Analytical study of fluid flow modeling by diffusivity equation including the quadratic pressure gradient term

摘要

Diffusivity equation which can provide us with the pressure distribution, is a Partial Differential Equation (PDE) describing fluid flow in porous media. The quadratic pressure gradient term in the diffusivity equation is nearly neglected in hydrology and petroleum engineering problems such as well test analysis. When a compressible liquid is injected into a well at high pressure gradient or when the reservoir possess a small permeability value, the effect of ignoring this term increases. In such cases, neglecting this parameter can result in high errors. Previous models basically focused on numerical and semi-analytical methods for semi-infinite domain. To the best of our knowledge, no analytical solution has yet been developed to consider the quadratic terms in diffusivity PDE of one-dimensional unsteady state fluid flow in rectangular coordinates and finite length.