.1

𝐾𝑂2𝑃 0.2 3 0.1 𝑌𝐻 0.63 1 0.0315

𝐾𝑁𝑂𝑃 0.5 2 0.1 𝑌𝑃𝐴𝑂 0.63 1 0.0315

𝐾𝐴𝑃 4 3 2 𝑌𝑃𝑂4 0.4 1 0.02

𝐾𝑁𝐻𝑃 0.05 3 0.025 𝑌𝑃𝐻𝐴 0.2 1 0.01

𝐾𝑃𝑆𝑃 0.2 3 0.1 𝑌𝐴 0.24 1 0.012

𝐾𝑃𝑃 0.01 3 0.005 𝑓𝑋𝐼 0.1 1 0.005

𝐾𝑃𝑃𝑃 0.01 3 0.005 𝑓𝑆𝐼 0 - 0.005

𝐾𝑀𝐴𝑋𝑃 0.34 2 0.068

𝐾𝐼𝑃𝑃𝑃 0.02 3 0.01 𝑆𝐹 influent 150 3 75

𝐾𝑃𝐻𝐴𝑃 0.01 3 0.005 𝑆𝐴 influent 0.01 3 0.005

𝑆𝐼 influent 0.01 3 0.005

𝜇𝐴 1 2 0.2 𝑆𝑁𝐻 influent 40 2 8

𝑏𝐴 0.15 3 0.075 𝑆𝑃𝑂4 influent 7 2 1.4

𝐾𝑂2𝐴 0.5 3 0.25 𝑋𝑆 influent 125 3 62.5

36

The parameters individual sensitivities calculated are listed in decreasing order, showing the

importance parameter ranking (Table 9) for the initial values 𝜃𝑖𝑛𝑖 and after parameter estimation

𝜃𝑒𝑛𝑑.

Table 9: Importance ranking at 𝜃𝑖𝑛𝑖 and 𝜃𝑒𝑛𝑑 for the top 30 parameters in activated sludge model The

potentially estimated parameters are indicated with an asterisk.

𝜃𝑖𝑛𝑖

𝜃𝑒𝑛𝑑

Rank Parameter 𝛿𝑗𝑚𝑠𝑞𝑟

Parameter 𝛿𝑗𝑚𝑠𝑞𝑟

1 𝑆𝑃𝑂4 influent 0.491 𝜇𝑃𝐴𝑂* 0.267

2 𝑘𝐻𝑌𝐷* 0.476 𝑘𝐻𝑌𝐷* 0.266

3 𝐾𝐹𝐻* 0.475 𝜇𝐻* 0.256

4 𝜇𝑃𝐴𝑂* 0.469 𝐾𝑂2𝐻 * 0.243

5 𝜇𝐻* 0.453 𝐾𝑋𝐻𝑌𝐷* 0.213

6 𝐾𝑋𝐻𝑌𝐷* 0.431 𝜇𝐴* 0.195

7 𝑋𝑆 influent 0.411 𝑏𝑃𝐴𝑂* 0.193

8 𝑆𝑁𝐻 influent 0.411 𝐾𝐹𝐻* 0.187

9 𝑆𝐹 influent 0.410 𝑖𝑃𝑋𝑆 0.181

10 𝑏𝑃𝑃* 0.408 𝑆𝑃𝑂4 influent 0.174

11 𝐾𝑁𝐻𝐻 * 0.406 𝑆𝑁𝐻 influent 0.138

12 𝐾𝑃𝑂4𝐻 * 0.406 𝐾𝑂2

𝐻𝑌𝐷* 0.119

13 𝐾𝐼𝑃𝑃𝑃 * 0.406 𝑞𝑓𝑒* 0.113

14 𝐾𝑃𝑆𝑃 * 0.406 𝑏𝑃𝐻𝐴* 0.111

15 𝑞𝑃𝑃* 0.406 𝑞𝑃𝐻𝐴* 0.108

16 𝑌𝐻 0.394 𝐾𝐴𝑃* 0.107

17 𝐾𝑀𝐴𝑋𝑃 * 0.374 𝑋𝑆 influent 0.085

18 𝜇𝐴* 0.160 𝑏𝐻* 0.082

19 𝐾𝑂2𝐻𝑌𝐷* 0.148 𝐾𝑃𝐻𝐴

𝑃 * 0.080

20 𝑞𝑓𝑒* 0.136 𝜂𝐻* 0.077

21 𝑏𝑃𝐴𝑂* 0.134 𝐾𝑂2𝐴 * 0.066

22 𝐾𝑂2𝐻 * 0.130 𝑏𝐴* 0.066

23 𝑏𝑃𝐻𝐴* 0.113 𝐾𝑁𝑂𝐻 * 0.054

24 𝑞𝑃𝐻𝐴* 0.111 𝑖𝑃𝑆𝐹 0.047

25 𝐾𝐴𝑃* 0.109 𝑌𝐻 0.044

26 𝑖𝑃𝑆𝐹 0.088 𝑆𝐹 influent 0.043

27 𝐾𝑃𝐻𝐴𝑃 * 0.084 𝑖𝑃𝑋𝐵 0.035

28 𝑏𝐻* 0.064 𝐾𝑂2𝑃 * 0.034

29 𝑖𝑃𝑋𝐵 0.063 𝐾𝐴𝐻* 0.034

30 𝑖𝑃𝑋𝑆 0.061 𝐾𝑁𝐻𝐴 * 0.029

The ranking in Table 9 shows that, at the initial moment, there is a high sensitivity of the model

towards the influent composition (𝑆𝑃𝑂4, 𝑋𝑆, 𝑆𝑁𝐻 and 𝑆𝐹 in influent), which reflects the importance

of substrate parameters. Hydrolysis rate, heterotrophic and PAO related kinetics are among the

ten most important parameters. The hydrolysis rate constant (𝑘𝐻𝑌𝐷) and hydrolysis saturation

coefficient for particulate COD (𝐾𝑋𝐻𝑌𝐷) are linked to the transformation of XS into readily available

substrate, presenting a great importance in the model. The maximum growth rates (𝜇𝐻 and 𝜇𝑃𝐴𝑂)

are directly linked to many processes, including organic matter and phosphorous removal,

heterotrophic and PAO biomass growth, justifying their high individual sensitivity. The third

parameter in the importance ranking is the fermentable substrate half saturation constant for

heterotrophs (𝐾𝐹𝐻) which is directly related to organic matter removal. These results reflect that

the substrate availability and kinetic parameters, such as maximum growth rate, half saturation

constant and decay rate contribute largely to the system dynamics.

37

5.2.2 Collinearity and identifiability index for AS

The identifiable analysis was limited to the 30 most important parameters listed in Table 9. From

these parameters, 22 were classified as potentially estimated from the available data (labeled by

an asterisk). Influent composition, stoichiometric parameters and conversion factors were

excluded, as more specific experimental data would be necessary to estimate them [6].

A subset K is considered identifiable if the model output is affected by each parameter contained

in it, which means a high local sensitivity and a high 𝜌𝐾 and also a low 𝛾𝐾, indicating that a change

in one of the parameters is not cancelled out by a change in another one contained in the same

subset [91] The 22 potential identifiable parameters are divided in groups ( hydrolysis, autotrophs,

heterotrophs and PAO). The collinearity and identifiability of all possible subsets combining them

were calculated. Table 10 lists the most relevant subsets and combinations limited to the

threshold 𝛾𝐾 <10 and highest.𝜌𝐾.

Table 10: Selected subsets formed from the potentially identifiable parameters the local sensitivity ranking,

their collinearity index (𝛾𝐾) and identifiability index (𝜌𝐾) before (𝜃𝑖𝑛𝑖) and after parameter estimation (𝜃𝑒𝑛𝑑)

𝜃𝑖𝑛𝑖 𝜃𝑒𝑛𝑑

Set Set Size

𝛾𝐾 𝜌𝐾

𝛾𝐾 𝜌𝐾 Parameters

Hydro

lysis

1 2 1.792 6.944 1.417 3.980 𝐾𝑋𝐻𝑌𝐷, 𝑘𝐻𝑌𝐷

2 2 1.028 4.549 1.149 2.823 𝐾𝑋𝐻𝑌𝐷, 𝐾𝑂2

𝐻𝑌𝐷

3 3 2.026 4.862 1.534 3.109 𝐾𝑋𝐻𝑌𝐷, 𝑘𝐻𝑌𝐷, 𝐾𝑂2

𝐻𝑌𝐷

Aut.

4 1 1.000 2.886 1.000 3.513 𝜇𝐴

Hete

rot.

5 2 1.394 7.811 2.363 2.978 𝜇𝐻, 𝐾𝐹𝐻

6 2 1.088 4.446 1.328 2.906 𝜇𝐻, 𝑞𝑓𝑒

7 3 1.489 5.246 4.439 2.156 𝜇𝐻, 𝐾𝐹𝐻, 𝑞𝑓𝑒

8 4 1.520 5.142 2.369 3.329 𝜇𝐻, 𝐾𝐹𝐻, 𝐾𝑂2

𝐻

9 4 1.677 3.456 2.396 2.633 𝜇𝐻, 𝐾𝐹𝐻, 𝑏𝐻, 𝐾𝑂2

𝐻

PA

O

10 2 1.000 8.448 1.000 4.808 𝜇𝑃𝐴𝑂

11 2 1.303 4.305 1.030 4.087 𝜇𝑃𝐴𝑂, 𝑏𝑃𝐴𝑂

12 3 2.758 2.622 6.046 1.980 𝜇𝑃𝐴𝑂, 𝑏𝑃𝐴𝑂 , 𝑏𝑃𝐻𝐴

13 4 2.610 2.479 2.121 2.033 𝜇𝑃𝐴𝑂, 𝑏𝑃𝐻𝐴, 𝐾𝑃𝐻𝐴𝑃

Com

bin

atio

ns

1, 4, 5, 10

6 5.841 4.568 3.012 3.442 𝐾𝑋𝐻𝑌𝐷, 𝑘𝐻𝑌𝐷, 𝜇𝐴, 𝜇𝐻, 𝐾𝐹

𝐻 , 𝜇𝑃𝐴𝑂

2, 4, 6, 10

6 2.661 3.802 4.600 3.059 𝐾𝑋𝐻𝑌𝐷, 𝐾𝑂2

𝐻𝑌𝐷, 𝜇𝐴, 𝜇𝐻, 𝑞𝑓𝑒, 𝜇𝑃𝐴𝑂

3, 4, 6, 10

7 2.769 3.939 1.845 3.034 𝐾𝑋𝐻𝑌𝐷, 𝑘𝐻𝑌𝐷, 𝐾𝑂2

𝐻𝑌𝐷, 𝜇𝐴, 𝜇𝐻, 𝑞𝑓𝑒, 𝜇𝑃𝐴𝑂

2, 4, 8, 10

7 3.752 3.763 3.752 3.763 𝐾𝑋𝐻𝑌𝐷, 𝐾𝑂2

𝐻𝑌𝐷, 𝜇𝐴, 𝜇𝐻, 𝐾𝐹𝐻 , 𝐾𝑂2

𝐻 , 𝜇𝑃𝐴𝑂

2, 4, 8, 11

8 4.719 3.194 4.719 3.194 𝐾𝑋𝐻𝑌𝐷, 𝐾𝑂2

𝐻𝑌𝐷, 𝜇𝐴, 𝜇𝐻, 𝐾𝐹𝐻 , 𝐾𝑂2

𝐻 , 𝜇𝑃𝐴𝑂, 𝑏𝑃𝐴𝑂

3, 4, 8, 10

8 7.751 3.554 5.698 2.773 𝐾𝑋𝐻𝑌𝐷, 𝑘𝐻𝑌𝐷, 𝐾𝑂2

𝐻𝑌𝐷, 𝜇𝐴, 𝜇𝐻, 𝐾𝐹𝐻 , 𝐾𝑂2

𝐻 , 𝜇𝑃𝐴𝑂

3, 4, 8, 11

9 7.825 3.070 8.564 2.421 𝐾𝑋

𝐻𝑌𝐷, 𝑘𝐻𝑌𝐷, 𝐾𝑂2𝐻𝑌𝐷, 𝜇𝐴, 𝜇𝐻, 𝐾𝐹

𝐻 , 𝐾𝑂2𝐻 , 𝜇𝑃𝐴𝑂,

𝑏𝑃𝐴𝑂

3, 4, 9, 11

10 7.836 2.643 9.017 2.178 𝐾𝑋

𝐻𝑌𝐷, 𝑘𝐻𝑌𝐷, 𝐾𝑂2𝐻𝑌𝐷, 𝜇𝐴, 𝜇𝐻, 𝐾𝐹

𝐻, 𝑏𝐻, 𝐾𝑂2𝐻 , 𝜇𝑃𝐴𝑂,

𝑏𝑃𝐴𝑂

3, 4, 9, 12

11 8.550 2.252 10.529 1.865 𝐾𝑋

𝐻𝑌𝐷, 𝑘𝐻𝑌𝐷, 𝐾𝑂2𝐻𝑌𝐷, 𝜇𝐴, 𝜇𝐻, 𝐾𝐹

𝐻, 𝑏𝐻, 𝐾𝑂2𝐻 , 𝜇𝑃𝐴𝑂,

𝑏𝑃𝐴𝑂, 𝑏𝑃𝐻𝐴

38

In Table 10, one can notice that some subsets present higher collinearity indexes (𝛾𝐾) than others.

Among the heterotrophs subsets, the subset number 9 has the highest collinearity indicating that

a simultaneous estimation of these four parameters would lead to a biased parameter tuning. The

same situation occurs in the PAO subsets. The subset 10, only containing

𝜇𝑃𝐴𝑂, presents a high identifiability in comparison to the other subsets. When 𝑏𝑃𝐴𝑂 or other

parameters are added, the subsets’ identifiability decrease and collinearity is more pronounced.

The process to select the better subset to calibrate the model was performed, first, analyzing the

collinearity, identifiability and, after that, using Aquasim to perform the parameter estimation,

following the method mentioned in section 4.3. In this process, the combination subsets of

heterotrophs, autotrophs, hydrolysis and PAO parameters (up to size 11) that presented a

collinearity index lower than 10 were tested.

