Rock Fractures and Fluid Flow Contemporary Understanding and Applications (1996) / Chapter Skim
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3 Physical Properties and Fundamental Processes in Fractures
3 Physical Properties and Fundamental Processes in Fractures
Pages 103-166
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From page 103... ...
This chapter emphasizes the results of theoretical and laboratory investigations. Theoretical studies, in combination with controlled laboratory tests, provide the fundamental physical properties and relationships between parameters that describe the processes of fluid flow and transport, seismic wave propagation, and electrical conduction.
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Fundamental to understanding these effects is a knowledge of how fracture void geometry changes under generalized stress conditions. Thus, the mechanical deformation of fractures is discussed in this section; the effects of this deformation on fluid flow and geophysical properties are discussed in subsequent sections.
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If the surfaces are not perfectly matched, as would be anticipated in many natural environments, there will be some regions where voids remain. Because the void space arises from a mismatch at some scale between the two surfaces of a fracture, a great deal of work has been done to quantify and model the statistics of fracture surfaces.
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Variations in ~ over different measurement scales indicate, however, that it may be unrealistic to extrapolate the power spectrum outside the range of measured wavelengths. Void Geometry Current understanding of the geometric properties of fracture void space has evolved from both experimental and theoretical investigations.
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. The composite topography contains only the mismatched parts of the surface roughness and represents the distribution of local apertures under essentially zero stress conditions (Figure 3.1~.
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(1990) showed that the statistical properties of local apertures can be derived directly from the statistical properties of each of the opposing fracture surfaces.
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A mismatch length scale Ac can be defined by the spatial frequency at which the ratio falls to one-half its high-frequency asymptotic value. For length scales greater than Ac the surfaces are closely matched, and for length scales less than Ac the surfaces are mismatched.
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. FIGURE 3.3 Composite SEM micrograph of Wood7s metal casts of two natural fractures showing void space at 33 MPa effective stress.
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Stress Effects on Fracture Void Geometry Deformation in a fracture can arise from either a change in fluid pressure or a perturbation of the stress field in the rock. The important stress for mechanical behavior and fluid flow in fractures is the effective stress, which is generally taken to be the normal stress on the fracture minus the fluid pressure (Terzaghi, 19361.
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Fracture surface roughness is one of the primary reasons for this coupling, as illustrated in Figure 3.4. This figure shows the distribution of voids and contacting asperities in an idealized representation of a very rough undeformed fracture.
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;;; .i~l- 1 1 ~ 1 1 0.02 0.04 0.06 0.08 0.1 0 0.12 (mm) FIGURE 3.5 Measurements of the closure of natural joints under normal stress canny.
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This process is illustrated in Figure 3.6, which shows a Wood's metal cast of the void space in a granite fracture at different stress levels. At low stress levels, there are only a few asperities of contact surrounded by large void areas.
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A consequence of volume conservation is that a given volumetric deformation corresponds to a small change in the average value of local apertures if there is a large areal percentage of voids or a large change in average aperture if there is a small areal percentage of voids. Thus, there is not a one-to-one correlation, as is often assumed, between mechanical closure and aperture closure in the fracture.
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They showed that this approach was essentially equivalent to that of the flat-crack model. Shear Stress Effects Application of shear stress to a fracture can have a significant impact on void geometry because of the potential for dilation associated with relative motions of the two surfaces.
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Although useful for conceptually describing the coupling between shear and normal stresses, the shearing of dilatant fractures under constant normal stress conditions as depicted schematically in Figures 3.7 and 3.8 usually does not occur in nature. Instead, as the fracture dilates, normal stress increases owing to the stiffness of the surrounding rock mass.
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From page 118... ...
Shearing processes can lead to formation of gouge and increasing anisotropy in permeability. SINGLE-PHASE FLUID FLOW IN FRACTURES Normal Stress Conditions Most of the work on fluid flow in single fractures has been carried out under normal stress conditions.
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From page 119... ...
This hysteresis is the result of slight mismatches between fracture surfaces, which produce additional pathways for fluid flow. As the load is applied, the surfaces can move slightly relative to each other, becoming better registered, or mated, and removing the effects of the mismatch.
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At the highest stress levels, all flow must pass through one or more "critical necks." These restrictions are more equant in shape than the surrounding voids. Thus, the flow rate approaches a value independent of stress at high stress levels but may be orders of magnitude lower than at low stress.
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From page 121... ...
Fracture openings in the field or from a core are commonly measured by using an automotive "feeler gauge." These are more nearly local aperture measurements rather than a representative distance between the fracture surfaces. In the laboratory the distance between fracture walls is often taken to be the measured mechanical closure relative to a maximum closure, under a load applied normal to the fracture surface.
