A Nonlocal Continuum Mechanics Model for Analyzing the Terahertz Flexural Wave Dispersion Characteristics of a Monolayer Graphene Embedded in Elastic Medium

We have developed a model-based processing technique for borehole dipole S-wave logging data to estimate formation shear slowness from the data. During dipole acoustic logging, the presence of the logging tool can significantly affect the dispersion characteristics of flexural waves. Therefore, modeling the effects of the tool is essential for model-based processing. We have determined that an equivalent-tool theory using only two parameters, tool radius, and modulus, can adequately model the flexural-wave-dispersion characteristics. We used this theory, together with a calibration procedure, to determine the tool parameters to formulate an inversion method for the logging data processing. Our use of the equivalent tool theory played an important role in fitting the theoretical dispersion curve to the actual flexural-wave-dispersion data, enabling fast processing of the field acoustic data. An advantage of this model-based method is its prediction power, which, in the absence of low-frequency dispersion data, allows for predicting formation shear slowness from the low-frequency limit of the model-fitted dispersion curve. We have also developed an application procedure of the method for field-data processing and demonstrated its effectiveness in the dispersion correction using field acoustic data from fast and slow formations.

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Mapping formation radial shear-wave velocity variation by a constrained inversion of borehole flexural-wave dispersion data

Geophysics ◽

10.1190/1.3502664 ◽

2010 ◽

Vol 75 (6) ◽

pp. E183-E190 ◽

Cited By ~ 19

Author(s):

Xiao-Ming Tang ◽

Douglas J. Patterson

Keyword(s):

Shear Wave ◽

Wave Velocity ◽

Shear Wave Velocity ◽

High Frequency ◽

Wave Dispersion ◽

Velocity Variation ◽

Flexural Wave ◽

Inversion Method ◽

Dispersion Characteristics ◽

Dispersion Data

We have developed a novel constrained inversion method for estimating a radial shear-wave velocity profile away from the wellbore using dipole acoustic logging data and have analyzed the effect of the radial velocity changes on dipole-flexural-wave dispersion characteristics. The inversion of the dispersion data to estimate the radial changes is inherently a nonunique problem because changing the degree of variation or the radial size of the variation zone can produce similar wave-dispersion characteristics. Nonuniqueness can be solved by developing a constrained inversion method. This is done by constraining the high-frequency portion of the model dispersion curve with another curve calculated using the near-borehole velocity. The constraint condition is based on the physical principle that a high-frequency dipole wave has a shallow penetration depth and is therefore sensitive to the near-borehole shear-wave velocity. We have validated the result of the constrained inversion with synthetic data testing. Combining the new inversion method with four-component crossed-dipole anisotropy processing obtains shear radial profiles in fast and slow shear polarization directions. In a sandstone formation, the fast and slow shear-wave profiles show substantial differences caused by the near-borehole stress field, demonstrating the ability of the technique to obtain radial and azimuthal geomechanical property changes near the wellbore.

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A NONLOCAL CONTINUUM MECHANICS MODEL TO ESTIMATE THE MATERIAL PROPERTY OF SINGLE-WALLED CARBON NANOTUBES

International Journal of Nanoscience ◽

10.1142/s0219581x1250007x ◽

2012 ◽

Vol 11 (01) ◽

pp. 1250007 ◽

Cited By ~ 6

Author(s):

S. NARENDAR ◽

S. GOPALAKRISHNAN

Keyword(s):

Carbon Nanotubes ◽

Continuum Mechanics ◽

Nonlocal Parameter ◽

Nonlocal Theory ◽

Accurate Estimate ◽

Continuum Models ◽

Nonlocal Continuum ◽

Length Scales ◽

Mechanics Model ◽

Carbon Carbon Bond

A subject of current technological interest is that of nanotechnology. It would appear that nonlocal continuum mechanics could potentially play a useful role in analysis related to nanotechnology applications. The present work explores this potential in the context of a specific application. The length scales associated with nanotechnology are often sufficiently small to call the applicability of classical continuum models into question. Atomic and molecular models, while certainly conceptually valid for small length scales, are difficult to formulate accurately and are almost always computationally intensive. Nonlocal continuum models represent attempts to extend the continuum approach to smaller length scales while retaining most of its many advantages. Therefore, continuum models need to be extended to consider the scale effect in nanomaterial studies. This can be accomplished through proposing nonlocal continuum mechanics models, where the internal size scale could be simply considered in constitutive equations as a material parameter. Usually, the magnitude of the nonlocal parameter e0, determines the nonlocal effect in the analysis. The modeling and analyses of nanostructures based on flexural displacement, require an accurate estimate of nonlocal scaling parameter. Such an attempt is made in the present work. From the present analysis, the value of the scale coefficient (e0a, a is carbon-carbon bond length) is recommended to be about 0.11 nm for the application of the nonlocal theory in the analysis of carbon nanotubes.

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