scholarly journals Investigating Spatial Heterogeneity within Fracture Networks using Hierarchical Clustering and Graph Distance Metrics

2021 ◽  
Author(s):  
Rahul Prabhakaran ◽  
Giovanni Bertotti ◽  
Janos Urai ◽  
David Smeulders
Keyword(s):  
Spatial Variation ◽  
Hierarchical Clustering ◽  
Similarity Measures ◽  
Fracture Network ◽  
Fracture Networks ◽  
Spatial Clusters ◽  
Network Modelling ◽  
Graph Similarity ◽  
Novel Approach ◽  
Fracture Development

Abstract. We investigate the spatial variation of 2D fracture networks digitized from the well-known Lilstock limestone pavements, Bristol Channel, UK. By treating fracture networks as spatial graphs, we utilize a novel approach combining graph similarity measures and hierarchical clustering to identify spatial clusters within fracture networks and quantify spatial variation. We use four graph similarity measures: fingerprint distance, D-measure, NetLSD, and portrait divergence to compare fracture graphs. The technique takes into account both topological relationship and geometry of the networks and is applied to three large fractured regions consisting of nearly 300,000 fractures spread over 14,200 sq.m. The results indicates presence of spatial clusters within fracture networks with that vary gradually over distances of tens of metres. One region is not influenced by faulting but still displays variation in background fracturing. Variation in fracture development in the other two regions are interpreted to be primarily influenced by proximity to faults that gradually gives way to background fracturing. Comparative analysis of the graph similarity-derived clusters with fracture persistence measures indicate that there is a general correspondence between patterns; however, additional variations are highlighted that is not obvious from fracture intensity and density plots. The proposed method provides a quantitative way to identify spatial variations in fracture networks which can be used to guide stochastic and geostatistical approaches to fracture network modelling.

scholarly journals Investigating spatial heterogeneity within fracture networks using hierarchical clustering and graph distance metrics

Solid Earth ◽  
2021 ◽  
Vol 12 (10) ◽  
pp. 2159-2209
Author(s):  
Rahul Prabhakaran ◽  
Giovanni Bertotti ◽  
Janos Urai ◽  
David Smeulders
Keyword(s):  
Spatial Variation ◽  
Hierarchical Clustering ◽  
Large Scale ◽  
Similarity Measures ◽  
Network Models ◽  
Fracture Network ◽  
Fracture Networks ◽  
Network Modelling ◽  
Graph Similarity ◽  
Novel Approach

Abstract. Rock fractures organize as networks, exhibiting natural variation in their spatial arrangements. Therefore, identifying, quantifying, and comparing variations in spatial arrangements within network geometries are of interest when explicit fracture representations or discrete fracture network models are chosen to capture the influence of fractures on bulk rock behaviour. Treating fracture networks as spatial graphs, we introduce a novel approach to quantify spatial variation. The method combines graph similarity measures with hierarchical clustering and is applied to investigate the spatial variation within large-scale 2-D fracture networks digitized from the well-known Lilstock limestone pavements, Bristol Channel, UK. We consider three large, fractured regions, comprising nearly 300 000 fractures spread over 14 200 m2 from the Lilstock pavements. Using a moving-window sampling approach, we first subsample the large networks into subgraphs. Four graph similarity measures – fingerprint distance, D-measure, Network Laplacian spectral descriptor (NetLSD), and portrait divergence – that encapsulate topological relationships and geometry of fracture networks are then used to compute pair-wise subgraph distances serving as input for the statistical hierarchical clustering technique. In the form of hierarchical dendrograms and derived spatial variation maps, the results indicate spatial autocorrelation with localized spatial clusters that gradually vary over distances of tens of metres with visually discernable and quantifiable boundaries. Fractures within the identified clusters exhibit differences in fracture orientations and topology. The comparison of graph similarity-derived clusters with fracture persistence measures indicates an intra-network spatial variation that is not immediately obvious from the ubiquitous fracture intensity and density maps. The proposed method provides a quantitative way to identify spatial variations in fracture networks, guiding stochastic and geostatistical approaches to fracture network modelling.