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From page 122... ...
10-5 10-6 ROCK FRACTURES AND FLUID FLOW ,_ , ~ _ , . "J ,.' I,.' _ ~ 'I "cubic law" prediction ~experimental 1 1 1 1 1 1 10-14 10-13 10-12 10-11 10-10 10-9 10-8 10-7 Flow Rate per unit Pressure Gradient (m4/Pa s)
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and Brown (1987) also showed that tortuosity results in a decreased flow, with the magnitude of the effect depending on the distribution and correlation of local apertures.
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From page 124... ...
They showed that flow rate decreased more rapidly than predicted by the cubic law and suggested that a large percentage of the head drop in a fracture occurred at the critical neck along the path of the largest connected local apertures.
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From page 125... ...
Such conditions are likely to occur in civil and mining works such as underground openings, dams, and slopes where the principal stress at the free surface is zero. Thermal and Chemical Effects A brief discussion of the thermal and chemical effects on fluid flow in a single fracture is given here.
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This process could affect flow by filling void space. Perhaps more importantly, it could also change the stiffness of the fracture.
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Although the fracture void volume was greater, the shape of the breakthrough curve was very similar to that obtained with the fracture in the mated condition. Additional work is needed to more quantitatively relate geometrical properties of the void space to transport properties.
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A variety of interesting results come from percolation theory, the most important being that the phase geometry is fractal and that a critical pressure exists where one phase forms an infinite connected cluster isolating the other phase (see Chapter 7 in Feder, 1988~. Numerical simulation of the percolation process on spatially correlated aperture networks has been used to evaluate phase structure as a function of pressure.
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From page 129... ...
comparable to those observed experimentally (Glass, 1993~. Processes by which a phase enters the fracture, including invasion from one edge of the fracture as discussed above, entry from the surrounding porous media, and entry through partitioning from the other phase, will significantly affect phase structure.
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to yield phase structure. In general, determination of the phase structure requires that the Navier
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Phase structures, however, may not be stable, and a variety of phenomena can occur, including viscous and gravitydriven fingering, flow pulsation, and blob flow (i.e., when one phase moves through another phase as a disconnected unit)
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. Flow pulsation and blob flow also have been documented to occur as flow rate through a stable gravity-driven finger is reduced (Nicholl et al., 1993b)
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This discontinuity affects the propagation of seismic waves according to the ratio of fracture size to the seismic wavelength. Considering that any seismic pulse consists of a spectrum of wavelengths, a single fracture will act as a discrete scatterer for those wavelengths that are longer or comparable in size.
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From page 134... ...
However, as long as the wavelength of the propagating wave is long compared to the spacing of the voids, an areal average value of the discontinuity in elastic displacements occurring at the voids can be assumed in calculations of the far-field reflected and transmitted wave fields. Such an approach is called a seismic displacement discontinuity model.
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From page 135... ...
where ~ is the areal average displacement in the plane of the fracture. The relationships between displacement in a fracture and the void geometry are discussed in detail later in this chapter under "Stress Effects on Fracture Void Geometry." Conceptually, K can be considered the tangent to the stress displacement curve obtained in a mechanical deformation test on a fracture (cf.
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o ROCK FRACTURES AND FLUID FLOW IRI \y 1 ~tgo tg (Zinc)
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3.13 and found good agreement between their results and those predicted from the seismic displacement discontinuity model. The seismic displacement discontinuity model has been compared with laboratory measurements on samples containing single natural fractures (Pyrak-Nolte, 1990a)
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Appendix 3.A discusses the theory underlying this model. Relationship to Hydraulic Properties The geometry and volume of the void space control fluid flow and (as discussed earlier, under "Shear Stress Conditions")
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Several variations of the formula exist that are considered to be more accurate for certain rock types. Archie's law is discussed in terms of the equivalent channel model by Walsh and Brace (1984~.
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However, if the fractures are connected, they will provide significant paths of conduction in the rock mass. Additionally, because the void space connectivity changes with stress, fracture conductivity is stress dependent.
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generated rough surfaces, and pairs of surfaces with the same fractal dimension were placed together to form a "fracture." Calculations of the volume flow rate and electric current fields of one such fracture are shown in Figure 3.16. The electric current is more diffuse over the fracture than the fluid flow.
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~_ ~_ . ~ ~1 / ~ ~ ~ Fluid Flow Electric Current FIGURE 3.17 Overlay of the left center portions of the flow fields shown in Figure 3.16.
