H13J-01
Numerical Simulation of Planar Fluid-Driven Fractures
Fluid-driven fractures are a class of tensile fractures that propagate in prestressed solid media due to internal pressurization by an injected viscous fluid. There are numerous examples of such fractures occurring in natural geological processes. The numerical simulation of fluid-driven fractures remains a particularly challenging computational problem, despite significant progress made since the first algorithms were developed in the 1970's. The major challenges stem from the dependence of the near-tip asymptotic form of the fracture width on the dominant physical process governing the propagation of the fracture and from the a priori unknown boundary of the fracture footprint. In this talk we describe a novel algorithm that is based on an implicit level set method to locate the free boundary. The algorithm exploits the applicable local tip asymptote to locate the unknown fracture front. The algorithm does not rely on the calculation of the normal front velocity from the pressure gradient field, which is typically singular at the tip. In fact, the implicit algorithm is able to provide accurate estimates of the normal velocity of the front by solving an appropriate nonlinear equation within each element of a small set of elements close to the fracture front. We provide numerous examples that demonstrate the robustness, efficiency, and accuracy of the algorithm for fractures that propagate in a variety of regimes: toughness dominated, viscosity dominated, and leak-off dominated.
H13J-02 INVITED
What Have We Learned About Fluid-Fracture Interaction in the Analog Aquifer/Reservoir at the Valley of Fire, Nevada?
The Jurassic aeolian Aztec Sandstone in the Valley of Fire State Park, Nevada, provides an exceptional natural laboratory to observe fluid-fracture interaction. This presentation is a summary of our investigations over the past decade and addresses: 1) how various fundamental types of fractures interacted with paleo-fluids; and 2) what we have learned about the hydrologic bases for these interactions. The oldest failure structures in the sandstone are a result of deformation localization of both shear band and compaction band types. These structures represent significant porosity and permeability reduction with respect to the undeformed rock as determined from image analyses and lattice-Boltzmann flow simulations, as well as from modeling the paleo-fluid fronts. The simplest failure structures are opening mode fractures or joints which conducted fluids in a fashion close to the idealized parallel plate model with well organized roughness. Sheared-joints which form by slip along pre- existing joints are the simplest shear fracture with slip on the order of millimeters to centimeters. There is abundant evidence that shearing enhanced the conductivity of these fractures. The physical bases of this phenomenon are thought to be dilation associated with slip across rough surfaces and increasing connectivity by linkage through splay fractures. Large-scale shear fractures or faults are always multi-component structures including slip surfaces, fault rocks, and damage zones which are composed of the simpler failure structures referred to above. Due to this complexity, the interaction between fluids and faults shows a wide range of variation. These effects are demonstrated using observation, laboratory measurements as well as upscaled permeability models. We conclude that the Valley of Fire analog aquifer/reservoir displays excellent examples of fluid-fracture interactions with a wide range of diversity, controlled primarily by the failure modes, and that flow modeling at various scales reveal the fundamental physical processes responsible for the nature of the observed interactions.
H13J-03 INVITED
A Simple Model for the Variation of the Transmissivity of a Rock Fracture under Normal Stress
A simple model is described that relates the normal stiffness of a fracture to the variation in transmissivity that occurs when the fracture is subjected to a normal load. The fracture is assumed to be represented by a row of evenly spaced, open elliptical channels (Myer, Int. J. Rock Mech., 2000). The normal stiffness of such a fracture is given exactly by the elasticity solution derived by Sneddon and Lowengrub ( Crack Problems in the Classical Theory of Elasticity, 1969). At zero load, these channels may have an arbitrary distribution of aspect ratios. As the normal load is increased, the channels close up sequentially, with those having smaller initial aspect ratios closing first, etc. As the stiffness depends on the number of open channels, and the normal stress required to completely close a channel depends on the initial aspect ratio, in principle the aspect ratio distribution determines the nonlinear stress-strain curve of the fracture. We can derive an explicit relation between the stress-strain curve and the aspect ratio distribution by considering the behavior of Sneddon and Lowengrub's equation in the limit of large contact area (in practice, greater than about 0.2). The transmissivity of such a fracture is given by the sum of the transmissivities of the various elliptical channels, as given by the well-known expression for flow through an elliptical tube (Landau and Lifschitz, Fluid Mechanics, 1959). The instantaneous aspect ratio of each tube can be expressed as a function of the normal stress, and so the overall transmissivity can be computed as a function of stress. This simple model has been applied to the classic data of Iwai ( PhD, UC Berkeley, 1976) on a granite fracture, with reasonable results. Obvious future extensions and refinements of the model include (a) use of Sneddon and Lowengrub's exact expression for the fracture compliance, rather than the approximation that assumes a high contact fraction, and (b) allowing the various flow channels to be connected in a two- dimensional network, rather than assuming that they are in parallel with each other. Nevertheless, the present simple version of this model is capable of providing a rationally based connection between fracture stiffness and transmissivity.
