scholarly journals Numerical study of the effect of cement defects on flexural-wave logging

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. D171-D177
Author(s):  
Ruolong Song ◽  
Hefeng Dong ◽  
Xueshan Bao
Keyword(s):  
Group Velocity ◽  
Numerical Study ◽  
Staggered Grid ◽  
Flexural Wave ◽  
Burial Depth ◽  
Flexural Waves ◽  
Wave Technique ◽  
Bond Evaluation ◽  
Pulse Echo ◽  
Leaky Lamb Wave

Cement-bond evaluation is needed for new wells and plug and abandonment activities. The ultrasonic leaky Lamb-wave (also called the flexural-wave) technique, in combination with the pulse-echo technique, has been widely used for cement-quality evaluation. Using a 2D time-domain staggered-grid stress-velocity finite-difference methodology, we have numerically investigated the attenuation and group velocity of flexural waves, and the scattering from defects, in the presence of a water-filled void in the cement annulus. The position, length, thickness, and burial depth of a defect are considered. The numerical study suggests that the combination of the attenuation and group velocity of the flexural wave allows for a discrimination between solids and liquids. The scattering from voids can be used to indicate the existence of a hidden defect, which cannot be detected by using the attenuation and group velocity if it is located larger than 5 mm away from the casing. The void signatures can even be used to characterize the geometry of the defect for neat cement. The numerical results provide improved understanding of flexural-wave logging results.

Fast and slow interaction of elastic waves with platonic clusters

2011 ◽  
Vol 467 (2136) ◽  
pp. 3509-3529 ◽  
Author(s):  
Michael H. Meylan ◽  
Ross C. McPhedran
Keyword(s):  
Elastic Waves ◽  
Early Time ◽  
Approximate Solutions ◽  
Wave Profile ◽  
Flexural Wave ◽  
Flexural Waves ◽  
Analytical Extension ◽  
Scattering Of Elastic Waves ◽  
Classical Models ◽  
The Time Domain

We study the scattering of elastic waves by platonic clusters in the time domain, both for plane wave excitations and for a specified initial wave profile. We show that we can use an analytical extension of our problem to calculate scattering frequencies of the solution. These allow us to calculate approximate solutions that give the flexural wave profile accurately in and around the cluster for large times. We also discuss the early-time behaviour of flexural waves in terms of the classical models of Sommerfeld and Brillouin.

scholarly journals Numerical Study on Surface Roughness Measurement Based on Nonlinear Ultrasonics in Through-Transmission and Pulse-Echo Modes

Materials ◽  
2021 ◽  
Vol 14 (17) ◽  
pp. 4855
Author(s):  
Maodan Yuan ◽  
Anbang Dai ◽  
Lin Liao ◽  
Yan Chen ◽  
Xuanrong Ji
Keyword(s):  
Surface Roughness ◽  
Numerical Study ◽  
Material Model ◽  
Nonlinearity Parameter ◽  
Fe Model ◽  
Roughness Measurement ◽  
Monitoring Method ◽  
Surface Roughness Measurement ◽  
Nonlinear Ultrasonics ◽  
Pulse Echo

Ultrasonic is one of the well-known methods for surface roughness measurement, but small roughness will only lead to a subtle variation of transmission or reflection. To explore sensitive techniques for surfaces with small roughness, nonlinear ultrasonic measurement in through-transmission and pulse-echo modes was proposed and studied based on an effective unit-cell finite element (FE) model. Higher harmonic generation in solids was realized by applying the Murnaghan hyperelastic material model. This FE model was verified by comparing the absolute value of the nonlinearity parameter with the analytical solution. Then, random surfaces with different roughness values ranging from 0 μm to 200 μm were repeatedly generated and studied in the two modes. The through-transmission mode is very suitable to measure the surfaces with roughness as small as 3% of the wavelength. The pulse-echo mode is sensitive and effective to measure the surface roughness ranging from 0.78% to 5.47% of the wavelength. This study offers a potential nondestructive testing and monitoring method for the interfaces or inner surfaces of the in-service structures.

scholarly journals Elastic properties of floating sea ice from air-coupled flexural waves

