Derivation of the Diphasic Biot’s Law for an Elastic Solid Matrix Containing Isolated Fluid Drops

2002 ◽  
pp. 151-160
Author(s):  
Thierry Clopeau ◽  
Jose Luis Ferrín ◽  
Andro Mikelic
Keyword(s):  
Elastic Solid ◽  
Solid Matrix

The Role of Terzaghi Effective Stress in Linearly Elastic Deformation

1983 ◽  
Vol 105 (4) ◽  
pp. 509-511 ◽  
Author(s):  
M. M. Carroll ◽  
N. Katsube
Keyword(s):  
Elastic Deformation ◽  
Effective Stress ◽  
Linear Elasticity ◽  
Simple Form ◽  
Pore Space ◽  
Elastic Solid ◽  
Solid Matrix ◽  
Pore Geometry ◽  
Average Strain

It has been shown that the overall strain of a fluid-filled porous elastic solid is not governed by the Terzaghi effective stress law. We show, in the context of anisotropic linear elasticity, that the overall strain may be resolved into a component which is the average strain of the solid matrix and a component due to change in relative pore geometry, and that the latter is determined by the Terzaghi effective stress. This leads to a simple form of the response laws and, in particular, to effective stress laws for overall strain (obtained previously) and for strain of the pore space.

Slug tests in a confined aquifer: experimental results in a large soil tank and numerical modeling

2002 ◽  
Vol 39 (1) ◽  
pp. 14-21 ◽  
Author(s):  
Robert P Chapuis ◽  
Djaouida Chenaf
Keyword(s):  
Numerical Modeling ◽  
Elastic Solid ◽  
Conservation Equation ◽  
Solid Matrix ◽  
Confined Aquifer ◽  
Slug Test ◽  
Slug Tests ◽  
Variable Head ◽  
Large Tank ◽  
Straight Lines

Variable-head (slug) tests in a confined aquifer can be interpreted using different methods that either consider or neglect the influence of the instantaneous deformation of an elastic solid matrix. This paper defines a unified interpretation for slug tests: it is based on the velocity graph describing the conservation equation underlying all methods. If the storativity S has no influence, the velocity graph is a straight line. If S has an influence, the theory considering this influence predicts the graph should be a curve. Numerous slug tests were performed in a large tank containing a confined aquifer. Other tests were used to determine independently the transmissivity T and S values of the confined aquifer which are compared with those obtained from slug tests. The velocity graphs of the slug tests provided straight lines instead of the smooth curves as predicted by the theory. A numerical analysis of these tests in the sand tank was performed using a finite element method. The analysis gave straight lines instead of curves for any S value and therefore confirmed the experimental observation (in velocity graphs) that slug test results do not depend of S and thus cannot be used to determine the S value.Key words: slug test, hydraulic conductivity, storativity, numerical modeling.

Rheological Model for a Nanoporous-Elasto-Hydrodynamic Composite Material

2013 ◽  
Vol 750 ◽  
pp. 100-103
Author(s):  
Claudiu Valentin Suciu ◽  
Shuuhei Fukui
Keyword(s):  
Composite Material ◽  
Rheological Model ◽  
Elastic Solid ◽  
Solid Matrix ◽  
Water Repellent ◽  
Water Molecules ◽  
Linear Elastic ◽  
Micro Particles ◽  
Hydrogel Matrix ◽  
Phase Water

This work proposes a rheological model for a nanoporous-elasto-hydrodynamic composite material (NPEHDCM), which can be obtained by mixing a colloid, consisted of water and water-repellent nanoporous silica micro-particles, with an adequate jellification agent. Hydrogel is modeled as a biphasic mixture consisted of a nanoporous hydrophilic isotropic and linear elastic solid matrix, and a liquid phase (water). At dynamic pressurization, water molecules exude from the hydrogel matrix and forcedly penetrate the nanopores of hydrophobic silica particles. Based on the proposed rheological model, the NPEHDCM can be suitably designed.

