scholarly journals A Computational Scheme for Evaluating the Stress Field of Thermally and Pressure Induced Unconventional Reservoir

Lithosphere ◽  
2021 ◽  
Vol 2021 (Special 1) ◽  
Author(s):  
Yao Fu ◽  
Xiangning Zhang ◽  
Xiaomin Zhou
Keyword(s):  
Stress Field ◽  
Pore Pressure ◽  
Transformation Strain ◽  
Computational Scheme ◽  
Unconventional Reservoir ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
Eshelby Inclusion ◽  
Fluid Production ◽  
Unconventional Resource

Abstract The fluid flow connecting the hydraulic fracture and associated unconventional gas or oil reservoir is of great importance to explore such unconventional resource. The deformation of unconventional reservoir caused by heat transport and pore pressure fluctuation may change the stress field of surrounding layer. In this paper, the stress distribution around a penny-shaped reservoir, whose shape is more versatile to cover a wide variety of special case, is investigated via the numerical equivalent inclusion method. Fluid production or hydraulic injection in a subsurface resource caused by the change of pore pressure and temperature within the reservoir may be simulated with the help of the Eshelby inclusion model. By employing the approach of classical eigenstrain, a computational scheme for solving the disturbance produced by the thermally and pressure induced unconventional reservoir is coded to study the effect of Biot coefficient and some other important factors. Moreover, thermo-poro transformation strain and arbitrarily orientated reservoir existing within the surrounding layer are also considered.

On the dynamic generalization of the anisotropic Eshelby ellipsoidal inclusion and the dynamically expanding inhomogeneities with transformation strain

2016 ◽  
Vol 01 (03n04) ◽  
pp. 1640001 ◽  
Author(s):  
Xanthippi Markenscoff
Keyword(s):  
Spherical Inclusion ◽  
Transformation Strain ◽  
Positive Definiteness ◽  
Equivalent Transformation ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
Chemical Phase ◽  
Eshelby Inclusion ◽  
Interior Domain

The self-similarly dynamically (subsonically) expanding anisotropic ellipsoidal Eshelby inclusion is shown to exhibit the constant stress “Eshelby property” in the interior domain of the expanding inclusion on the basis of dimensional analysis, analytic properties and the proof for the static inclusion alone. As an example of this property and the application of the dynamic Eshelby tensor (constant in the interior domain), it is shown that the Eshelby equivalent inclusion method always allows for the determination of the equivalent transformation strain for a self-similarly dynamically expanding inhomogeneous spherical inclusion when the Poisson's ratio is in the real range (positive definiteness of the strain energy). Thus, the solution of dynamically self-similarly expanding inhomogeneities (chemical phase change) with transformation strain can be obtained, as well as the driving force per unit area of the expanding inhomogeneity.

The Stress Field and Intensity Factor due to Crazes Formed at the Poles of a Spherical Inhomogeneity

1994 ◽  
Vol 61 (4) ◽  
pp. 803-808 ◽  
Author(s):  
Z. M. Xiao ◽  
K. D. Pae
Keyword(s):  
Stress Intensity Factor ◽  
Intensity Factor ◽  
Stress Field ◽  
Elastic Moduli ◽  
Superposition Principle ◽  
Numerical Examples ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
The Matrix ◽  
Good Agreement

The problem of two penny-shaped crazes formed at the top and the bottom poles of a spherical inhomogeneity has been investigated. The inhomogeneity is embedded in an infinitely extended elastic body which is under uniaxial tension. Both the inhomogeneity and the matrix are isotropic but have different elastic moduli. The analysis is based on the superposition principle of the elasticity theory and Eshelby’s equivalent inclusion method. The stress field inside the inhomogeneity and the stress intensity factor on the boundary of the craze are evaluated in the form of a series which involves the ratio of the radius of the penny-shaped craze to the radius of the spherical inhomogeneity. Numerical examples show the interaction between the craze and the inhomogeneity is strongly affected by the elastic properties of the inhomogeneity and the matrix. The conclusion deduced from the numerical results is in good agreement with experimental results given in the literature.

