NP7.1
Non-linear Waves and Fracturing

NP7.1

Non-linear Waves and Fracturing
Convener: Arcady Dyskin | Co-conveners: Elena Pasternak, Serge Shapiro, Sergey Turuntaev
vPICO presentations
| Thu, 29 Apr, 09:00–10:30 (CEST)

vPICO presentations: Thu, 29 Apr

Chairpersons: Arcady Dyskin, Elena Pasternak, Sergey Turuntaev
09:00–09:05
09:05–09:07
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EGU21-3584
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Highlight
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Klaus Regenauer-Lieb, Manman Hu, Qinpei Sun, and Christoph Schrank

We propose a mesoscopic thermodynamics approach for coupling multiphysics processes across scales in porous or multiphase media. In this multiscale reaction-diffusion formalism interactions of discrete phenomena at the local scale are seen as being subject to a larger scale Thermo-Hydro-Mechano-Chemical (THMC) thermodynamic force. When local interactions are incompatible with the large-scale thermodynamic stress field incompatibilities can arise which trigger accelerations resulting in meso-scale generalized thermodynamic fluxes of another (THMC) kind. The classical acoustic tensor localization criterion in plasticity theory is here understood as a standing wave solution of such acceleration waves. These classical zero-speed acceleration wave solutions are solitary waves, also known as solitons, and are interpreted in the reaction-diffusion formalism as self-diffusion dominated by harvesting all available energy from the cross-diffusional tails.

The more general case of non-zero traveling wave speed solutions is related to the cross-diffusion coefficients between different macro- and meso-scale thermodynamic THMC forces and fluxes. These cross-diffusion terms in the 4 x 4 THMC diffusion matrix are shown to lead to multiple diffusional P- and S-wave equations as THMC coupled, time-resolved dynamic solutions of the equation of motion. We show that the off-diagonal cross-diffusivities can give rise to a new class of waves also known as cross-diffusion waves or quasi-solitons. Their unique property is that for critical conditions cross-diffusion waves can funnel wave energy into a soliton wave focus.

Mathematically these solutions can be compared to events in ocean waves and optical fibers known as 'rogue waves' or 'high energy pulses of light' in lasers. In the context of hydromechanical coupling, a rogue wave would appear as a sudden fluid pressure spike on the future fault plane. This hydromechanically coupled fluid pressure P-wave instability is here interpreted as a trigger for the S-wave seismic moment release of a double couple dominated earthquake event. The proposed multiscale cascade of wave energy may apply to many other material instabilities.

 

 

How to cite: Regenauer-Lieb, K., Hu, M., Sun, Q., and Schrank, C.: Quasi-solitary multiscale cross-diffusion waves as a precursor to Earth instabilities, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3584, https://doi.org/10.5194/egusphere-egu21-3584, 2021.

09:07–09:09
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EGU21-8133
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ECS
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Manman Hu, Qingpei Sun, Christoph Schrank, and Klaus Regenauer-Lieb

Coupled Thermo-Hydro-Mechano-Chemical (THMC) patterns are ubiquitous in nature yet their origin is not yet fully understood. We propose a generic framework for pattern formation in terms of quasi-solitary wave instabilities that are triggered by cross-scale THMC-feedbacks considering a general topology of saturated porous media [1]. We identify the important aspect of cross-diffusion terms and present a linear stability analysis of the governing partial differential equations (pde’s). Multiple transient wave instabilities are found as solutions of the coupled THMC pde’s and in the standing wave limit (infinite time scale) these waves form the solitary wave patterns frozen into the geosystems at various scales.

Cross diffusion in a complex system is defined by the phenomenon that a gradient of one generalised thermodynamic force drives a generalised thermodynamic flux of another kind. Thermodynamic forces and fluxes in a THMC-system are defined as follows. Thermodynamic forces are the gradients of the THMC-system. The flux (T) represents Fourier’s law where thermal conductivity represents its characteristic diffusivity. The flux (H) describes Darcy’s law, where the diffusivity depends on the intrinsic permeability of the porous structure and the viscosity of saturating fluid. The flux (M) represents the incremental change in the solid-phase overstress adopting a Representative Elementary Volume (REV) formalism. The fluid phase within the REV, as an immediate environment surrounding the solid matrix, synchronously feels the pressure change, and vice versa. The flux (C) is Fick’s law, where chemical reaction and transport processes occur predominantly at/around the solid-fluid interfacial areas.

