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Add Koch parameters

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p.vanderwilt
2025-08-18 16:43:16 +02:00
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src/reaction_modules/asm3_class Koch.js Normal file
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const math = require('mathjs')
/**
* ASM3 class for the Activated Sludge Model No. 3 (ASM3). Using Koch et al. 2000 parameters.
*/
class ASM3 {
constructor() {
/**
* Kinetic parameters for ASM3 at 20 C. Using Koch et al. 2000 parameters.
* @property {Object} kin_params - Kinetic parameters
*/
this.kin_params = {
// Hydrolysis
k_H: 9., // hydrolysis rate constant [g X_S g-1 X_H d-1]
K_X: 1., // hydrolysis saturation constant [g X_S g-1 X_H]
// Heterotrophs
k_STO: 12., // storage rate constant [g S_S g-1 X_H d-1]
nu_NO: 0.5, // anoxic reduction factor [-]
K_O: 0.2, // saturation constant S_0 [g O2 m-3]
K_NO: 0.5, // saturation constant S_NO [g NO3-N m-3]
K_S: 10., // saturation constant S_s [g COD m-3]
K_STO: 0.1, // saturation constant X_STO [g X_STO g-1 X_H]
mu_H_max: 3., // maximum specific growth rate [d-1]
K_NH: 0.01, // saturation constant S_NH3 [g NH3-N m-3]
K_HCO: 0.1, // saturation constant S_HCO [mole HCO3 m-3]
b_H_O: 0.3, // aerobic respiration rate [d-1]
b_H_NO: 0.15, // anoxic respiration rate [d-1]
b_STO_O: 0.3, // aerobic respitation rate X_STO [d-1]
b_STO_NO: 0.15, // anoxic respitation rate X_STO [d-1]
// Autotrophs
mu_A_max: 1.3, // maximum specific growth rate [d-1]
K_A_NH: 1.4, // saturation constant S_NH3 [g NH3-N m-3]
K_A_O: 0.5, // saturation constant S_0 [g O2 m-3]
K_A_HCO: 0.5, // saturation constant S_HCO [mole HCO3 m-3]
b_A_O: 0.20, // aerobic respiration rate [d-1]
b_A_NO: 0.10 // anoxic respiration rate [d-1]
};
/**
* Stoichiometric and composition parameters for ASM3. Using Koch et al. 2000 parameters.
* @property {Object} stoi_params - Stoichiometric parameters
*/
this.stoi_params = {
// Fractions
f_SI: 0., // fraction S_I from hydrolysis [g S_I g-1 X_S]
f_XI: 0.2, // fraction X_I from decomp X_H [g X_I g-1 X_H]
// Yields
Y_STO_O: 0.80, // aerobic yield X_STO per S_S [g X_STO g-1 S_S]
Y_STO_NO: 0.70, // anoxic yield X_STO per S_S [g X_STO g-1 S_S]
Y_H_O: 0.80, // aerobic yield X_H per X_STO [g X_H g-1 X_STO]
Y_H_NO: 0.65, // anoxic yield X_H per X_STO [g X_H g-1 X_STO]
Y_A: 0.24, // anoxic yield X_A per S_NO [g X_A g-1 NO3-N]
// Composition (COD via DoR)
i_CODN: -1.71, // COD content (DoR) [g COD g-1 N2-N]
i_CODNO: -4.57, // COD content (DoR) [g COD g-1 NO3-N]
// Composition (nitrogen)
i_NSI: 0.01, // nitrogen content S_I [g N g-1 S_I]
i_NSS: 0.03, // nitrogen content S_S [g N g-1 S_S]
i_NXI: 0.04, // nitrogen content X_I [g N g-1 X_I]
i_NXS: 0.03, // nitrogen content X_S [g N g-1 X_S]
i_NBM: 0.07, // nitrogen content X_H / X_A [g N g-1 X_H / X_A]
// Composition (TSS)
i_TSXI: 0.75, // TSS content X_I [g TS g-1 X_I]
i_TSXS: 0.75, // TSS content X_S [g TS g-1 X_S]
i_TSBM: 0.90, // TSS content X_H / X_A [g TS g-1 X_H / X_A]
i_TSSTO: 0.60, // TSS content X_STO (PHB based) [g TS g-1 X_STO]
// Composition (charge)
i_cNH: 1/14, // charge per S_NH [mole H+ g-1 NH3-N]
i_cNO: -1/14 // charge per S_NO [mole H+ g-1 NO3-N]
};
/**
* Temperature theta parameters for ASM3. Using Koch et al. 2000 parameters.
