New Perforation Pressure Loss Correlations for Limited Entry Fracturing Treatments
Authors: El-Rabaa A.M. , Shah S.N. , Lord D.L. 
Published: December 2007

Abstract
Estimating the perforation pressure loss is an essential part in the design and analysis of hydraulic fracturing treatments. Accurate determination of perforation pressure loss for the rheologically complex fracturing fluids being used today can best be achieved through experimental study. Investigation of the perforation pressure loss for linear polymer solutions, crosslinked gels, and fracturing slurries has been conducted at the Fracturing Fluid Characterization Facility (FFCF) since 1994. Using the data acquired from these experiments, new correlations are developed to estimate the coefficient of discharge used in the orifice equation that governs the perforation pressure loss. The correlations can be used to accurately predict the coefficient of discharge for linear polymer solutions and titanium/borate-crosslinked gels. In addition, the slurry correlation can be utilized to determine the dynamic change in the coefficient of discharge for fracturing slurries due to erosion. The presented correlations are developed such that they can easily be incorporated into current fracturing simulators.

Introduction
Determining the pressure loss across the perforation is an essential part of the design and execution of hydraulic fracturing treatments. The accurate knowledge of perforation pressure becomes critical to the success of the treatment when the wellbore is connected to the formation through a limited number of perforations. This situation is encountered when fracturing multiple zones simultaneously (i.e., limited-entry treatment) or when reducing the perforated interval to inhibit the growth of multiple fractures (i.e., point source fracturing). In these cases, the pressure loss across the perforation is large enough to be a significant factor through out course of the treatment. Thus, prediction of perforation pressure loss becomes a key input in treatment simulation, execution, and analysis. Yet, the task of correctly estimating the perforation pressure loss is complicated by the flow mechanics of exotic modern fracturing fluids. Furthermore, the perforation erosion that takes place during the proppant placement stages of the treatment significantly affect the pressure loss estimation. A combined, theoretical and experimental, approach has to be used in understanding the perforation pressure loss under field conditions.
Currently, the industry is using a sharp-edged orifice equation to estimate the pressure drop across the perforation. This equation includes a kinetic energy correction factor, commonly known as the "coefficient of discharge," which is used in calculating the perforation pressure loss as follows:
(1)
Although the coefficient of discharge depends on fluid type and restriction (orifice) size, it is common practice to assume a fixed value for all fluids and perforation sizes. However, recent studies have shown that the coefficient of discharge can vary significantly with fluid viscosity and perforation size. Thus, a rough estimate for the coefficient of discharge can introduce a serious error in the predicted perforation pressure loss. For instance, an error of 10 % in the coefficient of discharge will result in a 25% error in the predicted pressure loss across the perforation. Luckily, for clean fracturing fluids, reliable estimates of the coefficient of discharge can be obtained from available experimental data. For fracturing slurries, on the other hand, good quality data and a robust approach for analysis are not available.
Laboratory data of perforation pressure loss for various slurries and different perforation sizes have been reported. Also, this study has included a discussion on the effects of flow rate, perforation size, and sand concentration on perforation erosion rate. P. 225^