Predicting variations of the least principal stress with depth: Application to unconventional oil and gas reservoirs using a log-based viscoelastic stress relaxation model

Knowledge of layer-to-layer variations of the least principal stress S-hmin with depth is essential for optimization of multistage hydraulic fracturing in unconventional reservoirs. Using a geomechanical model based on viscoelastic stress relaxation in relatively clay-rich rocks, we have developed a new method for predicting continuous S-hmin variations with depth. The method uses geophysical log data and S-hmin measurements from routine diagnostic fracture injection tests (DFITs) at several depths for calibration. We consider a case study in the Wolfcamp Formation in the Midland Basin, where geophysical logs and values of S-hmin from DFITs are available. We compute a continuous stress profile as a function of the well logs that fits all of the DFITs well. We use several machine-learning technologies, such as bootstrap aggregation (or bagging), to improve the generalization of the model and demonstrate that the excellent fit between predicted and observed stress values is not the result of over-fitting the calibration points. The model is then validated by accurately predicting hold-out stress measurements from four wells within the study area and, without recalibration, accurately predicting stress as a function of depth in an offset pad approximately 6 mi from the study area.