Multivariate Statistical Modelling of Water Quality Interdependencies in Produced Water from a Crude Oil Flow Station

To accurately predict the quality of wastewater generated by crude oil exploration activities, statistical models that capture multivariate interactions among co-varying parameters are required. Biochemical Oxygen Demand (BOD), Chemical Oxygen Demand (COD), Dissolved Oxygen (DO), Temperature, pH, and Conductivity of weekly produced water (260 readings over 5 years) from an oil flow station in Akwa Ibom State, Nigeria, were modelled using Pearson correlation, Principal Component Analysis (PCA) with Varimax rotation, Hierarchical Agglomerative Cluster Analysis (HACA), Multiple Linear Regression (MLR), and Vector Autoregression (VAR). Three components explained 74.3% of total parameter variance: the Organic Load Component (PC1, 36.3%), the Oxygen-Thermal Component (PC2, 23.2%), and the Ionic-pH Component (PC3, 14.8%). BOD and COD showed strong positive correlation (r = 0.72, p < 0.001), as did DO and Temperature (r = −0.61, p < 0.001). MLR models yielded R2 values of 0.71 (COD predicted from BOD and DO; out-of-sample RMSE = 20.4 mg/L) and 0.58 (DO predicted from Temperature and BOD; out-of-sample RMSE = 0.51 mg/L). VAR analysis identified BOD as a Granger-precedent predictor of COD at a two-week lag (F = 8.34, p = 0.003), and Temperature as a Granger-precedent predictor of DO (F = 11.62, p < 0.001). These results reflect predictive associations in the time series and do not imply physical causation. Cluster analysis delineated three quality regimes; none met Department of Petroleum Resources (DPR) discharge limits for BOD or DO, confirming systemic non-compliance at the study site. The models generated offer a basis for rapid characterisation of effluent quality and process control at Niger Delta flow stations.