Microfracture spacing distributions and the evolution of fracture patterns in sandstones

doi:10.1016/j.jsg.2017.04.001

Journal of Structural Geology

Volume 108, March 2018, Pages 66-79

https://doi.org/10.1016/j.jsg.2017.04.001 Get rights and content

Highlights

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A survey of microfracture spacings was collected from eight sandstone formations on three continents.
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Spacings from low-strain fracture sets are indistinguishable from random.
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Spacings from higher-strain fracture sets are systematically clustered.
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Fracture opening is progressively focused upon a subset of fractures, whose growth outpaces the rest.
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Fracture clustering results from interaction among coevally opening and sealing fractures.

Abstract

Natural fracture patterns in sandstone were sampled using scanning electron microscope-based cathodoluminescence (SEM-CL) imaging. All fractures are opening-mode and are fully or partially sealed by quartz cement. Most sampled fractures are too small to be height-restricted by sedimentary layers. At very low strains (<∼0.001), fracture spatial distributions are indistinguishable from random, whereas at higher strains, fractures are generally statistically clustered. All 12 large (N > 100) datasets show spacings that are best fit by log-normal size distributions, compared to exponential, power law, or normal distributions. The clustering of fractures suggests that the locations of natural factures are not determined by a random process. To investigate natural fracture localization, we reconstructed the opening history of a cluster of fractures within the Huizachal Group in northeastern Mexico, using fluid inclusions from synkinematic cements and thermal-history constraints. The largest fracture, which is the only fracture in the cluster visible to the naked eye, among 101 present, opened relatively late in the sequence. This result suggests that the growth of sets of fractures is a self-organized process, in which small, initially isolated fractures grow and progressively interact, with preferential growth of a subset of fractures developing at the expense of growth of the rest. Size-dependent sealing of fractures within sets suggests that synkinematic cementation may contribute to fracture clustering.

Introduction

The spacing of natural fractures is a well studied problem, in part because fracture spacing controls the probability of fracture intersection during tunneling or drilling (Narr, 1996). Statistics that can describe useful aspects of fracture spacing include the mean, which governs the overall expected frequency of fracture intersection, as well as the standard deviation, which describes the spatial regularity of the fractures. That is, a hypothetical fracture set may be perfectly regularly spaced, or highly clustered, with statistically random spacing occupying an intermediate position on the spatial regularity spectrum (Gillespie et al., 1999).

In the present study we focus on the spacing of opening-mode fractures that are fully or partially filled by mineral cements. In doing so we restrict our attention to fractures that demonstrably formed in the subsurface. As well, we can use mineral cements to support a genetic link between fractures in a geologic setting (Smith et al., 2014) and, in certain cases, to constrain the timing and fluid conditions of fracture opening (e.g., Becker et al., 2010). We discuss how our findings might also apply to the spacing of other types of fractures, such as magmatic dykes and barren fractures.

Geologic fractures are generally thought to initiate at flaws, based on the experimental work of Griffith (1921) as well as field evidence that large joints propagated from small joints located at fossils or sedimentary structures (e.g., Helgeson and Aydin, 1991, Savalli and Engelder, 2005). As such, the spacing of large fractures could reflect the spacing of flaws. However, it is commonly assumed that flaws are randomly dispersed throughout the host rock (e.g., Olson, 1993, Tang et al., 2008). The challenge in explaining fracture patterns, then, is how to start from an unorganized flaw distribution and produce a non-random pattern?

Regular spacing is commonly observed in stratified rocks (e.g., Ladeira and Price, 1981, Narr and Suppe, 1991). In such cases, fracture growth is commonly height-restricted and fracture spacing scales with the height of fractures, resulting in a periodic fracture spacing (Schöpfer et al., 2011). However, many highly clustered, and demonstrably non-random, fracture patterns have been identified, both in stratabound and non-stratabound fracture sets (see literature review in Hooker and Katz, 2015).

Various explanations of clustering have been proposed. Fractures can cluster in the vicinity of folds (Ogata et al., 2014) or faults (Putz and Sanderson, 2008). Diagenetic processes can create brittle zones that become preferentially fractured (Giorgioni et al., 2016). Sedimentary fabrics can be laterally anisotropic and produce spatially variable fracture patterns (Ogata et al., 2016). Finally, swarms of joints in the vicinity of magmatic dykes were attributed to tensile stresses related to dyke propagation (Delaney et al., 1986). This last example highlights the potential for fracture clustering to develop dynamically, during propagation, and therefore be inherent to fracture strain accumulation.

Furthermore, fractures visible to the naked eye (macrofractures) are commonly surrounded by microscopic fractures (microfractures), such that the largest fractures are bedding-bound and the smaller ones are not (Hooker et al., 2013). Consequently, even uniformly spaced, bedding-bound fracture patterns may have emerged from fracture growth that was initially unaffected by mechanical stratification.

