### 1. Introduction

^{2}of 0.955 and 0.91, respectively. Amr et al [10] conducted a study on three independent factors (ozone dosage, COD concentration, and reaction time) using RSM to evaluate the treatment of semi-aerobic stabilized leachate. The obtained optimum conditions were 70 g/m

^{3}ozone, 250 mg/L COD, and 60 min reaction time for 26.7, 7.1, and 92% removal for COD, NH

_{3}–N, and colour, respectively.

### 2. Materials and Methods

### 2.1. Synthetic Wastewater

### 2.2. Seed sludge and Experimental Apparatus

*COD*

*=*

_{out}*Effluent and COD*

*=*

_{in}*Influent*

^{−3}.d

^{−1}at a HRT of 24 h for the first three days of the start-up where it was operated in a batch mode, thereafter, the continuous mode was used. The OLR was thereafter increased in a stepwise manner according to the chosen HRT (6, 12 and 18 h) and it was maintained to enable the microorganisms to adapt to the new loadings until the system had attained stability. Upon HRT change, the reactor was run for a period of 50 d before changing to the next.

### 2.3. Analytical Methods

^{+6}) consumed and expressed in terms of its oxygen equivalence, was determined using close refluxing according to the standard method 5220D [16, 17]. Other parameters were determined as shown in Table S3.

### 2.4. Experimental Design and Procedure

#### 2.4.1. CCD

#### 2.4.2. BBD

*x*

*,*

_{n}*x*

*and Δ*

_{o}*x*

*represent the coded level, the real value, the centre point value and the variable step change, respectively.*

_{n}##### (3)

$${Y}_{i}={\beta}_{o}+{\mathrm{\Sigma}}_{i=1}^{k}{\beta}_{i}{X}_{i}+{\mathrm{\Sigma}}_{i=1}^{k}{\beta}_{ii}{X}_{i}^{2}+{\mathrm{\Sigma}}_{j=1}^{k-1}{\beta}_{ij}{X}_{i}{X}_{j}+C$$*β*

*,*

_{o}*β*

*,*

_{i}*β*

*and*

_{ii}*β*

*are constant, linear, quadratic, and cross factor interaction coefficients, respectively;*

_{ij}*X*

*and*

_{i}*X*

*represent the independent variables;*

_{j}*Y*

*is the predicted response; and*

_{i}*k*and

*c*are the number of factors and the residual terms, respectively. The significance of the model equations, individual parameters and factor interaction were evaluated by the analysis of variance (ANOVA) at a confidence intervals (CI) of 95% (

*ρ*= 0.05). Two-dimensional (2D) contour plots and three-dimensional (3D) surface responses were obtained after applying the developed quadratic models.

### 3. Results and Discussion

^{2}(0.9606; 0.9782), adjusted R

^{2}(0.9429; 0.9614) and predicted R

^{2}(0.8499; 0.8945) values for the CCD and BBD, respectively. All the models were significant with an insignificant lack of fit (LOF) at the 95% confidence level. The BBD based models had superlative values for the R

^{2}as compared with the CCD. The response models developed and their respective predicted values were then evaluated to validate the experimental results for the treatment of the wastewater using UASB. In addition, the models derived by the BBD seem to be simpler than the CCD, which had only 9 terms, whereas the CCD had 10. According to Zolgharnein et al. [6], the simplicity of the BBD makes it stand out from a theoretical statistical standpoint for better prediction. The response models, due to their complexity, validity, accuracy and operational interactions were then compared (section 3.1) with respect to their design’s performance.

