Numerous Fractures Research Articles

Modeling the Effect of Intersected Fractures on Oil Production Rate of Fractured Reservoirs by Embedded Fracture Continuum Approach

The homogenization of matrix and short fractures is one of the conventional approaches to deal with a plenty of fractures in different scales. However, the accuracy of this approach is still a question when long fractures and short fractures are distributed in the homogenized model. This paper describes a new hybrid method in which the long fractures will be modeled explicitly by the embedded fracture continuum approach and short fractures are considered through the homogenized technique. The author used this hybrid method to demonstrate the effect of fractures which are intersected to the well on the oil production rate as well as the elapsed time of a fractured reservoir in a depletion process. The advantages of the new hybrid method are easy assembling of numerous fractures into the model and incorporation of the complex fracture behaviour into the model.

Stability of femoral neck fracture fixation: A finite element analysis

Femoral neck fractures represent a relatively uncommon injury in the non-elderly population often resulting from high-energy trauma. Clinical outcome in these patients can be improved by optimizing surgical procedures and selecting appropriate fixation methods. The aim of this study was to develop a numerical fracture model to investigate the influence of critical mechanical factors on the stability of fixation methods for femoral neck fractures. The mechanical stability of fracture fixation was assessed through employing finite element models and simulating progressive consolidation of the fracture for a vertical femoral neck fracture (i.e. Pauwels type III in which the angle between the fracture line and the horizontal plane is greater than 70°). Mechanical performance was compared among three different fixation methods (cannulated screws, dynamic hip screw with de-rotational screw, and proximal femoral locking plate). Axial femoral head displacement varied from 2.3 mm for cannulated screws to 1.12 mm for proximal femoral locking plate, although dynamic hip screw with de-rotational screw indicated a value of 0.94 mm. Considering a consolidated fracture and full weight-bearing load case, average displacements of fracture fragments were obtained of about 1.5, 3 and 70 µm for dynamic hip screw with de-rotational screw, proximal femoral locking plate and cannulated screws methods, respectively. In terms of interfragmentary movements at the fracture site, outcomes of this study demonstrated that, in agreement with our previous experimental research, the dynamic hip screw with de-rotational screw implant is a more effective choice than cannulated screws and proximal femoral locking plate techniques for vertical femoral neck fractures in young patients. Thus, one may conclude that the use of dynamic hip screw with de-rotational screw, particularly during the early stages of bone healing, could provide suitable mechanical environments that facilitate direct bone formation and shorter healing times.

Analysis for effects of complex fracture network geometries on heat extraction efficiency of a multilateral-well enhanced geothermal system

The reservoir stimulation is important for the enhanced geothermal system (EGS), because it creates an effective fracture network to provide heat extraction channels for the working fluid to acquire commercial heat flow. Investigating heat extraction efficiencies of different fracture network geometries can provide suggestions for the EGS fracturing. This paper uses a 3D thermal-hydraulic-mechanical coupling model to study heat extraction efficiencies of 8 different fracture network geometries for a novel multilateral-well EGS. The effects of primary fracture stage quantity and position on the multilateral-well EGS efficiency are investigated. Contributions of primary and secondary fractures to the heat extraction of a multilateral-well EGS are compared. Heat extraction characteristics of a multilateral-well EGS with orthogonally intersecting fractures and bifurcated fractures are analyzed. Results indicate that the primary fracture stage quantity and fracturing position have significant effects on the multilateral-well EGS efficiency. A larger distance between the first stage fracture and lateral-well intersection is beneficial for the multilateral-well EGS efficiency. A multilateral-well EGS with bifurcated fractures has higher efficiency than orthogonal fractures. The fracturing operation of the multilateral-well EGS should focus on creating long secondary fractures to connect reservoir far from lateral wells rather than generating numerous fractures near lateral wells. Results provide significant suggestions for the fracturing operation of a multilateral-well EGS.

