Arrest of a radial hydraulic fracture upon shut-in of the injection

Möri, Andreas; Lecampion, Brice

doi:10.1016/j.ijsolstr.2021.02.022

Cited by 18 publications

(49 citation statements)

References 54 publications

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“…Neglecting these, the plot shows two clear changes in front deceleration. The first occurs once the injection stops (Möri & Lecampion 2021a), and the second once the upper tip has propagated further than 2𝑎, a characteristic radius we examine later. We interpret the second transition in the ascent speed to a shift in the process driving tip-line growth, from a radial injection-rate-driven fracture growth to buoyancy-driven fracturing, occurring once the upper tip of the fracture has propagated a given distance.…”

Section: Qualitative Insights From Numerical Simulations Of Fracture ...mentioning

confidence: 99%

“…Here we refer to the moment after injection when ascent becomes dominantly driven by buoyancy. This moment does not occur precisely at the end of injection; some ascent beyond that time is driven by the release of elastic energy stored during the injection phase, which drives a radial motion of the tip line (Möri & Lecampion 2021a). This energy is expended rapidly, after which buoyancy dominates in driving ascent.…”

Section: Early-time Ascent Ratementioning

confidence: 99%

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Ascent rates of 3D fractures driven by a finite batch of buoyant fluid

Davis¹,

Rivalta²,

Smittarello³

et al. 2023

Preprint

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Propagation of fluid-filled fractures by fluid buoyancy is important in a variety of settings, from magmatic dykes and veins to water-filled crevasses in glaciers. Industrial hydro-fracturing utilises fluid-driven fractures to increase the permeability of rock formations; the effect of buoyancy on fracture pathways in this context is typically neglected. Analytical approximations for the buoyant ascent rate facilitate quantitative estimates of buoyant effects. Such analysis exists for two-dimensional fractures, but real fractures are 3D. Here we present novel analysis to predict the buoyant ascent speed of 3D fractures containing a fixed-volume batch of fluid. We provide two estimates of the ascent rate: an upper limit applicable at early time, and an asymptotic estimate (proportional to t^(-2/3)) describing how the speed decays at late time. We infer and verify these predictions by comparison with numerical experiments across a range of scales and analogue experiments on liquid oil in solid gelatin. We find the ascent speed is a function of the fluid volume, density, viscosity and the elastic parameters of the host medium. Our approximate solutions can predict the ascent rate of fluid-driven fractures across a broad parameter space, including cases of water injection in shale and magmatic dykes. Our results demonstrate that both dykes and industrial hydro-fractures can ascend by buoyancy over a kilometre within a day.

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Section: Qualitative Insights From Numerical Simulations Of Fracture ...mentioning

confidence: 99%

Section: Early-time Ascent Ratementioning

confidence: 99%

Ascent rates of 3D fractures driven by a finite batch of buoyant fluid

Davis¹,

Rivalta²,

Smittarello³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Here, we have followed Mori & Lecampion (2021) and used the superscript V to denote the scaling for a fracture with a fixed injected volume V 0 at time t. The corresponding leak-off ( m-scaling) length/radius R V m(t) and aperture w V m(t) scalings for a hydraulic fracture with a fixed injected volume V 0 are…”

Section: Scaling Before Shut-inmentioning

confidence: 99%

“…Here, we have followed Mori & Lecampion (2021) and used the superscript to denote the scaling for a fracture with a fixed injected volume at time . The corresponding leak-off (-scaling) length/radius and aperture scalings for a hydraulic fracture with a fixed injected volume are The dimensionless toughness and leak-off parameters for a hydraulic fracture with a fixed injected volume are and , where …”

Section: Self-similarity Close To Closure – the Sunset Solutionmentioning

confidence: 99%

“…Since thus far there has been no rigorous treatment of a deflating and receding hydraulic fracture, current leak-off identification assumes that the hydraulic fracture deflates with the same footprint at the time of shut-in (Nolte 1979;Economides & Nolte 2000), and for stress measurement, there is no clear way to pinpoint the closure pressure from the pressure-time record. The propagation of radially symmetric hydraulic fractures between shut-in and arrest has been subjected to rigorous study only recently by Mori & Lecampion (2021), while, to our knowledge, existing models of recession have been purely numerical and accomplished by implementing a minimum aperture constraint whose magnitude is determined arbitrarily, which can impact the solution significantly (Desroches & Thiercelin 1993;Adachi et al 2007;McClure & Horne 2013;Mohammadnejad & Andrade 2016;Zanganeh, Clarkson & Hawkes 2017). Laboratory hydraulic fracture experiments in a porous solid rely on active acoustic monitoring in order to infer the fracture front locations as the hydraulic fracture evolves (De Pater et al 1996;van Dam, de Pater & Romijn 2000).…”

Section: Introductionmentioning

confidence: 99%

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Sunset similarity solution for a receding hydraulic fracture

Peirce

Detournay

2022

J. Fluid Mech.

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This paper derives approximate ‘sunset’ similarity solutions for receding plane strain and radially symmetric hydraulic fractures in permeable elastic media close to the point of closure. Local analysis is used to show that a receding hydraulic fracture has a linear aperture asymptote $\hat {w}\sim \hat {s}$ in the fracture tip, where $\hat {s}$ is the distance from the fracture front. Due to the regularity of the linear asymptote, it is possible to determine similarity solutions in the form of power series expansions, which, for integers $N\ge 2$ and values of the radius decay exponent $\gamma =1/N$ , can be shown to terminate to yield polynomial solutions for the fracture aperture of degree $N$ . Of this countable infinity of polynomial solutions, the final aperture profile as the fracture approaches closure is associated with the second-degree polynomial with $\gamma =1/2$ called the sunset solution. For the reverse time $t^{\prime }$ measured from closure, the sunset solution is characterized by $w\sim t^{\prime }$ and $R\sim t^{\prime 1/2}$ . Of all the admissible polynomial similarity solutions, the sunset solution is shown to form an attractor, as $t^{\prime }\rightarrow 0$ , for receding hydraulic fractures associated with a wide variety of points in parametric space. Using the sunset solution, it is possible to estimate the duration of recession, assuming that the fracture aperture and radius at the start of recession are given, and determine how it scales with a dimensionless shut-in parameter. As the fracture approaches closure, the term responsible for coupling the elastic force balance and fluid conservation becomes subdominant to the other terms in the lubrication equation, which reduces to a local kinematic relation between the decaying fracture aperture and the leak-off velocity. This fundamental decoupling of dynamics from kinematics results in the sunset solution being dependent on only a single material parameter – namely the leak-off coefficient. This isolation of the leak-off coefficient by the sunset solution opens the possibility to determine this parameter from laboratory or field measurements.

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Measurements of the Evolution of the Fluid Lag in Laboratory Hydraulic Fracture Experiments in Rocks

Liu

Lecampion

2022

Mechanics of Hydraulic Fracturing

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Arrest of a radial hydraulic fracture upon shut-in of the injection

Cited by 18 publications

References 54 publications

Ascent rates of 3D fractures driven by a finite batch of buoyant fluid

Ascent rates of 3D fractures driven by a finite batch of buoyant fluid

Sunset similarity solution for a receding hydraulic fracture

Measurements of the Evolution of the Fluid Lag in Laboratory Hydraulic Fracture Experiments in Rocks

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