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• Eriksen, Fredrik Kvalheim; Moura, Marcel; Jankov, Mihailo; Turquet, Antoine Leo & Måløy, Knut Jørgen (2022). Transition from viscous fingers to compact displacement during unstable drainage in porous media. Physical Review Fluids. 7(1). doi: 10.1103/PhysRevFluids.7.013901. Full text in Research Archive Show summary

  We describe a crossover from the viscous fingering instability to a compact invasion regime during viscously unstable drainage of porous media, and we investigate the underlying mechanisms of this compact fluid displacement. The study is based on a series of drainage experiments in a radial porous Hele-Shaw cell where we systematically vary the viscosity of the defending (wetting) fluid and the overpressure of the invading (nonwetting) fluid to map out the resulting invasion structures as a function of viscosity ratio and injection pressure. We show that above a threshold of injection pressure and viscosity ratio a more stable and compact invasion structure emerges within the viscous fingering patterns, i.e., a roughly circular displacement with viscous fingers on the outside. The onset of the stable displacement is found to begin at a rather low viscosity ratio M between the invading and defending fluids, i.e., when M≥10−3 for injection pressures of 3–5 kPa. We find that the ratio between the length of the outer fingers and the size of the compact invasion scales with the viscosity ratio and approaches a more or less constant value during growth, resulting in structures with proportionate growth and larger compact invasions for higher viscosity ratios. As opposed to the viscous fingering instability, we describe rich ganglion dynamics within the compact invasion structures and show that the pressure gradient is not screened by the outer fingers.

• Turquet, Antoine Leo; Toussaint, Renaud; Eriksen, Fredrik Kvalheim; Daniel, Guillaume; Lengline, Oliver & Flekkøy, Eirik Grude [Show all 7 contributors for this article] (2019). Source localization of microseismic emissions during pneumatic fracturing. Geophysical Research Letters. ISSN 0094-8276. 46(7), p. 3726–3733. doi: 10.1029/2019GL082198. Full text in Research Archive Show summary

  Localization of signals is a widely applied technique used in different areas of science telecommunication, medicine, or seismology. In this work, we study microseismic emissions due to stick‐slip events during pneumatic fracture in a transparent setup at laboratory scale and apply a localization method “Estimated Source Energy Homogeneity.” The seismic location results are compared with the image correlation results for displacement maps corresponding to the event times. We have observed (using optics and acoustics) that the movement starts inside the porous medium and progresses toward the channel tips, eventually causing channels to grow further. This finding could be of interest in understanding fluid‐induced earthquake nucleation processes. Similar to in‐site applications of pneumatic or fluid‐related fracturing, it shows that the area influenced extends beyond the fracture tips. This also shows why even after the end of pumping, we may get earthquakes, such as in the Basel case (Haring et al., 2008, https://doi.org/10.1016/j.geothermics.2008.06.002).

• Eriksen, Fredrik Kvalheim; Toussaint, Renaud; Turquet, Antoine Léo; Måløy, Knut Jørgen & Flekkøy, Eirik Grude (2018). Pressure evolution and deformation of confined granular media during pneumatic fracturing. Physical Review E (PRE). ISSN 2470-0045. 97(1), p. 1–19. doi: 10.1103/PhysRevE.97.012908. Full text in Research Archive Show summary

  By means of digital image correlation, we experimentally characterize the deformation of a dry granular medium confined inside a Hele-Shaw cell due to air injection at a constant overpressure high enough to deform it (from 50 to 250 kPa). Air injection at these overpressures leads to the formation of so-called pneumatic fractures, i.e., channels empty of beads, and we discuss the typical deformations of the medium surrounding these structures. In addition we simulate the diffusion of the fluid overpressure into the medium, comparing it with the Laplacian solution over time and relating pressure gradients with corresponding granular displacements. In the compacting medium we show that the diffusing pressure field becomes similar to the Laplace solution on the order of a characteristic time given by the properties of the pore fluid, the granular medium, and the system size. However, before the diffusing pressure approaches the Laplace solution on the system scale, we find that it resembles the Laplacian field near the channels, with the highest pressure gradients on the most advanced channel tips and a screened pressure gradient behind them. We show that the granular displacements more or less always move in the direction against the local pressure gradients, and when comparing granular velocities with pressure gradients in the zone ahead of channels, we observe a Bingham type of rheology for the granular paste (the mix of air and beads), with an effective viscosity μB and displacement thresholds ∇ Pc evolving during mobilization and compaction of the medium. Such a rheology, with disorder in the displacement thresholds, could be responsible for placing the pattern growth at moderate injection pressures in a universality class like the dielectric breakdown model with η = 2, where fractal dimensions are found between 1.5 and 1.6 for the patterns.

