Supplemental Information for A Combined Activated Sludge Anaerobic Digestion Model (CASADM) to Understand the Role of Anaerobic Sludge Recycling in Wastewater Treatment Plant Performance Michelle N. Young, Andrew K. Marcus, and Bruce E. Rittmann Appendix A.1: Modeling nomenclature Variable b C fd kUAP or EPS kj Ksubstrate Kinhibit Q ̂ V X Y γ Subscripts a Ac AD Amm Ax BAP Cl Cl-Sl Cl-St COD Ct DO EPS f h hyd in m n Description Decay rate Concentration Fraction of biodegradable biomass Formation rate of UAP or EPS Hydrolysis rate Half-maximum rate concentration Inhibition factor Volumetric flow rate Maximum utilization rate of substrate Volume Concentration of solids or biomass True yield Conversion factor Ammonium oxidizing bacteria Acetate Anaerobic digester Ammonium (NH4+-N) Anoxic tank Biomass associated products Clarifier Flow from clarifier to sludge thickener Flow from clarifier to stabilization tank Chemical oxygen demand Contact tank Dissolved oxygen Extracellular polymeric substances Fermenters Heterotrophs Hydrolysis Influent to the system Methanogens Nitrite oxidizing bacteria Units 1/t Ms/L3 1/t Ms/L3 Ms/L3 L3/t Ms/(Mx-t) L3 Mx/L3 Mx/Ms - Subscripts NaN NiN out P Sl Sl-AD Sl-super St UAP W Description Nitrate (NO3--N) Nitrite (NO2--N) Effluent from the system (from the clarifier) Single particles of PCOD Sludge thickener Sludge from the sludge thickener Supernatant from sludge thickener Stabilization tank Utilization associated products Wasting sludge from AD Units Appendix A.2: Modeling approach and mass balance equations Here, we explain our basic approach to modeling a complex wastewater treatment plant. All mathematical mass balance models are based on conservation of mass in a system: Accumulation Rate of rate of mass mass = within a entering system the system Rate of Generation Loss rate mass rate of of mass in + leaving mass in the the system the system system (A.1) A system that is at steady-state will have an accumulation rate term equal to zero. The first two terms on the RHS of the equation describe advective transfer of mass in and out of the system. The last two terms on the RHS describe the formation or utilization of mass via chemical or biological reactions. We begin by first identifying the different systems for modeling, which are illustrated in Figure 1 of the main text. We then identify the physical, chemical, and biological mechanisms and solid and soluble components that occur in the system; these are summarized in Table A.1. While the most typical physical mechanism is advective mass transport from tank to tank, separation also occurs in the settlers between a supernatant phase and a sludge phase. Table A.1. Solid and soluble components in the mathematical model Solid Components Heterotrophs Methanogens AOB NOB Fermenters PCOD Inert biomass EPS Soluble/Gaseous Components Substrate Biomass associated products (BAP) NH4+ Utilization associated products (UAP) NO2Acetate NO3 N2 Dissolved oxygen (DO) CH4 As stated in the main text, all biomass undergoes three common phenomena: substrate utilization for cell biomass synthesis, endogenous decay and respiration, and formation of SMP and EPS. However, environmental conditions in the activated sludge and anaerobic digestion processes will encourage a variety of other chemical/biological processes:  Aerobic utilization of acetate and COD by heterotrophs  Nitrification of NH4+ and NO2- by AOB and NOB, respectively, under aerobic conditions  Denitrification of NO2- and NO3- directly to N2 by heterotrophs without formation of intermediates in anoxic conditions  Fermentation of COD to acetate by fermenters in anaerobic conditions  Production of methane via