ABSTRACT: Geomechanical modeling of a reservoir has a very important role in all parts of a field lifecycle. In this paper, we demonstrate a new method for modeling the distribution of elastic properties in the whole reservoir using the concept of geomechanical units (GMUs). In this study, a GMU is a cluster of Young’s, Bulk and shear modulus, Poisson’s Ratio and unconfined uniaxial strength. To establish these GMUs we used eight wells and the Post-stack seismic data in the field of interest. Dynamic elastic parameters were computed from logging data of mentioned wells. To convert these dynamic parameters to static values, empirical equations were determined in a neighboring field of Salman, in the interval of Kangan and Dalan formations. In the next step, Multi-resolution graph-based clustering was applied to these static elastic parameters to construct five distinct GMUs. For three-dimensional modeling of GMUs, the 3D acoustic impedance model of the field was made by genetic inversion and used as a secondary parameter of Co-kriging. The amounts of elastic parameters of each GMU at the location of well number six in the final 3D model are found to be in good agreement with the known values of this well.
Geomechanics is a petroleum engineering sub-discipline developed to address the mechanical behavior of the reservoir and bounding rocks during exploration and production activities (Zoback, 2010; Aadnoy and Looyeh, 2011). In this regard, Three-dimensional modeling of geomechanical parameters plays a significant role in whole life of a reservoir. These models are used for seismic modeling, interpretation, hydraulic fracture design, assessing borehole stability and stress calculations in geological studies. Therefore, any improvement in one of these momentous applications could lead to better and more sufficient field development plans, at the same time save the considerable amount of money and operation time.
This study employs an efficient approach to construct a 3D reservoir geomechanical model based on the concept of Geomechanical Units (GMUs). A GMU is a single unit for design and modeling purposes. A GMU can be selected from logs, cores, or judgment (Dusseault, 2011). The advantages of GMU use in engineering studies have been discussed by a number of authors including Uwiera et al. (2011) and Nygaard (2010). In this work, a GMU is a set of rock mechanical properties, such as: Young’s modulus, bulk modulus, shear modulus, Poisson’s ratio, and uniaxial compressive strength. These elastic parameters are clustered by using different clustering methods to establish the best GMU. The purpose of using this method is to determine the distribution of elastic parameters in whole parts of the field of study. The Kangan and Dalan formations are the reservoir layers in the field of study. These formations are consisted of carbonate and dolomite (Figure 1).
ABSTRACT: This paper presents the theoretical formulation and numerical implementation of an anisotropic damage model for materials with intrinsic transverse isotropy, e.g. sedimentary rocks with a bedding plane. The direction dependent mechanical response is captured by utilizing four types of equivalent strains, for tension and compression, parallel and perpendicular to the bedding plane. The model is calibrated against triaxial compression test data, for different confinement and loading orientations. The variations of uniaxial tensile and compressive strengths with the orientation of the loading relative to the bedding follow the trends and magnitudes noted in experiments. Anisotropic non-local equivalent strains were used in the formulation to avoid localization and mesh dependence encountered with strain softening. Two different internal length parameters are used to distinguish the non-local effects along and perpendicular to the bedding. An arc length control algorithm is used to avoid convergence issues. Results of three-point bending tests confirm that the nonlocal approach indeed eliminates mesh dependency. Results show that the orientation and size of the damage process zone are direction dependent, and that materials with intrinsic transverse isotropy exhibit mixed fracture propagation modes except when the bedding aligns with the loading direction. Further research towards a multiscale hydro-mechanical fracture propagation scheme is undergoing.
Modeling fracture propagation in sedimentary rocks requires complex coupled constitutive equations to account for both intrinsic and stress-induced anisotropy, and regularized numerical methods to avoid mesh size dependence due to strain softening. Experiments revealed that rock maximum axial compressive strength is reached when weak planes are either parallel or perpendicular to the loading direction, and minimum strength is reached when weak planes are orientated 30° –60° with respect to the loading direction (Donath, 1961; Niandou et al., 1997; Pietruszczak and Mroz, 2001). In indirect tensile tests, the tensile strength is maximum when tensile stress is applied within the weak plane, and gradually decreases as the orientation angle between the tensile stress direction and the bedding plane increases (Mahjoub et al., 2015). State-of-the-Art constitutive models are either based on Continuum Damage Mechanics (CDM) or Micromechanics. In CDM, damage criteria and evolution laws for anisotropic materials depend on a second order fabric tensor to account for the direction dependency (Pietruszczak et al., 2007). In Micromechanics models, the expression of the free energy is obtained by solving a matrix-inclusion problem for a given set of crack families. Depending on the homogenization scheme, crack interaction may or may not be accounted for. Intrinsic anisotropy is accounted for by attributing different properties to crack families of different orientations (Chen et al., 2012). Once implemented in a Finite Element (FE) code, both CDM and micromechanics models suffer from mesh dependence if strain softening is considered for compression/tension. Several localization limiters can be used, e.g. the crack band theory, a non-local integration- based formulation or non-local differentiation-based formulation. However, the non-local effects of intrinsic anisotropy are usually not accounted for.
