What progress in quantifying fracture spatial arrangement?

Spatial arrangement is a fundamental characteristic of fracture arrays. The pattern of fault and opening-mode fracture positions in space defines structural heterogeneity and anisotropy in a rock volume, governs how faults and fractures affect fluid flow, and impacts our understanding of the initiation, propagation, and interactions during the formation of fracture patterns.

Fracture spatial arrangement

During the past decade, the need for meaningful documentation and accurate prediction of fracture patterns in the subsurface has become urgent. The spatial arrangement of faults and opening-mode fractures is a key aspect of structural heterogeneity and anisotropy in the upper elastofrictional crust.

Uncertainty about fundamental fault and fracture spatial patterns threatens engineering operations such as fluid injection underground, management of induced seismicity and the efficiency and success of fluid extraction, for example, in unconventional and deep hydrocarbon reservoirs, and geothermal systems.

Examples of cryptic but important arrangements include highly concentrated opening-mode fracture clusters that may locally breach reservoir cap rocks, account for abrupt differences in well performance, or, on broader regional scales, account for crustal fluid flow and ore deposit patterns.

Bulk rock strength and stiffness are also significantly influenced by the presence/absence of fractures and thus this attribute is sensitive to fracture patterns.

Fault and fracture patterns also provide evidence of structural growth processes. Increasingly, quantifying spatial arrangement is central to understanding pattern origins. How do patterns relate to mechanical stratigraphy, scale, loading conditions, growth processes and rates, interaction with concurrent geochemical processes, and other factors?

What is spatial arrangement?

In a 2018 review Laubach et al. defined spatial arrangement as follows. For faults and opening-mode fractures, spatial arrangement is the property possessed by an array that defines the position of constituent structures in the rock mass. Interpreted broadly, spatial arrangement is nearly synonymous with the field of structural geology—the arrangement of the parts of a rock mass, irrespective of scale, including spatial relationships between parts, their relative size and shape and the internal features of the parts.

In a narrower technical sense there are two complementary ways to view fracture spatial arrangement:

• As objects in space, where the position, orientation and abundance of the fractures are measured, usually in some geographical reference frame. This includes whether faults and fractures are closely or widely separated—their pattern of abundance—and whether they are regularly spaced or not.
• As objects in relation to one another (sometimes referred to as topology). Such measures are generally taken to be independent of scale and orientation and remain invariant under any continuous affine transformation.

In both cases, related issues are how patterns correlate and/or interact with host rock attributes, associated folds and faults over a range of scales, and with formative processes.

Challenges

Characterizing and understanding spatial arrangement has a range of challenges. Among these, how can spatial arrangement be quantified in 1, 2, and 3D? How can meaningful patterns be distinguished from random arrangements? What is the range of arrangements? How do they arise? What do different patterns signify? How do patterns vary with scale?

SDI efforts on spatial arrangement

Spatial arrangement has long been a focus of the Structural Diagenesis Initiative (SDI), including early successful models for explaining spatial clustering (Olson 2004), an award-winning method to quantify 1D spatial arrangement (Marrett et al. 2018), early field descriptions of fracture clusters (Laubach 1991; 1995), and a recent review (Laubach et al. 2018). New developments include 2D quantification methods, reconstructions of patterns through time, and models that account for the mechanical effects of cement.

So far, our published work has focused on spatial arrangement in space but in 2022 we proposed a new approach to defining fractures in relation to each other (node patterns) as part of a new protocol for fractured outcrop assessment.

Some of these developments are outlined in these published papers.

Broader implications & future directions in spatial arrangement research

The role of chemistry in fracture pattern development and opportunities to advance interpretations of geological materials. Laubach, S.E., Lander, R.H., Criscenti, L.J., et al., 2019.  Reviews of Geophysics, 57 (3), 1065-1111. doi:10.1029/2019RG000671 | view at publisher | blog post | BEG summary | view AGU Editor’s Vox | JSG press release

Review of fault & fracture spatial arrangements & introduction to special issue of Journal of Structural Geology on spatial arrangement.

• Spatial arrangement of faults and opening-mode fractures. Laubach, S.E., Lamarche, J., Gauthier, B.D.M., Dunne, W.M., Sanderson, D.J., 2017. Journal of Structural Geology | view at publisher 
  An overview & review of fracture patterns & discussion of future research directions.

