“…Bauer et al (2019) performed lattice Boltzmann numerical experiments in 3D porous media and laboratory experiments showing that the microstructural disorder of sphere packs and sandstones led to this type of porous media scaling. Also, Chaparian and Tammisola (2020) conducted numerical experiments to analyze the hydrodynamic features of yield-stress fluids flowing through 2D porous media under no-slip and sliding conditions, reporting the same type of porous media scaling in their Q vs. ∇ P datasets.…”
Section: Experimental Results: ∇ P Vs Q Measurementsmentioning
Fractures in geological formations constitute high-conductivity conduits which potentially act as preferential paths during fluid injection in soil remediation and reservoir engineering operations. Recently, the measurement of the pressure drop under different flow rates during the flow of yield stress fluids in porous media has been proposed as the basis for an environmentally friendly method to characterize the Pore Size Distribution. However, the Yield Stress fluids porosimetry Method (YSM) has still not been extended to the characterization of the hydraulic aperture distribution of rough-walled rock fractures. The potential interest of such an extension is intense, considering that the distinct characteristics of rock fractures vs the matrix represent a burden to other traditional porosimetry techniques. In the particular case of X-ray microtomography, time-consuming calibration is often needed, and serious difficulties arise due to beam hardening and reconstruction artifacts. The specific objective of the present investigation is to adapt YSM to the characterization of rough-walled rock fractures. For this purpose, the results of laboratory experiments in which a yield stress fluid was injected through two natural rock fractures were exploited, and the YSM model and algorithm was adapted to the particular topological and geometrical features of flows in fractures. Moreover, numerical experiments were performed at the scale of a single 2D channel with variable aperture to identify the dimension characterized by YSM and decipher the yielding behaviour of the fluids. The present findings show that YSM can be successfully used to characterize the distribution of hydraulic apertures of the flow channels in rough-walled rock fractures. Furthermore, the numerical results revealed that the plug of stagnant fluid is located in the central part of these flow channels and breaks close to the constrictions, forming islands of unyielded fluid.
“…Bauer et al (2019) performed lattice Boltzmann numerical experiments in 3D porous media and laboratory experiments showing that the microstructural disorder of sphere packs and sandstones led to this type of porous media scaling. Also, Chaparian and Tammisola (2020) conducted numerical experiments to analyze the hydrodynamic features of yield-stress fluids flowing through 2D porous media under no-slip and sliding conditions, reporting the same type of porous media scaling in their Q vs. ∇ P datasets.…”
Section: Experimental Results: ∇ P Vs Q Measurementsmentioning
Fractures in geological formations constitute high-conductivity conduits which potentially act as preferential paths during fluid injection in soil remediation and reservoir engineering operations. Recently, the measurement of the pressure drop under different flow rates during the flow of yield stress fluids in porous media has been proposed as the basis for an environmentally friendly method to characterize the Pore Size Distribution. However, the Yield Stress fluids porosimetry Method (YSM) has still not been extended to the characterization of the hydraulic aperture distribution of rough-walled rock fractures. The potential interest of such an extension is intense, considering that the distinct characteristics of rock fractures vs the matrix represent a burden to other traditional porosimetry techniques. In the particular case of X-ray microtomography, time-consuming calibration is often needed, and serious difficulties arise due to beam hardening and reconstruction artifacts. The specific objective of the present investigation is to adapt YSM to the characterization of rough-walled rock fractures. For this purpose, the results of laboratory experiments in which a yield stress fluid was injected through two natural rock fractures were exploited, and the YSM model and algorithm was adapted to the particular topological and geometrical features of flows in fractures. Moreover, numerical experiments were performed at the scale of a single 2D channel with variable aperture to identify the dimension characterized by YSM and decipher the yielding behaviour of the fluids. The present findings show that YSM can be successfully used to characterize the distribution of hydraulic apertures of the flow channels in rough-walled rock fractures. Furthermore, the numerical results revealed that the plug of stagnant fluid is located in the central part of these flow channels and breaks close to the constrictions, forming islands of unyielded fluid.
“…2016; Chaparian & Frigaard 2017 b ; Chaparian et al. 2020; Chaparian & Tammisola 2021), including those with particles. The mesh refinement nicely captures the yield surfaces after a few refinements.…”
Section: Methodology and Benchmarkingmentioning
confidence: 99%
“… and directions) are the characteristic lines of the hyperbolic momentum equations in a 2-D flow, known as the sliplines. Finding the sliplines does not require extensive computational effort and therefore this theory has been developed to compare with the viscoplastic ‘yield limit’ for many different problems such as particle sedimentation (Hewitt & Balmforth 2018; Chaparian & Frigaard 2017 a , b ; Chaparian & Tammisola 2021); swimming (Hewitt & Balmforth 2017; Supekar, Hewitt & Balmforth 2020); and different studies in slump/dam-break type problems (Dubash et al. 2009; Liu et al.…”
We use computational methods to determine the minimal yield stress required in order to hold static a buoyant bubble in a yield-stress liquid. The static limit is governed by the bubble shape, the dimensionless surface tension (
$\gamma$
) and the ratio of the yield stress to the buoyancy stress (
$Y$
). For a given geometry, bubbles are static for
$Y > Y_c$
, which we determine for a range of shapes. Given that surface tension is negligible, long prolate bubbles require larger yield stress to hold static compared with oblate bubbles. Non-zero
$\gamma$
increases
$Y_c$
and for large
$\gamma$
the yield-capillary number (
$Y/\gamma$
) determines the static boundary. In this limit, although bubble shape is important, bubble orientation is not. Two-dimensional planar and axisymmetric bubbles are studied.
“…. Figure 1.( a ) Slipline solution about a circular bubble (see Chaparian & Tammisola (2021) and Pourzahedi et al. (2021 a ) for more details).…”
Section: Problem Statementmentioning
confidence: 99%
“…The computational procedure has been validated extensively in our previous studies (Chaparian & Frigaard 2017; Chaparian et al. 2020; Chaparian & Tammisola 2021; Pourzahedi et al. 2021 a ), with the mesh adaptivity to capture yield surfaces to high resolution.…”
Viscoplastic fluids can hold bubbles/particles stationary by balancing the buoyancy stress with the yield stress – the key parameter here is the yield number
$Y$
, the ratio of the yield stress to the buoyancy stress. In the present study, we investigate a suspension of bubbles in a yield-stress fluid. More precisely, we compute how much is the gas fraction
$\phi$
that could be held trapped in a yield-stress fluid without motion. Here the goal is to shed light on how the bubbles feel their neighbours through the stress field and to compute the critical yield number for a bubble cloud beyond which the flow is suppressed. We perform two-dimensional computations in a full periodic box with randomized positions of the monosized circular bubbles. A large number of configurations are investigated to obtain statistically converged results. We intuitively expect that for higher volume fractions, the critical yield number is larger. Not only here do we establish that this is the case, but also we show that short-range interactions of bubbles increase the critical yield number even more dramatically for bubble clouds. The results show that the critical yield number is a linear function of volume fraction in the dilute regime. An algebraic expression model is given to approximate the critical yield number (semi-empirically) based on the numerical experiment in the studied range of
$0\le \phi \le 0.31$
, together with lower and upper estimates.
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