Thin Inclusions Research Articles

Effect of authigenic clay minerals and carbonate cements on quality of tight sandstone reservoirs: Insight from Triassic tight sandstones in the Huaqing area, Ordos Basin, Northern China

• Pore and throat structure can be characterized separately by XCT scanning. • Chlorite and illite produced most of the intercrystalline pores in tight sandstone . • Chlorite coatings are effective in preserving the large primary pore-throat. • The densification was completed by cementation instead of compaction. • Tight sandstone with high chlorite is the best quality reservoir in the Ordos Basin. As an important part of tight sandstone, authigenic clay minerals and carbonate cements have a strong influence on the densify of tight sandstone, but the details of these effects on pores and throats need be further clarified. The Ordos Basin is the second-largest sedimentary basin in China with the highest annual oil output and is characterized by tight sandstone. In this paper, the thin section, HPMI, XCT scanning and fluid inclusion homogenization temperature were combined to study the densification process of the tight sandstone in the Ordos Basin. The results show that early chlorite coating can effectively reduce further damage to the pore-throat space. But the pore-lining chlorite and illite led to reduce of the radius of intercrystalline micropores to <1 μm. After mechanical compaction, authigenic illite and the late ferrocalcite and ferrodolomite cements continued to grow and eventually complete the densification. Authigenic clay minerals and carbonate cements played contrasting role on evolving of pores and throats: tight sandstone with high chlorite showed obvious “right peak” PSD and TSD in XCT scanning with the largest number of throats, formed the best-quality reservoir; tight sandstone with high carbonate cement suggesting flat “right peak” TSD and increased the average length of throats; tight sandstone with high illite showed flat and “left shift” PSD and obvious “bimodal” TSD with the fewest number of throats, and formed the worst-quality reservoir.

Nonlinear Evolutionary Problem of Filtration Consolidation With the Non-Classical Conjugation Condition

Finite-element solutions of the initial-boundary value problem for a nonlinear parabolic equation in an inhomogeneous domain with the conjugation condition of a non-ideal contact were found. The initial boundary value problem is a mathematical model of an important technical problem of filtration consolidation of inhomogeneous soils. Inhomogeneity is considered in terms of the presence of thin inclusions, physicochemical characteristics of which differ from those of the main soil. The problem of longterm consolidation is especially pronounced in soils with low filtration coefficient. Low permeability of the porous medium causes deviation from the linear relationship between the pressure gradient and the filtration rate.Weak formulation of the problem is suggested, and the accuracy of the approximate finite element solution, its existence and uniqueness are substantiated for the case of Darcy’s nonlinear law. A test example and the effect of the nonlinear filtration law for thin inclusion on the dynamics of scattering of excess pressures in the entire area of the problem are considered.

Effect of the orientation distribution of thin highly conductive inhomogeneities on the overall electrical conductivity of heterogeneous material

Many natural composite materials contain systems of partially oriented thin low-resistivity inclusions (for example, water-saturated microcracks in a double porosity sedimentary formation). We have calculated the components of the electrical conductivity tensor of such materials as a function of crack density. The results were obtained for thin ellipsoidal inclusions with conductivity (electrical or thermal) much larger than the matrix conductivity. To calculate the effective conductivity, we have used the effective field method (EFM). We have obtained the explicit expressions for the effective parameters of inhomogeneous materials. The application of the EFM allows one to describe the influence of the peculiarities in the spatial distribution of inclusions on the effective properties of the medium. General explicit expressions, obtained in this work, are illustrated by calculation examples for inclusions, homogeneously distributed in the sector [-Beta, Beta], where Beta is the disorientation angle, and some continuous angle distribution functions. The calculations have shown that the spatial distribution of the crack-like inclusions strongly affects the conductive properties of the effective medium and the symmetry of their tensor.

Optimal control of thin elastic inclusion in an elastic body

Optimal control of thin elastic inclusion in an elastic body

Deformation and Strength Parameters of a Composite Structure with a Thin Multilayer Ribbon-like Inclusion.

Within the framework of the concept of deformable solid mechanics, an analytical-numerical method to the problem of determining the mechanical fields in the composite structures with interphase ribbon-like deformable multilayered inhomogeneities under combined force and dislocation loading has been proposed. Based on the general relations of linear elasticity theory, a mathematical model of thin multilayered inclusion of finite width is constructed. The possibility of nonperfect contact along a part of the interface between the inclusion and the matrix, and between the layers of inclusion where surface energy or sliding with dry friction occurs, is envisaged. Based on the application of the theory of functions of a complex variable and the jump function method, the stress-strain field in the vicinity of the inclusion during its interaction with the concentrated forces and screw dislocations was calculated. The values of generalized stress intensity factors for the asymptotics of stress-strain fields in the vicinity of the ends of thin inhomogeneities are calculated, using which the stress concentration and local strength of the structure can be calculated. Several effects have been identified which can be used in designing the structure of layers and operation modes of such composites. The proposed method has shown its effectiveness for solving a whole class of problems of deformation and fracture of bodies with thin deformable inclusions of finite length and can be used for mathematical modeling of the mechanical effects of thin FGM heterogeneities in composites.

