# Plant-Wide Models for Optimizing the Operation and Maintenance of BTEX-Contaminated Wastewater Treatment and Reuse

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Mathematical Model Development

#### 2.1.1. Biodegradation

_{r}. This ordinary differential equation (ODE) is generalized, and variables marked with the lower index must be expanded for each state variable in the model to be integrated over time by a solver algorithm. The liquid phase states generalized as L

_{i}may further be categorized based on the particle size, S

_{i}designating soluble components, C

_{i}applied for colloids and X

_{i}applied for particulates as follows:

_{i,in}—entering the tank, by Equation (2).

_{i}in Equation (4), is derived from the kinetic matrix by multiplying a stoichiometric coefficient (v

_{j,i}, regarding the interaction of the given process j with the state variable i) by process rates (r

_{j}for the process j), summing them up for every case where a given process affects the state variable (based on reading the matrix) [29].

_{i}, the mass rate of the process variable, which was seen earlier (regarding the liquid phase) as contributing to the component balance from Equation (1).

_{COD}m

^{−3}concentration units. These include dissolved benzene (S

_{BENE}), dissolved toluene (S

_{TENE}), dissolved ethylbenzene (S

_{EBENE}), dissolved xylene (S

_{XENE}), gaseous benzene (G

_{BENE}), gaseous toluene (G

_{TENE}), gaseous ethylbenzene (G

_{EBENE}) and gaseous xylene (G

_{XENE}). All the dissolved BTEX compounds undergo biodegradation under anaerobic, anoxic and aerobic conditions carried out by Ordinary Heterotrophic Organisms (X

_{OHO}) biomass. All the biological reactions are parallel reactions that completely mineralize the BTEX compounds to carbon dioxide and biomass. A complete list of rates and the model structure are disclosed as supplementary information in Appendix A (Table A1, Table A2, Table A3, Table A4, Table A5, Table A6, Table A7, Table A8, Table A9 and Table A10).

#### 2.1.2. Gas–Liquid Transfer

_{NTP}) and 293.15 K for temperature (T

_{NTP,K}).

_{Gi,air,inp}denotes the mass flow of gas i from the air supply and is calculated based on the composition of the input gas and the air flow based on the ideal gas law, as shown by Equation (7). Appendix C elaborates on the stoichiometry behind the equivalent molar mass MM

_{EQ,i}of each gaseous BTEX component derived from the theoretical oxygen demand.

_{Gi,air,outp}is calculated by Equation (8), where the concentrations expressed per liquid volume must be converted per volume of gas.

_{gas}. The gas hold-up is an input parameter, for which this paper uses a value of 0.01 m

^{3}

_{gas}m

^{−3}in case of aerated conditions and 0.001 m

^{3}

_{gas}m

^{−3}regarding non-aerated conditions [32]. The gas volumes at field conditions and standard conditions (V

_{gas}and V

_{gas,NTP}, respectively) are calculated by Equations (9) and (10).

_{gas}is determined by Equation (11) in accordance with EPA guidelines on dissolved oxygen saturation calculations [33].

_{v,T}is calculated by Equation (12) based on the water temperature and Antoine-coefficients, where a multiplication factor is used for unit conversion from mmHg to Pa.

_{air}is calculated by the barometric Equation (13), considering the elevation of the facility above sea level h

_{sea}(the molar mass of air MM

_{air}is converted from the unit g mol

^{−1}to kg mol

^{−1}). The parameter L

_{air}for the temperature lapse rate applies a value of 0.0065 K m

^{−1}[34].

_{sat,eff}is calculated by Equation (14), and in case there is no aeration, the diffuser submergence h

_{diff}is replaced by the total side water depth (h

_{r}). The saturation depth fraction f

_{h,sat,eff}may be assigned according to various approaches; the mid-depth concept provides reasonable accuracy in diffused aeration [35].

_{gas,outp,NTP}, which, physically, cannot be negative; this shall be reflected in the model code (e.g., using a maximum function).

_{gas,transfer,NTP}is derived from the summation of the individual gas component transfer molar flows, calculated by Equation (17).

_{L}a

_{i,bub,st,cw}—in clean water for a standard 20 °C temperature—and k

_{L}a

_{i,bub}—in wastewater at the field temperature—are calculated by Equations (20) and (21).

_{bub}is calculated by Equation (22) on a geometrical basis. Based on the literature review, in this study, the bubble Sauter mean diameter d

_{bub}is input as 0.003 m for aerated conditions and as 0.01 m under non-aerated conditions [32,36,37].

_{bub}is extended with the specific contact area between the water surface and the headspace, as shown by Equation (23).

_{L,i,bub,st,cw}are calculated using the respective diffusivities of volatile and soluble gas components by Equation (24) [38], relying on k

_{L,O2,bub,st,cw}as a model parameter with the input value of 0.54 m h

^{−1}[39]. BTEX-specific diffusion coefficients were averaged from values found in the scientific literature [40,41,42] and are disclosed in Appendix C (Table A12) The parameter for the fraction in the liquid side f

_{kL,i}equals 1 for all gases in this study, as they diffuse slowly through the liquid film, with the exception of 0.05 in the case of ammonia, due to its very high solubility [43].

_{L}a

_{O2,bub}is calculated by Equation (25), incorporating a further correction factor for diffuser fouling, an input parameter of aerated unit processes [45], which, in practice, is best adjusted knowing the diffuser age and the time of the last cleaning procedure [46]. For non-aerated conditions (and regarding coarse bubbles), the correction factor for fouling is not interpreted (equal to one).

_{L}a

_{O2,bub,st,cw}directly relates to the clean water performance of diffusers; thus, it is derived—according to Equation (26)—from the standard oxygen transfer rate involving air bubbles, SOTR

_{bub}.

_{bub}is derived from the specific standard oxygen transfer efficiency SSOTE, which describes the diffused aerator characteristics in clean water, as Equation (27) shows.

_{air,NTP,sp}[47].

_{air,NTP,sp}is calculated by Equation (29).

_{d,diff}, is calculated by Equation (30).

_{h,diff}, is calculated by Equation (31).

_{diff}is the ratio of the total diffuser area to the tank surface, as Equation (32) shows.

_{L}) estimated for the liquid surface. The clean water k

_{L}a

_{i,sur,st,cw}at standard conditions and the process water k

_{L}a

_{i,sur}for field conditions are calculated by Equations (33) and (34), respectively.

_{L,i,sur}is determined by Equation (35) using the same principle as for the gas bubble interface, as previously shown by Equation (24).

_{sur}is calculated by Equation (36), incorporating the multiplication factors f

_{cover}for reactor coverage and f

_{wave}for turbulence (waviness). The model inputs of 0.54 m h

^{−1}for k

_{L,O2,sur}and 1.9 for f

_{wave}in this study are adjusted based on the typical measured values of k

_{L}a

_{O2,sur}found in the relevant literature [53].

_{r}is defined by basin geometry, according to Equation (37).

_{i,bub,sat,st,cw}, standardized at 20 °C for clean water (thus requiring temperature conversion from 25 °C, used as the basis of Henry’s law), are modelled based on Equation (38). The variable for process water at field conditions, S

_{i,bub,sat,st}, is expressed by Equation (39). The values of the Henry’s law model parameters regarding BTEX contaminants were averaged in the process of the literature review [55,56,57] and are listed in Appendix C (Table A12).

_{partial,I,bub,st}, and for process conditions, p

_{partial,i,bub}, are calculated by Equations (40) and (41), respectively.

_{gas,bub}.

_{st,h,sat,eff}, is also compensated for the effective saturation depth, as diffuser testing in clean water involves the design submergence [58].

_{i,percent}, derived from the individual gas component molar concentrations and their sum.

