Transient Pressure Analysis in Partially Perforated Vertical Wells

Due to engineering or geological reasons, oil and gas wells are frequently completed using a partially perforated method. Complicated spatial distribution of perforation tunnels is too difficult to be considered in the conventional analytic solution model, and there is still short of a well test model regarding the partially perforated well. Therefore, this paper develops a 3D numerical well test model for partially perforated wells, which not only accurately describe the perforation tunnels distribution near the wellbore, but also consider the characteristics of perforation compacted zone, formation damaged zone, and permeability anisotropy. The 3D finite element method is utilized to conduct numerical solutions to the model, and the pressure response curves and pressure fields are obtained for the first time. Characteristics of the pressure response curves and pressure fields are studied as well as the effects of other factors, such as perforated position, perforation compacted zone, and formation damaged zone on the pressure response curve. The results show that the pressure response of partially perforated well is characterized by both totally perforated well and partially penetrated well. It not only has an early locally radial flow characteristic around the perforation tunnels, but also has an ellipsoidal (spherical) flow characteristic. Compared with perforation at either top or bottom, the perforation in the middle weakens the inter-perforation interference. The effect of perforation compacted zone can be replaced by reducing the effective perforation radius. The increase of perforation length can largely reduce the effect of formation damaged zone on the pressure response curve and productivity of partially perforated well. Finally, the total skin computing formula of the partially perforated well is verified by means of calculation of cases with different perforation lengths and different perforated level coefficients.