Summary
Using a combination of analytical calculations and 3D finite-element
simulation, we have developed a comprehensive skin-factor model for perforated
horizontal wells. In this paper, we present the mathematical model development
and validation by comparison with finite-element simulation results. With the
new perforation skin model, we then show how to optimize horizontal well
perforating to maximize well productivity.
A cased, perforated well may have lower productivity (as characterized by a
positive skin factor) relative to the equivalent openhole completion because of
two factors: the convergence of the flow to the perforations, and the blockage
of the flow by the wellbore itself. Because of the orientation of a horizontal
well relative to the anisotropic permeability field, perforation skin models
for vertical wells that consider these effects, notably the Karakas and Tariq
model (1991), are not directly applicable to perforated horizontal completions.
Using appropriate variable transformations, we derived a skin-factor model for
a horizontal perforated completion that is analogous to the Karakas and Tariq
(1991) vertical-well model. The empirical parameters in the model were
determined from an extensive 3D finite-element simulation study.
The results of the new model show that the azimuth of a perforation (the
angle between the perforation tunnel and the maximum permeability direction,
usually thought to be in the horizontal direction) affects the performance of
perforated completions in anisotropic reservoirs. When perforations are normal
to the maximum-permeability direction, perforations will enhance
horizontal-well flow compared with an openhole completion (a negative skin
factor). But if perforations are in the same direction as the maximum
permeability, significant positive skin will result. The new skin-factor model
provides a clear guide to the shot density, perforation orientation, and level
of perforation damage that is tolerable to create high-productivity perforated
completions in horizontal wells.
Introduction
A skin factor can be used to mathematically account for any deviations of
the flow and pressure field in the near-well vicinity from perfectly radial
flow to a wellbore of radius rw . A perforated completion
obviously has a flow and pressure field near the perforations that is not
perfectly radial. As shown by Karakas and Tariq (1991), the altered flow
characteristics near perforations can be conveniently divided into three parts:
the flow in a plane perpendicular to the wellbore, the blockage of flow to the
perforations by the wellbore itself, and the fully 3D flow resulting from the
asymmetric distribution of perforations along the wellbore. These effects on
the near-well flow field and the corresponding perforation skin factor
components are illustrated in Fig. 1.
Perforation skin models for vertical wells (Karakas and Tariq 1991; Harris
1966; Locke 1981; Klotz et al. 1974) have already been presented in many
papers. However, they are not directly applicable to a horizontal well because
the reservoir anisotropy in a horizontal well creates complex plane-flow
geometry normal to the well, which alters the flow efficiency of a perforated
completion. In this work, we present a new skin-factor model developed for a
cased, perforated horizontal well. From our observations, the 2D plane flow
skin, s2D , the wellbore blockage skin,
swb , and the 3D convergence skin, s3D , greatly depend on the magnitude of the permeability
anisotropy and the perforation angle measured from a horizontal plane. Our
model is based on the conventional perforation skin model for a vertical well
presented by Karakas and Tariq (1991).
Our perforation skin model is a semianalytical solution that is correlated
with numerical simulation results. The reliability of any empirical correlation
for perforation skin factors will depend on the accuracy of the numerical
simulations. The finite-element method (FEM), which is suitable for complex
flow geometry problems, has been widely applied by many authors (Karakas and
Tariq 1991; Klotz et al. 1974). In this study, we used the FEM to numerically
model the performance of perforated horizontal wells. Our model uses an
automatic and adaptive mesh generation program, GID (CIMNE 2006), to generate
the finite-element grid.
One of the great advantages of introducing a skin model for a perforated
well is that it can be easily incorporated into any existing model of reservoir
inflow performance or into a reservoir simulator. The modified perforation skin
model developed here gives optimized perforation conditions and helps us to
understand complex flow geometry in a horizontal perforated well. Using an
accurate finite-element simulator, we also show a verification of the
model.
© 2008. Society of Petroleum Engineers
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History
- Original manuscript received:
5 October 2004
- Meeting paper published:
22 September 2002
- Revised manuscript received:
17 January 2008
- Manuscript approved:
21 January 2008
- Version of record:
15 September 2008
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