The Law of Effective Stress for Rocks in Light of Results of Laboratory Experiments / Prawo Naprężeń Efektywnych Dla Skał W Świetle Wyników Badań Laboratoryjnych

2012 ◽  
Vol 57 (4) ◽  
pp. 1027-1044 ◽  
Author(s):  
Andrzej Nowakowski
Keyword(s):  
Pore Pressure ◽  
Effective Stress ◽  
Compression Test ◽  
Triaxial Compression ◽  
Volumetric Strain ◽  
Pore Fluid ◽  
Effective Pressure ◽  
Test Results ◽  
Strength Limit ◽  
The Law

Abstract This paper presents the results of laboratory tests carried out in order to formulate effective stress law. The law was sought for two different cases: first - when rock was treated as a porous Biot medium (Biot, 1941; Nur & Byerlee, 1971) and second - when the law was formulated according to definition of Robin (1973) developed by Gustkiewicz (1990) and Nowakowski (2007). In the first case coefficents (4) and (5) of the Biot equation (3) were were determined on the basis of compressibility test, in the second one effective pressure equation (9) and effective pressure value (11) were found on the basis of results of so called individual triaxial compression test (see Kovari et al., 1983) according to the methodology given by Nowakowski (2007). On the basis of Biot coefficients set of values was found that volumetric strain of the pore space described by a coefficient (5) was not dependent on the type of pore fluid and the pore pressure of only, while in case of volumetric strain of total rock described by coefficient (4) both the structure and texture of rock were important. The individual triaxial compression test results showed that for tested rock an effective pressure equation was a linear function of pore pressure as (15). The so called Rebinder effect (Rehbinder & Lichtman, 1957) might cause, that the α coefficient in equation (15) could assume values greater than one. This happened particularly in the case when the porous fluid was non-inert carbon dioxide. In case of inert pore fluid like kerosene the test results suggested that the a coefficient in equation (15) decreased while the differential strength limit was increasing. This might be caused by, so called, dillatancy strengthening (see Zoback & Byerlee, 1975). Another considered important parameter of the equation (15) was the value of the effective press p'. The results showed that the value of this parameter was practically independend on the pore fluid type. This conclusion was contrary to previous research (see, for example, Gustkiewicz et al., 2003 and Gustkiewicz, 1990) so these results should be treated with caution. There are no doubts, however, over p' increasing simultaneously with increase in Rσ1-σ3. Basically, the differential strength limit of the specimen is greater the greater is confining pressure applied to it. Thus, higher Rσ1-σ3 values are accompanied by higher p'.

Experimental investigation of the effect of compliant pores on reservoir rocks under hydrostatic and triaxial compression stress states

2019 ◽  
Vol 56 (7) ◽  
pp. 983-991
Author(s):  
Hua Yu ◽  
Kam Ng ◽  
Dario Grana ◽  
John Kaszuba ◽  
Vladimir Alvarado ◽  
...  
Keyword(s):  
Pore Pressure ◽  
Triaxial Compression ◽  
Matrix Material ◽  
Volumetric Strain ◽  
Confining Pressure ◽  
Differential Pressure ◽  
Sandstone Sample ◽  
Stress States ◽  
Rock Springs ◽  
Stage 1

The presence of compliant pores in rocks is important for understanding the stress–strain behaviors under different stress conditions. This paper describes findings on the effect of compliant pores on the mechanical behavior of a reservoir sandstone under hydrostatic and triaxial compression. Laboratory experiments were conducted at reservoir temperature on Weber Sandstone samples from the Rock Springs Uplift, Wyoming. Each experiment was conducted at three sequential stages: (stage 1) increase in the confining pressure while maintaining the pore pressure, (stage 2) increase in the pore pressure while maintaining the confining pressure, and (stage 3) application of the deviatoric load to failure. The nonlinear pore pressure – volumetric strain relationship governed by compliant pores under low confining pressure changes to a linear behavior governed by stiff pores under higher confining pressure. The estimated compressibilities of the matrix material in sandstone samples are close to the typical compressibility of quartz. Because of the change in pore structures during stage 1 and stage 2 loadings, the estimated bulk compressibilities of the sandstone sample under the lowest confining pressure decrease with increasing differential pressure. The increase in crack initiation stress is limited with increasing differential pressure because of similar total crack length governed by initial compliant porosity in sandstone samples.

Experimental assessment of the response of sands under shear–volume coupled deformation

2008 ◽  
Vol 45 (9) ◽  
pp. 1310-1323 ◽  
Author(s):  
S. Sivathayalan ◽  
P. Logeswaran
Keyword(s):  
Shear Strength ◽  
Boundary Conditions ◽  
Pore Pressure ◽  
Effective Stress ◽  
Strain Path ◽  
Stress Ratio ◽  
Volumetric Strain ◽  
Strain Paths ◽  
Pressure Boundary Conditions ◽  
Effective Stress Ratio