An Analysis of the Unconfined Compression of Articular Cartilage

1984 ◽  
Vol 106 (2) ◽  
pp. 165-173 ◽  
Author(s):  
C. G. Armstrong ◽  
W. M. Lai ◽  
V. C. Mow
Keyword(s):  
Fluid Flow ◽  
Articular Cartilage ◽  
Fluid Pressure ◽  
Constant Strain Rate ◽  
Elastic Solid ◽  
Solid Matrix ◽  
Unconfined Compression ◽  
Creep Stress ◽  
Internal Fluid ◽  
Equilibrium Response

Analytical solutions have been obtained for the internal deformation and fluid-flow fields and the externally observable creep, stress relaxation, and constant strain-rate behaviors which occur during the unconfined compression of a cylindrical specimen of a fluid-filled, porous, elastic solid, such as articular cartilage, between smooth, impermeable plates. Instantaneously, the “biphasic” continuum deforms without change in volume and behaves like an incompressible elastic solid of the same shear modulus. Radial fluid flow then allows the internal fluid pressure to equilibrate with the external environment. The equilibrium response is controlled by the Young’s modulus and Poisson’s ratio of the solid matrix.

Injection of Fluid Into a Layer of Deformable Porous Medium

1995 ◽  
Vol 48 (10) ◽  
pp. 722-726 ◽  
Author(s):  
Steven Barry ◽  
Geoffrey Aldis ◽  
Geoffry Mercer
Keyword(s):  
Porous Material ◽  
Point Source ◽  
Elastic Solid ◽  
Hankel Transform ◽  
Solid Matrix ◽  
Governing Equations ◽  
Elastic Parameters ◽  
Subcutaneous Injections ◽  
Deformable Porous Medium ◽  
One Dimensional

The flow of fluid from a point source into a layer of deformable porous material is considered. The main applications of this work are to subcutaneous injections and subterranean soil flows. The porous material is assumed to be an isotropic, homogeneous, linearly elastic solid. The governing equations are derived for an axisymmetric geometry using linear poro-elasticity and are applied to the situation of a point source at some height z = z0 with a line sink at a distance r = ρ. These are solved analytically using Hankel transform techniques with the Hankel inversion integrals calculated numerically. Results are given for the pressure contours and the displacement of the solid matrix for a variety of source heights and elastic parameters. These indicate the swelling of the medium and subsequent deformation of the free surface. Results indicate regions where one dimensional models may be applicable.

SYNTHETIC MICROSEISMOGRAMS: LOGGING IN POROUS FORMATIONS

Geophysics ◽  
1974 ◽  
Vol 39 (1) ◽  
pp. 14-32 ◽  
Author(s):  
J. H. Rosenbaum
Keyword(s):  
Narrow Band ◽  
Numerical Study ◽  
Wave Train ◽  
Elastic Solid ◽  
Wide Band ◽  
Plane Interface ◽  
Solid Matrix ◽  
Stoneley Wave ◽  
Biot’S Theory ◽  
Biot's Theory

Biot’s theory of wave propagation in a fluid‐filled porous elastic solid takes account of energy dissipation due to relative motion between viscous pore fluid and solid matrix. This theory has been applied to a numerical study of sound pulses propagating along a cylindrical borehole and along a plane interface. It is found that properties such as permeability affect the attenuation of the signal only at high frequencies. For the plane interface, the effect on the P-arrival is small; on the S-arrival it is moderate; and on the Stoneley‐wave it is large, but only if source and detector are close to the interface and the flow of fluid across the interface is relatively unrestricted. With a wide‐band signal, the low‐frequency pseudo‐Rayleigh wave can partially mask the S-arrival. Similar conclusions hold for the logging tool centered in the borehole, and arrivals other than the first P may be difficult to pick, especially for narrow‐band signals. The amplitude of the wave train arriving with approximately the tube‐wave velocity is particularly sensitive to the fluid‐transfer conditions at the borehole wall. The results suggest that acoustic permeability logging tools require high‐frequency signals: their performance could depend critically on the acoustic characteristics of mud cake in situ. Narrow‐band signals are not suitable for the identification of phases other than the first P-arrival; attenuation measurements probably must be based on the energies observed in gated sections of the pressure response. For signals in the seismic range, inelastic effects predicted by Biot’s theory are too small for the detection of formation properties, especially when thin impermeable beds are also present.

