Proppant transport in complex fracture networks
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Current hydraulic fracturing practice in unconventional resource development typically involves multiple fracturing stages, each consisting of the simultaneous creation of several fractures from a horizontal well. A large mass of proppant, often millions of pounds per well, is injected with the fluid to provide post-closure conductivity. Despite the large quantity of proppant used and its critical importance to well productivity, simple models are often applied to determine its placement in fractures. Propped or effective fracture lengths indicated by modeling may be 100 to 300% larger than the lengths inferred from production data. A common assumption is that the average proppant velocity due to pressure driven 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 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 computational fluid dynamics and discrete element method (CFD-DEM) that rigorously accounts for the both aspects of the problem. These simulations 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 proppant concentration and the ratio of proppant diameter to fracture width govern the relative velocity of proppant and fluid. Proppant settling velocity has been examined for small fracture widths to delineate the effect of several independent variables, including concentration. Simulations demonstrate that larger concentration increases the average settling velocity, in apparent contrast with much of the available literature, which indicates that increased concentration reduces settling velocity. However, this is due to the absence of displacement driven counter current fluid flow. This demonstrates that proppant settling in a hydraulic fracture is more complex than usually considered. 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 three-dimensional 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 rigorously. Two engineering fracture design parameters, injection rate and proppant diameter, have been varied to show the effect on proppant placement. This allows for an understanding of the relative importance of each and optimization of the treatment to a particular application. The presence of natural fractures in unconventional reservoirs can significantly contribute to well productivity. As proppant is transported along a hydraulic fracture, the presence of a dilated natural fracture forms a fluid accepting branch and may result in proppant entry. The proportion of proppant transported into a branch at steady state has been determined using the CFD-DEM approach and is presented via a dimensionless ‘particle transport coefficient’ through normalization by the proportion of fluid flowing into the branch. Reynolds number at the inlet, branch aperture and the angle of orientation between the main slot and branch, particle size and concentration each affect the transport coefficient. A very different physical process, which controls particle transport into a branch under certain conditions, is the formation of a stable particle bridge preventing subsequent particle transport into the branch. This phenomenon was observed in several simulation cases. The complete set of equations for a three-dimensional formulation of rectangular displacement discontinuity elements has been used to determine the width distribution of a hydraulic fracture and dilated natural fracture. The widths have been determined for several combinations of stress anisotropy, net pressure, hydraulic fracture height and length. The effect of the length, height and orientation of the natural fracture and the elastic moduli of the rock have also been examined. Of the cases examined, many show that natural fracture dilation does not occur. Further, of those cases where dilation is apparent, the proppant transport efficiency corresponding to the natural fracture width is significantly less than one and in many cases zero due to size exclusion. The location and orientation of the natural fracture do not significantly affect its width, while its length and the elastic moduli of the rock substantially change the width.