Some subsets, although presenting reasonable values of 𝛾𝐾 and 𝜌𝐾, leaded to extreme values in

the estimation process. For example, the parameter estimation performed with the first subset of

size 6 presented in Table 10 resulted in a 𝑘𝐻𝑌𝐷 of 30.96, more than 10 times its initial value. Such

high values do not correspond to the reality; therefore, subsets that leaded to these extreme

values were not taken into account.

Observing the combinations, the second subset of size 6 seems to be a combination of each

group’ subset with the lowest collinearity indexes. The first subset with size 7 differs from previous

one by adding the parameter 𝑘𝐻𝑌𝐷. Although the subset of size 7 presents a slightly higher

collinearity with this inclusion, it has a higher identifiability index and reached a better model

fitness evaluated by chi-square test: 922.60 for the overall system after calibration (while subset

of size 6 reached 985.6), with reasonable values for all the evaluated parameters. Other

combination subsets composed of a higher number of parameters presented an increasing

collinearity and lower identifiability indexes (subsets with size between 8 and 11). In addition, they

showed higher values in chi-square tests, leading to a weaker goodness of fit. In this way, the

parameter of size 7 (in bold in Table 10) was chosen to perform parameter estimation.

Although the parameter estimation was carried out based on subset’ identifiability, parameters

not included on this procedure (influent concentration, fractions and other considered not possible

to be estimated from the available data) can have a major impact on the results. For example,

SPO4 influent concentration at the first place and XS influent concentration at the 7th place on the

parameters importance ranking show that changes in these parameters have large influence on

the system. Since these parameter were kept fixed, their influence could bias the parameter

selection and estimation.

5.2.3 Parameter estimation for AS

The parameters were calibrated using model results and experimental measurements of effluent

with respect to COD, BOD, total Kjeldahl nitrogen and total phosphorous. In total, 352 iterations

were performed to achieve the minimum sum of squares of the weighted deviations. The total chi-

39

squared value, which was initially 1359.01, decreased to 922.60. The initial and estimated

parameters values are listed in Table 11.

Table 11: Parameters estimated from the subset with size 7.

Parameter Initial values [2] Estimated

𝑘𝐻𝑌𝐷 3.00 5.25

𝐾𝑋𝐻𝑌𝐷 0.10 0.08

𝐾𝑂2𝐻𝑌𝐷 0.20 0.37

𝜇𝐴 1.00 1.09

𝜇𝐻 6.00 5.26

𝑞𝑓𝑒 3.00 3.73

𝜇𝑃𝐴𝑂 1.00 1.07

After these parameter changes, new local sensitivities were calculated (Table 9 -

𝜃𝑒𝑛𝑑). The new collinearity index and identifiability index for the parameters subsets are also listed

in Table 10, under “𝜃𝑒𝑛𝑑”. One can notice that the values of local sensitivity

𝛿𝑗𝑚𝑠𝑞𝑟

decreased and the ranking suffered some changes. The parameters occupying the first

positions are the calibrated ones, what is expected due to their changes and influence on the

model. For example, 𝑘𝐻𝑌𝐷 increased from 3.00 to 5.25 d-1, allowing a higher hydrolysis rate and

reflecting the substrate (SF) availability in the system. The other parameters, such as maximum

growth rate were also adjusted in order to fit the model results to the lab experiments, influencing

directly in the biomass growth and removal efficiencies. Decreasing the maximum growth rate but

keeping decay rate constant leads to a lower effective growth rate, which affects directly the

system performance.

The subsets’ collinearity and identifiability indexes showed in Table 10, after calibration, suffered

significant changes. Observing the groups, one can notice that for hydrolysis, heterotrophs and

PAO, the identifiability of the subsets that compose the combination subset decreased. Only

autotrophs group (subset 4) presented an increased 𝜌𝐾. In relation to 𝛾𝐾, there was a decrease

for heterotrophs, indicating that the parameter tuning caused a lower interdependency between

these parameters. The selected subset of size 7 presented a slightly changes: 33.4% decrease

in 𝛾𝐾, indicating a lower collinearity between the parameters but a decrease of 22.3% in 𝜌𝐾.

The results after the model calibration improved slightly the model fitness to experimental data

(Figure 24 and Figure 25). The chi-squared tests, performed based on effluent concentrations for

BOD, COD, total Kjeldahl nitrogen and total phosphorous simulations and real data, are listed in

Table 12 in order to compare the model improvements.

Table 12: Chi-squared test and RMSE for initial and end values (after parameter estimation)

Chi-squared test

RMSE

𝜃𝑖𝑛𝑖 𝜃𝑒𝑛𝑑 𝜃𝑖𝑛𝑖 𝜃𝑒𝑛𝑑

BOD 879.63 688.29 15.64 g BOD.m-3 12.99 g BOD.m-3

COD 333.38 89.36 27.93 g COD.m-3 27.78 g COD.m-3

TKN 61.00 54.47 5.33 g N.m-3 4.55 g N.m-3

tP 85.05 90.49 2.22 g P.m-3 2.33g P.m-3

40

Figure 24: Organic matter concentration profiles (BOD and COD, respectively) after model calibration

Figure 25: Total Kjeldahl nitrogen and total phosphorous concentrations profiles, respectively, after model calibration.

As seen from Figure 24 and Figure 25, there is an improvement in the adjustment between

observed and predicted data when compared to the model outputs before calibration (Figure 17

and Figure 18). In addition, Table 12 presents the improvements achieved by the calibration

process. Both RMSE and chi-squared tests showed an improvement for BOD, COD and TKN.

5.2.4 Local sensitivity analysis for WSP

The waste stabilization ponds model was evaluated with respect to sensitivity. The potentially

identifiable parameters related to autotrophs, algae, P precipitation and other linked to nutrients

were not taken into account, since the nutrients are not well represented by the model. The

parameter values specified in literature, classes and uncertainties used in the sensitivity analysis

are listed in Table 13.

41

Table 13: Parameters analyzed in the WSP sensitivity, their respective values and uncertainties.

Parameter Value Class Δθ Parameter Value Class Δθ

𝜇𝐴𝑀𝐵 0.085 3 0.0425 𝐾𝑁𝐻𝐹𝐵 0.01 3 0.005

𝑏𝐴𝑀𝐵 0.008 3 0.004 𝐾𝑁𝑂𝐹𝐵 0.5 3 0.25

𝐾𝐴𝐴𝑀𝐵 56 3 28 𝐾𝑂2

𝐹𝐵 0.2 3 0.1

𝐾𝑁𝐻𝐴𝑀𝐵 0.01 3 0.005 𝐾𝑃

𝐹𝐵 0.01 3 0.005

𝐾𝑁𝑂𝐴𝑀𝐵 0.0005 3 0.00025

𝐾𝑂2𝐴𝑀𝐵 0.0002 3 0.0001 iNSF 0.03 2 0.006

𝐾𝑃𝐴𝑀𝐵 0.01 3 0.005 iNXB 0.07 1 0.0035

iNXI 0.02 2 0.004

𝜇𝐻𝑀𝐵 0.35 3 0.175 iNXS 0.04 2 0.008

𝑏𝐻𝑀𝐵 0.025 3 0.001 iPSF 0.01 3 0.005

𝐾𝐻2𝐻𝑀𝐵 0.13 3 0.065 iPXB 0.02 2 0.004

𝐾𝑁𝐻𝐻𝑀𝐵 0.01 3 0.005 iPXI 0.01 3 0.005

𝐾𝑁𝑂𝐻𝑀𝐵 0.0005 3 0.00025 iPXS 0.01 3 0.005

𝐾𝑂2𝐻𝑀𝐵 0.0002 3 0.0001

𝐾𝑃𝐻𝑀𝐵 0.01 3 0.005 𝑌𝐴𝑀𝐵 0.63 1 0.0315

𝑌𝐹𝐵 0.4 1 0.02

𝜇𝐻 6 3 3 𝑌𝐻𝑀𝐵 0.2 1 0.01

𝑏𝐻 0.4 2 0.08 𝑌𝐻 0.63 1 0.0315

𝜂𝐻 0.8 2 0.16 𝑓𝑋𝐼 0.1 1 0.005

𝐾𝐹𝐻 3.00 3 2 𝑓𝑆𝐼 0 - 0.005

𝐾𝐴𝐻 3.00 3 2 𝐾𝐻𝑌𝐷 1 3 0.5

𝐾𝑁𝐻𝐻 0.05 3 0.025

𝐾𝑁𝑂𝐻 0.5 2 0.1 𝑆𝐹 influent 150 3 75

𝐾𝑂2𝐻 0.2 3 0.1 𝑆𝐴 influent 0.01 3 0.005

𝐾𝑃𝐻 0.01 3 0.005 𝑆𝐼 influent 0.01 3 0.005

𝑆𝑁𝐻 influent 40 2 8

𝜇𝐹𝐵 6 3 3 𝑆𝑃𝑂4 influent 7 2 1.4

𝑏𝐹𝐵 0.02 3 0.01 𝑋𝑆 influent 125 3 62.5

𝐾𝐹𝐹𝐵 28 3 14

The parameters local sensitivities were calculated based on the COD and BOD related

parameters following the methodology presented in Section 4.3 , considering the results for SF,

SA, SI, XS in the three compartments.

Table 14: Importance ranking at 𝜃𝑖𝑛𝑖 for the top 30 parameters in WSP model. The potentially estimated

parameters are indicated with an asterisk.

𝜃𝑖𝑛𝑖

Rank Parameter 𝛿𝑗𝑚𝑠𝑞𝑟

Rank Parameter 𝛿𝑗𝑚𝑠𝑞𝑟

1 𝑖𝑃𝑋𝑆 4.967 16 𝐾𝑂2𝐻 * 0.033

2 𝑖𝑁𝑋𝐵 1.120 17 𝜇𝐴𝑀𝐵* 0.014

3 𝑌𝐻 1.027 18 𝐾𝐴𝐴𝑀𝐵* 0.011

4 𝐾𝐹𝐹𝐵* 0.495 19 𝜂𝐻* 0.009

5 𝐾𝑃𝑂4𝐻 * 0.243 20 𝑌𝐹𝐵 0.008

6 𝐾𝑁𝑂𝐹𝐵* 0.234 21 𝑆𝑁𝐻 influent 0.008

7 𝜇𝐻* 0.212 22 𝐾𝑁𝑂𝐻 * 0.007

8 𝐾𝑁𝐻𝐻 * 0.176 23 𝐾𝐴

𝐻* 0.007

9 𝑆𝐹 influent 0.141 24 𝑖𝑁𝑋𝐼 0.007

10 𝐾𝐹𝐻* 0.124 25 𝜇𝐹𝐵* 0.006

11 𝑋𝑆 influent 0.118 26 𝑏𝐹𝐵* 0.006

12 𝑖𝑁𝑋𝑆 0.117 27 𝑖𝑃𝑆𝐹 0.006

13 𝑆𝐼 influent 0.081 28 𝑌𝐴𝑀𝐵 0.006

14 𝑖𝑁𝑆𝐹 0.036 29 𝑖𝑃𝑋𝐵 0.005

15 𝑏𝐻* 0.035 30 𝑏𝐻𝑀𝐵* 0.004

42

Comparing with the sensitivity ranking for WSP (Table 14) and the one obtained for the AS model

(Table 9), one can notice that the three first values are too high, indicating problems in the

sensitivity analysis.

From the ranking, since the potentially identifiable parameters related to nutrients were not

included in the analysis, the importance of organic matter related parameters was over estimated.

For example, fractions of the influent components (SF, XS, SI) and biomass, such as 𝑖𝑃𝑋𝑆 and 𝑖𝑁𝑋𝐵

occupying the first two positions, have a great importance in the parameter ranking. On the other

hand, in the AS model, these type of parameters appeared only in the last positions. Other

parameters, such as influent SNH, which is at position 21 in the WSP parameters ranking, is clearly

important in the system because of its influence not only in algae, autotrophs, but also in

heterotrophs activity (denitrification) and nitrogen availability for biomass formation.

It is also important to highlight that the ranking revealed that the most important ones were

parameters that are not potentially estimated from available data (fractions 𝑖𝑃𝑋𝑆, 𝑖𝑁𝑋𝐵, yield 𝑌𝐻). It

means that these parameters have a significant impact in the model, however, would be kept

fixed in the identifiability analysis, what may cause biased parameter estimations. In addition, the

nutrients related parameters, which were omitted from the local sensitivity analysis, are related to

many COD or BOD processes, affecting identifiability process as a whole.

Considering that the model is not fully reliable and the limitations in the identifiability, the process

to identify a suitable subset for parameters estimation was not carried out. The original, not

calibrated WSP model was then used to evaluate the proposed scenarios.

5.3 Model simulations

5.3.1 Scenarios evaluation for AS

The calibrated AS model was used to assess the system removal efficiency and resilience in

different scenarios in respect to increased wastewater strength (as described in section 4.4.1).

For WSP, the non-calibrated model was used.

The activated sludge system was evaluated at its outlet for organic matter (BOD and COD) and

nutrients (TKN and tP). In the case of the WSP model, the system was only evaluated in relation

to the organic matter.

Observing the first graph in Figure 26, BOD removal efficiency, it is clear that the biodegradable

material is highly removed in most of the cases. The initial removal percentage is high, but it

quickly decreases. This behavior is related to the wastewater flow through the system and the

time it takes from the inlet to reach the outlet of the second compartment (around 1 day), where

the efficiency is measured. After this peak, the system starts to recover again, indicating

heterotrophic biomass growth and, consequently, organic matter removal. When the wastewater

strength increases sharply at day 2, there is a small increase in the efficiency, promoted by the

high availability of substrate and the high half-saturation constant for SA and SF for heterotrophs.

43

At day 7, the wastewater strength abruptly decreases, affecting XH growth and decreasing also

the BOD removal efficiency. From around day 13, the system efficiency was kept constant, close

to 100% for case 3, 97% for reference scenario and 94% for case 4.

Figure 26: Scenarios evaluation with changes in the wastewater strength for BOD, COD, TKN and tP.

The second graph shows the COD removal efficiency, which is clearly lower and with more

prominent peaks than in the previous graph. Since the COD takes into account the XS, the system

takes more time to recover from the peaks. As in the BOD, the abrupt influent concentration

increase favors the heterotrophs growth, promoting a higher COD removal at day 2 (maximum of

around 96%), which decreases until its lowest peak at day 7 (between 62 and 74% removal) when

the wastewater strength is reduced. After this point, the efficiency starts to increase again,

keeping a constant value after day 13 between 91% (for scenario 3) and 87% (for case 4).