2021 ◽  
Author(s):  
Rowan Romeyn ◽  
Alfred Hanssen ◽  
Bent Ole Ruud ◽  
Tor Arne Johansen
Keyword(s):  
Sea Ice ◽  
Elastic Properties ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Flexural Wave ◽  
Ice Thickness ◽  
Linear Filter ◽  
Flexural Stiffness ◽  
Flexural Waves ◽  
Impulsive Source

Abstract. Air-coupled flexural waves appear as wave trains of constant frequency that arrive in advance of the direct air-wave from an impulsive source travelling over a floating ice sheet. The frequency of these waves varies with the flexural stiffness of the ice sheet, which is controlled by a combination of thickness and elastic properties. We develop a theoretical framework to understand these waves, utilizing modern numerical and Fourier methods to give a simpler and more accessible description than the pioneering, yet unwieldly analytical efforts of the 1950's. Our favoured dynamical model can be understood in terms of linear filter theory and is closely related to models used to describe the flexural waves produced by moving vehicles on floating plates. We find that air-coupled flexural waves are a robust feature of floating ice-sheets excited by impulsive sources over a large range of thicknesses, and we present a simple closed-form estimator for the ice thickness. Our study is focussed on first-year sea ice of ~20–80 cm thickness in Van Mijenfjorden, Svalbard, that was investigated through active source seismic experiments over four field campaigns in 2013, 2016, 2017 and 2018. The air-coupled flexural frequencies for sea-ice in this thickness range are ~60–240 Hz. While air-coupled flexural waves for thick sea-ice have received little attention, the higher frequencies associated with thin ice on fresh water lakes and rivers are well known to the ice-skating community and have been reported in popular media. Estimation of ice physical properties, following the approach we present, may allow improved surface wave modelling and wavefield subtraction in reflection seismic studies where flexural wave noise is undesirable. On the other hand, air-coupled flexural waves may also permit non-destructive continuous monitoring of ice thickness and flexural stiffness using simple, relatively inexpensive microphones located in the vicinity of the desired measurement location, either above the ice-sheet or along the shoreline. In this case, naturally forming cracks in the ice may be an appropriate impulsive source capable of exciting flexural waves in floating ice sheets in a passive monitoring context.

Quaternion-based anisotropic inversion for flexural waves in horizontal transverse isotropic formations with unmatched sources: A synthetic example

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. A69-A74 ◽  
Author(s):  
Fuqiang Zeng ◽  
Wenzheng Yue ◽  
Chao Li
Keyword(s):  
Structural Information ◽  
Amplitude Ratio ◽  
Flexural Wave ◽  
Data Sets ◽  
Flexural Waves ◽  
P Waves ◽  
Source Type ◽  
Transverse Isotropic ◽  
Sonic Logging ◽  
Incident Waves

The anisotropy of elastic waves has been widely used to obtain structural information on formations in geosciences research. Flexural wave splitting is generally applied to evaluate anisotropy with geophysical inversion methods. Cross-dipole sonic logging has been widely used for anisotropic inversions in horizontal transverse isotropic formations. Traditional methods assume that fast and slow flexural waves are similar in shape and are not dispersive and that the radiation characteristics of the two orthogonal dipole sources are identical. The two above assumptions cannot be satisfied in field conditions. Therefore, the methods used in anisotropy inversion based on these assumptions will lead to inaccurate results. The introduction of the amplitude ratio (AR), the ratio of slow to fast flexural waves, which is not dependent on the source type, can eliminate the wave-shape assumption. Two data sets from orthogonally oriented receivers can be constructed as a quaternion array. Fast and slow flexural waves are the two main incident waves, and other arrivals such as P-waves can be taken as noise. The AR and a quaternion multiple signal classification algorithm are used to demonstrate how to improve the anisotropic inversion and avoid these assumptions. Compared with the traditional method, the new method presents better inversion results for the synthetic example with two different sources. We have determined that the inversion residual from the new objective function can be used to indicate the inversion quality.

scholarly journals Creating the Coupled Band Gaps in Piezoelectric Composite Plates by Interconnected Electric Impedance

