Monitoring the width of hydraulic fractures with acoustic waves

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 139-148 ◽  
Author(s):  
Jeroen Groenenboom ◽  
Jacob T. Fokkema
Keyword(s):  
Hydraulic Fracture ◽  
Acoustic Waves ◽  
Direct Determination ◽  
Time Lapse ◽  
Ultrasonic Waves ◽  
Hydraulic Fractures ◽  
Slip Model ◽  
Layer Model ◽  
Incident Wavelength ◽  
Linear Slip Model

During scaled hydraulic fracturing experiments in our laboratory, the fracture growth process is monitored in a time‐lapse experiment with ultrasonic waves. We observe dispersion of compressional waves that have propagated across the hydraulic fracture. This dispersion appears to be related to the width of the hydraulic fracture. This means that we can apply the dispersion measurements to monitor the width of the hydraulic fracture in an indirect manner. For a direct determination of the width, the resolution of the signal is required to distinguish the reflections that are related with two distinct fluid/solid interfaces delimiting the hydraulic fracture from its solid embedding. To make this distinction, the solid/fluid interfaces must be separated at least one eighth of a wavelength and represent sufficient impedance contrast. The applicability of the indirect dispersion measurement method however, extends to a fracture width that is in the order of 1% of the incident wavelength. The time‐lapse ultrasonic measurements allow us to relate the small difference in arrival time and amplitude between two measurements solely to the small changes in the width of the fracture. Additional experimental data show that shear waves are completely shadowed by hydraulic fractures, indicating that there is no acoustic contact mechanism at the fracture interface. Therefore we think it is appropriate to use a thin fluid‐filled layer model for these hydraulic fractures instead of the standard empirically oriented linear slip model. Nevertheless, the thin layer model is consistent with the linear‐slip model, if interpreted correctly. A comparison of width measurements inside the wellbore and width estimates by means of dispersion measurements close to the wellbore shows that the method can be successfully applied, at least under laboratory conditions, and that small changes in the width of the fracture are directly expressed in the dispersion of the transmitted signal. This opens the way for the important new application of width monitoring of hydraulic fractures.

Two-dimensional finite-difference seismic modeling of an open fluid-filled fracture: Comparison of thin-layer and linear-slip models

Geophysics ◽  
2005 ◽  
Vol 70 (4) ◽  
pp. T57-T62 ◽  
Author(s):  
Chunling Wu ◽  
Jerry M. Harris ◽  
Kurt T. Nihei ◽  
Seiji Nakagawa
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Thin Layer ◽  
Computational Cost ◽  
Seismic Wave Propagation ◽  
Thin Layers ◽  
Single Fracture ◽  
Slip Model ◽  
Layer Model ◽  
Linear Slip Model

Within the context of seismic wave propagation, fractures can be described as thin layers or linear-slip interfaces. In this paper, numerical simulations of elastic wave propagation in a medium with a single fracture represented by these two models are performed by 2D finite-difference codes: a variable-grid isotropic code for the thin-layer model and a regular-grid anisotropic code for the linear-slip model. Numerical results show excellent agreement between the two models for wavefields away from the fracture; the only discrepancy between the two is the presence of a slow wave traveling primarily within the fracture fluid of the thin-layer model. The comparison of the computational cost shows that modeling of the linear-slip model is more efficient than that of the thin-layer model. This study demonstrates that the linear-slip model is an efficient and accurate modeling approach for the remote seismic characterization of fractures.

Monitoring hydraulic fracture growth: Laboratory experiments

Geophysics ◽  
2000 ◽  
Vol 65 (2) ◽  
pp. 603-611 ◽  
Author(s):  
Jeroen Groenenboom ◽  
Dirkjan B. van Dam
Keyword(s):  
Shear Wave ◽  
Hydraulic Fracture ◽  
Acoustic Waves ◽  
Laboratory Experiments ◽  
Time Lapse ◽  
Small Scale ◽  
Fracture Characterization ◽  
Fracture Width ◽  
Validation Experiment ◽  
Fracture Growth

