SW-RheoPINN: Physics-Informed In-Line Estimation of Pipe-Effective Yield Stress from Pressure–Flow Measurements

Reliable in-line estimation of slurry rheology could improve the safety and control of pipeline-transfer operations, particularly in radioactive-waste processing where frequent manual sampling is undesirable. This study presents SW-RheoPINN, a physics-informed inverse pipe-rheometry framework for estimating pipe-effective yield stress and plastic viscosity from short windows of pressure-drop, mass-flow-rate, density, and pipe-geometry measurements. The framework combines a permutation-invariant sensor-window encoder with an analytical Bingham pipe-flow backbone, radial momentum balance, a regularized constitutive relation, cross-sectional mass conservation, and a tightly bounded velocity-profile correction for limited model discrepancy. SW-RheoPINN was evaluated using 20 two-state kaolin–water flow-loop experiments comprising 40 hydraulic states. In matched-physics synthetic tests with 2% multiplicative mass-flow noise, yield-stress recovery improved from R2=0.787 for two-state windows to R2=0.923 and R2=0.955 for three- and four-state windows, respectively; plastic-viscosity recovery improved from R2=0.937 to R2=0.967 and R2=0.961. For the experimental data, complete sensor-window reconstruction achieved a MAPE of 0.80% and R2=0.990. Because measured mass flow is an encoder input in this reconstruction, these metrics characterize inverse self-consistency rather than prospective prediction. A separate target-flow-withheld evaluation, in which the withheld mass flow was not supplied to the inverse model, achieved an RMSE of 0.108 kg.s-1, R2=0.790, and a median absolute percentage error of 3.55%. Prediction was strongest for compositions with repeatable hydraulic behavior and degraded when nominally similar experiments occupied distinct response states. Ablation and sensitivity analyses showed that strongly resolved high-yield conditions were largely insensitive to composition-related regularization, Papanastasiou sharpness, and correction capacity, whereas low-yield estimates were more model dependent. Misspecified-physics tests further showed that small hydraulic residuals do not necessarily imply unbiased rheological parameters. The inferred pipe-effective yield stresses retained the broad composition-dependent trend observed by offline rheometry, although absolute cross-scale agreement was limited. These results support SW-RheoPINN as a physics-constrained inference and diagnostic framework for identifying both well-supported and weakly resolved rheological states from standard process measurements.