Laura J. Pyrak-Nolte

Single fractures under normal stress: The relation between fracture specific stiffness and fluid flow

Abstract Fracture specific stiffness and fluid flow through a single fracture under normal stress are implicitly related through the geometry of the void space and contact area that comprise the fracture. Data from thirteen different rock samples, each containing a single fracture, show that relationships between fracture specific stiffness and fluid flow through a fracture fall into two general classes of behavior. Fractures either fall on a loosely-defined universal curve relating fluid flow to fracture specific stiffness, or else the flow is weakly dependent on fracture specific stiffness. The second relationship shows that flow decreases slowly with increasing fracture specific stiffness. The first relationship shows that flow decreases rapidly for increases in fracture specific stiffness. To understand this behavior, computer simulations on simulated single fractures were performed to calculate fluid flow, fracture displacement, and fracture specific stiffness as a function of normal stress. Simulated fractures with spatially correlated and uncorrelated aperture distributions were studied. Fractures with spatially uncorrelated aperture distributions tend to exhibit a weak dependence of fluid flow on fracture specific stiffness because these fractures tend to have multiple connected paths across the sample which can support flow with uniformly distributed contact area. Thus an increment in stress will increase the stiffness of the fracture without greatly reducing the amount of fluid flow. On the other hand, fractures with spatially correlated aperture distributions tend to belong to the universal relationship because correlated fractures tend to have only one or two dominant flow paths and the contact area is limited to a few regions resulting in a compliant fracture. Thus an increment in stress on a spatially correlated fracture will result in an increase in stiffness and rapid decrease in fluid flow. These spatial correlations in fracture void geometry can be differentiated in the laboratory based on the observed fracture specific stiffness–fluid flow relationship for a single fracture under normal loading.

The seismic response of fractures and the interrelations among fracture properties

In this paper the author presents a survey of current understanding of the interrelationships among the hydraulic, mechanical, seismic and geometrical properties of single natural factures. The paper also includes a discussion of the methods that have been developed to improve the measurement of fracture geometry including the measurement of fracture specific stiffness, which is the key link in interrelating the physical properties of a fracture. A new approach for determining fracture shear stiffness uses interface waves that propagate along fractures. (A)

Volumetric imaging of aperture distributions in connected fracture networks

We use x-ray computerized tomographic (CT) imaging to present quantitative aperture data for three-dimensional interconnected fracture networks imbedded in intact opaque rock samples several centimeters in length. X-ray images are obtained by injecting a high-density liquid metal into the fractured rock specimen under lithostatic conditions. The combination of tomographic reconstruction with gravimetric analysis makes it possible for the first time to obtain effective fracture aperture sizes to an accuracy of only several microns, located spatially within 300 microns. The apertures in the fracture network are spatially correlated over distances of 10 mm to 30 mm. The apertures of the intersections of the fractures were not found to be statistically larger in size than for the complete fracture network

Fracture interface waves

Interface waves on a single fracture in an elastic solid are investigated theoretically and numerically using plane wave analysis and a boundary element method. The finite mechanical stiffness of a fracture is modeled as a displacement discontinuity. Analysis for inhomogeneous plane wave propagation along a fracture yields two dispersive equations for symmetric and antisymmetric interface waves. The basic form of these equations are similar to the classic Rayleigh equation for a surface wave on a half-space, except that the displacements and velocities of the symmetric and antisymmetric fracture interface waves are each controlled by a normalized fracture stiffness. For low values of the normalized fracture stiffness, the symmetric and antisymmetric interface waves degenerate to the classic Rayleigh wave on a traction-free surface. For large values of the normalized fracture stiffness, the antisymmetric and symmetric interface waves become a body S wave and a body P wave, respectively, which propagate parallel to the fracture. For intermediate values of the normalized fracture stiffness, both interface waves are dispersive. Numerical modeling performed using a boundary element method demonstrates that a line source generates a P-type interface wave, in addition to the two Rayleigh-type interface waves. The magnitude of the normalized fracture stiffness is observed to control the velocities of the interface waves and the partitioning of seismic energy among the various waves near the fracture.

