# Coagulation: Determination of Key Operating Parameters by Multi-Response Surface Methodology Using Desirability Functions

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### Response Surface Method for Optimizing the Clarification Process

_{1}, X

_{2}, X

_{3}, …, X

_{k}are input vectors, and e is the error. The quadratic (second-order) model is a polynomial function that is frequently used, and is written as Equation (2):

_{0}, b

_{i}, b

_{ii}, and b

_{i}. However, good results are not always possible with these functions, if the problem is complex and involves many inputs and nonlinearities. The reason is that the coefficients cannot be adjusted if the data are sparse-like continuous functions that are described by polynomials. The p-value (or Prob. > F) is the probability that the result that will equal or exceed the value that was actually observed assuming that the model produces results that are accurate. The p-value can be determined by analysis of the variance (ANOVA). If the model’s Prob. > F and no term exceeds the level of significance (e.g., α = 0.05), one can consider the model to be acceptable within a (1 − α) confidence interval. Some investigators have used ANOVA to study the effect of inputs or process variables on process outputs [41,42]. If a problem has more than one outputs, the latter is termed MRS. Normally, it causes conflicting solutions, as the optimal configuration may vary significantly from one output to another. A compromise was suggested by Harrington [43]. It involves desirability functions for each output, Equations (3) and (4). It also involves an overall desirability. The latter is the mean value of the desirability (D) of each output (Equation (5)). Equations (3)–(5) can be described as:

_{r}is the model for prediction. It is beneficial to use a second-higher-degree polynomial to optimize responses [44]. In the desirability approach, each estimated response is transformed into a unit-less utility that is bounded by 0 < d

_{r}< 1. A higher value of d

_{r}signifies a more desirable response value. The optimization function of the R package v.1.6 [45] searches for a combination of importance factors (or weights of 1, 2 or −3) that satisfy the process criteria for each response and input.

#### 2.2. Experiments Design

## 3. Results and Discussion

#### 3.1. Experimental Results

#### 3.2. Analysis of Variance

^{–6}) on finTurb, whereas for s (p-value = 0.18584) and for T (p-value = 0.30660), its influence is much smaller. On the other hand, iniTurb has a certain influence on finTurb when it interacts with itself (p-value = 0.00484), as well as when it interacts with T (p-value = 0.00013). Finally, cuaDose has a notable influence on finTurb when it interacts with iniTurb (p-value = 0.00751) and with T (p-value = 0.00013). From Table 6, it is observed that for ECOTAN BIO 90D, there is no significant influence of any input on TSS, at least when the variables do not interact. However, Table 5 also shows that cuaDose has a notable influence when it interacts with t (p-value = 0.00041) and s (p-value = 0.05395). In addition, t has a notable influence when it interacts with s (p-value = 0.03045), and with T as well when it interacts with itself (p-value = 0.00699). From Table 7, it is observed that for ECOTAN BIO 100, there is a notable influence of s (p-value = 0.053178) on finTurb, whereas for t (p-value = 0.203000) its influence is limited. In addition, this table also shows that s has an important influence when it interacts with itself (p-value = 2.943 × 10

^{−5}) and when it interacts with cuaDose (p-value = 0.047805). On the other hand, iniTurb also has a notable influence when it interacts with T (p-value = 0.011558). In the same manner that occurs with ECOTAN BIO 90D, Table 8 shows that for ECOTAN BIO 100, there is no significant influence of any input on TSS, at least when the variables do not interact. However, in Table 8, it is observed that t and s have a notable influence on TSS when it interacts with itself (p-value = 0.02714 and p-value = 0.00619, respectively). These two variables also have a notable influence on cuaDose, which is also significantly influenced when it interacts with s (p-value = 0.00026), with iniTurb (p-value = 0.00137), and with itself (p-value = 0.01175). Finally, regarding ECOTAN BIO G150 (Table 9), it is observed that t, s and iniTurb have an important influence on finTurb (p-value = 0.03742, p-value = 0.04282 and p-value = 0.00116, respectively), and on cuaDose, where very low values are obtained for p-value (for s·cuaDose: p-value = 0.00077; and for iniTurb·cuaDose: p-value = 7.74 × 10

^{−5}). For this same coagulant, it is also observed that s and cuaDose have a significant influence on TSS (p-value = 0.04463 and p-value = 0.00141, respectively), while t also influences TSS when it is interacting with itself (p-value = 0.01602). T has no influence on TSS in any way.

_{k Experiment}are the experimentally obtained responses and Y

_{k Model}are responses from the quadratic models that RSM and m experiments produced. The prediction errors are shown in Table 11. The maximum error corresponds to TSS (the MAE equals to 0.14905 and the RMSE equals to 0.17981). The minimum error corresponds to finTurb (the MAE equals to 0.09261 and the RMSE equals to 0.11363).

