Physics-Guided Deep Neural Network to Characterize Non-Newtonian Fluid Flow for Optimal Use of Energy Resources

Numerical simulations of non-Newtonian fluids are indispensable for optimization and monitoring of several industrial processes such as crude oil transportation, nuclear cooling, geothermal and fossil fuel production. The governing equations derived for non-Newtonian fluid models result in nonlinear differential equations. Thus, increasing the complexity even for simple geometries. The cumbersome numerical computation and rudimentary empirical solutions hinder faster analysis over a wide range of parameters. However, machine and deep learning methods have higher accuracy but rely heavily on the quality and amount of training data, and the solution may become inconclusive if data is sparse. In this research, a novel algorithm (Herschel Bulkley Network) is introduced to simulate the non-Newtonian fluid flow in a pipe using data redundant deep neural network (DNN) for fully developed, laminar, and incompressible flow conditions. The objective of this investigation is to develop a physics dominated DNN solely driven by minimizing residuals from the Navier-Stokes based governing equations, establishing benchmark research. Herschel-Bulkley model is used to approximate the complex rheological behavior of a non-Newtonian fluid. The proposed DNN algorithm is structured to incorporate initial/boundary conditions in cylindrical coordinates and approximate the solution without the aid of any simulated or training data. The simulated results and analysis demonstrate an excellent agreement between the proposed algorithm and non-Newtonian fluids flow attributes. The detailed parametric analysis exhibits the competency of the proposed algorithm to explain the rheological features. Monte-Carlo simulation is performed by propagating uncertainty to investigate the dominant parameters affecting simulated results. The uncertainty in fluid consistency index is responsible for higher variance in the calculated flow rate, while the least variation is observed due to fluid behavior index uncertainty. The performance of the algorithm is validated with experimental datasets. The statistical error estimation exhibits a mean absolute error of 11.5%, and root mean squared error of 0.87. A comprehensive analysis on training unsupervised DNN and adjusted hyperparameters is also highlighted to achieve expedite convergence.