An Experimental Study of Coefficient of Discharge for Consistent Hole Perforating and the Effect on Limited Entry Designs

Abstract

In hydraulic fracturing, determining the perforation pressure loss is a critical step in the design strategy, on-site troubleshooting diagnostics and post-fracture analysis. Historically, the most widely assumed and thus unknown components in the perforation friction equationare the coefficient of discharge and the holistic perforation diameter. The perforation coefficient of discharge has long been assumed as a dynamic variable dependent on the amount of fluid and proppant pumped through the perforations. This variable becomes increasingly important when clusters are spaced closer together and fewer perforations are shot such as in a limited entry design. Limited entry is a perforating technique used to generate uniform fractures along the wellbore by creating appropriate pressure differentials from cluster to cluster. With the adoption of consistent hole perforating shaped charges, the perforating diameters are more consistent and predictable. While not all consistent hole shaped charges have low diameter variability, the perforating diameters downhole are no longer an unknown, particularly after the introduction of downhole cameras. Therefore, the coefficient of discharge is the only unknown variable remaining. This paper presents an experimental methodology to accurately define the true coefficient of discharge in common completions perforated by a known consistent hole shaped charge. The test setup is illustrated, detailed test steps are discussed, and experimental data with correlations of rate per perforation and discharge coefficient is presented. Completions tested included 4-1/2", 5", and 5-1/2" casings in common weights and grades. Various perforating strategies were examined such as single shot and angled shot. Critical parameters such as entry hole diameters were made by the actual shaped charges and measured before and after the test. Freshwater and slickwater were used as hydraulic fluid and circulated at real-world pump rates through each perforation to simulate the actual field flow conditions. Based on the study, several correlations for the coefficient of discharge of flow through a perforation are created considering casing thickness, entry hole diameter and rate per perforation for the given consistent hole shaped charges. These correlations can improve perforation and fracturing designs where perforation friction are important variables.