_{i,sur,sat,st,cw}in the case of clean water and S

_{i,sur,sat}regarding process water, are calculated by Equations (45) and (46).

_{i,atm}are defined as model constants, measured in volumetric percentages. Equations (47) and (48) quantify the partial pressure of gases in the atmosphere, p

_{partial,i,sur,st}for standardized conditions and p

_{partial,i,sur}for field conditions.

#### 2.1.3. Adsorption on Granular Activated Carbon

_{COD}into unit g

_{C}regarding the carbonaceous state variables and from unit g

_{N}into g

_{C}in case of organic nitrogen. The COD of organic substrates are interpreted using the concept of theoretical oxygen demand. Appendix D (Table A13) lists the ratios of COD (and N) to TOC. The continuous process flow model instantaneously calculates the carbon equivalent for all adsorbed components on the GAC bed volume based on the influent concentrations, using Equation (49). The removal efficiency Rem

_{GAC,i}was assigned to be 99% regarding BTEX components, 92% for a soluble unbiodegradable substrate and 90% in the case of VFA, as well as soluble biodegradable carbon and nitrogen [59,60].

_{C,ad,total}and the influent flow, the algebraic model can calculate the average replacement cycle frequency, knowing the set bed volume V

_{ac}and the TOC breakthrough capacity BTC.

_{m}in the mass fraction unit and the apparent density of the media ρ

_{ac}, both of which are design settings of the GAC model.

_{ac,cycle}.

_{C,ad,total}is monitored and compared to the BTC or the effluent TOC is monitored and compared to a TOC concentration threshold to trigger the bed replacement procedure. Regarding the volumetric load-based logic, the influent loading expressed in the number of bed volumes is registered and initiates the replacement process when it reaches the target volume ratio of the load per bed.

_{C,ad,total}is expressed directly as a sum of the accumulated C equivalent mass of pollutants per bed volume, following Equation (54).

_{i,ad,}, the adsorbed mass per bed volume of state variable i, is determined by differential equations that have to be solved by a numerical integrator. The derivative of L

_{i,ad}is expressed by Equation (55), describing GAC operational loading phases. The authors note that the same equation can also be used to account for potential impurities from backwash streams.

_{i,ad}is described simply using a zero-order rate expression, as seen in Equation (56). The accumulated mass per bed volume prior to the replacement L

_{i,ad,pre}shall be registered at the start of the replacement event, which is linearly decreased towards 0 throughout the duration of the bed replacement t

_{repl}.

_{GAC,i,actual}, depends on how saturated the granular medium is; based on EQ

_{C,ad,total}, the accumulated adsorbed components, a logistic saturation function expresses the drop compared to the defined initial removal ratio Rem

_{GAC,i}, as Equation (57) shows.

_{C,ad,total}, the midpoint concentration C

_{mid}is corrected for the asymmetry involving breakthrough curves, as pointed out by Equation (58).

_{mid,symm}, the midpoint concentration of the breakthrough curve without asymmetry correction, is derived from the BTC, the breakpoint fraction f

_{break}and the breakthrough curve slope sl

_{break}, using Equation (59). The drop in removal efficiency at the breakthrough point adsorption capacity is defined by f

_{break}. The slope and the two model parameters of the asymmetry correction term pow

_{mid,asymm}and magn

_{mid,asymm}were adjusted based on measured data involving breakthrough curves found in the relevant literature, and they can be re-estimated depending on the type of GAC media applied for the treatment [61,62]. The values of the parameters are disclosed in Appendix D (Table A13).

#### 2.2. Model Configuration

^{3}; with the effluent quality and quantity associated with the BSM1 use case, this ought to require bed replacement roughly every month, assuming that the bed density is 450 kg m

^{−3}and that the soluble organic carbon adsorption capacity of the bed is 0.2 g

_{C}g

_{AC}

^{−1}, estimated based on operational expertise. The MF and GAC units are backwashed in half-hour and daily cycles, respectively, for industrial safety reasons against solids depositing on the filter and the granular media. We note here that bed replacement can be calculated automatically in Sumo22 from the mass flow of the BTEX compounds removed, simulating how—in a full-scale treatment plant—the operators would remove exhausted granules and reinstall fresh granules periodically, whenever the breakpoint of the media is reached. After sedimentation, an additional re-aeration zone with the hydraulic retention time of 0.3 h—with coarse bubble aeration—is used to maintain sufficient dissolved oxygen levels required for the effluent quality. The influent quality regarding BTEX concentrations was characterized according to typical levels in municipal wastewater, containing 303 µg L

^{−1}of benzene, 290 µg L

^{−1}of toluene, 249 µg L

^{−1}of ethylbenzene and 933 µg L

^{−1}of xylene [64].

## 3. Results and Discussion

#### 3.1. SRT-Based Scenarios

#### 3.2. The Effect of Aeration Intensity

#### 3.3. GAC Operational Strategies

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

α | alpha (wastewater/clean water) correction factor for mass transfer coefficient |

a_{bub} | specific contact area between the gas bubble surface and liquid phase [m^{2} m^{−3}] |

a_{sur} | specific contact area between the surface gas and liquid phase [m^{2} m^{−3}] |

A_{diff,sp} | area per diffuser [m^{2}] |

A_{r} | liquid surface [m^{2}] |

β | beta (wastewater/clean water) correction factor for the saturation concentration |

BTC | TOC breakthrough capacity (in concentration unit) [g_{C} m^{−3}] |

BTC_{m} | TOC adsorption capacity (at breakpoint, in mass fraction unit) [g_{C} g_{AC}^{−1}] |

C_{mid} | midpoint concentration of breakthrough curve, with asymmetry correction [g_{C} m^{−3}] |

C_{mid,symm} | midpoint concentration of curve, without asymmetry correction [g_{C} m^{−3}] |

coeff_{lead,h,diff} | leading coefficient in a diffuser submergence correction term [m^{−1}] |

coeff_{lin,h,diff} | linear coefficient in a diffuser submergence correction term [m^{−1}] |

d_{bub} | bubble Sauter mean diameter [m] |

d_{diff} | diffuser density [m^{2} m^{−2}] |

D_{i,25} | diffusion coefficient of gas state variable i in water [m^{2} d^{−1}] |

div_{d,diff} | divisor value in a diffuser density correction term [m^{2} m^{−2}] |

ε | gas hold-up [m^{3}_{gas} m^{−3}] |

EQ_{C,ad,total} | carbon equivalent for all adsorbed components on a GAC bed [g C m^{−3}] |

exp_{SSOTE} | exponent in SSOTE correlation [d m^{−3}_{gas}] |

F | diffuser fouling factor |

F_{ac} | replaced activated carbon mass flow [g d^{−1}] |

f_{cover} | covered fraction of the reactor surface |

F_{Gi} | mass flow of gas phase state variable i [g d^{−1}] |

f_{h,sat,eff} | effective saturation depth fraction |

f_{kL,i} | fraction in the liquid side for the mass transfer of gas state variable i |

F_{Li} | mass flow of liquid phase state variable i [g d^{−1}] |

f_{wave} | waviness factor |

G_{i} | concentration of gas phase state variable i in off-gas, per liquid volume [g m^{−3}] |

G_{i,air,inp} | concentration of gas phase state variable i in the air input [%V V^{−1}] |

G_{i,atm} | concentration of gas phase state variable i in the atmosphere [%V V^{−1}] |

G_{i,percent} | concentration of gas phase state variable i in off-gas, percentage [%V V^{−1}] |

h_{diff} | diffuser submergence [m] |

h_{diff,floor} | diffuser height from floor [m] |

Henry_{i,dt} | temperature dependency factor for Henry coefficient of gas i [K] |

