Introduction

Productivity and injectivity in low-permeability rock formations are strongly dependent upon the well intersecting and hydraulically connecting with permeable fractures, whether natural or anthropogenic. The apertures and lengths of these connected fractures can be considered the dominant factors controlling permeability (Witherspoon et al. 1980), but tortuosity, contact area, fracture network connectivity, and roughness are also very important (Hyman et al. 2016; Makedonska et al. 2016; Zimmerman and Bovarsson 1996). In this study, we loosely use the term ‘fracture geometry’ to imply any or all physical spatial characteristics (i.e., length, height, twist, aperture, spacing, roughness, etc.). Fracture geometries are often complex, as opposed to simple planar features, due to changing stress states and the influence of heterogeneity and discontinuities throughout the rock mass (Aydin et al. 2006; Einstein and Dershowitz 1990; Hoek and Martin 2014).

Multiple intersecting fractures form complex fracture networks. These may include a combination of natural fractures, tensile hydraulic fractures, sheared weak discontinuities, and pressure solution interfaces (McClure and Horne 2014). Microseismic data acquired during hydraulic stimulation can be used to estimate the extent of these complex fracture networks, sometimes referred to as the stimulated reservoir volume (Mayerhofer et al. 2010). However, the actual geometry of these interconnected complex fracture networks is very difficult to characterize in situ (Warpinski et al. 1982a, b; Jeffrey et al. 1995). Fracture roughness, branching, and geometric complexity during hydraulic stimulation can cause increased frictional pressure losses and hinder proppant transport (Jeffrey et al. 2009), which in turn will affect fracture network permeability after fracture closure. Fracture tortuosity, roughness, and asperity contact area reduce fracture permeability (Detwiler and Morris 2014; Pyrak-Nolte and Morris 2000; Warpinski and Teufel 1987; Zimmerman and Bovarsson 1996). Branching and roughness increase fracture surface area. In natural rocks, it is impossible to confidently predict the geometry of stimulated fractures a priori because of uncertainty arising from heterogeneity and undetected or insufficiently characterized pre-existing fractures, even if only considering the targeted zone for stimulation. Therefore, it is important to understand the possible geometries of hydraulic stimulated fractures that are likely to occur in the field in order to better predict the effectiveness of a stimulation treatment. This is especially important in multi-stage hydraulic fracture treatments, where an optimal spacing of hydraulic fracture stimulation intervals along a horizontal well is thought to exist, such as for oil and gas or enhanced geothermal energy production.

In this study, we analyze three-dimensional hydraulic fracture geometry from a series of varied experiments in order to identify recurring patterns. The experiments included specimens of different materials with different sizes and different boundary conditions. Building from the well-known constitutive tensile and shear fractures, we identify the recurring higher-order patterns of offset fracture branching, traversing coalescence, and smooth fracture reorientation. These patterns occurred in homogeneous and heterogeneous materials and combine to form complex fracture networks. Identifying these common fracture structures elucidates geometrical features that are likely to influence fluid flow. We also evaluate the implications of these structures for proppant settling, fracture permeability, fracture surface area, and stimulated reservoir volume in the context of applications for oil and gas recovery, geothermal energy mining, waste disposal, and CO2 sequestration.

Background: hydraulic fracture geometry

Many hydraulic fracture experiments have been performed in rocks subjected to a variety of stress conditions. Some of these studies also present data regarding hydraulic fracture geometry. These studies generally found that hydraulic fracture geometry depends upon the rock stress-state, borehole and perforation geometry, fluid viscosity and injection rate, and rock structure and scale.

