Use of "digital core" module in SAE Fidesis to determine effective parameters of fractured porous media

2020 ◽  
Author(s):  
Vladimir Levin
Keyword(s):  
Heterogeneous Media ◽  
Effective Properties ◽  
Displacement Vector ◽  
Fractured Reservoirs ◽  
Periodicity Cell ◽  
Shear Deformations ◽  
Fractured Medium ◽  
Digital Core ◽  
The Relationship ◽  
Tangential Directions

<p>Development of the homogenization algorithms for the heterogeneous periodic and non-periodic materials has applications in different domains and considers different types of upscaling techniques (Fish, 2008, Bagheri, Settari, 2005, Kachanov et al. 1994, Levin et al. 2003).</p><p>The current presentation discusses an algorithm implemented in CAE Fidesys (Levin, Zingerman, Vershinin 2015, 2017) for calculating the effective mechanical characteristics of a porous-fractured medium (Myasnikov et al., 2016) at the scale of a periodicity cell dissected by a group of plane-parallel cracks modeled by elastic bonds with specified stiffnesses in the normal and tangential directions in accordance with the method of modeling cracks based on elastic bonds (Bagheri, Settari, 2005, 2006) In this case, the relationship between the components of the displacement vector and the force vector (normal stresses at the fracture’s boundaries) in the normal and tangential directions will be diagonal, neglecting the effects of dilatancy and shear deformations as a result of normal stresses.<br>The presentation also considers the general case of the relationship between displacements and forces along the fracture’s boundaries, taking into account shear deformations (which leads to an increase in the effective Young's modulus by 30%), and additionally a cell’s geometrical model is generalized by the presence of pores in the matrix’s material. The results of numerical studies on mesh convergence, the influence of periodicity cell sizes and fracture’s thicknesses on the computed effective properties are presented. A comparison between analytical (Kachanov, Tsukrov 1994, 2000) and numerical results obtained in CAE Fidesys for the effective elastic moduli estimation for particular cases of geometrical models of the periodicity cell is shown.<br>The developed algorithm is used to evaluate the effective mechanical properties of a digital core model obtained by the results of CT-scan data interpretation. A comparison is made with the results of laboratory physical core tests. Additionaly an algorithm implemented in CAE Fidesys and the results for the effective thermal conductivity and the effective coefficient of thermal expansion estimation are given for the considered test rock specimen.</p><p>The reported study was funded by Russian Science Foundation project № 19-77-10062. </p><p> </p><p> </p><ol><li>Bagheri, M., Settari, A. Effects of fractures on reservoir deformation and flow modeling // Can. Geotech. J. 43: 574–586 (2006) doi:10.1139/T06-024</li> <li>Bagheri, M., Settari, A. Modeling of Geomechanics in Naturally Fractured Reservoirs – SPE-93083-MS, SPE Reservoir Simulation Symposium, Houston, USA, 2005.</li> <li>Fish J., Fan R. Mathematical homogenization of nonperiodic heterogeneous media subjected to large deformation transient loading // International Journal for Numerical Methods in Engineering. 2008. V. 76. – P. 1044–1064.</li> <li>Kachanov M., Tsukrov I., Shafiro B. Effective moduli of a solid with holes and cavities of various shapes// Appl. Mech. Reviews. 1994. V. 47, № 1, Part 2. P. S151-S174.</li> </ol>

Effective Properties of Superconducting and Superfluid Composites

1998 ◽  
Vol 12 (29n31) ◽  
pp. 3063-3073 ◽  
Author(s):  
Leonid Berlyand
Keyword(s):  
Mathematical Model ◽  
Linear Problem ◽  
Effective Properties ◽  
Point Of View ◽  
Periodicity Cell ◽  
Unit Size ◽  
Composite Media ◽  
Homogenization Procedure

We consider a mathematical model which describes an ideal superfluid with a large number of thin insulating rods and an ideal superconductor reinforced by such rods. We suggest a homogenization procedure for calculating effective properties of both composite media. From the numerical point of view the procedure amounts to solving a linear problem in a periodicity cell of unit size.

Thermodynamics of stressed systems

2005 ◽  
Author(s):  
Boris S. Bokstein ◽  
Mikhail I. Mendelev ◽  
David J. Srolovitz
Keyword(s):  
Mechanical Properties ◽  
Thermodynamic Functions ◽  
School Child ◽  
Displacement Vector ◽  
Mechanical Deformation ◽  
Material Point ◽  
General Description ◽  
The Difference ◽  
Point To Point ◽  
The Relationship

