Perturbation Solutions for Flow in a Slowly Varying Fracture and the Estimation of Its Transmissivity

Wang, Zhihe; Xu, Chaoshui; Dowd, P. A.

doi:10.1007/s11242-019-01237-7

Cited by 11 publications

(15 citation statements)

References 34 publications

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“…The error associated with the second-order PS is of the third-order of ϵ and is therefore estimated to be small for fractures with gradual aperture change. The comparison study with the CFD simulation in Wang et al (2019) shows a mean absolute discrepancy of 1.6% for the PS in similar wedge-shaped cells when the inertial effects are moderate. However, further assessment may be conducted in the future to test comprehensively the proposed NRE in more fracture cases with different fracture void geometries.…”

Section: Water Resources Researchmentioning

confidence: 85%

A Nonlinear Version of the Reynolds Equation for Flow in Rock Fractures With Complex Void Geometries

Wang

Dowd

et al. 2020

Water Resources Research

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This study presents a nonlinear Reynolds equation (NRE) for single‐phase flow through rock fractures. The fracture void geometry is formed by connected wedge‐shaped cells at pore scale, based on the measured aperture field. An approximate analytical solution to two‐dimensional Navier‐Stokes equations is derived using the perturbation method to account for flow nonlinearity for wedge‐shaped geometries. The derived perturbation solution shows that the main contributors to the determination of general flow behaviors in local wedges are the degree of aperture variation relative to mean aperture, the ratio of aperture variation to wedge length, the Reynolds number, and the degree of wedge asymmetry. The transmissivity of the entire fracture is then solved with a field of local cell transmissivity that varies along both longitude and latitude directions on the fracture plane. The performance of the proposed NRE is tested against flow experiments and flow simulations by solving numerically the three‐dimensional Navier‐Stokes equations for three cases of rock fractures with different void geometries. Results from the proposed model are in close agreement with those obtained from simulations and experiments. As the Reynolds number increases, the pressure difference obtained from the NRE demonstrates the same nonlinear behavior as that obtained from the simulations. Overall, the mean discrepancy between the proposed model and flow simulations is 5.7% for Reynolds number ranging from 0.1 to 20, indicating that the proposed NRE can capture the flow nonlinearity in rock fractures.

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Section: Water Resources Researchmentioning

confidence: 85%

A Nonlinear Version of the Reynolds Equation for Flow in Rock Fractures With Complex Void Geometries

Wang

Dowd

et al. 2020

Water Resources Research

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“…Among these approximates, fractures are found to be well described by a series of connected wedges. Wang et al [37,38] used a wedge-shaped fracture to obtain the perturbation solution of pressure ∆p and flowrate Q under the pressure boundary condition. The perturbation parameter ε is selected as the relative aperture variation along the wedge length l in his study.…”

Section: Fluid Flow Modelmentioning

confidence: 99%

“…This section provides a brief description of the approach rather than a detailed derivation. A more detailed perturbation derivation can be viewed in Wang et al [37,38]. By perturbation analysis, the pressure difference can be made dimensionless and expressed as expanded series with a small parameter ε:…”

Section: Fluid Flow Modelmentioning

confidence: 99%

“…Furthermore, the deviation from the proposed heat transport model is reasonable when presented a diverging wedge with an angle that is 63.47°. The feature of the diverging and converging angle is mostly considered and reported for rock fractures [36,37,45] and therefore, the validity of the assumption is warranted in most cases. Additionally, the validity of the used flow perturbation solution in the fracture lies in the assumptions that the variation of aperture along the fracture length direction is small.…”

Section: Limitations Of Npctfmentioning

confidence: 99%

“…Additionally, the validity of the used flow perturbation solution in the fracture lies in the assumptions that the variation of aperture along the fracture length direction is small. However, Wang et al [37] discussed that the assumption can meet the geometry of most natural fractures.…”

Section: Limitations Of Npctfmentioning

confidence: 99%

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A Novel Procedure for Coupled Simulation of Thermal and Fluid Flow Models for Rough-Walled Rock Fractures

2021

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An enhanced geothermal system (EGS) proposed on the basis of hot dry rock mining technology has become a focus of geothermal research. A novel procedure for coupled simulation of thermal and fluid flow models (NPCTF) is derived to model heat flow and thermal energy absorption characteristics in rough-walled rock fractures. The perturbation method is used to calculate the pressure and flow rate in connected wedge-shaped cells at pore-scale, and an approximate analytical solution of temperature distribution in wedge-shaped cells is obtained, which assumes an identical temperature between the fluid and fracture wall. The proposed method is verified in Barton and Choubey (1985) fracture profiles. The maximum deviation of temperature distribution between the proposed method and heat flow simulation is 13.2% and flow transmissivity is 1.2%, which indicates the results from the proposed method are in close agreement with those obtained from simulations. By applying the proposed NPCTF to real rock fractures obtained by a 3D stereotopometric scanning system, its performance was tested against heat flow simulations from a COMSOL code. The mean discrepancy between them is 1.51% for all cases of fracture profiles, meaning that the new model can be applicable for fractures with different fracture roughness. Performance analysis shows small fracture aperture increases the deviation of NPCTF, but this decreases for a large aperture fracture. The accuracy of the NPCTF is not sensitive to the size of the mesh.

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The hydraulic conductivity of a shaped fracture with permeable walls

Municchi

Christov

2020

Preprint

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Perturbation Solutions for Flow in a Slowly Varying Fracture and the Estimation of Its Transmissivity

Cited by 11 publications

References 34 publications

A Nonlinear Version of the Reynolds Equation for Flow in Rock Fractures With Complex Void Geometries

A Nonlinear Version of the Reynolds Equation for Flow in Rock Fractures With Complex Void Geometries

A Novel Procedure for Coupled Simulation of Thermal and Fluid Flow Models for Rough-Walled Rock Fractures

The hydraulic conductivity of a shaped fracture with permeable walls

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