70 results found
Bird R, Paluszny A, Thomas RN, et al., 2023, Modelling of fracture intensity increase due to interacting blast waves in three-dimensional granitic rocks, International Journal of Rock Mechanics and Mining Sciences, Vol: 162, Pages: 1-15, ISSN: 0020-7624
The complexity of the physics of rock blasting is a longstanding modelling challenge. This work presents in detail a three-dimensional, material non-linear finite element based model for wave propagation, combined with a postprocessing procedure to determine the fracture intensity caused by blasting. The rock is described with the Johnson–Holmquist-2 constitutive model, an elastoplastic-damage model designed for brittle materials undergoing high strain rates and high pressures and fracturing; it is also combined with an instantaneous tensile failure model. Additionally, material heterogeneity is introduced into the model through variation of the material properties at the element level, ensuring jumps in strain. A detailed algorithm for the combined Johnson–Holmquist-2 and tensile failure model is presented and is demonstrated to be energy-conserving, and is complemented with an open-source MATLABTM implementation of the model. A range of sub-scale numerical experiments are performed to validate the modelling and postprocessing procedures, and a range of materials, explosive waves and geometries are considered to demonstrate the model’s predictive capability quantitatively and qualitatively for fracture intensity. Fracture intensities on 2D planes and 3D volumes are presented. The mesh dependence of the method is explored, demonstrating that mesh density changes maintain similar results and improve with increasing mesh quality. Damage patterns in simulations are self-organising, and form thin, planar, fracture-like structures that closely match the observed fractures in the experiments. The presented model is an advancement in realism for continuum modelling of blasts as it enables fully three-dimensional wave interaction, handles damage due to both compression and tension, and relies only on measurable material properties.
Saceanu MC, Paluszny A, Zimmerman RW, et al., 2022, Fracture growth leading to mechanical spalling around deposition boreholes of an underground nuclear waste repository, International Journal of Rock Mechanics and Mining Sciences, Vol: 152, ISSN: 0020-7624
This study presents a three-dimensional numerical analysis of multiple fracture growth leading to spalling around nuclear waste deposition boreholes. Mechanical spalling due to stress amplification after drilling is simulated using a finite element-based fracture growth simulator. Fractures initiate in tension based on a damage criterion and grow by evaluating stress intensity factors at each fracture tip. Tip propagation is multi-modal, resulting in final fracture patterns that are representative of both tensile and shear failure. Their geometries are represented by smooth parametric surfaces, which evolve during growth using lofting. The corresponding surface and volumetric meshes are updated at every growth step to accommodate the evolving fracture geometries. The numerical model is validated by comparing simulated fracture patterns against those observed in the AECL Underground Rock Laboratory Mine-By Experiment. It is subsequently calibrated to simulate fracture initiation and growth around boreholes drilled in the Forsmark granodiorite, subjected to a far-field anisotropic triaxial stress that corresponds to the in situ stress model from the Swedish Forsmark site. The deposition tunnel is implicitly simulated by attaching the deposition borehole to a free domain boundary.Several geomechanical cases are investigated, in which fracture growth is numerically evaluated as a function of in situ stress state, tunnel orientation, borehole geometry, total number of boreholes and borehole spacing. Numerical results show that spalling occurs in all cases, given the underground conditions at Forsmark, with borehole geometry, spacing and stresses affecting the extent of fracture nucleation and growth patterns.The uncertainty in underground stress conditions is evaluated through varying stress magnitudes and orientations relative to the tunnel floor. Whereas tunnel orientation influences the relative locations where fractures initiate with respect to the tunnel floor, frac
Iglauer S, Akhondzadeh H, Abid H, et al., 2022, Hydrogen Flooding of a Coal Core: Effect on Coal Swelling, GEOPHYSICAL RESEARCH LETTERS, Vol: 49, ISSN: 0094-8276
- Author Web Link
- Citations: 12
Thomas RN, Bird RE, Paluszny A, et al., 2022, Numerical Study of Three-dimensional Blast-induced Damage Patterns resulting from Simultaneous Borehole Blasting of Hard Rocks
Simultaneous detonation of charges in closely spaced boreholes is a commonly used blasting technique for fragmentation and construction. Blasting is a challenging phenomenon to model, due to the complexity of the mechanical deformation, fracturing, and fragmentation, and the spatial scales involved. Blast wave models must consider the possibility of constructive interference between separate waves in three-dimensions. A three-dimensional finite element method is used to study the induced damage in a general hard rock tunnel blast setting. The Johnson Holmquist-2 elastoplastic-damage model is used to quantify shear and tensile failure. In simulations with two blastholes separated by up to one meter, damage patterns emanating from boreholes interact to form self-organizing 'fracture-like' structures. Mechanical interaction between the two blasts is a function of the input charge wave properties, blasthole separation, and distance along the charge, with high concentrations of damage at the free boundary representing the tunnel wall. Constructive interference between the two blast waves is not shown to directly induce additional damage zones, and instead, interaction results from the overlap and slight extension of each blasthole's damage zone towards the other.
