Flow efficiency of perforated systems – a combined analytical and numerical treatment

Abstract

The effect of the spatial distribution of perforations on the flow from the reservoir to the wellbore for single phase liquid flow is studied. The reservoir is taken to be isotropic and, for most of the paper, the model used here assumes that the perforations and the wellbore are both undamaged. Thus, there is no change of permeability around the wellbore and perforations. The pressure/flow along a single perforation is studied in detail first and an integral equation is derived which can be solved numerically to give the pressure/flow everywhere along the perforation. The interaction of the perforations is considered by an approximation in which each perforation is represented by a point source of unknown strength positioned at the centre of the perforation. A simple ellipsoidal model of the perforation is also considered which provides a faster approach for evaluating the flow. The resulting flux of fluid from each perforation into the wellbore is presented numerically for the above-mentioned approximate methods and the comparison with the full numerical method is also made. For the ellipsoidal perforation, the modelling of the perforation skin effect (a mathematical treatment of pressure drops which is caused by perforation damage) is also described, but no detailed numerical results are given.