ABSTRACT: The Arbuckle group is a major geologic formation that is widely distributed in subsurface Oklahoma and Kansas. Understanding the geomechanical and petrophysical properties of the rock materials from these layers is of much interest for CO2 storage, salt water disposal, and injection induced seismicity problems. In this paper, we present some results of a geomechanical characterization effort to determine the rock mechanical properties of the Arbuckle Group and its bounding formations. Static and dynamic elastic modulus and Poisson’s ratio, shear strength, friction coefficient, and cohesion have been measured. The unconfined compressive strength (UCS) and Mohr-Coulomb failure envelop also have been estimated for every tested specimen. In addition, mechanical anisotropy of the rocks has been evaluated using both dynamic and static laboratory measurements. Furthermore, natural fracture properties have been measured under triaxial conditions. The characterizations of the rock mechanical properties of the Arbuckle group provide valuable data for ongoing numerical modeling of CO2 storage and seismicity in Oklahoma.
The Arbuckle group is a major geological formation in the midcontinent of the United States that underlies several important petroleum producing zones such as West Mayfield in Anadarko basin, Wilburton in Arkoma basin and Cottonwood Creek in Ardmore basin (Fritz et al., 2013). In the state of the Oklahoma, the Arbuckle group serves as the primary saltwater disposal zone. According to Oklahoma Corporation Commission (OCC), from 2010 to 2013, 14.47%-20.86% of SWD wells were completed in the Arbuckle group, and received 51.74% to 61.94% of the injected water volume (Murray, 2014). Understanding the rock and fracture properties of the Arbuckle geological formation would be beneficial to the well safety designs, and moreover, would provide reliable parameters for numerical modeling of production and seismicity. However, the literature contains very little to no data on the geomechanical properties of this important formation. Therefore, a laboratory geomechanical and petrophysical characterization program was developed to determine the much needed rock properties. Because actual core is not available, we used a block of the Arbuckle formation collected from outcrops in the Arbuckle Mountains in south-central Oklahoma along the I-35 in north of Carter County (34°22”6’, −97°8’45”), as shown in Fig. 1, where the rock was not highly weathered and resembled the actual cores reserved in the Oklahoma Petroleum Information Center (OPIC) (Morgan, 2015). A series of experiments have been carried out on eighteen specimens extracted from the block to measure various rock and fracture properties.
ABSTRACT: Layering-induced anisotropy of shale formations increases uncertainty in determining in-situ mechanical properties and stresses, thus increasing the risk associated with implementing advanced drilling and hydraulic stimulation in shales. We conduct simultaneous triaxial stress tests and ultrasonic wave propagation monitoring to quantify static and dynamic stiffness anisotropy in Mancos Shale. Two case studies evidence the impacts of (1) confining stress and (2) presence of pre-existing fractures, on dynamic-static transforms of Young’s moduli and Poisson’s ratios with increasing deviatoric stress. The first case shows that confining stress more heavily impacts dynamic mechanical properties than static. The effect is most prominent at high deviatoric stresses, where stress-induced damage increases the difference between dynamic and static Young’s moduli. The second case shows that samples with pre-existing fractures exhibit even higher differences between dynamic and static Young’s moduli than non-fractured (intact) and damaged rocks. Fractured samples exhibit ratios of Edyn/Est between 5:1 and 7:1, whereas intact samples generally remain near the 3:1 ratio. Pre- and post-test X-ray microtomography imaging confirm that bedding planes and pre-existing fractures act as planes of weakness, while sample layering causes mechanical stratigraphy, where changes in lithology may cause fractures to reorient. Results highlight the limitations of tangent linear elasticity moduli to explain complex deformational behavior in shales and the need for better models that address the strain-magnitude dependence of rock properties.
