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.

Upper-loss and lower-kick (UL–LK) events may occur in ultra-deep fractured carbonate formations when gas enters from a lower high-pressure zone while drilling fluid is lost to an upper low-pressure fracture. Because both flows can continue after shut-in, the wellbore remains incompletely closed. This study develops a transient wellbore-formation pressure model based on phase mass conservation and global volume balance, and introduces an effective gas–liquid partition coefficient to represent phase separation at the fracture inlet. The model shows that circulation loss limits bottomhole-pressure recovery, allowing gas influx to persist after shut-in. Relative to kick-only conditions, UL–LK conditions have a lower initial shut-in casing pressure (SICP) but a steeper subsequent buildup. A smaller partition coefficient, corresponding to preferential liquid loss, leaves more free gas in the wellbore and further increases the SICP buildup rate. A surface-pressure-based screening method was developed from contrasting SICP and shut-in drillpipe pressure (SIDPP) responses. When applied to five field cases, the method correctly identified three UL–LK cases and two kick-only cases. Its outcomes for five field cases agreed with the field interpretations. This framework supports post-shut-in pressure prediction and rapid screening without dedicated downhole measurements.