ASM1 Property Package
This package implements property relationships for the treatment of wastewater using an activated sludge biological reactor as provided in Henze, M. et al. (1987).
- This Activated Sludge Model no.1 (ASM1) property/reaction package:
supports ‘H2O’, ‘S_I’, ‘S_S’, ‘X_I’, ‘X_S’, ‘X_BH’, ‘X_BA’, ‘X_P’, ‘S_O’, ‘S_NO’, ‘S_NH’, ‘S_ND’, ‘X_ND’, and ‘S_ALK’ as components
supports only liquid phase
Sets
Description |
Symbol |
Indices |
|---|---|---|
Components |
\(j\) |
[‘H2O’, ‘S_I’, ‘S_S’, ‘X_I’, ‘X_S’, ‘X_BH’, ‘X_BA’, ‘X_P’, ‘S_O’, ‘S_NO’, ‘S_NH’, ‘S_ND’, ‘X_ND’, ‘S_ALK’] |
Phases |
\(p\) |
[‘Liq’] |
Components
Description |
Symbol |
Variable |
|---|---|---|
Soluble inert organic matter, S_I |
\(S_I\) |
S_I |
Readily biodegradable substrate S_S |
\(S_S\) |
S_S |
Particulate inert organic matter, X_I |
\(X_I\) |
X_I |
Slowly biodegradable substrate X_S |
\(X_S\) |
X_S |
Active heterotrophic biomass X_B,H |
\(X_{B,H}\) |
X_BH |
Active autotrophic biomass X_B,A |
\(X_{B,A}\) |
X_BA |
Particulate products arising from biomass decay, X_P |
\(X_P\) |
X_P |
Oxygen, S_O |
\(S_O\) |
S_O |
Nitrate and nitrite nitrogen, S_NO |
\(S_{NO}\) |
S_NO |
NH4 \(^{+}\) + NH \(_{3}\) Nitrogen, S_NH |
\(S_{NH}\) |
S_NH |
Soluble biodegradable organic nitrogen, S_ND |
\(S_{ND}\) |
S_ND |
Particulate biodegradable organic nitrogen, X_ND |
\(X_{ND}\) |
X_ND |
Alkalinity, S_ALK |
\(S_{ALK}\) |
S_ALK |
State variables
Description |
Symbol |
Variable |
Index |
Units |
|---|---|---|---|---|
Total volumetric flowrate |
\(Q\) |
flow_vol |
None |
\(\text{m}^3\text{/s}\) |
Temperature |
\(T\) |
temperature |
None |
\(\text{K}\) |
Pressure |
\(P\) |
pressure |
None |
\(\text{Pa}\) |
Component mass concentrations |
\(C_j\) |
conc_mass_comp |
[p] |
\(\text{kg/}\text{m}^3\) |
Alkalinity in molar concentration |
\(A\) |
alkalinity |
[p] |
\(\text{kmol HCO}_{3}^{-}\text{/m}^{3}\) |
Stoichiometric Parameters
Description |
Symbol |
Parameter |
Value at 20 C |
Units |
|---|---|---|---|---|
Yield of cell COD formed per g N consumed, Y_A |
\(Y_A\) |
Y_A |
0.24 |
\(\text{dimensionless}\) |
Yield of cell COD formed per g COD oxidized, Y_H |
\(Y_H\) |
Y_H |
0.67 |
\(\text{dimensionless}\) |
Fraction of biomass yielding particulate products, f_p |
\(f_P\) |
f_p |
0.08 |
\(\text{dimensionless}\) |
Mass fraction of N per COD in biomass, i_xb |
\(i_{XB}\) |
i_xb |
0.08 |
\(\text{dimensionless}\) |
Mass fraction of N per COD in particulates, i_xp |
\(i_{XP}\) |
i_xp |
0.06 |
\(\text{dimensionless}\) |
Kinetic Parameters
Description |
Symbol |
Parameter |
Value at 20 C |
Units |
|---|---|---|---|---|
Maximum specific growth rate for autotrophic biomass, mu_A |
\(µ_A\) |
mu_A |
0.5 |
\(\text{d}^{-1}\) |
Maximum specific growth rate for heterotrophic biomass, mu_H |
\(µ_H\) |
mu_H |
4.0 |
\(\text{d}^{-1}\) |
Half-saturation coefficient for heterotrophic biomass, K_S |
\(K_S\) |
K_S |
0.01 |
\(\text{kg COD/}\text{m}^{3}\) |
Oxygen half-saturation coefficient for heterotrophic biomass, K_O,H |
