Thin-finger growth and droplet pinch-off in miscible and immiscible displacements in a periodic network of microfluidic channels

Budek, Agnieszka; Garstecki, Piotr; Samborski, A.; Szymczak, Piotr

doi:10.1063/1.4935225

Cited by 14 publications

(29 citation statements)

References 59 publications

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“…From Figure 3A, the distance between these longest fingers is comparable to the length of their lengths. This is in agreement with the observation [41,42] that the long finger screens the area of a lateral extent approximately equal to its length. For the analysis of the growth rates of other fingers (see Figure S3A).…”

Section: Dissolution Finger Growth With Screening Effectsupporting

confidence: 93%

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Experimental Observation of Dissolution Finger Growth in Radial Geometry

Szymczak

Toussaint

et al. 2019

Front. Phys.

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Reaction-infiltration instability refers to the morphological instability of a reactive fluid front flowing in a soluble porous medium. This process is important for many naturally occurring phenomena, such as the weathering and diagenesis of rocks, dissolution in salt deposits and melt extraction from the mantle. This paper is focused on experiments on dissolution finger growth in radial geometries in an analog fracture. In the experiments, pure water dissolves a plaster sample forming one of the fracture walls in a Hele-Shaw cell with controlled injection rate and aperture. The flow is directed inwards to the center, and we observe the reaction-infiltration instability developing along the relatively long perimeter of the plaster. Our experimental results show a number of features consistent with the theoretical and numerical predictions on the finger growth dynamics such as screening and selection between the fingers. Statistical properties of the dissolved part evolution with time are also investigated.

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Section: Dissolution Finger Growth With Screening Effectsupporting

confidence: 93%

“…As a results, approximately half of the active fingers continue to grow while the other half cease to grow. The process then repeats itself, leading to the scale-free distribution of finger lengths [40,41].…”

Section: Dissolution Finger Growth With Screening Effectmentioning

confidence: 99%

Experimental Observation of Dissolution Finger Growth in Radial Geometry

Szymczak

Toussaint

et al. 2019

Front. Phys.

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“…Even though it was shown theoretically that the dissolution in laminated fractures is unstable, the corresponding wormholeformation process has not been studied. The only exception is the paper by Budek et al (2017), which, however, focused on highly idealized, smooth fracture geometries with the aim of understanding the dynamics of interactions between the dissolution fingers. Here, instead, we focus on realistic, self-affine, rough geometries of reactivated fractures in shales, generated from the power spectra (Eq.…”

Section: Characteristic Dissolutionmentioning

confidence: 99%

Wormhole Formation During Acidizing of Calcite-Cemented Fractures in Gas-Bearing Shales

et al. 2019

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A relatively large number of calcite-cemented fractures are present in gas-bearing shale formations. During hydraulic fracturing, some of these fractures will be reactivated and may become important flow paths in the resulting stimulated fracture network. On the other hand, the presence of carbonate lamina on fracture surfaces will have a hindering effect on the transport of shale gas from the matrix toward the wellbore. We investigate numerically the effect of low-pH reactive fluids on such fractures, and show that dissolution of the cement proceeds in a highly nonuniform manner. The morphology of the emerging flow paths ("wormholes") strongly depends on the thickness of the calcite layer. For thick carbonate layers, a hierarchical, fractal pattern appears, with highly branched wormhole-like channels competing for an available flow. For thin layers, the pattern is much more diffuse, with less-pronounced wormholes that merge easily with each other. Finally, for intermediate thicknesses, we observe a strong attraction between shorter and longer wormholes, which leads to the formation of islands of carbonate lamina surrounded by the dissolved regions. We argue that the wormholeformation processes are not only important for the increase of shale-gas recovery, but also can be used for retaining the fracture permeability, even in the absence of proppant.2019 SPE Journal 1 is the main driving process behind the cave formation in karst systems (Dreybrodt 1990;Hanna and Rajaram 1998;Cheung and Rajaram 2002;Szymczak and Ladd 2011). All these studies show that the dissolution of rock fractures is a strongly unstable process, with spontaneous focusing of the flow in high-porosity channels (wormholes). The instability here is, in fact, stronger than the corresponding instability in the dissolving porous media (Szymczak and Ladd 2011), with much weaker stabilization caused by diffusion. It needs to be stressed that both experimental and numerical studies of fracture dissolution have considered homogeneous soluble samples, in which aperture growth is potentially unlimited. In shales, the situation is fundamentally different, because the amount of soluble cement at a given place is finite and, thus, after a certain time, the cement fully dissolves, and the dissolution front moves farther downstream. As it turns out, a limited amount of soluble material significantly influences the dissolution patterns in fractures. Nevertheless, as we show in the present study, the dissolution front is still unstable, with an intense wormhole formation in the system. Besides serving as a means to increase the fracture-matrix transport, such a nonuniform dissolution is potentially important for retaining the fracture permeability even in the absence of proppant Wu and Sharma 2015). Whereas a uniformly etched fracture may close tightly under the load of overburden once the fluid pressure is removed, the nonuniform etching will tend to maintain the permeability. The less-dissolved regions will then act as supports to keep more-dissolved regions op...

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“…[45], which led to the conclusion that-if one discards the partially buried pipes the full length of which remain unknown-the length distribution is found to be consistent with a power-law. Such scale-invariant distributions are a characteristic feature of a large number of hierarchical growth processes [46], observed experimentally e.g., in some of the viscous fingering systems [47,48], dendritic sidebranches growth in crystallization [49] or crack propagation in brittle solids [50].…”

Section: Introductionmentioning

confidence: 99%

Influence of Layering on the Formation and Growth of Solution Pipes

Petrus

Szymczak

2016

Front. Phys.

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In karst systems, hydraulic conduits called solution pipes (or wormholes) are formed as a result of the dissolution of limestone rocks by the water surcharged with CO 2 . The solution pipes are the end result of a positive feedback between spatial variations in porosity in the rock matrix and the local dissolution rate. Here, we investigate numerically the effect of rock stratification on the solution pipe growth, using a simple model system with a number of horizontal layers, which are less porous than the rest of the matrix. Stratification is shown to affect the resulting piping patterns in a variety of ways. First of all, it enhances the competition between the pipes, impeding the growth of the shorter ones and enhancing the flow in the longer ones, which therefore grow longer. This is reflected in the change of the pipe length distribution, which becomes steeper as the porosity contrast between the layers is increased. Additionally, stratification affects the shapes of individual solution pipes, with characteristic widening of the profiles in between the layers and narrowing within the layers. These results are in qualitative agreement with the piping morphologies observed in nature.

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Thin-finger growth and droplet pinch-off in miscible and immiscible displacements in a periodic network of microfluidic channels

Cited by 14 publications

References 59 publications

Experimental Observation of Dissolution Finger Growth in Radial Geometry

Experimental Observation of Dissolution Finger Growth in Radial Geometry

Wormhole Formation During Acidizing of Calcite-Cemented Fractures in Gas-Bearing Shales

Influence of Layering on the Formation and Growth of Solution Pipes

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