Asymptotic Solutions of Penny-Shaped Inhomogeneities in Global Eshelby’s Tensor

2001 ◽  
Vol 68 (5) ◽  
pp. 740-750 ◽  
Author(s):  
Q. Yang ◽  
W. Y. Zhou ◽  
G. Swoboda
Keyword(s):  
Stress Field ◽  
Three Dimensional ◽  
Uniform Stress ◽  
Isotropic Matrix ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Equivalent Inclusion ◽  
Asymptotic Expressions ◽  
Eshelby’S Tensor ◽  
Uniform Stress Field

In this paper, a three-dimensional penny-shaped isotropic inhomogeneity surrounded by unbounded isotropic matrix in a uniform stress field is studied based on Eshelby’s equivalent inclusion method. The solution including the deduced equivalent eigenstrain and its asymptotic expressions is presented in tensorial form. The so-called energy-based equivalent inclusion method is introduced to remove the singularities of the size and eigenstrain of the Eshelby’s equivalent inclusion of the penny-shaped inhomogeneity, and yield the same energy disturbance. The size of the energy-based equivalent inclusion can be used as a generic damage measurement.

scholarly journals The dynamic generalization of the Eshelby inclusion problem and its static limit

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160256 ◽  
Author(s):  
Luqun Ni ◽  
Xanthippi Markenscoff
Keyword(s):  
Integral Form ◽  
Transformation Strain ◽  
The Self ◽  
Eshelby Tensor ◽  
Inclusion Problem ◽  
Static Limit ◽  
Governing System ◽  
Eshelby Inclusion ◽  
Interior Domain ◽  
Eshelby Problem

The dynamic generalization of the celebrated Eshelby inclusion with transformation strain is the (subsonically) self-similarly expanding ellipsoidal inclusion starting from the zero dimension. The solution of the governing system of partial differential equations was obtained recently by Ni & Markenscoff (In press. J. Mech. Phys. Solids ( doi:10.1016/j.jmps.2016.02.025 )) on the basis of the Radon transformation, while here an alternative method is presented. In the self-similarly expanding motion, the Eshelby property of constant constrained strain is valid in the interior domain of the expanding ellipsoid where the particle velocity vanishes (lacuna). The dynamic Eshelby tensor is obtained in integral form. From it, the static Eshelby tensor is obtained by a limiting procedure, as the axes' expansion velocities tend to zero and time to infinity, while their product is equal to the length of the static axis. This makes the Eshelby problem the limit of its dynamic generalization.

A Method to Evaluate the Elastic Properties of Ceramics-Enhanced Composites Undertaking Interfacial Delamination

2007 ◽  
Vol 336-338 ◽  
pp. 2513-2516
Author(s):  
Hua Jian Chang ◽  
Shu Wen Zhan
Keyword(s):  
Composite Materials ◽  
Present Method ◽  
Present Model ◽  
Constitutive Law ◽  
Layer Model ◽  
Interfacial Delamination ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
Micromechanical Approach ◽  
Properties Of Composites

A micromechanical approach is developed to investigate the behavior of composite materials, which undergo interfacial delamination. The main objective of this approach is to build a bridge between the intricate theories and the engineering applications. On the basis of the spring-layer model, which is useful to treat the interfacial debonding and sliding, the present paper proposes a convenient method to assess the effects of delamination on the overall properties of composites. By applying the Equivalent Inclusion Method (EIM), two fundamental tensors are derived in the present model, the modified Eshelby tensor, and the compliance tensor (or stiffness tensor) of the weakened inclusions. Both of them are the fundamental tensors for constructing the overall constitutive law of composite materials. By simply substituting these tensors into an existing constitutive model, for instance, the Mori-Tanaka model, one can easily evaluate the effects of interfacial delamination on the overall properties of composite materials. Therefore, the present method offers a pretty convenient tool. Some numerical results are carried out in order to demonstrate the performance of this model.

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