Summary
In this work, we present two simple formulas for the skin of a perforated
well caused by perforation damage: one for the reduction in permeability, and
one for the increase in non-Darcy flow coefficient (beta factor). They are
based on the inflow performance of a single perforation obtained by means of a
prolate-spheroidal flow model. This model rigorously accounts for the flow
convergence toward a perforation, especially near the tip of the perforation.
It provides a more realistic description of the inflow than a radial flow
model, the basis for the existing skin formulas proposed by McLeod (1983). In
the case of perforations with a large aspect ratio and a thin damaged zone, the
formula for the skin due to permeability reduction reduces to McLeod’s formula.
The formula for the non-Darcy skin yields a significantly larger skin than
predicted by the radial flow model, up to a factor 1.4 for large aspect ratios.
Finally, we demonstrate that perforated wells are much more liable to non-Darcy
flow than openhole wells, in particular if the perforations are severely
damaged.
Introduction
Oil and gas wells are commonly completed with production casing cemented in
place and perforated to enable fluids to enter the wellbore. The perforations
are created by perforating guns and have the form of straight elongated and
circular holes that stick into the formation perpendicular to the wall of the
wellbore. The perforation holes are surrounded by a damaged zone of crushed and
compacted rock. Typically, a perforation has a diameter of approximately a
quarter-in., a length of a few up to more than a dozen inches and a crushed
zone thickness of up to 1 in.
It has been long recognized that perforation damage may drastically impair
the flow efficiency of a perforated well. Not only is this caused by a lower
permeability in the crushed zone, but also by a higher inertial resistance
coefficient (non-Darcy flow coefficient), which is particularly important for
prolific, high-rate gas wells. Customarily, the inflow performance of a
perforated well is described by the radial openhole inflow formula, in which
the effect of the perforations (e.g. geometry, shot density, phasing, and
perforation damage) is included as a pseudo skin (Bell et al. 1995). The
current model for estimating the Darcy and non-Darcy skins due to perforation
damage was proposed by McLeod(1983). In this model the perforation is
represented by an open circular cylinder surrounded by a concentric crushed
zone of reduced permeability and enhanced non-Darcy flow coefficient, and the
inflow into this cylinder is assumed to be radial, perpendicular to its
axis.
© 2007. Society of Petroleum Engineers
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History
- Original manuscript received:
16 May 2005
- Revised manuscript received:
3 November 2006
- Manuscript approved:
9 November 2006
- Version of record:
20 June 2007
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