methanogenesis in anaerobic conditions  Consumption of SMP and EPS by heterotrophs and fermenters  Hydrolysis of PCOD and inactive biomass A discussion of specific mechanisms is in the next section. Table A.2 summarizes the generic mass balance equations (from Eqn. E.1) developed for each tank and the overall system for the hybrid and conventional processes. Note that the subscripts refer specifically to a tank, and C can refer to concentrations of soluble substrates or biomass. Table A.2. Mass balance equations for SWT’s hybrid and conventional processes, including equations for the overall system and each tank. Overall system Anoxic tank (Ax) Contact tank (Ct) Clarifier (Cl) Sludge thickener (Sl) Stabilization tank (St) Anaerobic digester (AD) Hybrid Conventional Hybrid Conventional where Appendix A.3: Model Features A.3.1. Dual-limitation Monod kinetics As established in Bae and Rittmann (1996), dual-limitation Monod kinetics are applied to describe situations in which the reaction rate is limited by the electron-donor concentration, electron-acceptor concentration, or both. For example, when COD is aerobically oxidized by heterotrophs, the reaction rate, r, is described as ̂( ̂ )( ) where ̂ is the maximum utilization rate of substrate (Ms/Mx-t), S and DO are COD substrate and dissolved oxygen (DO) concentrations (Ms/L3), respectively, KS and KDO are the substrate and DO half-maximum-rate concentrations (Ms/L3), respectively, and Xh is the concentration of heterotrophs (Mx/L3). Thus, if the electron donor or substrate concentrations are below saturation, the Monod term decreases and, under extreme limitation, becomes very small. A.3.2. Inhibition (or switch) factors To simplify the model implementation, we assumed that any mechanism could occur in any tank. Based on de Silva and Rittmann (2000), the level of activity of any mechanism is controlled through the application of an inhibition or switch factor. Different mechanisms described in this model can undergo inhibition if DO, nitrate (NO3-), and/or nitrite (NO2-) are present. The inhibition factor for DO is where Ks,DO is the inhibition factor for DO (M/L3). When the DO concentration is low, DOswitch is ~1, turning the switch on to describe processes under low DO concentrations. When the DO concentration is low, DOswitch is ~0, turning the switch off to inhibit processes under aerobic conditions. Similarly, the switch factors for NO2-, NO2,switch, and NO3-, NO3,switch, are: where Ks,NO2 and Ks,NO3 are the inhibition factors of NO2- and NO3- (M/L3), respectively, and NO2 and NO3 are the concentrations of NO2- and NO3- in the tank (M/L3), respectively. NO2and NO3- switches are ~1, the switches are turned on. These switches can be applied multiplicatively to describe several situations at once. For example, anaerobic conditions can be activated when the following switch expression is multiplied to an anaerobic rate equation: ( ) The NOx switches are added together as denitrification is dependent upon the total amount of NO2- and NO3- in the system. A.3.4. Application of the Unified Theory of EPS and SMP Laspidou and Rittmann (2002a, 2002b) outline the unified theory of EPS and SMP in their fundamental work. We modified their theory to expand its application to the variety of mechanisms presented in this paper. Consistent with Laspidou and Rittmann (2002a), all microorganisms produce EPS and UAP. Biomass yield is reduced as electrons are diverted to EPS and UAP formation by a factor of 1-kUAP-kEPS, where kUAP represents the fraction of electrons going to UAP formation (Ms/Ms) and kEPS represents the fraction of electrons going to EPS formation (Ms/Ms). The factor 1-kUAP-kEPS