A Field-Scale Model for Proppant Transport and Distribution in a Main–Branch Fracture System

Abstract

Proppant deposition changes the hydraulic resistance of connected fractures, while the resulting flow redistribution controls subsequent particle delivery. Resolving this feedback efficiently is important for evaluating field-scale proppant placement. This study develops an aperture-averaged model coupling suspended-particle transport, hindered settling, bed deposition and erosion, and junction flow partitioning. The downstream main fracture and branch fracture are represented as parallel hydraulic paths, with their resistances updated from the evolving mobile-flow region and slurry properties. Finite-volume transport and a nonlinear junction pressure balance provide the coupled solution. Comparisons with parallel-plate experiments and Fluent dense discrete phase model (DDPM) simulations reproduce the principal bed-height and placement-length trends. For the same 30 s benchmark, the wall-clock time decreases from 2847 s to 51.06 s, a reduction of 98.2%. A 150 m main fracture connected to a 50 m branch is then simulated for 1200 s. Increasing viscosity from 1 to 10 mPa·s lowers the maximum main-fracture bed height from approximately 8.9 to 1.4 m while extending placement. Increasing branch aperture from 3 to 7 mm raises the branch split ratio from 0.13 to 0.63 and shortens main-fracture placement from approximately 145 to 90 m. The results distinguish controls on particle delivery from controls on flow partitioning and provide a rapid basis for balancing main- and branch-fracture placement.