We carry out small‐scale hydraulic fracture experiments to investigate the physics of hydraulic fracturing. The laboratory experiments are combined with time‐lapse ultrasonic measurements with active sources using both compressional and shear‐wave transducers. For the time‐lapse measurements we focus on ultrasonic measurement changes during fracture growth. As a consequence we can detect the hydraulic fracture and characterize its shape and geometry during growth. Hence, this paper deals with fracture characterization using time‐lapse acoustic data. During fracture growth the acoustic waves generate diffractions at the tip of the fracture. The direct compressional and shear diffractions are used to locate the position of the tip of the fracture. More detailed analysis of these diffractions can be used to obtain information on the geometry and configuration of the fracture tip, including the creation of a zone that is not penetrated by fluid. Furthermore, it appears that the acoustic diffraction is generated mainly at the fluid front and only weakly at the dry tip. In addition, the wavefield that has been transmitted through the hydraulic fracture is measured. Shear‐wave transmissions are shadowed because the shear modulus vanishes inside the fluid‐filled fracture. From this observation we conclude that the fracture is mechanically open. In other words, no friction occurs related to the movement of fracture faces that are in mechanical contact. Compressional transmissions show a distinctive dispersion relative to the measurement in the unfractured medium. This dispersion can be used to determine the width (or aperture) of the fracture by fitting the measured dispersion with the theoretical prediction as a function of the unknown fracture width. We show that the width profile of the fracture can be reconstructed by using a set of transmission records with different source and receiver locations. By performing a validation experiment, we show that the width determination method is reliable, although the estimated fracture width is only a few percent of the incident wavelength. The strength of the method relies on time‐lapse measurements combined with fitting the changes in the measured waveforms during the experiment. The combination of diffractions and transmissions helps us visualize the dynamic process of hydraulic fracture growth. Hence, acoustic measurements with active sources prove their usefulness for fracture characterization.

Integrated characterization of hydraulic fracture treatments in the Barnett Shale: The Stocker geophysical experiment

2014 ◽  
Vol 2 (2) ◽  
pp. T111-T127 ◽  
Author(s):  
Baishali Roy ◽  
Bruce Hart ◽  
Anastasia Mironova ◽  
Changxi Zhou ◽  
Ulrich Zimmer
Keyword(s):  
Hydraulic Fracture ◽  
Horizontal Wells ◽  
Time Lapse ◽  
Seismic Facies ◽  
Barnett Shale ◽  
Hydraulic Fractures ◽  
Fracture Networks ◽  
Data Set ◽  
Stochastic Inversion ◽  
Wireline Logs

We integrated several independent geophysical and geologic methods to examine the effects of stratigraphic and structural heterogeneities on the growth of hydraulic fracture networks from two horizontal wells in the Barnett Shale, Fort Worth Basin, Texas. Our data set included time-lapse 3D seismic surveys, microseismic data, wireline logs, and distributed temperature sensing (DTS) data. We first created a local stratigraphic framework using wireline logs. In our area, the lower Barnett Shale consists of siliceous mudstones (the primary reservoir) intercalated with carbonate submarine fan deposits. The latter are low porosity (i.e., nonreservoir) and, if thick enough are potential baffles to the growth of hydraulic fractures. We used stochastic inversion to define the 3D distribution of fan lobes with much better resolution than could be obtained using deterministic inversion and obtained a geologically reasonable lithology prediction. The lowest of the fan lobes partially overlies the two horizontal wells, and its limits could be defined using wireline logs, the stochastic inversion, and seismic attributes (e.g., coherence, seismic facies classification). As suggested by the distribution of microseismic events, the extent of this lobe (locally up to 80 ft/24-m-thick) had a significant impact on the growth of the hydraulic fracture networks. The DTS data showed that high production correlates to dense microseismic activity in this area. Our time-lapse seismic analyses suggested that velocity changes induced by the hydraulic injections are detectable, although (largely because of logistical problems) the data were inadequately sampled to quantitatively define these changes. Alone, none of the analyses described herein provided an adequate understanding of the subsurface. However, once integrated, our multidisciplinary work provided a coherent, if still largely qualitative, understanding of the relationships between the geology and the growth of hydraulic fracture networks and some of the geophysical and engineering methods that can be used to define those links.

scholarly journals Numerical simulation of the laws of fracture propagation of multi-hole linear co-directional hydraulic fracturing

2021 ◽  
pp. 014459872198899
Author(s):  
Weiyong Lu ◽  
Changchun He
Keyword(s):  
Hydraulic Fracturing ◽  
Hydraulic Fracture ◽  
Minimum Principle ◽  
Fracture Propagation ◽  
Axial Direction ◽  
Rock Breaking ◽  
Hydraulic Fractures ◽  
Directional Hydraulic Fracturing ◽  
Fracture Intersection ◽  
Expansion Stage

