Similar construction method for non-Newtonian power-law fluid seepage models with elastic outer boundary conditions

In oil and gas engineering, non-Newtonian fluids are universal. Thus, studies on the seepage laws of non-Newtonian power-law fluids are of great importance and significance. In this paper, we introduced the definition of elastic coefficient based on the establishing elastic outer boundary conditions. We then set up a homogeneous well test model for non-Newtonian power-law fluids under elastic outer boundary conditions, considering wellbore reservoir and skin effect. The Laplace space solution of the bottom hole pressure was obtained using the similar structure method, and the double logarithmic characteristic curve was drawn using the Stehfest numerical inversion technique. Furthermore, the main parameters affecting the characteristic curve were analyzed. The experimental results showed that the early phase of the homogeneous well test curve can be affected by the wellbore storage coefficient. In addition, the mid-term seepage is greatly influenced by the power-law flow exponent and the skin factor, while the elastic coefficient predominantly acts on the later phase of fluid flow. We concluded that the introduction of the elastic outer boundary expands the traditional fixed form of ideal outer boundary conditions, enabling a more general representation of the seepage model. This approach provides a more effective theoretical basis for further exploration of the seepage law of the reservoir. Meanwhile, we simplify the calculation process of the solution model by the use of the similar structure method of the solution and point out a new research direction for solving the more complex seepage model.