In order to express the THMC feedback we write the governing reaction diffusion equations as coupled HM equations with generalized source terms depending on temperature, concentration, fluid pressure and solid overstress and further consider the cross-diffusion terms as a generic framework:

where h1>0, h2>0, h1+h2>0 are the cross-diffusion coefficients [2] triggering wave instabilities from solid-fluid interaction at the microscale. The capital D../Dt denotes the material derivative. In the case that h1=h2=0 the classical conservation laws are recovered, and no stationary waves are obtained. Propagating waves recorded in laboratory experiments and possible field applications are interpreted with this new approach.

[1] M.M. Hu, C. Schrank, K. Regenauer-Lieb. Cross-diffusion waves in hydro-poro-mechanics. Journal of the Mechanics and Physics of Solids, 2020. 135: 103632.

[2] V.K. Vanag and I.R. Epstein. Cross-diffusion and pattern formation in reaction–diffusion systems. Physical Chemistry Chemical Physics, 2009. 11(6): p. 897-912.

How to cite: Hu, M., Sun, Q., Schrank, C., and Regenauer-Lieb, K.: Cross-Diffusion Triggered Multiphysics Wave Instabilities, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8133, https://doi.org/10.5194/egusphere-egu21-8133, 2021.

09:09–09:11
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EGU21-5241
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Christian Boehmer

The Cosserat model generalises an elastic material taking into account the possible microstructure of the elements of the material continuum. In particular, within the Cosserat model the structured material point is rigid and can only experience microrotations, which is also known as micropolar elasticity. The propagation of elastic waves in such a medium is studied and we find two classes of waves, transversal rotational waves and longitudinal rotational waves, both of which are solutions of the nonlinear partial differential equations. For certain parameter choices, the transversal wave velocity can be greater than the longitudinal wave velocity.  We couple the rotational waves to linear elastic waves to study the behaviour of the coupled system and find wave-like solutions with differing wave speeds. In addition we also consider the so-called Cosserat coupling term. In this setting we seek soliton type solutions assuming small elastic displacements, however, we allow the material points to experience full rotations which are not assumed to be small.

How to cite: Boehmer, C.: Wave-like solutions in Cosserat micropolar elasticity, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-5241, https://doi.org/10.5194/egusphere-egu21-5241, 2021.

09:11–09:13
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EGU21-3588
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ECS
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Nazanin Nourifard, Elena Pasternak, and Maxim Lebedev

We designed and modified an experimental method to simultaneously measure the stress-strain (static moduli) and stress dependence of S and P-wave velocities of rocks (sandstone) under hydrostatic pressure by a Hoek’s cell. Dynamic moduli were calculated from the direct measurement of ultrasonic P- and S-wave velocities at a central dominant frequency of 1 MHz, while static moduli was recorded by strain gauges. The hydrostatic pressure was applied with a fixed rate at 1MPa/minute. We observed that the dynamic bulk moduli can be up to 44% higher than the static moduli in sandstones with porosity ranging from 8% to 24%. The results are in agreement with the existing empirical equations for soft rocks. Our experimental results demonstrate that the dynamic bulk’s modulus ranges from 4-13GPa, while the static bulk modulus ranges from 2-11GPa. We measured dynamic Young’s modulus and Poisson’s ratio at four different time periods (before applying the stress, right after the unloading, 20 days, and 60 days after the experiment) to investigate the effect of time on stress relaxation and eventually on the properties of the sandstones. All the samples showed an increase of Young’s modulus right after the stress application and then a gradual decrease of this value over time because of this relaxation; however, most of the samples could not reach the original state due to irreversible deformation at micro-level. Dynamic moduli show greater sensitivity to the irreversible deformations as compared to static moduli (even within the elastic limits). Dynamic moduli of porous material are also more sensitive to the microstructure than the static ones. Independent P and S-wave measurement for this study showed that the estimation of the S-wave velocity from the recorded P-wave velocity is not an accurate procedure and introduces a big error in the final calculation of the dynamic moduli. It also confirmed that by registering an accurate P-wave velocity the UCS (Unconfined Compressive Strength) value can be accurately estimated for sandstones. This demonstrates the great potential of dynamic studies as a non-destructive method to estimate this value for porous materials.

How to cite: Nourifard, N., Pasternak, E., and Lebedev, M.: Improved estimation method for dynamic bulk moduli of sandstones subjected to hydrostatic stress., EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3588, https://doi.org/10.5194/egusphere-egu21-3588, 2021.