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as a function of mechanical aperture (bm) and the rms height of the fracture surfaces (hrr~S)
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iS defined as the square of the ratio of the actual path length to the nominal path length. For channels of constant cross section, such as cylindrical tubes or parallel plates, the microscopic geometry can be used to predict the macroscopic permeability (K)
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~ 10 sol ~1 -2 10 10-3 10 D 2.5 10 slope=-2.93 4 ~ 2 slope=-1.98 1 1 1 1 1 1 10 Formation Factor 1o2 FIGURE 3.19 Permeability as a function of formation factor for a fracture composed of surfaces with fractal dimension D = 2.5. The permeability and formation factor were computed by using the hydraulic and electric apertures for the fracture.
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Both the geometric properties of the void space and the fracture surface roughness need to be described as stochastic processes. The change in fracture void geometry owing to an applied normal stress can be effectively modeled for many rock types, assuming the rock is a linearly elastic material.
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It is clear that these processes depend strongly on the statistical properties of the void space, including the interconnectivity and spatial distribution, but it is not yet clear what statistical measures are representative of typical fractures. Although direct measurement of flow properties is required, there is still a need for developing quantitative relationships between microscopic measurements of fracture void geometry and macroscopic flow properties.
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From page 148... ...
An area requiring further study is the effect of this localization on bulk effective properties that are measured in the field. Recent studies have indicated that qualitative, and perhaps quantitative, relationships exist between the hydrological properties of single fractures and their geophysical properties.
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The wavelength of the P-waves is about 0.1 m. The effects of the primary vertical fracture set on P-wave propagation are illustrated in Figure 3.A2.
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In other words, except for differences due to travel path length, it is assumed that pulses traveling between all boreholes would be identical to those propagating vertically between C1 and C2 were it not for the effects of the vertical fractures. Pulses propagating between C1 and C2 were therefore used as reference pulses.
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From page 151... ...
It is seen that the seismic displacement discontinuity theory is able to predict the ume delay, amplitude, and frequency characteristics of the measured pulse with a high degree of accuracy. For waves traveling between C3 and C4, six fractures were assumed because of the increased travel distance, but the stiffness of each fracture was held constant at 5 X lOii Pa/m.
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152 1.0 0.8 0.6 0.4 a) ~ 0.2 Q E ~ 0.0 ._ -0.2 ~0.4 ~0.6 ~0.8 -1.0 ROCK FRACTURES AND FLUID FLOW C3-C4 - ~ Measured .......
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From page 153... ...
Preferential flow associated with local fracture heterogeneity or differential supply of fluid will introduce finite-amplitude perturbations to the infiltration front, as shown in Figure 3.B 1 for a transparent analog system. The driving force in the advancing front is the sum of gravitational (Vg)
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From page 154... ...
The unstable front therefore bypasses significant portions of the fracture plane, advancing farther and faster than would be expected for an equivalent uniform front. The velocity of individual fingers is a function of system hydraulic parameters, Vc and Lf (Nicholl et al., 1992~.
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are wetted near field capacity of the analog fracture. Courtesy of R
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In addition, even in the connected regions, highly tortuous flow paths tend to bypass significant portions of the connected phase structure. This creates dead zones that do not actively participate in flow but communicate with active regions through diffusion.
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PHYSICAL PROPERTIES AND FUNDAMENTAL PROCESSES IN FRACTURES 157 FIGURE 3.C1 Steady-state wetted structure in a transparent analog fracture. Dark areas are filled with dyed water; light regions are entrapped air.
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736 ~ ~ ~ ~ Few FIGURE 3.C2 Tracer pulse consisUDg of clam water CutodDg the two-phasc wand secure in Figure 3.C1 Mom a constant Now bounds. From NichoH Ed Glass (1994~.
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PHYSICA f PROPERTIES AND FUNDAMENTAL PROCESSES IN FRACTURES 159 FIGURE 3.C3 Further development of the tracer pulse shown in Figure 3.C2. Note wholly isolated regions and dead zones that communicate by diffusion.
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1987. Fluid flow through rock joints: the effect of surface roughness.
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Pp. 375-382 in Rock Joints, Proceedings of the International Symposium on Rock Joints, Loen, Norway, W
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Pp. 203-210 in Rock Joints, Proceedings of the International Symposium on Rock Joints, Loen, Norway, W
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1990. Shear behavior of physical models of rock joints under constant normal stiffness conditions.
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Pp. 397-404 in Rock Joints, Proceedings of the International Symposium on Rock Joints, Loen, Norway, W
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1981. Tribology and the characterization of rock joints.
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From page 166... ...
1980. Validity of cubic law for fluid flow in a deformable rock fracture.
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