#### 3.3. Multi-Response Optimization

_{k,norm}are the normalized, experimental outputs of the models that were developed using RSM. The errors in the last columns concern the MAE and RMSE that were normalized for each variable in each clarification optimization scenario to be studied. The normalized MAE and RMSE that appear in the last two rows relate to the errors in the outputs variables that were examined. For example, Table 19, Table 20 and Table 21 show that the output variable that produce the greatest error in prediction for each of the three natural coagulants studied is the TSS variable (ECOTAN BIO 90D: MAE = 0.08, ECOTAN BIO 100: MAE = 0.08 and ECOTAN BIO G150: MAE = 0.29). These values correspond to the errors that appear in Table 13. In the latter table, the maximum MAE corresponds to the output variable TSS for the three natural coagulants that were studied. However, in Table 19, Table 20 and Table 21, the third optimization scenario has the highest MAE and RMSE values for the three studied coagulants. The reason for this may be that the samples of raw water in this optimization scenario required a high turbidity to analyze each of the natural coagulants to obtain the highest efficiency of turbidity removal and TSS. In this case, a greater initial turbidity of the raw water sample, also as a greater requirement in turbidity removal, could produce this maximum MAE for this scenario.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Scatter diagrams of ECOTAN BIO 90D: (

**a**) finTurb and (

**b)**TSS; ECOTAN BIO 100: (

**c**) finTurb and (

**d**) TSS; and ECOTAN BIO G150: (

**e**) finTurb and (

**f)**TSS.

pH | DQO (mg/L) | DBO (mg/L) | Nt (mg/L) | NH_{4} (mg/L) | Pt (mg/L) |
---|---|---|---|---|---|

7.48 | 306.71 | 147.84 | 34.21 | 18.54 | 4.26 |

Input | Notation | Magnitude | Levels | ||
---|---|---|---|---|---|

−1 | 0 | 1 | |||

time | t | sec | 30 | 75 | 120 |

speed | S | rpm | 50 | 75 | 100 |

temperature | T | °C | 10 | 15 | 20 |

initial turbidity | iniTurb | NTU | 40 | 90 | 140 |

coagulant dosage | cuaDose | mL | 1 | 3.5 | 6 |

Sample | Parameters of the Coagulation Process | ||||
---|---|---|---|---|---|

Time (t) (sec) | Speed (s) (rpm) | Temp (T) (°C) | Initial Turbidity (iniTurb) (NTU) | Coagulant Dosage (cuaDose) (mL) | |

