Prediction of Herschel–Bulkley Parameters for Water-Based Drilling Fluids Under Wide Temperature and Pressure Conditions Using Ambient-Condition Parameters

Accurate wellbore-pressure prediction is essential for safe drilling and pressure management in ultra-deep wells, where high temperature and pressure strongly alter drilling-fluid rheology. Existing rheological-parameter models are often calibrated for specific fluids and narrow temperature–pressure ranges, limiting their use in ultra-deep-well hydraulics. We measured three water-based drilling fluids at temperatures and pressures up to 210 °C and 206.5 MPa, compared seven rheological models, and developed a multidimensional evaluation method considering global fitting accuracy, extreme-condition performance, low-shear-rate representation, absolute shear-stress deviation, and model complexity. Using ambient-condition Herschel–Bulkley (H-B) parameters as baselines, we proposed a temperature–pressure (T-P)-coupled correction model requiring fluid-specific calibration to predict H-B parameters over the tested range. The fluids exhibited temperature-induced thinning, pressure-induced thickening, and shear-thinning behavior. The H-B model showed the best overall performance, with mean R2 values above 0.997 and mean absolute percentage errors below 2.5% for all fluids. Substituting the corrected parameters into the H-B equation yielded mean shear-stress errors no greater than 4.04%. Field validation showed that the T-P-coupled model reduced the mean circulating-pressure-loss error from 2.72% to 0.78%. This approach provides practical inputs for rheology estimation and circulating-pressure calculation in ultra-deep wells under wide temperature and pressure conditions.