Research on nonlinear spherical seepage model solution of fractal composite reservoir considering quadratic pressure gradient under elastic outer boundary

In order to break the limitation that only three ideal outer boundaries (infinity, constant pressure and closed) are considered in the traditional reservoir model, the paper introduces elasticity into the outer boundary condition, and establishes a nonlinear spherical seepage model for fractal composite reservoir that considers the quadratic pressure gradient, wellbore storage, skin factor and effective radius under the elastic outer boundary condition. The dimensionless bottom-hole pressure in real space is obtained by the process of variable substitution, similar construction method and numerical inversion, while the characteristic curves are plotted to analyze the influence laws of main parameters and elasticity. The results show that the ideal outer boundary conditions previously studied are only special cases of the elastic outer boundary conditions. Furthermore, the elastic outer boundary expands the scope of data interpretation, and makes the model more general. Meanwhile, it can be seen that the similar construction method is simpler and more effective than the traditional methods for solving nonlinear models. In addition, it is further demonstrated that neglecting the quadratic pressure gradient can cause large errors. This study not only provides a new idea for well testing analysis of reservoirs but also for solving more complex seepage models.