09:13–09:15
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EGU21-15534
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Serge Shapiro

In some regions a significant stress drop characterizes earthquakes induced by underground fluid injections or productions. In addition, long-term fluid operations in the underground can influence a seismogenic reaction of the rock per unit volume of the fluid involved. The seismogenic index is a quantitative characteristic of such a reaction. We derive a relationship between the seismogenic index and the stress drop. We propose a simple and rather general phenomenological model of the stress drop of induced earthquakes. Our model suggests that a high stress drop can result from a decrease in cohesion of initially inactive faults that are seismically activated by long-term fluid operations. On the one hand, the increasing stress drop can lead to an increase in the seismogenic index with the time of fluid operations. On the other hand, a production/injection caused change of the pore pressure can also cause a systematic increase in the stress drop. This can provide an additional contribution to the growth of seismogenic index (and thus to the seismic risk) with operation time of reservoirs.

The case study of Groningen gas field provides interesting information in this respect. A significant stress drop of some induced earthquakes at Groningen can be explained by activating preexisting cohesive normally-stressed fault systems. Seismic events on such faults lead to the drop of their cohesion due to the rupture process. This cohesion drop contributes directly to the earthquake stress drop. The production-related increase of the differential stress in the reservoir leads to an increasing number of seismically activated more cohesive faults. This leads in turn to an increasing seismogenic index. The seismogenic index seems to be quite low at Groningen. However, it increases systematically with the production time. One of reasons of this behavior can be related to the average cohesion of involved faults as it is mentioned above. An additional effect contributing to this increase is a systematically increasing stress drop due to the production-related pressure depletion increasing the effective stress in the reservoir. A growing seismogenic index can result in an increasing with time maximum possible magnitude, Mmax.

How to cite: Shapiro, S.: Mutual relations between stress drop of induced earthquakes and fault cohesion, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-15534, https://doi.org/10.5194/egusphere-egu21-15534, 2021.

09:15–09:17
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EGU21-9802
Qiang Xie, Yuxin Ban, Zhihui Wu, and Xiang Fu

The sliding surface deformation of the soil slope mainly presents progressive failure characteristics, and serial acoustic emission (AE) signals are generated during the deformation process of progressive landslide. A model test aiming at reproducing the typical shear surface deformation of a soil slope is designed. The displacement, AE data and corresponding time-frequency characteristics are comprehensively analyzed to evaluate the progressive deformation behavior. Comparisons with different granular backfills measurements show that cumulative AE count increase proportionally with the shear surface displacement, and the experiments demonstrate that the glass sand backfill exhibits remarkable AE detection characteristics and stronger correlation results. Significantly, AE signal exhibits variational dominant frequencies at different deformation stages, and there is the significant phenomenon that not only the low frequency signals generated with a significantly increase number, at the same time the continuous high frequency signals appear during the accelerating deformation stage. Furthermore, from the statistical trend of the energy percentage of the high frequency band into 312.5~500 kHz, it’s found that the correlative energy proportion occupies up to 15%, or even higher during the accelerating stage, indicating that the landslide may be about to enter a severely dangerous stage. The experiments show that the frequency characteristic of the AE signal can be effectively used as the early warning index, which may be the promising reference of the field warning monitoring for the soil progressive landslides.

How to cite: Xie, Q., Ban, Y., Wu, Z., and Fu, X.: Physical experiment investigation on progressive deformation of shear slip surface of the soil slope, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9802, https://doi.org/10.5194/egusphere-egu21-9802, 2021.

09:17–09:19
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EGU21-2542
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ECS
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Vasily Riga and Turuntaev Sergey

Seismicity associated with fluid injection into the subsurface is one of the most important issues worldwide. Fluid injection into or near a fault could lead to the fault sliding and to moderate or even hazardous seismic events. In the presented research, we study the single fault behavior under action of a single well injection near the fault. Various cases of initial conditions, system geometry, and friction properties of the fault are considered. To describe the friction on the fault we use two-parameter rate-and-state law. The fault has zones characterized by velocity-weakening and velocity-strengthening friction behavior. We analyze how location and size of the velocity-weakening zone and parameters of the friction law influence the fault sliding dynamics. We also consider how the fault sliding is changed when taking into account the rock poroelastic effects. As the result, we get conditions that are favorable for the occurrence of noticeable seismicity.

How to cite: Riga, V. and Sergey, T.: Numerical study of fault sliding under fluid injection, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2542, https://doi.org/10.5194/egusphere-egu21-2542, 2021.

