IWA Publishing

Parameter calibration results for models in Tables 1 and 2 are presented in Table 3. Calibrations were performed through three distinct model structures: the designation of the reaction order (n) as an integer for Equation (2) (e.g., models 1–9 in Table 3), calibration incorporating parameter n as a real number (e.g., models 10 and 11 in Table 3), and the most comprehensive calibration involving a flexible concentration of the stable component (⁠

⁠) instead of a designated

for a lower detection limit of the sensor (e.g., models 12–14 in Table 3).

Table 3

Calibrated parameters for candidate chlorine models with different hydraulic conditions

Model	Title	Parameter	Steady	40 min	20 min	10 min	5 min	2.5 min
1	1st order	k (day⁻¹)	0.479	0.440	0.397	0.286	0.240	0.185
2	2nd order	k (day⁻¹)	0.392	0.357	0.330	0.238	0.201	0.141
3	3rd order	k (day⁻¹)	0.318	0.285	0.270	0.195	0.166	0.105
4	4th order	k (day⁻¹)	0.260	0.244	0.244	0.163	0.139	0.078
5	Limited 1st order	k (day⁻¹)	0.488	0.458	0.397	0.292	0.244	0.188
6	Limited 2nd order	k (day⁻¹)	0.406	0.366	0.336	0.246	0.208	0.145
7	Limited 3rd order	k (day⁻¹)	0.334	0.305	0.275	0.206	0.175	0.110
8	Limited 4th order	k (day⁻¹)	0.278	0.250	0.250	0.175	0.156	0.084
9	Parallel 1st order	w	0.995	1.000	0.851	0.753	0.711	0.652
		k₁ (day⁻¹)	0.468	0.440	0.400	0.288	0.240	0.184
		k₂ (day⁻¹)	0.480	0.439	0.390	0.283	0.240	0.185
10	nth order	n	0.407	0.997	0.967	0.563	0.701	0.507
10	nth order	k (day⁻¹)	0.527	0.437	0.401	0.305	0.250	0.213
11	Limited nth order	n	0.390	0.980	0.945	0.547	0.683	0.478
11	Limited nth order	k (day⁻¹)	0.531	0.437	0.409	0.309	0.254	0.214
12	Combined ‘1 + 1’	w	0.942	0.992	0.959	0.903	0.859	0.792
		k₁ (day⁻¹)	0.479	0.440	0.399	0.287	0.240	0.185
		k₂ (day⁻¹)	0.478	0.440	0.390	0.276	0.238	0.185
		c* (mg/L)	0.000	0.000	0.000	0.000	0.000	0.000
13	Combined ‘1 + n’	w	0.125	0.332	0.314	0.259	0.083	0.015
		k₁ (day⁻¹)	0.407	0.995	0.974	0.248	0.082	0.057
		n	0.348	0.131	0.348	0.423	0.571	0.573
		k₂ (day⁻¹)	0.500	0.291	0.279	0.279	0.277	0.211
		c* (mg/L)	0.020	0.029	0.040	0.040	0.072	0.072
14	Combined ‘n + n’	w	0.424	0.304	0.261	0.204	0.192	0.191
		n₁	0.375	0.878	0.804	0.604	0.582	0.165
		k₁ (day⁻¹)	0.255	0.998	0.856	0.211	0.190	0.060
		n₂	0.364	0.069	0.433	0.501	0.628	0.651
		k₂ (day⁻¹)	0.438	0.295	0.295	0.263	0.219	0.187
		c* (mg/L)	0.034	0.003	0.011	0.032	0.037	0.045

Model	Title	Parameter	Steady	40 min	20 min	10 min	5 min	2.5 min
1	1st order	k (day⁻¹)	0.479	0.440	0.397	0.286	0.240	0.185
2	2nd order	k (day⁻¹)	0.392	0.357	0.330	0.238	0.201	0.141
3	3rd order	k (day⁻¹)	0.318	0.285	0.270	0.195	0.166	0.105
4	4th order	k (day⁻¹)	0.260	0.244	0.244	0.163	0.139	0.078
5	Limited 1st order	k (day⁻¹)	0.488	0.458	0.397	0.292	0.244	0.188
6	Limited 2nd order	k (day⁻¹)	0.406	0.366	0.336	0.246	0.208	0.145
7	Limited 3rd order	k (day⁻¹)	0.334	0.305	0.275	0.206	0.175	0.110
8	Limited 4th order	k (day⁻¹)	0.278	0.250	0.250	0.175	0.156	0.084
9	Parallel 1st order	w	0.995	1.000	0.851	0.753	0.711	0.652
		k₁ (day⁻¹)	0.468	0.440	0.400	0.288	0.240	0.184
		k₂ (day⁻¹)	0.480	0.439	0.390	0.283	0.240	0.185
10	nth order	n	0.407	0.997	0.967	0.563	0.701	0.507
10	nth order	k (day⁻¹)	0.527	0.437	0.401	0.305	0.250	0.213
11	Limited nth order	n	0.390	0.980	0.945	0.547	0.683	0.478
11	Limited nth order	k (day⁻¹)	0.531	0.437	0.409	0.309	0.254	0.214
12	Combined ‘1 + 1’	w	0.942	0.992	0.959	0.903	0.859	0.792
		k₁ (day⁻¹)	0.479	0.440	0.399	0.287	0.240	0.185
		k₂ (day⁻¹)	0.478	0.440	0.390	0.276	0.238	0.185
		c* (mg/L)	0.000	0.000	0.000	0.000	0.000	0.000
13	Combined ‘1 + n’	w	0.125	0.332	0.314	0.259	0.083	0.015
		k₁ (day⁻¹)	0.407	0.995	0.974	0.248	0.082	0.057
		n	0.348	0.131	0.348	0.423	0.571	0.573
		k₂ (day⁻¹)	0.500	0.291	0.279	0.279	0.277	0.211
		c* (mg/L)	0.020	0.029	0.040	0.040	0.072	0.072
14	Combined ‘n + n’	w	0.424	0.304	0.261	0.204	0.192	0.191
		n₁	0.375	0.878	0.804	0.604	0.582	0.165
		k₁ (day⁻¹)	0.255	0.998	0.856	0.211	0.190	0.060
		n₂	0.364	0.069	0.433	0.501	0.628	0.651
		k₂ (day⁻¹)	0.438	0.295	0.295	0.263	0.219	0.187
		c* (mg/L)	0.034	0.003	0.011	0.032	0.037	0.045

View Large

This Feature Is Available To Subscribers Only