A Novel Predictive Model for Drilling Fluid Rheological Parameters Across Wide Temperature–Pressure Ranges Using Symbolic Regression Algorithm

Accurate prediction of drilling fluid rheological parameters under high-temperature and high-pressure (HTHP) conditions is critical for reliable drilling hydraulics and wellbore pressure control in deep and ultra-deep wells. However, most existing empirical and semi-empirical rheological models are developed for limited temperature–pressure ranges and specific fluid formulations, which restrict their applicability and accuracy under HTHP conditions. In this study, systematic rheological experiments were conducted on multiple drilling fluid systems over wide temperature–pressure ranges (20–200 °C and 0.1–200 MPa). Based on the experimental data, a unified predictive model for key rheological parameters was developed using a symbolic regression (SR) algorithm. The model performance was evaluated using standard statistical metrics and compared with commonly used conventional models. Compared with conventional models, the proposed model shows stronger applicability for predicting the rheological parameters of the investigated oil-based and water-based drilling fluids over a wider temperature–pressure range. It effectively overcomes the limitations of existing models under HTHP conditions (150–200 °C and 80–200 MPa) and demonstrates improved prediction accuracy and robustness for both high- and low-density drilling fluids. The overall prediction errors are generally within approximately 10%. The results indicate that the proposed unified model provides a reliable and computationally efficient tool for predicting drilling fluid rheological parameters under HTHP conditions, facilitating its integration into wellbore hydraulics, wellbore pressure, and equivalent circulating density calculations in deep and ultra-deep well applications.