Power regressions of versus the parameters of chlorine decay models are presented in Table 6. The parameters of existing models are affected negatively by
and show strong correlations (R2 > 0.86). The parameter a (the proportional coefficient of regression equation) tends to decrease as the order n increases for the nth-order and limited nth-order models, and the converse tendency is apparent for the parameter b (the power coefficient of regression equation), except in the case of the fourth-order model, for which R2 values are small relative to those of other models (see Table 6).
Table 6
Regression equations between and model parameters (y) using y=axb and the corresponding determination coefficients (R2) for all models
| Model | y | X | a | b | R2 |
|---|---|---|---|---|---|
| 1st order | 1.869 | −2.487 × 10−1 | 0.980 | ||
| 2nd order | 1.670 | −2.611 × 10−1 | 0.958 | ||
| 3rd order | 1.474 | −2.741 × 10−1 | 0.928 | ||
| 4th order | 1.657 | −3.143 × 10−1 | 0.892 | ||
| Limited 1st order | 1.951 | −2.519 × 10−1 | 0.988 | ||
| Limited 2nd order | 1.677 | −2.578 × 10−1 | 0.959 | ||
| Limited 3rd order | 1.557 | −2.750 × 10−1 | 0.936 | ||
| Limited 4th order | 1.498 | −2.925 × 10−1 | 0.861 | ||
| Parallel 1st order | w | 1.845 | −1.151 × 10−1 | 0.968 | |
| k1 | 1.892 | −2.500 × 10−1 | 0.978 | ||
| k2 | 1.827 | −2.463 × 10−1 | 0.983 | ||
| nth | n | 2.868 | −1.861 × 10−1 | 0.740 | |
| k | 1.494 | −2.118 × 10−1 | 0.983 | ||
| Limited nth | n | 2.978 | −1.952 × 10−1 | 0.751 | |
| k | 1.513 | −2.120 × 10−1 | 0.977 | ||
| Combined ‘1 + 1’ | w | 1.426 | −6.217 × 10−1 | 0.975 | |
| k1 | 1.878 | −2.491 × 10−1 | 0.978 | ||
| k2 | 1.834 | −2.477 × 10−1 | 0.980 | ||
| w | 61.96 | −8.330 × 10−1 | 0.790 | ||
| Combined ‘1 + n’ | k1 | 230.3 | −9.147 × 10−1 | 0.941 | |
| n | 0.02066 | 3.857 × 10−1 | 0.816 | ||
| k2 | 0.4503 | −7.087 × 10−1 | 0.596 | ||
| c* | 0.0066 | 2.653 × 10−1 | 0.901 | ||
| w | 0.6310 | −1.379 × 10−1 | 0.892 | ||
| Combined ‘n+n’ | n1 | 10.39 | −4.009 × 10−1 | 0.717 | |
| k1 | 104.2 | −7.918 × 10−1 | 0.925 | ||
| n2 | 0.006321 | 5.443 × 10−1 | 0.680 | ||
| k1 | 0.6737 | −1.344 × 10−1 | 0.915 | ||
| c* | 6 × 10−5 | 7.537 × 10−1 | 0.855 |
| Model | y | X | a | b | R2 |
|---|---|---|---|---|---|
| 1st order | 1.869 | −2.487 × 10−1 | 0.980 | ||
| 2nd order | 1.670 | −2.611 × 10−1 | 0.958 | ||
| 3rd order | 1.474 | −2.741 × 10−1 | 0.928 | ||
| 4th order | 1.657 | −3.143 × 10−1 | 0.892 | ||
| Limited 1st order | 1.951 | −2.519 × 10−1 | 0.988 | ||
| Limited 2nd order | 1.677 | −2.578 × 10−1 | 0.959 | ||
| Limited 3rd order | 1.557 | −2.750 × 10−1 | 0.936 | ||
| Limited 4th order | 1.498 | −2.925 × 10−1 | 0.861 | ||
| Parallel 1st order | w | 1.845 | −1.151 × 10−1 | 0.968 | |
| k1 | 1.892 | −2.500 × 10−1 | 0.978 | ||
| k2 | 1.827 | −2.463 × 10−1 | 0.983 | ||
| nth | n | 2.868 | −1.861 × 10−1 | 0.740 | |
| k | 1.494 | −2.118 × 10−1 | 0.983 | ||
| Limited nth | n | 2.978 | −1.952 × 10−1 | 0.751 | |
| k | 1.513 | −2.120 × 10−1 | 0.977 | ||
| Combined ‘1 + 1’ | w | 1.426 | −6.217 × 10−1 | 0.975 | |
| k1 | 1.878 | −2.491 × 10−1 | 0.978 | ||
| k2 | 1.834 | −2.477 × 10−1 | 0.980 | ||
| w | 61.96 | −8.330 × 10−1 | 0.790 | ||
| Combined ‘1 + n’ | k1 | 230.3 | −9.147 × 10−1 | 0.941 | |
| n | 0.02066 | 3.857 × 10−1 | 0.816 | ||
| k2 | 0.4503 | −7.087 × 10−1 | 0.596 | ||
| c* | 0.0066 | 2.653 × 10−1 | 0.901 | ||
| w | 0.6310 | −1.379 × 10−1 | 0.892 | ||
| Combined ‘n+n’ | n1 | 10.39 | −4.009 × 10−1 | 0.717 | |
| k1 | 104.2 | −7.918 × 10−1 | 0.925 | ||
| n2 | 0.006321 | 5.443 × 10−1 | 0.680 | ||
| k1 | 0.6737 | −1.344 × 10−1 | 0.915 | ||
| c* | 6 × 10−5 | 7.537 × 10−1 | 0.855 |