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Transport in Porous Media

, 80:305 | Cite as

Flow Performance of Perforated Completions

  • Colin Atkinson
  • Franck MonmontEmail author
  • Alexander Zazovsky
Article

Abstract

A powerful approximate method for modeling the flow performance of perforated completions under steady-state conditions has been developed. The method is based on the representation of the perforation tunnels surrounding a wellbore by the equivalent elongated ellipsoids. This makes possible an analytical treatment of a 3D problem of steady-state flow in a porous medium with complex multiple production surfaces. The solution is obtained for a vertical wellbore fully penetrating through a horizontal formation in the presence of permeability anisotropy. The perforations are oriented horizontally, arranged in almost arbitrary patterns, repeating along the wellbore, and may have different lengths and shapes. The hydraulic resistances of perforations flowing inside them as well as the crushed zones around them with impaired permeability are neglected. The approximate solution found was verified by comparing the previous analytical/numerical solutions for a small number of perforations. This approach allows one to determine the local skin or the effective wellbore radius for any perforated interval, which can then be integrated into the conventional calculations of well productivity and used for the perforating gun selection during perforation job design.

Keywords

Well productivity Steady-state flow Skin Effective wellbore radius Productivity index Perforation Perforated completion Modeling 

List of Symbols

ai, bi, ci

Semi-axes of ellipsoids representing cylindrical perforation tunnels

dp

Diameter of the perforation tunnel

dw

Wellbore diameter

dwp

Equivalent openhole wellbore diameter at infinite shot density

D

Simulation domain

G

Dimensionless parameter used in Brooks’ correlation

h

Thickness of perforated interval with repeating perforation pattern

H

Perforated formation thickness

k

Formation permeability

kH

Horizontal permeability

kV

Vertical permeability

l

Depth of penetration

lp

Length of perforation tunnel

N

Shot density equal to number of tunnels per foot of perforated interval

p

Pressure

p0

Far-field formation pressure

pi

Superposed solution components

pw

Wellbore pressure

Δp

Drawdown pressure

Q

Steady-state production rate

rp

Radius of perforation tunnel

rw

Wellbore radius

re

Radius of far-field formation boundary

\({r{'}_{\rm w}}\)

Effective wellbore radius

S

Skin of perforated completion

v

Flow velocity

wij

Distance between centers of equivalent ellipsoids representing perforation tunnels

(xi, yi, zi)

Coordinates of centers of equivalent ellipsoids

X, Y, Z

Cartesian coordinates

αk

Permeability anisotropy ratio

\({\phi}\)

Porosity

\({\varphi _{i}}\)

Strengths of point sources representing far-field flows to ellipsoids

\({\phi}\)

Fundamental solution for steady-state flow into ellipsoidal cavity

Ω

Boundary of simulation domain

Λ

Productivity index of perforated completion

Λ0

Productivity index of openhole completion

Λ

Productivity index of perforated completion at infinite shot density

μ

Viscosity

Π

Productivity ratio

Π

Productivity efficiency

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Colin Atkinson
    • 1
    • 2
  • Franck Monmont
    • 2
    Email author
  • Alexander Zazovsky
    • 2
  1. 1.Department of MathematicsImperial College LondonLondonUK
  2. 2.Schlumberger Cambridge ResearchCambridgeEngland

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