Versatile numerical fractures removal for SPH-based free surface liquids

Numerical fractures severely impact the visual effects of SPH based free-surface liquid simulation, leading to surface tension artifact, particles clumping near the free-surface and thin features rupture in the free-surface. To tackle this issue, we first introduce a fast and accurate geometrical method to detect the free-surface particles and compute their normals for precise surface tension computation, avoiding surface-tension-like artifacts. Furthermore, we define a level-set function for each particle configuration and correct the miscalculated density induced by numerical fractures at free surface and solid boundary. In addition, we integrate our method into the PCISPH solver, which makes the SPH particles distributed more homogeneously, thereby improving the stability of the numerical simulation. We evaluate our method on a variety of benchmark examples, and experimental results show the proposed method can robustly, efficiently and realistically simulate the SPH-based free surface liquids.

Numerical study on heat extraction performance of a multilateral-well enhanced geothermal system considering complex hydraulic and natural fractures

The complex fracture network is necessary to provide flow and heat transfer channels for working fluid of an enhanced geothermal system (EGS). It is significant to compare heat extraction performances of different complex fracture networks and to provide suggestions for fracturing operation of an EGS. Based on a 3D thermal-hydraulic-mechanical coupled model, this paper studies heat extraction performances of 11 different complex fracture networks with natural and hydraulic fractures for a multilateral-well EGS. Effects of natural and non-planar fractures on multilateral-well EGS performance are investigated. Influences of primary fracture stage quantity on multilateral-well EGS performance are studied. Contributions of primary and secondary fractures to heat extraction of multilateral-well EGS are compared. Results indicate that natural fractures should be considered when accurately estimating multilateral-well EGS performance. The model with planar fracture networks overestimates production temperature and thermal power of multilateral-well EGS. It is suggested that 3 stages of primary fractures are beneficial for multilateral-well EGS performance. Fracturing operation of multilateral-well EGS should focus on generating long fractures to connect natural fractures far from lateral wells rather than inducing numerous fractures around lateral wells. Simulation results provide significant suggestions for the fracturing operation of multilateral-well EGS.

Dynamic coupling of analytical linear flow solution and numerical fracture model for simulating early-time flowback of fractured tight oil wells (planar fracture and complex fracture network)

Abstract Quantitative analysis of flowback data provides an early opportunity to interpret hydraulic fracture properties of fractured wells in unconventional reservoirs. In recent years, a number of studies have been dedicated to the analysis of single-phase flow data prior to hydrocarbon breakthrough and multi-phase flow data after hydrocarbon breakthrough during flowback. This study provides a new model to simulate flowback of fractured tight oil wells with planar fractures or a complex fracture network. In the model, fractures are discretized into a number of segments and the fully numerical method is used to model fracture flow. It is assumed that the pressure interference in the matrix caused by these fracture segments can be accounted using a no-flow boundary condition and that the drainage volumes of fracture segments form isolated regions to allow for linear flow from the matrix to each segment. To model this behavior, matrix flow is simulated using the analytical transient linear flow solution which is dynamically coupled with the fracture flow model by imposing continuity of pressure and flux on the fracture surfaces. The model is simple, but rigorous enough to take into account the important physics of the fracture system, including arbitrary fracture geometries and fracture conductivity distributions. The pressure and saturation gradients of each phase in fractures are accounted for. The ease of model setup and improved computational performance makes it convenient for practical application. The new model is verified with a commercial reservoir simulator. Investigation of the assumption of no-flow boundary condition for the pressure interference in the matrix caused by the fracture segments reveals that the assumption becomes poorer with increasing matrix permeability and decreasing fracture permeability. Flow regime analysis demonstrates that, for planar fractures, water exhibits an early transient linear flow period (first linear flow in the fracture) followed by boundary-dominated flow (first boundary-dominated flow in the fracture) prior to hydrocarbon breakthrough, after which a second transient linear flow in the fracture develops. The final flow period is boundary-dominated flow (second boundary-dominated flow in the fracture), indicating the end time of the flowback period. At this stage, oil will be the dominant phase in the fracture, and will exhibit transient linear flow in the matrix, which is the first flow-regime typically observed during the long-term production period. The case of a complex fracture network exhibits a similar sequence of flow regimes. The second transient linear flow for this case has not been discussed in the literature. The development of this flow period may be caused by the maintenance of fracture pressure, and decrease of water relative permeability due to hydrocarbon contribution from the matrix. A field example from western Canada exhibits the flow regimes noted above and is history-matched successfully using the new model. The results demonstrate the practical application of the new model for deriving reservoir/fracture properties from flowback data and for forecasting.

