In this preliminary study, we measured the roughness exponent for the fracture surfaces to be ζ ∼ 0.7, which is consistent with the morphology of fractures in materials with a disordered distribution of breaking strength [79]. Furthermore, the surface roughness was not observed to change after the durations of reactive flooding done in the experiments here (up to 41 hours). When investigating the evolution of the fracture apertures, we found that the regions with smaller initial apertures dissolved the most, while the regions with larger initial apertures had the most precipitation. This could perhaps be linked to the local flow velocity, which at a constant flux would be higher in the smaller apertures, providing more fresh water for reactions, while in the larger apertures the water would stay longer and deposit more chalk to the surface than is dissolved. For the shortest experiment (4 h), a pattern of dissolved lines along the flow direction was observed. The spatial correlation of reactions were found to increase with flow duration, first along the flow direction and later also in the perpendicular direction. We did not find a typical relationship between the change in fracture aperture and initial mid-plane.
Chapter 8
Conclusion and perspectives
This chapter is a summary of key findings together with some perspectives of future research.
For the invasion patterns during two-phase flow, we studied the typical patterns formed and characterized the surrounding deformations in the medium. The pat-terns are found to have similar fractal dimensions, around 1.5 and 1.6 for all bound-ary conditions, though the patterns show local differences depending on boundbound-ary conditions, where the invasion patterns in the open deformable medium changes the most as function of radius. For these invasion patterns, there is a transition with radius, with locally defined fractal dimensions, crossing over from around 1.7 - 1.8 initially, to 1.6 at an intermediate range and down towards 1.4 for the outer radii. The low outer fractal dimension indicates that the fingers cross over to a new instability, where 1 or 2 fingers come within a range from the outlet where beads become easier to displace, and grow on expense of the other fingers. This instability could be studied closer, e.g. evaluate how and where it begins as function of injec-tion pressure, how fast the radial finger growth is, and if the behavior changes with constant injection rate rather than injection pressure.
The area of the two-phase flow patterns is found to follow a Family-Vicsek scaling with time and radius, where the scaling exponent for the area as function of time is higher for more deformable systems, i.e. α = 1.45, 1.58 and 1.73 for the rigid, confined deformable and open deformable medium respectively. This indicates that the area of the invading clusters changes at a faster rate for more deformable media.
This, to our knowledge, newly measured exponent for viscous fingers in deformable porous media, calls for theoretical evaluation.
During experiments, the displacements outside the invasion patterns are directed radially outwards due to a viscous pressure gradient in the saturating liquid, while the displacements are directed perpendicularly away from the air-liquid interface close to the longest fingers. In the confined deformable system the viscous pressure gradient leads to a compaction of the medium until it becomes rigid, while in the open deformable medium we observe an initial compaction of the medium followed by decompaction. Further analysis on the deformations would be to compute the Laplace solution for the pressure field in the liquid, and characterize the granular rheology by comparing the pressure gradient with displacements. The correlation between the directions of displacement and the negative pressure gradient could be
evaluated to investigate to what degree and where the displacements are directed against the pressure gradient. Results from the confined deformable and open de-formable experiments could be compared to further investigate their differences and similarities.
In the study of air injection into dry dense granular media we have investigated both the patterns formed and the surrounding deformations together with simulated pressure fields. We found that the fractal dimensions for the developed channels in a confined dry granular medium was around 1.5 to 1.6, for injection pressures where the patterns were not too eroded by air flow. This is similar to the established fractal dimensions for viscous fingers in porous media, where randomly distributed capillary thresholds at the invasion front are responsible for the patterns being in a universality class modeled by the Dielectric Breakdown Model with η = 2 [2].
When investigating the deformations of the medium and simulated pressure fields, we found that the beads had a non-Newtonian, Bingham type rheology between the cell plates, which with noise in the thresholds can be responsible of placing the pattern growth into the same universality class as viscous fingers in porous media.
The influence of these thresholds on the patterns formed is of interest to investigate further, for example, will the patterns look more like viscous fingers in an empty Hele-Shaw cell if the thresholds are very low compared to the pressure gradient, i.e.
a rheology more like a Newtonian fluid? Will the patterns be rougher like viscous fingers in porous media if the thresholds are more significant and more disordered?
This could be tested by varying the properties of the cell, beads or interstitial fluid.
