The effective placement of proppant in a fracture has a dominant effect on well productivity. Existing hydraulic-fracture models simplify proppant-transport calculations to varying degrees. A common assumption applied is that the average proppant velocity caused by flow is equal to the average carrier-fluid velocity, while the settling-velocity calculation uses Stokes’ law. To more accurately determine the placement of proppant in a fracture, it is necessary to account for many effects not included in previous assumptions.

In this study, the motion of particles flowing with a fluid between fracture walls is simulated with a coupled computational-fluid-dynamics/discrete-element method (CFD/DEM) code that uses both particle dynamics and CFD calculations to account for both particles and fluid. These simulations (presented in metric units) determine individual particle trajectories as particle-to-particle and particle-to-wall collisions occur, and include the effect of fluid flow. The results show that the ratio of proppant diameter to fracture width governs the relative average velocity of proppant and fluid.

A proppant-transport model developed from the results of the direct numerical simulations and existing correlations for particle-settling velocity has been incorporated into a fully 3D hydraulic-fracturing simulator. This simulator couples fracture geomechanics with fluid-flow and proppant-transport considerations to enable the fracture geometry and proppant distribution in the main hydraulic fracture to be determined. For two typical shale-reservoir cases, the proppant placement and width distribution have been determined, allowing comparison at the hydraulic-fracture scale, including effects observed at the particle scale. This allows for optimization of the treatment to a specific application, and the results are presented in oilfield units, considered more familiar to our readers.