Dynamics of fracturing saturated porous media and self-organization of rupture

Analytical solutions and a vast majority of numerical ones for fracture propagation in saturated porous media yield smooth behavior while experiments, field observations and a few numerical solutions reveal stepwise crack advancement and pressure oscillations. To explain this fact, we invoke self-organization of rupture observed in fracturing solids, both dry and fully saturated, when two requirements are satisfied: i) the external drive has a much slower timescale than fracture propagation; and ii) the increment of the external load (drive) is applied only when the internal rearrangement of fracture is over. These requirements are needed to obtain clean Self Organized Criticality (SOC) in quasi-static situations. They imply that there should be no restriction on the fracture velocity i.e. algorithmically the fracture advancement rule should always be independent of the crack velocity. Generally, this is not the case when smooth answers are obtained which are often unphysical. Under the above conditions hints of Self Organized Criticality are evident in heterogeneous porous media in quasi-static conditions using a lattice model, showing stepwise advancement of the fracture and pressure oscillations. We extend this model to incorporate inertia forces and show that this behavior still holds. By incorporating the above requirements in numerical fracture advancement algorithms for cohesive fracture in saturated porous continua we also reproduce stepwise advancements and pressure oscillations both in quasi-static and dynamic situations. Since dynamic tests of dry specimens show that the fracture advancement velocity is not constant we replicate such an effect with a model of a debonding beam on elastic foundation. This is the first step before introducing the interaction with a fluid.

Mesh Size Effect on Numerical Fracture Strain of Aluminum Alloy plate A 2024-T3

Mesh Size Effect on Numerical Fracture Strain of Aluminum Alloy plate A 2024-T3

A comprehensive approach for mesoscale discrete element modelling of mechanical and fracture behavior of concrete

This paper describes a comprehensive approach for modelling mechanical and fracture behavior of concrete using discrete element method. Concrete is modelled at mesoscale as three phase material composed of aggregates, mortar and interface. Full aggregate grading curve is considered. A systematic approach has been used in this study to determine DEM micro parameters for each phase of concrete. The goal is to use same micro parameters irrespective of the specimen size and loading condition (tension, compression and bending). In each phase of concrete, local fracture is analyzed and discussed for different loading configurations in order to understand the role of aggregate, interface and matrix cracking. The numerical fracture pattern is compared with acoustic emission tests so as to identify the capacity of DEM to estimate the fracture process zone.

Numerical fracture analysis and model validation for disbonded honeycomb core sandwich composites

Disbond damage propagation in honeycomb core sandwich structures is investigated numerically and experimentally. A fully parametric two-dimensional finite element model of a disbonded honeycomb core sandwich specimen is presented. Energy release rate and mode-mixity were numerically determined using the Crack Surface Displacement Extrapolation (CSDE) method. An advanced method was adopted to obtain the homogenized mechanical properties of the honeycomb core based on the geometry of a single honeycomb cell and the material properties of the cell wall paper. The numerical model was benchmarked against CFRP/Nomex® Single Cantilever Beam (SCB) specimen tests and a closed-form semi-analytical model. The results show a close agreement between analytical, numerical and experimental energy release rate, as well as analytical and numerical mode-mixity. An extensive sensitivity analysis was also carried out and the effects of the geometry and the material properties of the SCB specimen on the energy release rate and mode-mixity have been investigated.