Directional rupture is one of the most important and most common problems related to rock breaking. The goal of directional rock breaking can be effectively achieved via multi-hole linear co-directional hydraulic fracturing. In this paper, the XSite software was utilized to verify the experimental results of multi-hole linear co-directional hydraulic fracturing., and its basic law is studied. The results indicate that the process of multi-hole linear co-directional hydraulic fracturing can be divided into four stages: water injection boost, hydraulic fracture initiation, and the unstable and stable propagation of hydraulic fracture. The stable expansion stage lasts longer and produces more microcracks than the unstable expansion stage. Due to the existence of the borehole-sealing device, the three-dimensional hydraulic fracture first initiates and expands along the axial direction in the bare borehole section, then extends along the axial direction in the non-bare hole section and finally expands along the axial direction in the rock mass without the borehole. The network formed by hydraulic fracture in rock is not a pure plane, but rather a curved spatial surface. The curved spatial surface passes through both the centre of the borehole and the axial direction relative to the borehole. Due to the boundary effect, the curved spatial surface goes toward the plane in which the maximum principal stress occurs. The local ground stress field is changed due to the initiation and propagation of hydraulic fractures. The propagation direction of the fractures between the fracturing boreholes will be deflected. A fracture propagation pressure that is greater than the minimum principle stress and a tension field that is induced in the leading edge of the fracture end, will aid to fracture intersection; as a result, the possibility of connecting the boreholes will increase.

scholarly journals Quantitative evaluation indexes of the spatial steering effect of directional perforation hydraulic fractures

2021 ◽  
pp. 014459872110102
Author(s):  
Lu Weiyong ◽  
He Changchun
Keyword(s):  
Quantitative Evaluation ◽  
Hydraulic Fracture ◽  
Deflection Angle ◽  
Hydraulic Fractures ◽  
Principal Stress Direction ◽  
Perforation Hole ◽  
Evaluation Indexes ◽  
Initiation Pressure ◽  
The Deflection Angle ◽  
Bending Fracture

To better evaluate the spatial steering effect of directional perforation hydraulic fractures, evaluation indexes for the spatial steering effect are first proposed in this paper. Then, these indexes are used to quantitatively evaluate existing physical experimental results. Finally, with the help of RFPA2D-Flow software, the influence of perforation length and azimuth on the spatial steering process of hydraulic fracture are quantitatively analysed using four evaluation indexes. It is shown by the results that the spatial deflection trajectory, deflection distance, deflection angle and initiation pressure of hydraulic fractures can be used as quantitative evaluation indexes for the spatial steering effect of hydraulic fractures. The deflection paths of directional perforation hydraulic fractures are basically the same. They all gradually deflect to the maximum horizontal principal stress direction from the perforation hole and finally represent a double-wing bending fracture. The deflection distance, deflection angle and initiation pressure of hydraulic fractures increase gradually with increasing perforation azimuth, and the sensitivity of the deflection angle to the perforation azimuth of hydraulic fractures also increases. With increasing perforation length, the deflection distance of hydraulic fractures increases gradually. However, the deflection angle and initiation pressure decrease gradually, as does the sensitivity.

scholarly journals Numerical simulation on the simultaneous stress interference of parallel multiple hydraulic fractures

2021 ◽  
pp. 014459872110019
Author(s):  
Weiyong Lu ◽  
Changchun He
Keyword(s):  
Principal Stress ◽  
Hydraulic Fracture ◽  
Stress Ratio ◽  
Fracture Network ◽  
Hydraulic Fractures ◽  
Fracture Spacing ◽  
Induced Stress ◽  
Minimum Principal Stress ◽  
Fracturing Process ◽  
Stress Ratios

During horizontal well staged fracturing, there is stress interference between multiple transverse fractures in the same perforation cluster. Theoretical analysis and numerical calculation methods are applied in this study. We analysed the mechanism of induced stress interference in a single fracture under different fracture spacings and principal stress ratios. We also investigated the hydraulic fracture morphology and synchronous expansion process under different fracture spacings and principal stress ratios. The results show that the essence of induced stress is the stress increment in the area around the hydraulic fracture. Induced stress had a dual role in the fracturing process. It created favourable ground stress conditions for the diversion of hydraulic fractures and the formation of complex fracture network systems, inhibited fracture expansion in local areas, stopped hydraulic fractures, and prevented the formation of effective fractures. The curves of the maximum principal stress, minimum principal stress, and induced principal stress difference with distance under different fracture lengths, different fracture spacings, and different principal stress ratios were consistent overall. With a small fracture spacing and a small principal stress ratio, intermediate hydraulic fractures were difficult to initiate or arrest soon after initiation, fractures did not expand easily, and the expansion speed of lateral hydraulic fractures was fast. Moreover, with a smaller fracture spacing and a smaller principal stress ratio, hydraulic fractures were more prone to steering, and even new fractures were produced in the minimum principal stress direction, which was beneficial to the fracture network communication in the reservoir. When the local stress and fracture spacing were appropriate, the intermediate fracture could expand normally, which could effectively increase the reservoir permeability.

scholarly journals Numerical Study of Elasto-Plastic Hydraulic Fracture Propagation in Deep Reservoirs Using a Hybrid EDFM–XFEM Method