Non-coercive problems for Kirchhoff–Love plates with thin rigid inclusion

Non-coercive problems for Kirchhoff–Love plates with thin rigid inclusion

Signorini-Type Problems over Non-Convex Sets for Composite Bodies Contacting by Sharp Edges of Rigid Inclusions

A new type of non-classical 2D contact problem formulated over non-convex admissible sets is proposed. Specifically, we suppose that a composite body in its undeformed state touches a wedge-shaped rigid obstacle at a single contact point. Composite bodies under investigation consist of an elastic matrix and a rigid inclusion. In this case, the displacements on the set, corresponding to a rigid inclusion, have a predetermined structure that describes possible parallel shifts and rotations of the inclusion. The rigid inclusion is located on the external boundary and has the form of a wedge. The presence of the rigid inclusion imposes a new type of non-penetration condition for certain geometrical configurations of the obstacle and the body near the contact point. The sharp-shaped edges of the obstacle effect such sets of admissible displacements that may be non-convex. For the case of a thin rigid inclusion, which is described by a curve and a volume (bulk) rigid inclusion specified in a subdomain, the energy minimization problems are formulated. The solvability of the corresponding boundary value problems is proved, based on analysis of auxiliary minimization problems formulated over convex sets. Qualitative properties of the auxiliary variational problems are revealed; in particular, we have found their equivalent differential formulations. As the most important result of this study, we provide justification for a new type of mathematical model for 2D contact problems for reinforced composite bodies.

EFFECT OF POURING TEMPERATURE AND DEGASSING ON THE CASTING QUALITY OF Al 6061: EXPERIMENTAL AND NUMERICAL STUDY

As one of important components of an airplane, body of airplane is required to have high value of strength to weight ratio. In this study, transient heat transfer of Al 6061 in a sand casting process was investigated both experimentally and numerically. The effects of different pouring temperatures (700, 720 and 740 °C) and presence of thin film and H2 inclusions are considered in the present study. Composition, XRD, metallography and tensile strength tests have been carried out to examine the casting product quality, before and after degassing, a process to remove the inclusions from the cast. Correspondingly, heat transfer simulations were carried out by taking into account the variation of pouring temperatures and the presence of inclusions. From the present experimental and numerical study, it was found that: (i) Degassing enhanced significantly the strength of Al 6061 product. The highest tensile strength value has been found to be 64.30 MPa, related to the pouring temperature of 700 °C with degassing, while the lowest one is 35.85 MPa associated with the pouring temperature of 700 °C without degassing . (ii) Pouring temperature did not affect significantly to the strength of Al 6061 product, especially when degassing process was carried out, and (iii) The presence of thin film and hydrogen gas inclusions affected the cooling rate of the metal slab. Overall, the cooling of the metal slab with thin film inclusion became slower, while the cooling of the metal slab with hydrogen gas inclusions became faster.

Mathematical modeling of the dynamic interaction of thin piezoceramic inclusion with elastic medium at axisymmetric torsion of the composite

Mathematical modeling of the dynamic interaction of thin piezoceramic inclusion with elastic medium at axisymmetric torsion of the composite

3D-1D coupling on non conforming meshes via a three-field optimization based domain decomposition

A new numerical approach is proposed for the simulation of coupled three-dimensional and one-dimensional elliptic equations (3D-1D coupling) arising from dimensionality reduction of 3D-3D problems with thin inclusions. The method is based on a well posed mathematical formulation and results in a numerical scheme with high flexibility in handling geometrical complexities. This is achieved by means of a three-field approach to split the 1D problems from the bulk 3D problem, and then resorting to the minimization of a properly designed functional to impose matching conditions at the interfaces. Thanks to the structure of the functional, the method allows the use of independent meshes for the various subdomains.

Elastic equilibrium of anisotropic bimaterial bodies with thin elastic anisotropic inclusions under longitudinal shear

Elastic equilibrium of anisotropic bimaterial bodies with thin elastic anisotropic inclusions under longitudinal shear

Effect of Frictional Slipping on the Strength of Ribbon-Reinforced Composite.

A numerical–analytical approach to the problem of determining the stress–strain state of bimaterial structures with interphase ribbon-like deformable inhomogeneities under combined force and dislocation loading has been proposed. The possibility of delamination along a part of the interface between the inclusion and the matrix, where sliding with dry friction occurs, is envisaged. A structurally modular method of jump functions is constructed to solve the problems arising when nonlinear geometrical or physical properties of a thin inclusion are taken into account. A complete system of equations is constructed to determine the unknowns of the problem. The condition for the appearance of slip zones at the inclusion–matrix interface is formulated. A convergent iterative algorithm for analytical and numerical determination of the friction-slip zones is developed. The influence of loading parameters and the friction coefficient on the development of these zones is investigated.

