Summary
The most crucial region with regard to affecting well productivity is the
perforated region. Considerable effort has been directed to study this subject
mathematically by many investigators, but they have been mainly focused on
single-phase flow, while two-phase flow has received less attention.
It has been demonstrated, first by Danesh et al. (1994) and subsequently by
other researchers (Henderson et al. 1995; Blom et al. 1997; Ali et al. 1997),
that the gas and condensate relative permeability (kr ) can
increase significantly by increasing the flow rate, contrary to the common
understanding. This effect, known as positive coupling, complicates the flow of
gas and condensate near the wellbore even further when it competes with the
inertial forces at higher velocities typical of those around perforation
tips.
The flow of gas and condensate in the perforated region was studied in this
work using a finite-element modeling approach. The model allows for changes in
fluid properties and accounts for the positive coupling and negative inertial
effects using a fractional-flow-based relative-permeability correlation. A
sensitivity analysis on the impact of perforation characteristics such as
density, phasing, length, and radius as well as that of fluid properties, rock
characteristics, wellbore radius, fractional flow, and rate on well
productivity was conducted, resulting in some valuable practical guidelines for
optimum perforation design.
Introduction
The effect of perforation characteristics on the well flow efficiency has
been studied by many investigators. Muskat presented the first analytical
treatment of the problem (1943). In his analysis, perforations were represented
by mathematical sinks distributed spirally around the wellbore but did not
extend into the formation. Other early investigators used the finite-difference
modeling technique to examine the productivity aspects of perforated
completions (Harris 1966; Hong 1975). However, because of the limitations of
the finite-difference method, these studies considered mostly unrealistic
perforation geometries to avoid mathematical complexities. Later investigators
applied the finite-element method, which models the geometry of the perforation
with greater precision (Locke 1981; Tariq 1987).
Tariq (1987) presented results of finite-element modeling of single-phase
steady-state flow in perforated completions with and without the non-Darcy
(inertial) effect for a linear core and a full 3D system. Although his results
for single-phase flow are widely used, there are reports on lack of required
accuracy at large perforation lengths and in the non-Darcy cases (Behie and
Settari 1993; Jamiolahmady et al. 2006a).
© 2007. Society of Petroleum Engineers
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History
- Original manuscript received:
21 March 2005
- Meeting paper published:
13 June 2005
- Revised manuscript received:
2 August 2006
- Manuscript approved:
9 October 2006
- Version of record:
20 March 2007
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