A New Skin Factor Model for Gravel-Packed Completions
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AbstractGravel packing is widely used in well completions to prevent sand production. An efficient gravel pack completion retains formation sand without creating significant additional pressure drop through the completion itself. To predict gravel-packed well performance, a completion model that calculates pressure drop for a gravel pack completion is necessary. In this paper, a theoretical turbulence skin factor model for cased-hole gravel-packed wells is presented that can be used to determine the effects of the gravel pack on well performance. The overall pressure drop through the gravel pack completion is divided into three parts; the pressure drop through the gravel between the casing and the screen, which is usually small and can be neglected; the pressure drop occurring through gravel in the perforation tunnels penetrating through the casing and cement and out into the formation; and the pressure drop outside the casing caused by flow converging to the perforations. This study is focused on the latter two pressure drops. Based on extensive 3D finite element simulation studies, the flow field in and around a gravel pack completion is approximated by a series of linear, radial, and hemispherical flow geometries, and the Forchheimer equation is then integrated along a simplified flowpath to obtain the pressure drop both inside and outside of the casing.The FEM simulation results show that the flow geometry of a cased, perforated, and gravel packed well greatly depends on the ratio of the formation permeability to the permeability of the gravel in the perforation tunnels. As the perforation tunnel permeability approaches the formation permeability, the flow geometry near the perforation through the casing is no longer linear but spherical as if there is no perforation in the formation. As a result, the conventional model of flow in the gravel packed perforations may give inaccurate results under these conditions. The new skin factor model accounts for the transition from linear to spherical flow as a function of the ratio of the formation to perforation tunnel permeabilities. This model also includes permeability damage in a perforation tunnel that significantly increases rate dependent (turbulent) skin effects. We used the model to determine the gravel pack conditions needed to insure that gravel pack skin factor is low and to minimize the effects of turbulence in the gravel pack in high rate wells. Guidelines for gravel permeability are presented based on these results.