1 | 30 | 100 | 20 | 40 | 1 |

2* | 75 | 75 | 15 | 90 | 3.5 |

3 | 120 | 50 | 10 | 40 | 6 |

4 | 30 | 50 | 20 | 40 | 6 |

5 | 30 | 50 | 20 | 140 | 1 |

6 | 30 | 100 | 20 | 140 | 6 |

7 | 75 | 75 | 15 | 90 | 1 |

8 | 30 | 100 | 10 | 140 | 6 |

9 | 75 | 75 | 15 | 40 | 3.5 |

10 | 120 | 50 | 10 | 140 | 1 |

11 | 30 | 50 | 10 | 140 | 1 |

12 | 75 | 75 | 15 | 90 | 3.5 |

13 | 75 | 75 | 15 | 90 | 3.5 |

14 | 30 | 50 | 10 | 40 | 6 |

15 | 120 | 100 | 20 | 40 | 1 |

16 | 120 | 100 | 20 | 40 | 6 |

17 | 120 | 100 | 10 | 40 | 1 |

18 | 30 | 75 | 15 | 90 | 3.5 |

19 | 120 | 50 | 20 | 40 | 1 |

20 | 75 | 75 | 15 | 90 | 6 |

21 | 120 | 100 | 10 | 140 | 6 |

22* | 75 | 75 | 15 | 90 | 3.5 |

23 | 120 | 50 | 20 | 140 | 6 |

24* | 75 | 75 | 15 | 90 | 3.5 |

25* | 75 | 75 | 15 | 90 | 3.5 |

26 | 75 | 75 | 15 | 140 | 3.5 |

27 | 75 | 75 | 20 | 90 | 3.5 |

28 | 120 | 50 | 20 | 140 | 1 |

29 | 75 | 50 | 15 | 90 | 3.5 |

30 | 30 | 100 | 20 | 40 | 6 |

31 | 75 | 100 | 15 | 90 | 3.5 |

32 | 30 | 50 | 20 | 140 | 6 |

33 | 30 | 50 | 10 | 140 | 6 |

34 | 120 | 50 | 10 | 140 | 6 |

35* | 75 | 75 | 15 | 90 | 3.5 |

36 | 30 | 100 | 20 | 140 | 1 |

37* | 75 | 75 | 15 | 90 | 3.5 |

38 | 120 | 100 | 20 | 140 | 1 |

39 | 30 | 50 | 10 | 40 | 1 |

40* | 75 | 75 | 15 | 90 | 3.5 |

41 | 120 | 50 | 20 | 40 | 6 |

42 | 75 | 75 | 10 | 90 | 3.5 |

43 | 30 | 100 | 10 | 40 | 1 |

44 | 120 | 100 | 20 | 140 | 6 |

45 | 120 | 100 | 10 | 40 | 6 |

46 | 120 | 50 | 10 | 40 | 1 |

47* | 75 | 75 | 15 | 90 | 3.5 |

48 | 30 | 50 | 20 | 40 | 1 |

49 | 30 | 100 | 10 | 140 | 1 |

50* | 75 | 75 | 15 | 90 | 3.5 |

51 | 120 | 75 | 15 | 90 | 3.5 |

52* | 75 | 75 | 15 | 90 | 3.5 |

33 | 30 | 100 | 10 | 40 | 6 |

54 | 120 | 100 | 10 | 140 | 1 |

Sample | Outputs | |||||
---|---|---|---|---|---|---|

ECOTAN BIO 90D | ECOTAN BIO 100 | ECOTAN BIO G150 | ||||

finTurb (NTU) | TSS (mg/L) | finTurb (NTU) | TSS (mg/L) | finTurb (NTU) | TSS (mg/L) | |

