Hydraulic-Fracture-Width Inversion Using Low-Frequency Distributed-Acoustic-Sensing Strain Data Part II: Extension for Multifracture and Field Application

SPE Journal ◽  
2021 ◽  
pp. 1-13
Author(s):  
Yongzan Liu ◽  
Ge Jin ◽  
Kan Wu ◽  
George Moridis
Keyword(s):  
Low Frequency ◽  
Accurate Estimation ◽  
Rate Data ◽  
Inversion Algorithm ◽  
Fracture Width ◽  
Strain Measurements ◽  
Strain Data ◽  
Measured Strain ◽  
Distributed Acoustic Sensing ◽  
The Individual

Summary Low-frequency distributed-acoustic-sensing (LF-DAS) strain data are direct measurements of in-situ rock deformation during hydraulic-fracturing treatments. In addition to monitoring fracture propagation and identifying fracture hits, quantitative strain measurements of LF-DAS provide opportunities to quantify fracture geometries. Recently, we proposed a Green’s function–based algorithm for the inversion of LF-DAS strain data (Liu et al. 2020b) that shows an accurate estimation of fracture width near the monitor well with single-cluster completions. However, multicluster completions with tighter cluster spacings are more commonly adopted in recent completion designs. One main challenge in the inversion of LF-DAS strain data under such circumstances is that strain measurements at fracture-hit locations by LF-DAS are not reliable, which makes the individual contribution of each fracture to the measured strain data indistinguishable. In this study, we first extended the inversion algorithm to handle multiple fractures, investigated the uncertainties of the inversion results, and proposed possible mitigation to the challenges raised by completion designs and field data acquisition through a synthetic case study. Ideally, there are available data on both sides of each fracture so that the inverted width of each fracture can be obtained with a negligible error. In reality, the strain data are usually limited, providing less constraint on the width of individual fracture. Nevertheless, the inversion results provide an accurate estimation of the width summation of all fractures. To evaluate the individual fracture width, a time-dependent constraint is added to the inversion algorithm. We assume that the width at the current timestep is dependent on the width at the previous step and the width variation between the two timesteps. The width variation can be roughly estimated from LF-DASstrain-rate data at the fracture-hit location. This extra constraint helps to improve the inversion performance. Finally, a field example is presented. We show the width summation of all fractures and the width of each individual fracture as a function of treatment time. The time-dependent width profiles show consistent trends with the LF-DASstrain-rate data. The calculated strains from the inverted model match well with the LF-DAS measured strain data. The findings demonstrate the potential of LF-DAS data for quantitative hydraulic-fracture characterization and provide insights on better use of LF-DAS data. The direct information on fracture width helps to calibrate fracturing models and optimize the completion designs.

Quantitative Hydraulic-Fracture Geometry Characterization with LF-DAS Strain Data: Numerical Analysis and Field Applications

2021 ◽  
Author(s):  
Yongzan Liu ◽  
Ge Jin ◽  
Kan Wu ◽  
George Moridis
Keyword(s):  
Hydraulic Fracture ◽  
True Strain ◽  
Low Frequency ◽  
Forward Model ◽  
Inversion Algorithm ◽  
Fracture Geometry ◽  
Fracture Width ◽  
True Value ◽  
Strain Data ◽  
Fracture Height

Abstract Low-frequency distributed acoustic sensing (LF-DAS) has been used for hydraulic fracture monitoring and characterization. Large amounts of DAS data have been acquired across different formations. The low-frequency components of DAS data are highly sensitive to mechanical strain changes. Forward geomechanical modeling has been the focus of current research efforts to better understand the LF-DAS signals. Moreover, LF-DAS provides the opportunity to quantify fracture geometry. Recently, Liu et al. (2020a;2020b) proposed an inversion algorithm to estimate hydraulic fracture width using LF-DAS data measured during multifracture propagation. The LF-DAS strain data is linked to the fracture widths through a forward model developed based on the Displacement Discontinuity Method (DDM). In this study, we firstly investigated the impacts of fracture height on the inversion results through a numerical case with a four-cluster completion design. Then we discussed how to estimate the fracture height based on the inversion results. Finally, we applied the inversion algorithm to two field examples. The inverted widths are not sensitive to the fracture height. In the synthetic case, the maximum relative error is less than 10% even when the fracture height is two times of the true value. After obtaining the fracture width, the fracture height can be estimated by matching the true strain data under various heights with a strong smooth weight. The error between the calculated strain and true strain decreases as the height is getting close to the true value. In the two field examples, the temporal evolutions of both width summation of all fractures and the width of each fracture show consistent behaviors with the field LF-DAS measurements. The calculated strain data from the forward model matches well with the field LF-DAS strain data. The results demonstrate the robustness and accuracy of the proposed inversion algorithm.

