Three-dimensional analytical solution for fluid-saturated transversely isotropic poroelastic multilayer formation

Abstract

According to the potential theory and mirror image method, the three-dimensional (3D) Green's functions of a fluid-saturated transversely isotropic multilayer formation with different thicknesses were first obtained. The exact 3D explicit closed analytical forms of the pressure increment and stress fields were expressed by simple functions which can be used to accurately calculate the full-field distribution under a fluid source. The numerical results reveal that the method had good convergence, high accuracy, and high stability. Based on this method, the effects of the modulus ratio, stratified characteristic, medium thickness, and medium stacking sequence on the 3D hydraulic coupling response of the medium were examined. Numerical results indicated that these parameters affected the behavior of the formation in different degrees. The main contributions of this study are as follows: (1) the anisotropy and stratified characteristic of the formation material are simultaneously considered; (2) the Green's functions are given as a simple explicit function for fluid-saturated multilayer transversely isotropic formation; and (3) the Green's function is a potential function that can be calculated as a boundary element to improve the calculation accuracy.