Experimental study on the discharge coefficient of perforation behaviors during hydraulic fracturing treatments

The discharge coefficient (C_d) affects the perforation pressure drop during the hydraulic fracturing treatments. Given the changes in completion procedures, especially with horizontal wells, this absence of research on the C_d value indicates that many times over-simplification of the term is applied in practice. The research outlined in this paper focuses solely on the C_d term and the various conditions that are encountered downhole and the resulting impacts on perforation friction.

This research provides an understanding into the influence of various factors on the discharge coefficient. Perforation hole size, perforation plate thickness, perforation hole geometry, downstream restrictions, friction reducer, fluid viscosity and horizontal behaviors are investigated in this work. In this study, a low pressure setup was built to investigate the effect of the previous factors on the discharge coefficient and subsequently the pressure loss through the perforations in hydraulic fracturing treatments.

The experimental results show that the perforation hole size does not impact the discharge coefficient. However, perforation plate thickness, friction reducer fluid loading and fluid viscosity has a positive relation with the discharge coefficient value. In other words, a clear increase in the C_d value was observed when these parameters were increased for all the conducted tests. For different perforation hole geometries, the results show that the smooth and tapered edge hole has a larger C_d value than the same shaped sharp-edge hole. When a downstream restriction is installed, the C_d value increases as the distance between the downstream reflection plate and the perforated plate increases. The results of the horizontal well behaviors show that the C_d value of the perforated horizontal casing is slightly higher than C_d value for the perforated plate. Overall, this study on the effect of influencing factors on the perforation C_d value can help form a better understanding of perforation pressure drop behaviors and modify the design of limited-entry techniques.