Development of a New Progressive Nonintrusive Theory to Reduce Computation Time with Particle-in-Fluid Flow Application

Abstract

Summary Solid-in-fluid flow studies and modeling approaches are categorized mainly based on the scale at which solid particles are modeled. Eulerian-Eulerian approaches treat solid at the same scale as fluid. These approaches are fast but suffer from improper physics and high dispersion effect due to averaging solid properties to upscale them to the fluid scale. Eulerian-Lagrangian methods try to solve the issue by modeling each particle individually. Modeling movement of each particle in fluid is complex, especially when modeling individual particle interaction with other particles and fluid is involved. Although such an approach is favorable due to its high accuracy in modeling solid behavior, it is computationally intensive and very time-consuming. It may take hours or even days to simulate a few seconds of a solid-in-fluid flow process when number of particles grows and goes beyond one thousand. In this paper, a theory is developed to reproduce and predict solid state variables such as location and velocity with a reasonable accuracy but at least four orders of magnitude faster. This solution uses the available information from previously finished simulations to build a progressive nonintrusive formulation based on the trajectory piecewise linearization (TPWL) theory that reproduces and predicts particles locations and velocities. Reproduction or prediction run accuracy is verified by comparing the results against a verification run and the reduction in computation time is also measured. The progressive nonintrusive formulation developed in this work is universal and is not limited to solid-in-fluid flow applications such as particle transport in wellbore or hydraulic fracture in petroleum engineering, and it can be applied to other engineering or science problems too.