Henry_{i,SATP} | Henry coefficient of gas i, standard (SATP) temperature (25 °C) [mol m^{−3} Pa^{−1}] |

h_{r} | reactor depth [m] |

h_{sat,eff} | effective saturation depth [m] |

h_{sea} | elevation above sea level [m] |

i_{C,i} | equivalent mass of soluble organic state variable i per unit mass of carbon [g g_{C}^{−1}] |

k_{L,i,bub,st,cw} | liquid-side mass transfer coefficient for gas bubbles, standard conditions [m d^{−1}] |

k_{L,i,sur,st,cw} | liquid-side mass transfer coefficient for liquid surface, standard conditions [m d^{−1}] |

k_{L}a_{i,bub} | volumetric mass transfer coefficient for gas bubbles, field conditions [d^{−1}] |

k_{L}a_{i,bub,st,cw} | volumetric mass transfer coefficient for gas bubbles, standard conditions [d^{−1}] |

k_{L}a_{i,sur} | volumetric mass transfer coefficient for liquid surface, field conditions [d^{−1}] |

k_{L}a_{i,sur,st,cw} | volumetric mass transfer coefficient for liquid surface, standard conditions [d^{−1}] |

L_{air} | temperature lapse rate for air pressure calculation [K m^{−1}] |

L_{i} | concentration of liquid phase state variable i [g m^{−3}] |

L_{i,ad} | adsorbed soluble organic state variable i mass per bed volume [g m^{−3}] |

M_{ac,cycle} | mass of activated carbon filled per cycle [g] |

magn_{mid,asymm} | magnitude of the breakthrough curve midpoint asymmetry correction term |

MM_{air} | molar mass of air [g mol^{−1}] |

MM_{EQ,i} | equivalent molar mass of gas phase state variable i [g mol^{−1}] |

n_{diff} | number of diffusers |

n_{gas,bub} | molar quantity of gas bubbles per unit liquid volume [mol m^{−3}] |

N_{repl} | activated carbon bed replacement cycle frequency [d^{−1}] |

p_{air} | air pressure at field elevation [Pa] |

p_{gas} | gas phase pressure [Pa] |

p_{NTP} | pressure at standard (NTP) conditions (101,325 Pa) [Pa] |

pow_{d,diff} | power value in a diffuser density correction term |

pow_{h,diff} | power value in a diffuser submergence correction term |

pow_{mid,asymm} | power of the breakthrough curve midpoint asymmetry correction term |

p_{partial,i,bub} | partial pressure of gas state variable i in the gas phase [Pa] |

p_{partial,i,bub,st} | partial pressure of gas state variable i in the gas phase, standard conditions [Pa] |

p_{partial,i,sur} | partial pressure of gas state variable i in the atmosphere [Pa] |

p_{partial,i,sur,st} | partial pressure of gas state variable i in the atmosphere, standard conditions [Pa] |

p_{st,h,sat,eff} | pressure at standard conditions and effective saturation depth [Pa] |

p_{v,T} | saturated vapor pressure of water at temperature T [Pa] |

θ | Arrhenius temperature correction factor for the mass transfer coefficient |

Q | volumetric flow of wastewater [m^{3} d^{−1}] |

Q_{air,NTP} | air flow at standard (NTP) conditions [m^{3}_{gas} d^{−1}] |

Q_{air,NTP,sp} | air flow per diffuser at standard (NTP) conditions [m^{3}_{gas} d^{−1}] |

Q_{gas,transfer,NTP} | gas transfer flow at standard (NTP) conditions [m^{3}_{gas} d^{−1}] |

Q_{gas,outp,NTP} | off-gas flow at standard (NTP) conditions [m^{3}_{gas} d^{−1}] |

ρ_{ac} | apparent density of granular activated carbon [g_{AC} m^{−3}] |

rateF_{i} | mass rate of state variable i [g d^{−1}] |

rate_{i} | reaction rate for the state variable [g m^{−3} d^{−1}] |

Rem_{GAC,i} | removal ratio of soluble organic state variable i by granular activated carbon |

r_{j} | process rate regarding process j (from Gujer matrix) [g m^{−3} d^{−1}] |

S_{i,bub,sat} | saturation concentration at the gas bubble interface [g m^{−3}] |

S_{i,bub,sat,st,cw} | saturation concentration at the gas bubble interface, standard conditions [g m^{−3}] |

S_{i,sur,sat} | saturation concentration at the atmospheric interface [g m^{−3}] |

S_{i,sur,sat,st,cw} | saturation concentration at the atmospheric interface, standard conditions [g m^{−3}] |

sl_{break} | slope of the breakthrough curve [m^{3} g_{C}^{−1}] |

S_{O2} | dissolved oxygen concentration [g_{O2} m^{−3}] |

SOTR_{bub} | standard oxygen transfer rate from bubbles [g d^{−1}] |

SSOTE | specific standard oxygen transfer efficiency [% m^{−1}] |

SSOTE_{0} | intercept in SSOTE correlation [% m^{−1}] |

SSOTE_{asym} | asymptote in SSOTE correlation [% m^{−1}] |

T | liquid temperature [°C] |

T_{air,K} | field air temperature [K] |

T_{K} | liquid temperature in an SI unit [K] |

T_{NTP,K} | temperature at standard (NTP) conditions (20 °C) [K] |

t_{repl} | duration of activated carbon bed replacement [d] |

T_{SATP,K} | temperature at standard (SATP) conditions (25 °C) [K] |

V_{ac} | activated carbon bed volume [m^{3}] |

V_{gas} | gas phase volume [m^{3}_{gas}] |

V_{gas,NTP} | gas phase volume at standard (NTP) conditions [m^{3}_{gas}] |

v_{j,i} | stoichiometric coefficient of state variable i in process j |

V_{r} | reactive volume [m^{3}] |

## Appendix A. Gujer Matrix Development

_{COD}m

^{−3}d

^{−1}units, with the exception of the elimination of surfactants, which is interpreted in d

^{−1}.

Symbol | Process Name |
---|---|

1 | OHO growth on VFAs, O_{2} |

2 | OHO growth on VFAs, NO_{x} |

3 | OHO growth on benzene, O_{2} |

4 | OHO growth on benzene, NO_{x} |

5 | OHO growth on toluene, O_{2} |

6 | OHO growth on toluene, NO_{x} |

7 | OHO growth on ethylbenzene, O_{2} |

8 | OHO growth on ethylbenzene, NO_{x} |

9 | OHO growth on xylene, O_{2} |

10 | OHO growth on xylene, NO_{x} |

11 | OHO growth on S_{B}, O_{2} |

12 | OHO growth on S_{B}, NO_{x} |

13 | S_{B} fermentation with high VFA (OHO growth, anaerobic) |

14 | S_{B} fermentation with low VFA (OHO growth, anaerobic) |

15 | Benzene fermentation with low VFA (OHO growth, anaerobic) |

16 | Toluene fermentation with low VFA (OHO growth, anaerobic) |

17 | Ethylbenzene fermentation with low VFA (OHO growth, anaerobic) |

18 | Xylene fermentation with low VFA (OHO growth, anaerobic) |

19 | OHO decay |

20 | NITO growth |

21 | NITO decay |

22 | AMETO growth |

23 | AMETO decay |

24 | HMETO growth |

25 | HMETO decay |

26 | X_{B} hydrolysis |

27 | X_{B} anaerobic hydrolysis (fermentation) |

28 | S_{N,B} ammonification |

29 | NO_{x} assimilative reduction |

30 | FeP precipitation |

31 | FeP redissolution |

32 | AlP precipitation |

33 | AlP redissolution |

34 | Elimination of surfactants |

35 | Methane gas transfer—bubbles |

36 | Hydrogen gas transfer—bubbles |

37 | Oxygen gas transfer—bubbles |

38 | Nitrogen gas transfer—bubbles |

39 | Benzene gas transfer—bubbles |

40 | Toluene gas transfer—bubbles |

41 | Ethylbenzene gas transfer—bubbles |

42 | Xylene gas transfer—bubbles |

43 | Methane gas transfer—surface |

44 | Hydrogen gas transfer—surface |

45 | Oxygen gas transfer—surface |

46 | Nitrogen gas transfer—surface |

47 | Benzene gas transfer—surface |

48 | Toluene gas transfer—surface |

49 | Ethylbenzene gas transfer—surface |

50 | Xylene gas transfer—surface |

S_{BENE} | S_{TENE} | S_{EBENE} | S_{XENE} | S_{B} | X_{B} | S_{U} | X_{U} | X_{E} | X_{OHO} | |
---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | |||||||||

