Fitting steady-state and transient models of the temperature and shear-rate-dependent rheology of waxy oils using symbolic regression and physics-informed neural networks

Reliable flow-assurance prediction for waxy crude oils requires constitutive models valid over offshore shear and temperature histories, where cooling drives crystallization, gelation, and history-dependent rheology. We critically evaluate three constitutive models using two model waxy oils, a paraffin-in-mineral-oil system, SIGMA, and Clarus-L, at 10 and 20 wt. % and final temperatures of 5–35 °C. Differential scanning calorimetry provides the crystalline wax volume fraction ϕ(T) as temperature-dependent input. For steady-state behavior, we compare the suspension of fractal aggregates (SoFA) model, a six-coefficient Python symbolic regression (PySR) expression, and a reduced eight-parameter fractal isotropic kinematic hardening (FIKH) model; full FIKH is fitted to transient data using physics-informed neural networks. SoFA reproduces monotonic flow-curve regions through temperature-specific fits but inconsistently captures the lowest-shear plateaus, particularly for Clarus-L. The PySR form was selected using SIGMA 10 wt. % intermediate-temperature validation data and then refitted per system. Both PySR and reduced-FIKH interpolate between end point calibration temperatures using ϕ(T). At a cooling shear rate of 500 s−1, transient-FIKH reproduces the 5 °C training trajectory, but agreement deteriorates upon transfer of these fitted parameters to predictions at higher temperatures. A single parameter set jointly calibrated to 500 and 100 s−1 histories increasingly underpredicts held-out 50 and 1 s−1 histories. Thus, PySR and reduced-FIKH interpolate steady-state response within calibrated temperature ranges, whereas transient-FIKH transfer across temperature and shear histories remains limited. These limitations show the need for models with richer wax-network descriptions; improved coupling among crystallization, shear history, and stress; multitimescale or state-dependent kinetics; and pipeline-relevant calibration.