09:19–09:21
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EGU21-5803
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Highlight
Elena Pasternak and Arcady Dyskin

Inter-sonic (faster than the shear wave velocity) propagation of zones of shear over faults are observed both in the Earth’s crust and in specially designed laboratory experiments. This is usually interpreted as propagation of shear fractures caused by postulated special fracture mechanisms. This interpretation is however at variance with experimental facts that shear fractures in solids do not propagate in their own planes, kinking instead. Extensive (and fast) in-plane shear fracture propagation seems to only be possible over pre-existing planes considerably weaker than the surrounding material. A limiting case of fracture propagation over such a weak plane is the propagation of a sliding zone resisted by friction only. Another limiting case is shearing over a narrow elastic layer (shear Winkler layer) without rupture. The shear Winkler layer models both traditional elastic connections (positive stiffness) and rotation of non-spherical particles of the fault gouge (negative stiffness), e.g. [1, 2].

In both cases propagation of sliding/shear zone also involve longitudinal deformation in the surrounding material. Using a configuration different from [3, 4] we demonstrate that the presence of the longitudinal deformation makes the sliding/shear zone propagate with p-wave velocity. Propagation of such zones create seismic signals with power spectra resembling those observed in earthquakes.

Acknowledgement.   AVD and EP acknowledge support from the Australian Research Council through project DP190103260.

How to cite: Pasternak, E. and Dyskin, A.: A mechanism of apparent inter-sonic propagation of shear fractures, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-5803, https://doi.org/10.5194/egusphere-egu21-5803, 2021.

09:21–09:23
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EGU21-3934
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ECS
Rui Xiang Wong, Elena Pasternak, and Arcady Dyskin

This study analyses a situation when a geological fault contains a section of anisotropic gouge with inclined symmetry axes (e.g. inclined layering), Bafekrpour et al. [1]. Such gouge in a constrained environment induces, under compression, asymmetric friction (different friction forces resisting sliding in the opposite directions). The rest of the gouge produces conventional symmetric friction. A mass-spring model of the gouge with asymmetric and symmetric friction sections is proposed consisting of a mass with asymmetric friction connected through a spring to another mass with symmetric friction. These masses are set on a base subjected to vibration. A parametric analysis is performed on this system. Two distinct characteristic regimes were observed: recurrent movement resembling stick-slip motion similar to predicted by [2] and sub-frictional movement. Recurrent movement arises when the inertial force is sufficient to overcome frictional force of a block with symmetric friction. Sub-frictional movement occurs when the inertial force is not sufficient to overcome frictional force of an equivalent system with only symmetric friction. The sub-frictional movement is produced by the force in the connecting spring increased due to the movement of the asymmetric friction block in the direction characterised by low friction. We formulate the criterion at which sub-frictional movement occurs. The occurrence of sub-frictional depends upon the relative mass of the symmetric and asymmetric friction sections, as well as the amplitude and driving frequency of the excitation. Power spectra of the produced vibrations are determined for both regimes. The results can shed light on mechanisms of sliding over pre-existing discontinuities and their effect on seismic event generation and propagation of hydraulic fractures in the presence of discontinuities.

[1] Bafekrpour, E., A.V. Dyskin, E. Pasternak, A. Molotnikov and Y. Estrin (2015), Internally architectured materials with directionally asymmetric friction. Scientific Reports, 5, Article 10732.

[2] Pasternak, E. A.V. Dyskin and I. Karachevtseva, 2020. Oscillations in sliding with dry friction. Friction reduction by imposing synchronised normal load oscillations. International Journal of Engineering Science, 154, 103313.

Acknowledgement. AVD and EP acknowledge support from the Australian Research Council through project DP190103260.

How to cite: Wong, R. X., Pasternak, E., and Dyskin, A.: Motion of masses with asymmetric and symmetric friction. Application to fault sliding, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3934, https://doi.org/10.5194/egusphere-egu21-3934, 2021.

