. 2021 Mar 3;55(6):3940–3955. doi: 10.1021/acs.est.0c05264

Table 1. Comparison among the Main Algae-Bacteria Models Available in the Literature for Wastewater Remediation^a.

	RWQM1	PHOBIA	modified RWQM1^b	modified ASM3	Bioalgae1	Bioalgae2	ALBA^b
Reference	Reichert, 2001	Wolf, 2007	Broekhuizen 2012	Arashiro, 2017	Solimeno, 2017	Solimeno, 2019	Casagli, 2021/this work
Model Structure/Characteristics
State variable (no.)	24	16	24	16	19	19	17
Biological processes (no.)	22	13	22	21	18	18	19
Parameters (no.)	120	75	138	47	94	108	72^c
Growth kinetic type	multiplicative	minimum	multiplicative	multiplicative	multiplicative	multiplicative	multiplicative/minimum^d
Dependence on organic and inorganic carbon	C_ORG	C_ORG, CO₂, HCO₃	C_ORG, CO₂, HCO₃, CO₃^2–	C_ORG	C_ORG, CO₂, HCO₃	C_ORG, CO₂, HCO₃	C_ORG, CO₂, HCO₃, CO₃^2–
Considered N-forms	NH₃, NH₄⁺, NO₃^–, NO₂^–	NH₃⁺, NO₃^–	NH₃, NH₄⁺, NO₃^–, NO₂^–, N₂	NH₄⁺, NO₃^–, NO₂^–	NH₃, NH₄⁺, NO₃^–, NO₂^–	NH₃, NH₄⁺, NO₃^–, NO₂^–	N_org, NH₃, NH₄⁺, NO₃^–, NO₂^– HNO₂, HNO₃, N₂
Considered P-forms	H₂PO₄^–, HPO₄^2–	-	H₂PO₄^–, HPO₄^2–	-	SPO4^e	SPO4^f	H₃PO₄, H₂PO₄^–, HPO₄^2–, PO₄^3–
Continuity check (mass conservation)	C, O, N, P	n.s.	C, O, N, P	(COD, N, P)	n.s.	n.s.	C, H, O, N, P, COD
Algal biomass composition	C₁₀₀H₂₃₂O₂₆N₁₄P	n.s.	C₁₀₀H₂₃₂O₂₆N₁₄P	C₁₀₆H₁₈₁O₄₅N₁₆P	C₁₀₀H₂₃₂O₂₆N₁₄P	C₁₀₀H₂₃₂O₂₆N₁₄P	C₁₀₀H₁₈₃O₄₈N₁₁P
Bacterial biomass composition	C₁₅₀H₃₃₅O₁₃N₃₀P	n.s.	C₁₅₀H₃₃₅O₁₃N₃₀P	C₅H₇O₂N	C₁₅₀H₃₃₅O₁₃N₃₀P	C₁₅₀H₃₃₅O₁₃N₃₀P	C₆₀H₈₇O₂₃N₁₂P
PAR model	Steele	Eilers and Peters	Smith	Poisson	Eilers and Peters	Eilers and Peters	Bernard and Remond
pH model	NH₄⁺, NH₃, CO₂, HCO₃, CO₃^2–, H₂PO₄^–, HPO₄^2–, Ca²⁺_, H⁺_, OH^–	NH₄⁺, NH₃, CO₂, HCO₃, CO₃^2–, H⁺_, OH^–_, Δ_CAT,AN	NH₄⁺, NH₃, CO₂, HCO₃, CO₃^2–, H₂PO₄^–, HPO₄^2–, Ca²⁺_, H⁺_, OH^–	-	NH₄⁺, NH₃, CO₂, HCO₃ CO₃^2–, H⁺_, OH^–	NH₄⁺, NH₃, CO₂, HCO₃, CO₃^2–, H⁺_, OH^–	NH₄⁺, NH₃, CO₂, HCO₃, CO₃^2–, H_3,PO₄, H₂PO₄^–, HPO₄^2–, PO₄^3–, NO₂^–, HNO₂, NO₃^–, HNO₃, H⁺, OH^–, Δ_CAT,AN, TA
pH growth dependence	-	-	Gaussian law	-	-	CPMI	CPM
Temperature simulation/growth dependence	-/Arrhenius	-	-/Arrhenius	-	-/Arrhenius	-/CTMI	√/CTMI
Ammonification	-	-	-	-	-	-	√
DO inhibition	-	-	-	-	√	√	√
NH₃ inhibition	-	-	-	-	-	-	√
Gas–liquid mass transfer	O₂	-	O₂	-	O₂, CO₂, NH₃	O₂, CO₂, NH₃	O₂, CO₂, NH₃, evaporation
Experimental Setup
Reactor type	river environment	laboratory incubator	raceway	cylindrical photobioreactor	raceway	cylindrical photobioreactor	raceway
Reactor installation/volume	outdoor	indoor(lab)/3L	outdoor/8 m³	indoor(lab)/2 L	outdoor/1 m³	indoor(lab)/4 L	outdoor/17 m³, 1 m³
Influent	wastewater discharge	MM	MWW	DSC	MWW	MWW	SWW, DSC
Calibration data set	-	-	365 d	√ (24 h)	√ (4 d)	√ (8 d)	√ (30 d)
Validation
Short-term dynamics	-	-		√ (24 h)	√ (4 d)	n.s.	3, 14 d
Long-term dynamics	-	-	330 d	-	√ (175 d)	-	√ (413 d, 189 d)
Sensitivity analysis	√	√	-	√	√	-	√
Seasonal analysis	-	-	-	-	-	-	√
Parameter uncertainty	√	-	-	√	-	-	√
Confidence intervals for model predictions	√	-	-	-	-	-	√

Abbreviations: √: implemented; n.s. not specified or provided in the relative publications; IC: Inorganic Carbon; DSC: Diluted Swine Centrate; MM: Mineral Medium; MWW: Municipal WasteWater; SWW: Synthetic Municipal WasteWater; TA: Total Alkalinity; CTMI: Cardinal Temperature Model with Inflection; CPMI: Cardinal pH Model with Inflection; CPM: Cardinal pH Model.

Demonstrative scale reactors (>5 m³).

Not including chemical constants, their temperature dependence, and stoichiometric coefficients.

In the ALBA model, only the Monod limitation terms relative to nutrients availability were implemented in the minimum function, while the dependence on inhibitory and environmental factors is multiplied for the minimum term (in the PHOBIA model, all the multiplicative terms considered are included in the minimum function).

P limitation term only on algae.

P limitation term on algae and bacteria.

Table 1. Comparison among the Main Algae-Bacteria Models Available in the Literature for Wastewater Remediationa.

Table 1. Comparison among the Main Algae-Bacteria Models Available in the Literature for Wastewater Remediation^a.