Growth of a crack produced by hydraulic fracture in a poroelastic medium

Morphodynamics during air injection into a confined granular suspension

“…This is indeed what is generally observed experimentally; in addition, for very large values of Ca, w does not go to zero but reaches a limiting value of about half the channel width. More precisely, the relative finger width = w/W is a function of the dimensionless control parameter 1/B = 12(W/b) 2 Ca, which involves the cell aspect ratio. The mean flow (averaged over the cell thickness) is governed by Darcy's law which reduces far away from the finger to: V = (b 2 /12Á)|∇P| with ∇P being the applied pressure gradient and V the flow velocity.…”

“…An even more complex situation is found when one considers the dynamics and the stability of a free interface within these granular suspensions. This situation is encountered widely both in nature or in industrial processes and due to their practical importance issues like flow induced reorganization of porous structures -often called poro-elasticity -have triggered many studies both in the geophysicist and the engineering communities [2,3]. A fundamental understanding of the involved processes is however still lacking.…”

A finite element approach to the simulation of hydraulic fractures with lag

“…In addition, we denote the second initial guess with two asterisks (**), which should yield the opposite, K < K;. In this article, we choose (26) for the first initial guess, which indicates a guess of no crack propagation. If this guess yields K' < K~, then we conclude that no crack propagation occurs, and we do not have to iterate further.…”

“…An example of this would be when strong plastic deformation is present, or when the rock exhibits a high degree of poroelastic behavior [24][25][26]. In those cases, boundary element methods are not so attractive because of the transient and inhomogeneous nature of the problem.…”

Modeling hydrofracture

“…This applies to leakage of hydrocarbons through low-permeability caprocks in sedimentary basins, fluid loss during ''leak-off'' tests carried out in subsurface drill holes, fluid ''blow out'' events in geysers, hydrothermal megaplumes and smaller fluid release events at the mid-ocean ridges, fluid release from crystallizing and cooling magmatic bodies, and fluid migration and veining following metamorphic devolatilization processes, and it may also be responsible for fracturing associated with the emplacement of dikes, sills, and other intrusive bodies in the Earth's crust. Existing studies of hydrofracturing include both theoretical analysis [Gordeyev, 1993;Valkó and Econimedes, 1995], simulation studies [Tzschichholtz et al, 1994;Tzschichholtz and Herrmann, 1995;Flornes, 2000;Herrmann and Roux, 1990], and real-scale empirical measurements during leakoff tests [Valkó and Econimedes, 1995]. Analogue experiments have also been carried out where the detailed evolution of the hydrofractures are made possible by transparent setups [Lemaire et al, 1991].…”