Hydraulic fracture diagnostics from Krauklis-wave resonance and tube-wave reflections

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. D171-D186 ◽  
Author(s):  
Chao Liang ◽  
Ossian O’Reilly ◽  
Eric M. Dunham ◽  
Dan Moos
Keyword(s):  
Hydraulic Fracture ◽  
Guided Waves ◽  
Navier Stokes ◽  
Fracture Aperture ◽  
Navier Stokes Equation ◽  
Fracture Geometry ◽  
Hydraulic Impedance ◽  
Resonance Frequencies ◽  
Tube Wave ◽  
Viscous Boundary

Fluid-filled fractures support guided waves known as Krauklis waves. The resonance of Krauklis waves within fractures occurs at specific frequencies; these frequencies, and the associated attenuation of the resonant modes, can be used to constrain the fracture geometry. We use numerical simulations of wave propagation along fluid-filled fractures to quantify fracture resonance. The simulations involve solution of an approximation to the compressible Navier-Stokes equation for the viscous fluid in the fracture coupled to the elastic-wave equation in the surrounding solid. Variable fracture aperture, narrow viscous boundary layers near the fracture walls, and additional attenuation from seismic radiation are accounted for in the simulations. We then determine how tube waves within a wellbore can be used to excite Krauklis waves within fractures that are hydraulically connected to the wellbore. The simulations provide the frequency-dependent hydraulic impedance of the fracture, which can then be used in a frequency-domain tube-wave code to model tube-wave reflection/transmission from fractures from a source in the wellbore or at the wellhead (e.g., water hammer from an abrupt shut-in). Tube waves at the resonance frequencies of the fracture can be selectively amplified by proper tuning of the length of a sealed section of the wellbore containing the fracture. The overall methodology presented here provides a framework for determining hydraulic fracture properties via interpretation of tube-wave data.

scholarly journals Lattice Numerical Simulations of Hydraulic Fracture Propagation and Their Geometry Evolution in Transversely Isotropic Formations

2021 ◽  
Vol 9 ◽  
Author(s):  
Dezhi Qiu ◽  
Jun Zhang ◽  
Yinhe Lin ◽  
Jinchuan Liu ◽  
Minou Rabiei ◽  
...  
Keyword(s):  
Hydraulic Fracture ◽  
Numerical Models ◽  
Fractured Reservoirs ◽  
Fracture Propagation ◽  
Propagation Mechanism ◽  
Fracture Aperture ◽  
Natural Interfaces ◽  
Fracture Geometry ◽  
Hf Propagation ◽  
The Impact

Accurate prediction of the fracture geometry before the operation of a hydraulic fracture (HF) job is important for the treatment design. Simplified planar fracture models, which may be applicable to predict the fracture geometry in homogeneous and continuous formations, fail in case of fractured reservoirs and laminated formations such as shales. To gain a better understanding of the fracture propagation mechanism in laminated formations and their vertical geometry to be specific, a series of numerical models were run using XSite, a lattice-based simulator. The results were studied to understand the impact of the mechanical properties of caprock and injection parameters on HF propagation. The tensile and shear stimulated areas were used to determine the ability of HF to propagate vertically and horizontally. The results indicated that larger caprock Young’s modulus increases the stimulated area (SA) in both vertical and horizontal directions, whereas it reduces the fracture aperture. Also, larger vertical stress anisotropy and tensile strength of caprock and natural interfaces inhibit the horizontal fracture propagation with an inconsiderable effect in vertical propagation, which collectively reduces the total SA. It was also observed that an increased fluid injection rate suppresses vertical fracture propagation with an insignificant effect on horizontal propagation. The dimensionless parameters defined in this study were used to characterize the transition of HF propagation behavior between horizontal and vertical HFs.

Intrinsic anisotropy in fracture permeability

2015 ◽  
Vol 3 (3) ◽  
pp. ST43-ST53 ◽  
Author(s):  
Mehdi Mokhtari ◽  
Azra N. Tutuncu ◽  
Gregory N. Boitnott
Keyword(s):  
Fluid Dynamics ◽  
Fluid Flow ◽  
Hydraulic Fracture ◽  
Numerical Data ◽  
Fracture Aperture ◽  
Fracture Permeability ◽  
Fracture Geometry ◽  
Mechanical Fracture ◽  
Proppant Transport ◽  
Intrinsic Anisotropy