1 | 20.09 | 598.3 | 31.11 | 696.0 | 30.20 | 227 |

2 | 12.67 | 203.7 | 36.10 | 689.0 | 27.30 | 600 |

3 | 11.71 | 42.0 | 17.99 | 318.0 | 33.30 | 327 |

4 | 19.10 | 48.0 | 25.00 | 631.0 | 41.30 | 414 |

5 | 34.90 | 658.0 | 22.50 | 134.0 | 41.70 | 432 |

6 | 9.60 | 107.8 | 21.60 | 394.0 | 25.90 | 91 |

7 | 12.85 | 273.3 | 35.30 | 528.0 | 32.70 | 585 |

8 | 13.11 | 392.0 | 35.40 | 110.0 | 41.30 | 201 |

9 | 9.60 | 119.5 | 27.90 | 429.0 | 36.70 | 586 |

10 | 6.83 | 413.0 | 13.51 | 555.0 | 11.50 | 291 |

11 | 15.30 | 368.0 | 28.90 | 507.0 | 19.10 | 609 |

12 | 9.20 | 302.0 | 27.50 | 694.3 | 23.90 | 535 |

13 | 11.90 | 396.0 | 25.70 | 629.0 | 30.40 | 551 |

14 | 28.90 | 641.9 | 22.20 | 5.0 | 53.90 | 32 |

15 | 10.04 | 514.7 | 23.80 | 423.0 | 35.10 | 238 |

16 | 6.95 | 611.3 | 22.60 | 29.3 | 21.70 | 261 |

17 | 6.45 | 249.0 | 22.30 | 414.0 | 40.70 | 332 |

18 | 18.2 | 761.9 | 46.70 | 285. | 63.90 | 771 |

19 | 9.57 | 354.6 | 10.70 | 507.0 | 35.30 | 514 |

20 | 13.10 | 596.0 | 41.20 | 134.0 | 39.50 | 27 |

21 | 5.87 | 563.9 | 7.63 | 482.0 | 48.00 | 38 |

22 | 8.70 | 707.3 | 37.20 | 505.0 | 32.20 | 690 |

23 | 13.18 | 362.0 | 28.70 | 629.0 | 46.30 | 620 |

24 | 8.43 | 387.0 | 27.40 | 463.0 | 30.20 | 708 |

25 | 6.62 | 261.2 | 29.90 | 230.0 | 33.60 | 709 |

26 | 12.6 | 388.5 | 22.70 | 289.0 | 14.10 | 235 |

27 | 9.80 | 576.0 | 32.10 | 398.0 | 27.40 | 561 |

28 | 19.80 | 57.0 | 9.83 | 128.0 | 14.88 | 377 |

29 | 8.67 | 423.9 | 30.20 | 652. | 21.40 | 390 |

30 | 21.30 | 141.0 | 26.70 | 190.0 | 37.90 | 215 |

31 | 15.20 | 355.0 | 19.80 | 827.9 | 22.70 | 211 |

32 | 6.30 | 75.8 | 20.30 | 410.0 | 55.90 | 166 |

33 | 20.10 | 229.0 | 53.70 | 528.0 | 30.00 | 546 |

34 | 6.82 | 160.6 | 66.50 | 242.0 | 36.20 | 571 |

35 | 9.63 | 539.2 | 39.00 | 648.0 | 14.81 | 260 |

36 | 16.10 | 430.0 | 13.00 | 592.0 | 17.00 | 255 |

37 | 4.97 | 395.1 | 39.80 | 227.0 | 28.24 | 473 |

38 | 10.70 | 220.0 | 31.90 | 396.0 | 14.55 | 670 |

39 | 34.30 | 443.0 | 28.70 | 703.0 | 39.80 | 534 |

40 | 14.60 | 525.8 | 49.80 | 687.0 | 28.26 | 198 |

41 | 6.63 | 550.0 | 28.60 | 97.0 | 47.70 | 4 |

42 | 7.68 | 139.0 | 49.20 | 490.0 | 45.70 | 357 |

43 | 15.60 | 539.1 | 17.30 | 475.0 | 37.00 | 383 |

44 | 7.65 | 529.0 | 5.83 | 523.0 | 22.10 | 276 |

45 | 14.34 | 769.0 | 20.90 | 403.0 | 33.30 | 275 |

46 | 8.45 | 215.2 | 25.40 | 312.0 | 43.70 | 307 |

47 | 9.10 | 618.6 | 60.90 | 470.0 | 23.80 | 486 |

48 | 17.55 | 598.5 | 35.10 | 472.0 | 30.20 | 420 |

49 | 23.10 | 673.0 | 24.90 | 623.0 | 21.50 | 463 |

50 | 12.80 | 390.5 | 47.50 | 419.2 | 31.20 | 467 |

51 | 17.82 | 752.0 | 38.70 | 101.0 | 29.60 | 520 |

52 | 3.87 | 392.0 | 19.50 | 246.0 | 30.70 | 604 |

53 | 32.60 | 464.0 | 13.60 | 24.0 | 44.10 | 74 |

54 | 6.83 | 164.0 | 12.53 | 880.0 | 12.46 | 432 |

Variable | Df ^{1} | Sum of Square | Mean Square | F Value | p-value |
---|---|---|---|---|---|

t | 1 | 916.346 | 916.346 | 53.236 | 8.428 × 10^{−6} |

t² | 1 | 323.793 | 323.793 | 18.811 | 9.867 × 10^{−5} |

s | 1 | 31.219 | 31.219 | 1.814 | 0.18584 |

t·s | 1 | 3.638 | 3.638 | 0.211 | 0.64825 |

T | 1 | 18.473 | 18.473 | 1.073 | 0.30660 |

t·T | 1 | 102.780 | 102.780 | 5.971 | 0.01917 |

T² | 1 | 57.522 | 57.522 | 3.342 | 0.07520 |

T·iniTurb | 1 | 2.850 | 2.850 | 0.166 | 0.68631 |

iniTurb² | 1 | 153.633 | 153.633 | 8.925 | 0.00484 |

t·cuaDose | 1 | 15.650 | 15.650 | 0.909 | 0.34620 |

s·cuaDose | 1 | 4.262 | 4.262 | 0.248 | 0.62155 |

T·cuaDose | 1 | 311.691 | 311.691 | 18.108 | 0.00013 |

iniTurb·cuaDose | 1 | 136.885 | 136.885 | 7.952 | 0.00751 |

cuaDose² | 1 | 30.343 | 30.343 | 1.763 | 0.19200 |

Residuals | 39 | 671.306 | 17.213 |

^{1}Degrees of freedom (Df).

Variable | Df ^{1} | Sum of Square | Mean Square | F Value | p-value |
---|---|---|---|---|---|

t | 1 | 12123.226 | 12123.226 | 0.486 | 0.48969 |

t² | 1 | 142.315 | 142.315 | 0.006 | 0.94016 |

t·s | 1 | 125559.858 | 125559.858 | 5.035 | 0.03045 |

s² | 1 | 5888.921 | 5888.921 | 0.236 | 0.62966 |

T | 1 | 45.924 | 45.924 | 0.002 | 0.96598 |

t·T | 1 | 47902.024 | 47902.024 | 1.921 | 0.17345 |

T² | 1 | 201652.233 | 201652.233 | 8.086 | 0.00699 |

iniTurb | 1 | 9905.698 | 9905.698 | 0.397 | 0.53212 |

iniTurb² | 1 | 164612.655 | 164612.655 | 6.601 | 0.01403 |

cuaDose | 1 | 53839.319 | 53839.319 | 2.159 | 0.14957 |

t·cuaDose | 1 | 371281.918 | 371281.918 | 14.888 | 0.00041 |

s·cuaDose | 1 | 98334.840 | 98334.840 | 3.943 | 0.05395 |

T·cuaDose | 1 | 74204.701 | 74204.701 | 2.976 | 0.09225 |

Residuals | 40 | 997539.737 | 24938.493 |

^{1}Degrees of freedom (Df).