Laser-based ultrasound detection using photorefractive quantum wells

We demonstrate a laser-based adaptive ultrasonic homodyne receiver using dynamic holography in AlGaAs/GaAs photorefractive multiple quantum wells. The dynamic hologram acts as an adaptive beamsplitter that compensates wavefront distortions in the presence of speckle and requires no path-length stabilization. The photorefractive quantum wells have the unique ability to achieve maximum linear homodyne detection regardless of the value of the photorefractive phase shift by tuning the excitonic spectral phase. We achieve a root mean square noise-equivalent surface displacement of 6.7×10−7 A(W/Hz)1/2.

Terrestrial Sequestration of CO2 – An Assessment of Research Needs

Publisher Summary This chapter provides a brief review of major characteristics of reservoir structures and lithologies serving as a guide to reservoir selection for CO 2 disposal. The chapter focuses on existing experience and uncertainties in reservoir characterization and response to CO 2 injection and long-term containment of sequestration sites. Special issues germane to CO 2 disposal arise in the assessment of depleted reservoirs, whose properties are known to have changed during single or repeated pore-pressure drawdown and fluid redistribution. Oil and gas reservoirs and aquifers share some common geometric elements. Generally, both are tabular bodies in which the fluid flow is constrained by upper and lower less-permeable lithologies. Primary aspects of CO 2 sequestration in geologic formations include the geohydrologic characterization, injection behavior, and long-term containment of supercritical CO 2 for storage in aquifers and reservoirs. The efficiency of a CO 2 enhanced oil-recovery flood depends strongly on the equilibrium phase behavior of mixtures of CO 2 with the oil.

Frequency dependence of fracture stiffness

The frequency dependence of fracture specific stiffness, for seismic or ultrasonic wave transmission, is shown to be a simple scaling property of fractures with spatially inhomogeneous distributions of stiffness. Different frequencies sample different subsets of the fracture geometry. Therefore the frequency dependence may be a simple consequence of fracture geometry and requires no additional dynamical mechanism. In this letter, the dynamic fracture stiffness is determined based on the displacement discontinuity model for wave transmission across a fracture. Local transmission coefficients are assumed to depend on the local static stiffness. For a fracture with a single value of static stiffness, the dynamic stiffness is frequency independent. A strongly inhomogeneous distribution of fracture stiffnesses produces a strong frequency dependence for the dynamic stiffness.

Wavelet analysis of velocity dispersion of elastic interface waves propagating along a fracture

A wavelet analysis is performed on seismic waveforms of elastic interface waves that propagate along a fracture. The wavelet analysis provides a direct quantitative measure of spectral content as a function of arrival time. We find that the spectral content of the interface wave signals is not stationary, but exhibits increasing frequency content for later arrival times, representing negative velocity dispersion. The dispersion increases from −11 m/sec/MHz to −116 m/sec/MHz as the stress on the fracture is increased from 3.5 kPa to 33 MPa. The negative velocity dispersion agrees with predictions from the displacement-discontinuity theory of the seismic response of fractures, and can be used to fit fracture stiffness.

Interface waves propagated along a fracture

Abstract The existence of interface waves along fractures depends on the specific stiffness of the fracture. With increasing fracture stiffness, the velocity of the interface wave increases and the spectral content of the signal is altered. We used interface wave measurements and wavelet analysis to examine the effect of normal and shear stresses on fracture shear stiffness. Fracture shear stiffness is more sensitive to changes in shear stress than to normal stress. Compressional waves propagated along a fracture appear to contain a delayed wave that is sensitive to changes in the fracture stiffness. Using acoustic wavefront imaging, we are able to visualize the delayed produced in the compressional-wave by the fracture from the spatial distribution of the arriving energy.

Approaching a universal scaling relationship between fracture stiffness and fluid flow.

A goal of subsurface geophysical monitoring is the detection and characterization of fracture alterations that affect the hydraulic integrity of a site. Achievement of this goal requires a link between the mechanical and hydraulic properties of a fracture. Here we present a scaling relationship between fluid flow and fracture-specific stiffness that approaches universality. Fracture-specific stiffness is a mechanical property dependent on fracture geometry that can be monitored remotely using seismic techniques. A Monte Carlo numerical approach demonstrates that a scaling relationship exists between flow and stiffness for fractures with strongly correlated aperture distributions, and continues to hold for fractures deformed by applied stress and by chemical erosion as well. This new scaling relationship provides a foundation for simulating changes in fracture behaviour as a function of stress or depth in the Earth and will aid risk assessment of the hydraulic integrity of subsurface sites.