An experimental study of the behaviour of an alluvial sand under different strain increment paths representing shear–volume coupled deformation is presented. Both pore pressure and pore volume change simultaneously in these tests. Linear strain paths with different levels of limiting volumetric strain and nonlinear strain paths that simulate different pore pressure boundary conditions were applied to the soil specimen in the laboratory. The strain paths imposed included both expansive and contractive volumetric deformation. Nonuniform excess pore pressures generated during earthquakes (on account of the heterogeneity in natural soils) often lead to such deformation in situ following the end of strong shaking. The shear strength of the soil could decrease significantly when the pore pressure boundary conditions result in volume inflow that leads to a considerable reduction of the effective confining stress. The rate of volume inflow plays a significant role on the resulting stress–strain and pore pressure responses. Both the peak and the minimum shear strength mobilized during the test were significantly dependent on the strain path. The effective stress ratio at the instant of peak pore pressure is independent of the strain path followed, and it is equal to the effective stress ratio noted at the instant of phase transformation in undrained tests.

scholarly journals Analysis of models for porosity evolution in reservoir during steam injection

2019 ◽  
pp. 91-105
Author(s):  
A A Kostina ◽  
M S Zhelnin ◽  
O A Plekhov
Keyword(s):  
Pore Pressure ◽  
Effective Stress ◽  
Balance Equation ◽  
Volumetric Strain ◽  
Gravity Drainage ◽  
Oil Viscosity ◽  
Fluid Filtration ◽  
Water Steam ◽  
Porosity Evolution ◽  
Steam Assisted Gravity Drainage

Depletion of traditional hydrocarbon reserves leads to the development of extracting methods for heavy crude oil and bitumen characterized by extremely high viscosity. The most effective technology is the steam-assisted gravity drainage. The aim of this method is to decrease oil viscosity by injection of hot steam into the reservoir. Increase of temperature, pore pressure and change of stress-strain state during this process significantly affect porosity which is the key storage parameter of the reservoir. This work is devoted to the analysis of models for porosity evolution during the steam-assisted gravity drainage process. The authors have developed an original model to describe steam-assisted gravity drainage which includes the mass balance equation for a three-phase flow, the energy balance equation involving latent heat due to vaporization/condensation of water/steam and Darcy’s law for fluid filtration. Numerical implementation of the proposed equations was based on the pressure-saturation algorithm. The results have shown a substantial qualitative and quantitative disagreement between the considered models. Coupling of porosity with volumetric strain leads to the rise of its magnitude. Models relating porosity to pore pressure show simultaneous existence of high-porous (near the injection well) and low-porous (near the production well) areas. In case when porosity is dependent on effective stress a circular area of a compacted soil is formed. Therefore, to obtain a correct estimation of the oil production rate in an arbitrary reservoir it is necessary to define the prevailing mechanism of porosity evolution (volumetric strain, pore pressure or effective stress).

Experimental Study on Mechanical Properties of Jurassic Soft Rock in Shajihai Mining Area of Xinjiang

2013 ◽  
Vol 353-356 ◽  
pp. 20-23
Author(s):  
Xiao Lei Wang ◽  
Shun Xi Yan ◽  
Guang Can Zhang
Keyword(s):  
Mechanical Properties ◽  
Compressive Strength ◽  
Compression Test ◽  
Mechanical Test ◽  
Triaxial Compression ◽  
Soft Rock ◽  
Mining Area ◽  
Surrounding Rock ◽  
Test Results ◽  
Support Design

According to the problemsof serious deformation of soft rock roadways and lack of system andcomprehensive study on surrounding rock characteristics and failure mechanismin Shajihai mining area, this paper carried out a series of mechanicalexperiments on the characteristics of surrounding rock in this area includinguniaxial compression test, triaxial compression test and water absorption propertiestest. Mechanical test results show that the compressive strength of surroundingrock of roadway is generally low, and mudstone compressive strength is thelargest which is 19.23 MPa, and compressive strength of the minimum is coalwhich is 11.32 MPa under natural condition. However sandstone and mudstone’sability of water absorbing is strong, and coal saturation strength issignificantly greater than that of mudstone and sandstone. Therefore, we shouldmake full use of the strength of coal in roadway layout and support design.

scholarly journals Influence of the initial hydrostatic pressure on contact area coefficient under drainage condition

2021 ◽  
Vol 276 ◽  
pp. 01023
Author(s):  
Chaoqun Feng ◽  
Pei Zhang ◽  
Chengshun Xu ◽  
Xiuli Du
Keyword(s):  
Hydrostatic Pressure ◽  
Pore Pressure ◽  
Effective Stress ◽  
Contact Area ◽  
Point Contact ◽  
Confining Pressure ◽  
Triaxial Tests ◽  
Test Results ◽  
Pressure Term ◽  
Pressure Factor

The expression of effective stress proposed by Terzaghi has always been questioned. Many correction formulas are modification of pore pressure term. The pore pressure factor is related to porosity, contact area and other factors. When the particles are in point contact, the expression of the effective stress is that proposed by Terzaghi, while for the surface contact particles, the actual effective stress increases the stress produced by pore pressure passing through the contact surface based on the Terzaghi effective stress. There are many factors that affect the development of contact area and pore pressure, therefore, a series of the drained triaxial tests were carried out on four groups of sand samples with different initial hydrostatic pressures to study the influence of different initial hydrostatic pressures on the effective stress due to the term of contact area (σα). The test results show that the shear strength is increases with the initial hydrostatic pressure under the same effective confining pressure, which indirectly indicates that the initial hydrostatic pressure increases the contact area stress.

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