Shale layering causes bed-parallel differences in rock properties, a component of mechanical stratigraphy (Laubach et al. 2009). Stratigraphic variations in mechanical properties are known to influence the growth of engineered fractures (Bosziak et al. 2014). A further element of bed-perpendicular anisotropy can be introduced by pre-existing fractures, which can impact rock stress-strain response (Bergbauer and Pollard 2004). Over geologic time, subsurface stresses may vary, which can cause natural fracturing. Chemical alteration (diagenesis) might stiffen natural fractures, therefore their orientations might not be aligned with current stresses or layering (Laubach et al. 2004). Consequently, the attributes and orientation of layering and diagenetically altered open fractures can impact rock mechanical behavior, engineered fracture growth, and rock failure under a range of loading paths. Layering and pre-existing fractures are suspected to influence the behavior of shales undergoing hydraulic fracture treatment (Suarez-Rivera et al. 2013, Gale et al. 2014).
ABSTRACT: A three-dimensional discrete dual lattice model is formulated to investigate the permeability and mechanical behavior of fracture-damaged shale. The mechanical lattice model simulates the granular internal structure of material at the grain level, and describes the heterogeneous deformation by means of discrete compatibility and equilibrium equations. A network of fluid transport elements built upon the mechanical lattice is used to simulate fluid flow along intergranular pores and cracks. The variation of permeability for cracked material is captured by coupling mechanical and transport lattice models. A numerical example of direct shear triaxial test on Utica shale is simulated by the formulated framework. Variation of shale shear strength with the angle between the vertical bedding plane and the shear plane is captured. The permeability of the fractured specimens was obtained by simulating water flowing along the specimens. The numerical results show that the simulated effect of cracking on the overall permeability is in general qualitative agreement with available experimental data.
Material characterization of gas/oil shale and shale-like rock, including study of their mechanical and hydraulic properties, is needed in many engineering practices such as hydraulic fracturing. Investigating the fracture- and damage-induced permeability variation of shale is necessary to understand and optimize oil and gas production. This involves quantifying damage and fracturing of material due to nucleation and propagation of microcracks and correlating permeability variations with damage by taking into account the multiscale nature of shale (Hyman et al., 2016; Li et al., 2016). Despite the urgent need to understand and characterize shale fracture permeability behavior, little work has been published to the best of authors’ knowledge.
Most experimental work related to the evolution of rock hydraulic properties with cracking and damage has investigated the permeability of prefractured (split or sawn) specimens (Gutierrez et al., 2000; Davy et al., 2007; Jobmann et al., 2010; Cho et al., 2013; Mokhtari et al., 2014). These studies clearly show that rock permeability is strongly related to density, spacing, orientation, width, and length of fractures within samples. Nevertheless, studies on shale permeability are substantially limited. It was suggested by researchers (Carey et al., 2015a; Carey et al., 2015b; Frash et al., 2016) that permeability studies of rocks fractured at in situ conditions through triaxial compression or direct shear tests better represent fracture properties in the subsurface than the ones using prefractured or artificial specimens.
ABSTRACT: For fundamental understanding of the roof fall, this research is focused on determining the time-delayed deformation. A series of triaxial single-stage creep tests was performed on Marcellus shale. The specimens were cored parallel and perpendicular to the bedding plane. X-ray diffraction tests were performed to determine the mineralogical composition of shale. The tests showed that the specimens were rich in carbonate content with minor percentage of clay minerals. A suite of uniaxial and triaxial compressive tests was performed on both parallel and perpendicular that determined their strength in different confining conditions. Finally, triaxial creep tests were performed to estimate the strength variation with orientation. Results from X-ray Diffraction (XRD), uniaxial and triaxial tested specimen showed the brittle behavior of shale. Specimens cored parallel to the bedding plane was found to be stiffer than the perpendicular specimens at different confining stresses. Higher confining stress led to the failure of specimens at higher angle of major shear failure plane to major principal stress. This was accompanied with lesser number of axial cracks and increase in the deformation of the specimen. Value of creep strain rate was found to be in correlation with differential stress on horizontal and vertical specimens.
The fundamental behavior of long-term strength deterioration in shale rock is not known. Various rock engineering structures such as underground coalmines have operating life of 30 years or greater and the challenge to maintain a stable roof is prime concern of ground control researchers. Mine Health and Safety Administration’s (MSHA) reports show that roof fall and rib rolls are the leading fatality factors. Operators have also left rider coal in the roof to prevent exposure of shale roof from humid mine environment. The approach has reduced the occurrence of roof failure however, long-term deformation of roof rock constituted with shale is still lacking. Presence of moisture and its effect on strength degradation has not been investigated at pore scale.