Zhang Y, Xu J, Tang X, et al., 2022, Determining the mechanical property of Martian rocks using accurate grain-based model
In the future, the extraterrestrial human activities, such as resources exploitation and base construction on Mars needs the aid of geotechnical engineering technology. Currently, there are only two approaches to obtain the Martian rock samples: sample-return activities by spacecraft and the collection of meteorites. However, meteorites are rare, expensive, arbitrarily sized and shaped, so it is difficult to process them into standard rock samples required by the traditional macroscale rock mechanics experiments (macro-RME). In the present work, the mechanical property of small-sized Martian meteorites was obtained by Accurate Grain-Based Modelling (AGBM) based on the microscale rock mechanics experiments (micro-RME). Firstly, the mineral composition and microstructure of NWA12564 Martian meteorites are achieved by the TESCAN Integrated Mineral Analyzer (TIMA). Secondly, the micromechanical properties of rock-forming minerals in meteorites was measured using nanoindentation tests. Thirdly, with the combination of micro-RME results and AGBM, the macroscale mechanical property of Martian rocks was able to be achieved using small and any-shaped meteorites. The present methodology is potential useful to estimate the mechanical property of Martian rocks using only arbitrarily shaped samples.
Burtonshaw JEJ, Paluszny A, Thomas RN, et al., 2022, The influence of hydraulic fluid properties on induced seismicity during underground hydrogen storage
Geological hydrogen storage is a promising technique to seasonally store surplus renewable energy at the large scale. Depleted gas reservoirs are currently being considered as potential storage sites for hydrogen. Induced seismicity is a key aspect of the sustainability and acceptance of both onshore and offshore gas storage and production. This study conducts a preliminary numerical assessesment of the deformation of a single three-dimensional fault that extends from the reservoir and into the caprock during the injection and storage of hydrogen over a period of weeks. Simulations are conducted with a three-dimensional finite element, fully coupled poroelastic code. Induced seismicity is quantified both in terms of tangential displacements on the fault surfaces, cumulative moment release, and maximum seismic event magnitudes. The reservoir is an anticlinal structure bound from above by a low permeability caprock, and below from a low permeability underburden. Mechanical properties are defined based on North Sea depleted gas reservoirs. The effect of injection fluid parameters such as density and viscosity are investigated. For hydrogen storage in depleted oil and gas reservoirs with proximate faults, some minor seismicity can be expected. According to these preliminary simulations, geological hydrogen storage appears to be operationally sustainable in terms of the magnitude of induced seismicity, at least for the injection volumes, rates and storage periods considered in this work. For the studied case, the maximal potential seismicity observed is of moment magnitude 2.1, with very few seismic events.
Burtonshaw J, Thomas R, Paluszny A, et al., 2021, Effect of Viscosity and Injection Rate on the Tensile and Shear Deformation Experienced By Interacting Hydraulic and Natural Fractures, 55th U.S. Rock Mechanics/Geomechanics Symposium - American Rock Mechanics Association (ARMA)
Bird RE, Paluszny A, Zimmerman RW, 2021, Application of the Displacement Discontinuity Model to a finite pulse wave impinging on a fracture
For a harmonic wave of single frequency impinging on a fracture, the Pyrak-Nolte displacement discontinuity model (DDM) can be used to determine the reflection and transmission coefficients of the resultant harmonic waves. However, it is often the case in the field that a wave impinging on a fracture will be a pulse of finite duration which contains a spectrum of frequencies. Here, for a P-wave impinging a fracture at normal incidence, the DDM is extended to consider arbitrarily shaped pulse waves using the discrete Fourier Transform. The method presented calculates two resultant spectra for the transmitted and reflected wave as well as their corresponding energy coefficients. The impinging pulse wave is made dimensionless with respect to a defined "characteristic"frequency; this allows for a dimensionless comparison to the energy response of a single frequency harmonic wave using the Pyrak-Nolte curves. The results show that the total reflected energy of a finite-pulse incoming wave will be lower than that of a harmonic wave having the same characteristic frequency.