2 | 1 | |||||||||

3 | −1/Y_{OHO,BTEX,ox} | 1 | ||||||||

4 | −1/Y_{OHO,BTEX,anox} | 1 | ||||||||

5 | −1/Y_{OHO,BTEX,ox} | 1 | ||||||||

6 | −1/Y_{OHO,BTEX,anox} | 1 | ||||||||

7 | −1/Y_{OHO,BTEX,ox} | 1 | ||||||||

8 | −1/Y_{OHO,BTEX,anox} | 1 | ||||||||

9 | −1/Y_{OHO,BTEX,ox} | 1 | ||||||||

10 | −1/Y_{OHO,BTEX,anox} | 1 | ||||||||

11 | −1/Y_{OHO,SB,ox} | 1 | ||||||||

12 | −1/Y_{OHO,SB,anox} | 1 | ||||||||

13 | −1/Y_{OHO,SB,ana} | 1 | ||||||||

14 | −1/Y_{OHO,SB,ana} | 1 | ||||||||

15 | −1/Y_{OHO,BTEX,ana} | 1 | ||||||||

16 | −1/Y_{OHO,BTEX,ana} | 1 | ||||||||

17 | −1/Y_{OHO,BTEX,ana} | 1 | ||||||||

18 | −1/Y_{OHO,BTEX,ana} | 1 | ||||||||

19 | 1 − f_{E} | f_{E} | −1 | |||||||

21 | 1 − f_{E} | f_{E} | ||||||||

23 | 1 − f_{E} | f_{E} | ||||||||

25 | 1 − f_{E} | f_{E} | ||||||||

26 | 1 | −1 | ||||||||

27 | 1 − f_{H2} | −1 | ||||||||

29 | −EEQ_{NO3} × X_{OHO}/X_{BIO,kin} | |||||||||

39 | 1 | |||||||||

40 | 1 | |||||||||

41 | 1 | |||||||||

42 | 1 | |||||||||

47 | 1 | |||||||||

48 | 1 | |||||||||

49 | 1 | |||||||||

50 | 1 |

S_{VFA} | |
---|---|

1 | −1/Y_{OHO,VFA,ox} |

2 | −1/Y_{OHO,VFA,anox} |

13 | (1 − Y_{OHO,SB,ana} − Y_{OHO,H2,ana,high})/Y_{OHO,SB,ana} |

14 | (1 − Y_{OHO,SB,ana} − Y_{OHO,H2,ana,low})/Y_{OHO,SB,ana} |

15 | (1 − Y_{OHO,SB,ana} − Y_{OHO,H2,ana,low})/Y_{OHO,SB,ana} |

16 | (1 − Y_{OHO,SB,ana} − Y_{OHO,H2,ana,low})/Y_{OHO,SB,ana} |

17 | (1 − Y_{OHO,SB,ana} − Y_{OHO,H2,ana,low})/Y_{OHO,SB,ana} |

18 | (1 − Y_{OHO,SB,ana} − Y_{OHO,H2,ana,low})/Y_{OHO,SB,ana} |

22 | −1/Y_{AMETO} |

X_{NITO} | X_{AMETO} | X_{HMETO} | |
---|---|---|---|

20 | 1 | ||

21 | −1 | ||

22 | 1 | ||

23 | −1 | ||

24 | 1 | ||

25 | −1 | ||

29 | −EEQ_{NO3} × X_{NITO}/X_{BIO,kin} | −EEQ_{NO3} × X_{AMETO}/X_{BIO,kin} | −EEQ_{NO3} × X_{HMETO}/X_{BIO,kin} |

S_{NHx} | S_{NOx} | S_{N2} | |
---|---|---|---|

1 | −i_{N,BIO} | ||

2 | −i_{N,BIO} | −(1 − Y_{OHO,VFA,anox})/(EEQ_{N2,NO3} × Y_{OHO,VFA,anox}) | (1 − Y_{OHO,VFA,anox})/(EEQ_{N2,NO3} × Y_{OHO,VFA,anox}) |

3 | −i_{N,BIO} | ||

4 | −i_{N,BIO} | −(1 − Y_{OHO,BTEX,anox})/(EEQ_{N2,NO3} × Y_{OHO,BTEX,anox}) | (1 − Y_{OHO,BTEX,anox})/(EEQ_{N2,NO3} × Y_{OHO,BTEX,anox}) |

5 | −i_{N,BIO} | ||

6 | −i_{N,BIO} | −(1 − Y_{OHO,BTEX,anox})/(EEQ_{N2,NO3} × Y_{OHO,BTEX,anox}) | (1 − Y_{OHO,BTEX,anox})/(EEQ_{N2,NO3} × Y_{OHO,BTEX,anox}) |

7 | −i_{N,BIO} | ||

8 | −i_{N,BIO} | −(1 − Y_{OHO,BTEX,anox})/(EEQ_{N2,NO3} × Y_{OHO,BTEX,anox}) | (1 − Y_{OHO,BTEX,anox})/(EEQ_{N2,NO3} × Y_{OHO,BTEX,anox}) |

9 | −i_{N,BIO} | ||

10 | −i_{N,BIO} | −(1 − Y_{OHO,BTEX,anox})/(EEQ_{N2,NO3} × Y_{OHO,BTEX,anox}) | (1 − Y_{OHO,BTEX,anox})/(EEQ_{N2,NO3} × Y_{OHO,BTEX,anox}) |

11 | −i_{N,BIO} | ||

12 | −i_{N,BIO} | −(1 − Y_{OHO,SB,anox})/(EEQ_{N2,NO3} × Y_{OHO,SB,anox}) | (1 − Y_{OHO,SB,anox})/(EEQ_{N2,NO3} × Y_{OHO,SB,anox}) |

