An Improved Model for Estimating Flow Impairment by Perforation Damage

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.