09:23–09:25
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EGU21-8858
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Sergey Turuntaev, Evgeny Zenchenko, Petr Zenchenko, Maria Trimonova, and Nikolai Baryshnikov

Acoustic transmission data obtained in laboratory experiment were used to estimate main stages of hydraulic fracture onset, growth and filling by fracturing fluid. Laboratory setup consists of two horizontal disks with a diameter of 750 mm, and a sidewall with an internal diameter of 430 mm. The disks and the sidewall form a pressure chamber with a diameter of 430 mm at a height of 70 mm. There are a number of holes in the disks and the sidewall that are used for mounting ultrasonic transducers, pressure sensors, as well as for fluid injections. As a model material, a mixture of gypsum with cement was used, which was poured into the chamber. The sample was saturated with water gypsum solution and loaded with vertical and two horizontal stresses using special chambers. The fracture was created by viscous fluid (mineral oil with viscosity 0.1 Pa*s) injection with a constant rate 0.2 cm3/s through a cased borehole (diameter 12 mm) with a horizontal slot, which was preliminary located in the center of the sample. Hydraulic fracturing monitoring was carried out by recording of ultrasonic pulses passing through the sample during fracturing. To separate the ultrasonic pulses, the frequency of their sending was used. After that, the envelope of each record fragment was constructed using the Hilbert transformation and its maximum was found. Comparison of the ultrasonic pulse amplitude variations and injection pressure led to the following observations. Initial decrease in the pulse amplitudes began before the maximum pressure was reached, which may indicate the hydraulic fracturing onset at a pressure less than the maximum. The amplitude decline occurs smoothly, so it is difficult to identify any characteristic point on these curves and, accordingly, it is difficult to establish an accurate time of the fracturing onset and the fracture rate. The fracture rate was estimated by different methods previously as ≈130 mm/s. After the decline, the pulse amplitudes started to increase, that was related with the injection fluid front propagation in the fracture. In contrast to the decline, the beginning of the amplitude growth was clearly detected. Taking into account the spatial locations of the ultrasonic pulse source, receivers, and fracture, it is possible to estimate the propagation velocity of the fracturing fluid front as ≈35 mm/s. After the increase, the ultrasonic pulse amplitudes started to decrease significantly (up to 3 times), which is probably due to the further expansion of the fracture aperture. On the transducers located closer to the well, this decline is maximum. When the injection is stopped, the ultrasonic pulse amplitudes began to grow again, which indicates the fracture closure as the injection pressure decrease. In the experiments on the fracture re-opening under various stress applied to the sample, a linear relationship between the fracture re-opening pressure and applied vertical stress was found. This type of relationship should be expected, but values of the relation parameters declined from the values suggested in theoretical research, which was explained by taken into account back-stresses and non-linear behavior of the sample material.

How to cite: Turuntaev, S., Zenchenko, E., Zenchenko, P., Trimonova, M., and Baryshnikov, N.: Dynamics of hydraulic fracture development according to acoustic transmission data, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8858, https://doi.org/10.5194/egusphere-egu21-8858, 2021.

09:25–09:27
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EGU21-5724
Arcady Dyskin and Elena Pasternak

Propagation of hydraulic fractures in rocks is often a non-smooth process, which leaves behind a number of rock bridges distributed all over the fracture. The bridges constrict the fracture opening and thus affect the determination of hydraulic fracture dimensions from the volume of pump-in fracturing fluid. This makes it necessary to detect the emergence of bridges and their concentration over the fracture surface.

Opening of hydraulic fractures in rocks is determined by a balance of pressure from the fracturing fluid and the normal component of the in-situ compressive stress. If an external excitation is applied (e.g. by a seismic wave), closure of the fracture is additionally resisted by the stiffness of fracturing fluid. Subsequently, a simple model of hydraulic fracture is presented by a bilinear spring with a certain stiffness in tension and a very high stiffness in compression. This constitutes so-called bilinear oscillator [1, 2] in which the compressive stiffness considerably exceeds the tensile one. The presence of bridges increases stiffness in tension thus reducing bilinearity of the modelling spring. Therefore the determination of the bilinearity is a first step in the reconstructing the effective stiffness of the bridges.  

We use the model of bilinear oscillator, identify multiple resonances and determine the first two harmonics (or first two peaks of in the power spectrum). The ratio of their amplitudes directly depends upon the bilinearity (ratio of compressive to tensile stiffnesses), hence the bilinearity is determinable from the amplitude ratio. Then the effective bridge stiffness can be estimated.

1. Dyskin, A.V., E. Pasternak and E. Pelinovsky, 2012. Periodic motions and resonances of impact oscillators. Journal of Sound and Vibration 331(12) 2856-2873. ISBN/ISSN 0022-460X, 04/06/2012.

2. Pasternak, E., A. Dyskinand Ch. Qi, 2020. Impact oscillator with non-zero bouncing point. International Journal of Engineering Science, 103203.

