scholarly journals The Influence of Rate of Change in Confining and Pore Pressure on Values of the Modulus of Compressibility of the Rock Skeleton and Biot’s Coefficient

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3056
Author(s):  
Andrzej Nowakowski
Keyword(s):  
Pore Space ◽  
Confining Pressure ◽  
Rate Of Change ◽  
Liquid Pressure ◽  
High Pressure Cell ◽  
Biot Coefficient ◽  
Biot’S Coefficient ◽  
Load Rate ◽  
Pore Liquid ◽  
Rock Skeleton

This work discusses the results of a study of the influence of rates of change of confining pressure on the result of a drained compressibility tests intended to determine the modulus of compressibility of a rock skeleton Ks. A series of cyclical compressibility tests was performed on samples of sandstone soaked in kerosene, for various rates of compression and decompression of the pressure liquid filling the cell and the pore volume of the sample. The studies showed that the deformability of the tested sample was directly proportional to the rate of change of the confining pressure. As a consequence, the value of the Ks modulus and Biot coefficient α decreased with increasing sample load rate. This phenomenon should be attributed primarily to equilibration of the liquid pressure inside the high-pressure cell with the liquid pressure in the sample pore space, caused by filtration of the pore liquid. These phenomena prove that the filtration process impacts the values of the modulus of compressibility of the rock skeleton Ks and of Biot coefficient α determined on the basis of the experiment. This is significant in the context of the use of Biot equations as constitutive equations for a porous rock medium.

scholarly journals Experimental Study of Stress-Seepage Coupling Properties of Sandstone under Different Loading Paths

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Xi Chen ◽  
Wei Wang ◽  
Yajun Cao ◽  
Qizhi Zhu ◽  
Weiya Xu ◽  
...  
Keyword(s):  
Elastic Modulus ◽  
Pore Pressure ◽  
Complex Loading ◽  
Friction Angle ◽  
Confining Pressure ◽  
Triaxial Tests ◽  
Compression Tests ◽  
Biot Coefficient ◽  
Cyclic Loading And Unloading ◽  
Loading And Unloading

The study on hydromechanical coupling properties of rocks is of great importance for rock engineering. It is closely related to the stability analysis of structures in rocks under seepage condition. In this study, a series of conventional triaxial tests under drained condition and hydrostatic compression tests under drained or undrained condition on sandstones were conducted. Moreover, complex cyclic loading and unloading tests were also carried out. Based on the experimental results, the following conclusions were obtained. For conventional triaxial tests, the elastic modulus, peak strength, crack initiation stress, and expansion stress increase with increased confining pressure. Pore pressure weakened the effect of the confining pressure under drained condition, which led to a decline in rock mechanical properties. It appeared that cohesion was more sensitive to pore pressure than to the internal friction angle. For complex loading and unloading cyclic tests, in deviatoric stress loading and unloading cycles, elastic modulus increased obviously in first loading stage and increased slowly in next stages. In confining pressure loading and unloading cycles, the Biot coefficient decreased first and then increased, which indicates that damage has a great impact on the Biot coefficient.

Biot coefficient is distinct from effective pressure coefficient

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. L27-L33 ◽  
Author(s):  
Tobias M. Müller ◽  
Pratap N. Sahay
Keyword(s):  
Pressure Coefficient ◽  
Fluid Pressure ◽  
Confining Pressure ◽  
Effective Pressure ◽  
Pore Scale ◽  
Biot Coefficient ◽  
Saturated Rock ◽  
Bulk Volume ◽  
The Difference ◽  
Pressure Changes

Within the Biot poroelasticity theory, the effective pressure coefficient for the bulk volume of a fluid-saturated rock and the Biot coefficient are one and the same quantity. The effective pressure coefficient for the bulk volume is the change of confining pressure with respect to fluid-pressure changes when the bulk volume is held constant. The Biot coefficient is the fluid volume change induced by bulk volume changes in the drained condition. However, there is experimental evidence showing a difference between these two coefficients, arguably caused by microinhomogeneities, such as microcracks and other compliant pore-scale features. In these circumstances, we advocate using the generalized constitutive pressure equations recently developed by Sahay wherein the effective pressure coefficient and the Biot coefficient enter as distinct quantities. Therein, the difference is attributed to the porosity effective pressure coefficient that serves as a measure for the deviation from the Biot prediction and accounts for microinhomogeneities. We have concluded that these generalized constitutive pressure equations offer a meaningful alternative to model observed rock behavior.

