ASM1 - Activated Sludge Model No. 1

IWA standard model for carbon and nitrogen removal with death-regeneration concept

Overview

ASM1 (Activated Sludge Model No. 1) is the foundational biokinetic model developed by the IWA Task Group on Mathematical Modelling. It describes carbon oxidation, nitrification, and denitrification in activated sludge systems using the death-regeneration concept.

When to Use

Recommended For

Conventional activated sludge
Nitrogen removal processes (MLE, Bardenpho, A2O)
Process optimization studies
Controller tuning
Teaching and training

Not Recommended For

Biological phosphorus removal (use ASM2d)
Storage-dominated processes (use ASM3)
Anaerobic systems (use ADM1)
High-rate processes with significant storage

State Variables

ASM1 uses 13 state variables:

Index	Symbol	Description	Unit
0	S_I	Soluble inert organics	mg COD/L
1	S_S	Readily biodegradable substrate	mg COD/L
2	X_I	Particulate inert organics	mg COD/L
3	X_S	Slowly biodegradable substrate	mg COD/L
4	X_BH	Active heterotrophic biomass	mg COD/L
5	X_BA	Active autotrophic biomass	mg COD/L
6	X_P	Particulate products from decay	mg COD/L
7	S_O	Dissolved oxygen	mg O2/L
8	S_NO	Nitrate nitrogen	mg N/L
9	S_NH	Ammonia nitrogen	mg N/L
10	S_ND	Soluble biodegradable organic N	mg N/L
11	X_ND	Particulate biodegradable organic N	mg N/L
12	S_ALK	Alkalinity	mol HCO3/m³

Processes

ASM1 includes 8 biological processes:

Process Summary

#	Process	Description
1	Aerobic heterotrophic growth	COD oxidation to biomass
2	Anoxic heterotrophic growth	Denitrification (NO3 → N2)
3	Aerobic autotrophic growth	Nitrification (NH4 → NO3)
4	Decay of heterotrophs	Death-regeneration
5	Decay of autotrophs	Death-regeneration
6	Ammonification	Organic N → NH4
7	Hydrolysis of X_S	Particulate → soluble COD
8	Hydrolysis of X_ND	Particulate → soluble org-N

Kinetic Equations

Process 1: Aerobic Heterotrophic Growth

$$\rho_1 = \mu_{H} \cdot \frac{S_S}{K_S + S_S} \cdot \frac{S_O}{K_{O,H} + S_O} \cdot X_{BH}$$

Process 2: Anoxic Heterotrophic Growth (Denitrification)

$$\rho_2 = \mu_{H} \cdot \eta_g \cdot \frac{S_S}{K_S + S_S} \cdot \frac{K_{O,H}}{K_{O,H} + S_O} \cdot \frac{S_{NO}}{K_{NO} + S_{NO}} \cdot X_{BH}$$

Process 3: Aerobic Autotrophic Growth (Nitrification)

$$\rho_3 = \mu_{A} \cdot \frac{S_{NH}}{K_{NH} + S_{NH}} \cdot \frac{S_O}{K_{O,A} + S_O} \cdot \frac{S_{ALK}}{K_{ALK} + S_{ALK}} \cdot X_{BA}$$

Process 4-5: Decay

$$\rho_4 = b_H \cdot X_{BH}$$ $$\rho_5 = b_A \cdot X_{BA}$$

Process 6: Ammonification

$$\rho_6 = k_a \cdot S_{ND} \cdot X_{BH}$$

Process 7-8: Hydrolysis

$$\rho_7 = k_h \cdot \frac{X_S/X_{BH}}{K_X + X_S/X_{BH}} \cdot \left[ \frac{S_O}{K_{O,H}+S_O} + \eta_h \cdot \frac{K_{O,H}}{K_{O,H}+S_O} \cdot \frac{S_{NO}}{K_{NO}+S_{NO}} \right] \cdot X_{BH}$$

Parameters

Default Kinetic Parameters (20°C)

Parameter	Symbol	Value	Unit	Description
μ_H	muH	6.0	1/d	Max heterotrophic growth rate
μ_A	muA	0.8	1/d	Max autotrophic growth rate
b_H	bH	0.62	1/d	Heterotrophic decay rate
b_A	bA	0.15	1/d	Autotrophic decay rate
k_h	kh	3.0	1/d	Hydrolysis rate
k_a	ka	0.08	m³/gCOD/d	Ammonification rate
η_g	etaG	0.8	-	Anoxic growth reduction
η_h	etaH	0.4	-	Anoxic hydrolysis reduction

Half-Saturation Coefficients

Parameter	Symbol	Value	Unit
K_S	KS	20.0	mg COD/L
K_O,H	KOH	0.2	mg O2/L
K_O,A	KOA	0.4	mg O2/L
K_NO	KNO	0.5	mg N/L
K_NH	KNH	1.0	mg N/L
K_X	KX	0.03	g XS/g XBH
K_ALK	KALK	0.1	mol/m³