Previous studies have identified many important trends between experimental parameters and resulting fracture geometries. Rock stresses are the dominant factor affecting fracture geometry with tensile hydraulic fractures preferentially orienting perpendicular to the minimum principal stress direction (Warpinski et al. 1982a, b; Zoback et al. 1977). The influence of the near-wellbore zone can add complexity to the fracture, where examples show that fractures tend to initiate with orientations parallel with the borehole axis even if the borehole is drilled parallel with the minimum principal stress (Hallam and Last 1991; Romero et al. 1995). It is relevant to note that these studies observed an offset branching pattern along the wellbore when hydraulic fractures initiated at an angle other than perpendicular to the minimum principal stress (Weijers et al. 1994), which is unlike the idealized curving pattern predicted by continuum theory (Abass et al. 1996; Valkó and Economides 1995). Perforations can affect fracture growth where misalignment between the perforations and the maximum principal rock stress can add tortuosity (Behrmann and Elbel 1991; Daneshy 1973). When the initial hydraulic fracture at the well is not perpendicular to the minimum principal field stress, twisting fractures can form as the fracture lengthens and far-field stress effects become dominant (Valkó and Economides 1995). Fluid viscosity and injection rate have a strong influence on propagating fracture geometry and its interaction with natural discontinuities (Beugelsdijk et al. 2000) where higher viscosities and flow rates can produce more planar fractures (Ishida et al. 2004) and very high injection rates, as with conflagration and explosive compounds, can produce more fracture branching (Cuderman and Northrop 1986; Wieland et al. 2006). Fluid–rock chemical interactions can affect fracture aperture distribution over time (Detwiler 2010). Permeation of fracture fluid into the matrix and frictional pressure losses with fluid flow through open fractures can reduce fracture aperture and length (Perkins and Kern 1961; Nordgren 1972; Geertsma and de Klerk 1969; Warpinski 1985).

Dimensional scale affects fracture geometry and roughness. For example, a small pre-existing fracture at 1 mm length will have a lesser effect on an intersecting 1 m hydraulic fracture than a 10 m pre-existing fracture. Most theoretical work concerning hydraulic fracture scaling focuses on continuum materials (de Pater et al. 1994; Johnson and Cleary 1991; Detournay et al. 2007), but field conditions and the laboratory use of natural rocks unavoidably include heterogeneity and discontinuity (Athavale and Miskimins 2008; Jeffrey et al. 2009; Mokhtari et al. 2014; Warpinski and Teufel 1987). We do not attempt to directly address the topic of discontinuous–heterogeneous scaling in this study; however, we do investigate hydraulically stimulated fractures in different-sized specimens and specimens that contain discontinuities ranging in size with respect to the specimens. From these, we find prevalent fracture patterns at a range of scales from sub-specimen to full specimen.

Uncertainty remains regarding the mechanisms for complex hydraulic fracture growth in heterogeneous and discontinuous rocks. A better understanding of this process can provide an improved means for evaluating complex fracture networks, whether actual or modeled. This in turn can lead to improved design of stimulation treatments.

Shear and tensile fracture identification

Fracture propagation can be categorized according to linear elastic fracture mechanics (LEFM) into one of the three principal directions of crack tip motion, (mode I) tensile opening, (mode II) in-plane shearing, and (mode III) out-of-plane shearing (Anderson 1991). These displacements can be determined after fracturing from characteristics such as texture, offset, and orientation with respect to the expected stress-field in which they were created (Aydin et al. 2006). Mixed mode fractures, including any combination of these three displacement modes, are common in rock because of natural heterogeneities and discontinuities. LEFM mechanics has been applied to hydraulic fracture breakdown pressure prediction and fracture propagation modeling for adequately homogeneous rock types, known stress conditions, and sufficiently characterized rock properties (Valkó and Economides 1995). When applied to natural fracture networks, LEFM is complicated by uncertainty in rock properties, heterogeneities, and pre-existing discontinuities. In this laboratory study, we assume shear- or tensile-dominated fractures by orientation with respect to known applied principal stresses. Tensile-dominated fractures are identified as those oriented perpendicular to the minimum principal stress. Shearing fractures occur at angles between the principal stresses.