As every school child knows, the difference between a solid and a liquid is that a liquid takes the shape of the container in which it is placed while the shape of a solid is independent of the shape of the container (providing the container is big enough). In other words, we must apply a force in order to change the shape of a solid. However, the thermodynamic functions described heretofore have no terms that depend on shape. In this chapter, we extend the thermodynamics discussed above to include such effects and therefore make it applicable to solids. However, since this is a thermodynamics, rather than a mechanics text, we focus more on the relationship between stress and thermodynamics rather than on a general description of the mechanical properties of solids. We start out discussion of mechanical deformation by describing the change of shape of a solid. We define the displacement vector at any point in the solid u(x, y, z) as the change in location of the material point (x, y, z) upon deformation: that is, ux(x, y, z) = x' - x, where the prime indicates the coordinates of the material that was at the unprimed position prior to the deformation. In linear elasticity, we explicitly assume that the displacement vector varies slowly from point to point within the solid where i and j denote the directions along the three axes, x, y, and z. Consider the small parallel-piped section of a solid with perpendicular edges shown in Fig. 7.1. We label the first corner as O, located at position (xO, yO, zO) and subsequent corners as A, B, . . . located at positions (xA, yA, zA), (xB, yB, zB), . . . The edge lengths are Δx, Δy, and Δz such that, for example, xA = xO + Δx. As a result of the deformation, the material originally at point O is displaced to point O' with coordinates (x'O, y'O, z'O).

EFFECT OF FRACTAL FRACTURES ON PERMEABILITY IN THREE-DIMENSIONAL DIGITAL ROCKS

Fractals ◽  
2019 ◽  
Vol 27 (01) ◽  
pp. 1940015 ◽  
Author(s):  
WEIFENG LV ◽  
GUOLIANG YAN ◽  
YONGDONG LIU ◽  
XUEFENG LIU ◽  
DONGXING DU ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Fractured Reservoirs ◽  
Three Dimensional ◽  
Absolute Permeability ◽  
Fracture Aperture ◽  
Fracture Networks ◽  
Discrete Fracture Networks ◽  
Discrete Fracture ◽  
The Relationship

The fracture has great impact on the flow behavior in fractured reservoirs. Fracture traces are usually self-similar and scale-independent, which makes the fractal theory become a powerful tool to characterize fracture. To obtain three-dimensional (3D) digital rocks reflecting the properties of fractured reservoirs, we first generate discrete fracture networks by stochastic modeling based on the fractal theory. These fracture networks are then added to the existing digital rocks of rock matrixes. We combine two low-permeable cores as rock matrixes with a group of discrete fracture networks with fractal characteristics. Various types of fractured digital rocks are obtained by adjusting different fracture parameters. Pore network models are extracted from the 3D fractured digital rock. Then the permeability is predicted by Darcy law to investigate the impacts of fracture properties to the absolute permeability. The permeability of fractured rock is subject to exponential increases with fracture aperture. The relationship between the permeability and the fractal dimension of fracture centers is exponential, as well as the relationship between permeability and the fractal dimension of fracture lengths.

scholarly journals Electromagnetic phenomena in heterogeneous media: Effective properties and local behavior

2006 ◽  
Vol 100 (4) ◽  
pp. 044902 ◽  
Author(s):  
Oriano Bottauscio ◽  
Alessandra Manzin ◽  
Valeria Chiadó Piat ◽  
Marco Codegone ◽  
Mario Chiampi
Keyword(s):  
Heterogeneous Media ◽  
Effective Properties ◽  
Local Behavior

Specifications for Hard Condensed Matter Specimens for Three-Dimensional High-Resolution Tomographies

2013 ◽  
Vol 19 (3) ◽  
pp. 726-739 ◽  
Author(s):  
P. Bleuet ◽  
G. Audoit ◽  
J.-P. Barnes ◽  
J. Bertheau ◽  
Y. Dabin ◽  
...  
Keyword(s):  
Sample Preparation ◽  
Heterogeneous Media ◽  
Effective Properties ◽  
Condensed Matter ◽  
Three Dimensional ◽  
Atom Probe ◽  
Preparation Technique ◽  
Ion Milling ◽  
Wide Range ◽  
Mechanical Machining

AbstractTomography is a standard and invaluable technique that covers a large range of length scales. It gives access to the inner morphology of specimens and to the three-dimensional (3D) distribution of physical quantities such as elemental composition, crystalline phases, oxidation state, or strain. These data are necessary to determine the effective properties of investigated heterogeneous media. However, each tomographic technique relies on severe sampling conditions and physical principles that require the sample to be adequately shaped. For that purpose, a wide range of sample preparation techniques is used, including mechanical machining, polishing, sawing, ion milling, or chemical techniques. Here, we focus on the basics of tomography that justify such advanced sample preparation, before reviewing and illustrating the main techniques. Performances and limits are highlighted, and we identify the best preparation technique for a particular tomographic scale and application. The targeted tomography techniques include hard X-ray micro- and nanotomography, electron nanotomography, and atom probe tomography. The article mainly focuses on hard condensed matter, including porous materials, alloys, and microelectronics applications, but also includes, to a lesser extent, biological considerations.