Stoichiometric Parameters

Parameter	Symbol	Value	Unit
Y_H	YH	0.67	g COD/g COD
Y_A	YA	0.24	g COD/g N
f_P	fP	0.08	-
i_XB	iXB	0.086	g N/g COD
i_XP	iXP	0.06	g N/g COD

Temperature Correction

$$k(T) = k(20) \cdot \theta^{(T-20)}$$

Temperature coefficients (θ):

Parameter Type	θ Value
Growth rates (μ_H, μ_A)	1.072
Decay rates (b_H, b_A)	1.029
Hydrolysis (k_h)	1.041
Ammonification (k_a)	1.029
Half-saturation (K_S, K_NH)	1.000

COD Fractionation

Influent COD Components

Fraction	Description	Typical %
S_S	Readily biodegradable	10-20%
S_I	Soluble inert	5-10%
X_S	Slowly biodegradable	40-50%
X_I	Particulate inert	15-25%
X_BH	Influent biomass	5-10%

Determination Methods

Respirometry: OUR tests for S_S
Flocculation: Filtration for soluble/particulate
BOD/COD ratio: Estimate biodegradable fraction
Default values: When no data available

API Endpoints

Model Information

http

GET /api/v1/asm1/info

Returns model metadata, state variable names, process names, and default parameters.

Calculate Process Rates

http

POST /api/v1/asm1/process-rates
Content-Type: application/json

{
  "stateVector": [30, 5, 1000, 50, 2500, 200, 500, 2.0, 5.0, 1.0, 2.0, 5.0, 5.0],
  "temperature": 20,
  "parameters": {
    "muH": 6.0,
    "YH": 0.67
  }
}

Calculate Derivatives

http

POST /api/v1/asm1/derivatives
Content-Type: application/json

{
  "stateVector": [30, 5, 1000, 50, 2500, 200, 500, 2.0, 5.0, 1.0, 2.0, 5.0, 5.0],
  "temperature": 20
}

Get Diagnostics

http

POST /api/v1/asm1/diagnostics
Content-Type: application/json

{
  "stateVector": [30, 5, 1000, 50, 2500, 200, 500, 2.0, 5.0, 1.0, 2.0, 5.0, 5.0],
  "temperature": 20
}

Returns:

Growth rates (aerobic/anoxic)
Nitrification/denitrification rates
Oxygen uptake rate
Minimum SRT estimates
Limiting factors

Oxygen Transfer Calculations

http

POST /api/v1/asm1/oxygen-transfer
Content-Type: application/json

{
  "kLa": 10.0,
  "volume": 5000,
  "actualDO": 2.0,
  "temperature": 20,
  "alpha": 0.65,
  "beta": 0.95,
  "diffuserDepth": 4.5
}

SRT Calculation

http

POST /api/v1/asm1/srt
Content-Type: application/json

{
  "volume": 8000,
  "mlss": 4000,
  "wasteSludgeFlow": 200,
  "wasteSludgeConcentration": 8000,
  "effluentFlow": 20000,
  "effluentSS": 15
}

Sludge Production

http

POST /api/v1/asm1/sludge-production
Content-Type: application/json

{
  "influentFlow": 20000,
  "influentBiocodCOD": 300,
  "effluentBiodCOD": 10,
  "influentXI": 50,
  "srt": 12
}

Aeration Design

http

POST /api/v1/asm1/aeration-design
Content-Type: application/json

{
  "oxygenUptakeRate": 50,
  "targetDO": 2.0,
  "volume": 5000,
  "temperature": 20,
  "alpha": 0.65,
  "beta": 0.95,
  "diffuserDepth": 4.5,
  "sote": 25
}

Configuration in ErgoPlanner

Enabling ASM1

Select biological reactor (CSTR, PFR, or Oxidation Ditch)
Set Calculation Mode to Advanced
Select Biokinetic Model: ASM1
Configure kinetic parameters (or use defaults)
Run simulation

Parameter Input

json

{
  "model": "asm1",
  "parameters": {
    "muH": 6.0,
    "muA": 0.8,
    "bH": 0.62,
    "bA": 0.15,
    "kh": 3.0,
    "ka": 0.08,
    "etaG": 0.8,
    "etaH": 0.4,
    "KS": 20.0,
    "KOH": 0.2,
    "KOA": 0.4,
    "KNO": 0.5,
    "KNH": 1.0,
    "KX": 0.03,
    "KALK": 0.1,
    "YH": 0.67,
    "YA": 0.24,
    "fP": 0.08,
    "iXB": 0.086,
    "iXP": 0.06
  }
}

Calibration Guidelines

Key Parameters to Calibrate

μ_H - Heterotrophic growth rate
Y_H - Heterotrophic yield
K_S - COD half-saturation
μ_A - Autotrophic growth rate
K_NH - Ammonia half-saturation
η_g - Denitrification factor

Calibration Procedure

Determine COD fractionation from respirometry
Match effluent COD with Y_H, μ_H
Match nitrification with μ_A, K_NH
Match denitrification with η_g
Verify dynamic response with step tests
Fine-tune temperature coefficients

