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).