Acknowledgement. The authors acknowledge support from the Australian Research Council through project DP190103260.

How to cite: Dyskin, A. and Pasternak, E.: Power spectrum of hydraulic fractures with constricted opening, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-5724, https://doi.org/10.5194/egusphere-egu21-5724, 2021.

09:27–09:29
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EGU21-13894
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ECS
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Mehdi Serati

An important issue in rapid brittle fracture is the limiting speed of crack propagation. It is widely believed that brittle mode I crack cannot propagate faster than the Rayleigh wave speed, or the speed of sound on a solid surface. Mode II cracks are also limited by longitudinal speed wave. The origin for this belief stems from the predictions of continuum mechanics. Once the crack speed reaches a theoretical upper limit in a material, which is most often larger than one fifth of the Rayleigh wave velocity, branching of a propagating crack occurs. To verify this hypothesis, this paper presents the results of an experimental program aimed at disclosing the size effect on the crack velocity in the Splitting Tensile Strength indirect test (i.e. the Brazilian Test) using high-speed photography techniques. Over 100 Brazilian tests with more than 10 different rock types at various diameters were prepared and tested according to the ASTM standard recommendations using either a servo hydraulic machine or an electromechanical load frame at a wide ranges of load/displacement rates. By adopting a high frame rate of above 100,000 frames per second (fps), crack initiation, propagation, and coalescence were captured to study the size effect on the crack speed and failure mode on the Brazilian test results.

How to cite: Serati, M.: Tensile Crack Speed in Brittle Rocks, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-13894, https://doi.org/10.5194/egusphere-egu21-13894, 2021.

09:29–09:31
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EGU21-14958
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ECS
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Victor Nachev and Sergey Turuntaev

Improved efficiency of hydraulic fracturing (HF) operations in complex reservoir rocks requires producing an extensive network of secondary fractures alongside the main fractures. The goal of the presented research is to find optimal stress-strain conditions yielding the most extensive network of secondary fractures at the microscale. The scope includes integrating results of microstructural characterization of tight gas reservoir rock samples and geomechanics. The study addresses the problem of hydraulic fracture optimization by suggesting stress-strain conditions to maximize fracture branching and, therefore, to optimize the drainage zone. We use a multidisciplinary approach including experimental data obtaining and numerical simulations. The first step is preparing a consistent set of 2D and 3D digital rock (DR) microscale models describing the experimental geometry, mineral composition and spatial distribution of mechanical properties of real rock samples. Geomechanical and petrophysical laboratory testing provide calibration/validation data for the DR models. Lab experiments include compressive and tensile strength testing coupled with digital image correlation, and X-ray computed tomography, 2D scanning electron microscopy coupled with mineralogy mapping. The preparation of DR models involves advanced 2D-to-3D and 3D-to-3D image registration techniques. The second step is a simulation of stress-strain states and fracture propagation in the models. We build simulation grids based on the mineral model and use a commercial mechanical simulator to simulate the fracture propagation at a microscale at given stress conditions. We applied the above approach to one of the most promising gas formations located in West Siberia, Russia. The reservoir rock features low permeability and pore dimensions down to tens of nanometers. Simulations delivered fracture networks for different loading conditions at the microscale. Simulation of typical geomechanical conditions allowed choosing reasonable stress-strain conditions that sustain the highest degree of formation fracturing. The research results may be applied to unconventional plays by increasing the efficiency of HF operation and maximizing production from isolated pore systems via establishing voids connectivity in the near-wellbore zone. The knowledge of the optimal stress-strain state for a near-wellbore zone will set the goal for HF propagation modeling at a wellbore scale. Using the approach, a geomechanical modeler would focus on designing main fractures, sustaining required stress-strain conditions in its vicinity, and thus producing the maximal amount of secondary microfractures. The results novelty is related with the simulation of 3D fracture propagation in highly heterogeneous reservoirs rocks taking into account its void space structure and fabric in geometry closest to real conditions.

How to cite: Nachev, V. and Turuntaev, S.: 3D Numerical Mineral Mechanical Modeling of Fracture Propagation in Complex Reservoirs Rocks at Microscale, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14958, https://doi.org/10.5194/egusphere-egu21-14958, 2021.