Bergsprungur og byggingar á höfuðborgarsvæðinu

Straddling the boundary between two of the major tectonic plates on Earth, Iceland offers unique conditions for engineering structures that require special attention. Urban areas are rapidly expanding into areas where the bedrock is cut by numerous active fractures and faults. The fissure swarm of the Krísuvík volcanic system runs through the outskirts of Reykjavík and other towns of the metropolitan area. Activity of its fractures mostly occurs during magmatic events along the Reykjanes Peninsula oblique rift on a thousand years timescale. Hazard caused by the fractures is mostly twofold: Relative displacement of the walls of the fracture during magmatic intrusion and small relative displacements during the passage of seismic waves from distant earthquakes may damage structures built across them. The risk of structural damage may most likely be reduced considerably by avoiding building structures across the fractures. We suggest a change in building practice in fractures areas to achieve that.

Uncertainty analysis of hydraulic fracture height containment in a layered formation

The prediction of hydraulic fracture height growth is of extreme interest in various engineering practices. To fully understand the dependence of the fracturing height in complex underground geological structures, it is crucial to develop theoretical and numerical hydraulic fracturing models to identify the key variables and their interactions to hydraulic fracture height containment. In this work, we adopt a three-dimensional hydro-mechanical coupling cohesive zone finite element model supported by logging data from a practical engineering project. A novel response surface method with Box–Behnken design is introduced to evaluate the statistical significance of tested variables and to forecast the optimal variable combinations for hydraulic fracture height. The key controlling variables are sorted according to their statistical significance from the analysis of variance, and only the minimum lateral stress ratios in mudstone layer and conglomerate layer are highly statistically significant. The minimum lateral in situ stress contrast is the predominant influence of fracture height containment regarding to their significant negative correlation, while the Young’s modulus contrast is probably not an important parameter in terms of direct control of fracture height. Upon optimization, 41 optimized variable combinations were achieved and could be served as references in regulating this engineering practice or even similar events.

A new SPH-based continuum framework with an embedded fracture process zone for modelling rock fracture

A new computational approach combining the Smooth Particle Hydrodynamics and a constitutive model that possesses an intrinsic length scale is proposed in this study for modelling rock fracture. In particular, a continuum-based size-dependent constitutive model with an embedded fracture process zone described by a cohesive model is adopted for modelling strain localisation in geomaterials. A length scale is introduced into the constitutive equations to describe the scale effect commonly observed in localised failure of geomaterials. The constitutive model is then employed in a mesh-free Taylor Smooth Particle Hydrodynamics (Taylor-SPH) framework to produce a new computational tool for rock fracture modelling. The key feature of the proposed numerical framework is that it describes the fracture geometry by a set of Lagrangian particles, which carry fracture information such as damage evolution and fracture orientation, thus bypassing the need to represent the fracture's topology and fracture orientation. To test the capability of this computational framework in simulating rock fracture behaviour, three mode-I numerical fracture tests including three-point bending test, Brazilian-disc test and semi-circular bending test are carried out and results validated with experimental data in the literature. The good agreement between numerical and experimental results suggests that the proposed method is a promising numerical approach to modelling rock fracture.

A Practical Methodology for Production-Data Analysis of Single-Phase Unconventional Wells With Complex Fracture Geometry

