Mosley, Kyle (Wood) | Baxter, Steven (Wood) | Hoek, Jaap (Wood) | Joyce, Steven (Wood) | Williams, Thomas (Wood) | Cottrell, Mark (Golder Associates Ltd.) | Fox, Aaron (Golder Associates Ltd.) | Hartley, Lee (Golder Associates Ltd.) | Aaltonen, Ismo (Posiva Oy) | Koskinen, Lasse (Posiva Oy) | Mattila, Jussi (Posiva Oy) | Suikkanen, Johannes (Posiva Oy) | Vanhanarkaus, Outi (Posiva Oy) | Selroos, Jan-Olof (Svensk Kärnbränslehantering AB (SKB))
Following ratification by the Finnish government in 2001, construction of the world’s first deep geological repository for spent nuclear fuel began in 2004 at Olkiluoto, an island off Finland’s south-west coast. The repository is situated at a depth of 400-450 m in the high-grade metamorphic bedrocks of the Fennoscandian shield, primarily composed of low-permeability Palaeoproterozoic gneisses and granites (Paulamäki et al., 2002). Construction and operation of the repository are fulfilled by Posiva, a nuclear waste management organisation. A key component of Posiva’s upcoming operational licence application is an updated site descriptive model (SDM), characterising the geological, hydrogeological and hydrogeochemical features of the island (Hartley et al., 2018). The updated model builds on several previous iterations of the Olkiluoto SDM (Hartley et al., 2010; Fox et al., 2012; Hartley et al., 2012; Hartley et al., 2017).
A primary objective of the updated SDM is to produce a quantitative description of the properties of naturally-occurring fractures in the bedrock. Groundwater flow through the void space of such fractures represents the principal transport pathway for any arising radionuclides, and is therefore a fundamental consideration for the long-term safety assessment of the repository. Fracture properties are pertinent to a number of geoscience disciplines including geology, rock mechanics, hydrogeology, solute transport and hydrogeochemistry. This work demonstrates how the discrete fracture network (DFN) methodology (e.g. Dershowitz, 1985) provides a conceptual framework in which these various disciplines can be integrated to develop a combined ‘hydrostructural’ model of fracturing, flow and transport processes at Olkiluoto.
MoFrac discrete fracture network (DFN) modeling software generates fracture network simulations with deterministic fractures constrained to known locations, and stochastic fractures conditioned to input data. A deterministic fracture network is generated through the modeling of a dataset that is representative of the lineaments typically found in a Canadian Shield environment. This model is used to constrain stochastic representations to observed fracture intensities and orientations. This study considers two- dimensional and three-dimensional length distributions and area distributions as constraints. Built-in metrics are used to analyze the size and orientation distributions of the stochastic models for comparison with the input data. Further calibration of constraints for these models is achieved by dividing fracture groups into subsets; this preprocessing task involves the definition of subsets of identified fracture groups based on orientation. The consistency and accuracy of the fracture network modeling are considered using three alternative conditioning methods. It was shown that generated fracture networks conform to the conditioning parameters for each method considered. Where multiple subsets were used to define fracture group parameters, resulting DFNs were more representative of the input data.
ABSTRACT: The fracture response of rock, as a quasi-brittle material, is highly sensitive to its microstructural design. We present a statistical damage formulation to model dynamic rock fracture. The damage model is rate-dependent and the corresponding damage evolution is a dynamic equation which introduces a timescale to the problem. The introduced timescale preserves mesh objectivity of the method with much less computational efforts in comparison with other conventional non-local formulations. We define a statistical field for rock cohesion to involve microstructure effects in the proposed formulation. The statistical field is constructed through the Karhunen-Loève (KL) method. The damage model is coupled with the elastodynamic equation. The final system of coupled equations is discretized by an asynchronous Spacetime Discontinuous Galerkin (aSDG) method. Robustness of the proposed formulation is shown though dynamic fracture simulation of rock under uniaxial compressive load. The numerical investigation indicates the importance of load amplitude and microstructure randomness on failure response of rock.