Hydraulic fracture experiments

In this study, we identify recurring hydraulic fracture patterns among a series of laboratory experiments. Details for each of the individual experiments are detailed in the prior work (Frash 2012, 2014; Frash et al. 2013a, b, 2014a, b, 2015a, b, c; Haas et al. 2013; Hampton et al. 2013; Revil et al. 2015). Table 1 gives an overview of the hydraulic stimulation experiments evaluated for this study, detailing the various specimen materials, injection fluids, and boundary conditions. Specimen materials included concrete, cement, granite, acrylic, and carbonate-rich shale, representing a large range of material types. Hydraulic fracture breakdown pressures were typically high due to scale effects from using small boreholes at 10 mm and 6 mm for cased and uncased intervals, respectively (Haimson and Zhao 1991). Available mechanical properties for each of these materials are given in Table 2 with additional description in the Appendix. Injection fluids included water, oil, and epoxies, as detailed in Table 3. Additional details and data for these experiments are available by reasonable request to the corresponding author.

Table 1 Summary of laboratory experiments in which hydraulic stimulation was performed by fluid injection into a borehole and after which fractures were mapped from a series of sequential cross sections
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Table 2 Properties of specimen materials used for the hydraulic stimulation experiments
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Table 3 Injection fluid properties as used in the hydraulic stimulation experiments
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Multiple hydraulic injection stages were executed for experiments P01-00, E01-00, E02-00, G01-00, G01-90, G01-92, and G01-93. Each injection stage included the possibility of new fracture growth; therefore, acoustic emission monitoring and/or real-time visual observation was used to estimate the location and timing of any new fractures activated or created by fluid injection. Pre-fracture inspections and a sequential series of post-fracture saw-cut cross sections were acquired from each of these experiments to measure hydraulically stimulated 3D fracture geometries. We find this saw-cut method to be more informative than the common method in the previous studies, where a hammer and chisel were used to mechanically split specimens parallel to the hydraulic fracture plane. Epoxy injection yielded the best fracture growth control, and the most pristine examples of complex fracture network geometry because fractures were better preserved and the path of injected fluid penetration into fractures and matrix was easily traceable, even when branching occured. Other methods such as X-ray tomography are available and have been successfully used for fracture identification in rocks, but these methods have difficulty resolving small-scale fracture structures within large specimens (Frash et al. 2016). For example, X-ray tomography would not be able to resolve 0.1 mm aperture fractures within a 300 mm × 300 mm × 300 mm cubic specimen at the current state of the technology.

Here, we first present results showing complex fracturing in acrylic specimens. Results from fracturing this relatively homogeneous and transparent acrylic material provide useful insight into understanding the experiments in opaque rocks and cements. Next, we present examples of recurring 3D fracture patterns observed at the full specimen scale, focusing on the least ambiguous results. Then, we show smaller, sub-specimen scale, fracture patterns where 2D evidence for similar structures to the large scale is found.

Complex fractures in acrylic

The most self-evident examples of simple tensile and shear fractures were acquired from A01-05, as shown in Fig. 1. The included photomicrographs were taken from cut cross sections through the hydraulic-fractured acrylic specimen. Injected epoxy (off-white/orange color) infilled the fractures in this experiment, preserving the fracture aperture during cross sectioning and enhancing contrast between fractures and the acrylic matrix. Similar fracture geometries were observed by eye in all of the acrylic specimens, but the tight residual fractures in A01-03 and A01-04 could not be easily photographed. Longitudinal tensile opening (mode I) was the dominant fracture type in the acrylic experiments. Shear-oriented fractures in the propagation direction (mode II) and perpendicular to the propagation direction (mode III) were observed within the tensile-dominated fractures.