Variable | Df ^{1} | Sum of Square | Mean Square | F Value | p-value |
---|---|---|---|---|---|

t | 1 | 166.585 | 166.585 | 1.675 | 0.203000 |

s | 1 | 394.790 | 394.790 | 3.970 | 0.053178 |

s² | 1 | 2208.677 | 2208.677 | 22.209 | 2.943 × 10^{−5} |

s·T | 1 | 11.438 | 11.438 | 0.115 | 0.736274 |

iniTurb | 1 | 0.034 | 0.034 | 0.000 | 0.985279 |

s·iniTurb | 1 | 223.193 | 223.193 | 2.244 | 0.141956 |

T·tubrIni | 1 | 696.807 | 696.807 | 7.007 | 0.011558 |

cuaDose | 1 | 118.417 | 118.417 | 1.191 | 0.281708 |

s·cuaDose | 1 | 414.589 | 414.589 | 4.169 | 0.047805 |

T·cuaDose | 1 | 311.029 | 311.029 | 3.128 | 0.084605 |

iniTurb·cuaDose | 1 | 298.428 | 298.428 | 3.001 | 0.090926 |

Residuals | 40 | 3977.917 | 99.448 |

^{1}Degrees of freedom (Df).

Variable | Df ^{1} | Sum of Square | Mean Square | F Value | p-value |
---|---|---|---|---|---|

t | 1 | 3433.556 | 3433.556 | 0.134 | 0.71620 |

t² | 1 | 134355.201 | 134355.201 | 5.242 | 0.02714 |

s | 1 | 11120.751 | 11120.751 | 0.434 | 0.51369 |

s² | 1 | 212994.469 | 212994.469 | 8.310 | 0.00619 |

T·iniTurb | 1 | 641.102 | 641.102 | 0.025 | 0.87509 |

s·cuaDose | 1 | 407001.590 | 407001.590 | 15.879 | 0.00026 |

T·cuaDose | 1 | 91379.561 | 91379.561 | 3.565 | 0.06592 |

iniTurb·cuaDose | 1 | 301130.135 | 301130.135 | 11.749 | 0.00137 |

cuaDose² | 1 | 177895.900 | 177895.900 | 6.941 | 0.01175 |

Residuals | 42 | 1076504.55 | 25631.061 |

^{1}Degrees of freedom (Df).

Variable | Df ^{1} | Sum of Square | Mean Square | F Value | p-value |
---|---|---|---|---|---|

t | 1 | 270.772 | 270.772 | 4.612 | 0.03742 |

t² | 1 | 329.885 | 329.885 | 5.619 | 0.02231 |

s | 1 | 255.758 | 255.758 | 4.357 | 0.04282 |

s² | 1 | 411.999 | 411.999 | 7.018 | 0.01124 |

s·T | 1 | 332.273 | 332.273 | 5.660 | 0.02186 |

iniTurb | 1 | 710.517 | 710.517 | 12.103 | 0.00116 |

T·iniTurb | 1 | 199.801 | 199.801 | 3.403 | 0.07195 |

s·cuaDose | 1 | 768.059 | 768.059 | 13.083 | 0.00077 |

iniTurb·cuaDose | 1 | 1120.611 | 1120.611 | 19.089 | 7.74 × 10^{−5} |

Residuals | 43 | 2524.340 | 58.706 |

^{1}Degrees of freedom (Df).

Variable | Df ^{1} | Sum of Square | Mean Square | F Value | p-value |
---|---|---|---|---|---|

t | 1 | 1423.529 | 1423.529 | 0.057 | 0.81278 |

t² | 1 | 158135.752 | 158135.752 | 6.312 | 0.01602 |

s | 1 | 107521.882 | 107521.882 | 4.292 | 0.04463 |

s² | 1 | 226926.055 | 226926.055 | 9.058 | 0.00446 |

T | 1 | 704.326 | 704.326 | 0.028 | 0.86767 |

t·T | 1 | 63037.289 | 63037.289 | 2.516 | 0.12036 |

T² | 1 | 40058.639 | 40058.639 | 1.599 | 0.21319 |

iniTurb | 1 | 10881.901 | 10881.901 | 0.434 | 0.51354 |

iniTurb² | 1 | 25196.398 | 25196.398 | 1.006 | 0.32181 |

cuaDose | 1 | 293880.040 | 293880.040 | 11.731 | 0.00141 |

s·cuaDose | 1 | 45925.039 | 45925.039 | 1.833 | 0.18317 |

cuaDose² | 1 | 85936.210 | 85936.210 | 3.430 | 0.07122 |

Residuals | 41 | 1027147.47 | 25052.377 |

^{1}Degrees of freedom (Df).

Coagulant | Outputs | Correlation | MAE ^{1} Train | RSMSE ^{2} Train |
---|---|---|---|---|

BIO 90D | finTurb | 0.87095 | 0.09261 | 0.11363 |

TSS | 0.73405 | 0.14905 | 0.18695 | |

BIO 100 | finTurb | 0.74100 | 0.11541 | 0.14416 |

TSS | 0.74466 | 0.13621 | 0.16444 | |

BIO G150 | finTurb | 0.79713 | 0.10266 | 0.13171 |

TSS | 0.71259 | 0.14427 | 0.17981 |

^{1}Mean Absolute Error (MAE),

^{2}Root Mean Squared Error (RMSE).