09:31–09:33
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EGU21-13328
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ECS
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Victoria Dochkina, Ilia Perepechkin, Natalia Zavialova, and Sergei Negodiaev

    Nowadays, none of widely used hydraulic fracturing simulators can simultaneously provide high calculation speed and sufficient physical reliability, which is crucial in engineering problems. Hence, an optimization of hydraulic fracturing simulation in terms of speed and accuracy is needed. It is possible to create a tool that will simultaneously solve the above-mentioned problems using Machine Learning methods. In that case, the simulation will have an accuracy close to the Planar3D model and almost instantaneous speed of calculation. The development of such a tool will simplify a selection of optimal injection parameters.
    This paper presents a Neural Network that approximates a planar three-dimensional hydraulic fracturing model. A feature of the proposed approximator is that it predicts the evolution of two-dimensional fracture aperture field. This is a key difference of this model from other approximators that predict well-defined parameters of the fracture geometry, such as half-length, height, etc. The availability of complete fracture geometry information allows highly accurate estimation of production and possible complications during hydraulic fracturing.
    The paper presents an ability of creating a Neural Network that will cover a wide range of production problems: from express simulation and optimization to accurate and physically reliable modeling.

How to cite: Dochkina, V., Perepechkin, I., Zavialova, N., and Negodiaev, S.: Application of Deep Learning for Planar 3D Hydraulic Fracturing Simulation, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-13328, https://doi.org/10.5194/egusphere-egu21-13328, 2021.

09:33–09:35
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EGU21-13309
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ECS
Helen Novikova and Mariia Trimonova

Recently, attention to the development of low-permeable reservoirs has been increasing. More and more attention is being paid to the search for various methods of data analysis of mini-hydraulic fracturing and computer modeling of the hydraulic fracturing process, which will simplify the entire procedure of hydraulic fracturing in a real field and reduce financial costs. The increase in interest is due to the fact that the results of the hydraulic fracturing are used to determine some important characteristics of the formation.

One of such important characteristics of a reservoir is permeability. In the course of this study, the data obtained from a series of laboratory experiments on mini-hydraulic fracturing were processed. The main goal was to determine the value of permeability of the medium in which the hydraulic fracture was formed and propagated, with the help of various standard methods. The second objective of the study was to compare the calculated values with real ones known from preliminary conducted laboratory experiments.

In the frame of the work, the laboratory experiments on mini-hydraulic fracturing were carried out using a special experimental setup [1]. The uniqueness of this experimental setup lies in the fact that it allows to perform a triaxial loading of the sample under consideration. The sample material was selected according to the similarity criteria between the fracturing process in the experiment and the fracturing process in the real field. These features make it possible to approximate the conditions of a laboratory experiment on hydraulic fracturing to real field conditions.

As a result, pressure-time dependencies were obtained for series of laboratory experiments. Further analysis of the curves was carried out in the time period after fracture closure.

In the course of data analysis, the flow regimes in the medium during the time period after fracture closure were estimated. After that, the values of permeability were calculated using approach introduced by Nolte [2, 3]. The permeability values were also estimated using the method proposed by Horner [4] and later modified by Nolte [5]. All theoretically obtained values were compared with real values of permeabilities.

Acknowledgements

The reported study was funded by RFBR, project number 20-35-80018, and state task 0146-2019-0007.

References

1. Trimonova M., Baryshnikov N., Zenchenko E., Zenchenko P., Turuntaev S.: “The Study of the Unstable Fracture Propagation in the Injection Well: Numerical and Laboratory Modelling,” (2017).

2. Nolte, K. G.: “Determination of Fracture Parameters from Fracturing Pressure Decline,” Las Vegas (1979).

3. Nolte, K. G.: “A General Analysis of Fracturing Pressure Decline With Application to Three Models,” (1986).

4. Horner, D. R.: “Pressure Build-Up in Wells,” Netherlands (1951).

5. Nolte, K. G., Maniere, J. L., Owens, K. A.: “After-Closure Analysis of Fracture Calibration Tests,” Texas (1997).

How to cite: Novikova, H. and Trimonova, M.: Permeability determination of the medium according to the analysis of laboratory hydraulic fracturing curves., EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-13309, https://doi.org/10.5194/egusphere-egu21-13309, 2021.