Effective conductivity of anisotropic media with crack-like inclusions and cracks of arbitrary shapes

The effective field method is applied to solution of the homogenization problem for anisotropic media containing random sets of thin inclusions of low conductivity (crack-like inclusions) or cracks. The derived expression for the tensor of effective conductivity of cracked media on the one hand, takes into account peculiarities of shapes and conductivity of thin inclusions, and on the other hand, reflect statistical properties of the inclusion distributions in the host medium. The crucial part of realization of the method is solution of the so-called one-particle problem that is the conductivity problem for an isolated inclusion embedded into an anisotropic host medium and subjected to a constant external field. This problem is reduced to solution of the integral equation for the potential jump on the middle surface of a thin inclusion. An efficient numerical method of solution of this equation is proposed. The integral equation is discretized by Gaussian approximating functions and reduced to a linear algebraic system for the coefficients of the approximation (the discretized problem). For Gaussian functions, the elements of the matrix of the discretized problem are calculated in explicit analytical forms (for isotropic host media) or they reduce to a standard 1D-integral (for arbitrary anisotropic host media) that can be tabulated. As a result, the matrix of the discretized problem is calculated fast. For inclusions with planar middle surfaces and regular grids of approximated nodes, this matrix has Toeplitz’ structure, and fast Fourier transform algorithm can be used for iterative solution of the discretized problem. The cases of a strongly anisotropic medium with circular, annular and square cracks are considered. Examples of solution of the homogenization problems for the medium containing cracks of various shapes are presented.

Generalized Solvability of a Parabolic Model Describing Transfer Processes in Domains with Thin Inclusions

Generalized Solvability of a Parabolic Model Describing Transfer Processes in Domains with Thin Inclusions

Erratum to: Asymptotic Justification of the Models of Thin Inclusions in an Elastic Body in the Antiplane Shear Problem

Erratum to: Asymptotic Justification of the Models of Thin Inclusions in an Elastic Body in the Antiplane Shear Problem

The problem of the partial delamination of the elastic interface thin inclusion in the conditions of longitudinal shear of the bimaterial

The problem of longitudinal displacement of a bi -material with a thin inclusion of arbitrary physical and mechanical nature at the interface of the matrix materials is considered. The bulk is loaded by normal compression and various force factors in the longitudinal direction. The possibility of partial delamination of a part of the boundary between the inclusion and the matrix, where dry friction slip occurs, is assumed. A complete system of equations for the formulated problem is constructed. It is proposed to construct the solution using the structural modular method of jump functions, a description of which is given. A condition for the appearance of a slip zone on the inclusion-matrix boundary is founded. A convergent iterative algorithm for numerically analytical determination of the size of this zone is developed.

Stress state near the cracks coming out from the ends of a thin rigid inclusion that is caused by the action of longitudinal shear waves

Stress state near the cracks coming out from the ends of a thin rigid inclusion that is caused by the action of longitudinal shear waves

An Iterative Method for Solving the Problem of Diffraction of Longitudinal Shear Waves on A System of Thin Rigid Inclusions

An Iterative Method for Solving the Problem of Diffraction of Longitudinal Shear Waves on A System of Thin Rigid Inclusions

Analytical model for miniaturized patch antenna on metaferrite-like substrate

In this study, a 2-D mathematical model of a high-directive microwave antenna with a miniaturized volume profile is developed analytically. The antenna is a rectangular patch antenna on a metaferrite substrate. The substrate is a parallelepiped-shaped dielectric matrix with periodically embedded thin cylindrical ferromagnetic inclusions of a circular cross section. It is assumed that the inclusions are fully or partially magnetized by an external DC bias magnetic field. It has been shown that the use of such a metamaterial substrate, instead of a dielectric one with the same values of permittivity and permeability, leads to a miniaturization of the volume profile of the antenna and an increase in its efficiency and power gain. The commercial electromagnetic software is used in the study to validate the proposed antenna model.

Modeling of deformation of the bimaterial with thin Non-linear interface inclusion

An incremental approach to solving the antiplane problem for bimaterial media with a thin, physically nonlinear inclusion placed on the materials interface is discussed. Using the jump functions method and the coupling problem of boundary values of the analytical functions method we reduce the problem to the system of singular integral equations (SSIE) on jump functions with variable coefficients allowing us to describe any quasi-static loads (monotonous or not) and their influence on the stress-strain state in the bulk. To solve the SSIE problem, an iterative analytical-numerical method is offered for various non-linear deformation models. Numerical calculations are carried out for different values of non-linearity characteristic parameters for the inclusion material. Their parameters are analyzed for a deformed body under a load of a balanced concentrated force system.