Materials ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 1656 ◽  
Author(s):  
Lin Li ◽  
Zhou Jiang ◽  
Yu Fan ◽  
Jun Li
Keyword(s):  
Band Gap ◽  
Piezoelectric Materials ◽  
Composite Plates ◽  
Forced Response ◽  
Band Gaps ◽  
Piezoelectric Composite ◽  
Flexural Wave ◽  
Response Analysis ◽  
Flexural Waves ◽  
Single Wave

In this paper, we investigate the coupled band gaps created by the locking phenomenon between the electric and flexural waves in piezoelectric composite plates. To do that, the distributed piezoelectric materials should be interconnected via a ‘global’ electric network rather than the respective ‘local’ impedance. Once the uncoupled electric wave has the same wavelength and opposite group velocity as the uncoupled flexural wave, the desired coupled band gap emerges. The Wave Finite Element Method (WFEM) is used to investigate the evolution of the coupled band gap with respect to propagation direction and electric parameters. Further, the bandwidth and directionality of the coupled band gap are compared with the LR and Bragg gaps. An indicator termed ratio of single wave (RSW) is proposed to determine the effective band gap for a given deformation (electric, flexural, etc.). The features of the coupled band gap are validated by a forced response analysis. We show that the coupled band gap, despite directional, can be much wider than the LR gap with the same overall inductance. This might lead to an alternative to adaptively create band gaps.

Numerical simulation of the Late Jurassic closure of the Vardar Tethys

2021 ◽  
Author(s):  
Nikola Stanković ◽  
Vesna Cvetkov ◽  
Vladica Cvetković
Keyword(s):  
Boundary Conditions ◽  
Numerical Simulations ◽  
Stokes Equations ◽  
Numerical Study ◽  
Phase Evolution ◽  
Staggered Grid ◽  
Second Phase ◽  
Weak Zone ◽  
Ongoing Research ◽  
Magmatic Complex

<p>We report updated results of our ongoing research on constraining geodynamic conditions associated with the final closure of the Vardar branch of the Tethys Ocean by means of application of numerical simulations (previous interim results reported in EGU2020-5919).</p><p>The aim of our numerical study is to test the hypothesis that a single eastward subduction in the Jurassic is a valid explanation for the occurrence of three major, presently observed geological entities that are left behind after the closure of the Vardar Tethys. These include: ophiolite-like igneous rocks of the Sava-Vardar zone and presumably subduction related Timok Magmatic Complex, both Late Cretaceous in age as well as Jurassic ophiolites obducted onto the Adriatic margin. In our simulations we initiate an intraoceanic subduction in the Early/Middle Jurassic, which eventually transitions into an oceanic closure and subsequent continental collision processes.</p><p>In the scope of our study numerical simulations are performed by solving a set of partial differential equations: the continuity equation, the Navier-Stokes equations and the temperature equation. To this end we used I2VIS thermo-mechanical code which utilizes marker in cell approach with finite difference discretization of equations on a staggered grid [Gerya et al., 2000; Gerya&Yuen, 2003].</p><p>The 2D model consists of two continental plates separated by two oceanic slabs connected at a mid-oceanic ridge. Intraoceanic subduction is initiated along the ridge by assigning a weak zone beneath the ridge. Time-dependent boundary conditions for velocity are imposed on the simulation in order to model a transient spreading period. The change of sign in plate velocities is found to be useful for both obtaining obduction / ophiolite emplacement [Duretz et al., 2016] and causing back-arc extension. Changes in velocities are linear in time. Simulations follow a three-phase evolution of velocity boundary conditions consisting of two convergent phases separated by a single divergent phase where spreading regime is dominant. Effect of duration and magnitude of the second phase on model evolution is also explored.</p><p>Our so far obtained simulations were able to reproduce the westward obduction and certain extension processes along the active (European) margin, which match the existing geological relationships. However, the simulations involve an unreasonably short geodynamic event (cca 15-20 My) and we are working on solving this problem with new simulations. </p>

Experimental and Numerical Study of Transport Phenomena in a Simulated Hydrothermal Crystal Growth System of Fluid-Saturated Porous Layer