is represented as “c” in Table A.3. EPS is hydrolyzed to BAP using first-order kinetics. BAP can then be consumed by microorganisms for growth. Only heterotrophs and fermenters utilize UAP and BAP, as they are heterotrophic, CODconsuming microorganisms. UAP and BAP consumption follows Monod-based substrate utilization kinetics. When UAP and BAP are utilized, microorganisms convert the energy to biomass based on a yield, Yp (Mx/Ms), which is assumed to be different than the direct utilization of other substrates. The microorganisms can produce additional EPS and SMP from utilization of UAP and BAP. A.3.4. Stoichiometric coefficients The half reaction for cell synthesis is (Rittmann & McCarty, 2001): where the biomass molecular formula is C5H7O2N (Rittmann and McCarty, 2001; Metcalf & Eddy, Inc., 2003). Thus, the conversion of cell biomass to COD, γo, can be determined by equating the substrates to their electron equivalents: Similarly, the amount of nitrogen in cells is Similar conversions can be performed for other substrates based on electron equivalents. For denitrification of NO3- and NO2- to N2 gas, the half reactions are To convert NO3- (γNaN) and NO2- (γNiN) to mgN/mgCOD, For acetate, the half reaction is To convert acetate to COD, γA, A critical part of the DO calculations is equating the DO utilized by AOB and NOB to the appropriate number of electron equivalents utilized. During nitrification, AOB convert NH4+ to NO2- via the half reaction To convert NH4+ to NO2- and express it as COD, NOB convert NO2- to NO3-, the half reaction is To convert NO2- to NO3- and express it as COD, Table A.3. Process, stoichiometry, and kinetics matrix. A blank cell indicates 0. 1 Process Aerobic metabolism of substrate by Xh Chemical components Substrate S PCOD Acetate UAP BAP Kinetic expression kUAP ( -1 kUAP ( -1 kUAP ( -1 c(1-γOYf) kUAP 2 Anoxic metabolism of substrate by Xh with NO3—N 3 Anoxic metabolism of substrate by Xh with NO2—N 4 Hydrolysis of inactive biomass 5 Anaerobic utilization of substrate by Xf 6 Aerobic metabolism of NO2--N by Xn ( 7 Aerobic metabolism of NH4+-N by Xa ( 8 Aerobic metabolism of acetate by Xh 9 Anoxic metabolism of acetate by Xh with NO3—N ̂ -1 -1 -1 kUAP kUAP ̂ ̂ )( ) )( ) )( ) ( ̂ ̂ ( ( ̂ ̂ ̂ ) )( ) )( ) )( )( ) ) Process Anoxic metabolism of acetate by Xh 10 with NO2—N 11 Chemical components Substrate S PCOD Acetate UAP Acetate utilization by Xm -1 kUAP -1 kUAP 12 Aerobic metabolism of UAP by Xh BAP Kinetic expression -(1kUAP) ( Anoxic metabolism of UAP and NO3--N by Xh -(1kUAP) ( 14 Anoxic metabolism of UAP and NO2--N by Xh -(1kUAP) ( 15 Metabolism of UAP by Xf 16 Aerobic metabolism of BAP by Xh kUAP -1 ( ̂ ̂ kUAP -1 ( 18 Anoxic metabolism of BAP and NO2--N by Xh kUAP -1 ( 19 Metabolism of BAP by Xf c(1-γOYf) kUAP -1 20 Hydrolysis of PCOD ̂ ) ̂ ) )( ( Anoxic metabolism of BAP and NO3--N by Xh -1 ̂ -(1kUAP) 17 1 )( ( 13 c(1-γOYf) ̂ ( )( ) )( ) ̂ )( ̂ ̂ ( ) ) ) )( ) )( ) ̂ kPP ) 21 Process Aerobic respiration by Xh Chemical components Substrate S PCOD Acetate UAP BAP Kinetic expression ( ) 22 Anoxic respiration by Xh during NO3--N utilization ( ) 23 Anoxic respiration by Xh during NO2--N utilization ( ) 24 Aerobic respiration by Xa ( ) 25 Aerobic respiration by Xn ( ) 26 Anaerobic respiration of Xf 27 Anaerobic respiration of Xm 28 Formation of BAP 29 Decay of Xh 1 1 khydEPS [ ] 30 Decay of Xa ( ) 31 Decay of Xn ( ) 32 Decay of Xf 33 Process Decay of Xm 34 UNITS Chemical components Substrate S PCOD Acetate UAP BAP Kinetic expression Process 1 2 3 Aerobic metabolism of substrate by Xh EPS Chemical components DO NH4+-N NO3--N -αh Anoxic metabolism of substrate by Xh with NO2--N ( 5 Anaerobic utilization