With regard to nitrogen, the system removal efficiency at the outlet first decreases between time

zero and day 1 (except for the reference scenario, which has a slightly increase at the beginning

due to the small N concentrations at the first days that still can be handled by the autotrophic

bacteria). An increase in the removal efficiency at day 2 occurs due to the abrupt rise in

44

wastewater strength, but it decreases as long as the ammonium concentration at the second

compartment goes up and the biomass cannot consume it quickly enough due to their slow

growth. Since the influent enters the system in the first compartment, it takes some time to reach

the second compartment outlet, delaying the effluent total nitrogen peak for around 1.5 days. This

shift causes a negative removal efficiency, which increases rapidly again, after the wastewater

strength goes back to normal concentrations. The removal efficiency stabilizes nearly day 13,

with values between 67% for reference scenario and zero for scenario 4.For total phosphorous,

the same behavior observed in TKN removal occurs. After day 13, the removal efficiency is

around 48% for the reference scenario and zero for scenario 4.

From the scenarios evaluation, one can notice that the system can handle higher wastewater

strengths for organic matter. Even scenario 4, with strength increased 50 times, showed a

reasonable removal with its lowest peak around 70% for BOD at day 1 and 94% in the stable

phase; showing that the system can still remove organic matter at acceptable levels. The scenario

3, with WW concentration increased in 10 times, presented a better performance than the other

scenarios in relation to organic matter, indicating that the organic matter promotes biomass

growth and allows it to handle such high concentrations. Nevertheless, the nutrients removal

efficiency is quickly diminished when the SNH/SPO4 concentrations increases. In fact, even for the

reference scenario, the nutrients removal is around 40-65% after the system stabilization, what is

significantly low and confirmed by the experiments carried out previously.

5.3.2 Scenarios evaluation for WSP

Since the model was not calibrated, the original one was used for WSP. The system removal

efficiency and resilience were evaluated in different scenarios, for BOD and COD, in respect to

increased wastewater strength (as described in section 4.4.1).

Observing the scenarios applied to the WSP model (Figure 27), one can notice that for BOD

(graph on left) the system has almost the same removal pattern for all scenarios. It shows that

the system can handle similarly different ranges of wastewater strength, from one to 50 times the

original pollutants concentration in a similar way. The system starts with removal efficiencies

between 97% (for lower WW strengths) and 99.9%. The tank initial conditions were the same for

all situations, so the initial pollutants concentrations affected the removal efficiency more

significantly in reference and first scenarios. The influent peak starts at day 2 and lasts until day

6, but it is only noticed at the outlet around day 11 due to the system HRT. After the peak, the

system recovers and reaches a removal efficiency of around 80%.

With respect to COD, the graph on right shows that until day 10, COD removal does not follow

the same pattern seem on the BOD graph. It happens due to the COD composition, which

includes XS and demands hydrolysis to first degrade it to readily available substrate. It causes

peaks in the outlet, what is noticed before day 10. After this point, the system efficiency decreases

down to around 75% in all scenarios and increases again as the influent peak diminishes. After

that, the system recover phase reaches removal efficiencies of around 89%.

45

Figure 27: Scenarios evaluation with changes in the wastewater strength for BOD and COD, evaluated at the system outlet.

It is important to underline the fact that the WSP system does not reach a stable phase after the

disturbances, as seen in AS graphs. It shows that the evaluated period of time was not enough

to describe the stability phase of the system.

5.3.3 Monte Carlo simulations

The uncertainties of the developed models were evaluated using the Monte Carlo simulations,

following the steps mentioned in section 4.4.2. Only input uncertainties (Δθ), linked to WW

composition and model parameters were considered, as listed in Table 8 for activated sludge

model and Table 13 for waste stabilization model. The uncertainties were based on the classes

proposed by Brun et al. [6], as in the identifiability analysis. The correlations between the

parameters were not taken into account, what could over- or underestimate the uncertainties [92].

The output probabilities are represented in a graphic way, by the mean, 10th and 90th percentiles.

The following graphs (Figure 28 and Figure 29) show the concentrations for reference scenario

(model output), the mean values and the uncertainties (percentiles) calculated in the Monte Carlo

simulations for AS and WSP models. In all cases, the influent concentrating peak is noticeable

(in smaller or larger extent) at the system outlet. At this point, the uncertainties are more

pronounced. In other words, the 10th and 90th percentiles are further away from the mean at the

influent concentration peaks, especially for BOD and COD.

According to Morgan and Henrion [93] the 500 simulations for AS ensure that, in a 95%

confidence level, the 50th percentile lies within the range of the 45.6 - 54.4th percentiles. For WSP,

the 50th percentile lies within 43.6 and 56.3% with 95% of confidence for 250 simulations

Observing the sensitivity ranking after calibration for AS (Table 9), it is clear that many of the top

important parameters (𝑘𝐻𝑌𝐷 , 𝜇𝐻 , 𝐾𝑂2𝐻 , 𝐾𝑋

𝐻𝑌𝐷 , 𝐾𝐹𝐻) are linked to organic matter, influencing directly

hydrolysis and heterotrophic activity, consequently COD and BOD removal. Therefore, the

46

changes in these parameters affect more drastically the model, increasing uncertainties as seen

in the graphs describing BOD and COD in AS system. For the WSP model, the importance ranking

presents BOD and COD related parameters (𝑌𝐻, 𝐾𝐹𝐹𝐵, 𝜇𝐻, 𝑆𝐹 influent, 𝐾𝐹

𝐻 ). However, since the

nutrient related parameters were not considered, the uncertainties analysis may be biased.

Figure 28: Reference scenario for the activated sludge model and the uncertainties associated with

calibrated model represented by the 10th and 90th percentiles

Figure 29: Reference scenario for the waste stabilization ponds model and the uncertainties associated with calibrated model represented by the 10th and 90th percentiles

The influent peaks contribute to the increasing in uncertainties due to its higher values. For

example, SF at its normal concentration in reference scenario varies from 75 to 225 gCOD.m-3

and, at the tripled concentration, from 225 to 675 gCOD.m-3 in the uniform distribution).

47

For AS, the proposed scenarios were evaluated in relation to their uncertainties, as seen in Figure

30 to Figure 33, showing the pollutants concentration over time. Due to the high computational

costs necessary to simulate WSP models, the Monte Carlo simulations were only calculated for

the reference scenario.

Figure 30: Scenario 1 (when the wastewater strength was increase twice) for the activated sludge model and the uncertainties associated to calibrated model represented by the 10th and 90th percentiles

Figure 31: Scenario 2 (when the wastewater strength was increased five times) for the activated sludge model and the uncertainties associated with the calibrated model represented by the 10th and 90th percentiles

48

Figure 32: Scenario 3 (when the wastewater strength was increased ten times) for the activated sludge model and the uncertainties associated to calibrated model represented by the 10th and 90th percentiles

Figure 33: Scenario 4 (when the wastewater strength was increased 50 times) for the activated sludge model and the uncertainties associated with the calibrated model represented by the 10th and 90th

percentiles

The different wastewater strength scenarios, in relation to their uncertainties, presented a similar

behavior between them. BOD and COD presented higher uncertainties than nutrients, what can

be related to their higher influent concentrations. In COD, the two peaks in the graphs can be

related to the beginning and end of the higher influent strength, causing even higher disturbances

49

in the system. The 10th and 90th percentiles for TKN were always closer to the mean when

compared to the others (COD, BOD and tP), indicating lower uncertainties linked to nitrogen. It

can also be explained from sensitivity analysis ranking, where only one parameter (𝜇𝐴) from the

top 10 is related to autotrophs and directly linked to nitrogen removal. For PAO, only two

parameters are directed linked to tP removal, however, the competition for organic matter with

heterotrophs and consume of the organic matter by PAO raise the influence of much more

parameters in phosphorous concentrations, contributing to higher uncertainties.

The uncertainties can be represented by cumulative distribution functions. In these graphs, the y-

axis represents the cumulative probability in which a model output (pollutant concentration) will

be equal or less to the correspondent value in the x-axis [92]. The uncertainties were compared

for AS scenarios at day 6, when the influent peak is more pronounced in the system outlet. The

COD (Figure 34, at top) presented increasing uncertainties for each scenario. Since the system

can handle higher concentrations of organic matter, there is a relatively narrow variation at the

system outlet, represented by the almost vertical curves in the first 4 scenarios. However, at the

last scenario, the system presented a more horizontal line, reflecting a higher uncertainty in the

system output behavior in these conditions. It is explained by the high input uncertainties and

smaller removal efficiency.

In respect to nutrients, the uncertainties related to total phosphorous are shown in Figure 34

(second graph). One can notice that the uncertainty spread in the first four situations is narrow,

reflecting in an almost vertical curve. For the last scenario, the uncertainties increased

significantly. It reflects the high influent uncertainties and the system behavior, which is not

capable to deal with such high phosphorous concentrations. However, it can be highlighted that

the tP uncertainty range at the last scenario is reasonably smaller than the COD. It can be linked

to the COD related parameters, which are higher and have higher influence on the system.

50

Figure 34: Cumulative distribution functions for COD and tP in the AS model, at day 6 in different scenarios.

51

6 CONCLUSIONS

Two mechanistic models were constructed in order to simulate conventional activated sludge

systems and waste stabilization pond systems, from that their removal efficiency and resilient

capacity could be evaluated. Their goodness of fit was assessed by comparing the model outputs

and the data from a case study of Panayiotis [74]. Subsequently, a systematic approach for

sensitivity and identifiability analyses were conducted. More specifically, due to the complexity of

these models, it is important to choose the subset of identifiable model parameters to be included

in a parameter estimation process. This approach, proposed by Brun et al. [6], includes a

preliminary parameter analysis and a subsequent iterative parameter subset selection and tuning

procedure. Finally, several scenarios were simulated to assess the robustness and resilience of

these systems against increased pollutants concentrations.

The activated sludge model, which included 19 processes was able to describe the removal

processes of organic matter and nutrients occurring in an aerobic followed by an anoxic tank,

characterizing the Wuhrmann configuration. The model development was based on the ASM2d

[2] framework and built in Aquasim, a software that showed to be valuable tool when dealing with

wastewater modeling. The AS model presented a significant good fit to the experimental data and

was able to describe the microbial processes happening in each compartment, such as organic

matter oxidation, nitrification-denitrification and biological phosphorous uptake. The calibration

procedure, based on the identifiability analysis approach, leaded to select one subset for

parameter tuning, avoiding collinearity problems. The chosen subset was composed of seven

identifiable parameters related to hydrolysis, heterotrophs, autotrophs and PAO, which that had

their original values altered by minimizing the sum of squares of the weighted deviations between

simulated and observed data. Hydrolysis rate constant (kHYD), which was on the second place in

importance ranking, suffered the most significant changes (from 3.00 d-1 to 5.25 d-1) in the

parameter tuning procedure, consequently increasing hydrolysis rate, influencing the substrate

availability and microbial activity. The calibration increased the model goodness of fit in 32%, in

comparison to the model outputs before parameter tuning.

In respect to the WSP, a model with three compartments (anaerobic, facultative and maturation

ponds) and 20 processes, was also developed using Aquasim. The simulated organic matter

removal presented a reasonable good fit to experimental data. The model output for nutrients

deviated much from the experimental data, showing that it does not reflect the reality. The WSP

presented many limitations, indicating that the development approach was not successful.

Therefore, the model was used only for BOD and COD simulations. In relation to the calibration

procedure (parameter identifiability), it was not carried out to completion due to model limitations

that hindered the identifiability procedure.

With regard to identifiability approach, it is a useful and systematic tool when dealing with models

containing a large number of parameters. However, in the parameter ranking built based on the

individual local sensitivities, some of the most important parameters (such as influent composition

52

and conversion factors) were kept fixed as they are considered not able to be estimated from the

available data, what may possibly lead to biased parameters estimation.

In both models the uncertainties were evaluated by a Monte Carlo simulation tool based only on

input uncertainties. These simulations showed that, at the influent peaks, the uncertainties are

higher since the system suffers a disturbance and the higher influent concentrations contribute in

a large extent to this uncertainty increase. In the proposed scenarios, the same behavior was

observed. The mean values, calculated from the 50th percentile in Monte Carlo simulations, in

some cases (especially for tP) differed significantly from the model output, indicating that the

model results may differ from the concentrations expected for 50% of the time. The WSP model,

evaluated at its reference scenario, presented slightly lower uncertainties due to a smaller number

of parameters considered in this Monte Carlo simulation (nutrient-related parameter were also

disregarded in the uncertainty analysis), what diverges from the reality. In addition, since the WSP

is a complex model, the Monte Carlo simulations were very computational demanding. For these

reasons, the Monte Carlo simulations were not carried out for the proposed scenarios in WSP.

The scenarios allowed the evaluation of AS and WSP models for increased concentration of

pollutants in wastewater influent. Both systems were efficient in removing organic matter, even at

increased wastewater strengths. With regard to nutrients, the AS showed a limited TKN removal

at the stability phase: around 67% for reference scenario and less than 50% in the proposed

scenarios; for tP, around 49% in the reference scenario and less than 25% for increased

wastewater strengths. Although the nutrients were not evaluated in the WSP model, the

experimental data revealed poor phosphorous removal (27% in average) and up to 29% for TKN

at the start of stable phase. These results show that the evaluated systems can handle high

concentrations of organic matter; however, TKN and tP are not removed at a high extent from

both systems. The lower pollutants removal rates in the WSP system, which did not agree with

the expected robustness of this method, seems to require further investigation and long term tests

in order to evaluate the system efficiency in more detail after stabilization.

Since both systems presented similar results for organic matter, the WSP method seems to be

an attractive alternative to AS, given its advantages over conventional treatment systems.

Nevertheless, it is clear that the WSP system setup needs to be improved in order to increase its

efficiency, especially for nutrients. In addition, the mathematical model needs to be further

developed in order to describe the system in a reliable way.

53

7 FUTURE RESEARCH

Municipal wastewater treatment systems are subject to variations in operation, flux, influent

composition and concentrations that influence significantly in system’s performance. In that way,

models showed to be a powerful method to deal with these complex systems, which cover a large

number of biological processes, parameters and variables. However, the developed models

presented some weaknesses that could be improved in order to develop a more reliable and

realistic model.