To lower the influence of the thresholds, maybe water could be injected into a water saturated medium instead of air into a dry one. Increased disorder in the thresholds for bead motion could be achieved by using fine grained sand instead of beads, or adding some roughness to the bottom plate of the cell, like a sandblasted plexiglass plate or a layer of sandpaper. In addition, simulations could be done where the beads and plates are frictionless, or where disordered friction could be added. Experiments can also be done to investigate how the patterns formed in a cell with open outer boundary and a rough bottom plate would change from the patterns formed in regular open cells.
The growth of the channel length with time was found to scale with injection pressure, and the growth can be modeled over time if the final length xf is known.
Before a critical time, the growth velocity is constant and scales with the injection pressure asPin3/2. After the critical time, the growth velocity follows a characteristic power law decay with time, v(t) ∼ tα with α = −2.5. The critical time is found to depend on the final channel length in addition to the injection pressure. To be able to describe the channel growth by the injection pressure alone, it is necessary to investigate how the final length xf depends on injection pressure and boundary conditions. In principle, a lot of data could be obtained quickly in repeated ex-periments where only the final length of the channel and the injection pressure is recorded. In addition, it is of interest to evaluate how the model for the channel growth proposed here would fit with experiments in other confined cells with e.g.
different cell gap, fluids, bead size, and cell dimensions. Perhaps, if the behavior described by this model can be fitted to a given system, it could be developed and upscaled for field applications.
In the late compacted stage of the experiments, we observed intermittent growth of the channel tips due to sudden bead rearrangements ahead of the channel. It is believed that the pressure gradient of the diffusing field suddenly overcomes the granular stress of jammed beads such that they rearrange. When this happens, the rearranging zone is compacted by the pressure gradient such that a zone closer to the channel is decompacted. As these beads compact, the channel expands a few mm. These stick-slip events could be investigated more in detail by first forming a developed channel at a lower pressure, start recording images at a zoomed in region around the most advanced channel, and then increase the injection pressure to induce further bead rearrangements. Together with the recording of acoustic emissions, this could be a nice experiment for the development of localization techniques and identification of characteristic emissions. Related work with acoustics is presented in the co-authored papers in the next chapter.
The results in the preliminary study of reactive flow in fractured chalk indicate that more dissolution occurs in initially narrow fracture apertures, while less disso-lution, or precipitation, occurs in initially larger fracture apertures. The correlation coefficient between initial fracture aperture and change in the fracture aperture was found to be -0.5 and -0.7 for experiments with 22.5 and 41 hours of reactive flow respectively. For the short 4 hour experiment, we observed a dissolution pattern of lines going roughly in the flow direction, not seen for the experiments which lasted longer. These are behaviors that should be investigated in further experi-ments, where various flow durations and flow rates should be tested. For example, preferably with a microscope that can efficiently profile the full fracture surfaces, experiments could be done where the fracture is profiled, flooded for some time, pro-filed, flooded again, and so on to make time lapse data. Full surface profiles could in addition make it easier to evaluate the fracture apertures, and enable correlations with larger offsets. The surface roughness exponent was not observed to change significantly for the durations of reactive flow we did (up to 41 hours), but it could be investigated as function of time in further experiments with longer durations. In addition, we designed a flow cell (not yet built) where the sample can be loaded parallel with, and perpendicular to the fracture plane in the diametrical direction, while the applied load is measured by force sensors. In future experiments, this cell could be used to characterize the effect of reactions on the solid stresses surrounding the evolving fractures.
Chapter 9
Co-authored papers
This chapter includes articles I have contributed to as a co-author during the work of this thesis, in particular contributing to the work with experiments and discussions.
9.1 Paper 4: Bridging aero-fracture evolution with the characteristics of the acoustic emissions in a porous medium
In this article, acoustic emissions during the same type of experiments as in chap-ters 5 and 6 are recorded and analyzed together with optical data from the high speed camera. The acoustic signals are recorded by piezoelectric sensors and shock accelerometers placed on the bottom plate of the cell. During experiments, air/solid interactions inside the cell create acoustic signals which are transmitted through the beads and excite the cell plates where the signals are recorded. Signature acoustic events are characterized in the Fourier spectrum and discussed together with the optical data to identify various sources, such as compaction of the medium, chan-nel formation and distinct events due to particle rearrangements in the compacted state. It is found that there is typically a transition between Type 1 and Type 2 events during the experiments, where Type 1 events are non-impulsive low fre-quency signals associated with channel formation and compaction of the medium, and Type 2 events are impulsive signals with energies spread over a wide range of frequencies, associated with sudden particle rearrangements in the compacted stage.