Sample | Parameters of the Coagulation Process | ||||
---|---|---|---|---|---|

Time (t) (sec) | Speed (s) (rpm) | Temp (T) (°C) | Initial Turbidity (iniTurb) (NTU) | Coagulant Dosage (cuaDose) (mL) | |

1 | 44 | 84 | 12.0 | 78 | 3.35 |

2 | 60 | 80 | 17.0 | 115 | 4.35 |

3 | 88 | 56 | 14.5 | 103 | 4.80 |

4 | 94 | 57 | 19.0 | 133 | 3.75 |

5 | 80 | 96 | 15.0 | 76 | 2.05 |

6 | 69 | 55 | 10.0 | 134 | 4.20 |

7 | 76 | 81 | 12.0 | 97 | 2.30 |

8 | 95 | 87 | 16.0 | 131 | 1.50 |

9 | 83 | 73 | 13.0 | 124 | 3.30 |

10 | 69 | 81 | 11.0 | 59 | 4.90 |

11 | 59 | 55 | 15.0 | 116 | 3.05 |

Errors | ECOTAN BIO 90D | ECOTAN BIO 100 | ECOTAN BIO G150 | |||
---|---|---|---|---|---|---|

finTurb (NTU) | TSS (mg/L) | finTurb (NTU) | TSS (mg/L) | finTurb (NTU) | TSS (mg/L) | |

MAE | 0.14902 | 0.1600 | 0.12016 | 0.17693 | 0.15815 | 0.17413 |

RMSE | 0.19515 | 0.22979 | 0.16307 | 0.21898 | 0.2145 | 0.23425 |

**Table 14.**The first clarification optimization scenario: all variables are considered to be equally important.

Coagulant | Parameters | Goal | Importance | Value | Desirability |
---|---|---|---|---|---|

ECOTAN BIO 90D | t | min | 1.0 | 67.197 | 0.587 |

s | min | 1.0 | 51.481 | 0.97 | |

T | min | 1.0 | 8.598 | 0.978 | |

iniTurb | min | 1.0 | 52.207 | 0.862 | |

cuaDose | inRange | 1.0 | 4.704 | 1.000 | |

finTurb | min | 1.0 | 12.057 | 0.736 | |

TSS | min | 1.0 | 5.010 | 1.000 | |

Overall Desirability | 0.841 | ||||

ECOTAN BIO 100 | t | min | 1.0 | 32.057 | 0.977 |

s | min | 1.0 | 59.857 | 0.803 | |

T | min | 1.0 | 12.027 | 0.882 | |

iniTurb | min | 1.0 | 41.924 | 0.831 | |

cuaDose | inRange | 1.0 | 5.441 | 1.000 | |

finTurb | min | 1.0 | 37.85 | 0.472 | |

TSS | min | 1.0 | 51.273 | 0.947 | |

Overall Desirability | 0.797 | ||||

ECOTAN BIO G150 | t | min | 1.0 | 36.344 | 0.93 |

s | min | 1.0 | 50.476 | 0.99 | |

T | min | 1.0 | 13.437 | 0.738 | |

iniTurb | min | 1.0 | 42.971 | 0.936 | |

cuaDose | inRange | 1.0 | 1.062 | 1.00 | |

finTurb | min | 1.0 | 38.788 | 0.479 | |

TSS | min | 1.0 | 343.679 | 0.557 | |

Overall Desirability | 0.774 |

**Table 15.**The second clarification optimization scenario: the energy consumption is minimized to obtain the highest efficiency of turbidity removal and TSS.

Coagulant | Parameters | Goal | Importance | Value | Desirability |
---|---|---|---|---|---|

