Managed Saffman-Taylor instability during overflush in hydraulic fracturing

Осипцов, А. Н.; Боронин, С. А.; Zilonova, Ekaterina; Desroches, J.

doi:10.1016/j.petrol.2017.10.018

Cited by 4 publications

(4 citation statements)

References 21 publications

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“…While the steady form of Darcy's law, which we employ, has been widely used to model steady flows in porous media, an unsteady form is often employed to capture unsteady effects. In oscillatory channel flow, the timescale associated with the unsteady term decreases to 5 6 of its LF limit value in the HF limit since the viscous layer depth decreases (i.e., the wall-normal velocity profile becomes more uniform) at sufficiently high frequencies [24]. The unsteady timescale ρM is related to the angular oscillation frequency ω = 2π f p through the Womersley number α = √ 3ρMω.…”

Section: Discussionmentioning

confidence: 99%

“…For example, amplifying instabilities can increase mixing efficiency in microfluidic applications [4]. Additionally, a recent model suggests that the structural integrity of hydraulic fractures can be improved when displacing the slurry used to hold the fracture open by allowing viscous fingering to dominate over density-based gravitational effects [5]. Further, viscous fingering affects the efficiency of CO 2 sequestration in terms of the pore-space utilized for long-term CO 2 storage in, e.g., saline aquifers [6].…”

Section: Introductionmentioning

confidence: 99%

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Control of instability by injection rate oscillations in a radial Hele-Shaw cell

et al. 2020

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Small spatial perturbations grow into fingers along the unstable interface of a fluid displacing a more viscous fluid in a porous medium or a Hele-Shaw cell. Mitigating this Saffman-Taylor instability increases the efficiency of fluid displacement applications (e.g., oil recovery), whereas amplifying these perturbations is desirable in, e.g., mixing applications. In this work, we investigate the Saffman-Taylor instability through analysis and experiments in which air injected with an oscillatory flow rate outwardly displaces silicone oil in a radial Hele-Shaw cell. A solution for linear instability growth that shows the competing effects of radial growth and surface tension, including wetting effects, is defined given an arbitrary reference condition. We use this solution to define a condition for stability relative to the constant flow rate case and make initial numerical predictions of instability growth by wave number for a variety of oscillations. These solutions are then modified by incorporating reference conditions from experimental data. The morphological evolution of the interface is tracked as the air bubble expands and displaces oil between the plates. Using the resulting images, we analyze and compare the linear growth of perturbations about the mean interfacial radius for constant injection rates with and without superimposed oscillations. Three distinct types of flow rate oscillations are found to modulate experimental linear growth over a constant phase-averaged rate of fluid displacement. In particular, instability growth at the interface is mildly mitigated by adding to the base flow rate provided by a peristaltic pump a second flow with low-frequency oscillations of small magnitude and, to a lesser extent, high-frequency oscillations of large amplitude. In both cases, the increased stability results from the selective suppression of the growth of large wave numbers in the linear regime. Contrarily, intermediate oscillations consistently destabilize the interface and significantly amplify the growth of the most unstable wave numbers of the constant flow rate case. Numerical predictions of low-frequency oscillations of opposite sign (initially decreasing) show promise of even greater mitigation of linear instability growth than that observed in this investigation. Looking forward, proper characterization of the unsteady, wetting, and nonlinear dynamics of instability growth will give further insight into the efficacy of oscillatory injection rates.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Control of instability by injection rate oscillations in a radial Hele-Shaw cell

et al. 2020

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“…Such fundamental understanding of fingering control can also be employed to minimize the risk of geomechanical phenomena during overflushing. In fact, it was shown (Osiptsov et al, 2018) that viscous fingering (occurring in Regime III) causes a non-uniform sweep of proppants in a fracture, which are important to distribute uniformly to prevents the fracture's collapse.…”

Section: Discussionmentioning

confidence: 99%

“…The natural heterogeneity and geometric variations of flow passages in these formations thus become even more pronounced during fracking. Once again, the instability of the interface between the fracking (displacing) fluid and the hydrocarbons (defending, or displaced, fluid) must be managed to ensure a high oil recovery rate, especially during overflushing (Osiptsov et al, 2018). As with EOR, it is desirable to displace a stable interface through the fractured rock so as to produce a "clean" sweep of the fracture, minimizing the oil or gas film layers left behind.…”

Section: Introductionmentioning

confidence: 99%

Computational Analysis of Interfacial Dynamics in Angled Hele-Shaw Cells: Instability Regimes

Municchi

Christov

2019

Transp Porous Med

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We present a theoretical and numerical study on the (in)stability of the interface between two immiscible liquids, i.e., viscous fingering, in angled Hele-Shaw cells across a range of capillary numbers (Ca). We consider two types of angled Hele-Shaw cells: diverging cells with a positive depth gradient and converging cells with a negative depth gradient, and compare those against parallel cells without a depth gradient. A modified linear stability analysis is employed to derive an expression for the growth rate of perturbations on the interface and for the critical capillary number (Cac) for such tapered Hele-Shaw cells with small gap gradients. Based on this new expression for Cac, a three-regime theory is formulated to describe the interface (in)stability: (i) in Regime I, the growth rate is always negative, thus the interface is stable; (ii) in Regime II, the growth rate remains zero (parallel cells), changes from negative to positive (converging cells), or from positive to negative (diverging cells), thus the interface (in)stability possibly changes type at some location in the cell; (iii) in Regime III, the growth rate is always positive, thus the interface is unstable. We conduct three-dimensional direct numerical simulations of the full Navier-Stokes equations, using a phase field method to enforce surface tension at the interface, to verify the theory and explore the effect of depth gradient on the interface (in)stability. We demonstrate that the depth gradient has only a slight influence in Regime I, and its effect is most pronounced in Regime III. Finally, we provide a critical discussion of the stability diagram derived from theoretical considerations versus the one obtained from direct numerical simulations.

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Integrated Approach to Optimize Flowback in Multi-stage Hydraulically Fractured Wells

Strizhnev,

Boronin,

Vainshtein

et al. 2024

Springer Series in Geomechanics and Geoengineering

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Managed Saffman-Taylor instability during overflush in hydraulic fracturing

Cited by 4 publications

References 21 publications

Control of instability by injection rate oscillations in a radial Hele-Shaw cell

Control of instability by injection rate oscillations in a radial Hele-Shaw cell

Computational Analysis of Interfacial Dynamics in Angled Hele-Shaw Cells: Instability Regimes

Integrated Approach to Optimize Flowback in Multi-stage Hydraulically Fractured Wells

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