13 | −i_{N,BIO} | ||

14 | −i_{N,BIO} | ||

15 | −i_{N,BIO} | ||

16 | −i_{N,BIO} | ||

17 | −i_{N,BIO} | ||

18 | −i_{N,BIO} | ||

19 | −f_{E} × (i_{N,XE} − i_{N,BIO}) | ||

20 | −1/Y_{NITO} − i_{N,BIO} | 1/Y_{NITO} | |

21 | −f_{E} × (i_{N,XE} − i_{N,BIO}) | ||

22 | −i_{N,BIO} | ||

23 | −f_{E} × (i_{N,XE} − i_{N,BIO}) | ||

24 | −i_{N,BIO} | ||

25 | −f_{E} × (i_{N,XE} − i_{N,BIO}) | ||

28 | 1 | ||

29 | 1 + EEQ_{NO3} × i_{N,BIO} | −1 | |

38 | 1 | ||

46 | 1 |

S_{N,B} | X_{N,B} | S_{PO4} | X_{P,B} | S_{O2} | S_{CH4} | S_{H2} | |
---|---|---|---|---|---|---|---|

1 | −i_{P,BIO} | −(1 − Y_{OHO,VFA,ox})/Y_{OHO,VFA,ox} | |||||

2 | −i_{P,BIO} | ||||||

3 | −i_{P,BIO} | −(1 − Y_{OHO,BTEX,ox})/Y_{OHO,BTEX,ox} | |||||

4 | −i_{P,BIO} | ||||||

5 | −i_{P,BIO} | −(1 − Y_{OHO,BTEX,ox})/Y_{OHO,BTEX,ox} | |||||

6 | −i_{P,BIO} | ||||||

7 | −i_{P,BIO} | −(1 − Y_{OHO,BTEX,ox})/Y_{OHO,BTEX,ox} | |||||

8 | −i_{P,BIO} | ||||||

9 | −i_{P,BIO} | −(1 − Y_{OHO,BTEX,ox})/Y_{OHO,BTEX,ox} | |||||

10 | −i_{P,BIO} | ||||||

11 | −i_{P,BIO} | −(1 − Y_{OHO,SB,ox})/Y_{OHO,SB,ox} | |||||

12 | −i_{P,BIO} | ||||||

13 | −i_{P,BIO} | Y_{OHO,H2,ana,high}/Y_{OHO,SB,ana} | |||||

14 | −i_{P,BIO} | Y_{OHO,H2,ana,low}/Y_{OHO,SB,ana} | |||||

15 | −i_{P,BIO} | Y_{OHO,H2,ana,low}/Y_{OHO,BTEX,ana} | |||||

16 | −i_{P,BIO} | Y_{OHO,H2,ana,low}/Y_{OHO,BTEX,ana} | |||||

17 | −i_{P,BIO} | Y_{OHO,H2,ana,low}/Y_{OHO,BTEX,ana} | |||||

18 | −i_{P,BIO} | Y_{OHO,H2,ana,low}/Y_{OHO,BTEX,ana} | |||||

19 | (1 − f_{E}) × i_{N,BIO} | (1 − f_{E}) × i_{P,BIO} | |||||

20 | −i_{P,BIO} | −(EEQ_{NO3} − Y_{NITO})/Y_{NITO} | |||||

21 | (1 − f_{E}) × i_{N,BIO} | (1 − f_{E}) × i_{P,BIO} | |||||

22 | −i_{P,BIO} | (1 − Y_{AMETO})/Y_{AMETO} | |||||

23 | (1 − f_{E}) × i_{N,BIO} | (1 − f_{E}) × i_{P,BIO} | |||||

24 | −i_{P,BIO} | (1 − Y_{HMETO})/Y_{HMETO} | −1/Y_{HMETO} | ||||

25 | (1 − f_{E}) × i_{N,BIO} | (1 − f_{E}) × i_{P,BIO} | |||||

26 | X_{N,B}/X_{B} | −X_{N,B}/X_{B} | X_{P,B}/X_{B} | −X_{P,B}/X_{B} | |||

27 | X_{N,B}/X_{B} | −X_{N,B}/X_{B} | X_{P,B}/X_{B} | −X_{P,B}/X_{B} | f_{H2} | ||

28 | −1 | ||||||

29 | EEQ_{NO3} × i_{P,BIO} | ||||||

30 | −f_{P,Fe} | ||||||

31 | f_{P,Fe} | ||||||

32 | −f_{P,Al} | ||||||

33 | f_{P,Al} | ||||||

35 | 1 | ||||||

36 | 1 | ||||||

37 | 1 | ||||||

43 | 1 | ||||||

44 | 1 | ||||||

45 | 1 |

S_{ALK} | X_{FeOH} | X_{FeP} | X_{AlOH} | X_{AlP} | |
---|---|---|---|---|---|

1 | (−i_{N,BIO} × CH_{NHx} − i_{P,BIO} × CH_{PO4}) | ||||

2 | (−(1 − Y_{OHO,VFA,anox})/(EEQ_{N2,NO3} × Y_{OHO,VFA,anox}) × CH_{NO3} − i_{N,BIO} × CH_{NHx} − i_{P,BIO} × CH_{PO4}) | ||||

3 | (−i_{N,BIO} × CH_{NHx} − i_{P,BIO} × CH_{PO4}) | ||||

4 | (−(1 − Y_{OHO,BTEX,anox})/(EEQ_{N2,NO3} × Y_{OHO,BTEX,anox}) × CH_{NO3} − i_{N,BIO} × CH_{NHx} − i_{P,BIO} × CH_{PO4}) | ||||

5 | (−i_{N,BIO} × CH_{NHx} − i_{P,BIO} × CH_{PO4}) | ||||

6 | (−(1 − Y_{OHO,BTEX,anox})/(EEQ_{N2,NO3} × Y_{OHO,BTEX,anox}) × CH_{NO3} − i_{N,BIO} × CH_{NHx} − i_{P,BIO} × CH_{PO4}) | ||||

7 | (−i_{N,BIO} × CH_{NHx} − i_{P,BIO} × CH_{PO4}) | ||||

8 | (−(1 − Y_{OHO,BTEX,anox})/(EEQ_{N2,NO3} × Y_{OHO,BTEX,anox}) × CH_{NO3} − i_{N,BIO} × CH_{NHx} − i_{P,BIO} × CH_{PO4}) | ||||

9 | (−i_{N,BIO} × CH_{NHx} − i_{P,BIO} × CH_{PO4}) | ||||

10 | (−(1 − Y_{OHO,BTEX,anox})/(EEQ_{N2,NO3} × Y_{OHO,BTEX,anox}) × CH_{NO3} − i_{N,BIO} × CH_{NHx} − i_{P,BIO} × CH_{PO4}) | ||||

11 | (−i_{N,BIO} × CH_{NHx} − i_{P,BIO} × CH_{PO4}) | ||||

12 | (−(1 − Y_{OHO,SB,anox})/(EEQ_{N2,NO3} × Y_{OHO,SB,anox}) × CH_{NO3} − i_{N,BIO} × CH_{NHx} − i_{P,BIO} × CH_{PO4}) | ||||

13 | (−i_{N,BIO} × CH_{NHx} − i_{P,BIO} × CH_{PO4}) | ||||

14 | (−i_{N,BIO} × CH_{NHx} − i_{P,BIO} × CH_{PO4}) | ||||

15 | (−i_{N,BIO} × CH_{NHx} − i_{P,BIO} × CH_{PO4}) | ||||

16 | (−i_{N,BIO} × CH_{NHx} − i_{P,BIO} × CH_{PO4}) | ||||

17 | (−i_{N,BIO} × CH_{NHx} − i_{P,BIO} × CH_{PO4}) | ||||

18 | (−i_{N,BIO} × CH_{NHx} − i_{P,BIO} × CH_{PO4}) | ||||

19 | −f_{E} × (i_{N,XE} − i_{N,BIO}) × CH_{NHx} | ||||

20 | ((−1/Y_{NITO} − i_{N,BIO}) × CH_{NHx} + 1/Y_{NITO} × CH_{NO3} − i_{P,BIO} × CH_{PO4}) | ||||

21 | −f_{E} × (i_{N,XE} − i_{N,BIO}) × CH_{NHx} | ||||

22 | (−i_{N,BIO} × CH_{NHx} − i_{P,BIO} × CH_{PO4}) | ||||

23 | −f_{E} × (i_{N,XE} − i_{N,BIO}) × CH_{NHx} | ||||

24 | (−i_{N,BIO} × CH_{NHx} − i_{P,BIO} × CH_{PO4}) | ||||

25 | −f_{E} × (i_{N,XE} − i_{N,BIO}) × CH_{NHx} | ||||

26 | X_{P,B}/X_{B} × CH_{PO4} | ||||

27 | X_{P,B}/X_{B} × CH_{PO4} | ||||

28 | CH_{NHx} | ||||

29 | ((1 + EEQ_{NO3} × i_{N,BIO}) × CH_{NHx} − CH_{NO3} + EEQ_{NO3} × i_{P,BIO} × CH_{PO4}) | ||||

30 | −f_{P,Fe} × CH_{PO4} | −1 | 1 | ||

31 | f_{P,Fe} × CH_{PO4} | 1 | −1 | ||

32 | −f_{P,Al} × CH_{PO4} | −1 | 1 | ||

33 | f_{P,Al} × CH_{PO4} | 1 | −1 |

S_{ALPHA} | G_{CH4} | G_{H2} | G_{O2} | G_{N2} | G_{BENE} | G_{TENE} | G_{EBENE} | G_{XENE} | |
---|---|---|---|---|---|---|---|---|---|

