Modeling of solids particle diversion to promote uniform growth of multiple hydraulic fractures

Solid particulate additives are sometimes used to promote the uniform growth of multiple hydraulic fractures in horizontal oil and gas wells. The principle is that solid particulates block, accumulate, and form larger porous plugging zones preferentially at entrances of fracture taking in the most fluid volume. These porous zones create fluid flow resistance or additional pressure loss; thereby, inhibiting the growth of these dominant fractures and diverting fluid to suppressed fractures. While this technology is promising, governing design parameters and ramifications of placing solids diverters inside the fracture remain unclear. This paper models the propagation of multi-fractures with diverter pressure losses induced by the porous plugging zones. The resulting non-linear hydraulic fracturing problem is solved numerically with an Implicit Level Set Algorithm (ILSA) for each time step and the mechanisms of diversion are illustrated by comparing and contrasting cases with and without particle diverter. In both cases, during the fluid ramp-up period (pumping rate gradually increases from 0 to fracturing rate ($Q_T$)), the injection can be equally distributed among fractures before the stress interference affects the fluid allocation (Phase I). Then, stress interference starts to partition more fluid into outer fractures and suppress the growth of the middle fracture (Phase II). Once the perforation friction loss is sufficient to counteract the stress interaction, injection begins to shift to the middle fracture, but still gives a significantly non-uniform fracture growth (Phase III). At this point, solid diverter particles are introduced, leading to three additional phases of growth. Phase IV introduces solid diverters to the treatment at a reduced pumping rate. Particles bridge, accumulate and create porous plugging zones at the flow entrance. A higher pressure drop in outer fractures diverts injection fluids to the middle fracture. Phase V resumes the treatment rate to $Q_T$ without diverter. The increased pump rate in turn increases the pressure drop in outer fractures and diverts more fluids to the middle fracture. This results in a rapid extension velocity for the middle fracture, enabling it to have the chance to catch up with the longer outer fractures (in Phase VI). This process is controlled by the interplay among stress interference, perforation friction loss, and diverting pressure drop. These simulations demonstrate that a model-based optimization could improve the effectiveness of the diverter technology and promote a uniform multi-fracture growth.