Beam model for hydraulic fracturing

Tzschichholz, F.; Herrmann, Hans J.; Roman, H. E.; Pfuff, M.

doi:10.1103/physrevb.49.7056

Cited by 34 publications

(25 citation statements)

References 12 publications

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“…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].…”

Section: Introductionmentioning

confidence: 99%

“…[5] Compared to existing simulation models [Tzschichholtz et al, 1994;Flornes, 2000;Maillot et al, 1999] the present model is the first to introduce a two-way coupling between solid deformations/fracture and pressure diffusion. This is essential in order to describe the fact that even thin fractures represent efficient pathways for the fluid pressure.…”

Section: Introductionmentioning

confidence: 99%

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Modeling hydrofracture

Flekkøy

2002

J. Geophys. Res.

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[1] We have developed a model to simulate the formation and evolution of hydraulic fractures. The model relies on a discrete spring network representation of the fracturing media and a continuum description of the fluid pressure that diffuses within it. The model is both versatile and efficient due to the lack of redundant components in the description of the fluid dynamics and the simple mechanics of the spring network. The model is validated quantitatively in a simple test case where it is shown that the pressure forces on the solid agree with theoretical predictions. Subsequently, it is applied to some simplified geological scenarios in order to explore some generic effects. While no attempt has been made to apply representative parameters for real geological systems, the model demonstrates that the fracture formation depends crucially on the way pressure diffuses into the rock, both in the case of a point pressure source and in the case of a sandwich or ''caprock'' geometry where high fluid pressure causes hydraulic fracturing of a lowpermeability ''lid'' layer. Finally, the continuum limit of the elastic system is obtained analytically in order to identify the proper macroscopic parameters that are needed when simulations are to be matched to real geological systems.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modeling hydrofracture

Flekkøy

2002

J. Geophys. Res.

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“…We have introduced a model [5] in which the imposed load represents a pressure that acts along the entire (inner) surface of the crack in a direction perpendicular to the surface (von Neumann boundary value problem). In this way, the point of application of the imposed load varies during the growth of the crack, a situation that describes the case of hydraulic fracturing more realistically than previous spring models.…”

Section: Introductionmentioning

confidence: 99%

Simulations of pressure fluctuations and acoustic emission in hydraulic fracturing

Tzschichholz

Herrmann

1995

Phys. Rev. E

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We consider a two dimensional lattice model to describe the opening of a crack in hydraulic fracturing. In particular we consider that the material only breaks under tension and the fluid has no pressure drop inside the crack. For the case in which the material is completely homogeneous (no disorder) we present results for pressure and elastic energy as a function of time and compare our findings with some analytic results from continuum fracture mechanics. Then we investigate fracture processes in strongly heterogeneous cohesive environments. We determine the cummulative probability distribution for breaking events of a given energetical magnitude (acoustic emission). Further we estimate the probabilty distribution of emission free time intervals. Finally we determine the fractal dimension(s) of the cracks.

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“…These models have later evolved into the beam model and the spring model of hydraulic fracturing, [34,33,35] and [11], respectively. The material strength in these models is represented by the strength of bonds like fuses, springs and beams.…”

Section: Fracture Criterionmentioning

confidence: 99%

“…The strength is initialized at the beginning of the simulation and it stays fixed (quenched disorder). The following distribution, taken from [34,33], is used…”

Section: Inhomogeneous Casementioning

confidence: 99%

Finite element modeling of hydraulic fracturing in 3D

Wangen

2013

Comput Geosci

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A procedure based on the finite element method is suggested for modelling of 3D hydraulic fracturing in the subsurface. The proposed formulation partitions the stress field into the initial stress state and an additional stress state caused by pressure build-up. The additional stress is obtained as a solution of the Biot-equations for coupled fluid flow and deformations in the rock. The fluid flow in the fracture is represented on a regular finite element grid by means of "fracture" porosity, which is the volume fraction of the fracture. The use of the fracture porosity allows for a uniform finite element formulation for the fracture and the rock, both with respect to fluid pressure and displacement. It is demonstrated how the fracture aperture is obtained from the displacement field. The model has a fracture criterion by means of a strain limit in each element. It is shown how this criterion scales with the element size. Fracturing becomes an intermittent process and each event is followed by a pressure drop. A procedure is suggested for the computation of the pressure drop. Two examples of hydraulic fracturing are given, when the pressure build-up is from fluid injection by a well. One case is of a homogeneous rock and the other case is an inhomogeneous rock. The fracture geometry, the well pressure, the new fracture area and the elastic energy released in each event are computed. The fracture geometry is three orthogonal fracture planes in the homogeneous case and it is a branched fracture in the inhomogeneous case.

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Beam model for hydraulic fracturing

Cited by 34 publications

References 12 publications

Modeling hydrofracture

Modeling hydrofracture

Simulations of pressure fluctuations and acoustic emission in hydraulic fracturing

Finite element modeling of hydraulic fracturing in 3D

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