Submitted:
10 February 2026
Posted:
11 February 2026
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Abstract

Keywords:
1. Introduction
1.1. Study Area

2. Materials and Methods
2.1. Sampling

2.2. Materials
2.3. Statistical Analysis and Model Evaluation
2.4. Model Graphs
2.5. Quality Assurance and Replication
2.6. Final Equation in Terms of Coded and Actual Factors
2.7. Response Surface Methodology
3. Results
3.1. Preliminary Experiments
3.2. Response Surface Methodology
3.2.1. Descriptive and FIT Statistics

3.3. External Model Validation
4. Discussion
4.1. Interpretation of Coagulant Performance and Mechanisms
4.2. Insights from RSM Optimization and Model Validity
4.3. Regulatory Compliance and Economic Viability
4.4. Limitations and Recommendations for Future Work
5. Conclusions
- Ferric chloride (FeCl3·6H2O) emerged as the most effective coagulant, achieving the highest and most consistent multi-parameter removal, particularly for turbidity and TSS, under alkaline conditions (pH 12, 30 mg/L). Aluminum sulfate provided robust performance, while Moringa oleifera, though cost-effective at low doses, exhibited a narrow optimal dosage window beyond which performance deteriorated due to restabilization.
- Statistically significant quadratic models were developed with high predictive accuracy (R2 > 0.97 for key parameters). External validation with independent experimental runs confirmed the models’ reliability for forecasting treatment outcomes within the defined operational space.
- Most significantly, the optimized process using FeCl3 produces an effluent that meets Botswana’s discharge standards for TSS (≤ 30 mg/L), COD (≤ 75 mg/L), and turbidity (≤ 10 NTU), directly addressing the plant’s core compliance failure.
- The research provides a clear, data-driven pathway for implementation. Coagulant dosing can be integrated into existing infrastructure between the trickling filters and humus tanks with modest capital investment. A preliminary economic analysis indicates operational costs are manageable, with FeCl3 representing the optimal balance of performance and reliability for ensuring consistent compliance.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
| WSP | Waste Stabilization Pond |
| TSS | Total Suspended Solids |
| TF | Trickling Filter |
| SS | Suspended Solids |
| RSM | Response Surface Methodology |
| RMSE | Root Mean Square Error |
| PWWTP | Palapye Wastewater Treatment Plant |
| PETRO | Pond Enhanced Treatment and Operation |
| OFAOT | One-Factor-at-a-Time |
| MRS | Multi-Response Surface |
| MP | Maturation Pond |
| HT | Humus Tank |
| FP | Facultative Pond |