With the goal of testing the relative importance of flaw distributions, sedimentary features, structures, and self-organization to the development of natural fracture patterns, this study presents microfracture spacing measurements, compiled from eight formations on three continents. The same data collection method was uniformly employed, over the same scale of observation, so that data can be compared over a range of structural settings. Fractures were measured in sandstones observed using SEM-CL, at a scale that we argue is sufficiently small to preclude height-restriction of most fractures by mechanically significant sedimentary bed boundaries. We perform statistical tests for the observed spacings to test whether natural microfractures are more or less clustered than would be predicted by a random arrangement of fractures.

To further investigate the processes that control fracture spacing, we examine the timing of opening of a cluster of fractures within the Triassic El Alamar Formation (Huizachal Group) of northeast Mexico, which is one of our sampling locations, using fluid-inclusion microthermometry and thermal history modeling. This study is the first that we know of to present independent timing evidence for a group of parallel, co-genetic fractures. We compare our results to previous models of fracture propagation and find support for previous theoretical models in which fracture clustering is the result of dynamic crack interaction during propagation.

Section snippets

Methods

The microfracture spacing dataset was assembled using rock samples collected from sandstones containing natural macrofractures (Table 1). Macrofracture patterns were observed either in core or in outcrop. Fracture spacing is defined as the distance between neighboring fractures, measured perpendicular to the fractures, along a single line of observation (scanline). In each sandstone the macrofractures are present in sub-parallel sets typically have a strike dispersion of less than 20° at a

Sample suite and fracture description

The sandstones studied reflect a variety of structural settings (Table 1). Each geologic setting was described in the Appendix of Hooker et al. (2014), which demonstrated that the aperture-size distributions of most individual datasets are well fit by power laws. Sandstones were selected for study based on the presence of one or more sets of fractures, identified as natural and reflecting geological processes by the presence of mineral cements that line or fill fractures.

Most scanlines were

Spacing data

Fracture strain, calculated as (sum of apertures)/(sum of spacings), ranges from 1 × 10⁻⁴ to 2 × 10⁻¹ (Table 1, Table 2). As detailed above, scanlines were drawn across vertical core samples, slant-core samples, and outcrop exposures, and so range in length from 20 to 2067 mm. Longer scanlines provide more robust sampling statistics, and are particularly important for analyzing low-strain, widely spaced fracture sets.

We quantified the irregularity of fracture spacing using the coefficient of

Interpretation of spacing statistics

No datasets has C_v significantly less than expected for random fracture locations (Fig. 3A), hence we do not interpret any datasets as regularly or periodically spaced. Furthermore, only three datasets, having N = 3, 4, and 6, have V′ lower than the lower-tail critical value for a uniform distribution (Table 2, Fig. 4B), for which we would interpret homogeneously distributed fracture strain. Of 60 total datasets, 39 exceed the critical value for either (18) or both (21) regular fracture spacing

Reconstructing a natural fracture array

Four sets of fractures are present in a canyon exposure of the Huizachal Group (Fig. 5). Each set comprises strike-parallel, steeply dipping, quartz- and calcite-cemented fractures. The relative timing of these four sets was constrained using crosscutting relationships by Laubach and Ward (2006), who labeled the sets A (earliest) through D (latest). Sample 44 of the fracture spacing dataset was measured from Set C at this location. Preliminary fluid-inclusion thermometry data in Laubach and

Discussion

Fracture strain related to fracture formation in sandstones appears to accumulate incrementally, as recorded in SEM-CL images of natural fractures, which generally contain crack-seal texture (Fig. 1; see also Hooker et al., 2014). It is not clear whether a crack-seal increment necessarily grew in a single discrete opening increment that was subsequently sealed, because each preserved increment could represent multiple smaller opening episodes that were later sealed, or the opening may have been

Conclusions

A survey of sandstone microfracture spacings from a range of formations and structural settings shows that natural microfractures are not regularly spaced. Rather, low-strain fracture sets have spatial distributions that are indistinguishable from random, whereas high-strain sets are systematically clustered. In a representative example from the Huizachal Group in northeastern Mexico, fluid-inclusion temperatures combined with burial history modeling suggest that large fractures are

Acknowledgments

This study was funded in part by grant DE-FG02-03ER15430 from Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy, by the GDL Foundation (field work), by the Fracture Research and Application Consortium, and by the Geology Foundation of the Jackson School of Geosciences, The University of Texas at Austin. We thank Hyein Ahn and Karen Black for SEM imaging, Peter Eichhubl, András Fall, Julia Gale, and Leonel Gomez

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