ABSTRACT: Geothermal energy, with its combination of very low CO2 emission rates and the possibility of providing electricity, has the potential of being a key factor in the global greenhouse gas emission reduction. Some geothermal systems, however, require stimulation to achieve economic production. To simulate the effectiveness of stimulation techniques, a synergy between dynamic flow simulators and geomechanical models is crucial. Especially in volcanic environments. Such systems are characterized by a high fracture density, fluids are generally stored in the pores of the rock mass, but the fracture network, rather than the connectivity of the pores, provides the conduits for fluids and heat to flow through the reservoir. Injecting fluid alters the stress field in the area. If the induced extra pressure is larger than the rock strength, it propagates tensile fractures in the rock, enhancing the conductivity and permeability. For smaller pressures, the reduction of the effective stress might cause hydro-shearing of existing fractures. Moreover, injecting fluid colder than the in situ temperature will generate thermal stresses, with similar effect on the fractures. To tackle all those aspects, we linked numerical simulators and analytical solutions to connect the evolving fluid properties and temperature with the changes in the stress field.
To reduce greenhouse gas emission in the atmosphere and the associated effects of global warming, it is key to make the stimulation of geothermal fields more efficient and economically more attractive. With its unique combination of an extremely low CO2 emission rate and the possibility of providing energy security, geothermal energy is rapidly becoming a very popular source of green energy. However, to achieve economic production, geothermal systems often need to be stimulated. The stimulation techniques aim to improve the permeability and connectivity of the geothermal system. This is achieved by creating new conduits or by enhancing the existing ones for the fluid, and the associated heat flow, in the geothermal reservoir. Common stimulation methods are:
Latham, J-P. (Imperial College London) | Yang, P. (Imperial College London) | Lei, Q. (Imperial College London) | Obeysekara, A. (Imperial College London) | Salinas, P. (Imperial College London) | Pavlidis, D. (Imperial College London) | Xiang, J. (Imperial College London) | Pain, C. C. (Imperial College London)
ABSTRACT: In quarries and mines, blocky rock masses are transformed by fracture of intact rock by the action of the detonation pressure of explosives, the blastpile fragment size distribution ultimately controlling the economics. Rock fragmentation prediction and blast design continues to this day to follow largely empirically calibrated equations. One source of inaccuracy of models such as Kuz-Ram is likely to be the lumping together of so-called uncontrollable i.e. geological parameters into one blastability factor to characterize the rock mass. Recent developments in numerical modelling have introduced the sophistication necessary to capture more of the key nonlinear and coupled processes that occur during rock blasting and to consider intact rock properties and jointing or discontinuities independently. The discontinuous computational approach adopted here is based on the combine finite-discrete element method (FEMDEM) coupled to a FEM multi-phase gas flow model with full equation of state. The fragment size distributions are compared for idealised scenarios drawn from simulated blasts with isotropic intact rock, rock with persistent and impersistent discontinuity sets i.e. with rock bridge ratios and different discontinuity spacing, all for identical detonation gas pressure. Results are discussed in the context of the rock structure’s effect on the dominant mechanisms of fragmentation.
Rock fragmentation by blasting is employed widely in mining and quarrying and is by far the most efficient initial method of comminution, see for example the extensive literature on blasting, e.g. Persson et al. (1993), JKMRC (1996), Jimeno et al. (1997). The economic and environmental drivers of these industries are highly dependent on the fragmentation size distribution as downstream load and haul and crusher efficiencies depend on such yield curves. Fragmentation prediction models are typically designed to combine practical bench and drill-hole layout geometries, sound physical principles based on explosive energy concentration to provide empirically derived size distribution outputs often characterised by best-fit two- or three-parameter cumulative distribution functions. The rock mass properties are acknowledged to be problematic for the prediction. On the commonly made assumption that a mine site or quarry site has a certain local geology, the blast designer is often content to use just one composite index for the blastability parameter in the model and perform field site adjustments based on actual blasting results. Prediction of blasted block size distributions, BBSDs (fragmentation curves, yield curves) is the subject of significant research effort as the possible error in prediction remains very high. Accuracy is limited because the geological conditions cannot easily be determined for every blast and the implementation of the blast design may suffer from practical constraints. Four approaches to fragmentation prediction were discussed in the context of quarry aggregates and large block (armourstone) production in Latham et al., (2006).
ABSTRACT: The Regional Connector Transit Corridor project provides a 3.0 km long connection for existing light rail transit lines in downtown Los Angeles, California. The project involves twin bored tunnels, cut-and-cover tunnels, three deep stations and one sequential excavation cavern that will encounter the Fernando Formation bedrock, which underlines the alluvium. The Fernando Formation consists of a poorly bedded to massive clayey siltstone to silty claystone that is poorly cemented and extremely weak to very weak per ISRM (1978). This paper presents the geotechnical engineering characteristics of the formation based on field investigation and laboratory testing.