Fig. 1
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Tensile (mode I), in-plane shear (shear; mode II), out-of-plane shear (tearing; mode III), and mixed-mode fractures observed in cross sections through the acrylic specimen A01-05. Marine epoxy (off-white color) infilled the fractures preserving their geometry for cross sectioning. Tensile fractures were dominant with some offset tensile fractures connected by shear fractures, forming larger coalesced fractures. Top right shows a view of the fractured specimen. Bottom right shows an internal X-ray computed tomography slice near the center of the injection interval

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A video of the A01-05 experiment (Frash et al. 2013c) reveals a staged progression to the hydraulic fracture’s propagation. This progression starts with epoxy filling pre-existing drilling-induced fractures along the borehole wall. At the breakdown injection pressure (i.e., peak pressure), these fractures begin to extend along their initial orientations, possibly dominated by mode I (tensile) opening. Then, at a critical amount of extension, these small tensile fractures begin to coalesce via new interconnecting fractures that likely include a mixture of shear modes. The tips of the shear-coalesced fracture fronts lag behind the tensile front with respect to radial distance from the borehole. This detail indicates that more strain is required to create the coalescing shear fractures than what is required to create the tensile fractures. The progression of fracture growth demonstrates that offset tensile fracture strands can simultaneously propagate on what could appear to be competing planes (e.g., stress shadowing) and later coalesce into a common fracture by shear (Fig. 1: mixed-mode example). The geometry in these experiments provides examples of: (1) hydraulic fractures propagating by different modes along segments within a larger coalesced fracture and (2) multiple fracture strands sharing a common plane closer to a common origin, even when they appear disconnected or separate from a 2D perspective.

Recurring fracture patterns at the specimen scale

It may not be immediately apparent how varied laboratory hydraulic fracture experiments can provide insight into complex fracturing processes in the subsurface. It is also common knowledge that natural rocks contain significant complexity (e.g., heterogeneity, discontinuity, anisotropy, nonlinearity, and variable stresses) that cannot be fully characterized across the relevant scales even using the most advanced available methods. In consequence and by subjective argument, it is useful to be able to identify recurring fracture geometries that occur across a range of material types subjected to differing boundary conditions. In this study, we categorize three characteristic 3D hydraulic fracture patterns of a higher order than simple tensile and shear modes. These higher-order patterns are proposed as constituents of even more complex fracture networks. Each higher-order fracture pattern hints at the origins of tortuosity, roughness, and branching and, in turn, has implications for hindered fluid flow and increased fracture surface area relative to more idealized fracture geometries. The three categorized fracture patterns include (1) offset branching, (2) traversing coalescence, and (3) smooth reorientation, as depicted in Fig. 2. Note that the ‘3D perspectives’ column in Fig. 2 shares a common boundary stress orientation with the x-axis being the minimum principal stress axis. The geometry shown for the complex network was produced from direct measurement (Frash et al. 2015a, b, c), while the other geometries are simplified from actual observations which tended to each include multiple fracture structures.

Fig. 2
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Categorization of fracture patterns created by hydraulic stimulation that combine to form complex fracture networks. Multiple perspectives are shown for each fracture pattern to depict their 3D structures, illustrate their 2D signatures, and provide evidence of their occurrence in the cement, granite, or shale experiments

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Simple tensile fractures are the simplest hydraulic fracture geometry and are a convenient assumed shape for modeling (de Pater et al. 1994; Perkins and Kern 1961; Nordgren 1972; Geertsma and de Klerk 1969). This geometry results from tensile-dominated fracture propagation radially away from the borehole and often exhibits an elliptical aperture profile (de Pater et al. 1994; Frash et al. 2014a, b). This was also the most commonly observed macro-scale fracture geometry with examples identified in all specimens except for E01-00—true-triaxially confined high-strength cement with brine injection and G01-92—triaxially confined granite with water injection. These laboratory results support the expectation that rock stresses, borehole orientation, and fluid parameters dominate over the influence of rock structure, particularly when high-viscosity fluids were used (de Pater et al. 1994; Ishida et al. 2004; Warpinski et al. 1982a, b).