Rock Deformation and Strain-Rate Characterization during Hydraulic Fracturing Treatments: Insights for Interpretation of Low-Frequency Distributed Acoustic-Sensing Signals

SPE Journal ◽  
2020 ◽  
Vol 25 (05) ◽  
pp. 2251-2264
Author(s):  
Yongzan Liu ◽  
Kan Wu ◽  
Ge Jin ◽  
George Moridis
Keyword(s):  
Strain Rate ◽  
Low Frequency ◽  
Fracture Propagation ◽  
Height Growth ◽  
Rock Deformation ◽  
Fracture Characterization ◽  
Fracture Width ◽  
Distributed Acoustic Sensing ◽  
Fracture Height ◽  
Specific Fracture

Summary Low-frequency distributed acoustic-sensing (LF-DAS) data are promising attributes for detecting fracture hits and fracture characterization. However, measured signals from different wells exhibiting various characteristics and mechanisms attributing to the difference are not well understood, which makes the interpretation of field LF-DAS data most challenging. In this study, our in-house hydraulic fracturing simulator is used to simulate fracture propagation. The induced rock deformation and corresponding strain-rate variations along offset monitor wells are analyzed and related to specific fracture features. The mechanisms for LF-DAS signals are investigated through five synthetic case studies with single fracture propagation. A typical strain-rate waterfall plot of LF-DAS measurements during the fluid injection phase of a fracturing treatment can be divided into two distinct regions. A heart-shaped extending region forms as the fracture approaches to the monitor well, indicating that the magnitude of extension keeps increasing as the fracture tip gets closer to the monitor well. After the fracture hits the monitor well, the extending region shrinks to a line (the field-measured data may be a wide band, depending on the spatial resolution of the measurement), and a two-wing compressing zone is observed, illustrating large compressional strain variations on both sides of the fracture. As the fracture continues propagating, the strain rate tends to be stable, the characteristics of which depend on specific fracture geometry and propagation conditions. The size and shape of observable signatures on LF-DAS data are directly influenced by fracture width, height, and height growth. Larger fracture width results in larger sizes of heart-shaped extending region and two-wing compressing region in the strain-rate waterfall plot. Larger fracture height also induces a larger heart-shaped extending region before the fracture hits. However, a fracture with larger height could lead to larger extension along the fiber near the fracture, which results in less overall compression and a zone of decreasing compression in the vicinity of the fracture as the fracture propagates away from the fiber after the fracture hit. This signature is more pronounced when the fracture height growth is considered. The interpretation of a field example with four clusters based on our forward physical modeling results indicates that, although the distinct signatures of field data are not as obvious as the simulation results because of low measurement resolution and unavoidable noise, they do convey valuable information on fracture characteristics. There is a shrinkage of the extending zone from a heart shape to a band at the fracture-hit time. During simultaneous multifracture propagation, fracture-hit time of each fracture, which determines the fracture propagation speed and perforation efficiency, can be identified. The discontinuous extending band after fracture hit could be attributed to the intermittent stop and restart of fracture propagation and relative fracture opening/closing. The results of this study help to better interpret the real-time LF-DAS data and provide critical insights into hydraulic fracture characterization using LF-DAS data.

Collective oscillations in bubble clouds

2011 ◽  
Vol 680 ◽  
pp. 114-149 ◽  
Author(s):  
ZORANA ZERAVCIC ◽  
DETLEF LOHSE ◽  
WIM VAN SAARLOOS
Keyword(s):  
Frequency Response ◽  
Acoustic Field ◽  
Low Frequency ◽  
Acoustic Energy ◽  
Viscous Damping ◽  
Edge States ◽  
Bubble Cloud ◽  
Collective Oscillations ◽  
The Individual ◽  
Bubble Oscillations

In this paper the collective oscillations of a bubble cloud in an acoustic field are theoretically analysed with concepts and techniques of condensed matter physics. More specifically, we will calculate the eigenmodes and their excitabilities, eigenfrequencies, densities of states, responses, absorption and participation ratios to better understand the collective dynamics of coupled bubbles and address the question of possible localization of acoustic energy in the bubble cloud. The radial oscillations of the individual bubbles in the acoustic field are described by coupled linearized Rayleigh–Plesset equations. We explore the effects of viscous damping, distance between bubbles, polydispersity, geometric disorder, size of the bubbles and size of the cloud. For large enough clusters, the collective response is often very different from that of a typical mode, as the frequency response of each mode is sufficiently wide that many modes are excited when the cloud is driven by ultrasound. The reason is the strong effect of viscosity on the collective mode response, which is surprising, as viscous damping effects are small for single-bubble oscillations in water. Localization of acoustic energy is only found in the case of substantial bubble size polydispersity or geometric disorder. The lack of localization for a weak disorder is traced back to the long-range 1/r interaction potential between the individual bubbles. The results of the present paper are connected to recent experimental observations of collective bubble oscillations in a two-dimensional bubble cloud, where pronounced edge states and a pronounced low-frequency response had been observed, both consistent with the present theoretical findings. Finally, an outlook to future possible experiments is given.

