The mechanics of fluid-driven fracture propagation through fracture networks is of central interest in gas and oil extraction procedures. A number of computational strategies have now been developed to simulate these processes although specific understanding of the propagation mechanics in the vicinity of pre-existing discontinuities or faults is still limited. This paper investigates the problem of formulating appropriate fluid branching logic at multiple flow path junctions and the influence of sudden contractions or expansions in the flow path channel width at discontinuity intersections. A plane strain model is assumed. A question of additional interest is the possible existence of a “fluid lag” region between the flow front and the mobilized fracture front. The paper explores some examples of flow propagation and branching through simple joint networks.
In recent years, the development of oil and gas from shale has proceeded quickly in the world due to the application of multi-stage fracturing technology in horizontal wells. It is imperative to study the poroelastic characteristics of the rock for modeling the performance of rock under in-situ conditions, thus ensuring the success of hydraulic fracturing. Biot's coefficient is one of the key poroelastic parameters for calculating the effective stress for creating artificial fractures in the shale formations. In this study, we propose anew method to measure the Biot's coefficient. Our method simplified the measuring procedures to obtain the Biot's coefficient by controlling the confining pressure, which isused to maintain the volume of the sample, while altering the pore pressure. Shales amples recovered form Bakken formation in Willistion Basin is tested using this method. The results of our experiments show that the Biot's coefficient of Bakken samples obtained from horizontal drilling and vertical drilling are significantly different from each other. This significant difference of Biot's coefficient with different drilling-direction provides scientists and engineers a solid base for in-situ stress analysis during multi stage hydraulic fracturing and reservoir depletion due to production.
Annavarapu, Chandrasekhar (Lawrence Livermore National Laboratory) | Settgast, Randolph (Lawrence Livermore National Laboratory) | Johnson, Scott (Lawrence Livermore National Laboratory) | Fu, Pengcheng (Lawrence Livermore National Laboratory) | Herbold, Eric B. (Lawrence Livermore National Laboratory)
We propose a stabilized approach based on Nitsche's method for enforcing contact constraints over crack surfaces. The proposed method addresses the shortcomings of conventional penalty and augmented Lagrange multiplier approaches by combining their attractive features. Similar to an augmented Lagrange multiplier approach, the proposed method has a consistent variational basis resulting in stronger enforcement of the non-interpenetration constraint. At the same time, the proposed method is purely displacement-based and alleviates the stability challenges common to mixed methods. The method also retains the computational efficiency of penalty approaches by eliminating the outer augmentation loop necessary for augmented Lagrangian approaches and resulting in smaller system matrices.
Pradhan, S. (SINTEF Petroleum Research) | Stroisz, A.M. (SINTEF Petroleum Research) | Fjæ, E. (SINTEF Petroleum Research) | Stenebråten, J. (SINTEF Petroleum Research) | Lund, H.K. (SINTEF Petroleum Research) | Sønstebø, E.F. (SINTEF Petroleum Research) | Roy, S. (The Institute of Mathematical Science)
Fracturing in reservoir rocks is an important issue for the petroleum industry - as productivity can be enhanced by a controlled fracturing operation. Fracturing also has a big impact on CO2 storage, geothermal installation and gas production at and from the reservoir rocks. Therefore, understanding the fracturing behavior of different types of reservoir rocks is a basic need for planning field operations towards these activities. In our study, the fracturing of rock sample is monitored by Acoustic Emission (AE) and post-experiment Computer Tomography (CT) scans. The fracturing experiments have been performed on hollow cylinder cores of different rocks - sandstones and chalks. Our analyses show that the amplitudes and energies of acoustic events clearly indicate initiation and propagation of the main fractures. The amplitudes of AE events follow an exponential distribution while the energies follow a power law distribution. Time-evolution of the radial strain measured in the fracturing-test will later be compared to model predictions of fracture size.
Murphy, M.M. (National Institute for Occupational Safety and Health (NIOSH)) | Esterhuizen, G.S. (National Institute for Occupational Safety and Health (NIOSH)) | Tulu, I.B. (National Institute for Occupational Safety and Health (NIOSH))
Fully grouted roof bolts increase the stability of a bedded mine roof by providing resistance to both vertical and horizontal displacements. The bolts provide suspension reinforcement from axial loads and lateral reinforcement from shear resistance effects. The lateral reinforcement provided by a roof bolt is difficult to observe in the field, but is often suggested by observation of roof failure cavities. However, these observations do not indicate whether bolt shear failure precedes or is a result of collapse. This paper highlights the use of a well-calibrated FLAC3D numerical model to investigate the shear resistance provided by a fully grouted bolt. The study first looks at analytical solutions to determine the necessary element size to obtain appropriate deflections of thin beams within FLAC3D. The study then compares different models demonstrating that the shear resistance provided by a fully grouted bolt has a limited impact on the overall stability of the mine roof. The model results indicate that the axial suspension effects of fully grouted bolts are more significant than the lateral reinforcement provided.
