|Theme||Visible||Selectable||Appearance||Zoom Range (now: 0)|
Reliable characterization of mechanical behavior (e.g., elastic properties) in anisotropic and heterogeneous formations require advanced methods for understanding the impacts of spatial distribution of rock components, pore structure, and pore pressure on mechanical properties. However, the existing methods for assessment of mechanical properties (e.g., effective elastic properties) such as effective medium models, assume constant stiffness values and idealized shapes for rock constituents and pores. These models also do not take into account coupled hydraulic and mechanical (HM) processes, which cause significant uncertainties in geomechanical evaluation. The objective of this paper is to investigate the effects of realistic spatial distribution of minerals, pore pressure, and pore structure on the effective elastic properties of rock-fluid systems.
In order to pursue this objective, we developed a pore-scale numerical simulator by satisfying conservation equations and considering the coupling among relevant HM processes. We adopted peridynamic theory to discretize the micro-/nano-scale medium. The inputs to the numerical modeling include pore-scale images of rock samples as well as mechanical and hydraulic properties of each rock constituent. We used micro-computed tomography (micro-CT) scan and focused ion beam (FIB) scanning electron microscope (SEM) images of rock samples to obtain a realistic micro-/nano-scale structure of both rock matrix and pore space. We then assigned realistic mechanical and hydraulic properties to each rock constituent within the pore-scale medium. The outcomes of numerical modeling include the variation of effective stress and the evolution of corresponding strain by honoring the variability in mechanical properties of rock components caused by their spatial distribution, size, pore pressure, and pore structure at the micro-/nano-scale level.
We successfully tested the reliability of the developed framework using results of an analytical solution for the case of consolidation. We then performed sensitivity analyses to quantify the effects of concentration and spatial distribution of rock components, divergence in mechanical properties of minerals, and pore structure on variations in effective elastic properties of rock components. For instance, the deformation of clay minerals dispersed in between the quartz minerals was approximately 60% less than that in clay minerals colonized next to the quartz under the same load. In the next step, we compared these mechanical characterizations with estimates obtained from the effective medium models. We observed measurable uncertainties (more than 15% depending on mineral content and distribution) in elastic properties of rock components estimated by the effective medium models such as self-consistent approximation. These uncertainties are associated with spatial distribution, shape, and size of minerals, which are not considered in those models. Such effective medium models also overlook the effects of pore structure and pore pressure on the mechanical properties. The results of coupled HM analysis for cases with the same mineral concentration but different pore structure revealed more than 12% error in estimates of effective mechanical properties.
Wang, Changzi (Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China) | Yao, Lu (Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China) | Wang, Shuqing (Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China) | He, Wentao (Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China)
ABSTRACT Initial defect and crack damage could pose a significant risk to the safety of the whole structure. To ensure the reliability level, the probabilistic residual ultimate strength of cracked plates under uniaxial compression is evaluated based on a Kriging-based Monte Carlo simulation method. Results demonstrate that the length and orientation of crack have a significant influence on the residual compressive strength, whereas they have a negligible effect on the initial stiffness. The initial deflection and transverse center-offset distance of crack have a remarkable effect on both the residual compressive strength and initial stiffness. INTRODUCTION Usually the ultimate strength of a structure under high waves or extreme loading conditions is evaluated using the deterministic method. However, different kinds of initial defects are usually inevitable for the ships and offshore structures since the manufacturing and working conditions are complicated (Saad-Eldeen et al., 2018; Cui et al., 2016; Xu et al., 2014). Crack is one of the most common damage that can usually be found at the structural discontinuities, welded joints and stress concentration regions (Saad-Eldeen et al., 2018; Cui et al., 2016). It is commonly acknowledged that not only the buckling performance but also the load bearing capacity of structures is significantly affected due to the existence of the cracks. The size, location and direction of the cracks are often different for different structures because of the uncertainty in the initiation and propagation of the crack.Therefore, it is significantly important to carry out the probabilistic assessment of ultimate strength under compressive load thoroughly during the damage-tolerant design and service life (Xu et al., 2019; Cui et al., 2017; Amlashi et al., 2008; Benson et al., 2013). With the introduction of damage tolerance approach, the reliability evaluation of the structure with initial defect has attracted more and more attention in ship and marine engineering. Risk-based inspection (RBI) has already been proposed to evaluate the optimal inspection and maintenance strategies of aged structures due to its advantages in identifying the primary factors among the basic random variables. Recently, within reliability-based approaches increasing attention has also been paid to quantifying the uncertainties of design variables via probabilistic models. Probabilistic modelling of ultimate strength mainly involves two aspects: the assessment of ultimate strength and the analysis of structural reliability. The ultimate strength assessment of cracked plates is usually associated with nonlinear structural behavior, which should rely on numerical approaches such as the nonlinear finite element analysis. Reliability analysis is a complex process that requires a huge number of numerical models (such as nonlinear finite element analysis (FEA) structural models), therefore, it is usually not suitable for local design of engineering structures because it is time-consuming and computationally intensive. To effectively solve this problem, alternative model-based methods are established as an effective technique to provide accurate reliability analysis with lower computational costs, such as polynomial response surface (Faravelli, 1989), artificial neural network (ANN) (Papadrakakis et al., 1996), support vector machine (SVM) (Vapnik, 2006) and kriging model (Matheron, 1973). Cui et al. (2019) predicted the probabilistic characteristics of the ultimate strength of typical bottom stiffened plate structures under local pitting accurately and efficiently based on gaussian process (GP), which is inserted with a new design point and integrated with a surrogate model. Gaspar et al. (2012) evaluated the failure probability and reliability of stiffened hull box girder plates under uniaxial compression and lateral pressure loads considering the effect of corrosion based on Monte Carlo simulation combined with response surface method. From the literature above, it is found that the reliability assessment of ultimate strength under compression load mainly focuses on the basic uncertainties, such as initial deformation and corrosion damage of the plate, the probabilistic ultimate strength investigation of the cracked plates are seldom reported.