of substrate by Xf ) ̂ ( ) ( Hydrolysis of inactive biomass Kinetic expression ( Anoxic metabolism of substrate by Xh with NO3--N 4 NO2--N -γNaN ̂ ( -γNiN ) ̂ ( )( ) )( ) )( ) γN ( ( ) Aerobic metabolism of NO2--N by 6 Xn -αn kUAP 7 Aerobic metabolism of NH4+-N by Xa -αa -(1- kUAP) 8 Aerobic metabolism of acetate by Xh c(1-YnγN) -1 ( c(1-YaγN) ( ̂ ( -αh ) ̂ ( ̂ ̂ ) )( ) )( ) )( ) Process 9 10 11 EPS Chemical components DO NH4+-N NO3--N Anoxic metabolism of acetate by Xh with NO3--N ( Anoxic metabolism of acetate by Xh with NO2--N ( ) NO2--N Kinetic expression -γNaN ̂ ( -γNiN ) ̂ ( 14 15 ( -αhp ( ) Anoxic metabolism of UAP and NO3--N by Xh ( Anoxic metabolism of UAP and NO2--N by Xh ( Metabolism of UAP by Xf )( ) ( ) 13 ) ( Acetate utilization by Xm 12 Aerobic metabolism of UAP by Xh )( ) ) ( -γNaN -γNiN ( ̂ )( ̂ ̂ ( ) ̂ ( ) ) )( ) )( ) ̂ ) Process 16 Aerobic metabolism of BAP by Xh 17 18 19 EPS Chemical components DO NH4+-N NO3--N NO2--N Kinetic expression ( -αhp ( ) Anoxic metabolism of BAP and NO3--N by Xh ( Anoxic metabolism of BAP and NO2--N by Xh ( ) ( -γNaN -γNiN ) ( ̂ )( ̂ ̂ ( Metabolism of BAP by Xf ( ) ) )( ) )( ) ̂ ) 20 Hydrolysis of PCOD 21 Aerobic respiration by Xh 22 Anoxic respiration by Xh during NO3--N utilization γN 23 Anoxic respiration by Xh during NO2--N utilization γN 24 Aerobic respiration by Xa -γO γN ( ) 25 Aerobic respiration by Xn -γO γN ( ) kPP -γO ( γN -γNaNγO -γNiNγO ) ( ) ( ) 26 Process Anaerobic respiration of Xf 27 Anaerobic respiration of Xm 28 Formation of BAP 29 Decay of Xh EPS Chemical components DO NH4+-N NO3--N NO2--N Kinetic expression γN γN -1 γN khydEPS [ ] 30 Decay of Xa ( ) 31 Decay of Xn ( ) 32 Decay of Xf 33 Decay of Xm 34 UNITS Process Aerobic metabolism of substrate by 1 Xh 2 Anoxic metabolism of substrate by Xh with NO3--N 3 Anoxic metabolism of substrate by Xh with NO2--N 4 Hydrolysis of inactive biomass 5 Anaerobic utilization of substrate by Xf 6 Aerobic metabolism of NO2--N by Xn 7 Aerobic metabolism of NH4+-N by Xa 8 Aerobic metabolism of acetate by Xh 9 Anoxic metabolism of acetate by Xh with NO3--N Chemical components N2 CH4 Biomass components Xh Xa Xn Kinetic expression γNaN γNiN ̂ ( cYh ̂ ( cYh -1 ̂ ( cYh -1 )( ) )( ) )( ) -1 ( cYn cYa cYh γNaN cYh ̂ ( ̂ ( ( ( ̂ ̂ ̂ ) )( ) )( ) )( )( ) ) Process Anoxic metabolism of acetate by Xh 10 with NO2--N 11 Chemical components N2 CH4 γNiN Biomass components Xh Xa Xn Kinetic expression ̂ ( cYh c(1YmγO) Acetate utilization by Xm 12 Aerobic metabolism of UAP by Xh )( ( cYp ( 13 Anoxic metabolism of UAP and NO3--N by Xh γNaN cYp ( 14 Anoxic metabolism of UAP and NO2--N by Xh γNiN cYp ( 15 Metabolism of UAP by Xf ̂ cYp ( ̂ ̂ 17 Anoxic metabolism of BAP and NO3--N by Xh γNaN cYp ( 18 Anoxic metabolism of BAP and NO2--N by Xh γNiN cYp ( 19 Metabolism of BAP by Xf 20 Hydrolysis of PCOD ̂ ̂ ) )( ( 16 Aerobic metabolism of BAP by Xh ) )( ) )( ) ̂ )( ̂ ̂ ( ) ) ) )( ) )( ) ̂ kPP ) 21 Process Aerobic respiration by Xh Chemical components N2 CH4 Biomass components Xh Xa Xn Kinetic expression ( ) 22 Anoxic respiration by Xh during NO3--N utilization γNaN γO ( ) 23 Anoxic respiration by Xh during NO2--N utilization γNiN γO ( ) 24 Aerobic respiration by Xa ( ) 25 Aerobic respiration by Xn ( ) 26 Anaerobic respiration of Xf 27 Anaerobic respiration of Xm 28 Formation of BAP 29 Decay of Xh 1 khydEPS [ -1 ] 30 Decay of Xa 31 Decay of Xn 32 Decay of Xf -1 -1 ( ) ( ) 33 Process Decay of Xm 34 UNITS Chemical components N2 CH4 fdγO Biomass components Xh Xa Xn Kinetic expression 1 Process Aerobic metabolism of substrate by Xh Biomass components Xf Xm Xi Kinetic expression ̂ ( ̂ 2 Anoxic metabolism of substrate by Xh with NO3--N ( 3 Anoxic metabolism of