New Correlation for Predicting Frictional Pressure Drop of Proppant-Laden Slurries Using Surface Pressure Data
Authors: Pandey Vibhas J. , Robert Joel A. 
Published: December 2007

Abstract
During a hydraulic fracturing treatment, it is important to ascertain the bottom hole pressure (BHP) in order to calculate the net pressure generated in the fracture. Net pressure trends are critical in the proppant stages because any incorrect interpretation may lead to an early termination of the treatment and hence the designed objectives may not be achieved. On other hand, continuing to pump the job even when a screen out is imminent may lead to a proppant pack in the tubular and may incur additional expenditure to clean up the well. In some treatments, BHP gauges, live annulus or dead strings may be used to monitor the net pressure. However, in most treatments such devices or methods may not be available. A majority of the hydraulic fracturing jobs, thus, rely on the pressures recorded at the surface to compute the net pressure.
This study utilizes the surface pressure recorded during the treatment to compute the friction pressure drops during the proppant stages. Over 150 hydraulic fracturing jobs were used for the study. Friction pressure multipliers were generated for several proppant concentrations using the friction pressure data obtained from these treatments. These multipliers were analyzed in the light of key parameters that could affect the proppant friction, namely, gel concentration, proppant density, tubular internal diameter, and average flow velocity. A correlation, capable of predicting proppant friction pressure exponent was generated using the above-mentioned variables. An average deviation of around 0.23% was observed when the results obtained from the correlation were compared with friction pressures calculated in cases where bottom hole pressures were measured. Further, proppant friction exponents obtained from the correlation were used in several other jobs that were not part of the initial study and reasonably good pressure history matches were obtained. The simple form of the correlation can be easily programmed in a spreadsheet and has proved to be an efficient tool in computing net pressures while monitoring the jobs where the bottom hole pressures are not measured.

Introduction
In comparison to the pad fluid, proppant-laden slurries are more complex to model because of the existence of two-phase flow consisting of base gel and solid proppant. On a typical hydraulic fracturing job, surface pressure shows a decreasing trend with the introduction of proppant stages. This reduction in surface pressure is primarily due to the increment in fluid density caused by the addition of solids in the fluid. A closer look however, reveals that the loss of pressure is not entirely due to an increase in hydrostatic pressure. This observed difference could be attributed to the additional friction pressure introduced because of the proppants. Major factors that contribute to increased friction pressures are proppant concentration, tubular size, flow rate, and slurry viscosity. For simplicity the proppant friction has been traditionally quantified as an increment to the base gel friction, so it can be included in existing models. Lack of proper modeling and theoretical understanding of the proppant-laden slurry, has however contributed to the limited data available in this field of investigation.

Literature Review
Historically, the researchers have found it relatively easy to generate theories for predicting friction pressure losses for Newtonian fluids in comparison to viscoelastic non-Newtonian fluids. The same can be extended to proppant-laden slurries, where there are several expressions for predicting friction pressures for slurries composed of Newtonian fluids and solid particles. However, there are not enough theories for how particles affect the friction pressure of highly non-Newtonian fluids.