1D spatial arrangement methods

• Correlation analysis of fracture arrangement in space. Marrett, R., Gale, J.F.W., Gomez, L., Laubach, S.E., 2018. Journal of Structural Geology. doi.org/10.1016/j.jsg.2017.06.012 | view at publisher
  A seminal paper on spatial arrangement concepts & methods that will set the standard for years to come; a breakthrough that will have a broad impact on fundamental & applied research.
• Microfracture spacing distributions and the evolution of fracture patterns in sandstones. Hooker, J.N., Laubach, S.E., Marrett, R., 2018. Journal of Structural Geology. doi.org/10.1016/j.jsg.2017.04.001 | view at publisher
  Reports first-ever rigorous reconstruction of size-distribution & spacing history of a fracture array.
• Multiscale spatial analysis of fracture arrangement and pattern reconstruction using Ripley’s K-Function. Shakiba, M., Lake, L.W., Gale, J.F.W., Pyrcz, M.J., 2022. Journal of Structural Geology, 155, doi.org/10.1016/j.jsg.2022.104531 | view at publisher
  1D spatial arrangement and pattern reconstruction using Ripley’s K
• Rigorizing the use of the coefficient of variation to diagnose fracture periodicity and clustering. Hooker, J., Marrett, R., Wang., Q., 2023. Journal of Structural Geology 168, 104830 | view at publisher

2D spatial arrangement methods

• Analysis of spatial arrangement of fractures in two dimensions using point process statistics. Corrêa, R.S.M., Marrett, R., Laubach, S.E., 2022. Journal of Structural Geology 163, 104726. | view at publisher
  A new 2D method that accounts for distributed attributes of fractures: orientation, length
• Stochastic reconstruction of fracture network pattern using spatial point processes Shakiba, M., Lake, L.W., Gale, J.F.W., Laubach, S.E., Pyrcz, M.J., , 2022. (in review) | view at publisher
  Taking spatial arrangement observations to pattern reconstruction
• Multiscale spatial analysis of fracture nodes in two dimensions. Shakiba, M., Lake, L.W., Gale, J.F.W., Laubach, S.E., Pyrcz, M.J., 2023. Marine & Petroleum Geology | view at publisher
  2D spatial arrangement that accounts for node patterns
• Characterization of spatial relationships between fractures from different sets using K-function analysis. Shakiba, M., Lake, L.W., Gale, J.F.W., Pyrcz, M.J., 2023. AAPG Bulletin doi:10.1306/11062222008 | view at publisher
• 2D spatial arrangement that accounts for multiple sets
  
• Scale-dependent fracture networks, Forstner, S.R., Laubach, S.E., 2022. Journal of Structural Geology, 165, 104748. | view at publisher
  A new approach account for inevitable scale dependencies in network characterization

1D spatial arrangement applications

• Quantifying opening-mode fracture spatial organization in horizontal wellbore image logs, core and outcrop: application to Upper Cretaceous Frontier Formation tight gas sandstones, USA. Li, J.Z., Laubach, S.E., Gale, J.F.W., Marrett, R.A., 2018. Journal of Structural Geology. doi.org/10.1016/j.jsg.2017.07.005 | view at publisher
  First quantitative account of fracture clustering in tight gas sandstone using subsurface & outcrop analog data
• Spatial arrangement and size distribution of normal faults, Buckskin Detachment upper plate, Western Arizona. Laubach, S.E., Hundley, T.H., Hooker, J.N., Marrett, R., 2018. Journal of Structural Geology. | view at publisher
  Applies the Marrett et al. methodology to intensely faulted rocks
• Natural fracture characterization in the Wolfcamp Formation at the Hydraulic Fracture Test Site (HFTS), Midland Basin, Texas. Gale, J.F.W., Elliott, S.J., Li, J.Z., Laubach, S.E. 2019. URTeC 644, Unconventional Resources Technology Conference, Denver, Colorado, USA, 22-24 July 2019 16 p. https://doi.org/10.15530/urtec-2019-644 | view at publisher
  Natural subsurface fracture spatial distributions in shale
• Quantified fracture (joint) clustering in Archean basement, Wyoming: application of Normalized Correlation Count method. Wang, Q., Laubach, S.E., Gale, J.F.W., Ramos, M.J., 2019. Petroleum Geoscience, 25, 415-428. doi:10.1144/petgeo2018-146 | view at publisher | blog post | Best of Petroleum Geoscience 2019
  Field example of clustering in basement rocks and tutorial on interpretation of NCC plots
• Characterizing subsurface fracture spatial distribution in the East Painter Reservoir anticline, Wyoming. Wang, Q., Narr, W., Laubach, S.E., 2020. SPE/AAPG/SEG Unconventional Resources Technology Conference, URTeC-3265, 12 p. doi: 10.15530/urtec-2020-3265 | view at publisher
  A preliminary account of spatial arrangement in long horizontal wells in an oil reservoir
• Fracture description of the HFTS-2 slant core, Delaware Basin, West Texas. Gale, J.F.W., Elliott, S.J., Rysak, B.G., Ginn, C.L., Zhang, N., Myers, R.D., Laubach, S.E., 2021. In SPE/AAPG/SEG Unconventional Resources Technology Conference. OnePetro. doi.org/10.15530/urtec-2021-5175 | view at publisher
  Spatial arrangement in shale of both natural and stimulation fractures
• Episodic reactivation of carbonate fault zones with implications for permeability – An example from Provence, Southeast France. Corrêa, R.S.M., Ukar, E., Laubach, S.E., Aubert, I., Lamarche, J., Wang, Q., Stockli, D., Stockli, L., Larson, T., 2022. Marine & Petroleum Geology 145, 105905. doi.org/10.1016/j.marpetgeo.2022.105905 | view at publisher
  Fault-related fracture clustering in context of diagenesis & fracture dating
• Quantification of the spatial arrangement of structural lineaments and deformation bands: Implications for the tectonic evolution of the eastern border of the Araripe Basin, NE Brazil. de Arruda Passos, V.S., de Miranda, T.S., Oliveira, J.T.C., Celestino, M.A.L., Corrêa, R.*, Topan, J.G., da Cruz Falcão, T. 2022. Journal of South American Earth Sciences, 118, 103934. | view at publisher
  Spatial arrangement and tectonic evolution
• The critical role of core in understanding hydraulic fracturing, Gale, J. F. W., Elliott, S. J., Rysak, B. G., Laubach, S. E., 2022. Geological Society, London, Special Publication 527, doi: https://doi.org/10.1144/SP527-2021-198. | view at publisher
  Summary of patterns seen in several different basins