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2610
Author(s):  
Wenzheng Liu ◽  
Qingdong Zeng ◽  
Jun Yao ◽  
Ziyou Liu ◽  
Tianliang Li ◽  
...  
Keyword(s):  
Plastic Deformation ◽  
Iterative Method ◽  
Hydraulic Fracture ◽  
Iterative Procedure ◽  
Fracture Propagation ◽  
Hydraulic Fractures ◽  
Zone Model ◽  
Dilatancy Angle ◽  
Proposed Model ◽  
Hydraulic Fracture Propagation

Rock yielding may well take place during hydraulic fracturing in deep reservoirs. The prevailing models based on the linear elastic fracture mechanics (LEFM) are incapable of describing the evolution process of hydraulic fractures accurately. In this paper, a hydro-elasto-plastic model is proposed to investigate the hydraulic fracture propagation in deep reservoirs. The Drucker–Prager plasticity model, Darcy’s law, cubic law and cohesive zone model are employed to describe the plastic deformation, matrix flow, fracture flow and evolution of hydraulic fractures, respectively. Combining the embedded discrete fracture model (EDFM), extended finite element method (XFEM) and finite volume method, a hybrid numerical scheme is presented to carry out simulations. A dual-layer iterative procedure is developed based on the fixed-stress split method, Picard iterative method and Newton–Raphson iterative method. The iterative procedure is used to deal with the coupling between nonlinear deformation with fracture extension and fluid flow. The proposed model is verified against analytical solutions and other numerical simulation results. A series of numerical cases are performed to investigate the influences of rock plasticity, internal friction angle, dilatancy angle and permeability on hydraulic fracture propagation. Finally, the proposed model is extended to simulate multiple hydraulic fracture propagation. The result shows that plastic deformation can enhance the stress-shadowing effect.

scholarly journals Ultrasonic Waves in Bubbly Liquids: An Analytic Approach

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1309
Author(s):  
P. R. Gordoa ◽  
A. Pickering
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Waves ◽  
Elliptic Functions ◽  
Coupled System ◽  
Ultrasonic Waves ◽  
Partial Differential ◽  
Special Cases ◽  
Spherical Bubbles

We consider the problem of the propagation of high-intensity acoustic waves in a bubble layer consisting of spherical bubbles of identical size with a uniform distribution. The mathematical model is a coupled system of partial differential equations for the acoustic pressure and the instantaneous radius of the bubbles consisting of the wave equation coupled with the Rayleigh–Plesset equation. We perform an analytic analysis based on the study of Lie symmetries for this system of equations, concentrating our attention on the traveling wave case. We then consider mappings of the resulting reductions onto equations defining elliptic functions, and special cases thereof, for example, solvable in terms of hyperbolic functions. In this way, we construct exact solutions of the system of partial differential equations under consideration. We believe this to be the first analytic study of this particular mathematical model.

scholarly journals Non-local dispersion and ultrasonic tunneling in concentrationally graded solids

2019 ◽  
Vol 21 (1) ◽  
pp. 54-62
Author(s):  
A. B. Shvartsburg ◽  
M. D. Malinkovich ◽  
A. M. Kislyuk
Keyword(s):  
Acoustic Waves ◽  
Travelling Waves ◽  
Ultrasonic Waves ◽  
Formal Similarity ◽  
Constant Elasticity ◽  
Transmittance Spectra ◽  
Local Dispersion ◽  
Total Transmission ◽  
Non Local ◽  
Spectral Ranges

The non-local dispersion of longitudinal ultrasonic waves is shown to appear in the heterogeneous solids due to continuous spatial distributions of their density and/or elasticity (gradient solids). This dispersion gives rise to the diversity of ultrasonic transmittance spectra, including the broadband total reflectance plateau, total transmission and tunneling spectral ranges. The ultrasonic wave fields in gradient solids, formed by interference of forward and backward travelling waves as well as by evanescent and antievanescent modes are examined in the framework of exactly solvable models of media with continuously distributed density and elasticity. Examples of transmittance spectra for both metal and semiconductor gradient structures are presented, and the generality of concept of artificial non-local dispersion for gradient composite materials is considered. It should also be noted that the wave equation for acoustic waves in gradient media with a constant elasticity modulus and a certain predetermined density distribution reduces to an equation describing the electromagnetic wave propagation in transparent dielectric media. This formal similarity shows that the concept of nonlocal dispersion is common for both optical and acoustic phenomena, which opens the way to the direct use of physical concepts and exact mathematical solutions, developed for gradient optics, to solve the corresponding acoustic problems.

Sign in / Sign up

Export Citation Format

Share Document