##### (4)

$$\begin{array}{l}\text{CCD-COD\hspace{0.17em}model\hspace{0.17em}actual}=\\ 169.37-2.701\text{HRT}-13.081\text{OLR}-19.971\text{pH}+\\ 1.14(\text{HRT}\times \text{OLR})+0.575(\text{HRT}\times \text{pH})+\\ 2.133(\text{OLR}\times \text{pH})-0.041({\text{HRT}}^{2})-0.101({\text{OLR}}^{2})+\\ 0.778\hspace{0.17em}({\text{pH}}^{2})-0.168\hspace{0.17em}(\text{HRT}\times \text{OLR}\times \text{pH})\end{array}$$##### (5)

$$\begin{array}{l}\text{CCD-COD\hspace{0.17em}model\hspace{0.17em}coded}=\\ 82.443+0.551\text{A}+0.307\text{B}-1.448\text{C}-\\ 0.786\text{AB}-3.114\text{AC}+0.401\text{BC}-{\text{A}}^{2}-\\ 1.238{\text{B}}^{2}+0.778{\text{C}}^{2}-3.533\text{ABC}\end{array}$$##### (6)

$$\begin{array}{l}\text{CCD-Biogas\hspace{0.17em}model\hspace{0.17em}actual}=\\ 21304.49+479.896\text{HRT}+21.593\text{OLR}-\\ 5719.225\text{pH}-19.675(\text{HRT}\times \text{OLR})-\\ 64.836(\text{HRT}\times \text{pH})-19.268(\text{OLR}\times \text{pH})+\\ 2.019({\text{HRT}}^{2})+17.462({\text{OLR}}^{2})+470.692\hspace{0.17em}({\text{pH}}^{2})+\\ 1.399\hspace{0.17em}(\text{HRT}\times \text{OLR}\times \text{pH})\end{array}$$##### (7)

$$\begin{array}{l}\text{CCD-Biogas\hspace{0.17em}model\hspace{0.17em}coded}=\\ 4168.13-16.85\text{A}-16.85\text{B}+76.37\text{C}-\\ 207.43\text{AB}-334.43\text{AC}-8.65\text{BC}+72.71{\text{A}}^{2}+\\ 213.9{\text{B}}^{2}+470.69{\text{C}}^{2}+29.39\text{A}\end{array}$$##### (8)

$$\begin{array}{l}\text{BBD-COD\hspace{0.17em}model\hspace{0.17em}actual}=\\ 161.29-0.856\text{HRT}-3.389\text{OLR}-\\ 17.363\text{pH}-0.00694(\text{HRT}\times \text{OLR})+\\ 0.102(\text{HRT}\times \text{pH})+0.4739(\text{OLR}\times \text{pH})+\\ 0.00429({\text{HRT}}^{2})+0.00776({\text{OLR}}^{2})+0.85\hspace{0.17em}({\text{pH}}^{2})\end{array}$$##### (9)

$$\begin{array}{l}\text{BBD-COD\hspace{0.17em}model\hspace{0.17em}coded}=\\ 82.443+0.551\text{A}+0.307\text{B}-1.448\text{C}-\\ 0.786\text{AB}-3.114\text{AC}+0.401\text{BC}-{\text{A}}^{2}-\\ 1.238{\text{B}}^{2}+0.778\text{C}2-3.533\text{ABC}\end{array}$$##### (10)

$$\begin{array}{l}\text{BBD-Biogas\hspace{0.17em}model\hspace{0.17em}actual}=\\ -6994.49+1055.50\text{HRT}-1089.921\text{OLR}+\\ 2640.099\text{pH}-16.22(\text{HRT}\times \text{OLR})-\\ 107.61(\text{HRT}\times \text{pH})+144.1(\text{OLR}\times \text{pH})-\\ 7.431({\text{HRT}}^{2})+17.648({\text{OLR}}^{2})-163.65\hspace{0.17em}({\text{pH}}^{2})\end{array}$$##### (11)

$$\begin{array}{l}\text{BBD-Biogas\hspace{0.17em}model\hspace{0.17em}coded}=\\ 4976.81+110.91\text{A}-162.5\text{B}-5.67\text{C}-\\ 340.63\text{AB}-645.63\text{AC}+504.35\text{BC}-267.52{\text{A}}^{2}+\\ 216.2{\text{B}}^{2}-163.65{\text{C}}^{2}\end{array}$$### 3.1. The Analysis of Variance (ANOVA) and Significance of the Models Using CCD and BBD

^{2}) for COD and biogas were 0.9617 and 0.9653, respectively. In addition, the R