34 | 1 | ||||||||

35 | −1 | ||||||||

36 | −1 | ||||||||

37 | −1 | ||||||||

38 | −1 | ||||||||

39 | −1 | ||||||||

40 | −1 | ||||||||

41 | −1 | ||||||||

42 | −1 |

Rate | |
---|---|

1 | µ_{OHO,T} × X_{OHO} × Msat_{SVFA,KVFA} × Msat_{SO2,KO2,OHO} × Msat_{SNHx,KNHx,BIO} × Msat_{SPO4,KPO4,BIO} × Msat_{SALK,KALK} |

2 | µ_{OHO,T} × X_{OHO} × η_{OHO,anox} × Msat_{SVFA,KVFA} × Msat_{SNOx,KNOx,OHO} × Minh_{SO2,KO2,OHO} × Msat_{SNHx,KNHx,BIO} × Msat_{SPO4,KPO4,BIO} × Msat_{SALK,KALK} |

3 | µ_{OHO,BENE,T} × X_{OHO} × Msat_{SBENE,KBENE} × Msat_{SO2,KO2,OHO} × Msat_{SNHx,KNHx,BIO} × Msat_{SPO4,KPO4,BIO} × Msat_{SALK,KALK} |

4 | µ_{OHO,BENE,T} × X_{OHO} × η_{OHO,anox} × Msat_{SBENE,KBENE} × Msat_{SNOx,KNOx,OHO} × Minh_{SO2,KO2,OHO} × Msat_{SNHx,KNHx,BIO} × Msat_{SPO4,KPO4,BIO} × Msat_{SALK,KALK} |

5 | µ_{OHO,TENE,T} × X_{OHO} × Msat_{STENE,KTENE} × Msat_{SO2,KO2,OHO} × Msat_{SNHx,KNHx,BIO} × Msat_{SPO4,KPO4,BIO} × Msat_{SALK,KALK} |

6 | µ_{OHO,TENE,T} × X_{OHO} × η_{OHO,anox} × Msat_{STENE,KTENE} × Msat_{SNOx,KNOx,OHO} × Minh_{SO2,KO2,OHO} × Msat_{SNHx,KNHx,BIO} × Msat_{SPO4,KPO4,BIO} × Msat_{SALK,KALK} |

7 | µ_{OHO,EBENE,T} × X_{OHO} × Msat_{SEBENE,KEBENE} × Msat_{SO2,KO2,OHO} × Msat_{SNHx,KNHx,BIO} × Msat_{SPO4,KPO4,BIO} × Msat_{SALK,KALK} |

8 | µ_{OHO,EBENE,T} × X_{OHO} × η_{OHO,anox} × Msat_{SEBENE,KEBENE} × Msat_{SNOx,KNOx,OHO} × Minh_{SO2,KO2,OHO} × Msat_{SNHx,KNHx,BIO} × Msat_{SPO4,KPO4,BIO} × Msat_{SALK,KALK} |

9 | µ_{OHO,XENE,T} × X_{OHO} × Msat_{SXENE,KXENE} × Msat_{SO2,KO2,OHO} × Msat_{SNHx,KNHx,BIO} × Msat_{SPO4,KPO4,BIO} × Msat_{SALK,KALK} |

10 | µ_{OHO,XENE,T} × X_{OHO} × η_{OHO,anox} × Msat_{SXENE,KXENE} × Msat_{SNOx,KNOx,OHO} × Minh_{SO2,KO2,OHO} × Msat_{SNHx,KNHx,BIO} × Msat_{SPO4,KPO4,BIO} × Msat_{SALK,KALK} |

11 | µ_{OHO,T} × Msat_{SB,KSB} × Minh_{SVFA,KVFA} × X_{OHO} × Msat_{SO2,KO2,OHO} × Msat_{SNHx,KNHx,BIO} × Msat_{SPO4,KPO4,BIO} × Msat_{SALK,KALK} |

12 | µ_{OHO,T} × η_{OHO,anox} × Msat_{SB,KSB} × Minh_{SVFA,KVFA} × X_{OHO} × Msat_{SNOx,KNOx,OHO} × Minh_{SO2,KO2,OHO} × Msat_{SNHx,KNHx,BIO} × Msat_{SPO4,KPO4,BIO} |

13 | µ_{FERM,OHO,T} × X_{OHO} × Logsat_{SVFA,KVFA,FERM} × Msat_{SB,KSB,ana} × Minh_{SO2,KO2,OHO} × Minh_{SNOx,KNOx,OHO} × Msat_{SNHx,KNHx,BIO} × Msat_{SPO4,KPO4,BIO} × Msat_{SALK,KALK} |

14 | µ_{FERM,OHO,T} × X_{OHO} × Loginh_{SVFA,KVFA,FERM} × Msat_{SB,KSB,ana} × Minh_{SO2,KO2,OHO} × Minh_{SNOx,KNOx,OHO} × Msat_{SNHx,KNHx,BIO} × Msat_{SPO4,KPO4,BIO} × Msat_{SALK,KALK} |

15 | µ_{FERM,OHO,BENE,T} × X_{OHO} × Loginh_{SVFA,KVFA,FERM} × Msat_{SBENE,KBENE,ana} × Minh_{SO2,KO2,OHO} × Minh_{SNOx,KNOx,OHO} × Msat_{SNHx,KNHx,BIO} × Msat_{SPO4,KPO4,BIO} × Msat_{SALK,KALK} |

16 | µ_{FERM,OHO,TENE,T} × X_{OHO} × Loginh_{SVFA,KVFA,FERM} × Msat_{STENE,KTENE,ana} × Minh_{SO2,KO2,OHO} × Minh_{SNOx,KNOx,OHO} × Msat_{SNHx,KNHx,BIO} × Msat_{SPO4,KPO4,BIO} × Msat_{SALK,KALK} |

17 | µ_{FERM,OHO,EBENE,T} × X_{OHO} × Loginh_{SVFA,KVFA,FERM} × Msat_{SEBENE,KEBENE,ana} × Minh_{SO2,KO2,OHO} × Minh_{SNOx,KNOx,OHO} × Msat_{SNHx,KNHx,BIO} × Msat_{SPO4,KPO4,BIO} × Msat_{SALK,KALK} |

18 | µ_{FERM,OHO,XENE,T} × X_{OHO} × Loginh_{SVFA,KVFA,FERM} × Msat_{SXENE,KXENE,ana} × Minh_{SO2,KO2,OHO} × Minh_{SNOx,KNOx,OHO} × Msat_{SNHx,KNHx,BIO} × Msat_{SPO4,KPO4,BIO} × Msat_{SALK,KALK} |

19 | b_{OHO,T} × X_{OHO} × (Msat_{SO2,KO2,OHO} + η_{b,anox} × Msat_{SNOx,KNOx,OHO} × Minh_{SO2,KO2,OHO} + η_{b,ana} × Minh_{SNOx,KNOx,OHO} × Minh_{SO2,KO2,OHO}) |

20 | µ_{NITO,T} × Msat_{SNHx,KNHx,NITO} × X_{NITO} × Msat_{SO2,KO2,NITO} × Msat_{SPO4,KPO4,BIO} × Msat_{SALK,KALK} |

