Hydraulic fracturing or fracking is a well stimulation technique for extracting hydrocarbons from naturally low (extra low) permeable oil and gas reservoirs. In this process water, proppant and chemicals are injected through the wellbore and from the perforation hole into the reservoir. The main goal of this treatment is to create artificial fluid path conduits in the formation and finally increase the permeability (and productivity) of the reservoirs.

One of the important factors which affects the near wellbore fluid pressure drop is the coefficient of discharge (Cd) which is a characteristic of the perforated hole in the wellbore tubular. The coefficient of discharge is defined as the ratio of the measured mass flow to the theoretical mass flow. The Cd depends on many factors and may change with time due to erosion caused by the injected sand, which was pumped into the formation. In this research, we investigated some of the factors that can affect the coefficient of discharge like the erosion of the perforated hole and the backpressure given by the fracture.

For this purpose, we have developed a new high-pressure high-flow rate setup for examining the effect of the following parameters which can alter the coefficient of discharge. More specifically we have investigated the effect of perforation hole size, perforation hole geometry and perforation shape on the Cd value at ambient conditions and with backpressure, before and after sand erosion. To do so, in a first step we have used machined holes with a clearly defined geometry and then compared the results with real perforated holes which were generated using various shaped charge designs. The coefficient of discharge was measured using water or gelled water with different pressure differentials and back-pressures. In our study, we have injected sand slurry for 30 minutes with a constant concentration. The flow rate and pressure drop were also recorded simultaneously during the injection of the sand.

Our results show how the erosion directly affects the Cd value and the subsequent pressure drop near the perforated hole. A clear increase of the Cd magnitude becomes visible only due to a change of the inlet geometry without changing the diameter. Also, the backpressure, which represents real fracking conditions, leads to a significant increase compared to the measurements at ambient outlet pressures.

The measured values before and after the erosion for real perforation holes differ from simple drilled holes. From the recorded results, it also seems that certain perforation shapes or geometries are more effected by erosion than others.

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