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

Anthropogenic fluid injections are known to induce earthquakes. The mechanisms involved are poorly understood, and our ability to assess the seismic hazard associated with geothermal energy or unconventional hydrocarbon production remains limited. We directly measure fault slip and seismicity induced by fluid injection into a natural fault. We observe highly dilatant and slow [~4 micrometers per second (μm/s)] aseismic slip associated with a 20-fold increase of permeability, which transitions to faster slip (~10 μm/s) associated with reduced dilatancy and micro-earthquakes. Most aseismic slip occurs within the fluid-pressurized zone and obeys a rate-strengthening friction law μ = 0.67 + 0.045ln(v/v₀) with v₀ = 0.1 μm/s. Fluid injection primarily triggers aseismic slip in this experiment, with micro-earthquakes being an indirect effect mediated by aseismic creep.

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Seismicity triggered by fluid injection–induced aseismic slip

The goal of this study is to review 18 significant enhanced geothermal system (EGS) sites and technologies that have been applied in the European Union, Japan, South Korea, Australia and the USA. The results of earlier cases indicate that the site characteristics, such as a transtensional type setting, are a key factor of successful EGS development. This study also introduces the Enhanced Geothermal Innovative Network for Europe (ENGINE), which focuses on developing high-temperature instruments for the characterization and exploitation of supercritical geothermal reservoirs, as well as the geothermal engineering integrating mitigation of induced seismicity in reservoirs (GEISER). The energy reserves in the upper 10 km of the earth's crust are approximately 1.3 × 1027 J, which could supply the global energy use for approximately 217 million years. The exploitable geothermal potential can reach 1200 GWe based on an estimated probability of 70%. In 2050, there will be more than 70 GWe of EGS based on an estimated probability of 85%. In view of the immature technologies for EGS, the US has funded a total of 0.22 billion USD from 2007 to 2013 to develop innovative exploration, reservoir stimulation, and sustainable reservoir technologies and economic analysis models for the commercialization of EGS. The crucial issue in Taiwan's geothermal development is the enhancement of the poor productivity of geothermal production wells. Based on foreign experience, increasing the productivity by adding reinjection wells in traditional hydrothermal fields should be a feasible approach for the development of EGS in Taiwan. The study suggests that Taiwan should establish a geothermal exploration database. In addition, the enhancement of geothermal production by developing reservoir simulation and reservoir maintenance technologies will lead to cost reductions. Finally, promoting traditional hydrothermal geothermal power plants to drive EGS development will allow for the stable expansion of Taiwan's geothermal industry.

A global review of enhanced geothermal system (EGS)

Fundamentals of Rock Mechanics

Boundary element methods in solid mechanics

An investigation of stimulation mechanisms in Enhanced Geothermal Systems

We utilize several lines of evidence to argue that slow slip on pre-existing fractures and faults is an important deformation mechanism contributing to the effectiveness of slick-water hydraulic fracturing for stimulating production in extremely low permeability shale gas reservoirs. First, we carried out rate and state friction experiments in the laboratory using shale samples from three different formations with a large range of clay content. These experiements indicated that slip on faults in shales comprised of less than about 30% clay is expected to propagate unstably, thus generating conventional microseismic events. In contrast, in formations containing more than about 30% clay are expected to slip slowly. Second, we illustrate through modeling that slip induced by high fluid pressure on faults that are poorly oriented for slip in the current stress field is expected to be slow, principally because slip cannot occur faster than fluid pressure propagates along the fault plane. Because slow fault slip does not generate high frequency seismic waves, conventional microseismic monitoring does not routinely detect what appears to be a critical process during stimulation. Thus, microseismic events are expected to give only a generalized picture of where pressurization is occurring in a shale gas reservoir during stimulation which helps explain why microseismicity does not appear to correlate with relative productivity. We review observations of long-period-longduration seismic events that appear to be generated by slow slip on mis-oriented fault planes during stimulation of the Barnett shale. Prediction of how pre-existing faults and fractures shear in response to hydraulic stimulation can help optimize field operations and improve recovery. Introduction Multi-stage hydraulic fracturing with slick-water in horizontal wells is an effective completion strategy for producing commercial quantities of natural gas from organic-rich shale gas formations. That said, the physical mechanisms responsible for reservoir stimulation are poorly understood. The prevalent paradigm is that diffusion of water out of the hydraulic fracture stimulates shear failure on multiple small, pre-existing fractures and faults in the shale. This shear slip creates a network of relatively permeable flow paths and thus enhances productivity from the extremely low permeability shale formations. Microseismic events recorded during hydraulic fracturing are evidence of this shear slip and the ‘clouds’ of microseismic events associated with multiple hydraulic fracturing stages in a well are generally assumed to define the stimulated rock volume (SRV) from which the gas is being produced (Warpinki et al., 2012). While this paradigm is generally useful, a simple mass balance calculation illustrates that the cumulative deformation associated with the microseismic events can account for only a small fraction of the production. In a single well, it has been shown that the number of microseismic events does not correlate with production from successive hydraulic fracturing stages (Moos et al., 2011). Production from five wells in the Barnett shale studied by Vermylen and Zoback (2011) does not correlate the number of microseismic events generated by hydraulic fracturing in each well even though the wells were stimulated in a similar manner. In this paper we argue that slow slip on numerous fault planes is occurring in shale gas reservoirs during stimulation. In fact, we believe this is likely to be the dominant deformation mechanism during hydraulic stimulation. The shear deformation associated with the slowly slipping faults is expected to create a network of multiple permeable planes surrounding the induced hydraulic fractures. In the sections below, we first review evidence of

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The Importance of Slow Slip on Faults During Hydraulic Fracturing Stimulation of Shale Gas Reservoirs

We describe a numerical investigation of seismicity induced by injection into a single isolated fracture. Injection into a single isolated fracture is a simple analog for shear stimulation in enhanced geothermal systems (EGS) during which water is injected into fractured, low permeability rock, triggering slip on preexisting large scale fracture zones. A model was developed and used that couples (1) fluid flow, (2) rate and state friction, and (3) mechanical stress interaction between fracture elements. Based on the results of this model, we propose a mechanism to describe the process by which the stimulated region grows during shear stimulation, which we refer to as the sequential stimulation (SS) mechanism. If the SS mechanism is realistic, it would undermine assumptions that are made for the estimation of the minimum principal stress and unstimulated hydraulic diffusivity. We investigated the effect of injection pressure on induced seismicity. For injection at constant pressure, there was not a signifi...

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Mark W. McClure

Papers

An investigation of stimulation mechanisms in Enhanced Geothermal Systems

The Importance of Slow Slip on Faults During Hydraulic Fracturing Stimulation of Shale Gas Reservoirs

Investigation of injection-induced seismicity using a coupled fluid flow and rate/state friction model

Slip-corrected liquid permeability and its effect on hydraulic fracturing and fluid loss in shale

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