scholarly journals Speech Identification with Temporal and Spectral Modification in Subjects with Auditory Neuropathy

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Vijaya Kumar Name ◽  
C. S. Vanaja
Keyword(s):  
Signal Processing ◽  
Speech Processing ◽  
Word Identification ◽  
Low Frequency ◽  
Auditory Neuropathy ◽  
Study Word ◽  
Spectral Modification ◽  
The Individual ◽  
High Pass ◽  
Speech Identification

Background. The aim of this study was to investigate the individual effects of envelope enhancement and high-pass filtering (500 Hz) on word identification scores in quiet for individuals with Auditory Neuropathy. Method. Twelve individuals with Auditory Neuropathy (six males and six females) with ages ranging from 12 to 40 years participated in the study. Word identification was assessed using bi-syllabic words in each of three speech processing conditions: unprocessed, envelope-enhanced, and high-pass filtered. All signal processing was carried out using MATLAB-7. Results. Word identification scores showed a mean improvement of 18% with envelope enhanced versus unprocessed speech. No significant improvement was observed with high-pass filtered versus unprocessed speech. Conclusion. These results suggest that the compression/expansion signal processing strategy enhances speech identification scores—at least for mild and moderately impaired individuals with AN. In contrast, simple high-pass filtering (i.e., eliminating the low-frequency content of the signal) does not improve speech perception in quiet for individuals with Auditory Neuropathy.

Hole-Drilling Residual Stress Profiling With Automated Smoothing

2007 ◽  
Vol 129 (3) ◽  
pp. 440-445 ◽  
Author(s):  
Gary S. Schajer
Keyword(s):  
Residual Stress ◽  
A Priori ◽  
Hole Drilling ◽  
Simple Method ◽  
Strain Measurements ◽  
Stress Solution ◽  
Strain Data ◽  
Data Content ◽  
Small Increments ◽  
Priori Information

An effective procedure is presented that allows stable hole-drilling residual stress calculations using strain data from measurements taken at many small increments of hole depth. This use of many strain measurements is desirable because it improves the data content of the calculation, and the statistical reliability of the residual stress results. The use of Tikhonov regularization to reduce the noise sensitivity that is characteristic of a fine-increment calculation is described. This mathematical procedure is combined with the Morozov criterion to identify the optimal amount of regularization that balances the competing tendencies of noise reduction and stress solution distortion. A simple method is described to estimate the standard error in the strain measurements so that the optimal regularization can be chosen automatically. The possible use of a priori information about the trend of the expected solution is also discussed as a further means of improving the stress solution. The application of the described method is demonstrated with some experimental measurements, and realistic results are obtained.

Strain Measurement by X-ray Diffraction Methods

1949 ◽  
Vol 1 (3) ◽  
pp. 211-224
Author(s):  
G. B. Greenough
Keyword(s):  
Strain Measurement ◽  
Plastic Anisotropy ◽  
Stress And Strain ◽  
Routine Method ◽  
X Ray Diffraction ◽  
Strain Measurements ◽  
X Ray ◽  
The Past ◽  
Polycrystalline Metals ◽  
The Individual

SummaryMany papers have been written on the measurement of strain by X-ray diffraction methods and on the interpretation of these strains in terms of stresses. Whereas, during the past few years, the experimental methods of determining the strains have. remained largely unchanged, research has shown that the older techniques for calculating stresses from strains are not always valid.In this paper an attempt is made to describe some of the principles of strain measurement by X-ray diffraction methods to those who are unfamiliar with the methods. The types of stress and strain systems which may exist in polycrystalline metals are then considered, particular attention being paid to the effect of the elastic and plastic anisotropy of the individual crystals. Some indication is given as to how the earlier methods of interpreting X-ray strain measurements should be modified, but no rigid routine method is proposed for use in a general case.

