Overflushing to displace the fracturing treatment away from the wellbore and into the fracture is common in multistage completions of horizontal wells in unconventional formations, but it can damage overall fracture performance by overly displacing proppant to leave the fracture unsupported or allowing gravity slumping to occur, again leaving unpropped area. A novel modeling approach was investigated to gain insight into the process and determine reliable bounds for overflushing.

From a fluid mechanics viewpoint, overflushing is displacement of a Hershel-Bulkley fluid by a power law fluid in a Hele-Shaw cell, leading to Saffman-Taylor instability at the fluids' interface. Most hydraulic fracturing simulators use power-law rheology. A novel numerical model accounting for the yield-stress behavior exhibited by proppant-laden slurries was developed using the lubrication approximation and includes transport equations for fluid volume fractions and a nonlinear elliptic equation for pressure with mixed-type boundary conditions. The pressure equation is solved with a fixed-point (Picard) iterations method, with the multigrid linear solver used at each iteration.

The model was validated against three sets of experiments in Hele-Shaw cells: gravitational slumping, displacement of Newtonian fluids with fingering, and displacement of a yield-stress fluid by a shear-thinning fluid, leading to formation of fractal fingering patterns. Good agreement is obtained. Based on fracture mechanics, we analyzed what portion of the fracture may be left unsupported before it is severely pinched during drawdown as a reliable bound for overflushing volumes. A parametric study was focused on the displacement of the yield-stress slurry by the overflushing fluid, varying overflush volume and rate and rheology contrast between slurry and displacing fluid. Qualitatively, when fingers of the overflushing fluid can be created at the overflush/slurry interface, large slurry pillars are preserved in the near-wellbore area, which may keep the fracture open; gravitational slumping is mitigated by the yield stress. Three scenarios occur, depending on slurry rheology: from slumping-dominated (low-viscosity base fluid in the slurry), through intermediate to a fingering-dominated scenario, where gravitational convection is suppressed by high viscosity of the slurry (~1 Pa s) and considerable yield stress (>1 Pa). The third scenario minimizes the geomechanical risks of overflushing by providing tiny fingers that are unlikely to be pinched out during fracture closure.

From the study, bounds for reliable overflushing are proposed, which are a lot more restrictive when the slurry base fluid does not exhibit a yield stress (e.g., for slickwater treating fluids).

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