Optimal Inflow Performance Relationship Equation for Horizontal and Deviated Wells in Low-Permeability Reservoirs

Abstract

After Vogel proposed a dimensionless inflow performance equation, with the rise of the horizontal well production mode, a large number of inflow performance relationship (IPR) equations have emerged. In the productivity analysis of deviated and horizontal wells, the IPR equation proposed by Cheng is mainly used. However, it is still unclear whether these inflow performance models (such as the Cheng, Klins-Majcher, Bendakhlia-Aziz, and Wiggins-Russell-Jennings types) are suitable for productivity evaluations of horizontal and deviated wells in low-permeability reservoirs. In-depth comparisons and analyses have not been carried out, which hinders improvements in the accuracy of the productivity evaluations of horizontal wells in low-permeability reservoirs. In this study, exploratory work was conducted in two areas. First, the linear flow function relationship used in previous studies was improved. Based on the experimental pressure-volume-temperature results, a power exponential flow function model was established according to different intervals greater or less than the bubble point pressure, which was introduced into the subsequent derivation of the inflow performance equation. Second, given the particularity of low-permeability reservoir percolation, considering that the reservoir is a deformation medium, and because of the existence of a threshold pressure gradient in fluid flow, the relationship between permeability and pressure was changed. The starting pressure gradient was introduced into the subsequent establishment of the inflow performance equation. Based on the above two aspects of this work, the dimensionless IPR of single-phase and oil-gas two-phase horizontal wells in a deformed medium reservoir was established by using the equivalent seepage resistance method and complex potential superposition principle. Furthermore, through regression and error analyses of the standard inflow performance data, the correlation coefficients and error distributions of six types of IPR equations applicable to deviated and horizontal wells at different inclination angles were compared. The results show that the IPR equation established in this study features good stability and accuracy and that it can fully reflect the particularity of low-permeability reservoir seepage. It provides the best choice of the IPR between inclined wells and horizontal wells in low-permeability reservoirs. The other types of IPR equations are the Wiggins-Russell-Jennings, Klins-Majcher, Vogel, Fetkovich, Bendakhlia-Aziz, and Harrison equations, listed here in order from good to poor in accuracy.