Paluszny A, Thomas RN, Saceanu MC, et al., 2020, Hydro-mechanical interaction effects and channelling in three-dimensional fracture networks undergoing growth and nucleation, JOURNAL OF ROCK MECHANICS AND GEOTECHNICAL ENGINEERING, Vol: 12, Pages: 707-719, ISSN: 1674-7755
The flow properties of geomechanically generated discrete fracture networks are examined in the context of channelling. Fracture networks are generated by growing fractures in tension, modelling the low permeability rock as a linear elastic material. Fractures are modelled as discrete surfaces which grow quasi-statically within a three-dimensional (3D) volume. Fractures may have their locations specified as a simulation input, or be generated as a function of damage, quantified using the local variation in equivalent strain. The properties of the grown networks are shown to be a product of in situ stress, relative orientation of initial flaws, and competitive process of fracture interaction and growth. Fractures grow preferentially in the direction perpendicular to the direction of maximum tension and may deviate from this path due to mechanical fracture interaction. Flow is significantly channelled through a subset of the fractures in the full domain, consistent with observations of other real and simulated fractures. As the fracture networks grow, small changes in the geometry of the fractures lead to large changes in the locations and scale of primary flow channels. The flow variability and formation of channels are examined for two growing networks, one with a fixed amount of fractures, and another with nucleating fractures. The interaction between fractures is shown to modify the local stress field, and in turn the aperture of the fractures. Pathways for single-phase flow are the results of hydro-mechanical effects in fracture networks during growth. These are the results of changes to the topology of the network as well as the result of mechanical self-organisation which occurs during interaction leading to growth and intersection.
Paluszny Rodriguez A, Graham CC, Daniels K, et al., 2020, Caprock integrity and public perception studies of carbon storage in depleted hydrocarbon reservoirs, International Journal of Greenhouse Gas Control, Vol: 98, ISSN: 1750-5836
Capture and subsurface storage of CO2 is widely viewed as being a necessary component of any strategy to minimise and control the continued increase in average global temperatures. Existing oil and gas reservoirs can be re-used for carbon storage, providing a substantial fraction of the vast amounts of subsurface storage space that will be required for the implementation of carbon storage at an industrial scale. Carbon capture and storage (CCS) in depleted reservoirs aims to ensure subsurface containment, both to satisfy safety considerations, and to provide confidence that the containment will continue over the necessary timescales. Other technical issues that need to be addressed include the risk of unintended subsurface events, such as induced seismicity. Minimisation of these risks is key to building confidence in CCS technology, both in relation to financing/liability, and the development and maintenance of public acceptance. These factors may be of particular importance with regard to CCS projects involving depleted hydrocarbon reservoirs, where the mechanical effects of production activities must also be considered. Given the importance of caprock behaviour in this context, several previously published geomechanical caprock studies of depleted hydrocarbon reservoirs are identified and reviewed, comprising experimental and numerical studies of fourteen CCS pilot sites in depleted hydrocarbon reservoirs, in seven countries (Algeria, Australia, Finland, France, Germany, Netherlands, Norway, UK). Particular emphasis is placed on the amount and types of data collected, the mathematical methods and codes used to conduct geomechanical analysis, and the relationship between geomechanical aspects and public perception. Sound geomechanical assessment, acting to help minimise operational and financial/liability risks, and the careful recognition of the impact of public perception are two key factors that can contribute to the development of a successful CCS project in a
Saceanu MC, Paluszny A, Zimmerman RW, et al., 2020, Numerical modelling of spalling around a nuclear waste storage deposition borehole using a fracture mechanics approach, 54th U.S. Rock Mechanics/Geomechanics Symposium
Fracture growth leading to mechanical spalling around a deposition borehole for disused nuclear fuel waste is modelled numerically. Simulations are conducted using a finite-element-based discrete fracture growth simulator, which computes deformation in the system based on the mechanical properties of the rock. Fractures are grown by computing stress intensity factors at each fracture tip, and the mesh is re-generated to accommodate the changing fracture geometries at every growth step. Several numerical models are created to explore the effect of boundary conditions on the initiation and development of spalling fractures at Forsmark, where the Swedish repository for nuclear waste is planned to be constructed. It is shown that the reported uncertainty in the principal stress magnitudes and orientations will affect the predicted fracture nucleation and growth patterns, and implicitly the final repository design. The potential effect of spalling on the structural integrity of the deposition borehole is illustrated for each stress scenario.