• Turquet, Antoine Léo; Toussaint, Renaud; Eriksen, Fredrik Kvalheim; Daniel, Guillaume; Koehn, Daniel & Flekkøy, Eirik Grude (2018). Microseismic Emissions During Pneumatic Fracturing: A Numerical Model to Explain the Experiments. Journal of Geophysical Research (JGR): Solid Earth. ISSN 2169-9313. 123(8), p. 6922–6939. doi: 10.1029/2017JB014613. Full text in Research Archive Show summary

  Modeling of fluid injection processes into a deformable porous medium is a challenging area of physics that has a wide range of applications like the food, construction, and petroleum industries. In this research, we investigate pneumatic fracturing of a porous medium experimentally and numerically in a Hele‐Shaw cell. In the experiments, we inject air into the porous medium (initially random loose packed) to create compaction, channeling, and fracturing while monitoring the cell with accelerometers and a high‐speed camera. Furthermore, we develop a numerical model in two steps: (1) a poroelastoplasticity‐based model to explain dynamic fluid pressure variations and (2) a solid stress model based on Janssen's theory. The contributions of the different pressure sources air in channels and solid stress in the experiments, and the simulations are compared with respect to amplitude and frequency. Afterward, the variations of the normal stress exerting on the plates are convolved with a Lamb Wave green function to generate acoustic emissions numerically. The physics behind the evolution of the experimentally recorded power spectrum of the out‐of‐plane plate vibrations are explained using numerical models. The frequency bands (in the simulated power spectra) are influenced by the size of the opened channels and the Hele‐Shaw cell and are in the same range with the experimentally measured peaks of the acoustic emissions.

• Mikkelsen, A; Khobaib, K; Eriksen, Fredrik Kvalheim; Måløy, Knut Jørgen & Rozynek, Z (2018). Particle-covered drops in electric fields: drop deformation and surface particle organization. Soft Matter. ISSN 1744-683X. 14(26), p. 5442–5451. doi: 10.1039/c8sm00915e. Full text in Research Archive Show summary

  Drops covered by adsorbed particles are a prominent research topic because they hold promise for a variety of practical applications. Unlocking the enormous potential of particle-laden drops in new material fabrication, for instance, requires understanding how surface particles affect the electrical and deformation properties of drops, as well as developing new routes for particle manipulation at the interface of drops. In this study, we utilized electric fields to experimentally investigate the mechanics of particle-covered silicone oil drops suspended in castor oil, as well as particle assembly at drop surfaces. We used particles with electrical conductivities ranging from insulating polystyrene to highly conductive silver. When subjected to electric fields, drops can change shape, rotate, or break apart. In the first part of this work, we demonstrate how the deformation magnitude and shape of drops, as well as their electrical properties, are affected by electric field strength, particle size, conductivity, and coverage. We also discuss the role of electrohydrodynamic flows on drop deformation. In the second part, we present the electric field-directed assembly and organization of particles at drop surfaces. In this regard, we studied various parameters in detail, including electric field strength, particle size, coverage, and electrical conductivity. Finally, we present a novel method for controlling the local particle coverage and packing of particles on drop surfaces by simply tuning the frequency of the applied electric field. This approach is expected to find uses in optical materials and applications.

• Eriksen, Fredrik Kvalheim; Toussaint, Renaud; Turquet, Antoine Léo; Måløy, Knut Jørgen & Flekkøy, Eirik Grude (2017). Pneumatic fractures in confined granular media. Physical Review E (PRE). ISSN 2470-0045. 95(6). doi: 10.1103/PhysRevE.95.062901. Full text in Research Archive Show summary

  We perform experiments where air is injected at a constant overpressure Pin , ranging from 5 to 250 kPa, into a dry granular medium confined within a horizontal linear Hele-Shaw cell. The setup allows us to explore compacted configurations by preventing decompaction at the outer boundary, i.e., the cell outlet has a semipermeable filter such that beads are stopped while air can pass. We study the emerging patterns and dynamic growth of channels in the granular media due to fluid flow, by analyzing images captured with a high speed camera (1000 images/s). We identify four qualitatively different flow regimes, depending on the imposed overpressure, ranging from no channel formation for Pin below 10 kPa, to large thick channels formed by erosion and fingers merging for high Pin around 200 kPa. The flow regimes where channels form are characterized by typical finger thickness, final depth into the medium, and growth dynamics. The shape of the finger tips during growth is studied by looking at the finger width w as function of distance d from the tip. The tip profile is found to follow w(d)∝ d β , where β = 0.68 is a typical value for all experiments, also over time. This indicates a singularity in the curvature d2d/dw2∼ κ ∼ d 1 − 2 β , but not of the slope dw/dd∼ d β − 1 , i.e., more rounded tips rather than pointy cusps, as they would be for the case β > 1 . For increasing Pin , the channels generally grow faster and deeper into the medium. We show that the channel length along the flow direction has a linear growth with time initially, followed by a power-law decay of growth velocity with time as the channel approaches its final length. A closer look reveals that the initial growth velocity v0 is found to scale with injection pressure as v0∝ P 3 2 in , while at a critical time tc there is a cross-over to the behavior v(t)∝ t − α , where α is close to 2.5 for all experiments. Finally, we explore the fractal dimension of the fully developed patterns. For example, for patterns resulting from intermediate Pin around 100–150 kPa, we find that the box-counting dimensions lie within the range DB∈ [ 1.53 , 1.62 ] , similar to viscous fingering fractals in porous media.

