Scattering by hydraulic fractures: Finite‐difference modeling and laboratory data

Geophysics ◽  
2000 ◽  
Vol 65 (2) ◽  
pp. 612-622 ◽  
Author(s):  
Jeroen Groenenboom ◽  
Joachim Falk
Keyword(s):  
Finite Difference ◽  
Hydraulic Fracture ◽  
Large Scale ◽  
Seismic Waves ◽  
Laboratory Data ◽  
Small Scale ◽  
Hydraulic Fractures ◽  
Grid Spacing ◽  
Fine Grid ◽  
Arrival Times

Reservoir production can be stimulated by creating hydraulic fractures that effectively facilitate the inflow of hydrocarbons into a well. Considering the effectiveness and safety of the operation, it is desirable to monitor the size and location of the fracture. In this paper we investigate the possibilities of using seismic waves generated by active sources to characterize the fractures. First, we must understand the scattering of seismic waves by hydraulic fractures. For that purpose we use a finite‐difference modeling scheme. We argue that a mechanically open hydraulic fracture can be represented by a thin, fluid‐filled layer. The width or aperture of the fracture is often small compared to the seismic wavelength, which forces us to use a very fine grid spacing to define the fracture. Based on equidistant grids, this results in a large number of grid points and hence computationally expensive problems. We show that this problem can be overcome by allowing for a variation in grid spacing in the finite‐difference scheme to accommodate the large‐scale variation in such a model. Second, we show ultrasonic data of small‐scale hydraulic fracture experiments in the laboratory. At first sight it is difficult to unravel the interpretation of the various events measured. We use the results of the finite‐difference modeling to postulate various possible events that might be present in the data. By comparing the calculated arrival times of these events with the laboratory and finite‐difference data, we are able to propose a plausible explanation of the set of scattering events. Based on the laboratory data, we conclude that active seismic sources can potentially be used to determine fracture size and location in the field. The modeling example of fracture scattering illustrates the benefit of the finite‐difference technique with a variation in grid spacing for comparing numerical and physical experiments.

2-D random media with ellipsoidal autocorrelation functions

Geophysics ◽  
1993 ◽  
Vol 58 (9) ◽  
pp. 1359-1372 ◽  
Author(s):  
L. T. Ikelle ◽  
S. K. Yung ◽  
F. Daube
Keyword(s):  
Aspect Ratio ◽  
Seismic Data ◽  
Random Media ◽  
Large Scale ◽  
Seismic Waves ◽  
Homogeneous Medium ◽  
Small Scale ◽  
Arrival Times ◽  
The Earth ◽  
Pulse Arrival

The integration of surface seismic data with borehole seismic data and well‐log data requires a model of the earth which can explain all these measurements. We have chosen a model that consists of large and small scale inhomogeneities: the large scale inhomogeneities are the mean characteristics of the earth while the small scale inhomogeneities are fluctuations from these mean values. In this paper, we consider a two‐dimensional (2-D) model where the large scale inhomogeneities are represented by a homogeneous medium and small scale inhomogeneities are randomly distributed inside the homogeneous medium. The random distribution is characterized by an ellipsoidal autocorrelation function in the medium properties. The ellipsoidal autocorrelation function allows the parameterization of small scale inhomogeneities by two independent autocorrelation lengths a and b in the horizontal and the vertical Cartesian directions, respectively. Thus we can describe media in which the inhomogeneities are isotropic (a = b), or elongated in a direction parallel to either of the two Cartesian directions (a > b, a < b), or even taken to infinite extent in either dimension (e.g., a = infinity, b = finite: a 1-D medium) by the appropriate choice of the autocorrelation lengths. We also examine the response of seismic waves to this form of inhomogeneity. To do this in an accurate way, we used the finite‐difference technique to simulate seismic waves. Special care is taken to minimize errors due to grid dispersion and grid anisotropy. The source‐receiver configuration consists of receivers distributed along a quarter of a circle centered at the source point, so that the angle between the source‐receiver direction and the vertical Cartesian direction varies from 0 to 90 degrees. Pulse broadening, coda, and anisotropy (transverse isotropy) due to small scale inhomogeneities are clearly apparent in the synthetic seismograms. These properties can be recast as functions of the aspect ratio [Formula: see text] of the medium, especially the anisotropy and coda. For media with zero aspect ratio (1-D media), the coda energy is dominant at large angles. The coda energy gradually becomes uniformly distributed with respect to angle as the aspect ratio increases to unity. Our numerical results also suggest that, for small values of aspect ratio, the anisotropic behavior (i.e., the variations of pulse arrival times with angle) of the 2-D random media is similar to that of a 1-D random medium. The arrival times agree with the effective medium theory. As the aspect ratio increases to unity, the variations of pulse arrival times with angle gradually become isotropic. To retain the anisotropic behavior beyond the geometrical critical angle, we have used a low‐frequency pulse with a nonzero dc component.