Thomas RN, Paluszny A, Zimmerman RW, 2020, Permeability of three‐dimensional numerically grown geomechanical discrete fracture networks with evolving geometry and mechanical apertures, Journal of Geophysical Research: Solid Earth, Vol: 125, ISSN: 2169-9313
Fracture networks significantly alter the mechanical and hydraulic properties of subsurface rocks. The mechanics of fracture propagation and interaction control network development. However, mechanical processes are not routinely incorporated into discrete fracture network (DFN) models. A finite element, linear elastic fracture mechanics‐based method is applied to the generation of three‐dimensional geomechanical discrete fracture networks (GDFNs). These networks grow quasi‐statically from a set of initial flaws in response to a remote uniaxial tensile stress. Fracture growth is handled using a stress intensity factor‐based approach, where extension is determined by the local variations in the three stress intensity factor modes along fracture tips. Mechanical interaction between fractures modifies growth patterns, resulting in nonuniform and nonplanar growth in dense networks. When fractures are close, stress concentration results in the reactivation of fractures that were initially inactive. Therefore, GDFNs provide realistic representations of subsurface networks that honor the physical process of concurrent fracture growth. Hydraulic properties of the grown networks are quantified by computing their equivalent permeability tensors at each growth step. Compared to two sets of stochastic DFNs, GDFNs with uniform fracture apertures are strongly anisotropic and have relatively higher permeabilities at high fracture intensities. In GDFN models, where fracture apertures are based on mechanical principles, fluid flow becomes strongly channeled along distinct flow paths. Fracture orientations and interactions significantly modify apertures, and in turn, the hydraulic properties of the network. GDFNs provide a new way of understanding subsurface networks, where fracture mechanics is the primary influence on their geometric and hydraulic properties.
Thomas R, Paluszny A, Zimmerman RW, 2020, Growth of three-dimensional fractures, arrays, and networks in brittle rocks under tension and compression, Computers and Geotechnics, Vol: 121, ISSN: 0266-352X
Concurrent growth of multiple fractures in brittle rock is a complex process due to mechanical interaction effects. Fractures can amplify or shield stress on other fracture tips, and stress field perturbations change continuously during fracture growth. A three-dimensional, finite-element based, quasi-static growth algorithm is validated for mixed mode fracture growth in linear elastic media, and is used to investigate concurrent fracture growth in arrays and networks. Growth is governed by fracture tip stress intensity factors, which quantify the energy contributing to fracture extension, and are validated against analytical solutions for fractures under compression and tension, demonstrating that growth is accurate even in coarsely meshed domains. Isolated fracture geometries are compared to wing cracks grown in experiments on brittle media. A novel formulation of a Paris-type extension criterion is introduced to handle concurrent fracture growth. Fracture and volume-based growth rate exponents are shown to modify fracture interaction patterns. A geomechanical discrete fracture network is generated and examined during its growth, whose properties are the direct result of the imposed anisotropic stress field and mutual fracture interaction. Two-dimensional cut-plane views of the network demonstrate how fractures would appear in outcrops, and show the variability in fracture traces arising during interaction and growth.
Iglauer S, Paluszny A, Rahman T, et al., 2019, Residual Trapping of CO2 in an Oil-Filled, Oil-Wet Sandstone Core: Results of Three-Phase Pore-Scale Imaging, GEOPHYSICAL RESEARCH LETTERS, Vol: 46, Pages: 11146-11154, ISSN: 0094-8276
- Author Web Link
- Citations: 3
Almulhim OA, Paluszny A, Thomas RN, et al., 2019, Fully-coupled three-dimensional finite element simulations of the interaction between a hydraulic fracture and a pre-existing natural fracture
Copyright 2019 ARMA, American Rock Mechanics Association. The effects of approach angle and matrix poroelasticity on three-dimensional fracture interactions are investigated by examining changes in stress intensity factors around hydraulic fracture tips. Additionally, the effect of the compressive stress induced by the hydraulic fracture (the “stress shadow effect”) on the natural fracture is explored. Fracture interaction is captured using three-dimensional interaction maps based on two interaction measures that quantify the magnitude and type of interaction. The results show that the stress conditions at the hydraulic fracture tip are more favorable for growth when interacting fractures have shallow approach angles, and the interaction reduces as the approach angle increases. For “high” permeability reservoirs, fluid leak-off causes the rock matrix to dilate, and generates a tensile stress that amplifies the local stress field. The increase in stress in the region ahead of the hydraulic fracture (the stress amplification zone) can cause natural fractures to open in tension before the hydraulic fracture intersects the natural fracture. The increase in matrix permeability causes earlier activation of natural fractures due to the additional stress induced by the dilated rock matrix.
Almulhim OA, Paluszny A, Thomas RN, et al., 2019, Fully-coupled three-dimensional finite element simulations of the interaction between a hydraulic fracture and a pre-existing natural fracture
The effects of approach angle and matrix poroelasticity on three-dimensional fracture interactions are investigated by examining changes in stress intensity factors around hydraulic fracture tips. Additionally, the effect of the compressive stress induced by the hydraulic fracture (the “stress shadow effect”) on the natural fracture is explored. Fracture interaction is captured using three-dimensional interaction maps based on two interaction measures that quantify the magnitude and type of interaction. The results show that the stress conditions at the hydraulic fracture tip are more favorable for growth when interacting fractures have shallow approach angles, and the interaction reduces as the approach angle increases. For “high” permeability reservoirs, fluid leak-off causes the rock matrix to dilate, and generates a tensile stress that amplifies the local stress field. The increase in stress in the region ahead of the hydraulic fracture (the stress amplification zone) can cause natural fractures to open in tension before the hydraulic fracture intersects the natural fracture. The increase in matrix permeability causes earlier activation of natural fractures due to the additional stress induced by the dilated rock matrix.
