Plug-and-perf fracturing stages with multiple perforation clusters have become common practice in the industry. However, it is usually unclear whether or not the fluid and proppant are distributed evenly among all clusters. In this study we present a method for computing the proppant distribution into each cluster in a fracturing stage. By integrating proppant transport into a multi-cluster hydraulic fracturing model and implementing a simple screenout criterion, we show that the proppant distribution in a fracturing stage can be very uneven with a strong bias towards the heel-side clusters even when the initial fluid distribution is uniform among all clusters.

In this work, we define the efficiency of proppant transport into a perforation by the proppant transport efficiency (PTE), which is defined as the mass fraction of proppant transported through a perforation relative to the total mass of proppant approaching the perforation. The dynamic proppant distribution in a fracturing stage is modeled using the PTE concept in 3 steps. First, a series of coupled computational fluid dynamics - discrete element method (CFD-DEM) simulations were performed to obtain PTE under controlled flow conditions. Then, the CFD-DEM simulation results were statistically analyzed to generate a PTE correlation as a function of wellbore, perforation, fluid, and proppant properties. Finally, the PTE correlation was incorporated into a multi-cluster hydraulic fracturing model to compute the dynamic distribution of fluid and proppant among multiple clusters in a fracturing stage.

Results from this work show that proppant concentration in the toe-side clusters can be several times higher than the injected concentration. This occurs because the high wellbore flow rate near the heel-side clusters provides proppant particles a large enough inertia that prevents them from turning into the perforations. Proppant concentration in the wellbore is thus increased as the slurry flows towards the toe side and the fluid preferentially leaks off from the heel side perforations. The highly concentrated slurry increases the screenout risk of the toe-side clusters. Our modeling results show that if toe-side clusters screen out at an early time of a proppant stage, fluid and proppant are re-distributed to the heel-side clusters. In such a case, cumulative fluid and proppant distributions will be heel-biased. Simulation results are compared with field observations and are shown to be completely consistent with DTS and DAS observations on proppant distribution made in three different studies.

The method presented in this work provides a way to quantify proppant transport at a wellbore scale. It shows that the uneven proppant distribution among perforation clusters is a function of fluid, perforation and proppant properties. An estimate of proppant placement in different perforation clusters can be computed for any pumping schedule and wellbore/perforation geometry using this method. This can be used to optimize perforation clusters that will result in a more even distribution of proppant in each cluster.

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