ECOTAN BIO 90D | t | min | 1.0 | 65.57 | 0.605 |

s | min | 1.0 | 52.019 | 0.960 | |

T | min | 1.0 | 8.569 | 0.980 | |

iniTurb | inRange | 1.0 | 127.612 | 1.000 | |

cuaDose | inRange | 1.0 | 3.162 | 1.000 | |

finTurb | min | 1.0 | 5.655 | 0.942 | |

TSS | min | 1.0 | 51.901 | 0.986 | |

Overall Desirability | 0.88 | ||||

ECOTAN BIO 100 | t | min | 1.0 | 31.967 | 0.978 |

s | min | 1.0 | 59.857 | 0.803 | |

T | min | 1.0 | 12.027 | 0.882 | |

iniTurb | inRange | 1.0 | 40.099 | 1.000 | |

cuaDose | inRange | 1.0 | 5.441 | 1.000 | |

finTurb | min | 1.0 | 37.882 | 0.472 | |

TSS | min | 1.0 | 50.807 | 0.948 | |

Overall Desirability | 0.791 | ||||

ECOTAN BIO G150 | t | min | 1.0 | 51.271 | 0.764 |

s | min | 1.0 | 50.858 | 0.983 | |

T | min | 1.0 | 13.779 | 0.712 | |

iniTurb | inRange | 1.0 | 133.808 | 1.000 | |

cuaDose | inRange | 1.0 | 3.781 | 1.000 | |

finTurb | min | 1.0 | 18.325 | 0.87 | |

TSS | min | 1.0 | 328.925 | 0.576 | |

Overall Desirability | 0.768 |

**Table 16.**The third clarification optimization scenario: the energy consumption is minimized to obtain the highest efficiency of turbidity removal and TSS, when the sample water is very turbid.

Coagulant | Parameters | Goal | Importance | Value | Desirability |
---|---|---|---|---|---|

ECOTAN BIO 90D | t | min | 1.0 | 49.463 | 0.784 |

s | min | 1.0 | 62.784 | 0.744 | |

T | min | 1.0 | 10.473 | 0.838 | |

iniTurb | max | 1.0 | 164.399 | 0.995 | |

cuaDose | inRange | 1.0 | 3.007 | 1.000 | |

finTurb | min | 1.0 | 9.222 | 0.828 | |

TSS | min | 1.0 | 51.098 | 0.987 | |

Overall Desirability | 0.857 | ||||

ECOTAN BIO 100 | t | min | 1.0 | 34.399 | 0.951 |

s | min | 1.0 | 55.619 | 0.888 | |

T | min | 1.0 | 20.819 | 0.514 | |

iniTurb | max | 1.0 | 184.576 | 0.998 | |

cuaDose | inRange | 1.0 | 3.490 | 1.000 | |

finTurb | min | 1.0 | 28.824 | 0.621 | |

TSS | min | 1.0 | 441.478 | 0.501 | |

Overall Desirability | 0.716 | ||||

ECOTAN BIO G150 | t | min | 1.0 | 51.271 | 0.764 |

s | min | 1.0 | 50.858 | 0.983 | |

T | min | 1.0 | 13.779 | 0.712 | |

iniTurb | max | 1.0 | 173.808 | 0.939 | |

cuaDose | inRange | 1.0 | 3.781 | 1.000 | |

finTurb | min | 1.0 | 18.325 | 0.87 | |

TSS | min | 1.0 | 328.925 | 0.576 | |

Overall Desirability | 0.794 |

**Table 17.**The fourth clarification optimization scenario: the turbidity and TSS are minimized when sample water is very cold and turbid.

Coagulant | Parameters | Goal | Importance | Value | Desirability |
---|---|---|---|---|---|

ECOTAN BIO 90D | t | inRange | 1.0 | 81.887 | 1.000 |

s | inRange | 1.0 | 53.278 | 1.000 | |

T | min | 1.0 | 8.567 | 0.980 | |

iniTurb | max | 1.0 | 160.591 | 0.966 | |

cuaDose | inRange | 1.0 | 5.267 | 1.000 | |

finTurb | min | 1.0 | 1.213 | 1.000 | |

TSS | min | 1.0 | 57.980 | 1.000 | |

Overall Desirability | 0.986 | ||||

ECOTAN BIO 100 | t | inRange | 1.0 | 110.137 | 1.000 |

s | inRange | 1.0 | 88.552 | 1.000 | |

T | min | 1.0 | 9.751 | 0.977 | |

iniTurb | max | 1.0 | 173.27 | 0.933 | |

cuaDose | inRange | 1.0 | 1.110 | 1.000 | |

finTurb | min | 1.0 | 24.719 | 0.689 | |

TSS | min | 1.0 | 429.117 | 0.515 | |

Overall Desirability | 0.754 | ||||

ECOTAN BIO G150 | t | inRange | 1.0 | 81.887 | 1.000 |

s | inRange | 1.0 | 53.278 | 1.000 | |

T | min | 1.0 | 10.261 | 0.980 | |

iniTurb | max | 1.0 | 177.957 | 0.966 | |

cuaDose | inRange | 1.0 | 5.267 | 1.000 | |

finTurb | min | 1.0 | 20.331 | 0.831 | |

TSS | min | 1.0 | 281.105 | 0.639 | |

Overall Desirability | 0.774 |

**Table 18.**The fifth clarification optimization scenario: the turbidity and TSS are minimized when the sample water is turbid and hot.