Lang P, Paluszny Rodriguez A, Morteza N, et al., 2018, Relationship between the orientation of maximum permeability and intermediate principal stress in fractured rocks, Water Resources Research, Vol: 54, Pages: 8734-8755, ISSN: 0043-1397
Flow and transport properties of fractured rock masses are a function of geometrical structures across many scales. These structures result from physical processes and states and are highly anisotropic in nature. Fracture surfaces often tend to be shifted with respect to each other, which is generally a result of stress‐induced displacements. This shift controls the fracture's transmissivity through the pore space that forms from the created mismatch between the surfaces. This transmissivity is anisotropic and greater in the direction perpendicular to the displacement. A contact mechanics‐based, first‐principle numerical approach is developed to investigate the effects that this shear‐induced transmissivity anisotropy has on the overall permeability of a fractured rock mass. Deformation of the rock and contact between fracture surfaces is computed in three dimensions at two scales. At the rock mass scale, fractures are treated as planar discontinuities along which displacements and tractions are resolved. Contact between the individual rough fracture surfaces is solved for each fracture at the small scale to find the stiffness and transmissivity that result from shear‐induced dilation and elastic compression. Results show that, given isotropic fracture networks, the direction of maximum permeability of a fractured rock mass tends to be aligned with the direction of the intermediate principal stress. This reflects the fact that fractures have the most pronounced slip in the plane of the maximum and minimum principal stresses, and for individual fractures transmissivity is most pronounced in the direction perpendicular to this slip.
Thomas RN, Paluszny A, Hambley D, et al., 2018, Permeability of observed three dimensional fracture networks in spent fuel pins, Journal of Nuclear Materials, Vol: 510, Pages: 613-622, ISSN: 0022-3115
The three-dimensional fracture network within a spent fuel pin is characterised using sequential grinding, and its permeability is numerically estimated. Advanced Gas-cooled Reactors (AGRs) produce spent fuel pins consisting of an outer steel cladding enclosing ceramic uranium dioxide (UO2) pellets. During irradiation, fuel pellets may undergo fracturing due to thermal, densification and swelling effects. Fracture patterns are usually observed on the surface of the pellet or through a cross section or longitudinal plane along the pellet. In this work, the three-dimensional fracture pattern within the pellet is characterised using an optical microscope. The pellet is progressively ground and polished, providing sequential cross sections, which together yield a three-dimensional discrete fracture pattern. Multiple large fractures grow to connect the cladding to the internal region of the pellet. Multiple surface fractures are observed that do not penetrate into the matrix of the pellet. The porosity of the UO2 and apertures of the fractures are estimated by sampling microscopic images. Darcy flow is numerically solved using the finite element method, computing flow through the matrix and fractures simultaneously. The equivalent tensorial permeability of the system is estimated for various approximate fracture apertures. The fracture network raises the permeability of the pellet by an order of magnitude.
Salimzadeh S, Paluszny Rodriguez A, Zimmerman RW, 2018, Effect of cold CO2 injection on fracture apertures and growth, International Journal of Greenhouse Gas Control, Vol: 74, Pages: 130-141, ISSN: 1750-5836
The injection of cold CO2 is modelled in three dimensions using a two-stage coupled thermoporoelastic model, with the aim of evaluating changes in apertures and potential growth of fractures. Non-isothermal flow is considered within the fractures and the rock matrix, and the two flow domains are coupled through a mass transfer term. The numerical model has been developed using standard finite elements, with spatial discretisation achieved using the Galerkin method, and temporal discretisation using finite differences. A full-scale field case geometric model, based on the Goldeneye depleted hydrocarbon reservoir in the North Sea, is developed and used for simulations. The in situ faults are modelled discretely as discontinuous surfaces in a three-dimensional matrix, including basement, reservoir, caprock and overburden layers. The faults are assumed initially to be low-permeable faults, with the same permeability as the caprock. However, the simulations show that their apertures (and as a result, their permeabilities) vary due to the thermoporoelastic effects caused by the injection of the relatively cold CO2. The change in the fracture apertures is mainly due to thermal effects; the reservoir layer undergoes contractions due to the cooling, significantly increasing fault aperture in the region of the fault within the reservoir, whereas the fault aperture is reduced in regions within the caprock. Propagation of fractures under thermoporoelastic loading is investigated. Results show that the distance to the injection well, as well as spatial orientation of fractures with respect to the injection well, affect aperture evolution and potential growth of fractures. A sensitivity analysis is performed on the parameters affecting the fracture growth: minimum normal stress acting on the fracture plane, dip angle of the fracture, and the contact friction coefficient. It is found that low friction, low normal contact stress, or high in situ shear stress on the fracture surface
Thomas RN, Paluszny A, Zimmerman RW, 2018, Effect of fracture growth velocity exponent on fluid flow through geomechanically-grown 3d fracture networks, 2nd International Discrete Fracture Network Engineering Conference
Copyright 2018 ARMA. Geomechanical discrete fracture networks (DFNs) are grown using a 3D finite element-based fracture mechanics simulator. The influence of the fracture growth rate exponent (β) on the resulting fracture geometry and hydraulic properties of networks is investigated. Previous work has found that β has a complex relationship with the final geometry of geomechanically-grown 2D DFNs. Realistic features evolve during the growth of DFNs as a result of the orientation of the principal stress axis and fracture interaction. High values of β cause interaction effects to be more pronounced, and irregular shaped fractures to be more common. Low values of β are found to produce networks with a balance between selective growth on preferentially oriented and interacting fractures, and significant increases in fracture surface area with computation time. The permeability of DFNs is significantly influenced by anisotropy, which develops in the axes perpendicular to the principal stress direction. For fracture networks with different β values, permeabilities along the principal axes are similar for the same total fracture void space.