* These parameters are used to adjust reaction rates based on temperature.
* @property {Object} temp_params - Temperature theta parameters
*/
this.temp_params = {
// Hydrolysis
theta_H: 0.04,
// Heterotrophs
theta_STO: 0.07,
theta_mu_H: 0.07,
theta_b_H_O: 0.07,
theta_b_H_NO: 0.07,
theta_b_STO_O: this._compute_theta(0.1, 0.2, 10, 20),
theta_b_STO_NO: this._compute_theta(0.05, 0.1, 10, 20),
// Autotrophs
theta_mu_A: 0.105,
theta_b_A_O: 0.105,
theta_b_A_NO: 0.105
};
this.stoi_matrix = this._initialise_stoi_matrix();
}
/**
* Initialises the stoichiometric matrix for ASM3.
* @returns {Array} - The stoichiometric matrix for ASM3. (2D array)
*/
_initialise_stoi_matrix() { // initialise stoichiometric matrix
const { f_SI, f_XI, Y_STO_O, Y_STO_NO, Y_H_O, Y_H_NO, Y_A, i_CODN, i_CODNO, i_NSI, i_NSS, i_NXI, i_NXS, i_NBM, i_TSXI, i_TSXS, i_TSBM, i_TSSTO, i_cNH, i_cNO } = this.stoi_params;
const stoi_matrix = Array(12);
// S_O, S_I, S_S, S_NH, S_N2, S_NO, S_HCO, X_I, X_S, X_H, X_STO, X_A, X_TS
stoi_matrix[0] = [0., f_SI, 1.-f_SI, i_NXS-(1.-f_SI)*i_NSS-f_SI*i_NSI, 0., 0., (i_NXS-(1.-f_SI)*i_NSS-f_SI*i_NSI)*i_cNH, 0., -1., 0., 0., 0., -i_TSXS];
stoi_matrix[1] = [-(1.-Y_STO_O), 0, -1., i_NSS, 0., 0., i_NSS*i_cNH, 0., 0., 0., Y_STO_O, 0., Y_STO_O*i_TSSTO];
stoi_matrix[2] = [0., 0., -1., i_NSS, -(1.-Y_STO_NO)/(i_CODNO-i_CODN), (1.-Y_STO_NO)/(i_CODNO-i_CODN), i_NSS*i_cNH + (1.-Y_STO_NO)/(i_CODNO-i_CODN)*i_cNO, 0., 0., 0., Y_STO_NO, 0., Y_STO_NO*i_TSSTO];
stoi_matrix[3] = [-(1.-Y_H_O)/Y_H_O, 0., 0., -i_NBM, 0., 0., -i_NBM*i_cNH, 0., 0., 1., -1./Y_H_O, 0., i_TSBM-i_TSSTO/Y_H_O];
stoi_matrix[4] = [0., 0., 0., -i_NBM, -(1.-Y_H_NO)/(Y_H_NO*(i_CODNO-i_CODN)), (1.-Y_H_NO)/(Y_H_NO*(i_CODNO-i_CODN)), -i_NBM*i_cNH+(1.-Y_H_NO)/(Y_H_NO*(i_CODNO-i_CODN))*i_cNO, 0., 0., 1., -1./Y_H_NO, 0., i_TSBM-i_TSSTO/Y_H_NO];
stoi_matrix[5] = [f_XI-1., 0., 0., i_NBM-f_XI*i_NXI, 0., 0., (i_NBM-f_XI*i_NXI)*i_cNH, f_XI, 0., -1., 0., 0., f_XI*i_TSXI-i_TSBM];
stoi_matrix[6] = [0., 0., 0., i_NBM-f_XI*i_NXI, -(1.-f_XI)/(i_CODNO-i_CODN), (1.-f_XI)/(i_CODNO-i_CODN), (i_NBM-f_XI*i_NXI)*i_cNH+(1-f_XI)/(i_CODNO-i_CODN)*i_cNO, f_XI, 0., -1., 0., 0., f_XI*i_TSXI-i_TSBM];
stoi_matrix[7] = [-1., 0., 0., 0., 0., 0., 0., 0., 0., 0., -1., 0., -i_TSSTO];
stoi_matrix[8] = [0., 0., 0., 0., -1./(i_CODNO-i_CODN), 1./(i_CODNO-i_CODN), i_cNO/(i_CODNO-i_CODN), 0., 0., 0., -1., 0., -i_TSSTO];
stoi_matrix[9] = [1.+i_CODNO/Y_A, 0., 0., -1./Y_A-i_NBM, 0., 1./Y_A, (-1./Y_A-i_NBM)*i_cNH+i_cNO/Y_A, 0., 0., 0., 0., 1., i_TSBM];