As a first recommendation, the experimental phase should be conceived and carried out in order

to supply the data necessary for model development. For example, influent and effluent from each

compartment could be characterized more in detail since its composition and representation in

fractions covered by the model components are crucial to determine the biochemical processes

occurring in the system.

Tests carried out in the experimental phase can provide valuable information. Respirometric

techniques (i.e. measurement of the oxygen utilization rate) could provide important information

to characterize aerobic rates and kinetic parameters, such as heterotrophic biomass

concentration, maximum growth and decay rate. It would allow more precise simulations, not

entirely centered on literature-based parameters and, consequently, a more trustworthy model

and minimized input uncertainties. In addition, more detailed information enables the use of more

sophisticated calibration protocols (BIOMATH [94] and STOWA protocols [95], as examples).

In respect to calibration, the parameter identifiability analysis outlined in Brun et al. [6] can be

improved. Additional analysis can be conducted with respect to the effects of fixed parameters

and their influences in parameter estimation in order to identify possible biases.

With regard to uncertainties, only the ones related to input parameter were considered in the

present models. In this way, identification of other possible sources of uncertainties, such as

model structure simplifications are recommended in order to avoid uncertainties underestimation.

In the Monte Carlo simulations, a higher number of samples could be used, increasing confidence.

In addition, correlation studies are also useful to identify the effects of one variable in relation to

others and avoid uncertainties underestimation.

Besides Aquasim, other software, e.g. WEST [96] and BioWin (EnviroSim Associates Ltd.,

Canada), could be used in order to achieve better results. In the AS models, the completely mixed

tanks are considered one-dimensional in space with ideal flow and other factors, such as

sedimentation and diffusion, are disregarded from the model. For the WSP, limitations related to

the sedimentation and diffusion of different substances are not taken into account in the

advective-diffusive compartments. Therefore, several simplifications are assumed, which may

affect the model’s performance and could be overcome using different softwares.

54

Moreover, the base used for the model development could also be further investigated. The

ASM2d, extensively applied in this work, has also limitations. For example, the model does not

cover the difference in yield for heterotrophs in aerobic/anoxic conditions and the competition

between glycogen accumulating organisms (GAO) and PAO in the activated sludge. These

assumptions lead to simplifications that are not always true, generating errors. In the WSP

system, the problems caused by assumptions and simplifications regard nutrients are much more

pronounced. The monitoring of pH, temperature, for example, would improve significantly the

nutrient removal processes, such as ammonia volatilization and phosphorous precipitation

Therefore, other approaches could be further investigated to improve the model reliability.

As further research, it is recommended the development of models based on full-size AS plants

or WSP, what would allow a more realistic model and the possibility of more reliable calibration

and validation.

55

8 REFERENCES

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60

9 APPENDICES

A. Activated sludge model

Appendix A.1: Gujer matrix, kinetic rate expressions and typical values for aerobic and anoxic processes occurring in AS system

Table 15: Activated sludge matrix, showing stoichiometric coefficients for all processes (first column) and components (first row) and COD conversion factors (last rows).

Component (i) → SF

gCOD.m-

3

SA

gCOD.m-

3

SI

gCOD.m-

3

SNH

gN.m-3 SNO

gN.m-3 SPO4

gP.m-3 SO2

gO2.m-3

SN2

gN.m-3

XA

gCOD.m-

3

XH

gCOD.m-

3

XPAO

gCOD.m-

3

XPP gP.m-

3

XPHA

gCOD.m-

3

XS

gCOD.m-

3

XI

gCOD.m-

3 Process (j) ↓

Hydrolysis

ρ17 Aerobic

hydrolysis 1 - fSI fSI

fSI.(iNSF -iNSI) + iNXS

-iNSF

fSI.(iPSF -iPSI) + iPXS

-iPSF -1

ρ18 Anoxic

hydrolysis 1 - fSI fSI

fSI.(iNSF -iNSI) + iNXS

-iNSF

fSI.(iPSF -iPSI) + iPXS

-iPSF -1

ρ19 Anaerobic hydrolysis

1 - fSI fSI fSI.(iNSF -

iNSI) + iNXS -iNSF

fSI.(iPSF -

iPSI) + iPXS -iPSF

-1

Heterotrophs

ρ1 Aerobic growth

on SF −

1

𝑌𝐻

−𝑖𝑁𝑋𝐵

+1

𝑌𝐻

𝑖𝑁𝑆𝐹

−𝑖𝑃𝑋𝐵

+1

𝑌𝐻

𝑖𝑃𝑆𝐹 1 −

1

𝑌𝐻

1

ρ2 Aerobic growth

on SA −

1

𝑌𝐻

−𝑖𝑁𝑋𝐵 −𝑖𝑃𝑋𝐵 1 −1

𝑌𝐻

1

ρ3 Anoxic growth of heterotrophs on SF (denitr.)

−1

𝑌𝐻

−𝑖𝑁𝑋𝐵

+1

𝑌𝐻

𝑖𝑁𝑆𝐹 −

1−𝑌𝐻

2.86𝑌𝐻

−𝑖𝑃𝑋𝐵

+1

𝑌𝐻

𝑖𝑃𝑆𝐹

1−𝑌𝐻

2.86𝑌𝐻

1

ρ4 Anoxic growth of heterotrophs on SA (denitr.)

−1

𝑌𝐻

−𝑖𝑁𝑋𝐵 −1−𝑌𝐻

2.86𝑌𝐻

−𝑖𝑃𝑋𝐵 1−𝑌𝐻

2.86𝑌𝐻

1

ρ5 Fermentation -1 1 𝑖𝑁𝑆𝐹 𝑖𝑃𝑆𝐹

61

ρ6 Decay of

heterotrophs

𝑖𝑁𝑋𝐵

− 𝑖𝑁𝑋𝑆

− 𝑓(𝑖𝑁𝑋𝐼

− 𝑖𝑁𝑋𝑆)

𝑖𝑃𝑋𝐵

− 𝑖𝑃𝑋𝑆

− 𝑓(𝑖𝑃𝑋𝐼

− 𝑖𝑃𝑋𝑆)

-1 1 − 𝑓𝑋𝐼 𝑓𝑋𝐼

Autotrophs

ρ7 Aerobic growth of autotrophs

(XA)

−𝑖𝑁𝑋𝐵

−1

𝑌𝐴

1

𝑌𝐴

−𝑖𝑃𝑋𝐵 −4.57−𝑌𝐴

𝑌𝐴

1

ρ8 Decay of

autotrophs

𝑖𝑁𝑋𝐵

− 𝑖𝑁𝑋𝑆

− 𝑓(𝑖𝑁𝑋𝐼

− 𝑖𝑁𝑋𝑆)

𝑖𝑃𝑋𝐵

− 𝑖𝑃𝑋𝑆

− 𝑓(𝑖𝑃𝑋𝐼

− 𝑖𝑃𝑋𝑆)

-1 1 − 𝑓𝑋𝐼 𝑓𝑋𝐼

Phosphorous Accumulating Organisms

ρ9 Storage of XPHA -1 YPO4 −𝑌𝑃𝑂4 1

ρ10 Aerobic storage

of XPP -1 −𝑌𝑃𝐻𝐴 1 −𝑌𝑃𝐻𝐴

ρ11 Anoxic storage

of XPP −

𝑌𝑃𝐻𝐴

2.86 -1

𝑌𝑃𝐻𝐴

2.86 1 −𝑌𝑃𝐻𝐴

ρ12 Aerobic growth

of XPAO −𝑖𝑁𝑋𝐵 −𝑖𝑃𝑋𝐵 1 −

1

𝑌𝑃𝐴𝑂

1 −1

𝑌𝑃𝐴𝑂

ρ13 Anoxic growth

of XPAO −𝑖𝑁𝑋𝐵

1 − 1/𝑌𝑃𝐴𝑂

2.86 −𝑖𝑃𝑋𝐵 −

1 − 1/𝑌𝑃𝐴𝑂

2.86 1 −

1

𝑌𝑃𝐴𝑂

ρ14 Decay of XPAO

𝑖𝑁𝑋𝐵

− 𝑖𝑁𝑋𝑆

− 𝑓(𝑖𝑁𝑋𝐼

− 𝑖𝑁𝑋𝑆)

𝑖𝑃𝑋𝐵

− 𝑖𝑃𝑋𝑆

− 𝑓(𝑖𝑃𝑋𝐼

− 𝑖𝑃𝑋𝑆)

-1 1 − 𝑓𝑋𝐼 𝑓𝑋𝐼

ρ15 Decay of XPP 1 -1

ρ16 Decay of XPHA 1 -1

Conversion Factors

gCOD/unit comp. 1 1 0 -4.57 0 -1 -1.71 1 1 1 0 1 1 1

gN/unit comp. iNSF 0 1 1 0 0 1 iNXB iNXB iNXB 0 0 iNXS iNXI

gP/unit comp. iPSF 0 0 0 1 0 0 iPXB iPXB iPXB 1 0 iPXS iPXI

62

Table 16: Processes listed in AS model and respective kinetic rate expressions.

