Application of polynomial type elastic outer boundary conditions in fractal composite reservoir seepage model

In this paper, the elastic function in the explanation of elastic outer boundary condition is regarded as polynomial functions of space variable $r$ and time variable $t$, and this is incorporated into the analysis of fractal composite reservoirs. The Laplace space solution the fractal composite reservoir models, which have polynomial elastic outer boundary conditions, is achieved through a modified method of similarity construction and the Gaver-Stehfest numerical inversion technique is used to derive the semi-analytical solutions for the models in actual space. Next, the polynomial elastic function is turned into a first-order function about time variable. Curves of pressure in non-dimensional well bottom under different quadratic pressure gradient terms and primary control factors are drawn by using MATLAB software and their impact on non-dimensional well bottom are analyzed. It is proved that the three impractical outer boundary conditions are only a particular case of the polynomial elastic outer boundary conditions. The research in this paper expands the discussion scope of elastic outer boundary conditions, and has strong reference significance.