Omani crude pipelines skip per-case CFD: a surrogate returns heat, head and power loss in milliseconds
Synopsis
Omani crude oil flows non-isothermally as a viscoplastic fluid, and predicting its heat and head losses has meant running high-fidelity CFD case by case, too slowly for real-time decisions. A physics-informed surrogate trained on 962 COMSOL simulations, with a dimensionless Rheological Heat-Loss Index (RHLI) as an input feature, now predicts total heat loss, head loss and total power loss together. Under five-fold cross-validation heat loss was the most learnable target, with cross-validated R² near 1; uncertainty quantification gave a mean calibration error of 0.0211 and 97.4% empirical 95% coverage, and SHAP ranked ambient temperature as the dominant heat-loss driver.
Interpretation
A single surrogate now returns heat loss, head loss and total power loss for a crude oil pipeline at once, instead of re-solving the flow and heat equations for every operating case. The prior route relied on high-fidelity CFD such as COMSOL per case, which limits parametric sweeps and real-time operational decisions. Training data are 962 COMSOL simulations over three serially connected segments with diameters of 0.106 m, 0.1524 m and 0.2032 m, with the crude oil treated as a Bingham–Papanastasiou viscoplastic fluid.
Physical quantities are built directly into the inputs so that learning is organized around rheological and heat-transfer relationships. Alongside Reynolds number, Bingham number and a Thermo-Hydraulic Ratio, the work constructs the dimensionless Rheological Heat-Loss Index RHLI, the ratio of viscous dissipation to yield-stress dissipation within a segment. Under five-fold cross-validation, tree ensembles reached cross-validated R² near 1 for heat loss and the Stacking Ensemble was the most stable across all three targets; quantile regression, conformal prediction and calibration gave a mean calibration error of 0.0211 and 97.4% empirical 95% coverage.
The model's importance ranking agrees with heat-transfer physics, with ambient temperature identified as the leading driver of heat loss. In the SHAP analysis ambient temperature contributes substantially more than mean temperature and the per-segment average temperatures. The ranking comes from SHAP feature importance and beeswarm plots for the best-performing heat-loss model, consistent with the oil-to-ambient temperature gradient governing heat dissipation.
Perspective
The conclusions rest on COMSOL simulation data for three serially connected AISI 1020 steel segments carrying Bingham–Papanastasiou viscoplastic crude oil, and do not yet include field-scale measurements; the authors propose incorporating real pipeline operational data for external validation and restricting the predictor set to design-stage inputs so the surrogate can be deployed without further CFD evaluation.
The authors state the model was trained for a specific three-segment configuration and rheological formulation, and may need retraining for other rheologies or pipeline topologies; heat-loss data cluster around plateaus near 500 W, 610 W and 725 W, and pinball loss at the extreme quantiles is markedly higher than at the median.