Strain localization in the form of compactive shear bands or compaction bands is often observed in high porosity rocks such as sandstones or limestones. In the present study, we theoretically investigate the possibility of strain localization in a high-porosity carbonate rock (calcarenite) by means of a continuum mechanics approach. A critical state elasto-plastic constitutive model has been employed for this purpose. We examine the constitutive and structural response by solving boundary value problems (BVPs) for calcarenite specimens subjected to axisymmetric loading conditions. In order to perform the numerical simulation in the post localization regime, the model is enhanced with a rate dependent regularization scheme. The results demonstrate that material heterogeneity, kinematic constraints and boundary effects govern the formation of various modes of localized deformation in the transitional regime between brittle fracture and ductile faulting. Indeed, the predicted macroscopic response is found to be in good agreement with observations available in the literature.
Underground storage is currently being considered by numerous countries as a long term solution for the disposal of high level nuclear waste. Research and design within each national program is generally tailored to a specific rock type, such as stable granitic plutons, bedded salt formations, clay, and sedimentary rocks ranging from limestone to shale. One important technical aspect of these designs is the accommodation of the mechanical impacts of thermal inputs (heating) from the fuel as it goes through the remainder of its life cycle. The results of experiments completed in a variety of different geological settings, including FEBEX by ENRESA in Grimsel, Switzerland, the Drift Scale Test (DST) at Yucca Mountain, the Äspö Pillar Stability Experiment (ASPE) from the Hard Rock Laboratory (HRL) in Sweden, and the Mine-By Experiment (MBE) by Atomic Energy Canada Limited’s (AECL) Underground Research Laboratory (URL), are analysed and compared to examine how thermal loading and the modelling process varies between different rock types.
Experimental study of a two cutters PDC bit-rock interaction shows that increase in the confining pressure reduces ROP through two mechanisms. The negative influences of confining pressure on the bit performance in addition to the rock strengthening under elevated borehole pressure (BHP), is the accumulation of crushed cuttings material in between the face of bit cutters and rock surface in the zone of penetration. The flow of crushed cuttings material on the surface of the PDC cutter causes additional confinement of the rock surface in the zone of the penetration due to friction.
On the other hand, utilizing a bit with an appropriate jet flow significantly improves ROP. In order to maximize the positive effect of bottom hole cleaning on ROP, the jet velocity has been raised to achieve cavitation condition by reducing the pressure with a high flow velocity ahead of the nozzles. However, the experimental results indicate that there are optimal conditions for applying a high velocity jet flow ahead of the bit, which yields maximum ROP when the cutters penetrate the rock mainly under the chamfer. After the effective cuttings removal condition, further increase in jet velocity no longer assists the bit to penetrate the rock faster.
In this study we will show how fractographic (i.e., fracture surface morphology) data of exfoliation fractures (i.e., fractures subparallel to landscape surfaces limited to near-surface rock masses) and three-dimensional numerical modeling can be used to infer orientations of principal rock mass stresses in topographically complex Alpine areas. Analysis of exfoliation fracture plumose axes, i.e., fractographic features that indicate main fracture propagation directions, and supposed local maximum compressive principal stress (σ1) orientations at the time of fracture formation, suggests complex directional trends of near-surface σ1 within trough valleys of the Grimsel region (central Swiss Alps). We investigated near-surface stress tensors with a threedimensional, elastic numerical model to 1. deduce evidence that plumose axes form parallel to σ1 in an overall compressive (farfield) stress field, and to 2. increase our knowledge of near-surface stress orientations in Alpine settings. Model results illustrate that superposition of topographic stresses with realistic horizontal strains reveals complex near-surface s1 trajectories that widely follow the patterns of plumose axes. The model results demonstrate large variations of stress orientations, which cannot be captured by small numbers of classical stress measurements. In-situ stress measurements support exfoliation fracture formation under compression and principal stress directions as inferred from our numerical model.
In tensile and low confinement conditions, the tensile strength plays a critical role in crack initiation and propagation. Being able to accurately determine the intact tensile strength as well as develop an appropriate failure criterion across the tensile and compressive (shear failure) regions, are critical components of any rock mechanics project. This paper presents a summary of both indirect and direct testing approaches to determine the intact tensile strength. A review of the reliability of each method as well as calibration factors to refine the estimates provided by indirect testing methods is presented. In order to more accurately capture the behaviour of the intact rock in the tensile region, a modified Hoek-Brown criterion consisting of a tension cutoff is introduced. Such an approach utilizes the Griffith theory of brittle failure and the generalized equation by Fairhurst to define the tensile strength, and can easily be incorporated with current curve fitting methods. Finally, a method for determining the tension cutoff for data sets without reliable tensile data is provided for preliminary assessment purposes.