Process Kinetic expression

Hydrolysis

ρ17 Aerobic hydrolysis 𝐾ℎ.𝑆𝑂2

𝐾𝑂2𝐻 + 𝑆𝑂2

.𝑋𝑆/𝑋𝐻

𝐾𝑋 + 𝑋𝑆/𝑋𝐻

. 𝑋𝐻

ρ18 Anoxic hydrolysis 𝐾ℎ. 𝜂𝐻

𝐾𝑂2𝐻

𝐾𝑂2𝐻 + 𝑆𝑂2

.𝑆𝑁𝑂

𝐾𝑁𝑂𝐻 + 𝑆𝑁𝑂

.𝑋𝑆/𝑋𝐻

𝐾𝑋 + 𝑋𝑆/𝑋𝐻

. 𝑋𝐻

ρ19 Anaerobic hydrolysis 𝐾ℎ . 𝜂𝑓𝑒

𝐾𝑂2𝐻

𝐾𝑂2𝐻 + 𝑆𝑂2

.𝐾𝑁𝑂

𝐻

𝐾𝑁𝑂𝐻 + 𝑆𝑁𝑂

.𝑋𝑆/𝑋𝐻

𝐾𝑋 + 𝑋𝑆/𝑋𝐻

. 𝑋𝐻

Heterotrophs

ρ1 Growth on SF 𝜇𝐻 .𝑆𝑂2

𝐾𝑂2𝐻 + 𝑆𝑂2

.𝑆𝑁𝐻

𝐾𝑁𝐻𝐻 + 𝑆𝑁𝐻

.𝑆𝑃𝑂4

𝐾𝑃𝐻 + 𝑆𝑃𝑂4

.𝑆𝐹

𝐾𝐹𝐻 + 𝑆𝐹

.𝑆𝐹

𝑆𝐹 + 𝑆𝐴

. 𝑋𝐻

ρ2 Growth on SA 𝜇𝐻 .𝑆𝑂2

𝐾𝑂2𝐻 + 𝑆𝑂2

.𝑆𝑁𝐻

𝐾𝑁𝐻𝐻 + 𝑆𝑁𝐻

.𝑆𝑃𝑂4

𝐾𝑃𝐻 + 𝑆𝑃𝑂4

.𝑆𝐴

𝐾𝐴𝐻 + 𝑆𝐴

.𝑆𝐴

𝑆𝐹 + 𝑆𝐴

. 𝑋𝐻

ρ3 Denitrification with

fermentable substrates (SF) 𝜇𝐻 . 𝜂𝐻

𝐾𝑂2𝐻

𝐾𝑂2𝐻 + 𝑆𝑂2

.𝑆𝑁𝑂

𝐾𝑁𝑂𝐻 + 𝑆𝑁𝑂

.𝑆𝑁𝐻

𝐾𝑁𝐻𝐻 + 𝑆𝑁𝐻

.𝑆𝑃𝑂4

𝐾𝑃𝐻 + 𝑆𝑃𝑂4

.𝑆𝐹

𝐾𝐹𝐻 + 𝑆𝐹

.𝑆𝐹

𝑆𝐹 + 𝑆𝐴

. 𝑋𝐻

ρ4 Denitrification with

fermentation products (SA) 𝜇𝐻 . 𝜂𝐻

𝐾𝑂2𝐻

𝐾𝑂2𝐻 + 𝑆𝑂2

.𝑆𝑁𝑂

𝐾𝑁𝑂𝐻 + 𝑆𝑁𝑂

.𝑆𝑁𝐻

𝐾𝑁𝐻𝐻 + 𝑆𝑁𝐻

.𝑆𝑃𝑂4

𝐾𝑃𝐻 + 𝑆𝑃𝑂4

.𝑆𝐴

𝐾𝐴𝐻 + 𝑆𝐴

.𝑆𝐴

𝑆𝐹 + 𝑆𝐴

. 𝑋𝐻

ρ5 Fermentation 𝑞𝑓𝑒 .𝐾𝑂2

𝐻

𝐾𝑂2𝐻 + 𝑆𝑂2

.𝐾𝑁𝑂

𝐻

𝐾𝑁𝑂𝐻 + 𝑆𝑁𝑂

.𝑆𝐹

𝐾𝐹𝐻 + 𝑆𝐹

. 𝑋𝐻

ρ6 Decay of heterotrophs 𝑏𝐻 . 𝑋𝐻

Autotrophs

ρ7 Growth of autotrophs 𝜇𝐴.𝑆𝑂2

𝐾𝑂2𝐴 + 𝑆𝑂2

.𝑆𝑁𝐻

𝐾𝑁𝐻𝐴 + 𝑆𝑁𝐻

.𝑆𝑃𝑂4

𝐾𝑃𝐴 + 𝑆𝑃𝑂4

. 𝑋𝐴

ρ8 Decay of autotrophs 𝑏𝐴. 𝑋𝐴

Phosphorous Accumulating Organisms

ρ9 Storage of XPHA 𝑞𝑃𝐻𝐴.𝑆𝐴

𝐾𝐴𝑃 + 𝑆𝐴

.𝑋𝑃𝑃/𝑋𝑃𝐴𝑂

𝐾𝑃𝑃𝑃 + 𝑋𝑃𝑃/𝑋𝑃𝐴𝑂

. 𝑋𝑃𝐴𝑂

ρ10 Aerobic storage of XPP 𝑞𝑃𝑃 .𝑆𝑂2

𝐾𝑂2𝑃 + 𝑆𝑂2

.𝑆𝑃𝑂4

𝐾𝑃𝑆𝑃 + 𝑆𝑃𝑂4

.𝑋𝑃𝐻𝐴/𝑋𝑃𝐴𝑂

𝐾𝑃𝐻𝐴𝑃 + 𝑋𝑃𝐻𝐴/𝑋𝑃𝐴𝑂

.𝐾𝑀𝐴𝑋

𝑃 − 𝑋𝑃𝑃/𝑋𝑃𝐴𝑂

𝐾𝐼𝑃𝑃𝑃 + 𝐾𝑀𝐴𝑋

𝑃 − 𝑋𝑃𝑃/𝑋𝑃𝐴𝑂

. 𝑋𝑃𝐴𝑂

ρ11 Anoxic storage of XPP 𝜌10. 𝜂𝑃 .𝐾𝑂2

𝑃

𝑆𝑂2

.𝑆𝑁𝑂

𝐾𝑁𝑂𝑃 + 𝑆𝑁𝑂

63

ρ12 Aerobic growth of XPAO 𝜇𝑃𝐴𝑂.𝑆𝑂2

𝐾𝑂2𝑃 + 𝑆𝑂2

.𝑆𝑁𝐻

𝐾𝑁𝐻𝑃 + 𝑆𝑁𝐻

.𝑆𝑃𝑂4

𝐾𝑃𝑃 + 𝑆𝑃𝑂4

.𝑋𝑃𝐻𝐴/𝑋𝑃𝐴𝑂

𝐾𝑃𝐻𝐴𝑃 + 𝑋𝑃𝐻𝐴/𝑋𝑃𝐴𝑂

. 𝑋𝑃𝐴𝑂

ρ13 Anoxic growth of XPAO 𝜌12. 𝜂𝑃 .𝐾𝑂2

𝑃

𝑆𝑂2

.𝑆𝑁𝑂

𝐾𝑁𝑂𝑃 + 𝑆𝑁𝑂

ρ14 Decay of XPAO 𝑏𝑃𝐴𝑂. 𝑋𝑃𝐴𝑂

ρ15 Decay of XPP 𝑏𝑃𝑃 . 𝑋𝑃𝑃

ρ16 Decay of XPHA 𝑏𝑃𝐻𝐴. 𝑋𝑃𝐻𝐴

Table 17: Typical values AS for stoichiometric and kinetic coefficients

Symbol Parameter Value and unit Reference

Conversion factors:

iNSI Nitrogen content of inert soluble COD SI 0.01 g N.g-1 COD ASM2d [2]

iNSF Nitrogen content in fermentable substrate SF 0.03 g N.g-1 COD ASM2d [2]

iNXB Nitrogen content in active biomass 0.07 g N.g-1 COD ASM2d [2]

iNXI Nitrogen content of inert particulate COD XI 0.02 g N.g-1 COD ASM2d [2]

iNXS Nitrogen content of slowly biodegradable substrate XS 0.04 g N.g-1 COD ASM2d [2]

iPSI Phosphorous content of inert soluble COD SI 0.00 g P.g-1 COD ASM2d [2]

iPSF Phosphorous content in fermentable substrate SF 0.01 g P.g-1 COD ASM2d [2]

iPXB Phosphorous content in active biomass 0.02 g P.g-1 COD ASM2d [2]

iPXI Phosphorous content of inert particulate COD XI 0.01 g P.g-1 COD ASM2d [2]

iPXS Phosphorous content of slowly biodegradable substrate XS 0.01 g P.g-1 COD ASM2d [2]

fXI Inert content in biomass 0.10 g COD. g-1 COD ASM2d [2]

fSI Production of SI in hydrolysis 0 g COD. g-1 COD ASM2d [2]

Hydrolysis

𝑘𝐻𝑌𝐷 Hydrolysis rate constant 3.00 d-1 ASM2d [2]

𝜂𝑁𝑂𝐻𝑌𝐷 Anoxic hydrolysis reduction factor 0.60 ASM2d [2]

𝜂𝑓𝑒𝐻𝑌𝐷 Anaerobic hydrolysis reduction factor 0.40 ASM2d [2]

𝐾𝑂2𝐻𝑌𝐷 Saturation/inhibition coefficient for oxygen 0.20 g O2.m

-3 ASM2d [2]

𝐾𝑁𝑂𝐻𝑌𝐷 Inhibition coefficient for nitrate 0.50 g N.m-3 ASM2d [2]

𝐾𝑋𝐻𝑌𝐷 Saturation/inhibition coefficient for particulate COD 0.10 g XS. g-1 XH ASM2d [2]

Heterotrophic organisms:

𝑌𝐻 Yield of heterotrophic bacteria 0.63 g COD.g-1 COD ASM2d [2]

𝜇𝐻 Maximum growth rate of heterotrophs 6.00 d-1 ASM2d [2]

𝐾𝑁𝐻𝐻 Ammonium half saturation constant for heterotrophs 0.05 g N.m-3 ASM2d [2]

𝐾𝑂2𝐻 Oxygen half saturation constant for heterotrophs 0.20 g O2.m

-3 ASM2d [2]

𝐾𝑁𝑂𝐻 Nitrate half saturation constant for heterotrophs 0.50 g N.m-3 ASM2d [2]

64

𝐾𝑃𝐻 Phosphorous half saturation constant of heterotrophs 0.01 g P.m-3 ASM2d [2]

𝐾𝐹𝐻 Fermentable substrate half saturation constant for heterotrophs 4.00 g COD.m-3 ASM2d [2]

𝐾𝐴𝐻 Fermentation products (acetate) half saturation constant for heterotrophs 4.00 g COD.m-3 ASM2d [2]

𝐾𝑓𝑒 Saturation coefficient for fermentation on SF 4.00 g COD.m-3 ASM2d [2]

𝑞𝑓𝑒 Maximum fermentation rate 3.00 g SF. g-1 XH d-1 ASM2d [2]

𝜂𝐻 Correction factor for 𝜇𝐻 under anoxic conditions 0.80 ASM2d [2]

bH Specific biomass decay rate of heterotrophs 0.40 d-1 ASM2d [2]

Autotrophic organisms:

𝑌𝐴 Yield of AOB on ammonia 0.24 g COD.g-1 N ASM2d [2]

𝜇𝐴 Maximum growth rate of autotrophs 1.00 d-1 ASM2d [2]

𝐾𝑁𝐻𝐴 Ammonium half saturation constant for autotrophs 1.00 g N.m-3 ASM2d [2]

𝐾𝑂2𝐴 Oxygen half saturation constant for autotrophs 0.50 g O2.m

-3 ASM2d [2]

𝐾𝑃𝐴 Phosphorous half saturation constant for autotrophs 0.01 g P.m-3 ASM2d [2]

𝑏𝐴 Specific biomass decay rate of autotrophs 0.15 d-1 ASM2d [2]

Phosphorous accumulating organisms (PAO):

YPAO Yield coefficient for PAO (biomass/PHA) 0.63 g COD.g-1 COD ASM2d [2]

YPO4 PP requirement (SPO4 release) for PHA storage 0.40 g P.g-1 COD ASM2d [2]

YPHA PHA requirement for PP storage 0.20 g COD.g-1 COD ASM2d [2]

𝜇𝑃𝐴𝑂 Maximum growth rate of PAO 1.00 d-1 ASM2d [2]

𝑞𝑃𝐻𝐴 Storage of XPHA (base XPP) rate constant 3.00 g XPHA. g-1 XPAO d-1 ASM2d [2]

𝑞𝑃𝑃 Storage of XPP rate constant 1.50 g XPP. g-1 XPAO d-1 ASM2d [2]

𝐾𝑃𝑃𝑃 Poly-phosphate saturation coefficient 0.01 g XPP. g-1 XPAO ASM2d [2]

𝐾𝑃𝑆𝑃 Phosphorous in storage of PP saturation coefficient 0.20 g P.m-3 ASM2d [2]

𝐾𝑀𝐴𝑋𝑃 Maximum ratio of XPP/XPAO 0.34 g XPP. g-1 XPAO ASM2d [2]

𝐾𝐼𝑃𝑃𝑃 Inhibition coefficient for PP storage 0.02 g XPP. g-1 XPAO ASM2d [2]

𝐾𝑃𝐻𝐴𝑃 PHA saturation coefficient 0.01 g XPHA. g-1 XPAO ASM2d [2]

𝐾𝑁𝐻𝑃 Ammonium half saturation constant for PAO 0.05 g N.m-3 ASM2d [2]

𝐾𝑂2𝑃 Oxygen half saturation constant for PAO 0.20 g O2.m

-3 ASM2d [2]

𝐾𝑁𝑂𝑃 Nitrate half saturation coefficient for PAO 0.50 g N.m-3 ASM2d [2]

𝐾𝑃𝑃 Phosphate (nutrient) half saturation constant for PAO 0.01 g P.m-3 ASM2d [2]

𝐾𝐴𝑃 Fermentation products (acetate) half saturation constant for PAO 4.00 g COD.m-3 ASM2d [2]

𝜂𝑃 Correction factor for 𝜇𝑃𝐴𝑂 under anoxic conditions 0.60 ASM2d [2]

𝑏𝑃𝐴𝑂 Specific biomass decay rate of XPAO 0.20 d-1 ASM2d [2]

𝑏𝑃𝑃 Specific biomass decay rate of XPP 0.20 d-1 ASM2d [2]

𝑏𝑃𝐻𝐴 Specific biomass decay rate of XPHA 0.20 d-1 ASM2d [2]

65

Appendix A.2: Mass balances for aerobic and anoxic processes occurring in AS system

Table 18: Mass balance for heterotrophs with respect to COD, nitrogen and phosphorous in the AS model

SF SA SNH4 SNO3 SPO4 SO2 SN2 XH XS XI COD balance / N balance / P balance

ρ1 Aerobic growth on SF −1

𝑌𝐻

−𝑖𝑁𝑋𝐵 +1

𝑌𝐻

𝑖𝑁𝑆𝐹 −𝑖𝑃𝑋𝐵 +1

𝑌𝐻

𝑖𝑃𝑆𝐹

1

−1

𝑌𝐻

1

(-1/YH)*1 + (-iNXB+iNSF/YH)*0 + (-iPXB+iPSF/YH)*0 + (1-1/YH)*(-1) + 1*1 = 0

(-1/YH)*iNSF + (-iNXB+iNSF/YH)*1 + (-iPXB+iPSF/YH)*0 + (1-1/YH)*0 + 1* iNXB = 0

(-1/YH)*iPSF + (-iNXB+iNSF/YH)*0 + (-iPXB+iPSF/YH)*1 + (1-1/YH)*0 + 1* iPXB = 0

ρ2 Aerobic growth on SA −1

𝑌𝐻

−𝑖𝑁𝑋𝐵 −𝑖𝑃𝑋𝐵

1

−1

𝑌𝐻

1

(-1/YH)*1 + (-iNXB)*0 + (-iPXB)*0 + (1-1/YH)*(-1) + 1*1 = 0 (-1/YH)*0 + (-iNXB)*1 + (-iPXB)*0 + (1-1/YH)*0 + 1* iNXB = 0 (-1/YH)*0 + (-iNXB)*0 + (-iPXB)*1 + (1-1/YH)*0 + 1* iPXB = 0

ρ3 Anoxic growth of

heterotrophs on SF (denitr.)

−1

𝑌𝐻

−𝑖𝑁𝑋𝐵 +1

𝑌𝐻

𝑖𝑁𝑆𝐹 −1−𝑌𝐻

2.86𝑌𝐻

−𝑖𝑃𝑋𝐵 +1

𝑌𝐻

𝑖𝑃𝑆𝐹 1−𝑌𝐻

2.86𝑌𝐻

1

(-1/YH)*1 + (-iNXB+iNSF/YH)*0 + (-(1-YH)/(2.86YH))*(-4.57) + (-iPXB+iPSF/YH)*0 + ((1-YH)/(2.86YH)) *(-1.71) + 1*1 = 0

(-1/YH)*iNSF + (-iNXB+iNSF/YH)*1 + (-(1-YH)/(2.86YH))*1 + (-iPXB+iPSF/YH)*0 + ((1-YH)/(2.86YH)) *1 + 1* iNXB = 0

(-1/YH)*iPSF + (-iNXB+iNSF/YH)*0 + (-(1-YH)/(2.86YH))*0 + (-iPXB+iPSF/YH)*1 + ((1-YH)/(2.86YH)) *0 + 1* iPXB = 0

ρ4 Anoxic growth of

heterotrophs on SA (denitr.)