Paluszny A, Thomas RN, Zimmerman RW, 2018, Finite element-based simulation of the growth of dense three-dimensional fracture networks, 52nd US Rock Mechanics / Geomechanics Symposium
Copyright © 2018 ARMA, American Rock Mechanics Association. The growth of fractures within a quasi-brittle rock is computed numerically with the aim of generating high-density geomechanically realistic three-dimensional discrete fracture patterns. Patterns are generated with a finite element-based discrete fracture propagation simulator, in which deformation and flow are numerically computed. These detailed multi-fracture growth simulations study the emergence of patterns as a function of the interaction of fractures and the mechanical effects of pattern evolution on the distribution of apertures in response to in situ stresses.
Salimzadeh S, Paluszny Rodriguez A, Nick HM, et al., 2018, A three-dimensional coupled thermo-hydro-mechanical model for deformable fractured geothermal systems, Geothermics, Vol: 71, Pages: 212-224, ISSN: 0375-6505
A fully coupled thermal-hydraulic-mechanical (THM) finite element model is presented for fractured geothermal reservoirs. Fractures are modelled as surface discontinuities within a three-dimensional matrix. Non-isothermal flow through the rock matrix and fractures are defined and coupled to a mechanical deformation model. A robust contact model is utilised to resolve the contact tractions between opposing fracture surfaces under THM loadings. A numerical model has been developed using the standard Galerkin method. Quadratic tetrahedral and triangular elements are used for spatial discretisation. The model has been validated against several analytical solutions, and applied to study the effects of the deformable fractures on the injection of cold water in fractured geothermal systems.Results show that the creation of flow channelling due to the thermal volumetric contraction of the rock matrix is very likely. The fluid exchanges heat with the rock matrix, which results in cooling down of the matrix, and subsequent volumetric deformation. The cooling down of the rock matrix around a fracture reduces the contact stress on the fracture surfaces, and increases the fracture aperture. Stress redistribution reduces the aperture, as the area with lower contact stress on the fracture expands. Stress redistribution reduces the likelihood of fracture propagation under pure opening mode, while the expansion of the area with lower contact stress may increase the likelihood of shear fracturing.
Paluszny A, Salimzadeh S, Zimmerman RW, 2018, Finite-Element Modeling of the Growth and Interaction of Hydraulic Fractures in Poroelastic Rock Formations, Hydraulic Fracture Modeling, Pages: 1-19, ISBN: 9780128129982
This chapter presents a finite element-based method for simulating the hydraulic fracturing process in porous rocks. The finite-element method is used to compute the mechanical deformation of the rock, and it accounts for the effects of poroelasticity, thermoelasticity, and fluid flow in both the fractures and the rock matrix, in a fully coupled manner. The fractures are represented in the mesh as fully three-dimensional objects, with evolving local apertures that are computed as part of the solution. Fracture growth is modeled using stress intensity factors, and the direction and rate of growth is evaluated individually at each fracture tip node. Specifically, the direction of fracture growth at each tip node is governed by the maximum circumferential stress criterion, and the extent of fracture growth is approximated using a Paris-type growth law. Contact between opposing fracture surfaces is handled using a gap-based augmented Lagrangian approach. Fracture growth is computed independently of the underlying mesh, and the fracture path is not constrained to follow the mesh. Instead, a new mesh is constructed after each time step, if the fracture has grown in that time step. This numerical framework is then applied to the growth of multiple hydraulic fractures in impermeable and permeable formations to investigate the effects of matrix permeability, matrix poroelasticity, and temperature contrast (between the rock and the injected fluid) on the growth and interaction of hydraulic fractures.