The Regional Connector Transit Corridor project consists of 3.0 km long new tracks of connection between a number of existing light rail transit lines in downtown Los Angeles. The project elements include three deep stations, one cavern using the sequential excavation method (SEM), segments of tunnels using a tunnel boring machine (TBM), and cut-and-cover guideway structures. The subsurface conditions along the tunnel alignment generally consist of artificial fill overlaying finer-grained alluvium (dominantly medium dense to dense sandy soils), underlain by coarser-grained alluvium (a wide variety of medium dense to dense sandy and gravely soils). Below the coarser-grained alluvium is the Fernando Formation, which is characterized as extremely weak to very weak sedimentary bedrock; a long segment of the project alignment will be excavated in this formation. The geologic profile along the alignment is shown in Figure 1.
2. OVERVIEW AND BASIC PROPERTIES
Based on a large number of geotechnical investigations performed for the project alignment, the Fernando Formation commonly consists of a weathered profile, ranging from “moderately weathered” to “highly weathered”, which overlays a “slightly weathered” to “fresh” profile. The thickness of the more weathered, weaker bedrock ranges from 0 to approximately 60 feet (1 foot = 0.305 m) along the project alignment. As shown on Figure 1, the thickest weathering underlies the high terrain in the vicinity of 2nd Street and Hope Street (i.e. from approximately Station 29+00 to 45+00 feet), where the depth to slightly weathered/fresh bedrock ranges from approximately 30 to 60 feet below the top of bedrock. The thickness of the more highly weathered bedrock decreases toward the flanks of the hill. Although bedrock is generally massive, the bedrock contains discontinuities that include bedding planes (bedding plane partings/bedding plane joints), joints and shears.
ABSTRACT: We examine P-wave propagation in a fractured medium using effective medium, explicit fractures, and localized effective medium representations of fracturing, to quantify their effectiveness. We model a published experiment with multiple parallel fractures. Initial models assume uniform fracture stiffness across all fractures. A methodology is presented for inverting a source from the experiment. We find that the waveforms from the three models do not match each other. For propagation parallel to the fractures, the explicit model performs best with excellent agreement with the experimental waveform. The waveform from the localized TI model is reasonably similar, matching arrival, predominant period, frequency content, but not amplitude. The TI model is a poor match with significant differences in period, amplitude and high frequency content. For perpendicular propagation, none of the models properly match the experimental waveform. All models reproduce the significant delay in arrival, but only the explicit and local TI models produce a reduction in period and frequency content mimicking the experiment. All models produce a reduction in amplitude but not to the degree of the experiment. An explicit model accounting for the effect of the non-uniform stress-field better matches the experiment, indicating similar developments are needed for the other two representations.
Fractures in rocks are significant in a number of engineering applications. For example, an assessment of rock fractures is extremely important for characterizing the effectiveness of the geological barrier to a nuclear waste disposal repository, as they can provide fluid pathways, increasing the rock permeability. By examining the full waveform from either active or passive seismic sources we can obtain information on fracturing as seismic waves interact with the fractures (e.g., Schoenberg, 1980). Many studies (e.g., Crampin, 1981, Hudson, 1981, Majer, et al., 1988, Rathore, et al., 1995, Kawai, et al., 2006, Tillotson, et al., 2011, de Figueiredo, et al., 2013, Ding, et al., 2014, Tillotson, et al., 2014) have assumed that the response of a large number of fractures, can be mapped into the overall effective behavior of the medium, by linking the elastic constants with the fracture density and orientation, leading to anisotropy in the wave velocities (effective medium modelling). An alternative approach is discrete fracture representation using displacement discontinuities. The model was introduced for seismic wave propagation by Schoenberg (1980) and has been studied by numerous authors, (e.g., Pyrak-Nolte, et al., 1990, Nakagawa, et al., 2002, Hildyard, 2007, Chichinina, et al., 2009b, Perino, et al., 2010, Fan & Sun, 2015, Shao, et al., 2015). Pyrak-Nolte et al. 1990 examined the displacement discontinuity model for elastic wave propagation through multiple parallel fractures, in an experiment using laminated steel plates to simulate natural fractures. Hildyard (2007) then showed that an explicit representation of the fractures could match the experimental recorded waveforms but only if the effect of a non-uniform loading on fracture stiffness was included. In this research we try to model this experiment on laminated steel block (Pyrak-Nolte, et al., 1990), using the numerical modelling code WAVE3D (Hildyard, et al., 1995) to demonstrate the resulting changes to seismic waveforms for both effective and discrete fracture models, in order to establish under what conditions each representation is most appropriate and how close the models are to producing real effects on waveforms.