−1

𝑌𝐻

−𝑖𝑁𝑋𝐵 −1−𝑌𝐻

2.86𝑌𝐻

−𝑖𝑃𝑋𝐵 1−𝑌𝐻

2.86𝑌𝐻

1

(-1/YH)*1 + (-iNXB)*0 + (-(1-YH)/(2.86YH)*(-4.57) + (-iPXB)*0 + ((1-YH)/(2.86YH) *(-1.71) + 1*1 = 0

(-1/YH)*0 + (-iNXB)*1 + (-(1-YH)/(2.86YH))*1 + (-iPXB)*0 + ((1-YH)/(2.86YH)) *1 + 1* iNXB =0

(-1/YH)*0 + (-iNXB)*0 + (-(1-YH)/(2.86YH))*0 + (-iPXB)*1 + ((1-YH)/(2.86YH)) *0 + 1* iPXB = 0

ρ5 Fermentation -1 1 iNSF iPSF (-1)*1 + (1)*1 = 0

(-1)* iNSF +1* iNSF +(1)*0 = 0 (-1)* iPSF + 1*iPSF (1)*0 = 0

ρ6 Decay of heterotrophs 𝑖𝑁𝑋𝐵 − 𝑖𝑁𝑋𝑆

− 𝑓(𝑖𝑁𝑋𝐼 − 𝑖𝑁𝑋𝑆)

𝑖𝑃𝑋𝐵 − 𝑖𝑃𝑋𝑆

− 𝑓(𝑖𝑃𝑋𝐼 − 𝑖𝑃𝑋𝑆) -1

1− 𝑓𝐼

𝑓𝐼

(iNXB-iNXS-f(iNXI-iNXS))*0 + (iPXB-iPXS-f(iPXI-iPXS))*0 + (-1)*1 + (1-fi)*1 + fi*1 = 0

(iNXB-iNXS-f(iNXI-iNXS))*1 + (iPXB-iPXS-f(iPXI-iPXS))*0 + (-1)* iNXB + (1-fi)* iNXS + fi* iNXI = 0

(iNXB-iNXS-f(iNXI-iNXS))*0 + (iPXB-iPXS-f(iPXI-iPXS))*1 + (-1)* iPXB + (1-fi)* iPXS + fi* iPXI = 0

Composition matrix

gCOD/unit comp. 1 1 0 -4.57 0 -1 -1.71 1 1 1

gN/unit comp. iNSF 0 1 1 0 0 1 iNXB iNXS iNXI

gP/unit comp. iPSF 0 0 0 1 0 0 iPXB iPXS iPXI

66

Table 19: Mass balance for autotrophs with respect to COD, nitrogen and phosphorous in the AS model

SNH4 SNO3 SPO4 SO2 XA XS XI COD balance / N balance / P balance

ρ7 Aerobic growth of autotrophs

−𝑖𝑁𝑋𝐵 −1

𝑌𝐴

1

𝑌𝐴

−𝑖𝑃𝑋𝐵 −4.57−𝑌𝐴

𝑌𝐴

1 (-iNXB-1/YA)*0 + (1/YA)*(-4.57) + (-iPXB)*0 + (-(4.57-YA)/YA)*(-1) + 1*1= 0

(-iNXB-1/YA)*1 + (1/YA)*1 + (-iPXB)*0 + (-(4.57-YA)/YA)*0 + 1*iNXB = 0 (-iNXB-1/YA)*0 + (1/YA)*0 + (-iPXB)*1 + (-(4.57-YA)/YA)*0 + 1*iPXB = 0

ρ8 Decay of

autotrophs

𝑖𝑁𝑋𝐵 − 𝑖𝑁𝑋𝑆

− 𝑓(𝑖𝑁𝑋𝐼

− 𝑖𝑁𝑋𝑆)

𝑖𝑃𝑋𝐵 − 𝑖𝑃𝑋𝑆

− 𝑓(𝑖𝑃𝑋𝐼

− 𝑖𝑃𝑋𝑆)

-1 1 − 𝑓𝐼 𝑓𝐼 (iNXB-iNXS-f(iNXI-iNXS))*0 + (iPXB-iPXS-f(iPXI-iPXS))*0 + (-1)*1 + (1-fi)*1 + fi*1 = 0

(iNXB-iNXS-f(iNXI-iNXS))*1 + (iPXB-iPXS-f(iPXI-iPXS))*0 + (-1)* iNXB + (1-fi)* iNXS + fi* iNXI = 0 (iNXB-iNXS-f(iNXI-iNXS))*0 + (iPXB-iPXS-f(iPXI-iPXS))*1 + (-1)* iPXB + (1-fi)* iPXS + fi* iPXI = 0

Composition matrix

gCOD/unit comp. 0 -4.57 0 -1 1 1 1

gN/unit comp. 1 1 0 0 iNXB iNXS iNXI

gP/unit comp. 0 0 1 0 iPXB iPXS iPXI

Table 20: Mass balance for PAO with respect to COD, nitrogen and phosphorous in the AS model

SA SNH4 SPO4 SO2 XPAO XPP XPHA XS XI COD balance / N balance / P balance

ρ9 Storage of

XPHA -1 𝑌𝑃𝑂4 −𝑌𝑃𝑂4 1

(-1)*1 + (YPO4)*0 + (-YPO4)*0 + 1*1 = 0 (-1)*0 + (YPO4)*0 + (-YPO4)*0 + 1*0 = 0 (-1)*0 + (YPO4)*1 + (-YPO4)*1 + 1*0 = 0

ρ10 Storage of

XPP -1 −𝑌𝑃𝐻𝐴 1 −𝑌𝑃𝐻𝐴

(-1)*0 + (-YPHA)*(-1) + 1*0 + (-YPHA)*1 = 0 (-1)*0 + (-YPHA)*0 + 1*0 + (-YPHA)*0 = 0 (-1)*1 + (-YPHA)*0 + 1*1 + (-YPHA)*0 = 0

ρ11 Aerobic

growth of XPAO

−𝑖𝑁𝑋𝐵 −𝑖𝑃𝑋𝐵 1 −1

𝑌𝐻

1 −1

𝑌𝐻

(-iPXB)*0 + (1-1/YH)*(-1) + 1*1 + (-1/YH)*1 = 0 (-iPXB)*0 + (1-1/YH)*0 + 1*iNXB + (-1/YH)*0 = 0 (-iPXB)*1 + (1-1/YH)*0 + 1*iPXB + (-1/YH)*0 = 0

ρ12 Decay of XPAO 𝑖𝑁𝑋𝐵 − 𝑖𝑁𝑋𝑆

− 𝑓(𝑖𝑁𝑋𝐼

− 𝑖𝑁𝑋𝑆)

𝑖𝑃𝑋𝐵 − 𝑖𝑃𝑋𝑆

− 𝑓(𝑖𝑃𝑋𝐼

− 𝑖𝑃𝑋𝑆) -1 1 − 𝑓𝐼 𝑓𝐼

(iNXB-iNXS-f(iNXI-iNXS))*0 + (iPXB-iPXS-f(iPXI-iPXS))*0 + (-1)*1 + (1-fi)*1 + fi*1 = 0

(iNXB-iNXS-f(iNXI-iNXS))*1 + (iPXB-iPXS-f(iPXI-iPXS))*0 + (-1)* iNXB + (1-fi)* iNXS + fi* iNXI = 0

(iNXB-iNXS-f(iNXI-iNXS))*0 + (iPXB-iPXS-f(iPXI-iPXS))*1 + (-1)* iPXB + (1-fi)* iPXS + fi* iPXI = 0

ρ13 Decay of XPP 1 -1 1*0 + (-1)*0 = 0 1*0 + (-1)*0 = 0 1*1 + (-1)*1 = 0

ρ14 Decay of XPHA 1 -1 1*1 + (-1)*1 = 0 1*0 + (-1)*0 = 0 1*0 + (-1)*0 = 0

Composition matrix

gCOD/unit comp. 1 0 0 -1 1 0 1 1 1

gN/unit comp. 0 1 0 0 iNXB 0 0 iNXS iNXI

gP/unit comp. 0 0 1 0 iPXB 1 0 iPXS iPXI

67

B. Waste Stabilization Pond Model

Appendix B1: Gujer matrix, processes and typical values for anaerobic and facultative ponds

Table 21: Matrix for the anaerobic pond, first pond composing the WSP system, showing stoichiometric coefficients for all processes (first column) and components (first row)

and COD conversion factors (last rows).

Component (i) → SF

gCOD.m-3

SA

gCOD.m-3 SNH

gN.m-3 SPO4

gP.m-3 SCH4

gCOD.m-3 SH2

gH.m-3 XFB

gCOD.m-3 XAMB

gCOD.m-3 XH2

gCOD.m-3 XS

gCOD.m-3 XI

gCOD.m-3 Process (j) ↓

ρ12 Hydrolysis of

particulate substrate 1 iNXS –iNSF iPXS –iPSF -1

ρ13 Anaerobic growth of

FB - 1/YFB

1

9(

−𝑌𝐹𝐵 + 1

𝑌𝐹𝐵

) -iNXB + iNSF/YFB -iPXB + iPSF/YFB 1

9(

−𝑌𝐹𝐵 + 1

𝑌𝐹𝐵

) 1

ρ14 Anaerobic growth of

AMB -1/YAMB -iNXB -iPXB ¼*(-1+1/YAMB) 1

ρ25 Anaerobic growth of

HMB -iNXB -iPXB ¼*(-1+1/YHMB) 1/8*(-1/YHMB) 1

ρ19 Decay of FB (fI-1)* iNXS+iNXB –

(fI*iNXI) (1-fI)* iPXS - iPXB – (fI*

iPXI) -1 1- fI fI

ρ20 Decay of AMB (fI-1) *iNXS+iNXB –

(fI*iNXI) (1-fI)* iPXS - iPXB – (fI*

iPXI) -1 1- fI fI

ρ26 Decay HMB -1 1- fI fI

gCOD/unit comp. 1 1 0 0 4 8 1 1 1 1 1

gN/unit comp. iNSF 0 1 0 0 0 iNXB iNXB iNXB iNXS iNXI

gP/unit comp. iPSF 0 0 1 0 0 iPXB iPXB iPXB iPXS iPXI

Table 22: Aerobic, anoxic and decay processes occurring in the facultative and maturation ponds (second and third ponds respectively in the WSP system).

Component (i) → SF

gCOD.m-

3

SA

gCOD.m-

3

SO2

gO2.m-3

SNH

gN.m-3 SNO

gN.m-3 SN2

gN.m-3 SPO4

gP.m-3

XH

gCOD.m-

3

XA

gCOD.m-

3

XALG

gCOD.m-

3

XS

gCOD.m-

3

XI

gCOD.m-

3 Process (j) ↓

Aerobic

ρ1 Algal growth on SNH 1 -iNALG -iPALG 1

ρ2 Algal growth on SNO 1+4.57

iNALG -iNALG -iPALG 1

68

ρ3 Aerobic growth of

HB on SF -1/YH 1- 1/YH -iNXB + iNSF/YH -iPXB + iPSF/YH 1

ρ4 Aerobic growth of

HB on SA -1/YH 1-1/YH -iNXB -iPXB 1

ρ5 Aerobic growth of

AB 1-4.57/YA -(iNXB +1/YA) 1/YA -iPXB 1

ρ30 Respiration of algae fIALG -1 iNALG - (fIALG *iNXI) iPALG - (fIALG *iPXI) -1 fIALG

Anoxic

ρ8 Anoxic growth of HB

on SF - 1/YH -(iNXB - iNSF/YH)

-(1-YH)/(2.86YH)

(1-YH)/2.86YH

-iPXB + iPSF/YH 1

ρ9 Anoxic growth of HB

on SA - 1/YH - iNXB -(1-YH)/2.86YH

(1-YH)/2.86YH

-iPXB 1

Decay

ρ17 Decay of HB (fI -1) *iNXS+iNXB -

(fI*iNXI)

iPXB - iPXS + fI*(iPXS

-iPXI) -1 1- fI fI

ρ18 Decay of AB (fI -1) *iNXS+iNXB - (fI

*iNXI)

iPXB - iPXS + fI *(iPXS

-iPXI) -1 1- fI fI

ρ16 Decay of Algae (fIALG -1) *iNXS+iNALG -

(fIALG *iNXI)

iPALG - iPXS + fIALG *(iPXS -iPXI)

-1 1- fIALG fIALG

gCOD/unit comp. 1 1 -1 0 -4.57 -1.71 0 1 1 1 1 1

gN/unit comp. iNSF 0 0 1 1 1 0 iNXB iNXB iNALG iNXS iNXI

gP/unit comp. iPSF 0 0 0 0 0 1 iPXB iPXB iPALG iPXS iPXI

Table 23: Phosphorous chemical processes precipitation and redissolution occurring in facultative and maturation ponds

Component (i) → SPO4

gP.m-3

SALK

mole HCO3-.m-3

XMeOH

gTSS.m-3 XMeP

gTSS.m-3 XTSS

gTSS.m-3 Process (j) ↓

ρ27 P Precipitation -1 0.048 -2.39 10 7.61

ρ28 P Redissolution 1 -0.048 2.39 -10 -7.61

gCOD/unit comp. 0 0 0 0 0

gN/unit comp. 0 0 0 0 0

gP/unit comp. 1 1 0 0 0.10

gTSS/unit comp. 0 0 0 1 1

Charge -1.5/31 -1.5/31 -1 0 0

69

Table 24: Processes listed in WSP model referring to anaerobic, aerobic, anoxic and phosphorous processes and their kinetic rate expressions