Example: MLE Process

Configuration

Zone	Volume	DO	Function
Anoxic	2,000 m³	<0.2 mg/L	Denitrification
Aerobic	6,000 m³	2.0 mg/L	COD oxidation, nitrification

Influent

Parameter	Value
Flow	20,000 m³/d
Total COD	400 mg/L
S_S	60 mg/L
S_NH	35 mg/L
TKN	40 mg/L

Expected Results

Parameter	Effluent
Total COD	<50 mg/L
S_NH	<1.0 mg/L
S_NO	5-8 mg/L
TN	<10 mg/L

Limitations

No biological P removal - PAOs not modeled (use ASM2d)
No storage - Assumes immediate growth on substrate
No N2O emissions - Intermediate products ignored
Death-regeneration - Simplified decay model
Single temperature - No spatial temperature variation
No inhibition kinetics - No substrate/product inhibition

Death-Regeneration Concept

ASM1 uses the death-regeneration hypothesis where:

Biomass decay produces slowly biodegradable substrate (X_S)
X_S is hydrolyzed to readily biodegradable substrate (S_S)
S_S is available for regrowth

This differs from the endogenous respiration model used in ASM3.

Implementation Details

State Vector Order

The 13-element state vector must follow this exact order:

[SI, SS, XI, XS, XBH, XBA, XP, SO, SNO, SNH, SND, XND, SALK]

Petersen Matrix

The stoichiometry is defined by a 13x8 Petersen matrix relating:

13 state variables (rows)
8 processes (columns)

Integration with Solvers

ASM1 provides CalculateDerivatives() method compatible with:

RK4 Solver (explicit, fixed step)
BDF Solver (implicit, variable step for stiff systems)

ASM2d - Adds biological P removal with PAO kinetics
ASM3 - Storage-based metabolism, endogenous respiration
ADM1 - Anaerobic digestion model

References

Henze, M. et al. "Activated Sludge Models ASM1, ASM2, ASM2d and ASM3" IWA Publishing, 2000
Grady, C.P.L. "Biological Wastewater Treatment" 3rd Edition
Rieger, L. et al. "Guidelines for Using ASMs"
Copp, J.B. "The COST Simulation Benchmark" COST Action 624

Clarification

Disinfection

Filtration

Membranes

ASM1 - Activated Sludge Model No. 1 ​

Overview ​

When to Use ​

Recommended For ​

Not Recommended For ​

State Variables ​

Processes ​

Process Summary ​

Kinetic Equations ​

Process 1: Aerobic Heterotrophic Growth ​

Process 2: Anoxic Heterotrophic Growth (Denitrification) ​

Process 3: Aerobic Autotrophic Growth (Nitrification) ​

Process 4-5: Decay ​

Process 6: Ammonification ​

Process 7-8: Hydrolysis ​

Parameters ​

Default Kinetic Parameters (20°C) ​

Half-Saturation Coefficients ​

Stoichiometric Parameters ​

Temperature Correction ​

COD Fractionation ​

Influent COD Components ​

Determination Methods ​

API Endpoints ​

Model Information ​

Calculate Process Rates ​

Calculate Derivatives ​

Get Diagnostics ​

Oxygen Transfer Calculations ​

SRT Calculation ​

Sludge Production ​

Aeration Design ​

Configuration in ErgoPlanner ​

Enabling ASM1 ​

Parameter Input ​

Calibration Guidelines ​

Key Parameters to Calibrate ​

Calibration Procedure ​

Example: MLE Process ​

Configuration ​

Influent ​

Expected Results ​

Limitations ​

Death-Regeneration Concept ​

Implementation Details ​

State Vector Order ​

Petersen Matrix ​

Integration with Solvers ​

Related Models ​

References ​

ASM1 - Activated Sludge Model No. 1

Overview

When to Use

Recommended For

Not Recommended For

State Variables

Processes

Process Summary

Kinetic Equations

Process 1: Aerobic Heterotrophic Growth

Process 2: Anoxic Heterotrophic Growth (Denitrification)

Process 3: Aerobic Autotrophic Growth (Nitrification)

Process 4-5: Decay

Process 6: Ammonification

Process 7-8: Hydrolysis

Parameters

Default Kinetic Parameters (20°C)

Half-Saturation Coefficients

Stoichiometric Parameters

Temperature Correction

COD Fractionation

Influent COD Components

Determination Methods

API Endpoints

Model Information

Calculate Process Rates

Calculate Derivatives

Get Diagnostics

Oxygen Transfer Calculations

SRT Calculation

Sludge Production

Aeration Design

Configuration in ErgoPlanner

Enabling ASM1

Parameter Input

Calibration Guidelines

Key Parameters to Calibrate

Calibration Procedure

Example: MLE Process

Configuration

Influent

Expected Results

Limitations

Death-Regeneration Concept

Implementation Details

State Vector Order

Petersen Matrix

Integration with Solvers

Related Models

References