Effects of Perforation-Entry Friction on Bottomhole Treating Analysis
Authors: Crump J.B. , Conway M.W. 
Published: December 2007

Summary
Analysis of field and laboratory data shows that variations in pressure drop caused by changing perforation-entry friction tends to influence the prediction of fracturing treatment performance. This paper presents experimental data on perforation-entry friction as it affects fracturing treatment design.
Prefracturing treatment planning practices include examination of numerous treating-pressure charts to determine formation type curves, which are used to anticipate fracturing treatment performance and screenout modes. Perforation-entry friction may vary greatly because of erosion of the perforation and new-wellbore fracture, and this changing friction pressure is often not properly accounted for in planning.
This paper presents discussion and data (laboratory and field) that show the degree of perforation erosion encountered in fracturing operations and proposed guidelines to determine when to alter pumping schedules to account for proppant erosion to perforations, cement sheath, and formation.

Introduction
Fluid rheology measurements, densimeters, and flowmeters, combined with recent advances in computing power, allow determination of bottomhole treating pressure (BHTP), pbht on a real-time basis. This pressure is actually the BHTP inside the casing. The true BHTP is the pressure inside the fracture. BHTP and formation bottomhole pressure (BHP) are used interchangeably.
The missing link and principal unknown in hydraulic fracturing is fracture-entry friction, pfef. It is usually assumed to be equal to zero, to be a constant, or to be a negligible influence on fracture treating pressure. Fracture-entry friction is the total pressure drop experienced by the fluid from the casing through the perforation and perforation tunnel to the fracture tip. Perforation friction, pf, is the pressure drop of the fluid passing through the restriction of the perforation in the casing. Current technology can determine the fracturing pressure in the casing but may not properly account for the changing BHTP caused by changing pfef. This paper addresses the changing pfef that occurs during pumping of sand-laden slurries.
Pioneering work by Nolte and Smith1 created increased industry awareness of the necessity for accurately determining formation BHP during a fracturing treatment. In an extension of Nolte and Smith's work. Conway et al.2 proposed the analysis and use of treating-pressure type curves to predict well type and screenout mode during the treatment. Many hydrocarbon zones are bounded by a delicate boundary layer that may be fractured by pressure a few hundred psi over design pressure. Analysis of the Nolte and Smith plot is used to determine whether the fracture has broken out of zone. Changing (decreasing) perforation friction pressure during a treatment can be interpreted on a Nolte and Smith plot as evidence of breaking out of zone.
Eq. 1 is used to calculate BHTP:Equation 1
wherepbht=BHTP,pw=wellhead pressure.ph=hydrostatic pressure.pt=pressure caused by fluid friction in tubulars, andpfef=pressure caused by fracture-entry friction.
Two calculated values are present in this equation, pt and pfef. Several recent papers3–5 described means by which the calculation of pt can be improved, particularly in the case of sand-laden slurries.
Components of fracture-entry friction include perforation friction, cetnent-sheath friction, formation damage (resulting from perforating), and fracture friction. Fracture friction can be calculated and depends on the fracture treatment design and fracture width. Formation damage can be minimized by shooting under-balanced,6,7 by proper design of perforation schedule, and by remedial acid cleanup jobs. Cement-sheath friction owing to perforating damage and its erosive properties is shown to have only a minor effect on total perforation-entry friction when slurries are pumped.
The major component of pfef is pf, which is detailed below. The other components of pfef are minor constituents. When sand-laden slurries are pumped at high differential pressure across perforations, pf changes constantly. Field and laboratory data have been combined to derive coefficients theoretically and empirically and to check this equation. The equation commonly used to predict pf isEquation 2
whereq=total flow rate,?=fluid density.np=number of perforations.d=perforation diameter, andKd=discharge coefficient.
Erosion of perforations in tubular goods and the subsequent drop in pf are the main points of emphasis in this paper. Laboratory data show that perforation-friction changes alone can cause errors in interpretation of Nolte and Smith plots.

Experimental Apparatus.
Three series of tests were run that pumped sand-laden slurries through perforated casing. Sand slurries are referred to by their concentration - i.e., pounds of sand per gallon of gelled fluid. Sand concentrations varied from 2 to 20 lbm/gal [240 to 2400 kg/m3], and differential pressure across the perforations ranged up to 1,500 psi [10.4 MPa].

Apparatus.
Three series of tests were run that pumped sand-laden slurries through perforated casing. Sand slurries are referred to by their concentration - i.e., pounds of sand per gallon of gelled fluid. Sand concentrations varied from 2 to 20 lbm/gal [240 to 2400 kg/m3], and differential pressure across the perforations ranged up to 1,500 psi [10.4 MPa].