Uniformity of proppant distribution among multiple perforation clusters affects treatment efficiency in multistage fractured wells stimulated using the plug-and-perf technique. Multiple physical phenomena taking place in the well and perforation tunnels can cause uneven proppant distribution among multiple clusters. The problem has been studied in the recent years with experimental and computational fluid dynamics (CFD) methods, which provide useful insights but are impractical for routine designs. Simplified models that incorporated the proppant transport efficiency (PTE) correlation derived from the CFD results in a hydraulic fracture model have been also presented in literature. In this paper, we present a numerical model that simulates the transient proppant slurry flow in the wellbore, considering proppant transport and settling including bed formation, rate- and concentration-dependent pressure drop, PTE, and dynamic pressure coupling with the hydraulic fractures. The model is efficient and is designed to be an independent wellbore transport model so it can be integrated with any fracture models, including fully 3D and/or complex fracture network models, for practical design optimization. The model predictions are compared and found to agree with previously published studies. Parametric studies demonstrate sensitivity of proppant distribution to grain size, fluid viscosity, and pumping rate for fixed perforation designs. Analysis of the simulation results shows that the dominant cause of uneven proppant distribution is proppant inertia. Possible slurry stratification is less important, except for the cases with relatively low flow rates and near toe clusters. Accordingly, proppant distribution is less sensitive to perforation phasing than to the number of perforations in clusters. Alterations of the number of perforations per cluster within a stage enable achieving more even proppant distribution.

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