| FeCl3·6H2O | Ferric chloride hexahydrate |
| DOE | Design of Experiment |
| COD | Chemical Oxygen Demand |
| CI | Confidence Interval |
| CCD | Central Composite Design |
| BOD | Biological Oxygen Demand |
| AS | Activated Sludge |
| AP | Anaerobic Pond |
| ANOVA | Analysis of Variance |
| Al2(SO4)3·18H2O | Aluminum sulfate octadecahydrate |
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| Input variable | Numeric Factor Levels | ||||
| -1.414 | -1 | 0 | +1 | + 1.414 | |
| Lower | Low | Centre | High | Higher | |
| pH | 8.38 | 9 | 10.5 | 12 | 12.6 |
| Al2(SO4)3.18H2O, mg/L | 2.93 | 5 | 10 | 15 | 17.1 |
| FeCl3.6H2O, mg/L | 5.86 | 10 | 20 | 30 | 34.1 |
| Moringa, mg/L | 0.76 | 2 | 5 | 8 | 9.2 |
| Al2(SO4)3.18H2O | FeCl3.6H2O | Moringa | |||
| pH | % Turbidity Removal | pH | % Turbidity Removal | pH | % Turbidity Removal |
| 2.0 | 46.5 | 2.0 | 70.0 | 2.0 | 69.2 |
| 3.5 | 62.3 | 3.0 | 75.6 | 4.0 | 63.8 |
| 6.1 | 76.0 | 6.1 | 85.6 | 6.1 | 76.1 |
| 7.1 | 84.3 | 9.6 | 92.0 | 9.0 | 96.4 |
| 11.0 | 81.5 | 11.8 | 96.9 | 11.1 | 97.7 |
| 12.2 | 92.7 | 12.4 | 98.9 | 12.4 | 98.5 |
| Dosage, | Turbidity, | Colour, | COD, | TSS, | Removal COD, | Removal TSS, | Removal Turbidity, | Removal Colour, | % Removal COD, | % Removal TSS, | % Removal Turbidity | % Removal Colour, |
| mg/L | NTU | mg/L Pt-co | mg/L O2 | mg/L | mg/L O2 | mg/L | NTU | mg/L Pt-co | % | % | % | % |
| 0 | 0.12 | 51 | 77 | 4 | 54 | 11 | 12.28 | 160 | 41.2 | 73.3 | 99.0 | 75.8 |
| 5 | 0.095 | 43 | 78 | 3 | 53 | 12 | 12.305 | 168 | 40.5 | 80.0 | 99.2 | 79.6 |
| 10 | 0.09 | 41 | 77 | 2 | 54 | 13 | 12.31 | 170 | 41.2 | 86.7 | 99.3 | 80.6 |
| 20 | 0.09 | 43 | 76 | 3 | 55 | 12 | 12.31 | 168 | 42.0 | 80.0 | 99.3 | 79.6 |
| 50 | 0.09 | 39 | 77 | 2 | 54 | 13 | 12.31 | 172 | 41.2 | 86.7 | 99.3 | 81.5 |
| 100 | 0.08 | 42 | 74 | 1 | 57 | 14 | 12.32 | 169 | 43.5 | 93.3 | 99.4 | 80.1 |
| Dosage, mg/L | Turbidity, NTU | Colour, mg/L Pt-co | COD, mg/L O2 | TSS, mg/L | Removal COD, mg/L O2 | Removal TSS, mg/L | Removal Turbidity, NTU | Removal Colour, mg/L Pt-co | % Removal Turbidity, NTU | % Removal Colour, mg/L Pt | % Removal COD, mg/L O2 | % Removal TSS, mg/L |
| 0 | 0.085 | 45 | 77 | 1 | 54 | 14 | 12.315 | 166 | 99.3 | 78.7 | 41.2 | 93.3 |
| 5 | 0.07 | 41 | 78 | 3 | 53 | 12 | 12.33 | 170 | 99.4 | 80.6 | 40.5 | 80.0 |
| 10 | 0.07 | 38 | 77 | 1 | 54 | 14 | 12.33 | 173 | 99.4 | 82.0 | 41.2 | 93.3 |
| 20 | 0.07 | 37 | 79 | 1 | 52 | 14 | 12.33 | 174 | 99.4 | 82.5 | 39.7 | 93.3 |
| 50 | 0.07 | 38 | 76 | 0 | 55 | 15 | 12.33 | 173 | 99.4 | 82.0 | 42.0 | 100.0 |
| 100 | 0.06 | 39 | 78 | 1 | 53 | 14 | 12.34 | 172 | 99.5 | 81.5 | 40.5 | 93.3 |
