During plug and perf completion, perforation pressure drop is used to encourage a uniform distribution of flow between clusters by overcoming stress shadowing, stress variability, and nonuniform breakdown pressure. However, proppant inertia, gravitational settling, and perforation erosion contribute to nonuniformity, even with an aggressive limited-entry design. In prior work, Dontsov (2023) developed a correlation for predicting proppant outflow from the wellbore as a function of slurry velocity, perforation phasing, and other parameters. In the present study, the Dontsov (2023) correlation is integrated into a wellbore dynamics simulator capturing key physical processes that control slurry and proppant outflow from the wellbore, such as erosion, stress shadowing, and near-wellbore tortuosity. The simulator is fast running and incorporated into a tool for Monte Carlo uncertainty quantification and design optimization. First, we run a series of sensitivity analysis simulations to evaluate the effect of key model inputs. The simulations demonstrate processes that can cause heel bias, toe bias, or heel/toe bias in the erosion distribution. Next, we apply the tool to analyze field datasets from the Eagle Ford and the Montney. Downhole imaging of erosion data enables model calibration. Calibration is necessary because differences in casing, cement, and formation properties cause differences in erosion behavior and flow distribution. Parameters controlling the magnitude of erosion and stress shadow are modified to match the trends observed from the downhole imaging. After calibration is performed, the model is applied to maximize the uniformity of proppant placement by optimizing perforation phasing, diameter, count, and cluster spacing.