21 | b_{NITO,T} × X_{NITO} × (Msat_{SO2,KO2,NITO} + η_{b,anox} × Msat_{SNOx,KNOx,NITO} × Minh_{SO2,KO2,NITO} + η_{b,ana} × Minh_{SNOx,KNOx,NITO} × Minh_{SO2,KO2,NITO} + m_{tox,ana}) |

22 | µ_{AMETO,T} × Hsat_{SVFA,AMETO} × X_{AMETO} × Minh_{SO2,KiO2,AMETO} × Minh_{SNOx,KNOx,AMETO} × Msat_{SNHx,KNHx,BIO} × Msat_{SPO4,KPO4,BIO} × Msat_{SALK,KALK} |

23 | b_{AMETO,T} × X_{AMETO} × (Msat_{SO2,KiO2,AMETO} + η_{b,anox} × Msat_{SNOx,KNOx,AMETO} × Minh_{SO2,KiO2,AMETO} + η_{b,ana} × Minh_{SNOx,KNOx,AMETO} × Minh_{SO2,KiO2,AMETO}) |

24 | µ_{HMETO,T} × Msat_{SH2,KH2,HMETO} × X_{HMETO} × Minh_{SO2,KiO2,HMETO} × Minh_{SNOx,KNOx,HMETO} × Msat_{SNHx,KNHx,BIO} × Msat_{SPO4,KPO4,BIO} × Msat_{SALK,KALK} |

25 | b_{HMETO,T} × X_{HMETO} × (Msat_{SO2,KiO2,HMETO} + η_{b,anox} × Msat_{SNOx,KNOx,HMETO} × Minh_{SO2,KiO2,HMETO} + η_{b,ana} × Minh_{SNOx,KNOx,HMETO} × Minh_{SO2,KiO2,HMETO}) |

26 | q_{HYD,T} × X_{BIO,kin} × MRsat_{XB,XBIO,kin,KHYD} × (Msat_{SO2,KO2,OHO} + η_{b,anox} × Msat_{SNOx,KNOx,OHO} × Minh_{SO2,KO2,OHO}) × Msat_{SALK,KALK} |

27 | q_{HYD,T} × X_{BIO,kin} × MRsat_{XB,XBIO,kin,KHYD} × η_{b,ana} × Minh_{SNOx,KNOx,OHO} × Minh_{SO2,KO2,OHO} × Msat_{SALK,KALK} |

28 | q_{AMMON,T} × S_{N,B} × X_{BIO,kin} |

29 | q_{ASSIM,T} × Msat_{SNOx,KNOx,ASSIM} × Minh_{SNHx,KiNHx,ASSIM} × X_{BIO,kin} |

30 | q_{FeOH,PREC,Me} × S_{PO4} × X_{FeOH} |

31 | q_{FeOH,DISSOL,Me} × X_{FeP} × Msat_{SALK,KALK} |

32 | q_{AlOH,PREC,Me} × S_{PO4} × X_{AlOH} |

33 | q_{AlOH,DISSOL,Me} × X_{AlP} × Msat_{SALK,KALK} |

34 | q_{ALPHA,O2} × X_{VSS} × damp_{ALPHA} × (S_{ALPHA,sat —} S_{ALPHA}) |

35 | k_{L}a_{GCH4,bub} × (S_{GCH4,bub,sat —} S_{CH4}) |

36 | k_{L}a_{GH2,bub} × (S_{GH2,bub,sat —} S_{H2}) |

37 | k_{L}a_{GO2,bub} × (S_{GO2,bub,sat —} S_{O2}) |

38 | k_{L}a_{GN2,bub} × (S_{GN2,bub,sat —} S_{N2}) |

39 | k_{L}a_{GBENE,bub} × (S_{GBENE,bub,sat —} S_{BENE}) |

40 | k_{L}a_{GTENE,bub} × (S_{GTENE,bub,sat —} S_{TENE}) |

41 | k_{L}a_{GEBENE,bub} × (S_{GEBENE,bub,sat —} S_{EBENE}) |

42 | k_{L}a_{GXENE,bub} × (S_{GXENE,bub,sat —} S_{XENE}) |

43 | k_{L}a_{GCH4,sur} × (S_{GCH4,sur,sat —} S_{CH4}) |

44 | k_{L}a_{GH2,sur} × (S_{GH2,sur,sat —} S_{H2}) |

45 | k_{L}a_{GO2,sur} × (S_{GO2,sur,sat —} S_{O2}) |

46 | k_{L}a_{GN2,sur} × (S_{GN2,sur,sat —} S_{N2}) |

47 | k_{L}a_{GBENE,sur} × (S_{GBENE,sur,sat —} S_{BENE}) |

48 | k_{L}a_{GTENE,sur} × (S_{GTENE,sur,sat —} S_{TENE}) |

49 | k_{L}a_{GEBENE,sur} × (S_{GEBENE,sur,sat —} S_{EBENE}) |

50 | k_{L}a_{GXENE,sur} × (S_{GXENE,sur,sat —} S_{XENE}) |

Symbol | Name | Expression |
---|---|---|

Msat(var; k) | Monod saturation | var/(k + var) |

Minh(var; k) | Monod inhibition | k/(k + var) |

MRsat(s;x;k) | Monod ratio saturation | (s/x)/(s/x + k) |

Logsat(var; halfval; slope) | Logistic saturation | 1/(1 + Exp((halfval − var) × slope)) |

Loginh(var; halfval; slope) | Logistic inhibition | 1/(1 + Exp((var − halfval) × slope)) |

Hsat(var; halfval; halfinh) | Haldane equation | var/(halfval + var + (var^{2}/halfinh)) |

## Appendix B. BTEX Kinetic and Stoichiometric Model Parameters

Ordinary Heterotrophic Organism Kinetics (OHO) | |||
---|---|---|---|

Symbol | Name | Value | Unit |

µ_{OHO,BENE} | Maximum specific growth rate of OHOs on benzene | 0.006 | d^{−1} |

µ_{OHO,TENE} | Maximum specific growth rate of OHOs on toluene | 0.014 | d^{−1} |

µ_{OHO,EBENE} | Maximum specific growth rate of OHOs on ethylbenzene | 0.014 | d^{−1} |

µ_{OHO,XENE} | Maximum specific growth rate of OHOs on xylene | 0.010 | d^{−1} |

µ_{FERM,OHO,BENE} | Fermentation growth rate of OHOs on benzene | 0.0030 | d^{−1} |

µ_{FERM,OHO,TENE} | Fermentation growth rate of OHOs on toluene | 0.0042 | d^{−1} |

µ_{FERM,OHO,EBENE} | Fermentation growth rate of OHOs on ethylbenzene | 0.0035 | d^{−1} |

µ_{FERM,OHO,XENE} | Fermentation growth rate of OHOs on xylene | 0.0050 | d^{−1} |

K_{BENE} | Half-saturation of benzene for OHOs | 6.8 | g_{COD} m^{−3} |

K_{TENE} | Half-saturation of toluene for OHOs | 14.8 | g_{COD} m^{−3} |

K_{EBENE} | Half-saturation of ethylbenzene for OHOs | 3.8 | g_{COD} m^{−3} |

K_{XENE} | Half-saturation of xylene for OHOs | 17.6 | g_{COD} m^{−3} |

K_{BENE,ana} | Half-saturation of benzene in fermentation by OHOs | 238 | g_{COD} m^{−3} |

K_{TENE,ana} | Half-saturation of toluene in fermentation by OHOs | 310 | g_{COD} m^{−3} |

K_{EBENE,ana} | Half-saturation of ethylbenzene in fermentation by OHOs | 67 | g_{COD} m^{−3} |

