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 and are often found to over-predict propped or effective fracture lengths by 100 to 300%. A common assumption is that the average proppant velocity due to flow is equal to the average carrier fluid velocity, while the settling velocity calculation uses Stokes’ law. To accurately determine the placement of proppant in a fracture, it is necessary to rigorously account for many effects not included in the above assumptions. In this study, the motion of particles flowing with a fluid between fracture walls has been simulated using a coupled CFD-DEM code that utilizes both particle dynamics and computational fluid dynamics calculations to rigorously account for both. These simulations determine individual particle trajectories as particle to particle and particle to wall collisions occur and include the effect of fluid flow and gravity. The results show that the proppant concentration and the ratio of proppant diameter to fracture width govern the relative velocity of proppant and fluid. Further, the dependencies of settling velocity on apparent fluid viscosity, proppant diameter and the density difference between the proppant and fluid predicted by Stokes’ law were found to apply. However, additional effects have been quantified and shown to substantially alter the predictions from Stokes’ law. Proppant concentration and slot flow Reynold’s number were both shown to modify the settling velocity predicted by Stokes’ law, as does the ratio of proppant diameter to slot width. The effect of leak-off was found to be negligible in terms of altering either the settling velocity or the relative velocity of proppant and fluid. The models developed from the direct numerical simulations have been incorporated into an existing fully 3-D hydraulic fracturing simulator. This simulator couples fracture geomechanics with fluid flow and proppant transport considerations to enable the fracture geometry and proppant distribution to be determined. Unlike all previous studies, these effects are included together and so are shown to be inter-dependent, allowing us for the first time to accurately model proppant transport. As noted above, proppant velocities have been accurately determined without simplifying approximations and with all relevant effects included, showing inter-dependence between the different effects. Two engineering fracture design parameters, injection rate and fluid rheology, have been varied to show the effect on proppant placement in a typical shale reservoir. This allows for an understanding of the relative importance of each and optimization of the treatment to a particular application.
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