scholarly journals Dynamic Loads and Response of a Spar Buoy Wind Turbine with Pitch-Controlled Rotating Blades: An Experimental Study

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3598
Author(s):  
Sara Russo ◽  
Pasquale Contestabile ◽  
Andrea Bardazzi ◽  
Elisa Leone ◽  
Gregorio Iglesias ◽  
...  
Keyword(s):  
Wind Speed ◽  
Wind Turbine ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Laboratory Data ◽  
Nonlinear Behavior ◽  
Offshore Wind ◽  
Small Scale ◽  
Wave Steepness ◽  
Design Factor

New large-scale laboratory data are presented on a physical model of a spar buoy wind turbine with angular motion of control surfaces implemented (pitch control). The peculiarity of this type of rotating blade represents an essential aspect when studying floating offshore wind structures. Experiments were designed specifically to compare different operational environmental conditions in terms of wave steepness and wind speed. Results discussed here were derived from an analysis of only a part of the whole dataset. Consistent with recent small-scale experiments, data clearly show that the waves contributed to most of the model motions and mooring loads. A significant nonlinear behavior for sway, roll and yaw has been detected, whereas an increase in the wave period makes the wind speed less influential for surge, heave and pitch. In general, as the steepness increases, the oscillations decrease. However, higher wind speed does not mean greater platform motions. Data also indicate a significant role of the blade rotation in the turbine thrust, nacelle dynamic forces and power in six degrees of freedom. Certain pairs of wind speed-wave steepness are particularly unfavorable, since the first harmonic of the rotor (coupled to the first wave harmonic) causes the thrust force to be larger than that in more energetic sea states. The experiments suggest that the inclusion of pitch-controlled, variable-speed blades in physical (and numerical) tests on such types of structures is crucial, highlighting the importance of pitch motion as an important design factor.

scholarly journals Characteristics of shallow thermally driven flow in the complex topography of the south-eastern Adriatic

2010 ◽  
Vol 28 (10) ◽  
pp. 1905-1922 ◽  
Author(s):  
M. T. Prtenjak ◽  
I. Tomažić ◽  
I. Kavčič ◽  
S. Đivanović
Keyword(s):  
Large Scale ◽  
Sea Breeze ◽  
Small Scale ◽  
The South ◽  
Fine Grid ◽  
Easterly Wind ◽  
Sodar Data ◽  
South Eastern ◽  
The North ◽  
Convergence Zones