Summary Forecasting coalbed-methane well performance in the Qinshui Basin is a key task for predicting future gas production. There is evidence suggesting that complex fracture geometry and multiple hydraulic-fracture networks might develop. Unfortunately, very limited work has been published on the production analysis of multiple-fractured vertical wells (MFVWs) in coalbed-methane reservoirs. To better understand the production performance of the MFVWs, a new, fast, and reliable methodology is presented in this paper. This semianalytical methodology is derived from an analytical reservoir solution and a numerical fracture solution. Dual-porosity, gas-diffusion, gas-adsorption, and stress-sensitivity effects are considered. Verification of the methodology is accomplished through comparison with synthetic-reservoir-simulation cases and with field-performance data. Good agreement is shown between results from the proposed methodology and those from a reservoir-simulation model. Results from this study indicate increasing transient-gas-production rate and cumulative gas recovery with increasing natural-fracture permeability, gas-storage coefficient, Langmuir volume, fracture conductivity, and fracture length. The transient gas-production rate and cumulative gas recovery were found to decrease with increasing stress-sensitivity coefficient. The parameters found to have the strongest and weakest effects on the gas-production rate were the natural-fracture permeability and the fracture conductivity, respectively. Results from this study on MFVWs in coalbed-methane reservoirs indicate fracture length is more important than fracture conductivity in terms of its effect on gas productivity.

On the tensile resistance of UHPC at impact

Ultra-High Performance Concrete (UHPC) is a new class of concrete which shows high strength and durability. In this paper experimental investigations on the dynamic properties of a low-silica UHPC are presented. By means of Hopkinson Pressure Bar experiments the dynamic elastic modulus and the tensile resistance of the material are determined. Additional numerical fracture simulations, based on a cohesive finite element technique, confirm the measured data and illustrate the possibilities to obtain predictive simulations.

Oncogenic Osteomalacia: The Search, Treatment, and Cure of a Debilitating Tumor

Objective: To present a rare case of oncogenic osteomalacia, describe the breadth of potential clinical symptoms, and review the underlying pathophysiology of this disorder. Methods: We report a case of oncogenic osteomalacia cured by surgical resection of a mesenchymal tumor. Results: A 48-year-old, wheelchair-dependent man presented to a tertiary care academic hospital with progressive back pain and diffuse weakness. Biochemical evaluation revealed elevated alkaline phosphatase, marked hypophosphatemia, phosphaturia, vitamin D deficiency, and elevated fibroblast growth factor 23, results that are concerning for oncogenic osteomalacia. Subsequent imaging showed extensive loss of vertebral height, numerous fractures, and ultimately identified an area suspicious for tumor in the right mandible, with concurrent uptake on octreotide scan. Segmental resection of the right mandible revealed a calcifying mesenchymal tumor. Following surgery there was a normalization of biochemistries and dramatic improvement in...

A new explanation on causes of fractures in the ancient City Wall, Nanjing: observation, measurement, and modeling

The ancient City Wall of Nanjing (CWN) has suffered various damages since it was built more than 600 years ago. Numerous fractures and dislocations can be found on the wall. Furthermore, deterioration or destruction on several segments of the wall often occurred soon after restoration work was done, and brings some threats again and again on the people who either walk or live near the wall. The characteristics of these damages and their causes are unclear. In this paper the major fractures and dislocations on CWN were investigated through a field survey. It was observed that the apertures and dislocations of the CWN are usually large near the ground surface and decrease upwards and the most active fractures are located in the segments of the wall along a fault in NWW direction (290°). Twelve joint meters were installed across those fractures and the changes of the fractures’ aperture were measured monthly from April, 2010 to December, 2011. The measured data show that the fractures’ apertures are changing with time significantly, and the maximum cumulative change of apertures is 2.3 mm during 20 months. 80 bases were installed for the GPS measurement on top of the wall, and each site was measured monthly for the same time period as the joint meter measurements, the position of the wall moves significantly with time and the range of the displacement is ± 15.00 mm with the largest value of 20.00 mm. Based on the field survey and measurement, it is hypothesized that the changes of the fractures’ aperture of the wall were caused by the non-uniform crustal movement. A three-dimensional mechanical modeling was built to test the hypothesis and the results confirmed the field observation. The findings from this study are significant and important to protect ancient walls and other human-made structures since the crustal movement may have never been considered before.