Abstract Spatial anisotropy and heterogeneity in petrophysical properties can significantly affect formation evaluation of hydrocarbon bearing formations. A common example is permeability anisotropy, which is a consequence of the depositional mechanisms of sediments. Additionally, the variation in spatial distribution of rock components and the effect of post-depositional processes on the physical and chemical structure of the rock constituents can strongly impact the directional dependency of petrophysical, electrical, and elastic properties. Therefore, image-based quantification of spatial distribution of rock constituents can be used for anisotropy evaluation. Assessment of anisotropy has been previously accomplished through use of pore-scale images. However, the discrete nature of this images gives a narrow picture of anisotropy in larger scales. Whole-core computed tomography (CT) scan images, despite revealing the distribution of rock components at a coarser scale, provide a continuous medium for anisotropy estimation. Assessment of anisotropy using three-dimensional (3D) CT-scan data and incorporation of that information in well-log-based formation evaluation is, however, not widely studied or practiced in the petroleum industry. The objectives of this paper are (a) to develop a method to quantify anisotropy utilizing whole-core 3D CT-scan image stacks, (b) to provide a semi-continuous measure of rock anisotropy, and (c) to show the value of the proposed method by means of estimation of directional-dependent elastic properties. First, we pre-process the raw whole-core CT-scan images to remove undesired image artifacts and to generate an image containing pixels representing only the recovered core material. Then, we segment each whole-core CT-scan image stack into distinctive phases. Then, we conduct numerical simulations of electric potential distribution in conjunction with streamline tracing techniques to quantify the electrical tortuosity of the continuous phase in each cartesian direction. We employed the tortuosity distribution values in each direction as a measure of rock anisotropy. Finally, we use a simulation model to estimate direction-dependent elastic properties. We applied the introduced method to dual energy whole-core CT-scan image stacks acquired in a siliciclastic depth interval. Estimates of rock anisotropy obtained using the proposed method agreed with the observed visual distribution of the segmented phase and the observed heterogeneity in available slabbed whole-core photos and 2D CT-scan images. Additionally, estimation of directional-dependent elastic properties demonstrated the value of the proposed method. Anisotropy results coincided with directional-dependent estimation of elastic properties. We observed measurable anisotropy in the 3D CT-scan image stacks, which is important to be quantitatively taken into account in petrophysical/ mechanical evaluation of this formation. A unique contribution of the proposed workflow is the use of core-scale image data for anisotropy estimation and the continuous nature of the anisotropy estimates when compared with workflows employing only pore-scale image data. It should also be noted that the proposed method can potentially be employed to identify the optimum locations to acquire core plugs for further assessment of rock anisotropy.
Abstract Most hydraulic fracturing models assume that the rock is homogeneous at a pore scale. However, reservoirs are highly heterogeneous at all length scales. Pore scale heterogeneity is evident from thin sections and scanning electron microscopic images (SEM). Heterogeneity at larger length scales is evident from logs and cores. In this paper, the effect of micro-scale (pore and core scale) heterogeneities caused by varying mineral composition and the presence of pores and microfractures, on fracture propagation has been investigated. A model that solves the solid displacements and fluid pressures both inside and outside the fracture and allows for the creation and propagation of multiple fractures is presented. This peridynamics-based hydraulic fracturing model is used to model the growth of multiple, complex fractures in a heterogeneous rock. Thin section and SEM images of rocks are used to represent the geometry of the rock grains and the pores in several rock samples. Far-field stresses are then applied and a fluid induced fracture is propagated in the rock matrix. The results of the model reveal that the stress distribution and the fracture geometry can be quite complex at the micro-scale. Fracture branching and turning is induced by variations in elastic moduli and stress concentration at the grain scale. The microstructure of the fracture is, therefore, determined by the geometry and distribution of mineral grains, their mechanical properties, and the initial stress anisotropy due to the co-existence of different mineral grains. A similar effect is observed at the core scale where differences in the microstructure of the rock can result in stress concentration at layer boundaries. For example, we show that the presence of a brittle mineral like calcite in the rock matrix causes fractures to branch at the mineral interface. Multiple fractures are shown to open, some that may not be in hydraulic contact with each other. As the fracture propagation continues, only the least tortuous path remains open. All other branches are bypassed hydraulically and are eventually closed. This fracture complexity occurs despite macroscopic stress anisotropy. Several examples of fracture propagation in rocks that are heterogeneous at a pore scale are provided to show that such fracture complexity should be expected in most lithologies. These results clearly show that while we have traditionally represented fractures as planes perpendicular to the minimum horizontal stress, the fracture surfaces may indeed be much more complex due to existence of different minerals grains with widely different mechanical properties. Cracks can form away from the crack tip along planes of weakness. These damage zones resulting from strains induced by fracture propagation may explain the creation of the stimulated reservoir volume (regions of enhanced permeability) around fractures in shale reservoirs.