Numerical Simulation of Complex Fracture Network Development by Hydraulic Fracturing in Naturally Fractured Ultratight Formations

2013 ◽  
Author(s):  
Hannes Hofmann ◽  
Tayfun Babadagli ◽  
Günter Zimmermann
Keyword(s):  
Fracture Network ◽  
Natural Fracture ◽  
Fracture Networks ◽  
Network Development ◽  
Complex Fracture ◽  
Fracture Patterns ◽  
Fracture Systems ◽  
Fracture Development ◽  
Complex Fracture Network ◽  
Treatment Designs

The creation of large complex fracture networks by hydraulic fracturing is imperative for enhanced oil recovery from tight sand or shale reservoirs, tight gas extraction, and Hot-Dry-Rock (HDR) geothermal systems to improve the contact area to the rock matrix. Although conventional fracturing treatments may result in bi-wing fractures, there is evidence by microseismic mapping that fracture networks can develop in many unconventional reservoirs, especially when natural fracture systems are present and the differences between the principle stresses are low. However, not much insight is gained about fracture development as well as fluid and proppant transport in naturally fractured tight formations. In order to clarify the relationship between rock and treatment parameters, and resulting fracture properties, numerical simulations were performed using a commercial Discrete Fracture Network (DFN) simulator. A comprehensive sensitivity analysis is presented to identify typical fracture network patterns resulting from massive water fracturing treatments in different geological conditions. It is shown how the treatment parameters influence the fracture development and what type of fracture patterns may result from different treatment designs. The focus of this study is on complex fracture network development in different natural fracture systems. Additionally, the applicability of the DFN simulator for modeling shale gas stimulation and HDR stimulation is critically discussed. The approach stated above gives an insight into the relationships between rock properties (specifically matrix properties and characteristics of natural fracture systems) and the properties of developed fracture networks. Various simulated scenarios show typical conditions under which different complex fracture patterns can develop and prescribe efficient treatment designs to generate these fracture systems. Hydraulic stimulation is essential for the production of oil, gas, or heat from ultratight formations like shales and basement rocks (mainly granite). If natural fracture systems are present, the fracturing process becomes more complex to simulate. Our simulation results reveal valuable information about main parameters influencing fracture network properties, major factors leading to complex fracture network development, and differences between HDR and shale gas/oil shale stimulations.

The influence of fracture networks on stability and geohazards of the Niagara Escarpment in southern Ontario

2021 ◽  
Author(s):  
Serena Formenti ◽  
Alexander Peace ◽  
John Waldron ◽  
Carolyn Eyles ◽  
Rebecca Lee
Keyword(s):  
Fluid Flow ◽  
Structural Stability ◽  
Fracture Network ◽  
Eastern United States ◽  
Fracture Networks ◽  
Network Modelling ◽  
Southern Ontario ◽  
Niagara Escarpment ◽  
Bedding Planes ◽  
Geologic Fractures

<p>The Niagara Escarpment is a geological feature comprised of highly fractured Ordovician and Silurian shales and carbonates stretching through southern Ontario and parts of the north-eastern United States. Differential erosion of the shale and carbonate strata has generated a steep cliff face bisecting the city of Hamilton, Ontario. Fractures occur throughout the cliff face and result in the formation of loose blocks of rock that are subject to erosion through rockfalls. This presents structural stability issues and an associated geohazard, which is of particular concern due to the proximity of the escarpment to city infrastructure. Previous work has alluded towards the role of geologic fractures in controlling erosion and stability of the Niagara Escarpment, but the causal mechanisms and extent to which these processes operate remains unclear. As such, the aim of this study is to quantify and analyse fracture networks using a combined field and numerical modelling-based approach to understand the distribution and nature of fractures throughout the escarpment, their connectivity, fluid flow properties, and relationship to structural stability. The location, orientation, and aperture of fractures were systematically quantified and documented around Hamilton. Data were plotted and analysed using the software Orient to identify clusters representative of fracture sets and to calculate average fracture set orientations and the respective confidence intervals. Three primary sets of geological fractures were identified including: 1) a near-vertical bedding confined set oriented north-south, 2) a near-vertical bedding confined set oriented east-west and 3) sedimentary bedding planes which have facilitated fracture migration and controlled resultant fracture geometry. Discrete fracture network modelling of these fracture sets in MOVE highlights their high degree of connectivity and indicates that the distribution and nature of these discontinuities are predominant controls on the locations and sizes of rock fragments generated on the cliff face resulting in rockfalls. Moreover, fracture-controlled porosity is a significant contributor to fluid flow throughout the escarpment. We conclude that geologic fractures present a first-order control on the stability of the Niagara Escarpment near Hamilton.</p>

Numerical Simulation of Complex Fracture Network Development by Hydraulic Fracturing in Naturally Fractured Ultratight Formations

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Hannes Hofmann ◽  
Tayfun Babadagli ◽  
Günter Zimmermann
Keyword(s):  
Fracture Network ◽  
Natural Fracture ◽  
Fracture Networks ◽  
Network Development ◽  
Complex Fracture ◽  
Fracture Patterns ◽  
Fracture Systems ◽  
Fracture Development ◽  
Complex Fracture Network ◽  
Treatment Designs

The creation of large complex fracture networks by hydraulic fracturing is imperative for enhanced oil recovery from tight sand or shale reservoirs, tight gas extraction, and hot-dry-rock (HDR) geothermal systems to improve the contact area to the rock matrix. Although conventional fracturing treatments may result in biwing fractures, there is evidence by microseismic mapping that fracture networks can develop in many unconventional reservoirs, especially when natural fracture systems are present and the differences between the principle stresses are low. However, not much insight is gained about fracture development as well as fluid and proppant transport in naturally fractured tight formations. In order to clarify the relationship between rock and treatment parameters, and resulting fracture properties, numerical simulations were performed using a commercial discrete fracture network (DFN) simulator. A comprehensive sensitivity analysis is presented to identify typical fracture network patterns resulting from massive water fracturing treatments in different geological conditions. It is shown how the treatment parameters influence the fracture development and what type of fracture patterns may result from different treatment designs. The focus of this study is on complex fracture network development in different natural fracture systems. Additionally, the applicability of the DFN simulator for modeling shale gas stimulation and HDR stimulation is critically discussed. The approach stated above gives an insight into the relationships between rock properties (specifically matrix properties and characteristics of natural fracture systems) and the properties of developed fracture networks. Various simulated scenarios show typical conditions under which different complex fracture patterns can develop and prescribe efficient treatment designs to generate these fracture systems. Hydraulic stimulation is essential for the production of oil, gas, or heat from ultratight formations like shales and basement rocks (mainly granite). If natural fracture systems are present, the fracturing process becomes more complex to simulate. Our simulations suggest that stress state, in situ fracture networks, and fluid type are the main parameters influencing hydraulic fracture network development. Major factors leading to more complex fracture networks are an extensive pre-existing natural fracture network, small fracture spacings, low differences between the principle stresses, well contained formations, high tensile strength, high Young’s modulus, low viscosity fracturing fluid, and large fluid volumes. The differences between 5 km deep granitic HDR and 2.5 km deep shale gas stimulations are the following: (1) the reservoir temperature in granites is higher, (2) the pressures and stresses in granites are higher, (3) surface treatment pressures in granites are higher, (4) the fluid leak-off in granites is less, and (5) the mechanical parameters tensile strength and Young’s modulus of granites are usually higher than those of shales.

scholarly journals The competition between fracture nucleation, propagation, and coalescence in dry and water-saturated crystalline rock

Solid Earth ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 375-387
Author(s):  
Jessica A. McBeck ◽  
Wenlu Zhu ◽  
François Renard
Keyword(s):  
Fracture Propagation ◽  
Fracture Network ◽  
Crystalline Rock ◽  
Pore Fluid ◽  
Fracture Networks ◽  
X Ray ◽  
Fracture Development ◽  
Dry Conditions ◽  
Water Saturated ◽  
Fracture Nucleation

Abstract. The continuum of behavior that emerges during fracture network development in crystalline rock may be categorized into three end-member modes: fracture nucleation, isolated fracture propagation, and fracture coalescence. These different modes of fracture growth produce fracture networks with distinctive geometric attributes, such as clustering and connectivity, that exert important controls on permeability and the extent of fluid–rock interactions. To track how these modes of fracture development vary in dominance throughout loading toward failure and thus how the geometric attributes of fracture networks may vary under these conditions, we perform in situ X-ray tomography triaxial compression experiments on low-porosity crystalline rock (monzonite) under upper-crustal stress conditions. To examine the influence of pore fluid on the varying dominance of the three modes of growth, we perform two experiments under nominally dry conditions and one under water-saturated conditions with 5 MPa of pore fluid pressure. We impose a confining pressure of 20–35 MPa and then increase the differential stress in steps until the rock fails macroscopically. After each stress step of 1–5 MPa we acquire a three-dimensional (3D) X-ray adsorption coefficient field from which we extract the 3D fracture network. We develop a novel method of tracking individual fractures between subsequent tomographic scans that identifies whether fractures grow from the coalescence and linkage of several fractures or from the propagation of a single fracture. Throughout loading in all of the experiments, the volume of preexisting fractures is larger than that of nucleating fractures, indicating that the growth of preexisting fractures dominates the nucleation of new fractures. Throughout loading until close to macroscopic failure in all of the experiments, the volume of coalescing fractures is smaller than the volume of propagating fractures, indicating that fracture propagation dominates coalescence. Immediately preceding failure, however, the volume of coalescing fractures is at least double the volume of propagating fractures in the experiments performed at nominally dry conditions. In the water-saturated sample, in contrast, although the volume of coalescing fractures increases during the stage preceding failure, the volume of propagating fractures remains dominant. The influence of stress corrosion cracking associated with hydration reactions at fracture tips and/or dilatant hardening may explain the observed difference in fracture development under dry and water-saturated conditions.

scholarly journals Numerical modeling of complex hydraulic fracture networks based on the discontinuous deformation analysis (DDA) method

2021 ◽  
pp. 014459872098153
Author(s):  
Yanzhi Hu ◽  
Xiao Li ◽  
Zhaobin Zhang ◽  
Jianming He ◽  
Guanfang Li
Keyword(s):  
Hydraulic Fracturing ◽  
Hydraulic Fracture ◽  
Fracture Network ◽  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Fracture Networks ◽  
Proposed Model ◽  
Discontinuous Deformation ◽  
Shale Reservoirs ◽  
Dda Method

Hydraulic fracturing is one of the most important technologies for shale gas production. Complex hydraulic fracture networks can be stimulated in shale reservoirs due to the existence of numerous natural fractures. The prediction of the complex fracture network remains a difficult and challenging problem. This paper presents a fully coupled hydromechanical model for complex hydraulic fracture network propagation based on the discontinuous deformation analysis (DDA) method. In the proposed model, the fracture propagation and rock mass deformation are simulated under the framework of DDA, and the fluid flow within fractures is simulated using lubrication theory. In particular, the natural fracture network is considered by using the discrete fracture network (DFN) model. The proposed model is widely verified against several analytical and experimental results. All the numerical results show good agreement. Then, this model is applied to field-scale modeling of hydraulic fracturing in naturally fractured shale reservoirs. The simulation results show that the proposed model can capture the evolution process of complex hydraulic fracture networks. This work offers a feasible numerical tool for investigating hydraulic fracturing processes, which may be useful for optimizing the fracturing design of shale gas reservoirs.

A Sensitivity Analysis for Effective Parameters on 2D Fracture-Network Permeability

2009 ◽  
Vol 12 (03) ◽  
pp. 455-469 ◽  
Author(s):  
Alireza Jafari ◽  
Tayfun Babadagli
Keyword(s):  
Sensitivity Analysis ◽  
Experimental Design ◽  
Fractured Reservoirs ◽  
Fracture Network ◽  
Static Model ◽  
Naturally Fractured Reservoirs ◽  
Single Fracture ◽  
Data Sets ◽  
Fracture Networks ◽  
Fractal Characteristics

