Non-Newtonian fluid flow dynamics in rotating annular media: Physics-based and data-driven modeling

A thorough understanding and accurate prediction of non-Newtonian fluid flow dynamics in rotating annular media are of paramount importance to numerous engineering applications. This is in particular relevant to oil and gas industry where this type of flow could occur during, e.g., drilling, well completion, and enhanced oil recovery scenarios. Here, mathematically we report on physical-based (numerical) and data-driven (intelligent) modeling of three-dimensional laminar flow of non-Newtonian fluids driven by axial pressure gradient in annular media that consist of a coaxially rotating inner cylinder. We focus on the dynamics of pressure loss ratio (PLR)—the ratio of total pressure loss in presence of rotation to that in stationary condition. We develop a novel and computationally efficient machine-learning based predictive model based on a Least Square Support Vector Machine (LSSVM) optimized with a Coupled Simulated Annealing (CSA) algorithm, which is trained and tested by 730 experimental data collected for this study. We then perform numerous CFD simulations governed by Navier-Stokes set of equations, which correspond to each of the experimental cases. Comparing the results with those obtained from a widely used empirical correlation for PLR, we find that the both of our numerical and machine-learning based models are more accurate and present a larger applicability domain. The predictive LSSVM model enjoys a supervised learning paradigm and leads to the highest accuracy, while the physically originated CFD approach captures more consistently the nonlinear behavior of PLR versus key system features. Following the validation of our models, we study the less understood effects of fluid viscosity, axial velocity and rotational velocity on PLR dynamics. We employ a dimensionless parameter analogous to Strouhal number and identify specific regimes where PLR shows a distinct behavior. Our study elucidates the role of shear-thinning effect and its interplay with inertial forces on the dynamical behavior of pressure loss (ratio) in rotating yield-power-law fluids.