Salimzadeh S, Usui T, Paluszny A, et al., 2017, Finite element simulations of interactions between multiple hydraulic fractures in a poroelastic rock, International Journal of Rock Mechanics and Mining Sciences, Vol: 99, Pages: 9-20, ISSN: 0020-7624
A fully coupled three-dimensional finite-element model for hydraulic fracturing in permeable rocks is utilised to investigate the interaction between multiple simultaneous and sequential hydraulic fractures. Fractures are modelled as surface discontinuities within a three-dimensional matrix. This model simultaneously accounts for laminar flow within the fracture, Darcy flow within the rock matrix, poroelastic deformation of the rock, and the propagation of fractures using a linear elastic fracture mechanics framework. The leakoff of fracturing fluid into the surrounding rocks is defined as a function of the pressure gradient at the fracture surface, the fluid viscosity, and the matrix permeability. The coupled equations are solved numerically using the finite element method. Quadratic tetrahedral and triangle elements are used for spatial discretisation of volumes and surfaces, respectively. The model is validated against various analytical solutions for plane-strain and penny-shaped hydraulic fractures. Several cases of simultaneous fracturing of multiple hydraulic fractures are simulated in which the effects of the various parameters (the in situ stresses, the distance between fractures, the permeability of the matrix, the Biot poroelastic coefficient, and the number of the fractures in a group) are investigated. The results show that the stress induced by the opening of the fractures, and the stress induced by the fluid leakoff, each have the effect of locally altering the magnitudes and orientations of the principal stresses, hence altering the propagation direction of the fractures. Opening of a fracture induces excessive compression (also known as the “stress shadow”) that causes adjacent fractures to curve away from each other. This excessive compression competes against the differential in situ stresses, which tend to cause the fracture to grow in the plane normal to the minimum in situ stress. The stress shadow effect is reduced by increasing th
Thomas RN, Paluszny A, Zimmerman RW, 2017, Quantification of fracture interaction using stress intensity factor variation maps, Journal of Geophysical Research. Solid Earth, Vol: 122, Pages: 7698-7717, ISSN: 2169-9356
Accurate and flexible models of fracture interaction are sought after in the fields of mechanics and geology. Stress intensity factors (SIFs) quantify the energy concentrated at the fracture tips and are perturbed from their isolated values when two fractures are close to one another. Using a three-dimensional finite element fracture mechanics code to simulate static fractures in tension and compression, interaction effects are examined. SIF perturbations are characterized by introducing three interaction measures: the circumferential and maximum SIF perturbation provide the “magnitude” of the effect of interaction, and the amplification to shielding ratio quantifies the balance between increased and decreased SIFs along the tip. These measures are used to demonstrate the change in interaction with fracture separation and to find the separation at which interaction becomes negligible. Interaction maps are constructed by plotting the values of the interaction measures for a static fracture as a second fracture is moved around it. These maps are presented for several common fracture orientations in tension. They explore interaction by highlighting regions in which growth is more likely to occur and where fractures will grow into nonplanar geometries. Interaction maps can be applied to fracture networks with multiple discontinuities to analyze the effect of geometric variations on fracture interaction.
Usui T, Salimzadeh S, Paluszny A, et al., 2017, Effect of poroelasticity on hydraulic fracture interactions, Sixth Biot Conference on Poromechanics 2017, Publisher: American Society of Civil Engineers, Pages: 2008-2015
This study investigates, by performing finite element-based simulations, the influence of fluid leak-off and poroelasticity on growth of multiple hydraulic fractures that initiate from a single horizontal well. In this research, poroelastic deformation of the matrix is coupled with fluid flow in the fractures, and fluid flow in the rock matrix, in three dimensions. Effects of the fluid leakoff and poroelasticity on the propagation of the neighboring fractures are studied by varying the matrix permeability, and the Biot coefficient. Simulation results show that the stress induced by the opening of the fractures, and the stress induced by the fluid leak-off, each have the effect of locally altering the magnitudes and orientations of the principal stresses, hence altering the propagation direction of the fractures. The stress induced by the opening of the fractures tends to propagate both of the fractures away from each other in a curved trajectory, whereas the effects of fluid leak-off and poroelasticity (i.e., a higher Biot coefficient) tend to straighten the curved trajectory.
