3.1 TPH Biodegradation
The degradation pathway for standard run 17 – 20 which serve as control for the study were similar having the same combined variables. TPH concentration degraded from 5,000 mg kg-1 to between 722 – 862 mg kg-1 in 90 days duration while maintaining 3 days/week turning rate. Standard runs 3, 4, 7, 8, 11, 12, 15, and 16 with moisture content of 50% had high slimy organic solvent floating on the surface. This made the admix semifluid in nature and easy to turn using hand trowel. When turning rate is effective and properly practice, the hydrocarbon contaminants becoming exposed to degrading agents and are therefore either completely degraded or mineralized . This is attributed to the over 80% TPH reduction recorded in standard run 16 after 90 days treatment.
Substrate addition also enhanced TPH degradation as it serves as energizer for the microbes. This served mainly as catalyst in microbes’ reproduction processes and consequent consumption of the TPH contaminants. Although higher concentration of substrate does not guarantee high TPH degradation, but when suitably combined with other parameters such as turning rate, high pH value and average moisture content; then a better degradation result can be obtained . As fertilizer application on crude oil contaminated site was well systemic and well calculated, TPH degradation result was less than 40%, this was mainly due to the low moisture content and high acidic values of the treated samples. Nwilo and Badejo  had similar results from their study in which NPK fertilizer was used in the treatment of soil collected from a spill site. TPH degradation was faster in samples with lower moisture content than samples with higher moisture content. The pH of the contaminated soil samples before treatment ranged from 2 – 5. An increase in pH values was observed as the treatment progress into day 15 to 70, the pH value ranged from 5.7 to 7.1 (neutral). The addition of fertilizer to hydrocarbon polluted soil samples had a catalyst effect on the treatment and the pH value increase from acidic range of 2 to neutral range of 6.8. The substrate applied caused an increase in the total nitrogenous content of the soil but as the treatment days increased from day 50 – 60, the nitrogen content decreased gradually. This could be linked to the soil bacterial consuming the nitrogen for the hydrocarbon degradation, thus reducing the available nitrogen as treatment time increases . In the cause of hydrocarbon degradation, nitrogen is lost in the atmosphere during nitrate ions conversion into gaseous nitrogen. This process utilizes biochemical reduction and it is initiated by denitrifying bacterial in the soil . In all the factorial setups for the hydrocarbon contamination treatment, there was significant TPH degradation and the bacterial population in all the setups increased exponentially. The petroleum degrading bacteria increased from 1.8E-0.1 to 3.6E+08 cfu/g during the treatment period. This increase confirms the loss of nitrogen which usually accompany degradation procedures [11,17]. This increment in petroleum degrading bacteria is in tandem with the findings of Oluwatuyi et. al.,  and Okonofua et al. . FD analysis of results was then employed to determine the variable with the most significant contribution in the TPH degradation procedure.
3.2 Factorial design of experiment
The response of TPHs on FD of experiment, used for variable screening hydrocarbon contaminant concentration of 5000 mg kg-1 within a period of 90 days is presented in Table 4. The minimum value of TPH is given as 450.43 mg kg-1 while the maximum value is 1393.04 mg kg-1. The calculated mean value is 921.44 mg kg-1 while the standard deviation is 302.48 mg kg-1. In assessing the worthiness of FD in screening the input variables based on their fundamental and important contributions, model standard error analysis was used based on Montgomery . Presented in Table 5 are the computed standard errors for the chosen response. From the result, a low standard error of 0.25 was achieved for both the individual and combine terms and effects. According to Jasmine and Mukherji , standard errors must be akin within a coefficient and the minimal the value is, the better. Similarly, the error values were lower than the model basic standard deviation (SD) of 1.0 suggesting that the FD was perfect for the screening process. To demonstrate for multicollinearity, the variance inflation factor (VIF) of the analysis was obtained all through as 1.0 representing a superb outcome as a perfect VIF should give 1.0. VIF's closer to 10 or greater than it are usually cause for concern, and this signifies that coefficients are basely calculated due to multicollinearity .
Furthermore, the Ri-squared values also gives zero which perfectly match an ideal Ri-square as high Ri-squared especially values above 1.0 shows that design terms are correlated utimately resulting to poor models. Table 6 presents the correlation matrix of the regression coefficient. It can be seen that, off diagonal matrix, the lower values obtained points out the fact that the model is well fitted and it is strengthened enough to pilot the design space thus adequately optimizing the chosen response variable. Also, the model leveages were computed in order to better understand the influencial effect of individual design points on the model’s predicted value. According to Meloun and Militky , leverage point indicates the extent of influence of an individual design point on the model's predicted values and it usually varies from 0 to 1. A leverage of 1 indicates that, the predicted value at a specific case will perfectly equal the observed value of the experiment, making the residual to be zero. The addition of leverage values in all cases equals the number of coefficients fit by the model, and the ultimate leverage an experiment can have is determined by 1/m, with m being the number of rounds the experiment was repeated. Leverages of 0.6750 calculated for in the factorial point indicate that, there is closeness between the predicted values and the experimental values. Hence, less or low residual value approves the sufficiency of the model.
