62 results found
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
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.
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
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.
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
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.
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.
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.
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, 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.
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.
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.
Paluszny A, Salimzadeh S, Tempone P, et al., 2017, Evaluating natural fracture growth in shale caprocks during cold CO<inf>2</inf> injection at the Heletz pilot site, Pages: 2988-2995
The potential growth of multiple fractures is investigated during the deformation of the caprock of a reservoir during the subsurface sequestration of CO2. Multiple scenarios of the interaction of pre-existing natural fractures are investigated, as a function of induced stress changes due to the temperature contrast between the injected CO2 and the reservoir. Simulations are performed at the field scale, on a simplified geologically-informed model of the Heletz pilot test site, Israel, in the framework of the EU-sponsored TRUST project. The potential reactivation and growth of pre-existing natural fractures is investigated. During cold injection, changes in the strain field around the well are tracked. The progression of the temperature plume is observed to cause a local release of stresses that in turn causes short propagation episodes, which mostly focus on downward growth. Although some upwards growth is modeled, growth is expected to prominently occur towards the reservoir.
Lang PS, Paluszny A, Zimmerman RW, 2016, Evolution of fracture normal stiffness due to pressure dissolution and precipitation, International Journal of Rock Mechanics and Mining Sciences, Vol: 88, Pages: 12-22, ISSN: 1873-4545
The normal stiffness of a fracture is a key parameter that controls, for example, rock mass deformability, the change in hydraulic transmissivity due to stress changes, and the speed and attenuation of seismic waves that travel across the fracture. Non-linearity of normal stiffness as a function of stress is often attributed to plastic yield at discrete contacts. Similar surface-altering mechanisms occur due to pressure solution and precipitation over larger timescales. These processes partition the fracture surfaces into a flattened contact region, and a rough free surface that bounds the void space. Under low loads, contact occurs exclusively over the flattened part, leading to rapid, exponential stiffening. At higher loads, contact occurs over the rough surface fraction, leading to the conventional linear increase of stiffness with stress. It follows that a relationship exists between the history of in situ temperature and stress state of a rock fracture, and its subsequent deformation behavior.
Ebigbo AOD, Lang PS, Paluszny A, et al., 2016, Inclusion-based effective medium models for the permeability of a 3D fractured rock mass, Transport in Porous Media, Vol: 113, Pages: 137-158, ISSN: 1573-1634
Effective permeability is an essential parameter for describing fluid flow through fractured rock masses. This study investigates the ability of classical inclusion-based effective medium models (following the work of Sævik et al. in Transp Porous Media 100(1):115–142, 2013. doi:10.1007/s11242-013-0208-0) to predict this permeability, which depends on several geometric properties of the fractures/networks. This is achieved by comparison of various effective medium models, such as the symmetric and asymmetric self-consistent schemes, the differential scheme, and Maxwell’s method, with the results of explicit numerical simulations of mono- and poly-disperse isotropic fracture networks embedded in a permeable rock matrix. Comparisons are also made with the Hashin–Shtrikman bounds, Snow’s model, and Mourzenko’s heuristic model (Mourzenko et al. in Phys Rev E 84:036–307, 2011. doi:10.1103/PhysRevE.84.036307). This problem is characterised by two small parameters, the aspect ratio of the spheroidal fractures, αα , and the ratio between matrix and fracture permeability, κκ . Two different regimes can be identified, corresponding to α/κ<1α/κ<1 and α/κ>1α/κ>1 . The lower the value of α/κα/κ , the more significant is flow through the matrix. Due to differing flow patterns, the dependence of effective permeability on fracture density differs in the two regimes. When α/κ≫1α/κ≫1 , a distinct percolation threshold is observed, whereas for α/κ≪1α/κ≪1 , the matrix is sufficiently transmissive that such a transition is not observed. The self-consistent effective medium methods show good accuracy for both mono- and polydisperse isotropic fracture networks. Mourzenko’s equation is very accurate, particularly for monodisperse networks. Finally, it is shown that Snow’
Nejati M, Paluszny A, Zimmerman RW, 2016, A finite element framework for modeling internal frictional contact in three-dimensional fractured media using unstructured tetrahedral meshes, Computer Methods in Applied Mechanics and Engineering, Vol: 306, Pages: 123-150, ISSN: 0045-7825
This paper introduces a three-dimensional finite element (FE) formulation to accurately model the linear elastic deformation of fractured media under compressive loading. The presented method applies the classic Augmented Lagrangian(AL)-Uzawa method, to evaluate the growth of multiple interacting and intersecting discrete fractures. The volume and surfaces are discretized by unstructured quadratic triangle-tetrahedral meshes; quarter-point triangles and tetrahedra are placed around fracture tips. Frictional contact between crack faces for high contact precisions is modeled using isoparametric integration point-to-integration point contact discretization, and a gap-based augmentation procedure. Contact forces are updated by interpolating tractions over elements that are adjacent to fracture tips, and have boundaries that are excluded from the contact region. Stress intensity factors are computed numerically using the methods of displacement correlation and disk-shaped domain integral. A novel square-root singular variation of the penalty parameter near the crack front is proposed to accurately model the contact tractions near the crack front. Tractions and compressive stress intensity factors are validated against analytical solutions. Numerical examples of cubes containing one, two, twenty four and seventy interacting and intersecting fractures are presented.
