Comparison of Symmetric and Asymmetric Schemes with Arithmetic and Harmonic Averaging for Fracture Flow on Cartesian Grids

Lavrov, Alexandre

doi:10.1007/s11242-022-01760-0

Cited by 2 publications

(2 citation statements)

References 44 publications

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“…Previous studies have reported that the geometry of rough-walled fractures significantly influences the flow properties of the rock masses [2,[10][11][12][13][14]. Zou et al [14] developed a two-dimensional (2D) finite volume method (FVM) code to examine the effects of the original wall surface roughness of fractures on fluid flow.…”

Section: Introductionmentioning

confidence: 99%

“…Gong et al [15,16] presented a new heavily parallelized, dynamic pore-network modeling platform that is capable of simulating two-phase flow in roughwalled fractures with high computational efficiency. Lavrov [13] performed four finite-difference schemes to numerically evaluate the fluid flow in rough-walled fractures. However, underground excavation and/or earthquakes can induce significant deformation of preexisting fractures in rock masses.…”

Section: Introductionmentioning

confidence: 99%

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Evolutions of Anisotropic Hydraulic Properties of Rough-Walled Rock Fractures under Different Shear Displacements

2023

Geofluids

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Four cylindrical sandstone samples were extracted from the original rectangular sample with a rough-walled fracture. Each drilling angle (θ) of cylindrical sandstone samples is different to consider the anisotropies of rough-walled rock fractures. For each sample, different flow velocities ranging from 0 m/s to 13 m/s were designed. For a given flow velocity, a series of different confining pressures ( σ n ), including 1.5 MPa, 2.5 MPa, and 3.5 MPa, were applied on the fractured samples. The hydraulic properties of each cylindrical sandstone sample were tested under different shear displacements ( u s ) and σ n . The results show that the hydraulic gradient ( J ) shows an increasing trend with the increment of σ n . With the increment of the Reynolds number ( Re ), the transmissivity ( T ) decreases in the form of the quadratic function. The normalized transmissivity ( T / T 0 ) decreases with the increment of J . The variations in T / T 0 with J can be divided into three stages. The first stage is that T / T 0 approximately holds a constant value of 1.0 when J is small indicating that the fluid flow is in the linear regime. The last two stages are that T / T 0 decreases with the continuous increase of J , and the reduction rate first increases and then decreases. The critical Reynolds’ number ( Re c ) of the sample angle with a drilling angle of 90° is different from that of other samples. The corresponding Re c is 6.52, 28.73, and 32.1 when the shear displacement u s = 2 mm , 3 mm, and 4 mm, respectively. The variations in Re c and J along different drilling angles are significantly obvious. When the confining pressure is large, the effect of anisotropy on Rec is much greater than that of confining pressure.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Evolutions of Anisotropic Hydraulic Properties of Rough-Walled Rock Fractures under Different Shear Displacements

2023

Geofluids

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Transmissivity Averaging in Fracture Flow on Self-affine Linear Profiles: Arithmetic, Harmonic, and Beyond

Lavrov

2023

Transp Porous Med

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Numerical modeling of unidirectional flow in self-affine fractures using the lubrication approximation requires averaging of the transmissivity between the nodes. Seven averaging techniques are reviewed: arithmetic averaging of transmissivity; harmonic averaging of transmissivity; two averaging techniques derived by cell-based collocation method; global reconstruction of profile by means of multiquadrics; arithmetic averaging of aperture; harmonic averaging of aperture. In order to evaluate the performance of the seven techniques in terms of pressure errors and hydraulic aperture errors, self-affine profiles of 1024 nodes with different Hurst exponents (0.4 to 0.8) are generated. Every second node is then removed, resulting in 512-node profiles. Apertures at removed nodes are used in reference flow simulations on the 512-node profiles. Then, simulations with the seven averaging techniques are performed on 512-node profiles. Errors are computed with regard to the results obtained in the reference simulations. Reconstruction with multiquadrics is found to provide superior accuracy on self-affine profiles, followed by harmonic averaging of transmissivity or harmonic averaging of the aperture (Some of the errors analyzed in this study are minimized with the two last mentioned schemes.). Multiquadrics reconstruction is found to provide the best accuracy also on a smooth periodic profile.

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Comparison of Symmetric and Asymmetric Schemes with Arithmetic and Harmonic Averaging for Fracture Flow on Cartesian Grids

Cited by 2 publications

References 44 publications

Evolutions of Anisotropic Hydraulic Properties of Rough-Walled Rock Fractures under Different Shear Displacements

Evolutions of Anisotropic Hydraulic Properties of Rough-Walled Rock Fractures under Different Shear Displacements

Transmissivity Averaging in Fracture Flow on Self-affine Linear Profiles: Arithmetic, Harmonic, and Beyond

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