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 physical, mechanical and morphological properties of a rock undergo substantial change when exposed to the extreme temperatures that are encountered in processes such as nuclear waste disposal, underground coal gasification (UCG) and building fires. An attempt has been made in this article to study the different physical and morphological changes that occur within Indian sandstone due to thermal treatment. Tests were performed on a thermally treated air-cooled and non-cooled set of samples in order to observe the change in the physico-morphological properties. Heating has a profound effect on the physical properties such as density, porosity and compression wave velocity (VP), which have been further explained by thin-section, X-ray diffraction (XRD) and scanning electron microscope (SEM) studies. Thermal analyses such as thermogravimetric analysis (TGA) and differential thermal analysis (DTA) were performed to observe the chemical changes occurring in the specimen. Since Dholpur sandstone is a quartz-dominant rock, the thermally induced chemical degradation is minimal in nature. DTA studies revealed the quartz inversion to occur at 579.19 °C. Structural changes that are caused due to the random alignment and the thermal anisotropic behaviour of different minerals lead to microcracking, thereby affecting the physical properties. This study will provide an understanding of the thermal behaviour of rocks and the relationship of the thermal behaviour with physico-mechanical behaviour. The study can prove useful while designing structures in processes such as UCG, nuclear waste disposal, deep mining and geothermal energy; the study can also enable the formation of a protocol to restore the structural integrity and aesthetic value of fire-damaged buildings.

Effects of thermal treatment on physico-morphological properties of Indian fine-grained sandstone

A slurry diffusion model of a single random-roughness fissure is established to consider the slurry and geological fracture coupling based on the Navier-Stokes equation. The slurry flow characteristics and coupling response in a rough fracture are investigated. The influencing mechanism of roughness on the slurry flow was revealed. The calculation model of effective aperture is determined in a rough fracture. The shear displacement effects on the slurry flow are studied. The results show that this slurry diffusion model can more accurately reflect the grouting. A rougher fracture has a great effect on the flow because of the larger low-speed domains. The pressure gradient and maximum diffusion velocity increase parabolically with changes in the relative roughness. The conventional flat-panel model can cause an increasing deviation rate for determination of grouting parameters. The coupling degree distribution is temporal with spatial variations, and increases with the time-dependent viscosity, roughness (decreasing effective aperture), and a shortening path. The viscosity is the key controlling factor in grouting pressure. The roughness response after shear displacement is more significant, further revealing that on-site grout splitting often occurs at the narrow undulating tip with high viscosity and shear on a rough flow surface. The rough fracture model considering fluid-solid coupling is more consistent with the grouting phenomenon in engineering. And the roughness and shear are the key geological factors of grout splitting.

Numerical investigation on a grouting mechanism with slurry-rock coupling and shear displacement in a single rough fracture

This study numerically investigates the effect of heat transfer between fluid and fracture walls on flow behavior in a single fracture. The process of heated flow through fracture models created with realistic rock surfaces is simulated by solving the Navier-Stokes equations and energy conservation equation. The simulation results show that the heat transfer has a significant effect on the viscosity of water in the fracture, but the effect on the density is negligible. With the influence of heat transfer, the fluid in the fracture exhibits nonlinear characteristics even though the flow rate is small. The Forchheimer equation is proven to well represent the nonlinearity induced by both the fracture geometry and the heat transfer. As the flow rate increases, the heat transfer effect gradually decreases. In addition, when the rock temperature is large enough, the fracture geometry effect becomes less prominent. The results in this study provide new insights in understanding the heat transfer–dependent fracture flow behavior and directing such experimental procedures in future.

Numerical investigation of heat transfer effect on flow behavior in a single fracture

Draa Sfar is a polymetallic (Zn–Pb–Cu) volcanogenic massive sulfide deposit with an actual resource of 13 Mt at 4.0% Zn and 1.3% Pb. It is part of the central Jbilets area known for its several Cu–Zn ore deposits. The ore is hosted in the upper Visean-Namurien sedimentary formation. Owing to the complexity of the geology of the ore deposits, numerical simulation approach was attempted to shed light into the temperature distribution, the circulation of the hydrothermal fluid and the genesis of massive sulfide ore bodies by evaluating the permeability, porosity, and thermal conductivity. On the basis of this simulation approach, the ore is predicted to be deposited at a temperature ranging between 230 and 290 °C. This temperature range is dependent on the pre-existing temperature of the discharge area where a metal-rich fluid precipitated the ore. The duration of the Draa Sfar ore body formation is predicted to be 15, 000 to 50, 000 years. Based on geological studies of Draa Sfar deposit together with the aforementioned results of the simulation approach, an ore genetic model for the massive sulfide ore bodies is proposed. In this model, the supply of ore-forming fluids is ensured by the combination of seawater and magmatic waters. Magma that generated rhyodacite dome acted as the heat source that remobilized the circulation of these ore-bearing fluids. The NW-SE trending faults acted as potential pathways for both the downward and upward migration of the ore-forming fluids. Due to their high permeability, the ignimbritic facies, host rocks of Draa Sfar ore bodies, have favored the circulation of the fluids. The mixing between the ore-forming fluids of magmatic origin and the descending seawaters and/or in situ pore waters led to the formation the ore bodies in 35,000 years. The position and size of the ore body, determined by the simulation approach, is consistent with the actual field geological data.

Numerical heat and fluid flow modeling of the Hercynian Draa Sfar polymetallic (Zn–Pb–Cu) massive sulfide deposit, Central Jbilets, Morocco

Understanding the flow behavior through fractures is critically important in a wide variety of applications. In many situations, the fluid flow can be highly irregular and non-linear in nature. Numerical simulation can be employed to simulate such conditions which are difficult to replicate in laboratory experiments. Therefore, a parametric study has been conducted on the fluid flow through micro-fracture over a large range of inlet pressure, fluid density, fluid viscosity, temperature, joint roughness coefficient (JRC), and fracture using finite element analysis. Irregular fracture profiles were created using Barton’s joint roughness coefficient. The Navier-Stokes (NS) equation was used to simulate the flow of water in those micro-fractures. The result showed that the fracture, fluid, and ambient conditions have a wide and varied effect on the fluid flow behavior. The interrelationship between these parameters was also studied. The model simulation provided result in the form of velocity and pressure drop profile, which can be used to determine the behavior of flow under different condition. The volumetric flow was calculated for each condition and has been plotted against the corresponding parameter to study the interrelationship.

Praksh Kumar Singh

Papers

Parametric study of factors affecting fluid flow through a fracture