H13J-04
A New Approach for Very Large Broadband Geophysical Monitoring of rock Deformations Into Deep Boreholes: The "High-Pulse Poroelasticity Protocol" (HPPP)
We present a new approach, called the "High-Pulse Poroelasticity Protocol" (HPPP), for a very large broadband geophysical monitoring of rock deformations into deep boreholes (from 200 m to 1 km depth). The HPPP consists in developing an innovative probe that allows the hydromechanical loading of rocks with synchronous fluid pressure – 3D deformations (translational components along and in the orthogonal plan of the borehole axis, and rotational components along the longitudinal axis) – seismic wave measurements over a broadband of frequencies (from static to dynamic [1-1,000 Hz]). In this protocol, the rock is subjected to a controlled source corresponding to a fast (few seconds) hydraulic pressure pulse (pressure wave) localized into a short injection chamber (from 1 to 3 m) which is isolated between two inflatable packers in a borehole. In the chamber, measurements are done with fibre-optic and acoustic sensors that makes possible to use a wide range of frequencies (1-1,000 Hz) and high accuracy (10-7) sampling of fluid pressure and 3D deformations. When the pressure wave is applied, several poroelastic effects are measured: (i) a static poroelastic response that is linked to the fluid diffusion in phase with mechanical deformation of the porous rock; (ii) a low-frequency slow Biot wave (P2 wave) associated with the motion out of phase of solid and fluid phases; (iii) a high-frequency pressure wave that is generated and converted to seismic waves (P1 and S waves) at the borehole wall. This new approach aims at determining the infinitesimal shear and axial components of the strain tensor within the rock crossed by a borehole. The HPPP also allows studying the relationships between elastic waves propagation and rock hydromechanical properties and state at an intermediate scale (mesoscopic scale), between the laboratory and crustal scales, in a volume of one to a few tens of meters around the borehole. This new approach was designed from previous pulse testing done in a fault zone with a first prototype of the HPPP probe capable of simultaneously measuring changes (with a high frequency [120 Hz] and high accuracy) in fluid pressure (± 1 kPa) and displacement normal to the fault (± 10-7 m). This prototype consisted of a fibre-optic fluid pressure and a fibre-optic normal displacement sensor fixed to the borehole walls by two anchors located on both sides of the fault which was isolated with two packers to create a 0.4 m injection chamber. Results indicated that fiber-optic measurements allow good capturing of all the high-frequency changes during the hydraulic pulse. The method appears useful for accurately measuring time discrepancies between pressure and deformation signals as small as a few milliseconds. Moreover, high-frequency measurement of the fault "pressure-deformation" poroelastic response allows highlighting of a loop-shaped evolution that is not observed in conventional laboratory or in situ experiments. Consequently, the HPPP approach will provide new data with axial and shear components of the strain tensor which will give us additional information for determination of the rock seismic and hydromechanical properties at various depths in the crust. Moreover, the HPPP will be adapted to study seismic and mechanical instability of fault zones under controlled hydraulic loading and localized in a point source.
H13J-05 INVITED
Stress-Versus-Permeability Relationships of Fractures From In Situ Experiments
Analysis of coupled hydrological and mechanical (HM) processes is of critical importance to many geological engineering practices. One key parameter in such analysis is a good estimate of the relationship between stress and permeability. A number of field studies for derivation of in situ stress-versus-permeability properties are reviewed, including borehole injection experiments, in situ block experiments, as well as recent data of permeability changes during eight years of heating and cooling in an underground large-scale heating experiment in highly fractured rock. It is concluded that because of great variability of hydraulic and mechanical properties in fractured rock, and the difficulties in using laboratory data for deriving in situ material properties, the stress versus permeability relationship of fractured rock masses are best characterized in situ.