Discontinuity shear was observed at some scale in all experiments with the most prominent examples identified in E01-00—true-triaxially confined high-strength cement with brine injection, E02-00—true-triaxially confined high-strength cement with oil injection, and S01-00—true-triaxially confined shale with epoxy injection. In each of these, large and prolific pre-existing discontinuities were hydrosheared by fluid injection because these fractures were weaker than the intact matrix rock (Mokhtari et al. 2014). The result from S01-00 was particularly interesting because a large shearing event occurred suddenly during low-rate constant-pressure injection at what was thought to be an injection pressure below the hydraulic fracture propagation pressure (Frash et al. 2015a, b, c). This indicates a transient effect where slow pressurization of a natural fracture eventually resulted in shear slip.

Offset fracture branching was observed in all specimens. At the field scale, similar hydraulic fracture branching has been described as a hydraulic fractured zone (Warpinski and Teufel 1987) or as a fracture band (Aydin et al. 2006). This structure often appears in cross sections as a set of unconnected or weakly connected sub-parallel hydraulic fractures. However, in many cases, these branches could be traced back to a common fracture plane closer to the injection well. Considering observations from the acrylic specimens, it is evident that these branches can propagate simultaneously, in parallel, overlapping, and in close proximity without significant competition from stress shadowing. The offset branching structure is significant for fluid flow. Lateral offsets in vertical fractures are likely to hinder proppant settling. Overlapping parallel branched fractures are likely to each have reduced aperture relative to a single fracture plane which will reduce both individual and cumulative hydraulic conductivities. Increased surface area from branched fractures will likely improve flow from matrix pores to the more conductive hydraulic fractures per length of the fracture, as well as enhance reactivity because new fracture surfaces tend to be highly reactive. The number of fracture branches does not appear to be predictable, but it is possible that they have some relation to distance from the well.

Traversing coalescence of branched fractures is a structure that sometimes occurred as branched fractures extended. It appears that this structure was the most common when branched fractures propagated in close proximity or that this structure caused branched fractures to propagate close together. Prominent examples of traversing coalescence were identified in A01-05—unconfined acrylic with epoxy injection and S01-00—true-triaxially confined shale with epoxy injection. The effects of traversing coalescence are likely to be the opposite of branching with a tendency to decrease fracture surface area, increase fracture aperture, and decrease tortuosity, especially as fracture size increases. The sequence of traversing coalescence occurring after branching is indicative of discontinuous processes in fracture propagation. This discontinuous nature of propagation is further supported by a known tendency for irregular pressure peaks during continuous injection stimulation (Frash et al. 2015a, b, c).

Smooth reorientation was most commonly observed as fractures transitioned from longitudinal with the wellbore in the near-well zone to be perpendicular to the minimum principal stress further from the well. This curvilinear geometry was less apparent in our experiments than in previous works that used larger wellbores and more homogeneous materials (Abass et al. 1996; Hallam and Last 1991; Romero et al. 1995; Weijers et al. 1994). Our most prominent examples of smooth reorientation were observed in E01-00—true-triaxially confined high-strength cement with brine injection and G01-90—true-triaxially confined granite with oil injection. Fracture branching was common amidst smooth reorientation. These branches generally arose from multiple tensile fracture initiation points along the well or by interaction with pre-existing fractures during propagation. Tortuosity due to smooth reorientation is likely to affect flow by increasing frictional pressure losses, especially near the wellbore.

Combinations of these recurring fracture structures yield complex fracture networks. A prominent example of a complex fracture network was observed in S01-00—true-triaxially confined shale with epoxy injection. This experiment produced a simple tensile planar bi-wing fracture, shear activation of a pre-existing discontinuity, and fluid penetration into bedding planes. Among these primary structures was evidence for offset fracture branching followed by traversing coalescence. No significant smooth reorientation of fractures was observed, likely because the injection well was drilled parallel to the maximum principal stress. Most fracture branching occurred at the small scale, but some branching also occurred at the macro-scale with influence from shear activated discontinuities. When offset fracture branches were traced back to the injection borehole, they were found to share a common plane. It is clear that the complex hydraulic fractures stimulated in this experiment penetrate a larger fracture volume and greater surface area than a simple tensile fracture alone would have.