stoi_matrix[10] = [f_XI-1., 0., 0., i_NBM-f_XI*i_NXI, 0., 0., (i_NBM-f_XI*i_NXI)*i_cNH, f_XI, 0., 0., 0., -1., f_XI*i_TSXI-i_TSBM];
stoi_matrix[11] = [0., 0., 0., i_NBM-f_XI*i_NXI, -(1.-f_XI)/(i_CODNO-i_CODN), (1.-f_XI)/(i_CODNO-i_CODN), (i_NBM-f_XI*i_NXI)*i_cNH+(1-f_XI)/(i_CODNO-i_CODN)*i_cNO, 0., 0., 0., 0., -1., f_XI*i_TSXI-i_TSBM];
return stoi_matrix[0].map((col, i) => stoi_matrix.map(row => row[i])); // transpose matrix
}
/**
* Computes the Monod equation rate value for a given concentration and half-saturation constant.
* @param {number} c - Concentration of reaction species.
* @param {number} K - Half-saturation constant for the reaction species.
* @returns {number} - Monod equation rate value for the given concentration and half-saturation constant.
*/
_monod(c, K) {
return c / (K + c);
}
/**
* Computes the inverse Monod equation rate value for a given concentration and half-saturation constant. Used for inhibition.
* @param {number} c - Concentration of reaction species.
* @param {number} K - Half-saturation constant for the reaction species.
* @returns {number} - Inverse Monod equation rate value for the given concentration and half-saturation constant.
*/
_inv_monod(c, K) {
return K / (K + c);
}
/**
* Adjust the rate parameter for temperature T using simplied Arrhenius equation based on rate constant at 20 degrees Celsius and theta parameter.
* @param {number} k - Rate constant at 20 degrees Celcius.
* @param {number} theta - Theta parameter.
* @param {number} T - Temperature in Celcius.
* @returns {number} - Adjusted rate parameter at temperature T based on the Arrhenius equation.
*/
_arrhenius(k, theta, T) {
return k * Math.exp(theta*(T-20));
}
/**
* Computes the temperature theta parameter based on two rate constants and their corresponding temperatures.
* @param {number} k1 - Rate constant at temperature T1.
* @param {number} k2 - Rate constant at temperature T2.
* @param {number} T1 - Temperature T1 in Celcius.
* @param {number} T2 - Temperature T2 in Celcius.
* @returns {number} - Theta parameter.
*/
_compute_theta(k1, k2, T1, T2) {
return Math.log(k1/k2)/(T1-T2);
}
/**
* Computes the reaction rates for each process reaction based on the current state and temperature.
* @param {Array} state - State vector containing concentrations of reaction species.
* @param {number} [T=20] - Temperature in degrees Celsius (default is 20).
* @returns {Array} - Reaction rates for each process reaction.
*/
compute_rates(state, T = 20) {
// state: S_O, S_I, S_S, S_NH, S_N2, S_NO, S_HCO, X_I, X_S, X_H, X_STO, X_A, X_TS
const rates = Array(12);
const [S_O, S_I, S_S, S_NH, S_N2, S_NO, S_HCO, X_I, X_S, X_H, X_STO, X_A, X_TS] = state;
const { k_H, K_X, k_STO, nu_NO, K_O, K_NO, K_S, K_STO, mu_H_max, K_NH, K_HCO, b_H_O, b_H_NO, b_STO_O, b_STO_NO, mu_A_max, K_A_NH, K_A_O, K_A_HCO, b_A_O, b_A_NO } = this.kin_params;
const { theta_H, theta_STO, theta_mu_H, theta_b_H_O, theta_b_H_NO, theta_b_STO_O, theta_b_STO_NO, theta_mu_A, theta_b_A_O, theta_b_A_NO } = this.temp_params;
// Hydrolysis
rates[0] = X_H == 0 ? 0 : this._arrhenius(k_H, theta_H, T) * this._monod(X_S / X_H, K_X) * X_H;
// Heterotrophs
rates[1] = this._arrhenius(k_STO, theta_STO, T) * this._monod(S_O, K_O) * this._monod(S_S, K_S) * X_H;
rates[2] = this._arrhenius(k_STO, theta_STO, T) * nu_NO * this._inv_monod(S_O, K_O) * this._monod(S_NO, K_NO) * this._monod(S_S, K_S) * X_H;
rates[3] = X_H == 0 ? 0 : this._arrhenius(mu_H_max, theta_mu_H, T) * this._monod(S_O, K_O) * this._monod(S_NH, K_NH) * this._monod(S_HCO, K_HCO) * this._monod(X_STO/X_H, K_STO) * X_H;
rates[4] = X_H == 0 ? 0 : this._arrhenius(mu_H_max, theta_mu_H, T) * nu_NO * this._inv_monod(S_O, K_O) * this._monod(S_NO, K_NO) * this._monod(S_NH, K_NH) * this._monod(S_HCO, K_HCO) * this._monod(X_STO/X_H, K_STO) * X_H;
rates[5] = this._arrhenius(b_H_O, theta_b_H_O, T) * this._monod(S_O, K_O) * X_H;
rates[6] = this._arrhenius(b_H_NO, theta_b_H_NO, T) * this._inv_monod(S_O, K_O) * this._monod(S_NO, K_NO) * X_H;
rates[7] = this._arrhenius(b_STO_O, theta_b_STO_O, T) * this._monod(S_O, K_O) * X_H;
rates[8] = this._arrhenius(b_STO_NO, theta_b_STO_NO, T) * this._inv_monod(S_O, K_O) * this._monod(S_NO, K_NO) * X_STO;
// Autotrophs
rates[9] = this._arrhenius(mu_A_max, theta_mu_A, T) * this._monod(S_O, K_A_O) * this._monod(S_NH, K_A_NH) * this._monod(S_HCO, K_A_HCO) * X_A;
rates[10] = this._arrhenius(b_A_O, theta_b_A_O, T) * this._monod(S_O, K_O) * X_A;
rates[11] = this._arrhenius(b_A_NO, theta_b_A_NO, T) * this._inv_monod(S_O, K_A_O) * this._monod(S_NO, K_NO) * X_A;
return rates;
}
/**
* Computes the change in concentrations of reaction species based on the current state and temperature.
* @param {Array} state - State vector containing concentrations of reaction species.
* @param {number} [T=20] - Temperature in degrees Celsius (default is 20).
* @returns {Array} - Change in reaction species concentrations.
*/
compute_dC(state, T = 20) { // compute changes in concentrations
// state: S_O, S_I, S_S, S_NH, S_N2, S_NO, S_HCO, X_I, X_S, X_H, X_STO, X_A, X_TS
return math.multiply(this.stoi_matrix, this.compute_rates(state, T));
}
}
module.exports = ASM3;