Paluszny A, Tang XH, Nejati M, et al., 2016, A direct fragmentation method with Weibull function distribution of sizes based on finite- and discrete element simulations, International Journal of Solids and Structures, Vol: 80, Pages: 38-51, ISSN: 0020-7683
A direct method is proposed to rapidly fragment bodies during impulse-based discrete element method simulations of multiple body interactions. The approach makes use of patterns and size distributions obtained both from experiments, and from numerical models that rigorously compute fragmentation by growing fractures explicitly. Weibull parameters approximate the fragment size distributions as a function of body size and relative contact velocity. Structured domain decomposition is applied on the colliding bodies directly, resulting in a low-cost fragmentation calculation that depends on relative velocity, but which does not require the computation of fracture growth nor explicit element de-bonding, but instead classifies pre-existing mesh elements into the newly fragmented sub-domains. The method is applied to the fragmentation of a single spherical rock fragment, to an irregularly shaped rock fragment, and to the crushing of an array of spherical rock fragments.
Salimzadeh S, Paluszny A, Zimmerman RW, 2016, Thermal effects during hydraulic fracturing in low-permeability brittle rocks, Pages: 45-50
A three-dimensional finite-element model for hydraulic fracturing has been developed that accounts for local thermal non-equilibrium between the injected fluid and host rock. The model also accounts for fluid flow and heat transfer within the fracture, heat conduction through the solid rock, deformation of the rock, and propagation of the fracture. Fluid flow through the fractures is modeled using the lubrication equation, and is fully coupled to the thermoelastic mechanical model through the pressure exerted by the fluid on the fracture walls, as well as by ensuring compatibility of fracture volumetric strains. Fractures are discretely modeled using triangular surfaces in an unstructured three-dimensional mesh. The growth of fractures is modeled using linear elastic fracture mechanics (LEFM), with the onset and direction of growth based on stress intensity factors that are computed for unstructured triangle-tetrahedral meshes. The model has been verified against analytical solutions available in the literature for penny-shaped (3D) fractures. A radial hydraulic fracture from a horizontal well is simulated to investigate the effects of the thermal non-equilibrium between the fracturing fluid and the host rock. For the case of very low matrix rock permeability, results show very little influence of thermal effects on the creation of hydraulic fractures.
Defoort T, Paluszny A, Zimmerman RW, 2016, Comparison of fracture mechanics and damage mechanics approaches to simulate three-point bending and double-notch shear experiments on rock samples, Pages: 1265-1271
Three-point-bending and double-notch shear experiments are modeled using a continuum damage mechanics approach, and an explicit fracture mechanics approach, for both homogeneous and heterogeneous rocks. The local damage approach uses the Mazars isotropic damage model. In the explicit fracture simulations, fractures are represented as explicit surfaces within a three-dimensional unstructured mesh comprised of isoparametric quadratic tetrahedra and quarter point tetrahedra. Heterogeneities in strength, stiffness and toughness are introduced in a random manner within ±50% of the average values. A characteristic length is used to define the size of element clusters having uniform properties. Both approaches are used to evaluate the influence of material heterogeneity on crack propagation and interaction. Both models reproduce well the experimental results for homogeneous rocks. While in the damage model the mesh is fixed and refined globally, the discrete approach only requires refinement around the fracture tips. In the three-point-bending and double-notch shear simulations, the damage mechanics approach is more realistic in that it leads to rougher crack surfaces. However, the fracture mechanics model predicts lower curvature of the fracture, which better corresponds to experimental observations. Both approaches predict that the presence of heterogeneities seems to diminish fracture interaction.
Nejati M, Paluszny A, Zimmerman RW, 2015, A disk-shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes, International Journal of Solids and Structures, Vol: 69-70, Pages: 230-251, ISSN: 0020-7683
A novel domain integral approach is introduced for the accurate computation of pointwise J-integral and stress intensity factors (SIFs) of 3D planar cracks using tetrahedral elements. This method is efficient and easy to implement, and does not require a structured mesh around the crack front. The method relies on the construction of virtual disk-shaped integral domains at points along the crack front, and the computation of domain integrals using a series of virtual triangular and line elements. The accuracy of the numerical results computed for through-the-thickness, penny-shaped, and elliptical crack configurations has been validated by using the available analytical formulations. The average error of computed SIFs remains below 1% for fine meshes, and 2–3% for coarse ones. The results of an extensive parametric study suggest that there exists an optimum mesh-dependent domain radius at which the computed SIFs are the most accurate. Furthermore, the results provide evidence that tetrahedral elements are efficient, reliable and robust instruments for accurate linear elastic fracture mechanics calculations.
Alyafei N, Raeini AQ, Paluszny Rodriguez A, et al., 2015, A Sensitivity Study of the Effect of Image Resolution on Predicted Petrophysical Properties, TRANSPORT IN POROUS MEDIA, ISSN: 0169-3913
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