Spectral method for modeling waves in cylindrical poroelastic structures.

Abstract

The modeling of propagating modes in poroelastic fluid‐saturated cylindrical structures is important for the interpretation of acoustic and seismic measurements in hydrocarbon wells as well as laboratory measurements on core samples. In order to obtain the velocities of different modes the roots of the appropriate dispersion equation have to be found. This is a very difficult task especially when some layers are represented by poroelastic materials with frequency‐dependent attenuation. A new technique is presented for modeling those modes, which adopts a spectral method to discretize the underlying partial differential equations using Chebyshev differentiation matrices. The corresponding system of linear equations can then be solved as a generalized eigenvalue problem. This means that, for a given frequency, the eigenvalues correspond to the slownesses of different modes. This approach is implemented for an arbitrary number of cylindrical fluid and solid layers as well as poroelastic layers. In addition to the dispersion, the attenuation curves are computed as well as radial profiles of displacements and stresses for various frequencies. The resulting approach can be used to model wave propagations in open and completed boreholes surrounded by permeable formations. This can pave the way to invert for formation and completion permeability from acoustic measurements.