Constraints on Pipe Friction and Perforation Cluster Efficiency from Water Hammer Analysis
Authors: Dunham Eric M. , Zhang Junwei , Moos Dan 
Published: January 2023

Abstract
Pressure losses from pipe and perforation friction control the relation between wellhead pressure and pressure at the mouth (entrance) of hydraulic fractures. Because both pipe and perforation friction are proportional to flow rate squared, standard step-down tests that rely on the steady pressure response at a set of injection rates cannot uniquely determine pipe and perforation friction. We introduce a novel method to resolve this nonuniqueness by analyzing the water hammer response, measured by high-rate pressure sensors at the wellhead, following abrupt rate steps during shut-in following a stimulation treatment. Constraints on perforation friction permit quantification of the number of active perforations connecting to fractures and hence perforation cluster efficiency.
Our method requires a shut-in procedure with abrupt drops in injection rate to produce water hammer oscillations (tube waves propagating between the wellhead and current stage). The rate drop is accompanied by a drop in wellhead pressure as a tube wave propagates away from the wellhead, decelerating the fluid behind it. Pipe friction attenuates this wave, such that the local flow rate remains higher at depth than near the wellhead. This expands the fluid, causing additional depressurization at the wellhead until the arrival of the reflected wave from the stage. The Darcy-Weisbach pipe friction factor is determined from the depressurization rate. At high background flow rates, the reflected wave amplitude is controlled by perforation friction with minimal sensitivity to fracture properties.
The claims above are substantiated by numerical simulations of tube wave propagation and reflection from perforation clusters connected to hydraulic fractures. We then present two case studies in which the method is applied data from hydraulic fracturing treatments in two stages in different wells targeting the Wolfcamp and Bone Spring Formations, Permian Basin. The inferred pipe friction factor is 2×10−3, an order of magnitude smaller than for turbulent water flow, but consistent with the use of friction reducers and pumping company pressure loss tables. The measured perforation friction is higher than predictions based on a standard formula involving fluid density, discharge coefficient, entry hole diameter, and design number of holes. This suggests not all clusters connect to fractures; the inferred cluster efficiency is 67% (Case-A, Wolfcamp) and 84% (Case-B, Bone Spring).
This work extends simulation and inversion capabilities utilizing wellhead data to nonlinear problems involving tube wave interactions with hydraulic fractures and perforations. The ability to independently constrain pipe and perforation friction resolves nonuniqueness of step rate tests. Rapid inversion enables us to deliver real-time measurements of perforation cluster efficiency, pipe and perforation friction that complement traditional fracture diagnostics. Combined with acoustic pulsing to quantify near-well flow resistance, the method provides a noninvasive, cost-effective means of monitoring of the critical connection between the well and fractures during simulation treatment. The method can be used to diagnose and treat problems such as uneven fluid distribution across clusters.