A Geostatistical Heterogeneity Metric for Spatial Feature Engineering

Abstract

AbstractHeterogeneity is a vital spatial feature for subsurface resource recovery predictions, such as mining grade tonnage functions, hydrocarbon recovery factor, and water aquifer draw-down predictions. Feature engineering presents the opportunity to integrate heterogeneity information, but traditional heterogeneity engineered features like Dykstra-Parsons and Lorenz coefficients ignore the spatial context; therefore, are not sufficient to quantify the heterogeneity over multiple scales of spatial intervals to inform predictive machine learning models. We propose a novel use of dispersion variance as a spatial-engineered feature that accounts for heterogeneity within the spatial context, including spatial continuity and sample data and model volume support size to improve predictive machine-learning-based models, e.g., for pre-drill prediction and uncertainty quantification. Dispersion variance is a generalized form of variance that accounts for volume support size and can be calculated from the semivariogram-based spatial continuity model. We demonstrate dispersion variance as a useful predictor feature for the case of hydrocarbon recovery prediction, with the ability to quantify the spatial variation over the support size of the production well drainage radius, given the spatial continuity from the variogram and trajectory of the well. We include a synthetic example based on geostatistical models and flow simulation to show the sensitivity of dispersion variance to production. Then we demonstrate the dispersion variance as an informative predictor feature for production forecasting with a field case study in the Duvernay formation.