09:35–09:37
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EGU21-2491
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ECS
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Nikolay Baryshnikov, Evgeniy Zenchenko, and Sergey Turuntaev

Currently, a number of studies showing that the injection of fluid into the formation can cause induced seismicity. Usually, it is associated with a change in the stress-strain state of the reservoir during the pore pressure front propagation. Modeling this process requires knowledge of the features of the filtration properties of reservoir rocks. Many researchers note the fact that the measured permeability of rock samples decreases at low pressure gradients. Among other things, this may be due to the formation of boundary adhesion layers with altered properties at the interfaces between the liquid and solid phases. The characteristic thickness of such layer can be fractions of a micron, and the effect becomes significant when filtering the fluid in rocks with a comparable characteristic pore size. The purpose of this work was to study the filtration properties of rock samples with low permeability at low flow rates. Laboratory modeling of such processes is associated with significant technical difficulties, primarily with the accuracy limit of measuring instruments when approaching zero speed values. The technique used by us to conduct the experiment and data processing allows us to study the dependence of the apparent permeability on the pore pressure gradient in the range of 0.01 MPa/m, which is comparable to the characteristic pressure gradients during the development of oil fields. In the course of the study, we carried out laboratory experiments on limestone core samples, during which the dependencies of their apparent permeability on the pore pressure gradient were obtained. We observed a significant decrease in their permeability at low flow rates. In the course of analyzing the experimental results, we proposed that a decrease in apparent permeability may occur due to the effect of even a small amount of residual gas in the pore space of the samples. This has been confirmed by additional experiments. The possibility of clogging of core sample pore space must be considered when conducting when conducting laboratory studies of the core apparent permeability.

How to cite: Baryshnikov, N., Zenchenko, E., and Turuntaev, S.: Possible Reason of the Dependence of an Apparent Permeability on the Pressure Gradient at low Flow Rates in Laboratory Study, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2491, https://doi.org/10.5194/egusphere-egu21-2491, 2021.

09:37–09:39
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EGU21-1867
Yong Li, Weiqiu Kong, Weishen Zhu, Guannan Wu, Zhiheng Wang, Feng Dai, and Chen Wang

Abstract: Based on laboratory direct shear tests and discrete element theory, the crack propagation and coalescence mechanism and numerical simulation of cement mortar specimens considering the combined actions of internal hydraulic pressure and shear force were carried out. We completed the filling of the internal hydraulic pressure in the cement mortar specimens with preexisting flaws, and performed the direct shear tests on the specimens. In the numerical analysis, the pipe domain model in the two dimensional particle flow code (PFC2D) was modified owing to the high brittleness and low permeability of the cement mortar particles in the numerical model. We also modified the calculation rules of the interaction between the fluid and cement mortar particles, and proposed an improved fluid-solid coupling model which is more suitable for the high brittle cement mortar. Under the action of internal hydraulic pressure, a tensile region existed at the tip of the preexisting flaws of the cement mortar specimen, which can also explain the crack initiation and propagation along the horizontal shear direction during the stage of crack initiation. However, the fissure water pressure was not completely dissipated because of the high brittleness of the cement mortar and the existence of a large number of micro-cracks in the failure area, which finally resulted in a relatively concentrated horizontal compressive stress, and roughly formed a compressive region with a smaller stress along the horizontal shear direction.

How to cite: Li, Y., Kong, W., Zhu, W., Wu, G., Wang, Z., Dai, F., and Wang, C.: Crack propagation and coalescence characteristics of rock-like specimen containing preexisting flaws subjected to internal hydraulic pressure and shear force, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1867, https://doi.org/10.5194/egusphere-egu21-1867, 2021.

09:39–09:41
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EGU21-1519
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ECS
Hongyu Wang, Arcady Dyskin, Phil Dight, and Elena Paternak

An experimental study of post-peak behaviour of rock models in uniaxial compression under different controlling methods is presented. A series of mortar samples with different compositions are firstly tested into post-peak stages using the axial strain control. In axial strain control, all types of mortar samples including pure cement samples have unavoidable sudden failure beyond the peak stress at different stages, and therefore only limited post-peak stress-strain curves can be captured. In order to capture the post-peak stress-strain curves beyond the sudden failure, a failure control method based on controlling the rate of lateral strain is proposed in this study. Using this method, post-peak stress-strain curves with positive modulus could be obtained for class II behaviour. The failure modes of the samples tested in both axial strain control and failure control show similarity. Also, the failure-controlled experiments indicate that despite the unstable fracture growth in the samples being considerable after peak stress, it may not lead to the uncontrolled sudden failure of the whole sample but could produce a class II stress-strain curve.

How to cite: Wang, H., Dyskin, A., Dight, P., and Paternak, E.: Class II post-peak behaviour of cementitious material in uniaxial compression, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1519, https://doi.org/10.5194/egusphere-egu21-1519, 2021.

09:41–10:30