Novel Mathematical Models for Prediction of Spent Engine oil Interactions with Vernonia amygdalina Leaf Extract

Aims: The michaelis-menten biokinetic model was used for the determination of key biokinetic parameters; maximum specific rate constant ( and michaelis-menten constant ( including  the total polycyclic aromatic hydrocarbon (TPAH) degradation rate equation in the biostimulation of spent engine oil (SEO) – contaminated soil  using vernonia amygdalina leaf (bitter leaf) extract. Study Design:  Single factor experiment in a randomized complete block design (RCBD) was used in this study. Place and Duration of Study: Research farm, Rivers state university, Port-Harcourt, Nigeria, between April 2023 and May 2023. Methodology: TPAH was quantified by the standard method, according to USEPA method using gas chromatography-mass spectrometry (GC-MS). The experiment consisted of 4 reactors replicated thrice including the control (Labelled A to D) comprised of soil, SEO and bitter leaf extract in the ratios of 8:1:0.5, 8:1:1, 8:1:1.5, and 8:1:0, respectively, after 8 weeks of treatment. Results: The results obtained shows that TPAH concentration dropped by 42.3 – 63.9% from 98.73mg/kg-1 with an average reduction of 52% was achieved in all treatment reactors. The average of   was 4.4mg/kg-week and   was 79.2mg/kg while the TPAH degradation was deduced as  at any TPAH concentration. The validation of the developed model indicates a high coefficient of determination (2) ranging from 0.927 to 0.992 and a low root mean square error of 9.08 to 20.81mg/kg. This statistical tool effectively shows the potential of the model to predict TPAH concentration in the biostimulation of spent engine oil-polluted soil using bitter leaf extract Conclusion: Up to 63.9% TPAH reduction was achieved for the stated period. The evaluation results show the potential of the model to predict TPAH in the biostimulation of SEO–contaminated sandy loam soil using bitter leaf extract.