Coagulant | Parameters | Goal | Importance | Value | Desirability |
---|---|---|---|---|---|

ECOTAN BIO 90D | t | inRange | 1.0 | 45.363 | 1.000 |

s | inRange | 1.0 | 79.840 | 1.000 | |

T | max | 1.0 | 20.926 | 0.942 | |

iniTurb | max | 1.0 | 136.59 | 0.966 | |

cuaDose | inRange | 1.0 | 5.455 | 1.000 | |

finTurb | min | 1.0 | 3.964 | 0.997 | |

TSS | min | 1.0 | 4.730 | 1.000 | |

Overall Desirability | 0.976 | ||||

ECOTAN BIO 100 | t | inRange | 1.0 | 92.101 | 1.000 |

s | inRange | 1.0 | 78.240 | 1.000 | |

T | max | 1.0 | 31.458 | 0.931 | |

iniTurb | max | 1.0 | 138.785 | 0.964 | |

cuaDose | inRange | 1.0 | 1.197 | 1.000 | |

finTurb | min | 1.0 | 13.487 | 0.874 | |

TSS | min | 1.0 | 20.112 | 1.000 | |

Overall Desirability | 0.941 | ||||

ECOTAN BIO G150 | t | inRange | 1.0 | 62.737 | 1.000 |

s | inRange | 1.0 | 99.463 | 1.000 | |

T | max | 1.0 | 20.050 | 0.767 | |

iniTurb | max | 1.0 | 139.986 | 0.980 | |

cuaDose | inRange | 1.0 | 2.5140 | 1.000 | |

finTurb | min | 1.0 | 5.4220 | 1.000 | |

TSS | min | 1.0 | 194.109 | 0.752 | |

Overall Desirability | 0.774 |

**Table 19.**Experimental outputs that were obtained according to the five clarification optimization scenarios for ECOTAN BIO 90D.

Opt. Scenario | Experimental Values Obtained | |||
---|---|---|---|---|

finTurb | TSS | MAE | RMSE | |

1st Scenario | 0.86 | 0.02 | 0.07 | 0.10 |

2nd Scenario | 0.48 | 0.76 | 0.10 | 0.10 |

3rd Scenario | 0.65 | 0.72 | 0.12 | 0.13 |

4th Scenario | 0.01 | 0.90 | 0.05 | 0.07 |

5th Scenario | 0.20 | 0.01 | 0.03 | 0.04 |

MAE | 0.07 | 0.08 | ||

RMSE | 0.08 | 0.10 |

**Table 20.**Experimental outputs that were obtained according to the five clarification optimization scenarios for ECOTAN BIO 100.

Opt. Scenario | Experimental Values Obtained | |||
---|---|---|---|---|

finTurb | TSS | MAE | RMSE | |

1st Scenario | 0.87 | 0.05 | 0.08 | 0.09 |

2nd Scenario | 0.82 | 0.06 | 0.10 | 0.13 |

3rd Scenario | 0.62 | 0.80 | 0.11 | 0.14 |

4th Scenario | 0.48 | 0.84 | 0.08 | 0.10 |

5th Scenario | 0.03 | 0.01 | 0.02 | 0.02 |

MAE | 0.07 | 0.08 | ||

RMSE | 0.10 | 0.11 |

**Table 21.**Experimental outputs that were obtained according to the five clarification optimization scenarios for ECOTAN G150.

Opt. Scenario | Experimental Values Obtained | |||
---|---|---|---|---|

finTurb | TSS | MAE | RMSE | |

1st Scenario | 0.98 | 0.62 | 0.20 | 0.27 |

2nd Scenario | 0.37 | 0.55 | 0.18 | 0.25 |

3rd Scenario | 0.48 | 0.57 | 0.21 | 0.25 |

4th Scenario | 0.37 | 0.75 | 0.12 | 0.13 |

5th Scenario | 0.03 | 0.20 | 0.12 | 0.15 |

MAE | 0.05 | 0.29 | ||

RMSE | 0.06 | 0.30 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Corral Bobadilla, M.; Lorza, R.L.; Escribano García, R.; Somovilla Gómez, F.; Vergara González, E.P. Coagulation: Determination of Key Operating Parameters by Multi-Response Surface Methodology Using Desirability Functions. *Water* **2019**, *11*, 398.
https://doi.org/10.3390/w11020398

**AMA Style**

Corral Bobadilla M, Lorza RL, Escribano García R, Somovilla Gómez F, Vergara González EP. Coagulation: Determination of Key Operating Parameters by Multi-Response Surface Methodology Using Desirability Functions. *Water*. 2019; 11(2):398.
https://doi.org/10.3390/w11020398

**Chicago/Turabian Style**

Corral Bobadilla, Marina, Rubén Lostado Lorza, Rubén Escribano García, Fátima Somovilla Gómez, and Eliseo P. Vergara González. 2019. "Coagulation: Determination of Key Operating Parameters by Multi-Response Surface Methodology Using Desirability Functions" *Water* 11, no. 2: 398.
https://doi.org/10.3390/w11020398