• Turkaya, Semih; Toussaint, Renaud; Eriksen, Fredrik Kvalheim; Lengline, Oliver; Daniel, Guillaume & Flekkøy, Eirik Grude [Show all 7 contributors for this article] (2016). Note: Localization based on estimated source energy homogeneity. Review of Scientific Instruments. ISSN 0034-6748. 87:096101(9), p. 1–3. doi: 10.1063/1.4962407. Full text in Research Archive
• Eriksen, Fredrik Kvalheim; Toussaint, Renaud; Måløy, Knut Jørgen & Flekkøy, Eirik Grude (2015). Invasion patterns during two-phase flow in deformable porous media. Frontiers in Physics. 3(81). doi: 10.3389/fphy.2015.00081. Full text in Research Archive Show summary

  We study the formation of viscous fingering and fracturing patterns that occur when air at constant overpressure invades a circular Hele-Shaw cell containing a liquid-saturated deformable porous medium—i.e., during the flow of two non-miscible fluids in a confined granular medium at high enough rate to deform it. The resulting patterns are characterized in terms of growth rate, average finger thickness as function of radius and time, and fractal properties. Based on experiments with various injection pressures, we identify and compare typical pattern characteristics when there is no deformation, compaction, and/or decompaction of the porous medium. This is achieved by preparing monolayers of glass beads in cells with various boundary conditions, ranging from a rigid disordered porous medium to a deformable granular medium with either a semi-permeable or a free outer boundary. We show that the patterns formed have characteristic features depending on the boundary conditions. For example, the average finger thickness is found to be constant with radius in the non-deformable (ND) system, while in the deformable ones there is a larger initial thickness decreasing to the ND value. Then, depending on whether the outer boundary is semi-permeable or free there is a further decrease or increase in the average finger thickness. When estimated from the flow patterns, the box-counting fractal dimensions are not found to change significantly with boundary conditions, but by using a method to locally estimate fractal dimensions, we see a transition in behavior with radius for patterns in deformable systems; In the deformable system with a free boundary, it seems to be a transition in universality class as the local fractal dimensions decrease toward the outer rim, where fingers are opening up like fractures in a paste.

• Turkaya, Semih; Toussaint, Renaud; Eriksen, Fredrik Kvalheim; Zecevic, Megan; Daniel, Guillaume & Flekkøy, Eirik Grude [Show all 7 contributors for this article] (2015). Bridging aero-fracture evolution with the characteristics of the acoustic emissions in a porous medium. Frontiers in Physics. 3. doi: 10.3389/fphy.2015.00070. Full text in Research Archive Show summary

  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, CO2 sequestration 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 exponent p ≈ 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.

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• Moura, Marcel; Eriksen, Fredrik Kvalheim; Jankov, Mihailo; Turquet, Antoine Leo; Hansen, Alex & Måløy, Knut Jørgen (2024). Experiments on transient and steady-state flows in porous media: the transition from viscous fingers to compact displacement during unstable drainage flows. Full text in Research Archive
• Moura, Marcel; Eriksen, Fredrik Kvalheim; Jankov, Mihailo; Turquet, Antoine Leo & Måløy, Knut Jørgen (2022). Transition from viscous Fingers to compact displacement during unstable drainage in porous media. Full text in Research Archive
• Moura, Marcel; Eriksen, Fredrik Kvalheim; Jankov, Mihailo; Turquet, Antoine Léo & Måløy, Knut Jørgen (2022). Transition from viscous fingers to compact displacement during unstable drainage in porous media. Full text in Research Archive
• Moura, Marcel; Reis, Paula Kozlowski Pitombeira; Eriksen, Fredrik Kvalheim; Turquet, Antoine Léo; Flekkøy, Eirik Grude & Toussaint, Renaud [Show all 8 contributors for this article] (2022). Complexity: “More is Different” also in porous media flows. Full text in Research Archive
• Moura, Marcel; Eriksen, Fredrik Kvalheim; Jankov, Mihailo; Turquet, Antoine Léo & Måløy, Knut Jørgen (2022). Transition from viscous fingers to compact displacement during unstable drainage in porous media. Full text in Research Archive
• Moura, Marcel; Eriksen, Fredrik Kvalheim; Turquet, Antoine Leo; Flekkøy, Eirik Grude; Toussaint, Renaud & Jankov, Mihailo [Show all 7 contributors for this article] (2021). Complexity: “More is Different” also in porous media flows. Full text in Research Archive
• Turquet, Antoine Leo; Toussaint, Renaud; Eriksen, Fredrik Kvalheim; Flekkøy, Eirik Grude & Måløy, Knut Jørgen (2020). Reverse Engineering Earthquakes using Lab-scale Replicas: Application to Mw5. 5 2017 Pohang Earthquake. Full text in Research Archive
• Moura, Marcel; Dumazer, Guillaume; Eriksen, Fredrik Kvalheim; Måløy, Knut Jørgen; Flekkøy, Eirik Grude & Toussaint, Renaud (2018). Marangoni induced fracturing in two-dimensional frictional flows. Full text in Research Archive

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