Geospatial Prediction of Geochemical Properties of Produced Water Samples: Application of Dual Kriging-Gradient Boosting Method

Abstract The geochemical assessment of produced water has a practical impact for operational decisions in oil and gas reservoir management. As a general practice, kriging and other geo-statistical interpolation methods are deployed to estimate values at unsampled location away from well control. A key disadvantage of spatial Gaussian process models (e.g., kriging) is their assumption of a linear relationship between response variable (water salinity) and the predictor variables (such as elemental concentration of Na, Cl, Ca, HCO3, SO4). Resulting predictions for spatial data analysis are discontinuous over space, and machine-learning (ML) algorithms tend to ignore geo-spatially coherent structure of input data. In order to overcome the limitation of Gaussian process models, kriging and gradient tree boosting algorithms were combined as a novel practical solution to ensure an optimum predictability of spatial and temporal geochemical variations. As a proof of concept, a historical geochemical dataset of produced water from national exploration and production areas was recovered from the USGS National Geochemical Database with an extended collection of measured values of chemical-physical parameters (TDS, density, pH), and elemental concentrations (Na, Ca, K, Mg, Ba, Sr, Cl, HCO3 and SO4). The USGS dataset was utilized to choose an appropriate "target" variable (such as TDS) and use remaining predictor variables as "features" which constitutes the input for supervised ML framework used. A detailed exploratory statistical data analysis for input features was performed using correlation matrix, analysis of probability distribution and quantile-quantile plots (Q-Q plot). Geochemical data analytics with Piper and Gaillardet end-member diagrams provided an automated characterization of recovered fluids for given stratigraphic formations. The application of coupled gradient-boosting and universal kriging methods improved the prediction for target variables that deviated from the assumed normal distribution (Gaussian assumption). This method will overcome inherent limitations of kriging method associated with non-Gaussian predictive variables, especially at unsampled locations. The proposed numerical technique represents a generalized geo-statistical tool to predict different geochemical parameters in the reservoir ahead of the drill bit.