NetworkGT: A GIS tool for geometric and topological analysis of two-dimensional fracture networks

Fractures rarely occur individually but more usually as networks of numerous fractures whose arrangement, abundance, and interaction control the mechanical and transport properties of rock masses. Of particular importance are the distributions and spatial variations of different geometric (locations, orientation, length, etc.) and topological (intersections, connectivity, etc.) attributes of fractures in a network. Geographical Information Systems (GIS) provide a means to map and digitize two-dimensional fracture networks from a variety of field and remote sensing data and to display the results in the form of quality maps. We introduce NetworkGT, an open-source toolbox for ArcGIS capable of efficient sampling, analysis, and spatial mapping of geometric and topological attributes of two-dimensional fracture networks. The toolbox helps to extract and plot geometric and topological information from a given two-dimensional fracture network including: rose diagrams, plots of frequency distribution and topology, and maps of topological parameters. Using a fracture network example from offshore NW Devon, United Kingdom, we illustrate the practicality and effectiveness of the toolbox. This includes computing a contour grid with 1326 subsampled regions within the fracture network, which is used to demonstrate the quantitative capabilities of the toolbox and the ability to spatially map important network properties. The toolbox will help to facilitate the increasing application of geometry and topology in the analysis and comparison of fracture networks at a range of scales. Furthermore, the integration of the NetworkGT toolbox into ArcGIS allows two-dimensional fracture networks to be interpreted, mapped, and fully analyzed within the same software package.

Numerical simulation of two-dimensional problems of creep crack growth with material damage consideration

Approach for numerical simulation of the process of the creep crack growth taking into account the hidden material damage is proposed. The approach is based on the application of finite element creep modeling, accompanied by damage. For calculations, the FEM Creep software package is used. Using the proposed algorithm for rebuilding the grid with the removal of the destroyed elements, the current picture of deformation and fracture is analyzed. This takes into account the growing level of damage during the crack motion in each element. Numerical fracture simulation data are used to determine the constants in the differential creep fracture propagation equation. As an example, the creep fracture of planar specimens with sharp notches in their plane is considered. The material of the specimens is a high-temperature nickel-based alloy EI 867 at a temperature of 950 °C. Calculations are carried out for different values of the load. For different times, finite element grids with remote elements are shown. Graphs of the dependence of crack length on time are built. Comparison of numerical and calculated data obtained with the motion equation of a crack shows their acceptable coincidence. The possibility of using the proposed approach for obtaining constants in the equation of crack motion as an alternative to the existing experimental one is discussed.

Analytical and numerical fracture analysis of pressure vessel containing wall crack and reinforcement with CFRP laminates

This paper concentrates on the analytical and numerical calculation of the critical internal load for a pressure vessel containing a longitudinal edge crack or cracks. Initially, the vessel’s capacity is analyzed based on the theoretical fracture methods for seven material properties, different crack lengths, and vessel’s wall thickness. Theses analyses are conducted using an extended finite element method (XFEM) to observe its accuracy and applicability. In problems with complex configuration of crack, it’s difficult to use theoretical method for analyzing the structure. Therefore, after verifying the XFEM with excellent accuracy, several analyses are made for different cases. By employing the XFEM, the effects of having multiple cracks along the vessel’s circumference, crack width along the vessel’s wall, crack location on the internal or external edge of the vessel, and applying the FRP laminates to reinforce the vessel are investigated. Besides, the effect of mode II (sliding mode) on behavior of vessel and the elastic-plastic analysis are analytically studied. Results show that the critical internal pressure for a single cracked and a multiple cracked vessel are the same unless two cracks be very close to each other. Increasing the crack width decreases the critical pressure meaningfully. It is also shown that the vessel is more vulnerable to fail by external crack than an internal crack with similar length and width. Also, the cracked bodies are reinforced with FRP laminates which proves that laminates with higher modulus of elasticity have more effect on the critical internal pressure. Moreover, the elastic-plastic analysis does not have significant influence on critical pressure load due to small plastic zone.