Neural Network-Based Prediction Model for High Temperature and High Pressure Rheological Parameters of Water-Based Drilling Fluids

The rheological behavior of drilling fluids under HTHP conditions is critical for ensuring drilling safety and performing reliable wellbore hydraulic calculations. However, many traditional prediction methods require the prior selection of a constitutive model and the fitting of intermediate rheological parameters, and may fail to clearly characterize the nonlinear effects of temperature and pressure at different shear rates. In this study, a HTHP rheometer was used to investigate the shear-stress response of a fixed-formulation WBDF over temperature and pressure ranges of 50–220 °C and 50–200 MPa, respectively, at six shear rates ranging from 5.11 to 1021.38 s−1. At constant pressure, shear stress generally decreased with increasing temperature and tended to stabilize or increase slightly in the medium-to-high temperature range. At constant temperature, shear stress increased with increasing pressure at all six shear rates. At high shear rates, the effect of pressure was mainly reflected by an overall increase in shear stress, whereas at low shear rates the pressure effect became more pronounced at elevated temperatures. A KART-NN model inspired by the Kolmogorov–Arnold representation theorem was developed using temperature and pressure as input variables and shear stress as the output variable. Separate models were established for the six shear rates and quantitatively compared with MLP and SVR-RBF using identical training and random hold-out test samples. On the random hold-out test subset, KART-NN achieved a mean RMSE of 0.00814 Pa, a mean MAE of 0.00342 Pa, and a mean R2 of 0.99990. KART-NN achieved the lowest RMSE at five of the six shear rates and the lowest MAE at all six shear rates. Additional grouped validation using completely held-out temperature and pressure conditions yielded mean pooled R2 values of 0.9857 and 0.9937, respectively, providing a more conservative assessment of model generalization. The proposed framework directly maps temperature and pressure to shear stress without requiring intermediate constitutive-parameter fitting and can provide rheological inputs for wellbore hydraulic calculations within the investigated formulation and HTHP domain.