| Dosage, mg/L | Turbidity, NTU | Colour, mg/L Pt | COD, mg/L | TSS, mg/L | Removal Turbidity, NTU | Removal Colour, mg/L Pt | COD Removal, mg/L | TSS Removal , mg/L | % Removal Turbidity |
% Removal Colour | % COD Removal, | % TSS Removal |
| 0 | 0.09 | 49 | 82 | 3 | 12.31 | 162 | 49 | 12 | 99.3 | 76.8 | 37.4 | 80.0 |
| 5 | 0.07 | 48 | 81 | 2 | 12.33 | 163 | 50 | 13 | 99.4 | 77.3 | 38.2 | 86.7 |
| 10 | 0.08 | 51 | 83 | 2 | 12.32 | 160 | 48 | 13 | 99.4 | 75.8 | 36.6 | 86.7 |
| 20 | 0.09 | 61 | 85 | 4 | 12.31 | 150 | 46 | 11 | 99.3 | 71.1 | 35.1 | 73.3 |
| 50 | 0.11 | 73 | 96 | 2 | 12.29 | 138 | 35 | 13 | 99.1 | 65.4 | 26.7 | 86.7 |
| 100 | 0.165 | 117 | 106 | 6 | 12.235 | 94 | 25 | 9 | 98.7 | 44.5 | 19.1 | 60.0 |
| Trickling filter effluent Characterization | Coagulant Stock Solution (10 g/l) | ||||
| Turbidity, NTU | 50.7 | Fil. Turb, NTU: | 4 | Coagulant Name | pH |
| Colour, mg/L, Pt-co | 762 | Fil. Colour, mg/L, Pt-co | 147 | Al2(SO4)3.18H2O | 3.7 |
| COD, mg/L | 202 | FeCl3.6H2O | 2.12 | ||
| TSS, mg/L | 65 | Moringa | 6.25 | ||
| Response | Model | Lack of FIT | FIT Statistics | |||||
| F values | P value |
F values | P value | R2 | Adj R2 | Pred. R2 | Adq. precision | |
| Turbidity | 114.47 | <0.0001 | 1.7 | 0.1789 | 0.9764 | 0.9676 | 0.9481 | 41.4541 |
| Colour | 244.43 | <0.0001 | 1.58 | 0.2161 | 0.9869 | 0.9828 | 0.9796 | 66.5861 |
| COD | 118.25 | <0.0001 | 1.71 | 0.1834 | 0.9718 | 0.9636 | 0.9456 | 47.2574 |
| TSS | 21.22 | <0.0001 | 0.9832 | 0.5234 | 0.8908 | 0.8488 | 0.7668 | 16.2008 |
| Run | Parameter | Predicted Value | Actual Value | Percent Error (%) | RMSE* |
| 1 | Turbidity (NTU) | 0.45 | 0.47 | 4.3 | 0.41 NTU |
| Colour (mg/L Pt-Co) | 42.1 | 44.5 | 5.4 | 8.7 mg/L | |
| COD (mg/L O2) | 58.3 | 62.8 | 7.2 | 5.2 mg/L | |
| TSS (mg/L) | 3.2 | 3.4 | 5.9 | 1.8 mg/L | |
| 2 | Turbidity (NTU) | 0.38 | 0.36 | 5.6 | 0.41 NTU |
| Colour (mg/L Pt-Co) | 38.7 | 40.2 | 3.7 | 8.7 mg/L | |
| COD (mg/L O2) | 61.5 | 65.1 | 5.5 | 5.2 mg/L | |
| TSS (mg/L) | 2.8 | 2.9 | 3.4 | 1.8 mg/L | |
| 3 | Turbidity (NTU) | 0.52 | 0.50 | 4.0 | 0.41 NTU |
| Colour (mg/L Pt-Co) | 45.3 | 47.8 | 5.2 | 8.7 mg/L | |
| COD (mg/L O2) | 55.8 | 60.3 | 7.5 | 5.2 mg/L | |
| TSS (mg/L) | 3.5 | 3.7 | 5.4 | 1.8 mg/L | |
| Average | All Parameters | - | - | 5.4 | - |
| Overall RMSE | - | - | - | - | See below |
| Parameter | Botswana Standard (Typical Limit) | Optimized Effluent Value (FeCl3) | Compliance Status |
| TSS | ≤ 30 mg/L | 1 mg/L | Fully Compliant |
| COD | ≤ 75 mg/L | 55 mg/L | Fully Compliant |
| Turbidity | ≤ 10 NTU | 0.07 NTU | Fully Compliant |
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