A Large-Scale Experiment-Based Perforation Erosion Evolution Model and Its Field Application

Summary During multicluster hydraulic fracturing in horizontal wells, the erosion of perforations by proppant-laden slurry dynamically alters the perforation diameter d and discharge coefficient Cd, causing a continuous decline in perforation friction and severely compromising the effectiveness of limited-entry fracturing design. Existing erosion models are mostly derived from small-scale laboratory experiments and cannot faithfully represent the high pump rate, high injection pressure, and large proppant volume conditions encountered in modern completion operations. To address this limitation, a field-scale perforation erosion evaluation system was independently constructed in this study, and a series of systematic erosion experiments covering varying pump rates, proppant concentrations, fracturing fluid viscosities, and proppant types/mesh sizes were conducted using casing used in actual fracturing operations. Based on the measured pressure drop data, the diameter erosion coefficient α and the roundness erosion coefficient β were back-calculated. A bidirectional stepwise regression algorithm was then introduced to establish empirical correlations between the erosion coefficients and key engineering design parameters, thereby eliminating the need for costly iterative experiments for each specific fracturing treatment. Furthermore, by coupling the wellbore pressure balance and mass conservation equations, a dynamic evolution model incorporating multicluster and multiperforation flow competition and nonuniform erosion was developed. Evaluation against the continuous-pumping experiments (Experiments 8–10) yielded final-perforation-diameter errors of 1.31–2.45% and perforation-friction-pressure errors of 1.41–3.37%. Compared with the static d and Cd model, the proposed model reduced the average pressure-prediction error from 54.25% to 2.48%. For Experiment 6, the proposed model reduced the final-diameter and pressure-prediction errors from 7.66% to 2.41% and from 14.79% to 2.93%, respectively, relative to the fixed erosion coefficient model. These reductions indicate that dynamically predicting the erosion coefficients can significantly enhance the predictive accuracy for perforation parameters and perforation friction. Using downhole camera data from two horizontal wells in the Mahu conglomerate reservoir, the model reproduced the overall distributions of post-treatment perforation diameters, with mean relative errors of 7.54% and 7.42%, respectively. The integrated workflow established in this study provides a low-cost, high-accuracy engineering tool for predicting perforation friction evolution and optimizing extreme limited-entry fracturing design parameters.