In situ TEM observations of melting in nanosized eutectic Pb-Cd inclusions embedded in Al

1996 ◽  
Vol 54 ◽  
pp. 986-987
Author(s):  
S. Hagège ◽  
U. Dahmen ◽  
E. Johnson ◽  
A. Johansen ◽  
V.S. Tuboltsev
Keyword(s):  
Electron Microscope ◽  
Melt Spinning ◽  
Ternary Alloys ◽  
Solid Matrix ◽  
Eutectic System ◽  
In Situ Tem ◽  
In Situ Observation ◽  
Orientation Relationships ◽  
Transmission Electron

Small particles of a low-melting phase embedded in a solid matrix with a higher melting point offer the possibility of studying the mechanisms of melting and solidification directly by in-situ observation in a transmission electron microscope. Previous studies of Pb, Cd and other low-melting inclusions embedded in an Al matrix have shown well-defined orientation relationships, strongly faceted shapes, and an unusual size-dependent superheating before melting.[e.g. 1,2].In the present study we have examined the shapes and thermal behavior of eutectic Pb-Cd inclusions in Al. Pb and Cd form a simple eutectic system with each other, but both elements are insoluble in solid Al. Ternary alloys of Al (Pb,Cd) were prepared from high purity elements by melt spinning or by sequential ion implantation of the two alloying additions to achieve a total alloying addition of up to lat%. TEM observations were made using a heating stage in a 200kV electron microscope equipped with a video system for recording dynamic behavior.

The internal stability of an elastic solid

2000 ◽  
Vol 80 (12) ◽  
pp. 2827-2840 ◽  
Author(s):  
J. W. Morris Jr, C. R. K Renn
Keyword(s):  
Elastic Solid ◽  
Internal Stability

Stabilization of pH in Solid-matrix Hydroponic Systems

HortScience ◽  
1993 ◽  
Vol 28 (10) ◽  
pp. 981-984 ◽  
Author(s):  
Jay Frick ◽  
Cary A. Mitchell
Keyword(s):  
Seed Yield ◽  
Seed Oil ◽  
Exchange Resin ◽  
Cation Exchange Resin ◽  
Solid Matrix ◽  
Resin Bead ◽  
Resin Beads ◽  
Hydroponic Systems ◽  
Ethanesulfonic Acid ◽  
Substrate Ph

2-[N-morpholino] ethanesulfonic acid (MES) buffer or Amberlite DP-1 (cation-exchange resin beads) were used to stabilize substrate pH of passive-wicking, solid-matrix hydroponic systems in which small canopies of Brassica napus L. (CrGC 5-2, genome: ACaacc) were grown to maturity. Two concentrations of MES (5 or 10 m m) were included in Hoagland 1 nutrient solution. Alternatively, resin beads were incorporated into the 2 vermiculite: 1 perlite (v/v) growth medium at 6% or 12% of total substrate volume. Both strategies stabilized pH without toxic side effects on plants. Average seed yield rates for all four pH stabilization treatments (13.3 to 16.9 g·m-2·day-1) were about double that of the control (8.2 g·m-2·day-1), for which there was no attempt to buffer substrate pH. Both the highest canopy seed yield rate (16.9 g·m-2·day-1) and the highest shoot harvest index (19.5%) occurred with the 6% resin bead treatment, even though the 10 mm MES and 12% bead treatments maintained pH within the narrowest limits. The pH stabilization methods tested did not significantly affect seed oil and protein contents.

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