Furthermore, the Type 1 events are found to evolve during the channel growth with increasing mean frequency, and when the channel is developed there is a cross over to Type 2 events. The accumulated number of Type 2 events after the cross-over are found to follow a modified Omori law, similar to the stick-slip relaxation events which follows a big earthquake at real scale. The paper was published in Frontiers in Physics in September 2015.
PAPER 4
ORIGINAL RESEARCH The University of Tokyo, Japan Loic Vanel, Université Claude Bernard Lyon 1, France
*Correspondence:
Semih Turkaya, Centre National de la Recherche Scientifique UMR 7516, Institut de Physique du Globe de Strasbourg, Université de Strasbourg, 5 Rue Rene Descartes, 67084 Strasbourg, France turkaya@unistra.fr
Specialty section:
This article was submitted to Interdisciplinary Physics, a section of the journal Frontiers in Physics
Received:29 June 2015 Accepted:21 August 2015 Published:08 September 2015
Citation:
Turkaya S, Toussaint R, Eriksen FK, Zecevic M, Daniel G, Flekkøy EG and Måløy KJ (2015) Bridging aero-fracture evolution with the characteristics of the acoustic emissions in a porous medium.
Front. Phys. 3:70.
doi: 10.3389/fphy.2015.00070
Bridging aero-fracture evolution with the characteristics of the acoustic emissions in a porous medium
Semih Turkaya1*, Renaud Toussaint1, Fredrik K. Eriksen1, 2, Megan Zecevic3, Guillaume Daniel3, Eirik G. Flekkøy2and Knut J. Måløy2
1Centre National de la Recherche Scientifique, Institut de Physique du Globe de Strasbourg, Université de Strasbourg, Strasbourg, France,2Department of Physics, University of Oslo, Oslo, Norway,3Magnitude, Sainte Tulle, France
The characterization and understanding of rock deformation processes due to fluid flow is a challenging problem with numerous applications. The signature of this problem can be found in Earth Science and Physics, notably with applications in natural hazard understanding, mitigation or forecast (e.g., earthquakes, landslides with hydrological control, volcanic eruptions), or in industrial applications such as hydraulic-fracturing, steam-assisted gravity drainage, CO2sequestration operations or soil remediation. Here, we investigate the link between the visual deformation and the mechanical wave signals generated due to fluid injection into porous medium. In a rectangular Hele-Shaw Cell, side air injection causes burst movement and compaction of grains along with channeling (creation of high permeability channels empty of grains). During the initial compaction and emergence of the main channel, the hydraulic fracturing in the medium generates a large non-impulsive low frequency signal in the frequency range 100 Hz–10 kHz. When the channel network is established, the relaxation of the surrounding medium causes impulsive aftershock-like events, with high frequency (above 10 kHz) acoustic emissions, the rate of which follows an Omori Law. These signals and observations are comparable to seismicity induced by fluid injection. Compared to the data obtained during hydraulic fracturing operations, low frequency seismicity with evolving spectral characteristics have also been observed. An Omori-like decay of microearthquake rates is also often observed after injection shut-in, with a similar exponentp≈0.5 as observed here, where the decay rate of aftershock follows a scaling law dN/dt ∝ (t−t0)−p. The physical basis for this modified Omori law is explained by pore pressure diffusion affecting the stress relaxation.
