Permeability of a fracture with cylindrical asperities

Kumar, Sunil; Zimmerman, Robert W.; Bodvarsson, G.S.

doi:10.1016/0169-5983(91)90053-l

Cited by 26 publications

(27 citation statements)

References 17 publications

(36 reference statements)

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“…Kumar et al (1991) investigated fluid flow between two parallel plane walls with randomly distributed, monodisperse cylindrical obstacles, which were considered as an analog of contact areas in natural rock fractures. Kumar et al (1991) investigated fluid flow between two parallel plane walls with randomly distributed, monodisperse cylindrical obstacles, which were considered as an analog of contact areas in natural rock fractures.…”

Section: 1002/2017jb014509mentioning

confidence: 99%

“…Figure 11 compares the numerically determined fracture permeabilities Darin and Huitt (1960), Lee (1969), Walsh (1981), and Kumar et al (1991), and the dashed lines give the effective permeability calculated using the differential effective medium (DEM) model developed based on the drag force formula from Spielman and Goren (1968). Between an empty fracture and an obstacle fraction of f = 0.3 the transmissivity drops 2 orders of magnitude, then again almost 2 orders of magnitude between f = 0.3 and f = 0.7 and almost an order of magnitude between f = 0.7 and f = 0.8.…”

Section: Effective Transmissivity Of a Fracture With Obstacles-numerimentioning

confidence: 99%

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The Effective Transmissivity of a Plane‐Walled Fracture With Circular Cylindrical Obstacles

Jasinski

Dąbrowski

2018

JGR Solid Earth

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Stimulated and propped fractures provide the conductive pathways in low matrix permeability rocks. We study the impact of fracture aperture and proppant size and fraction on the effective transmissivity of a stimulated fracture filled with a partial monolayer of proppant grains. The proppant grains are treated as circular cylindrical obstacles, and the fracture walls are planar. The key geometric parameters are the obstacle fraction f and the ratio between the fracture aperture and the obstacle diameter α. We use three‐dimensional Stokes flow numerical simulations to demonstrate that the fracture flow model given by the Reynolds equations may largely overestimate the flow rate. To circumvent the inability of the Reynolds model to fulfill the no‐slip boundary condition at the rims of the obstacles, we use the Brinkman flow model adapted to the case of fracture flow. The relative difference between the effective transmissivities computed with the Stokes and Brinkman models for systems with multiple obstacles is below 10% for fractions up to 0.5. We use the Brinkman model to study the effective transmissivity of a plane‐walled fracture with circular cylindrical obstacles. Systematic numerical simulations show that the normalized effective transmissivity is predominantly dependent on f and α, and the effects of obstacle ordering are minor. The presented numerical results can be used by petroleum engineers for estimating transmissivities of propped fractures under in situ conditions. The model can also be applied to microfluidic systems and for deriving first‐order estimates of the effective transmissivity of rough‐walled, natural fractures with load‐bearing contact areas.

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Section: 1002/2017jb014509mentioning

confidence: 99%

Section: Effective Transmissivity Of a Fracture With Obstacles-numerimentioning

confidence: 99%

The Effective Transmissivity of a Plane‐Walled Fracture With Circular Cylindrical Obstacles

Jasinski

Dąbrowski

2018

JGR Solid Earth

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“…For the fracture, we will use the characteristic curves that were derived by of the hydrological parameters for the fracture are taken to be k =5.5 x 10-m (per fracture), S , = 1.0, S, =O.O, va =-1.65 x lo3 Pa, and n =2.89. If the permeability b2/12 of a smooth-walled channel is modified to account for fracture roughness and contact area (see Kumar et al, 1991;Zimmerman et al, 1991cZimmerman et al, ,1992, this single--27 -fracture permeability is seen to be consistent with a fracture whose aperture is on the order of 1OOp. The volumes of the fracture elements were chosen to correspond to an aperture of 800pm, however.…”

Section: Horizontal Flow Along a Single Leaky Fracturementioning

confidence: 99%

Transient dual-porosity simulations of unsaturated flow in fractured rocks

Zimmerman¹,

Hadgu²,

Bodvarsson³

1995

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DISCLAIMER ABSTRACTThis report describes the development and use of a semi-analytical dual-porosity simulator for unsaturated flow in fractured rock masses. Fluid flow between the fracture network and the matrix blocks is described by a nonlinear equation that relates the imbibition rate to the local difference in liquid-phase pressure between the fractures and the matrix blocks. This equation is a generalization of the Warren-Root equation, but is accurate in both early and late time regimes. The fracture/matrix interflow equation has been incorporated into a computational module that acts as a source/sink term for fracture elements; this module is compatible with the unsaturated flow simulator TOUGH. Flow processes are then simulated using only fracture elements in the computational grid. This semi-analytical dual-porosity module has been tested with TOUGH on various problems involving transient flow in fracturedporous media, and compared with simulations performed using explicit discretization of the matrix blocks. The new semi-analytical dual-porosity model accurately simulates flow processes in unsaturated fractured rocks, and typically requires an order of magnitude less computational time than do simulations using fully-discretized matrix blocks.

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“…For Newtonian fluids, Yang et al (2002) developed a mathematical model for the flow of water through a channel impregnated with a polymer gel that is treated as an elastic and deformable porous medium. Kumar et al (1991) investigated the permeability of a rock fracture. The attempts to include porous media in the flows of complex fluids need some new physical parameters besides non-Newtonian fluid parameters.…”

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confidence: 99%

Approximate Analytical Solutions for Flow of a Third-Grade Fluid Through a Parallel-Plate Channel Filled with a Porous Medium

Aksoy

Pakdemi̇rli̇

2009

Transp Porous Med

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The flow of a non-Newtonian fluid through a porous media in between two parallel plates at different temperatures is considered. The governing momentum equation of third-grade fluid with modified Darcy's law and energy equation have been derived. Approximate analytical solutions of momentum and energy equations are obtained by using perturbation techniques. Constant viscosity, Reynold's model viscosity, and Vogel's model viscosity cases are treated separately. The criteria for validity of approximate solutions are derived. A numerical residual error analysis is performed for the solutions. Within the validity range, analytical and numerical solutions are in good agreement.

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Permeability of a fracture with cylindrical asperities

Cited by 26 publications

References 17 publications

The Effective Transmissivity of a Plane‐Walled Fracture With Circular Cylindrical Obstacles

The Effective Transmissivity of a Plane‐Walled Fracture With Circular Cylindrical Obstacles

Transient dual-porosity simulations of unsaturated flow in fractured rocks

Approximate Analytical Solutions for Flow of a Third-Grade Fluid Through a Parallel-Plate Channel Filled with a Porous Medium

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