Small-scale fracture patterns

Microscopic inspection of the cut cross sections from the laboratory hydraulic fracture experiments revealed fracture complexity similar to the macroscopic scale, as shown in Fig. 3. At the macroscopic perspective, this complexity is often lumped into the description of roughness and generated fines (i.e., loose particles). Experiments using epoxy injection provided the best detail on microscopic fracture structures and produced the examples shown in Fig. 3. From observation, simple tensile fractures included propagation by void nucleation and coalescence and by transgranular fracturing. Shear activation was typically observed with intergranular fracturing; however, microscale intergranular fracturing was also observed within macro-scale simple tensile fractures. A special case of microscale fracturing included granular fracture bifurcation which is a branching process likely related to offset branching. Another special case included transportable grain release where fracture propagation was found to mobilize fine-sized particles. Without a detailed analysis or support from granular fracture models, evaluations of the mechanisms by which these structures arise would be merely hypothetical. The implications of these mechanisms are more self-evident, where void nucleation, fracture coalescence, and intergranular fracturing all contribute to fracture roughness which in turn causes increased frictional pressure losses in flowing fluids. Transportable grain release is an interesting special case, in that transportable fines could act as natural proppant or flow-blocking particles. Granular fracture bifurcation is another interesting special case, in that it creates increased surface area within macroscopic fractures and also potentially contributes to macroscopic branching.

Fig. 3
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Microscopic fracture patterns with examples from the experiments

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Conclusions

Building on fundamental simple tensile hydraulic fractures and shear activation of pre-existing discontinuities, we proposed the three higher-order fracture geometries of offset branching, traversing coalescence, and smooth reorientation, as depicted in Fig. 2. Combinations of these geometries yield complex fracture networks that are observable across dimensional scales. We observed them via laboratory experiments conducted using a variety of materials subjected to a variety of conditions. Observations of fracture geometries were best via cut cross sections and injection of clearly traceable fluids such as epoxy. In both homogeneous and heterogeneous materials, offset fracture branching was often found to share a common fracture closer to the point of injection. This common fracture was coalesced from smaller close-proximity tensile-dominated branches via traversing shear-oriented fractures that lagged behind the tensile fracture front. Smooth fracture reorientation was prevalent when the injection borehole was not aligned with a principal stress direction. In this case, hydraulic fractures that initiated semi-longitudinally along the wellbore would twist and reorient to be perpendicular to the minimum principal stress further from the point of injection. Instances of offset branching and traversing coalescence were observed amidst the reorienting fracture. The three proposed higher-order fracture geometries are not new fracturing modes but rather recurring manifestations of mixed fracture modes.

Evidence that higher-order complex fracture geometries occur and identification of common structures for these geometries provide useful insight related to hydraulic fracture stimulations. For example, well stimulation methods that encourage fracture branching could provide increased fracture surface area and increased stimulated reservoir volumes for a given amount of injected fluid volume. This would be beneficial for increasing oil and gas recovery because it will connect the stimulated well to more of the rock matrix. Also in this process, offset fracture branches would beneficially limit proppant settling to within semi-isolated vertical segments of fractures. Possible methods for encouraging branching include low-viscosity or low-rate injection with slickwater or gas fracs. For an opposite example, stimulation methods that encourage simple tensile fracturing or traversing coalescence could result with more conductive and open fractures that counteract tortuosity. Possible methods for this include high-rate or high-viscosity fluid injection using gels or more horsepower. In practice, complex fractures should be expected in hydraulic fracture stimulation and accurate modeling of these structures with consideration of the common patterns could contribute to more efficient development of natural gas and geothermal energy resources or disposal sites for waste or CO2.