H13J-06
Experimental observation of coupled geochemical alteration and geomechanical deformation of discrete variable-aperture fractures
Flow through fractures is controlled by the magnitude and variability of apertures within the fracture. Geochemical reactions and applied stresses can both alter fracture apertures leading to changes in transmissivity that are difficult to predict with existing models. Previous experimental studies in fixed displacement fractures have shown that flow of reactive fluids can lead to different dissolution patterns that are controlled by the Peclet (Pe ~ advection/diffusion) and Damkohler (Da ~ reaction/advection) numbers and range from relatively uniform dissolution throughout the fracture (high Pe, low Da) to development of distinct channels (low Pe, high Da). These results demonstrate that during uniform dissolution the smallest aperture regions dissolve more quickly than the larger apertures, leading to a smoothing of the fracture aperture field. This suggests that the addition of normal stresses, which can be significant in many subsurface environments, may lead to closure of the fracture surfaces under conditions of net dissolution from the fracture surfaces. We have developed an experimental system that allows application of a uniform confining stress to transparent analog, variable-aperture fractures during reactive fluid flow experiments. The fractures are fabricated by mating a rough, nonreactive surface (glass) with a smooth reactive surface (KH2PO4). Using this apparatus, we have conducted a series of dissolution experiments under steady confining pressure. Because the fractures are transparent, we can apply light transmission techniques to accurately (± 3 μm) measure fracture apertures at high spatial resolution (80 x 80 μm) over the entire flow field during dissolution experiments. Results show that fracture transmissivity initially increases as the fracture surfaces dissolve. However, gradual erosion of contacts leads to an accumulation of stress in the contacts until the remaining contacts deform resulting in sudden decreases in fracture transmissivity. This process repeats leading to periodic transmissivity oscillations over the duration of the experiments. This work was performed under the auspices of the U.S. Department of Energy by University of California, Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.
H13J-07
Interactions Between Fluid and Fractures During Well Tests in Fractured Rock
Deformation during hydraulic well tests causes basic aquifer properties to change, and the displacement signal can be interpreted to improve characterization of fractured aquifers. These conclusions are based on results and analyses of hydromechanical well tests, which involve measuring and interpreting displacements of rock along with the transient pressure signal resulting from hydraulic well tests. We used a precision extensometer between packers to measure axial displacements during slug and pumping tests in fractured biotite gneiss. The field data from several 100 tests show that fractures typically open or close with an apparent normal compliance of 1 to 5 microns of displacement per m of head change in the wellbore, although some fractures were stiffer than this. The displacement is a hysteretic function of the well bore pressure; that is, displacements are smaller earlier in the test than they are at the same pressure late in the test. This hysteretic behavior can be predicted using a discrete fracture model that considers coupled fluid flow and elastic deformation. Both field and theoretical data indicate that during well tests the apparent compliance of a formation can increase by a factor of 10 or more. Compliance is proportional to storativity, so a 10-fold increase in compliance means that the storativity increases by a factor of 10. During slug tests, the fracture continues to open while the wellbore pressure falls early in the test, which produces the peculiar result of a negative storativity. These changes in S stabilize and approach the value determined by interpreting typical hydraulic well tests at late times when relatively isolated fractures are tested. However, a different result occurs when the primary fracture being tested is cross-cut by other fractures roughly parallel to the borehole. The cross-cutting fractures cause water to leak out of the primary fracture, changing the pressure distribution within it, and reducing the resulting displacement. The transmissivity of a fracture is proportional to the cube of its aperture, so relatively small changes in aperture can cause significant changes in T. For example, normalized transmissivity of biotite gneiss is sensitive to pressure by approximately 0.01/m to 0.04/m (this means that T varies by 1 to 4 percent per m of drawdown). Pressure sensitive T has been reported in soft sedimentary formations, but it appears to be significant in some situations in fractured gneiss. Displacements during hydromechanical well tests are sensitive to the properties and geometries of fractures in the vicinity of the well, so inverse methods can be used to estimate characteristics of fracture networks. Recent analyses have predicted the occurrence of leakage and blockages in primary fractures, which appear to be confirmed with interference tests in nearby boreholes. Preliminary results also suggest that it may be possible to identify fractures that are softened by weathering or stiffened by mineralization. http://www.ces.clemson.edu/hydro/murdoch/Research/Hydromechanics/index%20hm.htm