Nonintrusive Reduced Order Modeling of Particle in Fluid Flow – Proppant Transport

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Understanding proppant flow and its distribution in a hydraulic fracture is essential to determine the well conductivity and productivity. Proppant transport in a hydraulic fracture is an example of the broader topic of solid-in-fluid flow. Among existing modeling approaches, the Eulerian – Lagrangian method which models fluid in meso scale using Computational Fluid Dynamic (CFD) schemes and solid particles in micro scale using Discrete Element Methods (DEM) is the most accurate approach to determine the location and velocity of particles. But since this method models solid particles individually, it is impossible to simulate a field scale proppant transport problem with the present computation facilities. In addition to the number of particles, the very small time step size required to capture all collisions among particles and calculate collision forces is another factor that makes this type of simulation computationally intensive. Therefore, a solution that reduces the computation time while maintaining the accuracy of the results is highly desired. In this research, a novel progressive nonintrusive will be developed to substitute the complex governing equations with approximating functions. These radial basis approximating functions are generated based on the snapshot data collected from available simulations for different sets of input variables. This progressive nonintrusive approach not only can reproduce the available runs with a very high accuracy, but also can predict the particles behaviour for a new set of input variables. Using such a nonintrusive approach reduces the run time at least two to three orders of magnitude. The model order reduction is used to reduce the computation time furthermore. Proper Orthogonal Decomposition (POD) method, which works with snapshots data as well, is used to find and size a reduced space that the full order nonintrusive model is projected into it. The dimensionality gain decreases the required calculations, and the resulted reduced variables are transformed back to the full space. Comparing the results with the CFD – DEM approach exact solution shows that the developed nonintrusive reduced order model for particle-in-fluid flow can reduce the computation time several orders of magnitude with acceptable accuracy in estimating particles locations and velocities.

Nonintrusive, reduced order modeling, proppant, particle, radial basis function, hydraulic fracture