Construction and Application of a Quantitative Perforation Erosion Model Based on Field Experiments

Perforation erosion is one of the critical factors influencing the effectiveness of hydraulic fracturing and the productivity of oil and gas wells. This study developed a mathematical model for perforation erosion based on the field experimental data and theoretical analysis. This model comprehensively considers the effects of the rate of change in perforation diameter and the flow coefficient. Through field experiments, the values of the perforation diameter correlation coefficient (α) and the flow coefficient correlation coefficient (β) were determined. The wear behavior of perforations under high-pressure sand-carrying fluid conditions was thoroughly investigated, and the primary factors influencing perforation erosion were systematically analyzed. The results indicate that perforation erosion under high-pressure sand-carrying fluid conditions undergoes two distinct stages: the roundness erosion stage, characterized by a sharp pressure drop (greater than 30%) and the diameter erosion stage, marked by a gradual pressure decline (less than 5%), ultimately forming a trumpet-shaped perforation channel. The study further revealed that larger proppants cause significantly severe erosion than smaller proppants, resulting in 18.19% greater perforation diameter enlargement. In comparison tests, ceramic proppants produced 16.87% more diameter expansion than quartz sand under identical erosion conditions. Innovatively, this study proposes a "limited entry and temporary plugging" synergistic composite process. The timing of temporary plugging and the selection criteria for diverter size were clarified and optimized by determining the critical perforation friction for limited-entry failure based on inter-cluster stress differences. Field applications demonstrate that the optimized approach reduces erosion rates by 35-50%, improves fracture uniformity to over 80%, and increases single-well productivity by 18-25%. This research provides a quantitative basis and practical guidance for optimizing fracturing operation parameters, offering significant insights for enhancing the efficiency and productivity of hydraulic fracturing in oil and gas wells.