Abstract. Characteristics of thermally induced flow, namely the sea breeze, are investigated along the south-eastern Adriatic. The chosen period 24–25 April 2006 favoured sea breeze development and simultaneously allowed a comparison of the large-scale wind influence (north-westerly wind versus south-easterly wind) and the complex terrain on the local circulations. Particular attention is paid to the small-scale formation of the wind field, convergence zones (CZs), channelling flows and small scale eddies, especially in the vicinity of two airports in the central part of south-eastern Adriatic. The results are based on wind measurements (from meteorological surface stations, radiosoundings, satellite data and sodar data) and further supplemented by model data at fine grid spacing. This study shows the formation of numerous irregular daytime and nighttime CZs, which occurred along the coastline in the lee of mountains and over the larger, elongated islands. The results show that the above mentioned airports are surrounded by daytime CZ formations within the lowermost 1000 m and associated updrafts of 1 m s−1, especially if CZs are maintained by the north-westerly large-scale winds. Whereas the daytime CZ was generated due to merged sea breezes, the weaker and shallower nighttime CZs were formed by wind convergence of the seaward breezes, and significantly modified by the large-scale flow of the topography (e.g., accelerated flow in the sea channels and substantial swirled flows around the islands). The passes between the coastal mountain peaks changed the inflow penetration, provoking the increase in wind speed of the channelled flow. The strongest sea breeze channelling was observed above the valley of the Neretva River, where the onshore flow reached 40 km inland with a strength of 8 m s−1, and the highly asymmetric offshore part was confined within the sea channel.

Experiments on surface deformation arising from a subsurface fracture

1995 ◽  
Vol 32 (6) ◽  
pp. 1024-1034 ◽  
Author(s):  
Gang Wang ◽  
Maurice B. Dusseault ◽  
Jerzy T. Pindera
Keyword(s):  
Large Scale ◽  
Surface Deformation ◽  
Scale Effects ◽  
Model Simulation ◽  
Laboratory Data ◽  
Nonlinear Problems ◽  
Laboratory Simulation ◽  
Scale Model ◽  
Laboratory Model ◽  
Hydraulic Fractures

Laboratory model simulation of large-scale earth processes is rarely undertaken because of scale effects, nonlinearity, and questions of representativeness with respect to the real case. Hydraulic fractures generate distortion fields that can be measured with high precision both in the laboratory and in the field. A combination of field and laboratory data allows us to test our ability to measure displacements, make forward predictions, and invert real measurements; thus it is important to have some means of simulation, other than purely numerical simulation. This paper contains the results of a set of experiments on the surface deformation arising from a pressurized fracture, using laser holography and Fizeau interferometry of noncontacting techniques to precisely sample the displacement field above a scale model. The results are remarkably accurate and consistent, and compare reasonably well with analytical and numerical model predictions. The techniques have potential applications in geomechanics and geotechnical engineering for laboratory study of various linear and nonlinear problems. Key words : laboratory simulation, holographic, Fizeau interferometry, hydrofractures.

scholarly journals Sea-ice deformation in a coupled ocean–sea-ice model and in satellite remote sensing data

2017 ◽  
Vol 11 (4) ◽  
pp. 1553-1573 ◽  
Author(s):  
Gunnar Spreen ◽  
Ron Kwok ◽  
Dimitris Menemenlis ◽  
An T. Nguyen
Keyword(s):  
Sea Ice ◽  
Power Law ◽  
Large Scale ◽  
Remote Sensing Data ◽  
Satellite Observations ◽  
Small Scale ◽  
Grid Spacing ◽  
Model Solutions ◽  
Realistic Representation ◽  
The Right

Abstract. A realistic representation of sea-ice deformation in models is important for accurate simulation of the sea-ice mass balance. Simulated sea-ice deformation from numerical simulations with 4.5, 9, and 18 km horizontal grid spacing and a viscous–plastic (VP) sea-ice rheology are compared with synthetic aperture radar (SAR) satellite observations (RGPS, RADARSAT Geophysical Processor System) for the time period 1996–2008. All three simulations can reproduce the large-scale ice deformation patterns, but small-scale sea-ice deformations and linear kinematic features (LKFs) are not adequately reproduced. The mean sea-ice total deformation rate is about 40 % lower in all model solutions than in the satellite observations, especially in the seasonal sea-ice zone. A decrease in model grid spacing, however, produces a higher density and more localized ice deformation features. The 4.5 km simulation produces some linear kinematic features, but not with the right frequency. The dependence on length scale and probability density functions (PDFs) of absolute divergence and shear for all three model solutions show a power-law scaling behavior similar to RGPS observations, contrary to what was found in some previous studies. Overall, the 4.5 km simulation produces the most realistic divergence, vorticity, and shear when compared with RGPS data. This study provides an evaluation of high and coarse-resolution viscous–plastic sea-ice simulations based on spatial distribution, time series, and power-law scaling metrics.