Brittle materials have a significant role in various applications: glasses, ceramics, concrete, bone, etc. These types of materials are susceptible to sudden rupture by cracking as they have many microdefects and microcracks. Before reaching the ultimate load capacity of a material sample, existing microcracks and microdefects propagate at microscale. At ultimate capacity, microscale degradation processes coalescence and cause fracture initiation at macroscale. Macroscale degradation continues under a softening process until the material completely fails.
An important aspect in fracture of rock, and in general quasi-brittle materials, is the effect of microstructure on their fracture response. As shown in  due to the high sensitivity of these materials to their defects, even for the same loading and geometry set-up, different fracture patterns can be observed. Same observations are made in  where high variations on material response, especially beyond elastic range—e.g., ultimate load and fracture energy— were observed due to sample to sample variations. Size effect is another consequence of the high sensitivity of response to microscale defects, as for example demonstrated in [3,4]. In fact, the Weibull's weakest link model [5,6] has proven very effective in capturing the size effect and statistical variation of fracture strength. We have used the Weibull model in the context of an interfacial damage model to capture statistical fracture response of rock, in hydraulic fracturing , fracture under dynamic compressive loading , and in fragmentation studies [9,10]. However, as will be discussed below, these models first can become quite expensive due to the use of a sharp interface model for fracture and second are not derived from a homogenization approach.
Sharp interface (SI) models represent fracture on crack surfaces. Some examples include the linear elastic fracture mechanics (LEFM) model, cohesive models [11,12], and interfacial damage models [13-15]. Each of these models has its own advantages/disadvantages. SI models explicitly track real pattern of fractures, but their implementation is cumbersome and their computational cost is high. Also, in applications such as multiscale methods, it is hard to track explicit discontinuities in all scales of interest. If it is even possible, the computation cost will be extremely high. These facts have lead many efforts to develop fracture models based on continuum mechanics.
Faskhoodi, Majid M. (Schlumberger) | Boskovic, Drazenko (Schlumberger) | Zhmodik, Alexey (Schlumberger) | Qiuguo, Li (Schlumberger) | Michi, Oscar P. (Schlumberger) | Ramanathan, Venkateshwaran (Schlumberger) | Ogunyemi, Taofeek (Schlumberger)
This paper presents a novel approach in statistical analysis of well performance of multistage fractured wells completed in specific part of Montney. For the first time, both geological and hydraulic fracture parameters were considered in analysis with objective of finding most influential parameters that impact deliverability of wells. Results from single point statistical analysis were further extended to unsupervised discrete classification using neural-network to bin the reservoir. Binning classification was then used to design and optimize hydraulic fracture parameters.
Rezaei, A. (University of Houston) | Siddiqui, F. (University of Houston) | Bornia, G. (Texas Tech University) | Soliman, M. Y. (University of Houston) | Rafiee, M. (StatOil) | Morse, S. (Texas Tech University)
ABSTRACT: The Displacement Discontinuity Method (DDM) is one of the most popular numerical methods in simulating hydraulic fracturing problems. Despite its superior advantages in solving fracture modeling problems, this method becomes computationally expensive when the number of degrees of freedom (DOF) increases. An example takes place in the study of two-dimensional fracturing problems with multiple fractures propagating from one or more wells. It would also occur in three-dimensional problems where typically the number of elements exceeds a few thousands. Additionally, including poroelasticity into the problem makes this method even more computationally expensive because of the necessity to build a time-marching procedure. The Fast Multipole Method (FMM) is a computational method to efficiently compute matrix-vector products with a controllable error. Unlike the conventional Boundary Element Method (BEM), in FMM the interaction between far-field sources and influenced points are calculated by initially concentrating a cluster of far-field sources into a separate point, then the effect of these concentrated forces on each influenced point is calculated.
