An Improved Ball Sealer Model for Well Stimulation

Abstract

Abstract Ball sealers are commonly applied in fracturing and acidizing treatments for diverting treatment fluid to the desired zones by plugging perforations. It has proven that injecting ball sealers is a low-cost and efficient method for diversion. To predict the effectiveness of ball sealers, an improved ball sealer seating model is developed by introducing the maximum seating efficiency and random functions to capture the stochastic nature of ball-sealer plugging. The new model can predict ball sealer performance with different ball densities in vertical, deviated and horizontal wells. The traditional ball sealer model was originally designed for vertical wells, where ball sealers with different densities have similar behavior. However, for deviated and horizontal wells, the seating of buoyant and dense balls is more complicated. Buoyant balls tend to plug the perforations at the top of wellbore, and dense balls tend to plug the perforations at the bottom of wellbore. Thus, the traditional ball sealer model cannot be applied in these wells. A maximum seating efficiency for each ball is introduced in the new model, which is obtained by correlations based on experimental results. To describe the stochastic nature of ball sealer seating on perforations, a random number is assigned to each ball sealer, and a range is assigned to each perforation based on the ratio between flow rates through the perforations and flow rate in the wellbore. With the improved model, it can predict seating efficiency of ball sealers for all types of well with buoyant, neutral and dense balls. The results are showing that the seating efficiency of ball sealers predicted by the model can match the experimental results, which validates the model. Based on the simulation results, when ball sealers with mixed densities are pumped into deviated or horizontal wells, the seating efficiency is better than pumping ball sealers with only one density. For vertical wells, the benefit of mixing densities is minimal.