3D Elastic finite-difference modeling of seismic motion using staggered grids with nonuniform spacing

1999 ◽  
Vol 89 (1) ◽  
pp. 54-68
Author(s):  
Arben Pitarka
Keyword(s):  
Finite Difference ◽  
Large Scale ◽  
Sampling Rate ◽  
Point Sources ◽  
Staggered Grid ◽  
Uniform Grid ◽  
Grid Spacing ◽  
Nonuniform Grids ◽  
Velocity Models ◽  
Finite Fault

Abstract This article provides a technique to model seismic motions in 3D elastic media using fourth-order staggered-grid finite-difference (FD) operators implemented on a mesh with nonuniform grid spacing. The accuracy of the proposed technique has been tested through comparisons with analytical solutions, conventional 3D staggered-grid FD with uniform grid spacing, and reflectivity methods for a variety of velocity models. Numerical tests with nonuniform grids suggest that the method allows sufficiently accurate modeling when the grid sampling rate is at least 6 grid points per shortest shear wavelength. The applicability for a finite fault with non-uniform distribution of point sources is also confirmed. The use of nonuniform spacing improves the efficiency of the FD methods when applied to large-scale structures by partially avoiding the spatial oversampling introduced by the uniform spacing in zones with high velocity. The significant reduction in computer memory that can be obtained by the new technique improves the efficiency of the 3D-FD method at handling shorter wavelengths, larger areas, or more realistic 3D velocity structures.

scholarly journals Experimental and Numerical Investigation on Basic Law of Dense Linear Multihole Directional Hydraulic Fracturing

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Xin Zhang ◽  
Yuqi Zhang
Keyword(s):  
Hydraulic Fracturing ◽  
Hydraulic Fracture ◽  
Large Scale ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
In Situ Stress ◽  
Hydraulic Fractures ◽  
Directional Hydraulic Fracturing ◽  
Basic Law

Using the dense linear multihole to control the directional hydraulic fracturing is a significant technical method to realize roof control in mining engineering. By combining the large-scale true triaxial directional hydraulic fracturing experiment with the discrete element numerical simulation experiment, the basic law of dense linear holes controlling directional hydraulic fracturing was studied. The results show the following: (1) Using the dense linear holes to control directional hydraulic fracturing can effectively form directional hydraulic fractures extending along the borehole line. (2) The hydraulic fracturing simulation program is very suitable for studying the basic law of directional hydraulic fracturing. (3) The reason why the hydraulic fracture can be controlled and oriented is that firstly, due to the mutual compression between the dense holes, the maximum effective tangential tensile stress appears on the connecting line of the drilling hole, where the hydraulic fracture is easy to be initiated. Secondly, due to the effect of pore water pressure, the disturbed stress zone appears at the tip of the hydraulic fracture, and the stress concentration zone overlaps with each other to form the stress guiding strip, which controls the propagation and formation of directional hydraulic fractures. (4) The angle between the drilling line and the direction of the maximum principal stress, the in situ stress, and the hole spacing has significant effects on the directional hydraulic fracturing effect. The smaller the angle, the difference of the in situ stress, and the hole spacing, the better the directional hydraulic fracturing effect. (5) The directional effect of synchronous hydraulic fracturing is better than that of sequential hydraulic fracturing. (6) According to the multihole linear codirectional hydraulic fracturing experiments, five typical directional hydraulic fracture propagation modes are summarized.

