ABSTRACT
Knowledge of the minimum horizontal principal stress (Shmin) is essential for geo-energy utilization. Shmin direct measurements are costly, involve high-risk operations, and provide only discrete values of the required quantity. Other methods were developed to interpret a continuous stress sequence from sonic logs. These methods usually require some ‘horizontal tectonic stress’ correction for calibration and rarely match sections characterized by stress profiling due to viscoelastic stress relaxation. Recently, several studies have tried to predict the stress profile by an empirical correlation corresponding to an average strain rate through geologic time or by using machine learning technologies. Here, we used the Bayesian Physics-Based Machine Learning framework to identify the relationships among the viscoelastic parameter distributions and to quantify statistical uncertainty. More specifically, we used well logs data and ISIP measurements to quantify the uncertainty of the viscoelastic-dependent stress profile model. Our results show that the linear regression approach suffers from higher uncertainty, and the Gaussian process regression Shmin prediction shows a relatively smaller uncertainty distribution. Extracting the lithology logs from the prediction model improves each method's uncertainty distribution. We show that the density and the porosity logs have a superior correlation to the viscoplastic stress relaxation behavior.
INTRODUCTION
Comprehensive recognition of the least principal stress is essential for economic multistage hydraulic fracturing stimulation design. It is well established that hydraulic fractures propagate perpendicular to the least principal stress and that the stress profile prominent the hydraulic fractures generation in both the lateral and horizontal direction (Fisher et al., 2012; Hubbert and Willis, 1957; Kohli et al., 2022; Valkó and Economides, 1995; Zoback et al., 2022)c. In other words, the stress layering could act as a ‘frac barrier’ that limits fracture development in discrete directions and promotes progress in different directions (Singh et al., 2019). Detailed knowledge of the least principal stress profile is significant for hydraulic fracture growth assessment, proppants technology optimization, and efficient landing zone detection (Pudugramam et al., 2022). Traditionally, these considerations were aligned with the oil and gas industry. Still, today, they have substantial implications for enhanced geothermal system development, carbon storage integrity, and in a broader sense, a safe path for a carbon neutrality economy.