Michio Kurashige

SIMULATED EFFECTIVE THERMAL CONDUCTIVITY OF SINTERED, RANDOMLY PACKED SPHERES AND STATISTICAL STRUCTURES OF PACKINGS

Effective thermal conductivity of sintered spherical particles is estimated by a computer simulation. The simulation consists of (i)simulated random packing of equal spheres by a method of rigid sphere free fall into a virtual box, (ii) finite element method (FEM) estimation of the thermal resistance of a sintered pair of spheres, and (iii) simulated heat conduction tests of a random network, as a model of sintered particles, of thermal resistors with the estimated resistance; these tests yield the effective conductivity of sintered spherical particle aggregates. Statistical structures of the random packings of spheres are examined. The random packings constructed are standard loose random packings. The cumulative diameter distribution of circles appearing on cross-sections of the packings is in complete agreement with the theoretical prediction for all three orthogonal directions, implying that the packing structures are isotropic. And, despite this result, the zenithal distribution of branch ori...

Simulated effect of box size and wall on porosity of random packings of spherical particles

SummaryEffects of the size of the box which spherical particles are deposited into on the porosity of a resulting particle aggregate have been simulated and examined, particularly to find out if the extrapolation method often used by experimenters is certainly right; this method is based on the empirical fact that the porosity is inversely proportional to the box size. The simulation justified the inverse proportionality and demonstrated that the porosity obtained by the simulated extrapolation coincides with that by the simulation with use of conventional cyclic boundary conditions. This coincidence implies the extrapolation gives the right experimental results of porosities and also that the conventional cyclic boundary condition method is a really strong method to construct a random packing of “infinite” extent by simulation. An effect of the box wall has also been explored in view of area porosisties and cumulative distribution of diameters of circles appearing on aggregate cross-sections. Furthermore, slopes of the straight line of the porosity versus ratio of the particle diameter to the box size have been discussed in terms of two statistical geometry models.

Simulated Effective Elastic Moduli and Wave Velocities in Water-Saturated Sintered Glass-Beads

SummaryEffective elastic moduli of sintered glass-beads and wave phase velocities in this sintered material saturated by water are estimated by a computer simulation. The simulation consists of (A) simulated random packing of equal spheres, (B) FEM estimation of the spring constants of 6 degrees of freedom for a “sintered” pair of spheres, and (C) simulated tensile tests of a “random network”, as a model of sintered glass-beads, of springs with the estimated spring constants; these tests yield the effective elastic moduli of sintered spherical particle aggregates. And (D) use of these moduli in Biots simplified formulae gives phase velocities for the first compressional and shear bulk waves. Results of the simulation are compared with the estimates based on the self-consistent models and those by experiments. The simulated results are in good agreement with the experimental ones.

Mechanical response of a water-saturated core sample under opposite diametrical loadings

SummaryBy use of the theory of poroelasticity, the analytical solutions were obtained for mechanical responses of a water-saturated core sample subjected to opposite diametrical loadings that vary like a step function of time (Problem I) and a linearly increasing function of time (Problem II). These loadings correspond to elastic moduli tests (by Hondros) and indirect tensile strength tests (the Brazilian tests) of dry brittle materials, respectively. The analysis showed how the diffusion of pore fluid affects these tests, if the tests are carried out for fluid-saturated samples. Furthermore, the accuracy of the Stehfest numerical Laplace inversion was checked based on the analysis. In addition, a method of determining poroelastic moduli was proposed.

Analysis of ink flow in a mimeograph printer based on the mechanics of fluid-filled poroelastic solids

SummaryTo understand some main ink flow mechanisms in a mimeograph printer, the continuum mechanics theory of fluid-saturated porous solids is applied to analyze the ink flow through screens and a printing master, which are modeled by a fluid-filled poroelastic single layer. The layer is assumed to be pressed by a press roller from below and to be subjected from above to the hydrodynamic lubrication pressure induced between a printing drum and an ink roller. Nonlinear elasticity of the layer and dependence of the permeability on its deformation are taken into account. The numerical results show some important results: e.g., squeezing-out of the ink from the layer by the layer compaction by the press roller plays an important role, especially for the case where the compression duration is small in comparison with the characteristic time of the ink-filled poroelastic layer.

Finite shearing of a FRR block with a circular hole

SummaryBy using the idealized theory of fiber-reinforced materials, an exact equilibrium solution is obtained for the finite shearing of a rubber block reinforced by fibers in the shearing direction and weakened by a circular hole. Deformed configurations of the hole and block ends are obtained in explicit forms. It is found that the infinite normal stress occurs along the fiber lines tangent to the hole while the infinite hydrostatic pressure along the normal lines tangent to the hole. The edge stress around the hole obtained in an explicit form can be reduced to that given by the infinitesimal theory of anisotropic elasticity for the infinite ratio of elastic moduli when the block is infinite in length. These results are also presented in the figures.

Integral Equations for a 3D Crack in a Fluid-Saturated Poroelastic Infinite Space of Transversely Isotropic Permeability. Case of Anisotropy Axis Perpendicular to Crack Face.

A pair of integral equations are derived for a non-uniformly pressurized vertical planar crack of arbitrary shape in a fluid-saturated, poroelastic, infinite space of transversely isotropic permeability with its anisotropy axis perpendicular to crack surface, by using the fundamental solutions obtained in a previous paper and the concept of a dislocation segment. This anisotropy assumption is more realistic for many oil reservoirs. The equations obtained relate normal tractions and fluid pressure on the crack faces to crack opening gradients and fluid injection rate per unit fracture area and include the known integral equations for an isotropic permeability as a limiting case. These integral equations are intended to be implanted in a 3D hydraulic fracturing simulator.

ROUGH SIZE ESTIMATION OF A THERMALLY FRACTURED ZONE IN AN INFINITE HOT ROCK MASS

Abstract Concerning the extraction of geothermal energy from a deep thermal reservoir by the downhole coaxial heat exchanger with a thermally insulated inner pipe proposed by Morita et al, we obtained rough estimates of a size of the fractured zone induced by thermal stresses due to injecting cold water into the hot rock mass through the pipe. We assumed complete spherical symmetry of the temperature and stress fields. At the rough estimation, we considered three typical or extreme cases. (1) The fracturing affects neither the loading capacity of a fractured rock mass nor the temperature distribution within the formation. (2) The fractured zone completely loses its loading capacity and is fully invaded by the borehole water. No disturbance of the fracturing makes any difference in the temperature. (3) The rock formation is assumed to have an appropriately increased fictitious conduction substituted for the heat transfer enhanced by the expected convection within the fractured zone in order to discuss the ...