Spatial arrangement, topology, and diagenesis

• Scale-dependent fracture networks, Forstner, S.R., Laubach, S.E., 2022. Journal of Structural Geology, 104748. | view at publisher
  A new approach account for inevitable scale dependencies in network characterization

Spatial arrangement and geomechanical models

• Predicting fracture swarms – the influence of subcritical crack growth and the crack-tip process zone on joint spacing in rock, Olson, J.E., 2004. In Cosgrove, J.W., Engelder, T., eds, The initiation, propagation, and arrest of joints and other fractures, Geological Society of London Special Publication 231, 73-87. | view at publisher
  A model that accounts for fracture clustering
• Coupling diagenesis and mechanics for more realistic simulation of natural fracture pattern development, Lee, B., Olson, J.E., Laubach, S.E., 2022. Proceedings, Second International Meeting for Applied Geoscience & Energy, AAPG IMAGE 2022. | view at publisher
  A fully 3D model that takes the mechanical effects of cement into account

Early field accounts of clustering

• Fault and joint swarms in a normal fault zone. Laubach, S.E., Mace, R.E., Nance, H.S., 1995. In: Rossmanith, H.-P., ed.. Mechanics of Jointed and Faulted Rock, Balkema, Rotterdam, 305-309. | view
  Fracture clusters in Austin Chalk in long excavations
• Fracture patterns in low-permeability-sandstone gas reservoir rocks in the Rocky Mountain region. Laubach, S. E., 1991, Society of Petroleum Engineers, SPE Paper No. 21853, p. 501–510. doi:10.2118/21853-MS | view at publisher
  Fracture clusters (swarms) in various sandstones and coal, western U.S.

Research in progress

Work is in progress further developing and applying 1 and 2D methods and perfecting extension to 3D, developing geomechanical models that fully account for the processes that govern spatial arrangement and comparing model results to nature, reconstructing how fracture patterns evolve through time, and investigating the scale dependencies of patterns. In the later category, our research is investigating aspects of how fractures relate to one another over ranges of scale.

Software

Software used to analyze spatial arrangement is available via the source publications listed above. These include:

• Joints; Joints2D with diagenesis (Olson 2004; Lee et al. in preparation)
• CorrCount (Marrett et al. 2018); CorrCount 2D (Corrêa et al. 2022)
• Ripley’s K software (Shakiba et al. 2022 a,b,c)
• R code for calculating C_V significance (Wang et al., in review; Hooker et al., 2023)

A user’s guide to the Marrett et al. 2018 program CorrCount is available upon request.

Awards

Clustered or random? A best paper award | Structural Diagenesis Initiative (utexas.edu)

Acknowledgements

Our research on spatial arrangement is funded by grant DE-SC0022968, ‘Reconstructing and Predicting Fracture Pattern Evolution’ from Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy