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

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.

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Hybrid Analytical and Numerical Approach for Modeling Fluid Flow in Simplified Three-Dimensional Fracture Networks

Geofluids ◽

10.1155/2020/3583817 ◽

2020 ◽

Vol 2020 ◽

pp. 1-14

Author(s):

D. Roubinet ◽

S. Demirel ◽

E. B. Voytek ◽

X. Wang ◽

J. Irving

Keyword(s):

Fluid Flow ◽

Three Dimensional ◽

Fracture Network ◽

Numerical Approach ◽

Fracture Networks ◽

Surrounding Matrix ◽

Mesh Free ◽

Fracture Scale ◽

The Impact ◽

Numerical Approaches

Modeling fluid flow in three-dimensional fracture networks is required in a wide variety of applications related to fractured rocks. Numerical approaches developed for this purpose rely on either simplified representations of the physics of the considered problem using mesh-free methods at the fracture scale or complex meshing of the studied systems resulting in considerable computational costs. Here, we derive an alternative approach that does not rely on a full meshing of the fracture network yet maintains an accurate representation of the modeled physical processes. This is done by considering simplified fracture networks in which the fractures are represented as rectangles that are divided into rectangular subfractures such that the fracture intersections are defined on the borders of these subfractures. Two-dimensional analytical solutions for the Darcy-scale flow problem are utilized at the subfracture scale and coupled at the fracture-network scale through discretization nodes located on the subfracture borders. We investigate the impact of parameters related to the location and number of the discretization nodes on the results obtained, and we compare our results with those calculated using reference solutions, which are an analytical solution for simple configurations and a standard finite-element modeling approach for complex configurations. This work represents a first step towards the development of 3D hybrid analytical and numerical approaches where the impact of the surrounding matrix will be eventually considered.

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Modelling large-scale fractured reservoirs efficiently for geothermal energy and groundwater flow

10.5194/egusphere-egu2020-9278 ◽

2020 ◽

Author(s):

Simon Oldfield ◽

Mikael Lüthje ◽

Michael Welch ◽

Florian Smit

Keyword(s):

Fluid Flow ◽

Geothermal Energy ◽

Large Scale ◽

Fractured Reservoirs ◽

Fracture Network ◽

Natural Fracture ◽

Fracture Networks ◽

Persistent Problem ◽

Fracture Evolution ◽

Rapid Generation

Large scale modelling of fractured reservoirs is a persistent problem in representing fluid flow in the subsurface. Considering a geothermal energy prospect beneath the Drenthe Aa area, we demonstrate application of a recently developed approach to efficiently predict fracture network geometry across an area of several square kilometres.Using a strain based method to mechanically model fracture nucleation and propagation, we generate a discretely modelled fracture network consisting of individual failure planes, opening parallel and perpendicular to the orientation of maximum and minimum strain. Fracture orientation, length and interactions vary following expected trends, forming a connected fracture network featuring population statistics and size distributions comparable to outcrop examples.Modelled fracture networks appear visually similar to natural fracture networks with spatial variation in fracture clustering and the dominance of major and minor fracture trends.Using a network topology approach, we demonstrate that the predicted fracture network shares greater geometric similarity with natural networks. Considering fluid flow through the model, we demonstrate that hydraulic conductivity and flow anisotropy are strongly dependent on the geometric connection of fracture sets.Modelling fracture evolution mechanically allows improved representation of geometric aspects of fracture networks to which fluid flow is particularly sensitive. This method enables rapid generation of discretely modelled fractures over large areas and extraction of suitable summary statistics for reservoir simulation. Visual similarity of the output models improves our ability to compare between our model and natural analogues to consider model validation.

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Properties of a pair of fracture networks produced by triaxial deformation experiments: insights on fluid flow using discrete fracture network models

Hydrogeology Journal ◽

10.1007/s10040-016-1468-x ◽

2016 ◽

Vol 25 (3) ◽

pp. 813-827 ◽

Cited By ~ 2

Author(s):

Ghislain Trullenque ◽

Rishi Parashar ◽

Clément Delcourt ◽

Lucille Collet ◽

Pauline Villard ◽

...

Keyword(s):

Fluid Flow ◽

Network Models ◽

Fracture Network ◽

Discrete Fracture Network ◽

Fracture Networks ◽

Triaxial Deformation ◽

Discrete Fracture

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An alternative method to evaluate fracture network efficiency to fluid flow

10.5194/egusphere-egu2020-4799 ◽

2020 ◽

Author(s):

Giampaolo Proietti ◽

Valentina Romano ◽

Alessia Conti ◽

Maria Chiara Tartarello ◽

Sabina Bigi

Keyword(s):

Fluid Flow ◽

Numerical Models ◽

Computational Cost ◽

Fracture Network ◽

Fractured Reservoir ◽

Fracture Networks ◽

Alternative Method ◽

Main Challenge ◽

Hydraulic Behaviour ◽

Wide Range

Fracture networks exist at a wide range of scale in the earth crust and strongly influence the hydraulic behaviour of rocks, providing either pathways or barriers for fluid flow. Many oil, gas, geothermal and water supply reservoirs form in fractured rocks. The main challenge is the development of numerical models that describe adequately the fracture networks and the constitutive equations governing the physical processes in fractured reservoir. The hydraulic properties of fracture networks, derived from Discrete Fracture Network (DFN), models are commonly used to populate continuum equivalent models at reservoir scale, to reduce the computational cost and the numerical complexity. However, the efficiency of fracture networks to fluid flow is strongly tied to their connectivity and spatial distribution, that continuum models are not able to capture explicitly.In this work we used field data and synthetic models to introduce a new parameter to evaluate the efficiency of fracture networks to fluid flow, reflecting a range of variability in fracture network characteristics (e.g. P32, number of fractures, stress field). This alternative method allows to model fractured systems at reservoir scale, in a variety of geological settings, using exclusively a DFN approach.

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

Solid Earth ◽

10.5194/se-12-2159-2021 ◽

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.

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

10.5194/se-2021-45 ◽

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.

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Modeling Coupled Fracture-Matrix Fluid Flow in Geomechanically Simulated Fracture Networks

SPE Reservoir Evaluation & Engineering ◽

10.2118/77340-pa ◽

2005 ◽

Vol 8 (04) ◽

pp. 300-309 ◽

Cited By ~ 67

Author(s):

Zeno G. Philip ◽

James W. Jennings ◽

Jon E. Olson ◽

Stephen E. Laubach ◽

Jon Holder

Keyword(s):

Fluid Flow ◽

Finite Difference ◽

Flow Simulation ◽

Fracture Network ◽

Fracture Aperture ◽

Grid Cells ◽

Fracture Networks ◽

Fracture Permeability ◽

Fracture Length ◽

Fracture Patterns

Summary In conventional reservoir simulations, gridblock permeabilities are frequently assigned values larger than those observed in core measurements to obtain reasonable history matches. Even then, accuracy with regard to some aspects of the performance such as water or gas cuts, breakthrough times, and sweep efficiencies may be inadequate. In some cases, this could be caused by the presence of substantial flow through natural fractures unaccounted for in the simulation. In this paper, we present a numerical investigation into the effects of coupled fracture-matrix fluid flow on equivalent permeability. A fracture-mechanics-based crack-growth simulator, rather than a purely stochastic method, was used to generate fracture networks with realistic clustering, spacing, and fracture lengths dependent on Young's modulus, the subcritical crack index, the bed thickness, and the tectonic strain. Coupled fracture-matrix fluid-flow simulations of the resulting fracture patterns were performed with a finite-difference simulator to obtain equivalent permeabilities that can be used in a coarse-scale flow simulation. The effects of diagenetic cements completely filling smaller aperture fractures and partially filling larger aperture fractures were also studied. Fractures were represented in finite-difference simulations both explicitly as grid cells and implicitly using nonneighbor connections (NNCs) between grid cells. The results indicate that even though fracture permeability is highly sensitive to fracture aperture, the computed equivalent permeabilities are more sensitive to fracture patterns and connectivity. Introduction High-permeability fracture networks in a matrix system can create high-conductivity channels for the flow of fluids through a reservoir, producing larger flow rates and, therefore, larger apparent permeabilities. The presence of fractures can also cause early breakthrough of the displacing fluid and lead to poorer sweep efficiencies in displacement processes. A better understanding of reservoir performance in such cases may be obtained by including the details of the fluid flow in fractures in a coupled fracture-matrix reservoir flow model. It is very difficult to directly measure interwell fracture-network geometry in sufficient detail to model its effect on reservoir behavior. Thus, most modeling approaches have been statistical, using data from outcrop and wellbore observations to determine distributions of fracture attributes such as fracture length, spacing, and aperture to randomly populate a field. In this paper, we use a mechanistic approach to generate the fracture patterns. Attributes of the fracture network depend on the applied boundary conditions and material properties.

