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

Fundamentals of Rock Mechanics

Boundary element methods in solid mechanics

Fluid Mechanics of Hydraulic Fracturing: a Review

Supercritical geothermal systems are very high-temperature geothermal systems that are located at depths near or below the brittle–ductile transition zone in the crust where the reservoir fluid is assumed to be in the supercritical state, that is for pure water, temperature and pressure are, respectively, in excess of 374 °C and 221 bar. These systems have garnered attention in recent years as a possible type of unconventional geothermal resource due to their very high enthalpy fluids. Supercritical conditions are often found at the roots of volcanic-hosted hydrothermal systems. More than 25 deep wells drilled in geothermal fields such as The Geysers, Salton Sea, and on Hawaii (USA), Kakkonda (Japan), Larderello (Italy), Krafla (Iceland), Los Humeros (Mexico), and Menengai (Kenya) have encountered temperatures in excess of 374 °C, and in some cases have encountered magma. Although fluid entries were documented for some of these wells, it remains an open question if permeability can be maintained at high enthalpy conditions. The IDDP-1 well at Krafla encountered magma, and ended up producing very high enthalpy fluids; however, these fluids were very corrosive and abrasive. Innovative drilling and well completion techniques are therefore needed to deal with the extreme temperatures and aggressive fluid chemistry compositions of these systems. New efforts are underway in Japan (northern Honshu), Italy (Larderello), Iceland (Reykjanes peninsula and Krafla), Mexico (Los Humeros), USA (Newberry), and New Zealand (Taupo Volcanic Zone) to investigate supercritical systems. Here, we review past studies, describe current research efforts, and outline the challenges and potential opportunities that these systems provide for international collaboration to ultimately utilize supercritical geothermal systems as a geothermal energy resource.

/pdf/utilizing-supercritical-geothermal-systems-a-review-of-past-2wj6373io7.pdf

Utilizing supercritical geothermal systems: a review of past ventures and ongoing research activities

Fully Coupled Hydromechanical Simulation of Hydraulic Fracturing in 3D Discrete-Fracture Networks

Simulation of proppant transport with gravitational settling and fracture closure in a three-dimensional hydraulic fracturing simulator

https://repositories.lib.utexas.edu/bitstream/handle/2152/30030/Tianyu_Li_Thesis.pdf?sequence=2

Thermal breakthrough calculations to optimize design of a multiple-stage Enhanced Geothermal System

Fully Coupled Hydromechanical Simulation of Hydraulic Fracturing in Three-Dimensional Discrete Fracture Networks

Comparison of Pseudo-3D and Fully-3D Simulations of Proppant Transport in Hydraulic Fractures, Including Gravitational Settling, Formation of Proppant Banks, Tip-Screen Out, and Fracture Closure

Sogo Shiozawa

Papers

Fully Coupled Hydromechanical Simulation of Hydraulic Fracturing in 3D Discrete-Fracture Networks

Simulation of proppant transport with gravitational settling and fracture closure in a three-dimensional hydraulic fracturing simulator

Thermal breakthrough calculations to optimize design of a multiple-stage Enhanced Geothermal System

Fully Coupled Hydromechanical Simulation of Hydraulic Fracturing in Three-Dimensional Discrete Fracture Networks

Comparison of Pseudo-3D and Fully-3D Simulations of Proppant Transport in Hydraulic Fractures, Including Gravitational Settling, Formation of Proppant Banks, Tip-Screen Out, and Fracture Closure