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

This study focuses on the transport properties and permeability evolution characteristics of fluid flow through thermally treated rock samples containing single fractures. First, splitting fractures were generated in cylindrical granite samples after high-temperature exposure (25–800 °C). Then a series of water flow tests through both intact and fractured samples were conducted in a triaxial cell under different confining pressures (10–30 MPa) and varying inlet hydraulic pressures (0.4–6 MPa). The results show that as the temperature increases from 25 to 800 °C, the standard deviations of the 3D spatial distribution parameters, including the asperity height, slope angle, and aspect direction of the fracture surface mesh element planes, all increase, indicating gradually increasing fracture surface roughness. The relationships between the pressure gradient and flow rate of intact samples, fractured rock samples, and the fractures themselves can all be well fitted using the Forchheimer’s law. Both linear and nonlinear coefficients in the Forchheimer’s law increase with increasing confining pressure. An exponential function is used to evaluate the equivalent permeability of intact samples based on temperature levels. The permeability undergoes an increasing trend as the temperature increases due to thermally induced defects, but undergoes a decreasing trend as the confining pressure increases due to defect closure. Two representative types of flow characteristics through the fractured rock samples, dominated by either the rock matrix or fracture flow, are identified. In the temperature range of 25–800 °C, the critical Reynolds number of the fractures declines, which first remains generally constant for temperatures of 25–400 °C and then experiences a dramatic decrease for temperatures of 400–800 °C. The nonlinear coefficient bf in Forchheimer’s law versus the hydraulic aperture eh curves displays a decreasing trend following a power-law relationship. The Forchheimer’s law results are evaluated by plotting the normalized transmissivity against the pressure gradient. An increase in the confining pressure shifts the fitted curves downward. As the temperature increases, the contribution of the matrix to the overall discharge capacity of the fractured rock samples gradually enhances, while that for the fractures weakens. The reduction extent in permeability of the rough-walled fractures is more remarkable than that of the matrix under an applied confining pressure.

Experimental Study of Nonlinear Flow Behaviors Through Fractured Rock Samples After High-Temperature Exposure

Effect of surface morphology on fluid flow in rough fractures: A review

Influences of connectivity and conductivity on nonlinear flow behaviours through three-dimension discrete fracture networks

The instability of rock slopes and underground engineering structures is usually caused by shear sliding along discontinuities, such as joints or faults, which are usually non-persistent It is important to study the shear failure behavior of non-persistent joints to better understand the instability mechanism of jointed rock masses In this research, rock-like samples containing multiple non-persistent joints were prepared and used for direct shear tests under constant normal load The test results showed that the shear failure of multiple non-persistent joints usually involves multiple coalescence modes of rock bridges, which are affected by joint configurations and normal stress Under the same normal stress, the shear strength, and dilation behavior are mostly dominated by joint persistency, which essentially determines the roughness of the macroshear fracture surface Furthermore, the acoustic emission characteristics of non-persistent joints were evaluated by the hit rate, energy rate, and b value A lower b value, indicating a more intense shear failure, is usually related to a smaller joint persistency and medium joint spacing Finally, the cracking process, force evolution, and micro-cracking mechanism of multiple non-persistent joints were revealed using particle flow code

Experimental and Numerical Investigation on Shear Failure Behavior of Rock-like Samples Containing Multiple Non-Persistent Joints

Hydraulic properties of 3D rough-walled fractures during shearing: An experimental study

Coupled THM (thermal-hydromechanical) processes have become increasingly important in studying the issues affecting subsurface flow systems. CO2 permeability of the fracture in caprock is a key factor that affects sealing efficiency of caprock. A new model associated with coupled THM processes that shows a good reliability was derived. Then, based on the COMSOL multiphysics software, a series of numerical calculations were performed on caprock models with a single fracture subject to coupled THM effects. Transmissivity of the fracture as a function of fracture angle, overburden pressure, fluid pressure difference, injected CO2 temperature, and the initial fracture aperture was elucidated, respectively. Average transmissivity of the fracture undergoes an increase by 1.74 times with the fracture angle (45°–90°), 2-3 orders of magnitude with the fluid pressure difference (5–30 MPa), and 4-5 orders of magnitude with the initial fracture aperture (0.05–0.5 mm), while it decreases by 3-4 orders of magnitude as overburden pressure increases from 30 to 80 MPa. Injected CO2 temperature has a small impact on the fracture permeability. This work provides an alternative tool to enrich the numerical modeling for the assessment of CO2 caprock sealing efficiency.

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Huidong Wang

Papers

Hydraulic properties of 3D rough-walled fractures during shearing: An experimental study

CO2 Permeability Analysis of Caprock Containing a Single Fracture Subject to Coupled Thermal-Hydromechanical Effects