An analytical model for predicting the productivity of perforated wells

In this work, we present an analytical model for the prediction of the productivity of perforated wells. The basic building block of the model is an analytical solution for single-phase Darcy flow to a single perforation in a semi-infinite porous medium. We have expanded this solution to describe the flow to a well with regularly spaced arrays of equidistant perforations along the wellbore wall. The end result is a formula for the perforation skin as a function of perforation length and radius, shot density, perforation phasing, permeability anisotropy, perforation damage and formation damage. Partially perforated wells can be handled with the help of the total skin formula of Jones and Watts [Jones, L.G., Watts, J.W., 1971. Estimating Skin Effect in a Partially Completed Damaged Well. J. Pet. Technol. (February), 249–252.]. The results of the model compare fairly well with the results of previous numerical flow simulations. The model can be readily implemented in a standard spreadsheet program and may be used as an alternative to the current semi-analytical method of Karakas and Tariq [Karakas, S.M., Tariq, S.M., 1991. Semianalytical Productivity Models for Perforated Completions. SPE Prod. Eng. (February), 73–82.]. It is shown that this method does not properly account for permeability anisotropy, which results in overly optimistic well productivities, particularly in the presence of perforation and formation damage.