Fracture apertures

We can use the calculated reaction rates (Fig. 26.3) to compute how rapidly quartz precipitation seals the fracture. The sealing rate, the negative rate at which fracture aperture changes, can be expressed as... 

Metamorphic fracture apertures range from the micrometer scale (Ramsay, 1980 Etheridge et al., 1984) to mm or cm scales (Ague, 1995). 

Fig. 1. Empirical relation between joint roughness (JRC) and the hydraulic (e) and mechanical (E) fracture aperture (after Barton et al., 1985).

Fig. 2 shows a horizontal cross-section through NGFs coupled shear flow test (CSFT) cell. This biaxial cell allows fractured samples (14 x 12 x 5 cm) to be displaced by a maximum 8 mm under controlled fracture normal stresses and temperatures up to 80°C. Variation in fracture aperture (dilation) is measured by a total of four displacement gages, whereas shear displacement is measured by a total of two gages. The flow measurements, as illustrated in Fig. 2, measure the total flow in the direction of the fracture plane and do not differentiate between fracture and matrix flow. To quantify the matrix flow component, tests on non-fractured samples with the same principal geometry as the fractured tests and under the same stress conditions, were conducted in the CSFT cell. 

Keller, A.A., P.V. Roberts, and M.J. Blunt. 1999. Effect of fracture aperture variations on the dispersion of contaminants. Water Resour. Res. 35 55-63. 

Water residence time X Distance along flow direction z Distance into matrix 5 Fracture aperture f Flow porosity p Matrix porosity... 

Abstract This paper presents a model for the simulation of two phase flow phenomena in deformable fractured rocks. The main problem is that gas pressure may play an important role on the mechanical behavior specially if discontinuities exist or develop. Fracture aperture changes and fracture failure are accounted by the model. Aperture of the discontinuity is used as the main variable for permeability and capillary pressure variations. Injection pressures that show peak values before steady state regime is attained are obtained with the model as shown in some simulations performed. 

Figure 2. Stress-strain behavior coupled to fracture aperture changes.

Figure 2 shows the general stress-strain behaviour coupled to aperture changes. A threshold strain (e ) defines the initiation of fracture aperture. A strain corresponding to failure is indicated (ci). Failure is achieved when the normal stress reaches the tensile strength (o,). e , ei and o, are model parameters. 

The fact that this model considers elastic and inelastic fracture aperture or closure has already been discussed in the literature. For instance, Renner et al (2000) investigated the behaviour of fractured argillaceous rocks including permeability variations induced by changes in confining pressures. In this work crack dimensions and permeability are correlated by means a model that takes into account elastic crack closure and crack closure controlled by inelastic processes. This later is explained by asperity indentation when rough crack walls contact each other. 

Figure 6 shows the evolution of gas pressure at the injection point and the gas flow rate at the outflow point. It can be observed that after a period of gas pressure increase corresponding to the desaturation of the injection layer, gas starts to penetrate in the medium. Figure 7 shows degree of saturation for both the fracture and the rock matrix. Gas flow takes place through the fracture because permeability is higher than in the matrix and because desaturation is easier than in the matrix. Due to fracture aperture, permeability increases and the air entry pressure decreases. 

Finally, figure 8 shows the evolution of intrinsic permeability as a result of fracture aperture. It can be observed that changes in permeability take place as soon as gas is injected due to the assumed... 

Figure 13. Change in (a) driving differential pressure (end-to-end) with time, and evaluation of fracture aperture, as a proxy for (b) permeability change. Overlain on (b) are evaluations of permeability change constrained only on initial permeability magnitude and mass removal rate dM/dt. [Modifiedfrom Polak et ai, 2004].

Figure 14. Scan of the fractured limestone sample pre- (above) and post-test (below). Growth in the fracture aperture occurs during the test. CT number measured across the sample confirms growth of the aperture as a "wormhole. [ Polak et ai. 2004].

The current model for converting fracture deformation behavior to changes in fracture permeability utilizes only the normal deformation component. The fracture permeability is calculated using the predicted fracture apertures with the cubic law ... 

In this study, the current fracture aperture b depends on the current effective normal stress a . according an exponential function ... 

Figure 7 presents the calculated THM-induced changes in air permeability. These changes are caused by the combined effect of TH-induced changes in fracture moisture content (Figure 5) and TM-induced changes in fracture aperture (Figure 6). Near the heat source, permeability decreases mainly because of fracture closure, but is also affected by TH-induced wetting and drying. Away from the heat source, a zone of increased permeability has developed as a result of the opening of vertical fractures (Figure 7, near borehole section 74 4).

Figure 7. Calculated changes in air-permeability (k/k, = Ft) as a result ofTH-induced changes in liquid fracture saturation and TM-induced changes in fracture aperture...

Finally, the sensitivity of fracture aperture to block size and fracture length was analysed. Fracture networks with domain sizes of 5 m x 5 m and 10 mx 10 m revealed differences in median hydraulic apertures of less than 0.5 pm. Even with a block size of 15mxl5m and effectively infinitely long fractures, the change in median hydraulic aperture remained less than I pm. It can be concluded that the size of the REV determined for flow only is also suitable for mechanical calculations, and that, for the assumed spatial distribution and orientation of fracturing, fracture length has only a minor impact on the hydraulic aperture distribution. 

Considerable variability of fracture apertures is simulated even at depths of 500 m - 1000 m as observed in actual fractured rock at depth (e.g. Brace 1980, Armitage et al. 1996). 

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