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Investigating the effects of intersection flow localization in equivalent-continuum-based upscaling of flow in discrete fracture networks

Solid Earth ◽

10.5194/se-12-2235-2021 ◽

2021 ◽

Vol 12 (10) ◽

pp. 2235-2254

Author(s):

Maximilian O. Kottwitz ◽

Anton A. Popov ◽

Steffen Abe ◽

Boris J. P. Kaus

Keyword(s):

Fluid Flow ◽

Cell Size ◽

Fracture Network ◽

Fracture Networks ◽

Flow Localization ◽

Computational Costs ◽

Pipe Model ◽

Hydraulic Aperture ◽

Discrete Fracture ◽

Equivalent Continuum

Abstract. Predicting effective permeabilities of fractured rock masses is a crucial component of reservoir modeling. Its often realized with the discrete fracture network (DFN) method, whereby single-phase incompressible fluid flow is modeled in discrete representations of individual fractures in a network. Depending on the overall number of fractures, this can result in high computational costs. Equivalent continuum models (ECMs) provide an alternative approach by subdividing the fracture network into a grid of continuous medium cells, over which hydraulic properties are averaged for fluid flow simulations. While continuum methods have the advantage of lower computational costs and the possibility of including matrix properties, choosing the right cell size to discretize the fracture network into an ECM is crucial to provide accurate flow results and conserve anisotropic flow properties. Whereas several techniques exist to map a fracture network onto a grid of continuum cells, the complexity related to flow in fracture intersections is often ignored. Here, numerical simulations of Stokes flow in simple fracture intersections are utilized to analyze their effect on permeability. It is demonstrated that intersection lineaments oriented parallel to the principal direction of flow increase permeability in a process we term intersection flow localization (IFL). We propose a new method to generate ECMs that includes this effect with a directional pipe flow parameterization: the fracture-and-pipe model. Our approach is compared against an ECM method that does not take IFL into account by performing ECM-based upscaling with a massively parallelized Darcy flow solver capable of representing permeability anisotropy for individual grid cells. While IFL results in an increase in permeability at the local scale of the ECM cell (fracture scale), its effects on network-scale flow are minor. We investigated the effects of IFL for test cases with orthogonal fracture formations for various scales, fracture lengths, hydraulic apertures, and fracture densities. Only for global fracture porosities above 30 % does IFL start to increase the systems permeability. For lower fracture densities, the effects of IFL are smeared out in the upscaling process. However, we noticed a strong dependency of ECM-based upscaling on its grid resolution. Resolution tests suggests that, as long as the cell size is smaller than the minimal fracture length and larger than the maximal hydraulic aperture of the considered fracture network, the resulting effective permeabilities and anisotropies are resolution-independent. Within that range, ECMs are applicable to upscale flow in fracture networks.

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Equivalent continuum-based upscaling of flow in discrete fracture networks: The fracture-and-pipe model

10.5194/se-2020-208 ◽

2021 ◽

Author(s):

Maximilian O. Kottwitz ◽

Anton A. Popov ◽

Steffen Abe ◽

Boris J. P. Kaus

Keyword(s):

Fluid Flow ◽

Numerical Simulations ◽

Fractured Rock ◽

Fracture Network ◽

Fracture Networks ◽

Computational Costs ◽

Pipe Model ◽

Discrete Fracture ◽

Fractured Rock Masses ◽

Equivalent Continuum

Abstract. Predicting effective permeabilities of fractured rock masses is a key component of reservoir modelling. This is often realized with the discrete fracture network (DFN) method, where single-phase incompressible fluid flow is modelled in discrete representations of individual fractures in a network. Depending on the overall number of fractures, this can result in significant computational costs. Equivalent continuum models (ECM) provide an alternative approach by subdividing the fracture network into a grid of continuous medium cells, over which hydraulic properties are averaged for fluid flow simulations. While this has the advantage of lower computational costs and the possibility to include matrix properties, choosing the right cell size for discretizing the fracture network into an ECM is crucial to provide accurate flow results and conserve anisotropic flow properties. Whereas several techniques exist to map a fracture network onto a grid of continuum cells, the complexity related to flow in fracture intersections is often ignored. Here, numerical simulations of Stokes-flow in simple fracture intersections are utilized to analyze their effect on permeability. It is demonstrated that intersection lineaments oriented parallel to the principal direction of flow increase permeability in a process termed intersection flow localization (IFL). We propose a new method to generate ECM's that includes this effect with a directional pipe flow parametrization: the fracture-and-pipe model. Our approach is tested by conducting resolution tests with a massively parallelized Darcy-flow solver, capable of representing the full permeability anisotropy for individual grid cells. The results suggest that as long as the cell size is smaller than the minimal fracture length and larger than the maximal hydraulic aperture of the considered fracture network, the resulting effective permeabilities and anisotropies are resolution-independent. Within that range, ECM's are applicable to upscale flow in fracture networks, which reduces computational expenses for numerical permeability predictions of fractured rock masses. Furthermore, incorporating the off-diagonal terms of the individual permeability tensors into numerical simulations results in an improved representation of anisotropy in ECM's that was previously reserved for the DFN method.

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