A Mathematical Thermal Hydraulic-Mechanical Coupling Model for Unsaturated Porous Media

2014 ◽  
Vol 602-605 ◽  
pp. 365-369
Author(s):  
Jun Yan ◽  
Yin Qi Wei ◽  
Hong Cai
Keyword(s):  
Porous Media ◽  
Solid Mechanics ◽  
Coupling Effect ◽  
Coupling Model ◽  
Unsaturated Porous Media ◽  
Liquid Pressure ◽  
Mechanical Coupling ◽  
The Earth ◽  
Highly Nonlinear ◽  
Pore Liquid

s: Temperature, seepage and deformation are the important parts of the engineering geological mechanics both in water conservancy and hydropower engineering since there are highly nonlinear complex coupling effect between each other. In this paper, the earth and rock mass are classified as continuous porous media. The thermal constitutive relation of porous media and motion regularity of pore fluid are deduced from the basic theory of solid mechanics, hydraulics, and thermodynamics. Based on momentum, mass and energy conservation equations, the multi-field controlling equations of unsaturated porous media are given, in which the unknown variables include displacements, pore liquid pressure, pore gas pressure, temperature, and porosity.

scholarly journals Empirical Formula for Dynamic Biot Coefficient of Sandstone Samples from South-West of Poland

Energies ◽  
2021 ◽  
Vol 14 (17) ◽  
pp. 5514
Author(s):  
Dariusz Knez ◽  
Mohammad Ahmad Mahmoudi Zamani
Keyword(s):  
Elastic Moduli ◽  
Confining Pressure ◽  
Open Pit ◽  
High Porosity ◽  
Empirical Correlations ◽  
Biot Coefficient ◽  
South West ◽  
Dynamic Elastic Moduli ◽  
Skempton Coefficient ◽  
Low Porosity

In this research, two empirical correlations have been introduced to calculate the dynamic Biot coefficients of low-porosity and high-porosity sandstone samples from two open pit mines located in South-West Poland. The experiments were conducted using an acoustic velocity measurement apparatus. Under the undrained condition, firstly, the confining pressure was increased in increments of 200 psi, and the values of pore pressure and dynamic elastic modulus were recorded. This experiment was continued until the Skempton coefficient remained in the range of 0.98–1. Secondly, an experiment on the same sample was conducted under drained conditions, and the corresponding dynamic elastic moduli were calculated. Then, using the calculated dynamic elastic moduli, the dynamic Biot coefficient was determined for each sample under different confining pressure. Finally, two empirical correlations were formulated for each sandstone category. The results demonstrate that, as the confining pressure increases, the Biot coefficient decreases from 0.79 to 0.50 and from 0.84 to 0.45 for low-porosity and high-porosity samples, respectively. Furthermore, as the porosity increases, the sandstone behavior increasingly approaches that of soil. The empirical correlations can be used for sandstone formations with the same porosity in projects where there is not a measurement method for the Biot coefficient.

scholarly journals Thermodynamics of snow metamorphism due to variations in curvature

1980 ◽  
Vol 26 (94) ◽  
pp. 291-301 ◽  
Author(s):  
S. C. Colbeck
Keyword(s):  
Grain Growth ◽  
Pore Space ◽  
Large Temperature ◽  
Radius Of Curvature ◽  
Liquid Content ◽  
Liquid Pressure ◽  
Vapor Diffusion ◽  
Liquid Saturation ◽  
Wet Snow ◽  
Seasonal Snow Cover

AbstractIn the absence of imposed temperature gradients, the metamorphism of dry snow is dominated by the slow process of vapor diffusion between surfaces of different radii of curvature. This process is so slow in a seasonal snow cover (where temperatures normally change on the scale of hours or days) that vapor migration is usually dominated by the imposed temperature gradient. Thus radius of curvature contributes to but does not control metamorphism except for short periods in very fresh snow. As opposed to dry snow, liquid-saturated snow (i.e. pore space filled by the melt) is metamorphosed by heat flow arising from relatively large temperature differences among the particles. Grain growth in liquid-saturated snow is rapid because of the large temperature differences at nearly constant liquid pressure. In wet snow with low liquid content (2-5% by volume), grain growth is dominated by vapor diffusion (as in dry snow) so grain growth is much slower than under conditions of liquid saturation.

