Calculation of Perforated Vertical and Horizontal Well Productivity in Low-Permeability Reservoirs

Abstract

Summary This paper presents the productivity formulas of a perforated vertical well on the basis of the dual-radial-flow model and then presents the productivity formulas of horizontal wells on the basis of disturbing elliptical flow theory. The threshold pressure gradient (TPG) is used to characterize the seepage characteristics of low-permeability reservoirs. By combing the above formulas, the authors proposed the productivity formulas of perforated horizontal wells in a low-permeability reservoir on the basis of the triple-radial-flow model. The formulas are derived considering the cases of the damaged zone being penetrated and being partially penetrated. At the same time, the flow patterns of single-phase flow and oil/water two-phase flows are considered. Sensitivity analysis on the performance of the perforated well shows that the productivity increases with the increase of the length of the horizontal well, penetration depth, shot density, perforation diameter, and phasing, and it decreases with the increase of TPG, compaction thickness, and crush degree of the crushed zone; the influence of the length of the horizontal well, TPG, penetration depth, shot density, compaction degree, phasing, perforation diameter, and compaction thickness on the productivity is in descending order.