Process Kinetic expression

ρ12 Hydrolysis 𝐾ℎ𝑦𝑑 . 𝑋𝐹𝐵

ρ13 Anaerobic growth of FB 𝜇𝐹𝐵.𝑆𝐹

𝐾𝐹𝐹𝐵 + 𝑆𝐹

.𝐾𝑂2

𝐹𝐵

𝐾𝑂2𝐹𝐵 + 𝑆𝐴

.𝐾𝑁𝑂

𝐹𝐵

𝐾𝑁𝑂𝐹𝐵 + 𝑆𝑁𝑂

.𝑆𝑁𝐻

𝐾𝑁𝐻𝐹𝐵 + 𝑆𝑁𝐻

.𝑆𝑃𝑂4

𝐾𝑃𝐹𝐵 + 𝑆𝑃𝑂4

. 𝑋𝐹𝐵

ρ14 Anaerobic growth of AMB 𝜇𝐴𝑀𝐵.𝑆𝐴

𝐾𝐴𝐴𝑀𝐵 + 𝑆𝐴

.𝐾𝑂2

𝐴𝑀𝐵

𝐾𝑂2𝐴𝑀𝐵 + 𝑆𝑂2

.𝐾𝑁𝑂

𝐴𝑀𝐵

𝐾𝑁𝑂𝐴𝑀𝐵 + 𝑆𝑁𝑂

.𝑆𝑁𝐻

𝐾𝑁𝐻𝐴𝑀𝐵 + 𝑆𝑁𝐻

.𝑆𝑃𝑂4

𝐾𝑃𝐴𝑀𝐵 + 𝑆𝑃𝑂4

𝑋𝐴𝑀𝐵

ρ26 Anaerobic growth of HMB 𝜇𝐻𝑀𝐵.𝑆𝐻2

𝐾𝐻2𝐻𝑀𝐵 + 𝑆𝐻2

.𝐾𝑂2

𝐻𝑀𝐵

𝐾𝑂2𝐻𝑀𝐵 + 𝑆𝑂2

.𝐾𝑁𝑂

𝐻𝑀𝐵

𝐾𝑁𝑂𝐻𝑀𝐵 + 𝑆𝑁𝑂

.𝑆𝑁𝐻

𝐾𝑁𝐻𝐻𝑀𝐵 + 𝑆𝑁𝐻

.𝑆𝑃𝑂4

𝐾𝑃𝐻𝑀𝐵 + 𝑆𝑃𝑂4

𝑋𝐻𝑀𝐵

ρ19 Decay of FB 𝑏𝐹𝐵. 𝑋𝐹𝐵

ρ20 Decay of AMB 𝑏𝐴𝑀𝐵 . 𝑋𝐴𝑀𝐵

ρ26 Decay of HMB 𝑏𝐻𝑀𝐵. 𝑋𝐻𝑀𝐵

ρ1 Algae growth on SNH 𝜇𝐴𝐿𝐺 . 𝑓(𝐿).𝑆𝑁𝐻

𝐾𝑁𝐻𝐴𝐿𝐺 + 𝑆𝑁𝐻

.𝑆𝑃𝑂4

𝐾𝑃𝐴𝐿𝐺 + 𝑆𝑃𝑂4

. 𝑋𝐴𝐿𝐺

ρ2 Algae growth on SNO 𝜇𝐴𝐿𝐺 . 𝑓(𝐿).𝑆𝑁𝑂

𝐾𝑁𝑂𝐴𝐿𝐺 + 𝑆𝑁𝑂

.𝑆𝑃𝑂4

𝐾𝑃𝐴𝐿𝐺 + 𝑆𝑃𝑂4

.𝐾𝑁𝐻

𝐴𝐿𝐺

𝐾𝑁𝐻𝐴𝐿𝐺 + 𝑆𝑁𝐻

. 𝑋𝐴𝐿𝐺

ρ3 Aerobic growth of HB on SF 𝜇𝐻 .𝑆𝐹

𝐾𝑆𝐹𝐻 + 𝑆𝐹

.𝑆𝐹

𝑆𝐹 + 𝑆𝐴

.𝑆𝑂2

𝐾𝑂2𝐻 + 𝑆𝑂2

.𝑆𝑁𝐻

𝐾𝑁𝐻𝐻 + 𝑆𝑁𝐻

.𝑆𝑃𝑂4

𝐾𝑃𝐻 + 𝑆𝑃𝑂4

. 𝑋𝐻

ρ4 Aerobic growth of HB on SA 𝜇𝐻 .𝑆𝐴

𝐾𝑆𝐴𝐻 + 𝑆𝐴

.𝑆𝐴

𝑆𝐹 + 𝑆𝐴

.𝑆𝑂2

𝐾𝑂2𝐻 + 𝑆𝑂2

.𝑆𝑁𝐻

𝐾𝑁𝐻𝐻 + 𝑆𝑁𝐻

.𝑆𝑃𝑂4

𝐾𝑃𝐻 + 𝑆𝑃𝑂4

. 𝑋𝐻

ρ5 Aerobic growth of AB 𝜇𝐴.𝑆𝑁𝐻

𝐾𝑁𝐻𝐴 + 𝑆𝑁𝐻

.𝑆𝑂2

𝐾𝑂2𝐴 + 𝑆𝑂2

.𝑆𝑃𝑂4

𝐾𝑃𝐴 + 𝑆𝑃𝑂4

𝑋𝐴

ρ16 Decay of Algae 𝑏𝐴𝐿𝐺 . 𝑋𝐴𝐿𝐺

ρ30 Respiration of Algae 𝑏𝑅𝑒𝑠𝐴𝐿𝐺 .

𝑆𝑂2

𝐾𝑂2𝐴𝐿𝐺 + 𝑆𝑂2

. 𝑋𝐴𝐿𝐺

ρ17 Decay of HB 𝑏𝐻 . 𝑋𝐻

ρ18 Decay of AB 𝑏𝐴. 𝑋𝐴

ρ8 Anoxic growth of HB on SF 𝜇𝐻 . 𝜂𝐻 .𝑆𝐹

𝐾𝐹𝐻 + 𝑆𝐹

.𝑆𝐹

𝑆𝐹 + 𝑆𝐴

.𝐾𝑂2

𝐻

𝐾𝑂2𝐻 + 𝑆𝑂2

.𝑆𝑁𝑂

𝐾𝑁𝑂𝐻 + 𝑆𝑁𝑂

.𝑆𝑁𝐻

𝐾𝑁𝐻𝐻 + 𝑆𝑁𝐻

.𝑆𝑃𝑂4

𝐾𝑃𝐻 + 𝑆𝑃𝑂4

. 𝑋𝐻

ρ9 Anoxic growth of HB on SA 𝜇𝐻 . 𝜂𝐻 .𝑆𝐴

𝐾𝐴𝐻 + 𝑆𝐴

.𝑆𝐴

𝑆𝐹 + 𝑆𝐴

.𝐾𝑂2

𝐻

𝐾𝑂2𝐻 + 𝑆𝑂2

.𝑆𝑁𝑂

𝐾𝑁𝑂𝐻 + 𝑆𝑁𝑂

.𝑆𝑁𝐻

𝐾𝑁𝐻𝐻 + 𝑆𝑁𝐻

.𝑆𝑃𝑂4

𝐾𝑃𝐻 + 𝑆𝑃𝑂4

. 𝑋𝐻

ρ28 P Precipitation 𝑘𝑃𝑅𝐸 . 𝑆𝑃𝑂4. 𝑋𝑀𝑒𝑂𝐻

ρ29 P Redissolution 𝑘𝑅𝐸𝐷 . 𝑋𝑀𝑒𝑃 . 𝑆𝐴𝐿𝐾/(𝐾𝐴𝐿𝐾 + 𝑆𝐴𝐿𝐾)

70

Table 25: Typical values for stoichiometric and kinetic coefficients related to WSPs.

Symbol Parameter: Value: Reference:

Nitrogen

iNSI Nitrogen content of inert soluble COD SI 0.01 g N.g-1 COD ASM2d [2]

iNSF Nitrogen content in fermentable substrate SF 0.03 g N.g-1 COD ASM2d [2]

iNXB Nitrogen content in active biomass 0.07 g N.g-1 COD ASM2d [2]

iNXI Nitrogen content of inert particulate COD XI 0.03 g N.g-1 COD ASM2d [2]

iNXS Nitrogen content of slowly biodegradable substrate XS 0.04 g N.g-1 COD ASM2d [2]

iNALG Nitrogen content in algae 0.063 g N.g-1 COD Peng et al. [97]

Phosphorous

iPSI Phosphorous content of inert soluble COD SI 0.00 g P.g-1 COD ASM2d [2]

iPSF Phosphorous content in fermentable substrate SF 0.01 g P.g-1 COD ASM2d [2]

iPXB Phosphorous content in active biomass 0.02 g P.g-1 COD ASM2d [2]

iPXI Phosphorous content of inert particulate COD XI 0.01 g P.g-1 COD ASM2d [2]

iPXS Phosphorous content of slowly biodegradable substrate XS 0.01 g P.g-1 COD ASM2d [2]

iPALG Phosphorous content in algae 0.01 g P.g-1 COD Reichert et al. [4]

𝑘𝑃𝑅𝐸 Rate constant for P precipitation 1.00 m3 (g Ca(OH)2)−1 d−1 ASM2d [2]

𝑘𝑅𝐸𝐷 Rate constant for P redissolution 0.60 d-1 ASM2d [2]

Algae (XALG)

𝜇𝐴𝐿𝐺 Maximum growth rate of algae 2 d-1 Reichert et al. [4]

𝐾𝑁𝐻𝐴𝐿𝐺 Ammonium half saturation coefficient for algae 0.01 g N.m-3 Chao et al. [98]

𝐾𝑁𝑂𝐴𝐿𝐺 Nitrate half saturation coefficient for algae 0.01 g N.m-3 Chao et al. [98]

𝐾𝑃𝐴𝐿𝐺 Phosphorous half saturation coefficient for algae 0.02 g P.m-3 Reichert et al. [4]

𝐾𝑂2𝐴𝐿𝐺 Oxygen half saturation coefficient for algae 0.2 g O2.m

-3 Reichert et al. [4]

𝑏𝐴𝐿𝐺 Specific biomass decay rate of algae 0.1 d-1 Reichert et al. [4]

𝑏𝑅𝑒𝑠𝐴𝐿𝐺 Specific biomass respiration rate of algae 0.1 d-1 Reichert et al. [4]

Autotrophic nitrifying bacteria (XA)

𝑌𝐴 Yield of autotrophic bacteria 0.24 g COD.g-1 N ASM2d [2]

𝜇𝐴 Maximum growth rate of autotrophs 2 d-1 Sah et al. [72]

𝐾𝑂2𝐴 Oxygen half saturation coefficient for autotrophs 0.5 g O2.m

-3 ASM2d [2]

𝐾𝑁𝐻𝐴 Ammonium half saturation coefficient for autotrophs 0.2 g N.m-3 Sah et al. [72]

𝐾𝑁𝑂𝐴 Nitrate half saturation coefficient for autotrophs 0.50 g N.m-3 ASM2d [2]

𝐾𝑃𝐴 Phosphorous half saturation coefficient for autotrophs 0.01 g P.m-3 ASM2d [2]

𝑏𝐴 Specific biomass decay rate of autotrophs 0.015 d-1 Sah et al. [72]

Heterotrophic bacteria (XH)

𝑌𝐻 Yield of heterotrophic bacteria 0.63 g COD.g-1 COD ASM2d [2]

𝜇𝐻 Maximum growth rate of heterotrophs 6.00 d-1 ASM2d [2]

𝐾𝐴𝐻 Fermentation products (acetate) half saturation coefficient for heterotrophs 4.00 g COD.m-3 ASM2d [2]

𝐾𝑂2𝐻 Oxygen half saturation coefficient for heterotrophs 0.20 g O2.m

-3 ASM2d [2]

71

𝐾𝑁𝐻𝐻 Ammonium half saturation coefficient for heterotrophs 0.05 g N.m-3 ASM2d [2]

𝐾𝐹𝐻 Fermentable substrate half saturation coefficient for heterotrophs 3.00 g COD.m-3 Sah et al. [72]

𝐾𝑁𝑂𝐻 Nitrate half saturation coefficient for heterotrophs 0.50 g N.m-3 ASM2d [2]

𝐾𝑃𝐻 Phosphorous half saturation coefficient of heterotrophs 0.01 g P.m-3 ASM2d [2]

𝜂𝐻 Correction factor for 𝜇𝐻under anoxic conditions 0.80 ASM2d [2]

bH Specific biomass decay rate of heterotrophs 0.40 d-1 ASM2d [2]

Fermenting bacteria (XFB)

𝑌𝐹𝐵 Yield of fermenting bacteria 0.053 g COD.g-1 COD Langergraber et al. [5]

𝜇𝐹𝐵 Maximum growth rate of fermenting bacteria 6.00 d-1 Sah et al. [72]

𝐾𝐹𝐹𝐵 Fermentable substrate half saturation coefficient for fermenting bacteria 28 g COD.m-3 Langergraber et al. [5]

𝐾𝑂2𝐹𝐵 Oxygen half saturation coefficient for fermenting bacteria 0.20 g O2.m

-3 Langergraber et al. [5]

𝐾𝑁𝑂𝐹𝐵 Nitrate half saturation coefficient for fermenting bacteria 0.50 g N.m-3 Langergraber et al. [5]

𝐾𝑁𝐻𝐹𝐵 Ammonium half saturation coefficient for fermenting bacteria 0.01 g N.m-3 Langergraber et al. [5]

𝐾𝑃𝐹𝐵 Phosphorous half saturation coefficient for fermenting bacteria 0.01 g P.m-3 ASM2d [2]

𝑏𝐹𝐵 Specific biomass decay rate of fermenting bacteria 0.02 d-1 Langergraber et al. [5]

Acetotrophic methanogenic bacteria (XAMB)

𝑌𝐴𝑀𝐵 Yield of AMB 0.032 g COD.g-1 COD Kalyuzhnyi and Fedorovich [99]

𝜇𝐴𝑀𝐵 Maximum growth rate of AMB 0.085 d-1 Kalyuzhnyi and Fedorovich [99]

𝐾𝑂2𝐴𝑀𝐵 Oxygen inhibition coefficient for AMB 0.0002 g O2.m

-3 Rousseau [100]

𝐾𝑁𝑂𝐴𝑀𝐵 Nitrate half saturation coefficient for AMB 0.0005 g N.m-3 Rousseau [100]

𝐾𝐴𝐴𝑀𝐵 Fermentation products (acetate) half saturation coefficient for AMB 56 g COD.m-3 Kalyuzhnyi and Fedorovich [99]

𝐾𝑁𝐻𝐴𝑀𝐵 Ammonium half saturation coefficient for AMB 0.01 g N.m-3 Rousseau [100]

𝐾𝑃𝐴𝑀𝐵 Phosphorous half saturation coefficient for AMB 0.01 g P.m-3 Sah et al. [72]

𝑏𝐴𝑀𝐵 Specific biomass decay rate of AMB 0.008 d-1 Kalyuzhnyi and Fedorovich [99]

Hydrogenotrophic methanogenic bacteria (XHMB)

𝑌𝐻𝑀𝐵 Yield of HMB 0.022 g COD.g-1 COD Kalyuzhnyi and Fedorovich [99]

𝜇𝐻𝑀𝐵 Maximum growth rate of HMB 0.35 d-1 Kalyuzhnyi and Fedorovich [99]

𝐾𝐻2𝐻𝑀𝐵 Hydrogen gas half saturation coefficient for HMB 0.13 g COD.m-3 Kalyuzhnyi and Fedorovich [99]

𝐾𝑂2𝐻𝑀𝐵 Oxygen inhibition coefficient for HMB 0.0002 g O2.m

-3 Rousseau [100]

𝐾𝑁𝑂𝐻𝑀𝐵 Nitrate inhibition coefficient for HMB 0.0005 g N.m-3 Rousseau [100]

𝐾𝑃𝐻𝑀𝐵 Phosphorous half saturation coefficient for AMB 0.01 g P.m-3 Sah et al. [72]

𝑏𝐻𝑀𝐵 Specific biomass decay rate of HMB 0.025 d-1 Kalyuzhnyi and Fedorovich [99]

Other parameters

𝐾𝐻𝑌𝐷 Half saturation coefficient for hydrolysis 1 g COD. g-1 COD Effebi et al. [101]

𝐾𝐴𝐿𝐾 Saturation coefficient for alkalinity 0.50 mole HCO3-.m-3 ASM2d [2]

𝑓𝐼𝐴𝐿𝐺 Inert content in algae (fraction of XI formed during algal decay) 0.1 g COD. g-1 COD Peng et al. [97]

𝑓𝐼 Inert content in bacteria (fraction of XI formed during bacterial decay) 0.1 g COD. g-1 COD ASM2d [2]

𝑓𝑆𝐼 Fraction of SI formed during hydrolysis 0 g COD. g-1 COD ASM2d [2]

𝑓(𝐿) Attenuation of light (based on simplification of Lambert Beer law and mean depth of pond) - Sah et al. [72]

