The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

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VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

The flow of homogeneous fluids through porous media: analogies with other physical problems

A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering

This paper provides a review of hydromechanical (HM) couplings in fractured rock, with special emphasis on HM interactions as a result of, or directly connected with human activities. In the early 1960s, the coupling between hydraulic and mechanical processes in fractured rock started to receive wide attention. A series of events including dam failures, landslides, and injection-induced earthquakes were believed to result from HM interaction. Moreover, the advent of the computer technology in the 1970s made possible the integration of nonlinear processes such as stress–permeability coupling and rock mass failure into coupled HM analysis. Coupled HM analysis is currently being applied to many geological engineering practices. One key parameter in such analyses is a good estimate of the relationship between stress and permeability. Based on available laboratory and field data, it was found that the permeability of fractured rock masses tends to be most sensitive to stress changes at shallow depth (low stress) and in areas of low in-situ permeability. In highly permeable, fractured rock sections, fluid flow may take place in clusters of connected fractures which are locked open as a result of previous shear dislocation or partial cementation of hard mineral filling. Such locked-open fractures tend to be relatively insensitive to stress and may therefore be conductive at great depths. Because of the great variability of HM properties in fractured rock, and the difficulties in using laboratory data for deriving in-situ material properties, the HM properties of fractured rock masses are best characterized in situ.

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The role of hydromechanical coupling in fractured rock engineering

The failure of brittle rocks during compression is preceded by the formation, growth, and coalescence of microcracks. Elastic wave velocities are reduced in the presence of open microcracks and fractures and may therefore be used to monitor the progressive damage of the rock. In general, these microcracks are not randomly oriented, and the rock displays an elastic anisotropy. The elastic anisotropy due to cracks can be expressed in terms of a second-rank and fourth-rank crack density tensor. For open cracks the contribution of the fourth-rank crack density tensor to the elastic wave velocities is small. These results are compared with recent measurements of the ultrasonic compressional and shear wave velocities for propagation parallel and perpendicular to an increasing axial stress applied at constant confining stress to Berea sandstone. Inversion of the velocity measurements indicates that the microcracks propagate parallel to the maximum compressive stress, in agreement with current rock mechanics theory. A reasonable fit to the data is obtained using only the second-rank crack density tensor even though, at high confining stress, the cracks are expected to be in partial contact along their length. This is consistent with the model of elastic wave propagation in a medium containing partially contacting fractures published by White. However, measurements of off-axis wave velocities are required to fully quantify the contribution of the fourth-rank crack density tensor.

Microcrack-induced elastic wave anisotropy of brittle rocks

Evaluation of mechanical rock properties using a Schmidt Hammer

The classic Mandel solution associated with the well-known Mandel–Cryer effect is re-examined. Using Biot theory of poroelasticity, the solution of the Mandel problem is extended to include material transverse isotropy, as well as the compressibility of the pore fluid and the solid constituents of the soil–rock skeleton. Le resultat classique de Mandel, associe a l'effet bien comnnu de Mandel—Cryer, est reexaminee. En utilisant la theorie poro-e1astique de Blot, la solution du probleme de Mandel est etendue afin d'introduire l'anisotropie transverse du materiau, ainsi que la compressibilite des fluides presents dans les pores et celle des constituants solides du squelette du sol ou de la roche.

Mandel's problem revisited

Fracability Evaluation in Shale Reservoirs - An Integrated Petrophysics and Geomechanics Approach

An Integrated Petrophysics and Geomechanics Approach for Fracability Evaluation in Shale Reservoirs

Cubical granite specimens were fractured by borehole pressurization of 1 cP water, 80 cP oil and via a urethane sleeve. Viscous oil tends to generate thick and planar cracks with few branches, while water tends to generate thin and wavelike cracks with many secondary branches. While penetrating fluids extended cracks rapidly, pressurization via a urethane sleeve led to stepwise crack extension. Fault-plane solutions of AE (Acoustic Emission) events indicated that shear-type mechanisms were dominant during water injection and sleeve pressurization, whereas tensile-type mechanisms were dominant during oil injection. These results could be helpful in optimizing stimulation treatments in the petroleum industry.

Jean-Claude Roegiers

Papers

Evaluation of mechanical rock properties using a Schmidt Hammer

Mandel's problem revisited

Fracability Evaluation in Shale Reservoirs - An Integrated Petrophysics and Geomechanics Approach

An Integrated Petrophysics and Geomechanics Approach for Fracability Evaluation in Shale Reservoirs

Influence of Fluid Viscosity on the Hydraulic Fracturing Mechanism