Study Investigates Factors Affecting Coefficient of Discharge in Stimulation
Authors: Carpenter Chris 
Published: August 2021

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 200612, “The Role of Backpressure and Perforation-Hole Erosion on the Magnitude of the Coefficient of Discharge in Hydraulic Fracturing Stimulation,” by Davood M. Yosefnejad, Bernd Fricke, and Joern Loehken, DynaEnergetics Europe, et al., prepared for the 2020 SPE Virtual Europec Conference, 1–3 December. The paper has not been peer reviewed.
One of the important factors affecting the near-wellbore-fluid pressure drop is the coefficient of discharge (Cd). In the complete paper, the authors investigate some of the factors that can affect Cd, such as the erosion of the perforated hole and the backpressure given by the fracture. The paper studies the effect of perforation hole size, geometry, and shape on the Cd value at ambient conditions and with backpressure, before and after sand erosion.

Setup Specifications and Materials
For this study, a high-pressure, high-flow setup was built for Cd measurements, as well as a second setup in which the holes can be eroded by proppant-laden slurries. The test cell was the same for both setups. The holders of the plates were stainless steel and connected to 7-in. pipes approximately 4 ft long on each side. In all the experiments, the flow rate and inlet and outlet pressure data were recorded simultaneously vs. injection time by high-precision sensors. All experiments were carried out at an ambient temperature of 15–28°C.
For these flow-test experiments, only water was used, circulated with different pressure differentials to determine the effect of pressure on Cd magnitude. In addition, backpressure was applied through the needle valve to simulate real reservoir conditions and to compare the Cd value with the tests under ambient conditions.
The flow rate range of the pump was 1–7 bbl/min at maximum pressures of approximately 2,000 psi. Erosion tests have been performed for 30 minutes with a near-constant flow rate (approximately 1 bbl/min), constant pressure (approximately 200 psi), and constant sand concentration. For the erosion test, a viscosity of approximately 10 cp was used. The sand concentration was kept at 1 to 2 lbm/gal to keep the erosion rate low, which would allow distinguishing between shape-driven changes in Cd and changes caused by an increase of the hole size.
The study used machined holes and holes created by differently shaped charges, which also differed in size and geometry. A description of these holes, and associated shaped-charge tests, is provided in the complete paper.

Experimental Results and Discussion
Generic Holes. In the first sets of experiments, generic holes with different entrance-hole diameters were used. The experiment began with the lowest inlet pressure, which gradually was increased to the maximum pressure. The outlet pressure was kept constant at an ambient pressure. The flow rate increased because of the increase in differential pressure. After reaching the maximum pressure, the inlet pressure was kept constant and the choke on the outlet side was closed step by step to establish a backpressure, which led to a decrease in differential pressure. Surprisingly, the flow rate stayed constant until the differential pressure surpassed 700 psi.