Measurement of Dynamic Strain

1943 ◽  
Vol 10 (2) ◽  
pp. A85-A92
Author(s):  
C. O. Dohrenwend ◽  
W. R. Mehaffey
Keyword(s):  
High Speed ◽  
Shock Loading ◽  
Low Frequency ◽  
Dynamic Strain ◽  
Time Axis ◽  
Low Frequencies ◽  
Strain Measurements ◽  
Moving Vehicles ◽  
Machine Parts ◽  
Dynamic Strains

Abstract The measurement of dynamic strains of both high and low frequency give rise to a variety of problems in instrumentation. Two types of equipment and circuits designed and used by the authors are discussed in detail. The first type based on the amplitude-modulated method is for low frequencies from zero to about 15 per cent of the carrier frequency of 1025 cycles per sec. The equipment has application to strain measurements varying from static values to those produced in moving vehicles, various machine parts, structures such as crane bridges, in fact all strain measurements where the frequency is 150 cycles per sec or less. The second type of equipment discussed is a potentiometer type and is for high-frequency strain measurements from 100 cycles per sec to 8000 cycles per sec. This high-speed equipment is conveniently used for impact strain, such as produced in hammer blows, shock loading, forging equipment, and impact-factor determination. Both units are designed to be used with a cathode-ray oscillograph which lends itself to a variety of recording methods. The methods discussed include both the type where the time axis is obtained by sweeping the oscilloscope beam on a stationary film and where the time axis is obtained mechanically.

Combining Distributed Acoustic Sensing and Beamforming in a Volcanic Environment on Mount Meager, British Columbia.

2021 ◽  
Author(s):  
Sara Klaasen ◽  
Patrick Paitz ◽  
Jan Dettmer ◽  
Andreas Fichtner
Keyword(s):  
British Columbia ◽  
Power Distribution ◽  
High Frequency ◽  
Low Frequency ◽  
Volcanic Tremor ◽  
Extreme Environment ◽  
Volcanic Complex ◽  
Acoustic Sensing ◽  
Distributed Acoustic Sensing ◽  
Volcanic Environment

<p>We present one of the first applications of Distributed Acoustic Sensing (DAS) in a volcanic environment. The goals are twofold: First, we want to examine the feasibility of DAS in such a remote and extreme environment, and second, we search for active volcanic signals of Mount Meager in British Columbia (Canada). </p><p>The Mount Meager massif is an active volcanic complex that is estimated to have the largest geothermal potential in Canada and caused its largest recorded landslide in 2010. We installed a 3-km long fibre-optic cable at 2000 m elevation that crosses the ridge of Mount Meager and traverses the uppermost part of a glacier, yielding continuous measurements from 19 September to 17 October 2019.</p><p>We identify ~30 low-frequency (0.01-1 Hz) and 3000 high-frequency (5-45 Hz) events. The low-frequency events are not correlated with microseismic ocean or atmospheric noise sources and volcanic tremor remains a plausible origin. The frequency-power distribution of the high-frequency events indicates a natural origin, and beamforming on these events reveals distinct event clusters, predominantly in the direction of the main peaks of the volcanic complex. Numerical examples show that we can apply conventional beamforming to the data, and that the results are improved by taking the signal-to-noise ratio of individual channels into account.</p><p>The increased data quantity of DAS can outweigh the limitations due to the lower quality of individual channels in these hazardous and remote environments. We conclude that DAS is a promising tool in this setting that warrants further development.</p>

HEART RATE VARIABILITY RELATED TO N95 RESPIRATOR USE IN INTERNS DURING COVID-19 PANDEMIC

2021 ◽  
pp. 69-70
Author(s):  
Pakanati Sujana ◽  
Venkata Mahesh Gandhavalla ◽  
K. Prabhakara Rao
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Low Frequency ◽  
Protective Equipment ◽  
Short Term ◽  
Non Invasive ◽  
Critical Components ◽  
The Individual ◽  
N95 Respirators ◽  
Respiratory Droplets

Introduction: COVID19 is caused by SARS-CoV-2 which is primarily transmitted through respiratory droplets and contact routes. WHO recommended the use of personal protective equipment (PPE) for prevention and N95 respirators are critical components of PPE. Breathing through N95 respirator will impart stress in the individual and that can be assessed by heart rate variability (HRV). HRV measures the variation in time between each heartbeat controlled by autonomic nervous system (ANS), which is a non invasive reliable index to identify the ANS imbalances. Aims And Objectives: This study is aimed at assessing the HRV of Interns working in COVID19 wards using N95 respirators. Methodology: This study included 100 interns in whom short term HRV was recorded using the standard protocol. Lead II of ECG was recorded using AD instruments (ADI) 8channel polygraph and HRV was analysed using Labchart 8pro software. The recordings were taken before and 1hour after wearing N95 respirator. Results: Overall HRV (SDRR) was found to decrease signicantly after wearing N95 respirator for 1hr (p=0.000). Similarly, indices representing the parasympathetic component ( RMSSD and HF ) were also found to decrease signicantly with the use of N95 respirator. Low frequency (LF) power and LF/HF ratio increased signicantly with N95 respirator use (p=0.000). Conclusion: We conclude that using N95 respirator increased sympathetic activity reecting decreased HRV in our subjects Hence we recommend that it is better to change the duty pattern for interns.

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