A NEW 3D FINITE ELEMENT METHOD FOR CALCULATING THE PRODUCTIVITY RATIO OF A PERFORATED WELL

In order to get more accurate and comprehensive productivity ratios, this paper presents a 3D steady dimensionless porous flow model for perforated wells. A new 3D finite element modeling method is developed. The numerical solution is obtained using fine tetrahedral meshes and a parallel computing method. By comparing the calculated results with the results of the traditional methods, it shows that precision of Karakas method is higher than that of Hagoort method. However, the Karakas method still has some variable-dependent errors, meaning that it cannot be used under certain conditions and with specific values of some parameters. The proposed finite element method is more useful than the Karakas method in calculating the productivity ratios of certain perforated wells with specific phase angles or impacts from pollution. The effects of actual perforation geometry, formation damaged zones, perforation compacted zones, and reservoir permeability anisotropy on productivity ratios were also analyzed, and the results show that increasing perforation length tends to increase productivity. Additionally, there are optimal values for both perforation density and perforation phase angle, and shooting through the formation damaged zone around the wellbore is the most effective way to reduce the effect of damaged zones on productivity. Perforation compacted zones and those with low vertical permeability dramatically reduce productivity. This study provides theoretical guidance to improve the completion design and predict the productivity of perforated wells.