Contrary to the assumption in cubic law, the surface of fractures has some degree of roughness, which impacts their fluid dynamics. Incorporating the effect of roughness can improve the simulation of fluid flow in fractures and faults, as well as proppant transport in hydraulic fracturing. To investigate the effect of roughness on the fluid flow, we created a fracture using the Brazilian test, and its roughness was measured using a laser profilometer. Experimental permeability measurements showed a reduction in permeability as the effective stress increased. However, the unmatching surfaces of the fracture prevented its complete mechanical closure. Numerical simulations of the fluid dynamics were conducted on the measured fracture geometry. We determined that the hydraulic fracture aperture is less than the mechanical fracture aperture and that there was anisotropy in the fracture permeability. The ratio of hydraulic fracture aperture to mechanical fracture aperture, as well as anisotropy in fracture permeability, increased when the fracture aperture decreased. The anisotropy in fracture permeability was 45% at the lowest simulated fracture aperture. Integrating the experimental and numerical data, we estimated the fracture porosity and fracture permeability.

Data Analytics to Help Improve Hydraulic Fracture Geometry Prediction Using Support Vector Regression: Case Study

2020 ◽  
Author(s):  
Avinash Wesley ◽  
Bharat Mantha ◽  
Ajay Rajeev ◽  
Aimee Taylor ◽  
Mohit Dholi ◽  
...  
Keyword(s):  
Support Vector Regression ◽  
Hydraulic Fracture ◽  
Data Analytics ◽  
Support Vector ◽  
Fracture Geometry

scholarly journals An Incompressible Polymer Fluid Interacting with a Koiter Shell

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Dominic Breit ◽  
Prince Romeo Mensah
Keyword(s):  
Moving Boundary ◽  
Classical Model ◽  
Elastic Shell ◽  
Planck Equation ◽  
Navier Stokes ◽  
Flexible Shell ◽  
Navier Stokes Equation ◽  
Shell System ◽  
Forward Equation ◽  
Polymer Fluid

AbstractWe study a mutually coupled mesoscopic-macroscopic-shell system of equations modeling a dilute incompressible polymer fluid which is evolving and interacting with a flexible shell of Koiter type. The polymer constitutes a solvent-solute mixture where the solvent is modelled on the macroscopic scale by the incompressible Navier–Stokes equation and the solute is modelled on the mesoscopic scale by a Fokker–Planck equation (Kolmogorov forward equation) for the probability density function of the bead-spring polymer chain configuration. This mixture interacts with a nonlinear elastic shell which serves as a moving boundary of the physical spatial domain of the polymer fluid. We use the classical model by Koiter to describe the shell movement which yields a fully nonlinear fourth order hyperbolic equation. Our main result is the existence of a weak solution to the underlying system which exists until the Koiter energy degenerates or the flexible shell approaches a self-intersection.

scholarly journals Effects of Salt Tracer Volume and Concentration on Residence Time Distribution Curves for Characterization of Liquid Steel Behavior in Metallurgical Tundish

Metals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 430
Author(s):  
Changyou Ding ◽  
Hong Lei ◽  
Hong Niu ◽  
Han Zhang ◽  
Bin Yang ◽  
...  
Keyword(s):  
Residence Time ◽  
Time Distribution ◽  
Residence Time Distribution ◽  
Mass Concentration ◽  
Distribution Curve ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Residence Time Distribution Curve ◽  
Tracer Solution ◽  
Time Distribution Curve

The residence time distribution (RTD) curve is widely applied to describe the fluid flow in a tundish, different tracer mass concentrations and different tracer volumes give different residence time distribution curves for the same flow field. Thus, it is necessary to have a deep insight into the effects of the mass concentration and the volume of tracer solution on the residence time distribution curve. In order to describe the interaction between the tracer and the fluid, solute buoyancy is considered in the Navier–Stokes equation. Numerical results show that, with the increase of the mass concentration and the volume of the tracer, the shape of the residence time distribution curve changes from single flat peak to single sharp peak and then to double peaks. This change comes from the stratified flow of the tracer. Furthermore, the velocity difference number is introduced to demonstrate the importance of the density difference between the tracer and the fluid.

Wavelet-distributed approximating functional method for solving the Navier-Stokes equation

1998 ◽  
Vol 115 (1) ◽  
pp. 18-24 ◽  
Author(s):  
G.W. Wei ◽  
D.S. Zhang ◽  
S.C. Althorpe ◽  
D.J. Kouri ◽  
D.K. Hoffman
Keyword(s):  
Stokes Equation ◽  
Functional Method ◽  
Navier Stokes ◽  
Navier Stokes Equation

scholarly journals Generalized Navier–Stokes Equations and Dynamics of Plane Molecular Media

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 288
Author(s):  
Alexei Kushner ◽  
Valentin Lychagin
Keyword(s):  
Carbon Dioxide ◽  
Internal Structure ◽  
Stokes Equation ◽  
Hydrogen Cyanide ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

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