Keywords: fracturing, lamb waves, acoustic emissions, power spectral evolution, Hele-Shaw cell
1. Introduction
Fluid flow [1,2], rock deformation [3] and granular dynamics [4] by themselves are very large scientific domains to investigate individually [5]. However, the idea of putting them together via a system of deformable porous medium with a fluid flow makes the phenomena even harder to understand. Rapid changes in the porosity of the medium due to fluid flow, channeling and fracturing via momentum exchange with the flow make understanding the mechanics of the system a challenge [6–9]. Hydraulic fracturing of the ground is a good example for this coupled behavior of solid and fluid phases. First, the pressure of the flow creates fissures and cracks which
Turkaya et al. Bridging aero-fracture evolution with acoustics
changes the permeability of the initial rock. Then, a flowing mixture of fine sand and chemicals helps maintain this cracked state by penetrating the newly opened areas. By jamming and/or cementing the newly-formed channels and cracks, possible relaxation after injection is prevented. Thus, a more permeable state of the rock is preserved after injection for various types of industrial applications. Recently, various well-stimulation projects have attempted to use pressurized gas (N2, CO2), instead of water, to trigger fracturing within reservoirs for several reasons (e.g., to avoid wasting water, to sequestrate CO2, environmental risks due to chemicals etc.) [10–12]. In this study, contrary to conventional fracturing methods, the fractures are induced using air injection.
Monitoring, predicting and controlling fracture evolution during hydraulic-fracturing, steam-assisted gravity drainage, or CO2 sequestration operations is a key goal [13–16]. One possibility for monitoring is to use generated acoustic emissions during those operations. In the hydraulic fracturing industry, the typical monitoring devices consist of geophones and seismometers. However, the interpretation of the signals during fast deformations of porous media due to fast fluid flow is not simple. Particularly, the measurements of deformations are usually difficult to achieve in an opaque medium, and the source of the seismic waves and acoustic emissions can be complex. The study of microseismicity during well operations is routinely done in the industry, but its interpretation is often delicate [17–19].
In this paper, we present an experimental study using a purpose-built setup allowing channeling and fracturing due to fluid flow, where we can observe the deformations optically using a fast camera and transparent setup, and simultaneously record the mechanical waves emitted by the complex channels and fractures created. Both signals, optical and acoustic/microseismic, are then analyzed. They display a complex evolution of the source geometry, and of the spectral characteristics. The experimental setup designed to achieve this consists of a rectangular Hele-Shaw cell filled with 80 microns diameter grains, mixed with fluid (air). The linear cell has three lateral sealed boundaries and a semi-permeable one enabling fluid (but not solid) flow. During the experiments, air is injected into the system from the side opposite to the semi-permeable boundary so that the air penetrates into the solid and at high injection pressures makes a way to the semi-permeable boundary via the creation of channels and fractures - or at low injection pressures, directly using the pore network.
For a similar system of aerofractures in a Hele-Shaw cell, a numerical model was conducted by Niebling et al. [20].
These models were also compared with experiments for further development and validation [20–24]. Same kind of experiments—but without acoustic monitoring—with a Hele-Shaw cell have also been conducted. Johnsen et al. worked on the coupled behavior by air injection into the porous material both in fluid saturated and non-saturated cases to study multiphase flow numerically and experimentally [23,25,26]. Aero-granular coupling in a free falling porous medium in a vertical Hele-Shaw cell was studied numerically and experimentally by Vinningland et al. [27–29]. Varas et al. conducted experiments of air injection into the saturated porous media in a Hele-Shaw cell [30, 31]
and in a cylinder box [32]. Eriksen et al. and McMinn et al.
worked on injecting gas into a saturated deformable porous medium [Eriksen et al., submitted;33]. Sandnes et al. classified different regimes of fingering of porous media in a Hele-Shaw cell [34]. Rust et al. developed a closed-system degassing model using volcanic eruption data [35]. Holtzman et al. also studied air induced fracturing where they identified different invasion regimes [36]. Furthermore, a recent study was conducted by Eriksen et al. where the air injection causes bubbles in a fluid-grain mixture [37].
The equivalent of microseismicity monitoring in the lab is the tracking of acoustic events. Hall et al. compared recorded acoustic emissions with the digital image correlation to track crack propagation in the rock samples [38]. Valès et al. used acoustic emissions to track strain heterogeneities in Argilite rocks [39]. Some studies have started to look at sources directly, both optically and acoustically, in various problems to characterize the different source mechanisms [40–44]. Farin et al. conducted some experimental studies on rockfalls and avalanches where he monitors those phenomena using acoustic emissions [45].
Stojanova et al. worked on fracture of paper using acoustic emissions created during crack propagation [46–48]. During the current experiments, acoustic signals are recorded using different
Stojanova et al. worked on fracture of paper using acoustic emissions created during crack propagation [46–48]. During the current experiments, acoustic signals are recorded using different