A Semi-Analytical Model for Gas–Water Two-Phase Productivity Prediction of Carbonate Gas Reservoirs

Abstract

The productivity prediction of gas wells in carbonate gas reservoirs is greatly affected by the characteristics of gas–water two-phase flow and fracture seepage parameters. Compared with numerical simulation, the productivity prediction based on the analytical model is fast and widely used, but the traditional analytical model is fairly simplified while dealing with the nonlinear problem of the two-phase seepage equation, leading to a large discrepancy in the results of dynamic analysis. To solve this problem, this paper considers the characteristics of gas–water two-phase flow in the reservoir and fracture, uses the dual-medium model to characterize the stress sensitivity of the fracture and reservoir, and establishes a gas–water two-phase productivity prediction model for carbonate gas reservoirs. Combining the flowing material balance equation with the Newton iteration method, the nonlinear parameters of the percolation model are updated step by step with the use of average formation pressure, and the gas–water two-phase model is linearized through successive iterations to obtain the semi-analytical solution of the model. The accuracy of the model was verified using a comparison with the results of commercial numerical simulation software and field application, the gas–water two-phase productivity prediction curve was obtained, and the influence of sensitive parameters on productivity was analyzed. The results show that: (1) the semi-analytical solution method can efficiently deal with the gas–water two-phase nonlinear seepage problem and obtain the productivity prediction curve of carbonate gas wells rapidly and (2) the water production of the carbonate gas reservoir seriously affects the productivity of gas wells. During the development process, the production pressure difference should be reasonably controlled to reduce the negative impact of stress sensitivity on productivity performance.