72

Appendix B.2: Mass balances for aerobic, anoxic and anaerobic processes occurring in WSP

Table 26: Mass balance for anaerobic processes occurring in anaerobic ponds

Component (i) → SF

gCOD.m-

3

SA

gCOD.m-3 SNH

gN.m-3 SPO4

gP.m-3 SCH4

gCOD.m-3 SH2

gH.m-3

XFB

gCOD.m-

3

XAMB

gCOD.m-

3

XHMB

gCOD.m-

3

XS

gCOD.m-

3

XI

gCOD.m-

3

Process (j) ↓

ρ12 Hydrolysis of particulate substrate

1 iNXS –iNSF iPXS –iPSF -1

1*1 + 0 + 0 + (-1)*1 = 0 1* iNSF + (iNXS –iNSF)*1 + 0 + (-1)*

iNXS = 0 1* iPSF + 0 + (iPXS – iPSF)*1 + (-1)*

iPXS = 0

ρ13 Anaerobic

growth of FB - 1/YFB

1

9(

−𝑌𝐹𝐵 + 1

𝑌𝐹𝐵

) -iNXB +

iNSF/YFB -iPXB +

iPSF/YFB

1/9*(-1+1/YFB)

1

(- 1/YFB)*1 + 1/9((-YFB +1) /YFB)*1 + 1/9((-YFB +1) /YFB)*8 + 1*1 = 0

(- 1/YFB)* iNSF + 0 + (-iNXB + iNSF/YFB)*1 + 0 + 1* iNXB = 0 (- 1/YFB)* iPSF + 0 + (-iPXB + iPSF/YFB)*1 + 0 + 1*iPXB = 0

ρ14 Anaerobic

growth of AMB -1/YAMB -iNXB -iPXB

¼*(-1+1/YAMB)

1

(-1/YAMB)*1 + 0 + 0 + (¼*(-1+1/YAMB))*4 + 1*1 = 0

0 - iNXB*1 + 0 + 0 + 1* iNXB = 0 0 + 0 - iPXB*1 + 0 + 1* iPXB = 0

ρ25 Anaerobic

growth of HMB -iNXB -iPXB

¼*(-1+1/YHMB)

1/8*(-1/YHMB)

1

0 + 0 + (¼*(-1+1/YHMB))*4 + (1/8*(-1/YHMB))*8 + 1*1 = 0

-iNXB*1 + 0 + 0 + 0 + 1* iNXB = 0 -iPXB*1 + 0 + 0 + 0 + 1* iPXB = 0

ρ19 Decay of FB (fI-1)*

iNXS+iNXB – (fI*iNXI)

(1-fI)* iPXS

- iPXB – (fI* iPXI)

-1 1- fI fI

0 + 0 -1*1 + (1- fI)*1 + fI *1 = 0 ((fI-1)* iNXS+iNXB – (fI*iNXI))*1 + 0 -1*

iNXB + (1- fI)* iNXS + fI * iNXI = 0 0 + ((1-fI)* iPXS - iPXB – (fI* iPXI))*1 -1* iPXB + (1- fI)* iPXS + fI * iPXI = 0

ρ20 Decay of AMB (fI-1)

*iNXS+iNXB – (fI*iNXI)

(1-fI)* iPXS

- iPXB – (fI* iPXI)

-1 1- fI fI

0 + 0 -1*1 + (1- fI)*1 + fI *1 = 0 ((fI-1)* iNXS+iNXB – (fI*iNXI))*1 + 0 -1*

iNXB + (1- fI)* iNXS + fI * iNXI = 0 0 + ((1-fI)* iPXS - iPXB – (fI* iPXI))*1 -1* iPXB + (1- fI)* iPXS + fI * iPXI = 0

ρ26 Decay HMB (fI-1)

*iNXS+iNXB – (fI*iNXI)

(1-fI)* iPXS

- iPXB – (fI* iPXI)

-1 1- fI fI

0 + 0 -1*1 + (1- fI)*1 + fI *1 = 0 ((fI-1)* iNXS+iNXB – (fI*iNXI))*1 + 0 -1*

iNXB + (1- fI)* iNXS + fI * iNXI = 0 0 + ((1-fI)* iPXS - iPXB – (fI* iPXI))*1 -1* iPXB + (1- fI)* iPXS + fI * iPXI = 0

gCOD/unit comp. 1 1 0 0 4 8 1 1 1 1 1

gN/unit comp. iNSF 0 1 0 0 0 iNXB iNXB iNXB iNXS iNXI

gP/unit comp. iPSF 0 0 1 0 0 iPXB iPXB iPXB iPXS iPXI

73

Table 27: Mass balance for aerobic, anoxic and decay processes occurring in the facultative/maturation ponds

Component (i) → SF

gCOD.m-

3

SA

gCOD.m-

3

SO2

gO2.m-3

SNH

gN.m-3 SNO

gN.m-3 SN2

gN.m-3 SPO4

gP.m-3

XH

gCOD.m-

3

XA

gCOD.m-

3

XALG

gCOD.m-

3

XS

gCOD.m-

3

XI

gCOD.m-

3 COD balance / N balance / P balance

Process (j) ↓

Aerobic

ρ1 Algal growth

on SNH 1 -iNALG -iPALG 1

1*(-1) + (-iNALG)*0 + 1*1 = 0 1*(0) + (-iNALG)*1 + (-iPALG)*0 + 1*iNALG = 0 1*(0) + (-iNALG)*0 + (-iPALG)*1 + 1*iPALG = 0

ρ2 Algal growth

on SNO

1+4.57* iNALG

-iNALG -iPALG 1

(1+4.57 iNALG)*(-1) + (-iNALG)*(-4.57) + (-iPALG)*(0) + 1*1 = 0

(1+4.57 iNALG)*(0) + (-iNALG)*(1) + (-iPALG)*(0) + 1* iNALG = 0

(1+4.57 iNALG)*(0) + (-iNALG)*(0) + (-iPALG)*(1) + 1* iPALG = 0

ρ3 Aerobic

growth of HB on SF

-1/YH 1- 1/YH -iNXB + iNSF/YH -iPXB + iPSF/YH

1

(-1/YH)*1 + (1-1/YH)*(-1) + (-iNXB)*0 + (-iPXB)*0 + 1*1 = 0

(-1/YH)*0 + (1-1/YH)*(0) + (-iNXB)*1 + (-iPXB)*0 + 1*iNXB = 0

(-1/YH)*0 + (1-1/YH)*(0) + (-iNXB)*0 + (-iPXB)*1 + 1*iPXB = 0

ρ4 Aerobic

growth of HB on SA

-1/YH 1-1/YH -iNXB -iPXB 1

(-1/YH)*1 + (1-1/YH)*(-1) + (-iNXB + iNSF/YH)*0 + (-iPXB + iPSF/YH)*0 + 1*1 = 0

(-1/YH)*iNSF + (1-1/YH)*0 + (-iNXB + iNSF/YH)*1 + (-iPXB + iPSF/YH)*0 + 1*iNXB = 0

(-1/YH)*iPSF + (1-1/YH)*0 + (-iNXB + iNSF/YH)*0 + (-iPXB + iPSF/YH)*0 + 1*iPXB = 0

ρ5 Aerobic

growth of AB

1-(4.57) /YA

-(iNXB +1/YA) 1/YA -iPXB 1

(1-4.57/YA)*(-1) + (-(iNXB +1/YA))*0 + (1/YA)*(-4.57) + (-iPXB)*0 + 1*1 = 0

(1-4.57/YA)*0 + (-(iNXB +1/YA))*1 + (1/YA)*1 + (-iPXB)*0 + 1* iNXB = 0

(1-4.57/YA)*0 + (-(iNXB +1/YA))*0 + (1/YA)*0 + (-iPXB)*1 + 1* iPXB = 0

ρ30 Respiration of

algae fIALG -1

iNALG - (fIALG *iNXI)

iPALG -

(fIALG *iPXI) -1 fIALG

(fIALG -1)*(-1)+0+0+(-1)*1+ ( fIALG)*1 = 0 0+1*( iNALG-(fIALG *iNXI))+0+(-1)* iNALG +

fIALG* iNXI = 0 0+0+1*( iPALG-(fIALG *iPXI))+(-1)* iPALG +

fIALG* iPXI = 0

Anoxic

ρ8 Anoxic growth of HB on SF

- 1/YH -(iNXB - iNSF/YH)

-(1-YH)/ (2.86YH)

(1-YH)/ (2.86YH)

-iPXB + iPSF/YH

1

(-1/YH)*1 + (-iNXB)*0 + -((1-YH)/2.86YH)*(-

4.57) + ((1-YH)/2.86YH)*(-1.71) + (-iPXB)*0 +1*1 = 0

74

(-1/YH)*0 + (-iNXB)*1 + -((1-YH)/2.86YH)*1 +

((1-YH)/2.86YH)*1 + (-iPXB)*0 + 1* iNXB = 0

(-1/YH)*0 + (-iNXB)*0 + -((1-YH)/2.86YH)*0 +

((1-YH)/2.86YH)*0 + (-iPXB)*1 + 1* iPXB = 0

ρ9 Anoxic growth of HB on SA

- 1/YH - iNXB -(1-YH)/ (2.86YH)

(1-YH)/ (2.86YH)

-iPXB 1

(-1/YH)*1 + (-(iNXB - iNSF/YH))*0 + (-(1-

YH)/2.86YH)*(-4.57) + ((1-YH)/2.86YH)*(-1.71) + (-iPXB + iPSF/YH)*0 + 1*1 = 0

(-1/YH)* iNSF + (-(iNXB - iNSF/YH))*1 + (-(1-

YH)/2.86YH)*1 + ((1-YH)/2.86YH)*1 + (-iPXB

+ iPSF/YH)*0 + 1*iNXB = 0

(-1/YH)* iPSF + (-(iNXB - iNSF/YH))*1 + (-(1-

YH)/2.86YH)*1 + ((1-YH)/2.86YH)*1 + (-iPXB

+ iPSF/YH)*0 + 1*iPXB = 0

Decay

ρ17 Decay of HB (fI -1)

*iNXS+iNXB - (fI*iNXI)

iPXB - iPXS

+ fI*(iPXS -iPXI)

-1 1- fI fI

((fI -1) *iNXS+iNXB - (fI *iNXI))*0 + (iPXB - iPXS + fI

*(iPXS -iPXI))*0 + (-1)*1 + (1- fI)*1 + (fI)*1 = 0

((fI -1) *iNXS+iNXB - (fI *iNXI))*1 + (iPXB - iPXS + fI

*(iPXS -iPXI))*0 + (-1)* iNXB + (1- fI)* iNXS + (fI)* iNXI = 0

((fI -1) *iNXS+iNXB - (fI *iNXI))*0 + (iPXB - iPXS + fI fI

*(iPXS -iPXI))*1 + (-1)*iPXB + (1- fI)*iPXS + (fI)* iPXI = 0

ρ18 Decay of AB (fI -1)

*iNXS+iNXB - (fI *iNXI)

iPXB - iPXS

+ fI *(iPXS -iPXI)

-1 1- fI fI

((fI -1) *iNXS+iNXB - (fI *iNXI))*0 + (iPXB - iPXS + fI

*(iPXS -iPXI))*0+ (-1)*1 + (1- fI)*1 + fI *1 = 0

((fI -1) *iNXS+iNXB - (fI *iNXI))*1 + (iPXB - iPXS + fI

*(iPXS -iPXI))*0+ (-1)* iNXB + (1- fI)* iNXS + fI fI * iNXI = 0

((fI -1) *iNXS+iNXB - (fI *iNXI))*1 + (iPXB - iPXS + fI

*(iPXS -iPXI))*0+ (-1)* iNXB + (1- fI)* iNXS + fI * iNXI

= 0

ρ16 Decay of

Algae

(fIALG -1) *iNXS+iNALG - (fIALG *iNXI)

iPALG - iPXS

+ fIALG *(iPXS -iPXI)

-1 1- fIALG fIALG

((fIALG-1) *iNXS+iNALG - (fIALG *iNXI))*0 + (iPALG - iPXS + fIALG *(iPXS -iPXI))*0 + (-1)*1 + (1- fIALG)*1

+ (fIALG)*1 = 0

((fIALG -1) *iNXS+iNALG - (fIALG *iNXI))*1 + (iPALG - iPXS + fIALG *(iPXS -iPXI))*0 + (-1)*iNALG + (1-

fIALG)* iNXS + (fIALG)* iNXI = 0

((fIALG -1) *iNXS+iNALG - (fIALG *iNXI))*0 + (iPALG - iPXS + fIALG *(iPXS -iPXI))*1 + (-1)* iPALG + (1-

fIALG)* iPXS + (fIALG)* iPXI = 0

gCOD/unit comp. 1 1 -1 0 -4.57 -1.71 0 1 1 1 1 1

gN/unit comp. iNSF 0 0 1 1 1 0 iNXB iNXB iNALG iNXS iNXI

gP/unit comp. iPSF 0 0 0 0 0 1 iPXB iPXB iPALG iPXS iPXI

75

Table 28: Mass balance for phosphorous precipitation and redissolution

Component (i) → SPO4

gP.m-3

SALK

mole HCO3-.m-3

XMeOH

gTSS.m-3 XMeP

gTSS.m-3 XTSS

gTSS.m-3

COD balance / N balance / P balance / TSS balance /

Charges Balance Process (j) ↓

ρ27 P Precipitation -1 0.048 -2.39 10 7.61

0 0

(-1)*1+0+0+(10)*0.1+0 = 0 0+0+(-2.39)*1+10*(1)+7.61*(-

1) = 0 (-1)*(-1.5/31)+0.048*(-1)

+0+0+0 = 0

ρ28 P Redissolution 1 -0.048 2.39 -10 -7.61

0 0

1*1+0+0+(-10)*0.1+0 = 0 0+0+(-2.39)*1+(-10)*(1)+

(-7.61)*(-1) = 0 1*(-1.5/31)+(-0.048)*(-1)

+0+0+0 = 0

gCOD/unit comp. 0 0 0 0 0

gN/unit comp. 0 0 0 0 0

gP/unit comp. 1 0 0 0.10 0

gTSS/unit comp. 0 0 1 1 -1

Charge -1.5/31 -1 0 0 0

Adapted from Fe(OH)3 as presented on ASM2d [2] for Ca(OH)2.