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Equivalent Modelling For Perturbation Analysis

IP.com Disclosure Number: IPCOM000241975D
Publication Date: 2015-Jun-11

Publishing Venue

The IP.com Prior Art Database

Abstract

Equivalent modelling for perturbation analysis is provided. In one possible implementation, an equivalent model can be constructed in which an artificial boundary (such as, for example, a rigid boundary) can be put inside a formation beyond a region of perturbations to trap leaky energy. In one possible aspect, an equivalence between a new model and an original model can be defined in terms of dispersion slowness. Also, in one possible implementation, a radial position of the artificial boundary can be a function of frequency for a particular dispersion curve.

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EQUIVALENT MODELLING FOR PERTURBATION ANALYSIS

                    BACKGROUND
[0001] Forward modelling of borehole dispersion curves can be conducted in the presence of a scanning tool in a cased-hole surrounded by a slow formation. In such a scenario, dispersions like the Stoneley and the dipole flexural dispersions can become leaky. Together with leaky modes (such as leaky compressional dispersions from monopole and dipole), energy can be radiated into the formation such that the displacement fields, as well as the stress and strain fields, can radially grow to infinity. This can result in conditions that preclude the use of existing perturbation theory both to compute the dispersion curves for radially varying formations, and to model where other kinds of heterogeneities exist.

                     SUMMARY
[0002] Equivalent modelling for perturbation analysis is provided. In one possible implementation, an equivalent model can be constructed in which an artificial boundary (such as, for example, a rigid boundary) can be put inside a formation beyond a region of perturbations to trap leaky energy. In one possible aspect, an equivalence between a new model and an original model can be defined in terms of dispersion slowness. Also, in one possible implementation, a radial position of the artificial boundary can be a function of frequency for a particular dispersion curve.

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           BRIEF DESCRIPTION OF THE DRAWINGS
[0003] Fig. 1 illustrates an example configuration of a fluid-filled cased borehole in the presence of a scanner tool surrounded by a homogeneous formation with an artificial rigid boundary;

[0004] Fig. 2 illustrates an example radial position of the artificial boundary of the equivalent model as a function of frequency for the leaky dispersion modes;

[0005] Fig. 3 illustrates an example comparison of the leaky dispersions between the original and the equivalent models for the model of a fluid-filled cased borehole;

[0006] Fig. 4 illustrates an example radial profile;

[0007] Fig. 5 illustrates an example comparison of the leaky dispersions of a monopole source between mode-search results using the original model and the perturbation analysis result using the equivalent models for the model of a fluid-filled cased borehole;

[0008] Fig. 6 illustrates an example comparison of the leaky dispersions of a dipole source between mode-search result using the original model and the perturbation analysis result using the equivalent models for the model of a fluid- filled cased borehole;

[0009] Fig. 7 illustrates an example radial profile;

[0010] Fig. 8 illustrates an example comparison of the leaky dispersions of a monopole source between mode-search results using the original model and the perturbation analysis result using the equivalent models for the model of a

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fluid-filled cased borehole;

[0011] Fig. 9 illustrates an example comparison of the leaky dispersions of a dipole source between mode-search result using the original model and the perturb...