K_{XENE,ana} | Half-saturation of xylene in fermentation by OHOs | 615 | g_{COD} m^{−3} |

Stoichiometric yields | |||

Symbol | Name | Value | Unit |

Y_{OHO,BTEX,ox} | Yield of OHOs on BTEX under aerobic conditions | 0.55 | g X_{OHO} g S_{BTEX}^{−1} |

Y_{OHO,BTEX,anox} | Yield of OHOs on BTEX under anoxic conditions | 0.35 | g X_{OHO} g S_{BTEX}^{−1} |

Y_{OHO,BTEX,ana} | Yield of OHOs on BTEX under anaerobic conditions | 0.10 | g X_{OHO} g S_{BTEX}^{−1} |

## Appendix C. Gas Transfer, Aeration and BTEX Model Parameters

Henry Coefficients | |||
---|---|---|---|

Symbol | Name | Value | Unit |

Henry_{BENE,25} | Henry coefficient for benzene at 25 °C | 1.70 × 10^{−3} | mol m^{−3} Pa^{−1} |

Henry_{BENE,dt} | Henry’s law temperature dependency factor of benzene | 4150 | K |

Henry_{TENE,25} | Henry coefficient for toluene at 25 °C | 1.50 × 10^{−3} | mol m^{−3} Pa^{−1} |

Henry_{TENE,dt} | Henry’s law temperature dependency factor of toluene | 4150 | K |

Henry_{EBENE,25} | Henry coefficient for ethylbenzene at 25 °C | 1.27 × 10^{−3} | mol m^{−3} Pa^{−1} |

Henry_{EBENE,dt} | Henry’s law temperature dependency factor of ethylbenzene | 5100 | K |

Henry_{XENE,25} | Henry coefficient for xylene at 25 °C | 1.56 × 10^{−3} | mol m^{−3} Pa^{−1} |

Henry_{XENE,dt} | Henry’s law temperature dependency factor of xylene | 4083 | K |

Diffusion coefficients | |||

Symbol | Name | Value | Unit |

D_{BENE,25} | Diffusion coefficient of benzene in water at 25 °C | 9.13 × 10^{−5} | m^{2} d^{−1} |

D_{TENE,25} | Diffusion coefficient of toluene in water at 25 °C | 7.89 × 10^{−5} | m^{2} d^{−1} |

D_{EBENE,25} | Diffusion coefficient of ethylbenzene in water at 25 °C | 7.27 × 10^{−5} | m^{2} d^{−1} |

D_{XENE,25} | Diffusion coefficient of xylene in water at 25 °C | 7.08 × 10^{−5} | m^{2} d^{−1} |

Oxygen transfer efficiency correlation parameters | |||

Symbol | Name | Value | Unit |

SSOTE_{0} | Intercept in SSOTE correlation | 7.77 | % m^{−1} |

exp_{SSOTE} | Exponent (absolute value) in SSOTE correlation | 0.01041 | d m^{−3}_{gas} |

SSOTE_{asym} | Asymptote in SSOTE correlation | 5.75 | % m^{−1} |

div_{d,diff} | Divisor value in a diffuser density correction term | 0.1173 | m^{2} m^{−2} |

pow_{d,diff} | Power value in a diffuser density correction term | 0.1329 | |

coeff_{lead,h,diff} | Leading coefficient in a diffuser submergence correction term | 0.011 | m^{−1} |

pow_{h,diff} | Power value in a diffuser submergence correction term | 1.6031 | |

coeff_{lin,h,diff} | Linear coefficient in a diffuser submergence correction term | −0.0229 | m^{−1} |

Specific molecular masses | |||

Symbol | Name | Value | Unit |

MM_{EQ,GBENE} | Equivalent molar mass of benzene | 239.97 | g_{COD} mol^{−1} |

MM_{EQ,GTENE} | Equivalent molar mass of toluene | 287.96 | g_{COD} mol^{−1} |

MM_{EQ,GEBENE} | Equivalent molar mass of ethylbenzene | 335.95 | g_{COD} mol^{−1} |

MM_{EQ,GXENE} | Equivalent molar mass of xylene | 335.95 | g_{COD} mol^{−1} |

## Appendix D. GAC Model Parameters

State Variable Equivalent Mass Ratios to Carbon | |||
---|---|---|---|

Symbol | Name | Value | Unit |

i_{C,VFA} | COD-to-carbon-mass ratio of VFA | 5.33 | g_{COD} g_{C}^{−1} |

i_{C,BENE} | COD-to-carbon-mass ratio of benzene | 19.98 | g_{COD} g_{C}^{−1} |

i_{C,TENE} | COD-to-carbon-mass ratio of toluene | 23.98 | g_{COD} g_{C}^{−1} |

i_{C,EBENE} | COD-to-carbon-mass ratio of ethylbenzene | 27.97 | g_{COD} g_{C}^{−1} |

i_{C,XENE} | COD-to-carbon-mass ratio of xylene | 27.97 | g_{COD} g_{C}^{−1} |

i_{C,SB} | COD-to-carbon-mass ratio of readily biodegradable substrate | 3.20 | g_{COD} g_{C}^{−1} |

i_{C,SU} | COD-to-carbon-mass ratio of soluble unbiodegradable organics | 2.80 | g_{COD} g_{C}^{−1} |

i_{C,SN,B} | Nitrogen-to-carbon-mass ratio of soluble biodegradable organic N | 1.17 | g_{N} g_{C}^{−1} |

Breakthrough curve parameters | |||

Symbol | Name | Value | Unit |

f_{break} | Breakpoint fraction | 0.05 | |

sl_{break} | Breakthrough curve slope | 0.00015 | m^{3} g^{−1} |

pow_{mid,asymm} | Power of the midpoint asymmetry correction term | 20.00 | |

magn_{mid,asymm} | Magnitude of the midpoint asymmetry correction term | 0.50 |

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**Figure 1.**Modified BSM1 test configuration for modelling examples of BTEX removal. Arrows represent the direction of the fluid flow.

Parameter | Value | Unit |
---|---|---|

Influent properties | ||

Flow | 18,446 | m^{3} d^{−1} |

COD | 360 | g_{COD} m^{−3} |

Filtered COD | 144 | g_{COD} m^{−3} |

TOC | 114 | g_{C} m^{−3} |

TKN | 47 | g_{N} m^{−3} |

NH_{4}-N | 30 | g_{N} m^{−3} |

Tank dimensions | ||

Anoxic 1 zone volume | 1000 | m^{3} |

Anoxic 2 zone volume | 1000 | m^{3} |

Aerobic 1 zone volume | 1333 | m^{3} |

Aerobic 2 zone volume | 1333 | m^{3} |

Aerobic 3 zone volume | 1333 | m^{3} |

Clarifier surface area | 1500 | m^{2} |

Clarifier depth | 4 | m |

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**MDPI and ACS Style**

Bencsik, D.; Wadhawan, T.; Házi, F.; Karches, T.
Plant-Wide Models for Optimizing the Operation and Maintenance of BTEX-Contaminated Wastewater Treatment and Reuse. *Environments* **2024**, *11*, 88.
https://doi.org/10.3390/environments11050088

**AMA Style**

Bencsik D, Wadhawan T, Házi F, Karches T.
Plant-Wide Models for Optimizing the Operation and Maintenance of BTEX-Contaminated Wastewater Treatment and Reuse. *Environments*. 2024; 11(5):88.
https://doi.org/10.3390/environments11050088

**Chicago/Turabian Style**

Bencsik, Dániel, Tanush Wadhawan, Ferenc Házi, and Tamás Karches.
2024. "Plant-Wide Models for Optimizing the Operation and Maintenance of BTEX-Contaminated Wastewater Treatment and Reuse" *Environments* 11, no. 5: 88.
https://doi.org/10.3390/environments11050088