Paluszny A, Zimmerman RW, 2017, Modelling of primary fragmentation in block caving mines using a finite-element based fracture mechanics approach, Geomechanics and Geophysics for Geo-Energy and Geo-Resources, Vol: 3, Pages: 121-130, ISSN: 2363-8419
The growth of fractures around an undercut of a block cave is simulated. A finite element based approach is used, in which fractures are represented as non-planar 3D surfaces that grow in response to boundary stresses and interaction. A new mesh is recreated at each step to compute the displacement field. Stress intensity factors are computed around fracture tips using a technique that computes the interaction integral over a virtual disk. Fracture geometry is updated using Paris and Schöllmann propagation laws, and a geometric fracture pattern ensues from the simulation. The growth of fractures is examined in the lower 20 m of a mine at 812 m depth. The growth of 30, 60 and 90 fractures is examined. Realistic extraction schedules for over 100 draw points control the rate of mass extraction. The effect of rock bridges as overburden stress shields is investigated. Bridges are modelled by constraining the vertical displacement of the top boundary. This case is compared to a Neumann-type overburden stress boundary condition in which the overburden is felt throughout the top of the cave. In both cases, fractures grow to form a dome shape above and around the cave during extraction. For the case of a fixed top boundary, fracture growth is observed away from the cave, while in the direct overburden stress case, fractures tend to grow close to the cave. Over-arching fractures concentric to the undercut continue to grow as the cave progresses.
Salimzadeh S, Paluszny A, Zimmerman RW, 2017, Three-dimensional poroelastic effects during hydraulic fracturing in permeable rocks, International Journal of Solids and Structures, Vol: 108, Pages: 153-163, ISSN: 0020-7683
A fully coupled three-dimensional finite-element model for hydraulic fractures in permeable rocks is presented, and used to investigate the ranges of applicability of the classical analytical solutions that are known to be valid in limiting cases. This model simultaneously accounts for fluid flow within the fracture and rock matrix, poroelastic deformation, propagation of the fractures, and fluid leakage into the rock formation. The model is validated against available asymptotic analytical solutions for penny-shaped fractures, in the viscosity-dominated, toughness-dominated, storage-dominated, and leakoff-dominated regimes. However, for intermediate regimes, these analytical solutions cannot be used to predict the key hydraulic fracturing variables, i.e. injection pressure, fracture aperture, and length. For leakoff-dominated cases in permeable rocks, the asymptotic solutions fail to accurately predict the lower-bound for fracture radius and apertures, and the upper-bound for fracture pressure. This is due to the poroelastic effects in the dilated rock matrix, as well as due to the multi-dimensional flow within matrix, which in many simulation codes is idealised as being one-dimensional, normal to the fracture plane.
Paluszny A, Salimzadeh S, Zimmerman RW, 2017, Finite-Element Modeling of the Growth and Interaction of Hydraulic Fractures in Poroelastic Rock Formations, Hydraulic Fracture Modeling, Pages: 1-19, ISBN: 9780128129999
This chapter presents a finite element–based method for simulating the hydraulic fracturing process in porous rocks. The finite-element method is used to compute the mechanical deformation of the rock, and it accounts for the effects of poroelasticity, thermoelasticity, and fluid flow in both the fractures and the rock matrix, in a fully coupled manner. The fractures are represented in the mesh as fully three-dimensional objects, with evolving local apertures that are computed as part of the solution. Fracture growth is modeled using stress intensity factors, and the direction and rate of growth is evaluated individually at each fracture tip node. Specifically, the direction of fracture growth at each tip node is governed by the maximum circumferential stress criterion, and the extent of fracture growth is approximated using a Paris-type growth law. Contact between opposing fracture surfaces is handled using a gap-based augmented Lagrangian approach. Fracture growth is computed independently of the underlying mesh, and the fracture path is not constrained to follow the mesh. Instead, a new mesh is constructed after each time step, if the fracture has grown in that time step. This numerical framework is then applied to the growth of multiple hydraulic fractures in impermeable and permeable formations to investigate the effects of matrix permeability, matrix poroelasticity, and temperature contrast (between the rock and the injected fluid) on the growth and interaction of hydraulic fractures.
Defoort T, Paluszny A, Zimmerman RW, et al., 2017, Numerical study of the contact between a chamfered cylindrical PDC cutter and the rock, Pages: 3147-3153
Numerical rock cutting simulations are performed for different cutter configurations. Special attention is given to the contact region between the cutter and the rock. Frictional contact is solved using a Gap Based Augmented Lagrangian approach, in order to minimize the interpenetration error that is present in the less expensive penalty approach, while reducing finite element accumulation time compared to the standard Lagrangian method. Numerical experiments are performed with a single cylindrical cutter of radius 16 mm, a back rake of 15°, a depth of cut of 4 mm, and two different chamfers: a 0.3 mm chamfer at 15°, and a 0.5 mm chamfer at 45°. The number of Uzawa iterations required for the interpenetration error to have minimal impact on cutting forces is estimated, and the accuracy of the penalty approach is emphasized. Contact tractions are shown, suggesting areas where the mesh should be refined. A suitable mesh size is given for both chamfer geometries. The influence of the friction coefficient on cutting forces is evaluated, suggesting a cutter configuration insensitive to the value of the friction coefficient within a realistic range.
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