Summary Fracture-network mapping and estimation of its permeability constitute two major steps in static-model preparation of naturally fractured reservoirs. Although several different analytical methods were proposed in the past for calculating fracture-network permeability (FNP), different approaches are still needed for practical use. We propose a new and practical approach to estimate FNP using statistical and fractal characteristics of fracture networks. We also provide a detailed sensitivity analysis to determine the relative importance of fracture-network parameters on the FNP in comparison to single-fracture conductivity using an experimental-design approach. The FNP is controlled by many different fracture-network parameters such as fracture length, density, orientation, aperture, and single-fracture connectivity. Five different 2D fracture data sets were generated for random and systematic orientations. In each data set, 20 different combinations of fracture density and length for different orientations were tested. For each combination, 10 different realizations were generated. The length was considered as constant and variable. This yielded a total of 1,000 trials. The FNPs were computed through a commercial discrete-fracture-network (DFN) modeling simulator for all cases. Then, we correlated different statistical and fractal characteristics of the networks to the measured FNPs using multivariable-regression analysis. Twelve fractal (sandbox, box counting, and scanline fractal dimensions) and statistical (average length, density, orientation, and connectivity index) parameters were tested against the measured FNP for synthetically generated fracture networks for a wide range of fracture properties. All cases were above the percolation threshold to obtain a percolating network, and the matrix effect was neglected. The correlation obtained through this analysis using four data sets was tested on the fifth one with known permeability for verification. High-quality match was obtained. Finally, we adopted an experimental-design approach to identify the most-critical parameters on the FNP for different fracture-network types. The results are presented as Pareto charts. It is believed that the new method and results presented in this paper will be useful for practitioners in static-model development of naturally fractured reservoirs and will shed light on further studies on modeling and understanding the transmissibility characteristics of fracture networks. It should be emphasized that this study was conducted on 2D fracture networks and could be extended to 3D models. This, however, requires further algorithm development to use 2D fractal characteristics for 3D systems and/or development of fractal measurement techniques for a 3D system. This study will provide a guideline for this type of research.

On the multiscale quantification of fracture network geometry from lineament maps of crystalline basement units

2021 ◽  
Author(s):  
Alberto Ceccato ◽  
Giulia Tartaglia ◽  
Giulio Viola ◽  
Marco Antonellini
Keyword(s):  
Statistical Analysis ◽  
Scaling Laws ◽  
Numerical Models ◽  
Regional Scale ◽  
Fracture Network ◽  
Crystalline Basement ◽  
Fracture Networks ◽  
Spatial Organisation ◽  
Robust Analysis ◽  
Network Properties

<p>Fractured crystalline basement units are attracting increasing attention as potential unconventional reservoirs for natural (oil, heat and water) resources and as potential waste (nuclear, CO<sub>2</sub>) disposal sites. The focus of the current efforts is the characterisation of the structural permeability of fractured crystalline basement units, which is primarily related to the geology, geometry, and spatial characteristics of fracture networks. Fracture network properties may be scale–dependent or independent. Thus, a multi–scale characterisation of fracture networks is usually recommended to quantify the scale–variability of properties and, eventually, the related predictive scaling laws. Fracture lineament maps are schematic representations of fracture distributions obtained from either manual or automated interpretation of 2D digital models of the earth surface at different scales. From the quantitative analysis on fracture lineament maps, we can retrieve invaluable information on the scale–dependence of fracture network properties.</p><p>Here we present the results of the quantification of fracture network and fracture set properties (orientation, length, spacing, spatial organisation) from multi– (outcrop to regional) scale 2D lineament maps of two crystalline basement study areas of Western Norway (Bømlo island and Kråkenes). Lineament maps were obtained from the manual interpretation of orthophotos and 2D digital terrain models retrieved from UAV–drone and LiDAR surveys.</p><p>Analyses aimed at the quantification of: (i) scaling laws for fracture length cumulative distributions, defined through a statistically–robust fitting method (Maximum Likelihood Estimations coupled with Kolmogorov–Smirnov tests); (ii) variability of orientation sets as a function of scale; (iii) spatial organisation of fracture sets among scales; (iv) fractal characteristics of fracture networks (fractal exponent). Results suggest that: (i) a statistical analysis considering variable censoring and truncation effects allows to confidently define the best–fitting scaling laws; (ii) the analysis of orientation variability of fracture sets among different scales may provide important constraints about the geometrical complexity of fracture and fault zones; (iii) the statistical analysis of 2D spacing variability and fracture intensity can be adopted to quantify fracture spatial organisation at different scales.</p><p>A statistically robust analysis of the scaling laws, length distributions, spacing, and spatial organisation of lineaments on 2D maps provides reliable results also where only partial or incomplete dataset/lineament maps are available. Such properties are the fundamental input parameters for conceptual (geologic) and numerical (discrete fracture network, DFN) models of fractured crystalline basement reservoirs. Therefore, a statistically robust analysis of fracture lineament maps may help to improve the accuracy of conceptual and numerical models.</p>

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