Prediction of In Situ Stress in Ultra-Deep Carbonate Reservoirs Along Fault Zone 6 of the Shunbei Ordovician System Based on a Two-Parameter Coupling Model with Nonlinear Perturbations

The Ordovician No. 6 fault zone reservoir in the Shunbei Oilfield exhibits ultra-deep-burial, high-pressure, and high-temperature conditions. Its pronounced tectonic control and significant heterogeneity render traditional in situ stress prediction methods—based on linear elasticity and anisotropy assumptions—inadequate for accurately characterizing the evolution and uncertainty of carbonate reservoir stiffness. Therefore, quantitatively predicting the development patterns and distribution characteristics of the Shunbei No. 6 structural fault zone is crucial for the exploration and development of Ordovician carbonate reservoirs in the Shunbei region. This study integrates wave impedance inversion with high-confining-pressure PFC particle flow biaxial test results to establish a constitutive calibration system consistent with seismic and experimental data. It introduces a nonlinear weakening function incorporating higher-order derivative constraints to fuse structural fracture and effective stress weakening effects, enabling dynamic correction of elastic parameters. This approach establishes a novel in situ stress prediction model. Simulation results indicate a predicted range for maximum horizontal principal stress between 201 and 261 MPa, with minimum horizontal principal stress ranging from 124 to 173 MPa. Predicted stress values for three key wells exhibit measurement errors within 6.92% compared to actual logging data, displaying a zoned spatial distribution consistent with regional tectonic stress evolution patterns. Simultaneously, sensitivity analysis reveals that the Young’s modulus fitting accuracy improved from 0.89 to 0.95, with a 43% reduction in mean square error, with the proportion of outliers reduced to below 1%. This significantly enhances response continuity and numerical stability in high-gradient disturbance zones and stiffness drop regions. The new model explicitly incorporates the nonlinear coupling between fracture geometry and pore pressure disturbance into the parameter field, eliminating systematic bias along fracture zones. Higher-order derivative constraints suppress numerical oscillations in high-gradient areas, stabilizing variance and preventing anomaly propagation. Residual distributions exhibit enhanced symmetry and reduced spatial autocorrelation, effectively suppressing numerical oscillations and divergence in complex fracture zones while significantly improving stress prediction accuracy for the study area. Overall, this research provides novel methodologies for predicting in situ stresses in ultra-deep carbonate reservoirs, offering engineering guidance and parameterization references for scheme deployment in complex fractured karst systems.