Influences of Coal Properties on the Principal Permeability Tensor during Primary Coalbed Methane Recovery: A Parametric Study

Coal permeability is intrinsically anisotropic because of the cleat structure of coal. Therefore, coal permeability can be denoted by a second-order tensor under three-dimensional conditions. Our previous paper proposed an analytical model of the principal permeability tensor of coal during primary coalbed methane (CBM) recovery. Based on this model, 18 modeling cases were considered in the present study to evaluate how the principal permeabilities were influenced by representative coal properties (the areal porosity, the internal swelling ratio, and the Young modulus) during primary CBM recovery. The modeling results show that with regard to the influences of the areal porosity on the principal permeabilities, an increase in cleat porosity reduces the sensitivity of each principal permeability to pore pressure change. The magnitudes of the principal permeabilities are positively proportional to the internal swelling ratio. The principal permeabilities thus tend to monotonically increase with a depletion in the pore pressure when the internal swelling ratio increases. Because the internal swelling ratio represents the extent of gas-sorption-induced matrix deformation, an increase in the internal swelling ratio increases desorption-induced matrix shrinkage and thus induces an increase in permeability. The principal permeabilities are positively proportional to the isotropic principal Young moduli and the synchronously changing anisotropic principal Young moduli. On the other hand, the principal Young modulus within the plane of isotropy influences the principal permeabilities within this plane in diverse patterns depending on both the dip angle of the coalbed and the pitch angle of the cleat sets. The principal permeability perpendicular to the plane of isotropy is positively proportional to this principal Young modulus, and this correlation pattern is independent of both the dip angle and pitch angle.

Defining Parameters of Shear Resistance on Oil Shale Samples

The research environment is a transversely isotropic model, which is characterized with constant physical mechanical properties in different directions in the plane of isotropy, and a different properties in the direction perpendicular to the plane of isotropy. For defining parameters of shear resistance of shale (transversely isotropic model) in three mutually perpendicular directions, it is necessary to prepare 9 (nine) samples, size (8x8x8) [c, using the Mor-Coulomb's law, where the destruction of rock happens in plane of the least resistance to shear. This paper presents results got from tests performed in geomechanical laboratory.

Further Investigation and Application of the Principle of Correspondence Between Elastic and Piezoelectric Problems

In the present work, the recently established principle of correspondence between the elastic and the piezoelectric problems for the transversely isotropic materials has been applied to obtain the solution of the problem of interaction of two tangential forces and a penny-shaped crack. The problem under consideration is described as follows: a penny-shaped crack in the unbounded piezoelectric medium is interacting with two tangential forces of the same magnitude acting in the same direction and applied arbitrarily but symmetrically with respect to the crack plane, which is a plane of isotropy. Some further investigation of the principle of correspondence is made and the important limiting conditions are stated.

Thermoelastic Equilibrium of Bodies in Generalized Cylindrical Coordinates

Using the method of separation of variables, an exact solution is constructed for some boundary value and boundary-contact problems of thermoelastic equilibrium of one- and multilayer bodies bounded by the coordinate surfaces of generalized cylindrical coordinates ρ, α, 𝑧. ρ, α are the orthogonal coordinates on the plane and 𝑧 is the linear coordinate. The body, occupying the domain Ω = {ρ 0 < ρ < ρ 1, α 0 < α < α 1, 0 < 𝑧 < 𝑧1}, is subjected to the action of a stationary thermal field and surface disturbances (such as stresses, displacements, or their combinations) for 𝑧 = 0 and 𝑧 = 𝑧1. Special type homogeneous conditions are given on the remainder of the surface. The elastic body is assumed to be transversally isotropic with the plane of isotropy 𝑧 = const and nonhomogeneous along 𝑧. The same assumption is made for the layers of the multilayer body which contact along 𝑧 = const.

Elastic fields due to defects in transversely isotropic bimaterials

A method for obtaining the analytic solution of the elastic fields due to defects such as inclusions, dislocations, disclinations, and point defects in transversely isotropic bimaterials is presented. The bimaterial consists of two semi-infinite transversely isotropic solids either perfectly bonded together or in frictionless contact with each other at a planar interface which is parallel to the plane of isotropy of both solids. The elastic solution is expressed in terms of the hexagonal stress vectors for the double force and the double force with moment. Closed form solutions for inclusions with pure dilatational eigenstrain, straight dislocation and disclination lines, circular, dislocation loops, and point defects are presented.

On the Indentation of a Transversely Isotropic Half-Space With Application to Thin Solid Lubricant Films

In this investigation, the contact between a model rigid ellipsoidal asperity and the surface of an oriented solid lubricant film has been simulated using an analysis developed previously for contact of a transversely isotropic half-space. In this case, unlike most previous work, the plane of isotropy is oriented normal to the plane of contact, instead of parallel. Under this condition, the contact patch is of a general elliptical form, depending on the shape and orientation of the model asperity and on the elastic constants of the solid lubricants. Several applicable material compositions are examined using the analysis, and the influence of asperity shape and elastic constants in relation to friction and potential design of solid lubricant formulations is discussed.

Green’s Functions for Two-Phase Transversely Isotropic Materials

Closed-form solutions are obtained for the Green’s function problems of point forces applied in the interior of a two-phase material consisting of two semi-infinite transversely isotropic elastic media bonded along a plane interface. The interface is parallel to the plane of isotropy of both media. The solutions are applicable to all combinations of elastic constants. The present solution reduces to Sueklo’s expression when the point force is normal to the plane of isotropy and (C11C33)1/2 ≠ C13 + 2C44 for both phases. When the elastic constants of one of the phases are set to zero, the solution can be reduced to the Green’s function for semi-infinite media obtained by Michell, Lekhnitzki, Hu, Shield, and Pan and Chou. The Green’s function solution of Pan and Chou for an infinite transversely isotropic solid can be reproduced from the present expression by setting the elastic constants of both phases to be equal. Finally, the Green’s function for isotropic materials can also be obtained from the present solution by suitable substitution of elastic constants.

Determination of Elastic Constants for Human Femurs

The elastic properties of the bone constituting human femurs have been determined from measurements of the velocities of ultrasonic compressional and shear waves through wet, embalmed bone samples. The bone has been shown to be a transversely isotropic material with the axis of symmetry parallel to the longitudinal axis of the bone. The values of the elastic constants were determined to be: c11=6860±330MPaE3=5500MPac12=2700±570MPaE1=4990MPac13=3760±1570MPaν31=0.39c33=8480±760MPaν12=0.20c44=2240±180MPaG31=2240MPa where the 3-axis is that of rotational symmetry and the 1- and 2-axes are in the plane of isotropy.