Modulus—porosity relations, Gassmann’s equations, and the low‐frequency elastic‐wave response to fluids

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1355-1363 ◽  
Author(s):  
Richard C. Nolen‐Hoeksema
Keyword(s):  
Elastic Wave ◽  
Pore Space ◽  
Low Frequency ◽  
Biot Coefficient ◽  
Convenient Tool ◽  
Wave Response ◽  
Wave Properties

Gassmann’s equations relate the low‐frequency drained and undrained elastic‐wave response to fluids. This tutorial explores how different modulus—porosity relationships affect predictions of the low‐frequency elastic‐wave response to fluids based on Gassmann’s equations. I take different modulus—porosity relations and substitute them into Gassmann’s equations through the framework moduli. The results illustrate the range of responses to fluids and can be summarized in a nomograph of the effective fluid coefficient, which quantifies the change in the pore‐space modulus ([Formula: see text]) in response to a change in fluid modulus ([Formula: see text]). Two ratios control the effective fluid coefficient: the ratio of the fluid modulus to the solid‐grain modulus ( [Formula: see text]) and the ratio of the Biot coefficient to porosity ([Formula: see text]). The effective fluid coefficient nomograph is a convenient tool for estimating how low‐frequency elastic‐wave properties will respond to changes in reservoir fluids.

Fuel Controller Design in a Once-Through Subcritical Steam Generator System

1978 ◽  
Vol 100 (1) ◽  
pp. 189-196 ◽  
Author(s):  
Yu-Hwan Lin ◽  
R. S. Nielsen ◽  
A. Ray
Keyword(s):  
Steam Generator ◽  
Controller Design ◽  
Rate Of Change ◽  
Normal Operation ◽  
Generator System ◽  
Stable Operating ◽  
Operating Level ◽  
Flash Tank ◽  
Load Rate ◽  
Power Generation System

Established techniques have been applied for modeling a once-through subcritical steam generator in an oil-fired 386 MW(e) power generation system. The model was used to design a fuel controller which was implemented in the actual plant. The resulting minimum stable operating level of the system has been reduced from 220 MW(e) to flash tank level of 130 MW(e), and the customary load rate-of-change during normal operation improved from approximately 2 MW/min to 9 MW/min.

Effects of pore and differential pressure on compressional wave velocity and quality factor in Berea and Michigan sandstones

Geophysics ◽  
1997 ◽  
Vol 62 (4) ◽  
pp. 1163-1176 ◽  
Author(s):  
Manika Prasad ◽  
Murli H. Manghnani
Keyword(s):  
Quality Factor ◽  
Wave Velocity ◽  
Pore Space ◽  
Confining Pressure ◽  
Compressional Wave ◽  
Differential Pressure ◽  
Berea Sandstone ◽  
Compressional Wave Velocity ◽  
Stress Coefficient ◽  
Space Deformation

Compressional‐wave velocity [Formula: see text] and quality factor [Formula: see text] have been measured in Berea and Michigan sandstones as a function of confining pressure [Formula: see text] to 55 MPa and pore pressure [Formula: see text] to 35 MPa. [Formula: see text] values are lower in the poorly cemented, finer grained, and microcracked Berea sandstone. [Formula: see text] values are affected to a lesser extent by the microstructural differences. A directional dependence of [Formula: see text] is observed in both sandstones and can be related to pore alignment with pressure. [Formula: see text] anisotropy is observed only in Berea sandstone. [Formula: see text] and [Formula: see text] increase with both increasing differential pressure [Formula: see text] and increasing [Formula: see text]. The effect of [Formula: see text] on [Formula: see text] is greater at higher [Formula: see text]. The results suggest that the effective stress coefficient, a measure of pore space deformation, for both [Formula: see text] and [Formula: see text] is less than 1 and decreases with increasing [Formula: see text].

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