Core Phases Observed with AlpArray

2020 ◽  
Author(s):  
On Ki Angel Ling ◽  
Simon Stähler ◽  
Domenico Giardini ◽  
Kasra Hosseini ◽  
The AlpArray Working Group
Keyword(s):  
Large Scale ◽  
Seismic Waves ◽  
Incidence Angle ◽  
Body Wave ◽  
Sampling Rate ◽  
European Alps ◽  
S Wave ◽  
Arrival Times ◽  
The Core ◽  
Ray Path

&lt;p&gt;In most seismic tomographic models, the first P and/or S wave data generated by regional and teleseismic events are used to conduct tomographic inversion. Despite the abundance and precise measurement of the first body wave arrival times, the non-uniform distribution of their ray path leads to a lower resolution in the mantle below 1000km in depth. Curiously, there are particularly few ray paths sampling the lowermost mantle below dense seismic arrays, due to the limited incidence angle range of P and S waves. Previous studies have demonstrated the importance of core phases, resulting from reflection and/or conversion of seismic waves at the core discontinuities, in seismic tomography by improving the ray path coverage and constraining the structures in the lower mantle. Therefore, adding core-grazing phases (Pdiff, Sdiff) as well as core phases (e.g. PKP, PKIKP, SKS) in tomography could deliver high-resolution tomographic images of deep mantle structures in poorly resolved regions and may even reveal undiscovered features.&lt;/p&gt;&lt;p&gt;To increase the topographic resolution in the Alpine region, the AlpArray Initiative deployed about 250 temporary stations alongside the local permanent stations in the European Alps forming a greater AlpArray seismic network. This large-scale network provides a dense sampling rate and high-quality seismic data across the region, which gives us a unique opportunity to observe core phases coming from all directions in such a large aperture. We investigate the visibility of core phases observed with AlpArray and find that it is uniquely suited to observe high order core phases (P&amp;#8217;P&amp;#8217;, PcPPcPPKP, PKPPKPPKP) from sources in Alaska, Japan, and Sumatra in a distance range of 60-110 degrees. We show some array processing methods to improve the resolution of seismic observation and examine the waveforms in different frequency ranges. We find significant deviations in core phase amplitudes from predictions which are most likely linked to other structures directly above the core mantle boundary and can serve to test tomographic models in this depth region. The insight gained from this modelling is used to discuss the usability of core phases in future tomographic studies.&lt;/p&gt;

scholarly journals Experimental Study on Crack Extension Rules of Hydraulic Fracturing Based on Simulated Coal Seam Roof and Floor

Geofluids ◽  
2022 ◽  
Vol 2022 ◽  
pp. 1-12
Author(s):  
Lu Gao ◽  
Xiangtao Kang ◽  
Gun Huang ◽  
Ziyi Wang ◽  
Meng Tang ◽  
...  
Keyword(s):  
Coal Seam ◽  
Hydraulic Fracturing ◽  
Principal Stress ◽  
Hydraulic Fracture ◽  
Large Scale ◽  
Confining Pressure ◽  
Maximum Principal Stress ◽  
Hydraulic Fractures ◽  
True Triaxial ◽  
Extension Direction

Hydraulic fracturing can increase the fracture of coal seams, improve the permeability in the coal seam, and reduce the risk of coal and gas outburst. Most of the existing experimental specimens are homogeneous, and the influence of the roof and floor on hydraulic fracture expansion is not considered. Therefore, the hydraulic fracturing test of the simulated combination of the coal seam and the roof and floor under different stress conditions was carried out using the self-developed true triaxial coal mine dynamic disaster large-scale simulation test rig. The results show that (1) under the condition of triaxial unequal pressure, the hydraulic fractures are vertical in the coal seam, and the extension direction of hydraulic fractures in the coal seam will be deflected, with the increase of the ratio of the horizontal maximum principal stress to the horizontal minimum principal stress. The angle between the extension direction of the hydraulic fracture and the horizontal maximum principal stress decreases. (2) Under the condition of triaxial equal confining pressure, the extension of hydraulic fractures in the coal seam are random, and the hydraulic fracture will expand along the dominant fracture surface and form a unilateral expansion fracture when a crack is formed. (3) When the pressure in one direction is unloaded under the condition of the triaxial unequal pressure, the hydraulic fractures in the coal seam will reorientate, and the cracks will expand in the direction of the decreased confining pressure, forming almost mutually perpendicular turning cracks.

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