In this study, a novel technique known as black-box fast multipole method (bbFMM) is used to improve the computational efficiency of a poroelastic displacement discontinuity hydraulic fracture model while keeping its accuracy. This method is used to develop an efficient poroelastic hydraulic fracture simulator. Then, the simulator is used to examine the computational effectiveness and the accuracy of the new approach against the conventional displacement discontinuity approach in calculating stresses, displacements and pore pressure. A comparison between efficiency and precision of the developed fast multipole model and the conventional displacement discontinuity model is presented. Several cases of discrete fracture problems with large degrees of freedom are tested. Results show that the new approach reduces the computation time and memory compared to the conventional approach. The applicability of the developed model in hydraulic fracturing problems is also demonstrated. Because of this increase in computational performance, this method can be applied to poroelasticity problems which require such computations at each time step. Unlike the regular method, calculations using the FMM algorithm may be accomplished in a reasonable time.
Fereshtenejad, Sayedalireza (Seoul National University) | Song, Jae-Joon (Seoul National University) | Afshari, Mohammad Karim (Islamic Azad University) | Bafghi, Alireza Yarahmadi (Yazd University) | Laderian, Asghar (Arak University) | Safaei, Homayon (University of Isfahan)
The first step to determine mechanical and hydraulic properties of rock masses is the evaluation of geometrical characterizations of discontinuities. Discrete Fracture Network models have been developed to model the geometrical properties of discontinuities. Among all the discontinuity properties, shape is the most controversial. In previous Discrete Fracture Network models, discontinuities were considered as planar surfaces while in some fields, curve-shaped discontinuities could be observed. Folding is the most common factor in the creation of curve-shaped discontinuities in mines and engineering works. In this research, a practical 3D geometrical method has been introduced to model folded layers using Fourier analysis and Spline function. Based on the proposed method, a practical MATLAB script named RocFold was developed. Finally, to evaluate the applicability and the feasibility of the proposed model and script, a typical folded structure in Anjire lead and zinc mine in Isfahan province, Iran was applied.
Discrete Fracture Network (DFN) models have been developed to model the geometrical properties of discontinuities by statistical values and distributions of these characteristics evaluated from analysis of core logging and outcrops mapping. Different conceptual models are applied to build DFN models, and each of them is based on specific relationships between characteristics such as location of fracture, termination, and fracture shape. The earliest model developed to represent fracture systems was based upon the assumption that all fractures can be defined by three sets of unbounded orthogonal fractures (Dershowitz & Einstein 1988). The basic model defined by Snow (1965) consists of orthogonal sets of parallel-unbounded fractures, with a constant spacing between the fractures within each set. Baecher disk model (disk-shaped discontinuities) has been developed by Baecher et al. (1977) and Barton (1978) simultaneously and was one of the first well-characterized discrete fracture models. The ordinary Baecher model has been further on developed to account for fracture terminations at intersections with pre-existing fractures and for more general fracture shapes (Geier et al. 1989 and Dershowitz et al. 1998). Veneziano (1978) introduced a method for adaptation of the concept of Poisson plane fractures to bounded fractures (Veneziano model). Dershowitz (1984) remedied the disadvantage of the Veneziano model that fracture intersections and fracture edges do not coincide. Other than the mentioned models, some other practical conceptual models have been proposed for the modeling of fracture network, such as geostatistical and fractal models.
This paper provides a brief summary of a continuous research programme by the authors since 2004, and highlights the research approach, achievements and outstanding issues for conceptual understanding, laboratory testing and mathematical modeling of the coupled stress-shear-fluid flow-solute transport processes of rock fractures. The focuses are put on stress and shear induced fluid flow anisotropy, transport pass channeling, and impact of considering different retardation mechanisms in single fractures of crystalline rocks, typically granites, due to its importance for the performance and safety assessments of geological radioactive waste disposal projects.