QVOA analysis: P-wave attenuation anisotropy for fracture characterization

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. C37-C48 ◽  
Author(s):  
Tatiana Chichinina ◽  
Vladimir Sabinin ◽  
Gerardo Ronquillo-Jarillo
Keyword(s):  
Wave Reflection ◽  
Wave Attenuation ◽  
Fractured Reservoirs ◽  
Anisotropy Parameter ◽  
P Wave ◽  
Fracture Parameters ◽  
Fractured Medium ◽  
Seismic Quality Factor ◽  
Pp Wave ◽  
Attenuation Anisotropy

This paper investigates [Formula: see text]-anisotropy for characterizing fractured reservoirs — specifically, the variation of the seismic quality factor [Formula: see text] versus offset and azimuth (QVOA). We derive an analytical expression for P-wave attenuation in a transversely isotropic medium with horizontal symmetry axis (HTI) and provide a method (QVOA) for estimating fracture direction from azimuthally varying [Formula: see text] in PP-wave reflection data. The QVOA formula is similar to Rüger’s approximation for PP-wave reflection coefficients, the theoretical basis for amplitude variation with angle offset (AVOA) analysis. The technique for QVOA analysis is similar to azimuthal AVO analysis. We introduce two new seismic attributes: [Formula: see text] versus offset (QVO) gradient and intercept. QVO gradient inversion not only indicates fracture orientation but also characterizes [Formula: see text]-anisotropy. We relate the [Formula: see text]-anisotropy parameter [Formula: see text] to fractured-medium parameters and invert the QVO gradient to estimate [Formula: see text]. The attenuation parameter [Formula: see text] and Thomsen-style anisotropy parameter [Formula: see text] are found to be interdependent. The attenuation anisotropy magnitude strongly depends on the host rock’s [Formula: see text] parameter, whereas the dependence on fracture parameters is weak. This complicates the QVO gradient inversion for the fracture parameters. This result is independent of the attenuation mechanism. To illustrate the QVOA method in synthetic data, we use Hudson’s first-order effective-medium model of a dissipative fractured reservoir with fluid flow between aligned cracks and random pores as a possible mechanism for P-wave attenuation.

scholarly journals Geomechanical key parameters of the process of hydraulic fracturing propagation in fractured medium

2019 ◽  
Vol 74 ◽  
pp. 58 ◽  
Author(s):  
Rouhollah Basirat ◽  
Kamran Goshtasbi ◽  
Morteza Ahmadi
Keyword(s):  
Hydraulic Fracturing ◽  
Numerical Models ◽  
Fractured Reservoirs ◽  
Natural Fracture ◽  
Propagation Path ◽  
Fracture Density ◽  
Strength Parameters ◽  
Propagation Process ◽  
Fractured Medium ◽  
Hf Propagation

Hydraulic Fracturing (HF) is a well-stimulation technique that creates fractures in rock formations through the injection of hydraulically pressurized fluid. Because of the interaction between HF and Natural Fractures (NFs), this process in fractured reservoirs is different from conventional reservoirs. This paper focuses mainly on three effects including anisotropy in the reservoir, strength parameters of discontinuities, and fracture density on HF propagation process using a numerical simulation of Discrete Element Method (DEM). To achieve this aim, a comprehensive study was performed with considering different situations of in situ stress, the presence of a joint set, and different fracture network density in numerical models. The analysis results showed that these factors play a crucial role in HF propagation process. It also was indicated that HF propagation path is not always along the maximum principal stress direction. The results of the numerical models displayed that the affected area under HF treatment is decreased with increasing the strength parameters of natural fracture and decreasing fracture intensity.

Две модели резинокордного слоя

2021 ◽  
Vol 27 (2) ◽  
pp. 191-204
Author(s):  
С. В. Шешенин ◽  
◽  
Икунь Ду ◽  
Keyword(s):  
Effective Properties ◽  
Boundary Effect ◽  
Phenomenological Approach ◽  
Elastic Potential ◽  
Homogeneous Material ◽  
Periodicity Cell ◽  
Periodic Cell ◽  
Material Parameters ◽  
Local Problems ◽  
Hyper Elastic

Breker layers in a pneumatic tire are an important part in the tire construction. These layers have a metal cord resulting in substantial bending stiffness. When homogenizing such layers, a “shave” method is applied to the breaker layer. This results in a thinner layer having adequate stiffness in both tension and bending. In this work, a phenomenological approach is used to obtain the effective properties of a homogeneous anisotropic hyper elastic material of an equivalent layer. Two models utilize transverse isotropic or orthotropic potential used to describe the homogenized properties. Comparison is made between these models for the “shaved” rubber-cord layer based on numerical experiments. In both cases, the potentials are built on the basis of the Treloar or Mooney potentials. Note that in the case of an inhomogeneous thin layer, the traditional definition of homogenization needs to be modified. In previous works of the authors, it was proposed to determine 3D averaged elastic properties of a layer by surrounding it with a homogeneous material. This makes it possible to correctly take into account the fact that the boundary effect from the upper to lower surfaces that penetrates through the whole periodicity cell. A set of local problems formulated for the periodicity cell is proposed. This set is sufficient for determining elastic potential material parameters. Nonlinear local problems on a periodic cell are solved and the material constants of the elastic potential are determined. The applicability of the orthotropic potential (second model) is determined for the “shaved” layer. It was found that orthotropic properties are manifested relative to longitudinal shears. The results show the suitability of the proposed potential and the scheme for determining the material parameters.

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