3.3 Strength assessment of factorial model
To assess the strength of the factorial model towards an effective screening and optimization of the input variables, based on their significant contributions, one-way analysis of variance (ANOVA) was done for the response variable (Table 7). This was used to examine if the model is significant or not and to also measure the important contributions of individual variable. From the analysis in Table 7, the Model F-value of 56.24 connotes that the model is significant owing to the fact that there is only 0.01% probability that a "Model F-Value" with high value could occur due to noise. When the values of "Prob > F" are < 0.05, it indicate that the model terms are significant while values ˃ 0.1 indicate the model terms are not significant [39, 40]. Therefore, the terms A, D, AD, BC and CD are all significant model terms. Also, 22.47 gotten for the "Curvature F-value" means that there exist significant curvature in the design space. This is mostly estimated by the difference between the average of the factorial points and that of the center points, and there is just 0.15% chance that a "Curvature F-value" with high value could occur as noise. Furthermore, 0.60 gotten for the "Lack of Fit F-value" connotes that, it is not significant when compared with the pure error but on the other hand, there is a 71.07% probability that a "Lack of Fit F-value" could occur due to noise. In Table 8, the goodness of fit statistics were used to formalize the sufficiency of the factorial model regarding its potential to screen the input variables based on their significant contribution. From the statistical analysis, the "Predicted R-Squared" value of 0.9188 is in logical agreement with the "Adj R-Squared" value of 0.9684. According to Singh et al. , obtaining an adequate precision shows an adequate signal to noise ratio ˃ 4 as been desirable. Thus, the computed ratio of 20.367 as shown in Table 8 connotes an adequate signal. This model outcome therefore shows that it can be used to pilot the design space and properly screen the input variables while also determine their optimum value.
3.4 Input parameters and generated equation
The significant contributions of each input variables were determined using pareto chart. Pareto chart is a graphical presentation of input variables in order of their ranking. Statistical tool was used to generate Pareto’s chart (Fig. 3) for the selected input variables. The result shows that the variables contributed to the hydrocarbon degradation in varying proportion with turning rate, pH, moisture content and mass of substrate all contributing 82.79%, 4.36%, 0.48% and 0.046% respectively. Furthermore, the most fitting equation which depict both the combine interactions and individual effects of the significant input variables (pH, moisture content, mass of substrate and turning rate) against the mesured response (total petroleum hydrocarbon TPH) is provided based on the coded variables and the actual factors which are shown in Eqs. 4 and 5. Either of these two equations can be used in the estimation of the predicted TPH values which is shown in column 3 of Table 9. The predicted TPH values are then compared with the measured values to obtain the residual and the cook’s distance shown in columns 4 and 9 in Table 9. In factorial design study, only terms without coefficients (zero coefficient) are left out in TPH evaluation using either coded or actual factors, hence the inclusion of AB and BD.
The symptomatic case statistics showing the observed values of the response covariant (TPH) against the predicted values is shown in Table 9. This symptomatic case statistics vividly present a clear and deep understanding into the model strength and the adequacy of the factorial design model.
3.5 Model validation
To further evaluate the accuracy of the prediction and established the appropriateness of factorial design of experiment, the observed and predicted values of TPH was gotten via a reliability plot as shown in Fig. 4. The r2 = 0.9865 which represent the coefficient of determination was utilized in affirming the eligibility of the factorial design in reducing the TPH. An adequate statistical analysis output must first be used to check the satisfactoriness level of any model before its acceptance. Thus, to examine the statistical properties of the factorial design model, the normal probability plot of studentized residual shown in Fig. 5 was used to evaluate the regularity of the calculated residuals. The plot of residuals which represent the standard deviation of actual values based on the predicted values was adopted to ascertain if the residuals (observed – predicted) follows a normal distribution pattern. It was depicted that, the computed residuals are normally and approximately distributed which indicates the degree of satisfaction of the developed model developed. Furthermore, in the analysis, to determine the availability of a possible outlier, cook’s distance plot was generated (Fig. 6). This cook’s distance is a phenomenon that measures the degree at which the regression can change if the outlier is excluded from the analysis. A particular point having a high distance value relative to the other points can possibly be an outlier and should therefore be investigated . From Fig. 6, the plot has an upper bound and lower bound of 1.00 and 0.00 respectively; therefore, experimental values below the lower bound (0.00) or above the upper bounds (1.00) are termed as outliers which must be adequately investigated. Fortunately, the data of this analysis are free of possible outliers thus showing forth the adequacy of the experimental data. A 3D surface response plot was also provided to study the effects of combine input variables on the response (Fig. 7). It can be seen that the plot depicts the connection between the input variables (pH and turning rate) and the response variable (TPH) and also provide a comprehensible concept of the factorial model. In addition to this, the colour of the surface gets darker towards the turning rate which connotes that a higher turning rate leads to a reduction in TPH. This observation is in tandem with the work of Agarry and Ogunleye .
3.6 Numerical optimizaton
The numerical optimization was finally done to be sure of the desirability of the absolute model. Design expert was adopted in the numerical optimization phase in order to minimize the TPH and determine the optimum pH, moisture content, mass of substrate and the turning rate. The numerical optimization interphase presents the objective function (Fig. S1) with production of twenty (20) optimal solutions (Table 10). From the analysis, turning rate of 5 times a week, with pH of 6.01, moisture content of 10% and substrate mass of 1.00 kg will result in a minimum TPH value of 635.907 with a reliability value of 98.60%. The ramp solution showing the graphical representation of the best solution (Fig. S2) while the desirability chart depicting the veracity with which the model can predict the values of the chosen input variables and the similar response is presented in Fig. 8. From the outcome on the chart, it can be inferred that the developed and optimized model using factorial design and numerical optimization method respectively, predicted the TPH by an accuracy level of 97.83%.