Rocks are natural geological materials containing fractures of different origins, sizes, mineral fillings, weathering degrees, orientations, termination patterns, thickness and shapes, and especially surface roughness features. In addition, rocks in-situ are under stress, caused by dynamicmovements in the upper crust of the Earth, such as tectonic plate movements, earthquakes, land uplifting/subsidence, glaciation cycles and tides, in addition to gravity. A rock mass is also a fractured porous medium containing fluids in either liquid or gas phases (e.g. water, oil, natural gases and air), under complex in-situ conditions of stresses, heating or cooling, freezing or thawing, fluid pressures, and complicated geochemical reactions, with connected fractures most often serve as the major energy and mass transport pathways and most active areas of geochemical reactions, especially for fractured hard crystalline rocks. This is the reason why the coupled thermal (T), hydraulic (H), mechanical (M) and chemical (C) processes is an issue of importance in the field of rock mechanics.
The terms “discontinuity” and “fracture” are used interchangeably in the rock mechanics literature. The term “fracture” is adopted throughout this paper as a collective term for all types of natural or artificial discontinuities such as faults, joints, dykes, fracture zones and other types of weakness surfaces or interfaces, unless specifically stated otherwise. The rock fractures are usually not just open voids with fresh and smooth surfaces. Their surfaces (or walls) are often rough, weathered and fully or partially filled with precipitated minerals, and their relative positions are often modified by geological history and loading conditions, such as opening, closing, faulting or shearing, with large or small relative displacements. The complexity in the surface topography makes understanding and quantitative representation of the physical-chemical behavior and rock fracture properties difficult issues.
Horizontal wells with multistage hydraulic fracturing stimulation become the common practice in developing tight and shale gas reservoirs. For gas condensate reservoirs, heavier components in the gas phase start dropping and decrease the gas mobility due to a relative-permeability relationship as reservoir pressure drops below the saturation pressure. Therefore, modeling the condensate banking along hydraulic fractures becomes critical in understanding the productivity loss, the hydraulic fracturing job design as well as the field production optimization. In addition, along with pressure depletion, the stress dependent permeability must be taken into account either by an approximation derived from lab experiments inside a finite difference flow simulator or modeling separately by a finite element geomechanics code.
A condensate fluid pseudoization that reduces nine hydrocarbon components to a pseudo three components mixture is presented in this paper. The control volume based multiphase multi-components thermal simulator FATS is utilized in modeling the condensate banking inside the hydraulic fractures and surrounding matrix blocks. A K-value interpolation algorithm is developed and validated by a two-phase envelope generated by an Equation of State (EOS). FATS results are validated by the EOS based reservoir simulator GEM.
A compositional simulation model is coupled with reservoir geomechanics in this study to investigate the interaction of stress changes and its effects on multiphase flow along fractures. A modular coupled approach is implemented for solving the stress and flow equations at each time step by the iteration between the reservoir simulator and geomechanical module. Pressure and temperature changes occurring in the reservoir simulator are passed to the geomechanical simulator to compute the changing of stress and strain and updating porosity and permeability simultaneously. Simulation results show that fracture conductivity reduction is due to the combination of condensate banking and changing of the effective stress along hydraulic fractures.
This paper presents a review of a systematic research program for understanding scale and stress effects on transport behaviours of fractured crystalline rocks, using a hybrid discrete element and particle tracking approach. The motivation is the importance of understanding stress effects on behaviours of contaminant transport in fractured crystalline rocks, an important issue of rock mechanics for environmental safety assessments of many rock engineering projects. The study is divided into three steps. The first step is a basic study that established the mathematical platform for deriving the conditions, criteria, basic approaches and test case results for investigating stress and scale effects on hydraulic behavior of the fractured rock concerned. At the second step, based on outstanding issues drawn from the first step, the study was extended to consider effects of the correlation between the fracture aperture and size (represented by trace length) on the permeability of the fractured rock, and uncertainties in deriving equivalent continuum properties of fractured rocks. The third step added the particle/solute transport processes to the mathematical platform, including different retardation mechanisms, so that impact of stress on safety can be directly evaluated, even it can only be done conceptually. The obtained results show that stress, scale and inter-parameter correlations of the fracture system geometry are dominant issues for understanding and characterization of coupled hydro-mechanical processes of fractured rocks and play a significant role for understanding the mass transport behaviour in them, with direct impact on geo-environmental safety.