An analytical flow model for multistage fractured horizontal well with elastic outer reservoir boundary

Currently, the analytical flow models for multistage fractured horizontal well that describe the seepage flow laws in unconventional tight oil and gas reservoirs mostly assume the traditional idealized reservoir outer boundaries, which are closed, constant pressure, or infinite. However, these three traditional types of idealized outer boundaries cannot adapt to some actual situations in reservoir engineering, in which the outer reservoir boundary can show an elastic feature. To address this issue, based on an engineering background of shale gas reservoir development, conception of elastic outer boundary condition is introduced for the first time, and a novel physical flow model and its mathematical model for multistage fractured horizontal wells with elastic outer reservoir boundary are established. Through defining pseudo gas pressure, the mathematical model is linearized, and then, the semi-analytical solution of the model is obtained by using Laplace transform. Finally, the novel model was applied to analyze the actual production data from parent wells in shale gas reservoirs, which suffer from reservoir energy replenishment through fluid injection into infill wells. The results show that the typical curve fitting for the production data is well improved by using our model. It largely increases the accuracy of production forecast. Moreover, the elastic outer boundary condition in this model can cover all the three types of traditional idealized boundaries. The research greatly improves the accuracy and applicability of the analytical flow model for multistage fractured horizontal wells. All in all, it provides an important theoretical foundation on seepage flow mechanics for dynamic production data analysis and well testing technologies in the development of unconventional oil and gas fields.