Abstract:The formation of a fracture network is a key process for many geophysical and industrial practices from energy resource recovery to induced seismic management. We focus on the initial stage of a fracture network formation using experiments on the symmetric coalescence of two equal coplanar, fluid-driven, penny-shaped fractures in a brittle elastic medium. Initially, the fractures propagate independently of each other. The fractures then begin to interact and coalesce, forming a bridge between them. Within an i… Show more
“…O'Keeffe et al. 2018) has also made promising progresses in recent years. Figure 1.The interaction of gravity currents generated by simultaneous injection of two fluids of distinct density into a porous layer of permeability , porosity , length and thickness .…”
The interactions of upper (lighter) and lower (heavier) gravity currents are closely related to fluid-phase resource recovery in porous layers and cleaning of confined spaces. The addition of a second current increases the sweep efficiency of fluid displacement. In this paper, we first derive two ordinary differential equations to describe the interaction of gravity currents in the quasi-steady regime. Two asymptotic regimes are identified, characterised by whether or not the two currents attach to each other, depending on whether the source fluxes are large enough. In the attached regime, a symmetry condition is also identified that describes whether or not the pumping and buoyancy forces balance each other. The model also leads to analytical solutions for the interface shape of the interacting currents in both the detached and attached regimes and for both symmetric and asymmetric currents. For symmetric currents, analytical solutions can also be obtained for the pressure distribution along cap rocks and the sweep efficiency of flooding processes. A particularly interesting aspect is that the displaced fluid remains quiescent at any steady state, regardless of whether the currents attach to each other. Correspondingly, the interface shape of the currents can be described by relatively simple equations and solutions, as if the currents propagate independently in unconfined porous layers. Time transition towards quasi-steady solutions is provided, employing time-dependent numerical solutions of two coupled partial differential equations for dynamic current interaction.
“…O'Keeffe et al. 2018) has also made promising progresses in recent years. Figure 1.The interaction of gravity currents generated by simultaneous injection of two fluids of distinct density into a porous layer of permeability , porosity , length and thickness .…”
The interactions of upper (lighter) and lower (heavier) gravity currents are closely related to fluid-phase resource recovery in porous layers and cleaning of confined spaces. The addition of a second current increases the sweep efficiency of fluid displacement. In this paper, we first derive two ordinary differential equations to describe the interaction of gravity currents in the quasi-steady regime. Two asymptotic regimes are identified, characterised by whether or not the two currents attach to each other, depending on whether the source fluxes are large enough. In the attached regime, a symmetry condition is also identified that describes whether or not the pumping and buoyancy forces balance each other. The model also leads to analytical solutions for the interface shape of the interacting currents in both the detached and attached regimes and for both symmetric and asymmetric currents. For symmetric currents, analytical solutions can also be obtained for the pressure distribution along cap rocks and the sweep efficiency of flooding processes. A particularly interesting aspect is that the displaced fluid remains quiescent at any steady state, regardless of whether the currents attach to each other. Correspondingly, the interface shape of the currents can be described by relatively simple equations and solutions, as if the currents propagate independently in unconfined porous layers. Time transition towards quasi-steady solutions is provided, employing time-dependent numerical solutions of two coupled partial differential equations for dynamic current interaction.
“…The elastic stress in the medium leads to the growth of a penny-shaped fluid-filled fracture in the direction of minimum confining stress. The propagation of such fractures has been studied extensively as it is essential to the modelling of more complex geological situations, including those involving a finite medium (Bunger & Detournay 2005), complex fluids (Barbati et al 2016;Hormozi & Frigaard 2017;Lai et al 2018) and interacting fractures (O'Keeffe et al 2018b). Seminal work on the stress distribution in a penny-shaped fracture (Sneddon & Mott 1946) and the injection of viscous fluids to form fractures (Khristianovic & Zheltov 1955;Barenblatt 1956) led to the development of self-similar solutions for fractures whose propagation is limited by the viscous dissipation in the fluid (Spence & Sharp 1985).…”
Section: Introductionmentioning
confidence: 99%
“…2018) and interacting fractures (O'Keeffe et al. 2018 b ). Seminal work on the stress distribution in a penny-shaped fracture (Sneddon & Mott 1946) and the injection of viscous fluids to form fractures (Khristianovic & Zheltov 1955; Barenblatt 1956) led to the development of self-similar solutions for fractures whose propagation is limited by the viscous dissipation in the fluid (Spence & Sharp 1985).…”
Displacement flows are common in hydraulic fracturing, as fracking fluids of different composition are injected sequentially in the fracture. The injection of an immiscible fluid at the centre of a liquid-filled fracture results in the growth of the fracture and the outward displacement of the interface between the two liquids. We study the dynamics of the fluid-driven fracture, which is controlled by the competition between viscous, elastic and toughness-related stresses. We use a model experiment to characterize the dynamics of the fracture for a range of mechanical properties of the fractured material and fracturing fluids. We form the liquid-filled pre-fracture in an elastic brittle matrix of gelatin. The displacing liquid is then injected. We record the radius and aperture of the fracture, and the position of the interface between the two liquids. In a typical experiment, the axisymmetric radial viscous flow is accommodated by the elastic deformation and fracturing of the matrix. We model the coupling between elastic deformation, viscous dissipation and fracture propagation, and recover the two fracturing regimes identified for single-fluid injection. For the viscous-dominated and toughness-dominated regimes, we derive scaling equations that describe the crack growth due to a displacement flow and show the influence of the pre-existing fracture on the crack dynamics through a finite initial volume and an average viscosity of the fluids in the fracture.
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