2000 ◽  
Author(s):  
D. Mishra ◽  
A. Pal ◽  
N. Nemick ◽  
A. K. Saha ◽  
V. Prasad ◽  
...  
Keyword(s):  
Temperature Field ◽  
Porous Layer ◽  
Hydrothermal System ◽  
Numerical Study ◽  
Transport Phenomena ◽  
Composite Layer ◽  
Staggered Grid ◽  
Working Fluid ◽  
Hydrothermal Crystal Growth ◽  
Numerical Predictions

Abstract A simulated, non-pressurized hydrothermal system consisting of a fluid-superposed porous layer is fabricated and used for visualization and measurement of the temperature field using liquid crystal thermography. The system is used for various boundary conditions with pure glycerine as the working fluid and the porous layer is made of 3mm diameter glass beads. Experimental data is recorded using a color CCD camera and flow visualization is obtained through a long exposure video photography. A calibration is performed to relate the temperature with scattered colors at an orthogonal angle to the incoming white light sheet. Quantitative temperature data is obtained through this calibration and compared with the numerical predictions. For numerical studies the system is modeled as a composite layer of fluid and porous charge using the Darcy-Brinkman-Forchheimer flow model. A two-dimensional curvilinear algorithm using finite volume technique with a non-staggered grid is used to simulate the temperature field and transport phenomena for various Rayleigh–Darcy number combinations of varying aspect ratio. The results, for the first time, make an attempt towards understanding the transport process in hydrothermal system through both numerical simulation and experimental validation.

Numerical Study of Density-Currents Using the Non-Staggered Grid Fractional-Step-Method

2000 ◽  
Author(s):  
J. Rafael Pacheco ◽  
Arturo Pacheco-Vega ◽  
Sigfrido Pacheco-Vega
Keyword(s):  
Numerical Study ◽  
Density Variation ◽  
Staggered Grid ◽  
Mapping Technique ◽  
Fractional Step ◽  
Density Currents ◽  
Step Method ◽  
Fractional Step Method ◽  
New Approach ◽  
Flow Equations

Abstract A new approach for the solution of time-dependent calculations of buoyancy driven currents is presented. This method employs the idea that density variation can be pursued by using markers distributed in the flow field. The analysis based on the finite difference technique with the non-staggered grid fractional step method is used to solve the flow equations written in terms of primitive variables. The physical domain is transformed to a rectangle by means of a numerical mapping technique. The problems analyzed include two-fluid flow in a tank with sloping bottom and colliding density currents. The numerical experiments performed show that this approach is efficient and robust.

scholarly journals Study of Abnormal Group Velocities in Flexural Metamaterials

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Hong Woo Park ◽  
Joo Hwan Oh
Keyword(s):  
Group Velocity ◽  
Periodic Structure ◽  
Three Dimensional ◽  
Wave Dispersion ◽  
Abnormal Behavior ◽  
Flexural Wave ◽  
Negative Group ◽  
One Dimensional ◽  
Optical Branch ◽  
Negative Group Velocity

Abstract Generally, it has been known that the optical branch of a simple one-dimensional periodic structure has a negative group velocity at the first Brillouin zone due to the band-folding effect. However, the optical branch of the flexural wave in one-dimensional periodic structure doesn’t always have negative group velocity. The problem is that the condition whether the group velocity of the flexural optical branch is negative, positive or positive-negative has not been studied yet. In consequence, who try to achieve negative group velocity has suffered from trial-error process without an analytic guideline. In this paper, the analytic investigation for this abnormal behavior is carried out. In particular, we discovered that the group velocity of the optical branch in flexural metamaterials is determined by a simple condition expressed in terms of a stiffness ratio and inertia ratio of the metamaterial. To derive the analytic condition, an extended mass-spring system is used to calculate the wave dispersion relationship in flexural metamaterials. For the validation, various numerical simulations are carried out, including a dispersion curve calculation and three-dimensional wave simulation. The results studied in this paper are expected to provide new guidelines in designing flexural metamaterials to have desired wave dispersion curves.

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