\(K_{O,H}\) |
K_OH |
0.0002 |
\(\text{kg -COD/}\text{m}^{3}\) |
Oxygen half-saturation coefficient for autotrophic biomass, K_O,A |
\(K_{O,A}\) |
K_OA |
0.0004 |
\(\text{kg -COD/}\text{m}^{3}\) |
Nitrate half-saturation coefficient for denitrifying heterotrophic biomass, K_NO |
\(K_{NO}\) |
K_NO |
0.0005 |
\(\text{kg NO}_{3}\text{-N/}\text{m}^{3}\) |
Decay coefficient for heterotrophic biomass, b_H |
\(b_H\) |
b_H |
0.3 |
\(\text{d}^{-1}\) |
Decay coefficient for autotrophic biomass, b_A |
\(b_A\) |
b_A |
0.05 |
\(\text{d}^{-1}\) |
Correction factor for mu_H under anoxic conditions, eta_g |
\(η_g\) |
eta_g |
0.8 |
\(\text{dimensionless}\) |
Correction factor for hydrolysis under anoxic conditions, eta_h |
\(η_h\) |
eta_h |
0.8 |
\(\text{dimensionless}\) |
Maximum specific hydrolysis rate, k_h |
\(k_h\) |
k_h |
3.0 |
\(\text{d}^{-1}\) |
Half-saturation coefficient for hydrolysis of slowly biodegradable substrate, K_X |
\(K_X\) |
K_X |
0.1 |
\(\text{dimensionless}\) |
Ammonia Half-saturation coefficient for autotrophic biomass, K_NH |
\(K_{NH}\) |
K_NH |
1.0 |
\(\text{kg NH}_{3}\text{-N/}\text{m}^{3}\) |
Ammonification rate, k_a |
\(k_a\) |
k_a |
0.00005 |
\(\text{m}^{3}\text{/}\text{kg COD . d}\) |
Properties
Description |
Symbol |
Variable |
Index |
Units |
|---|---|---|---|---|
Fluid specific heat capacity |
\(c_p\) |
cp |
None |
\(\text{J/kg/K}\) |
Mass density |
\(\rho\) |
dens_mass |
[p] |
\(\text{kg/}\text{m}^3\) |
Process Rate Equations
Description |
Equation |
|---|---|
Aerobic growth of heterotrophs |
\(ρ_1 = µ_{H}(\frac{S_{S}}{K_{S}+S_{S}})(\frac{S_{O}}{K_{O,H}+S_{O}})X_{B,H}\) |
Anoxic growth of heterotrophs |
\(ρ_2 = µ_{H}(\frac{S_{S}}{K_{S}+S_{S}})(\frac{K_{O,H}}{K_{O,H}+S_{O}})(\frac{S_{NO}}{K_{NO}+S_{NO}})η_{g}X_{B,H}\) |
Aerobic growth of autotrophs |
\(ρ_3 = µ_{A}(\frac{S_{NH}}{K_{NH}+S_{NH}})(\frac{S_{O}}{K_{O,A}+S_{O}})X_{B,A}\) |
Decay of heterotrophs |
\(ρ_4 = b_{H}X_{B,H}\) |
Decay of autotrophs |
\(ρ_5 = b_{H}X_{B,H}\) |
Ammonification of soluble organic nitrogen |
\(ρ_6 = k_{a}S_{ND}X_{B,H}\) |
Hydrolysis of entrapped organics |
\(ρ_7 = k_{H}(\frac{X_{S}/X_{B,H}}{K_{X}+(X_{S}/X_{B,H})})[(\frac{S_{O}}{K_{O,H}+S_{O}})+η_{h}(\frac{K_{O,H}}{K_{O,H}+S_{O}})(\frac{S_{NO}}{K_{NO}+S_{NO}})]X_{B,H}\) |
Hydrolysis of entrapped organic nitrogen |
\(ρ_7 = k_{H}(\frac{X_{S}/X_{B,H}}{K_{X}+(X_{S}/X_{B,H})})[(\frac{S_{O}}{K_{O,H}+S_{O}})+η_{h}(\frac{K_{O,H}}{K_{O,H}+S_{O}})(\frac{S_{NO}}{K_{NO}+S_{NO}})]X_{B,H}(X_{ND}/X_{S})\) |
Scaling
Scaling for the ASM1 property package has yet to be implemented.
References
[1] Henze, M., Grady, C.P.L., Gujer, W., Marais, G.v.R., Matsuo, T., “Activated Sludge Model No. 1”, 1987, IAWPRC Task Group on Mathematical Modeling for Design and Operation of Biological Wastewater Treatment. https://belinra.inrae.fr/doc_num.php?explnum_id=4467
[2] Alex, J. et al. Benchmark Simulation Model no.1 (BSM1). Lund University, 2008, 5-6. https://www.iea.lth.se/publications/Reports/LTH-IEA-7229.pdf