^{2}of the COD and biogas-based models using the BBD were 0.9752 and 0.9802, respectively. In both occurrences the R

^{2}values were found to be greater than 0.8 indicating a good fit of the models. Each of the model terms evaluated by the F-test showed 5% significance level (

*p*< 0.05) with a

*p*-value (probability) of 95% confidence level. The CCD and BBD F-values for COD (47.70; 3.37) and biogas (3.31; 9.02) implied that there was less than 2% chance that an F-value that large could occur due to error. Hence, the significant terms with

*p*-values less than 0.05 were considered as significant terms, whilst those with

*p*≥ 0.05 were considered as limited terms. The high hierarchal were of the model terms with

*p*-values greater than or equal to 0.05, which had limited influence on the response were also excluded. The adequate precision measured the signal to noise ratio.

^{2}values, which satisfied the adjustment of the models to suit the experimental data. This demonstrated a good agreement between the experimental data and the predicted results (Table S4 and S5). Furthermore, the ANOVA results showed a desirable and coherent agreement with the adjusted R

^{2}. Therefore, the use of the quadratic models could be used to optimize the system under the same given condition instead of the conventional method.

### 3.2. Diagnostic Checking of the Fitted Models Using CCD and BBD

### 3.3. The Three-dimensional (3D surface) Plots of the Models

### 3.4. Numerical Evaluation of the Effect of pH, OLR and HRT on the Response

^{−3}.d

^{−1}and 3 kg.m

^{−3}.d

^{−1}, respectively.

^{−3}.d

^{−1}) at low HRT (8 h) could result in high VFA, which might have inhibited the biogas production and decrease the degradability of the COD. Thus, within the pH range of 6.5–7.2, the COD removal and biogas production increased, whilst below 6.5, the efficiency of the system was inhibited. This agree with the report by Lettinga and Pol [15 Lettinga and Pol [15] and Torkian et al. [18 Torkian et al. [18]. They reported that a decrease in pH below 6.5 could hinder the methanogenic microorganism activities thus declining biogas production. At a lower pH, an accumulation of VFA could occur and a minimal buffering capacity of the UASB is induced thereby inhibiting the methanogenic activity.

^{−3}.d

^{−1}and at a shorter HRT of less than 8 h was found to be detrimental to the methanogens. Thus, the high OLR (10 kg.m

^{−3}.d

^{−1}) resulted in poor performance of the system, due to overload of the substrate, which supersedes the microorganism. At a lower HRT, there is a reduction in the contact time for the breaking down of the organic components, therefore impeding the performance of methanogens present in the system such that the conversion of the high COD or the acetates into biogas is limited. Operating at an optimal region of the OLR (3–5 kg.m

^{−3}.d

^{−1}) was found suitable to prevent the washout of the organic matter in the effluent and increased the treatable desirability of the system. At higher OLR, a possible washout of organic matter could occur.

### 4. Conclusions

^{−3}.d

^{−1}and 3 kg.m

^{−3}.d

^{−1}for CCD and BBD, respectively. Both designs were found suitable in predicting high treatability performance of the UASB above 90%. Based on the confirmation test, the BBD model prediction (biogas 5,955.4 ± 225.3 mL/d; COD 81.5 ± 1.014%) was found to be in good agreement with the experimental results (biogas 5,800 mL/d; COD 80.8%). Conversely, the BBD produced a high desirability efficiency of 94% as opposed to the CCD of 92%. The models obtained were found to be predictive, adequate and significant at 95% confidence level. RSM is an effective and economically viable alternative technique that can be adapted for optimizing various wastewater treatment processes to favourably maximise the output. Operating the UASB at HRT (8 to 15 h), OLR (3 to 5 kg.m

^{−3}.d

^{−1}) and pH (6.5 to 7.2) were found to be workable conditions to maximise the outputs. Furthermore, the UASB is an effective and reliable process for the treatment and generation of biogas from wastewaters. In addition, this area can be of economic interest to stakeholders for protecting the environment and producing green energy as well as reducing the footprint of greenhouse gases.