substrate by Xh with NO2--N ( 4 Hydrolysis of inactive biomass 5 Anaerobic utilization of substrate by Xf 6 Aerobic metabolism of NO2--N by Xn ( 7 Aerobic metabolism of NH4+-N by Xa ( 8 Aerobic metabolism of acetate by Xh ( 9 Anoxic metabolism of acetate by Xh with NO3--N ( 10 Anoxic metabolism of acetate by Xh with NO2--N ( 11 Acetate utilization by Xm ̂ )( ) )( ) )( ) ( cYf cYm ̂ ̂ ̂ ̂ ̂ ̂ ) )( ) )( ) )( ) )( ) )( ) ( ̂ ) 12 Process Aerobic metabolism of UAP by Xh Biomass components Xf Xm Xi Kinetic expression ( Anoxic metabolism of UAP and NO3--N 13 by Xh ( 14 Anoxic metabolism of UAP and NO2--N by Xh ( 15 Metabolism of UAP by Xf 16 Aerobic metabolism of BAP by Xh ( 17 Anoxic metabolism of BAP and NO3--N by Xh ( Anoxic metabolism of BAP and NO2--N 18 by Xh ( ̂ )( ̂ ̂ ( cYp ̂ ) )( ) )( ) ̂ ) )( ̂ ̂ 19 Metabolism of BAP by Xf 20 Hydrolysis of PCOD 21 Aerobic respiration by Xh ( 22 Anoxic respiration by Xh during NO3--N utilization ( ( cYp ) )( ) )( ) ̂ ) kPP ) ) Process Anoxic respiration by Xh during NO2--N 23 utilization Biomass components Xf Xm Xi Kinetic expression ( ) 24 Aerobic respiration by Xa ( ) 25 Aerobic respiration by Xn ( ) 26 Anaerobic respiration of Xf 27 Anaerobic respiration of Xm 28 Formation of BAP 29 Decay of Xh khydEPS [ 1-fd ] 30 Decay of Xa 1-fd 31 Decay of Xn 1-fd 32 Decay of Xf 33 Decay of Xm 34 UNITS 1-fd -1 -1 1-fd ( ) ( ) Inhibition terms for processes limited by nitrate, nitrite, and dissolved oxygen concentrations are defined as: Nitrite: Nitrate: Dissolved oxygen: Coefficients: c= 1 – kUAP – kEPS γO = 160/113 mgCOD/mgVSS γN = 14/113 mgN/mgVSS γA = 64/60 mgCOD/mgAcetate γNiN = 14/24 mgNO2--N/mgCOD γNaN = 14/40 mgNO3--N/mgCOD [ ( )] Table A.4. Microorganisms’ kinetic and stoichiometric parameters Heterotrophs Subscript h Kinetic Parameters Symbol Units True yield Substrate Yj mgVSS/mgCOD 0.45 coefficient SMP Yp mgVSS/mgCOD Maximum Substrate mgCOD/mgVSS-d 10 ̂ utilization rate UAP mgCOD/mgVSS-d 1.8 ̂ BAP Acetate Half-maximum Substrate rate Acetate concentration DO UAP BAP NO2- or NO3UAP formation rate EPS formation rate Hydrolysis rate EPS PCOD Decay rate Fraction of biodegradable biomass Inhibition factor ̂ AOB a NOB n Fermenters f Methanogens m 0.33 0.2 0.077 3.1 -- 0.083 0.5 13 -- 10 1.8 --- mgCOD/mgVSS-d 0.5 -- -- 0.5 -- ̂ KS,j KAc,j KDO,j KUAP,j KBAP,j KN.j mgAc/mgVSS-d mgCOD/L mgAc/L mgDO/L mgCOD/L mgCOD/L mgN/L 8.1 10 10 0.2 100 85 0.2 -1.5 -0.5 --1.5 -2.7 -0.68 --2.7 -10 --100 85 -- 7 -30 ----- kUAP kEPS khyd kp b,j fd mgCOD/mgCOD mgCOD/mgCOD 1/d 1/d 1/d - 0.04 0.03 Ks,l 0.3 mgDO/L mgN/L j denotes the biomass subscript, l denotes the chemical species subscript. DO 0.2 -- 0.15 0.05 0.18 0.17 0.22 0.15 0.8 NO2-0.2 NO3-0.2 Appendix A.4: References Bae, W., & Rittmann, B. E. (1996). A Structured Model of Dual-Limitation Kinetics. Biotechnology and Bioengineering, 49(6), 683-689. de Silva, D., & Rittmann, B. E. (2000). Nonsteady-State Modeling of Multispecies Activated Sludge Processes. Water Environment Research, 72(5), 554-565. Laspidou, C. S., & Rittmann, B. E. (2002a). A Unified Theory for Extracellular Polymeric Substances, Soluble Microbial Products, and Active and Inert Biomass. Water Research, 2711-2720. Laspidou, C. S., & Rittmann, B. E. (2002b). Non-steady State Modeling of Extracellular Polymeric Substances, Soluble Microbial Products, and Active and Inert Biomass. Water Research, 1983-1992. Metcalf & Eddy, Inc. (2003). Wastewater Engineering: Treatment and Reuse (4th ed.). (I. Metcalf & Eddy, Ed.) New York: McGraw-Hill. Rittmann, B. E., & McCarty, P. L. (2001). Environmental Biotechnology: Principles and Applications (1st ed.). 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