US 11,567,228 B2 · Acoustic dispersion curve identification based on reciprocal condition number

Abstract

To generate dispersion curves for acoustic waves in a radially layered system, a matrix M containing solutions to the wave equation subject to the boundary conditions of the system is constructed. The reciprocal condition number (RCN) of the matrix M is determined as a function of acoustic wave frequency and slowness. The local minima of the RCN in the frequency-slowness plane produces the dispersion curves corresponding to allowable acoustic modes in the system. A sensitivity analysis which identifies the dispersion curves dependent on a selected parameter. The dispersion curves independent of the perturbed parameters are eliminated by perturbing the modeling parameters and generating the RCN of the perturbed matrix M and then subtracting the RCN values of the unperturbed matrix M, leaving the dispersion curves that exhibit dependence on the selected parameter.

Claims20

Dependent claims

A method comprising:

detecting, by one or more acoustic sensors, acoustic waves within a formation;
obtaining, by a dispersion curve generator, a matrix M of functions based, at least in part, on first acoustic wave equations for an m layer system corresponding to a combination of the formation and a wellbore in the formation, wherein the first acoustic wave equations represent the acoustic waves;
determining, by the dispersion curve generator, at least one of a condition number and a reciprocal condition number of the matrix M as a function of frequency and slowness;
generating, by the dispersion curve generator, dispersion curves as a function of frequency and slowness based on local minima of the reciprocal condition number of the matrix M;
and
determining one or more petrophysical properties of the formation based on the dispersion curves.

3 more elements

One or more non-transitory machine-readable media comprising program code for generating dispersion curves, the program code to:

detect, by one or more acoustic sensors, acoustic waves within a formation;
generate, by a dispersion curve generator, a matrix M of functions based, at least in part, on first acoustic wave equations for an m layer system corresponding to a combination of the formation and a wellbore in the formation, wherein the first acoustic wave equations represent the acoustic waves;
determine, by the dispersion curve generator, at least one of a condition number and a reciprocal condition number of the matrix M as a function of frequency and slowness;
generate, by the dispersion curve generator, dispersion curves as a function of frequency and slowness based on local minima of the reciprocal condition number of the matrix M;
and
determine one or more petrophysical properties of the formation based on the dispersion curves.

3 more elements

An apparatus comprising:

a processor;
and
a machine-readable medium having program code executable by the processor to cause the apparatus to,
detect, by one or more acoustic sensors, acoustic waves within a formation;
generate, by a dispersion curve generator, a matrix M of functions based, at least in part, on first acoustic wave equations for an m layer system corresponding to the formation and a wellbore in the formation, wherein the first acoustic wave equations represent the acoustic waves;
determine, by the dispersion curve generator, at least one of a condition number and a reciprocal condition number of the matrix M as a function of frequency and slowness;
generate, by the dispersion curve generator, dispersion curves as a function of frequency and slowness based on local minima of the reciprocal condition number of the matrix M;
and
determine one or more petrophysical properties of the formation based on the dispersion curves.

6 more elements

Dependencies are inferred from the claim text.

Acoustic dispersion curve identification based on reciprocal condition number

Life of this patent

Acoustic dispersion curve identification based on reciprocal condition number

Life of this patent

Abstract

Claims20