Linear filtration waves in a layered heterogeneous formation

Abstract

Solutions to the problem of a filtration-wave pressure field in a layered inhomogeneous medium with a pressure pulse specified on the left boundary are obtained. The problem statement contains a two-dimensional wave equation in the central layer, a wave equation that takes into account the predominance of vertical motion in the environment, symmetry conditions in the center of the formation, equality of pressures and flows at the interfaces, the absence of disturbances of the filtration wave field at the initial moment of time and at an infinite distance from the source of disturbance. The article found an exact solution to the problem obtained using the Laplace–Carson and the Fourier transform of sine, an asymptotic solution and an exact solution for the special case of a homogeneous medium. It is shown that when the formal parameter tends to zero, the exact solution coincides with the main asymptotic approximation. The tendency of the thickness of the central layer to infinity reduces the solution for a layered inhomogeneous medium to an expression describing the pressure fields in a homogeneous medium. Spatiotemporal dependencies describing the dynamics of the pressure pulse in layered inhomogeneous and homogeneous media were constructed, and the general properties and features of linear filtration waves in layered inhomogeneous and homogeneous layers were studied.