Generalization of Gassmann equations for porous media saturated with a solid material

Geophysics ◽  
2007 ◽  
Vol 72 (6) ◽  
pp. A75-A79 ◽  
Author(s):  
Radim Ciz ◽  
Serge A. Shapiro
Keyword(s):  
Numerical Simulations ◽  
Elastic Properties ◽  
Pore Space ◽  
Viscoelastic Model ◽  
Solid Material ◽  
Filling Material ◽  
Porous Rocks ◽  
Pore Filling ◽  
Effective Elastic Properties ◽  
New Model

Gassmann equations predict effective elastic properties of an isotropic homogeneous bulk rock frame filled with a fluid. This theory has been generalized for an anisotropic porous frame by Brown and Korringa’s equations. Here, we develop a new model for effective elastic properties of porous rocks — a generalization of Brown and Korringa’s and Gassmann equations for a solid infill of the pore space. We derive the elastic tensor of a solid-saturated porous rock considering small deformations of the rock skeleton and the pore infill material upon loading them with the confining and pore-space stresses. In the case of isotropic material, the solution reduces to two generalized Gassmann equations for the bulk and shear moduli. The applicability of the new model is tested by independent numerical simulations performed on the microscale by finite-difference and finite-element methods. The results show very good agreement between the new theory and the numerical simulations. The generalized Gass-mann model introduces a new heuristic parameter, characterizing the elastic properties of average deformation of the pore-filling solid material. In many cases, these elastic moduli can be substituted by the elastic parameters of the infill grain material. They can also represent a proper viscoelastic model of the pore-filling material. Knowledge of the effective elastic properties for such a situation is required, for example, when predicting seismic velocities in some heavy oil reservoirs, where a highly viscous material fills the pores. The classical Gassmann fluid substitution is inapplicable for a configuration in which the fluid behaves as a quasi-solid.

Modeling effective elastic properties of digital rocks using a new dynamic stress-strain simulation method

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. MR163-MR174
Author(s):  
Wei Zhu ◽  
Luanxiao Zhao ◽  
Rui Shan
Keyword(s):  
Boundary Condition ◽  
Elastic Properties ◽  
Dynamic Stress ◽  
Simulation Method ◽  
Staggered Grid ◽  
Fluid Viscosity ◽  
Porous Rocks ◽  
Stress Strain ◽  
Effective Elastic Properties ◽  
Wide Range

We have developed a dynamic stress-strain simulation methodology to compute effective elasticity on digital rocks in a wide range of frequency based on the rotated staggered grid finite-difference method. The primary advantage of this simulator lies in characterizing the anisotropic behavior of complex porous rocks by setting specified boundary conditions along specified directions: The edges perpendicular to the propagating wave are applied with a strain boundary condition, and the edges parallel to the propagating wave are applied with a periodic boundary condition. The accuracy of the simulator is validated by comparing the simulating results in microinhomogeneous porous media containing randomly distributed inclusions and aligned oriented cracks, with that obtained by effective medium theories of self-consistent approximation in isotropic and anisotropic domains. This dynamic simulator can successfully capture anisotropic magnitude of rocks containing needle-like inclusions with different degrees of alignment. For real digital rock saturated with viscoelastic fluids, it is able to predict the dependence of velocities and attenuating factors on the frequency. We found that the magnitude of dispersion increases with the increase of pore fluid viscosity. Therefore, this method offers a robust and effective tool to compute effective elastic properties and anisotropy for real complex porous rocks.

scholarly journals Impact of the cracks lost in the imaging process on computing linear elastic properties from 3D microtomographic images of Berea sandstone

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. R95-R104 ◽  
Author(s):  
Yang Zhang ◽  
M. Nafi Toksöz
Keyword(s):  
Numerical Simulations ◽  
Elastic Properties ◽  
Rock Physics ◽  
Clay Content ◽  
Laboratory Measurements ◽  
Berea Sandstone ◽  
Effective Elastic Properties ◽  
Crack Distribution ◽  
Aspect Ratios ◽  
Effective Media

With the current developments in imaging/computational techniques and resources, computational rock physics has been emerging as a new field of study. Properties of rocks are examined by carrying out extensive numerical simulations on rocks that have been digitized using high-resolution X-ray CT scans. The ultimate goal of computational rock physics is to supplement the traditional laboratory measurements, which are time consuming, with faster numerical simulations that allow the parameter space to be explored more thoroughly. We applied the finite-element method to compute the static effective elastic properties from 3D microtomographic images of Berea sandstone saturated with different fluids. From the computations, we found discrepancies between the numerical results and the laboratory measurements. The reason for such a problem is the loss of small features, such as fine cracks and micropores, in the digitized matrix during the imaging and aggregation process. We used a hybrid approach, combining the numerical computation and the effective media theories — the differential effective medium model and the Kuster-Toksöz model — to deduce the lost cracks by a very fast simulated annealing method. We analyzed the sensitivity of the inverted results — the distributions of crack aspect ratios and concentrations — to the clay content. We found that the inverted crack distribution is not so sensitive to clay content. Compared with the effect of cracks on the computed effective elastic properties, clay has only a secondary effect. Our approach can recover the lost cracks and is capable of predicting the effective elastic properties of the rocks from the microtomographic images for different fluid saturations. Compared with the traditional inversion schemes, based only on the effective media theories, this hybrid scheme has the advantage of utilizing the complex microstructures that are resolved in the imaging process, and it helps define the inversion space for crack distribution.

On the Mechanical Behavior of the Orthotropic Cord-Rubber Composite

1976 ◽  
Vol 4 (4) ◽  
pp. 219-232 ◽  
Author(s):  
Ö. Pósfalvi
Keyword(s):  
Mechanical Behavior ◽  
Uniaxial Tension ◽  
Elastic Properties ◽  
Large Deformations ◽  
Virtual Work ◽  
Poisson's Ratio ◽  
Principle Of Virtual Work ◽  
Effective Elastic Properties ◽  
Rubber Composite ◽  
Mooney Equation

Abstract The effective elastic properties of the cord-rubber composite are deduced from the principle of virtual work. Such a composite must be compliant in the noncord directions and therefore undergo large deformations. The Rivlin-Mooney equation is used to derive the effective Poisson's ratio and Young's modulus of the composite and as a basis for their measurement in uniaxial tension.

scholarly journals Use of Image Correlation to Measure Macroscopic Strains by Hygric Swelling in Sandstone Rocks

2021 ◽  
Vol 11 (6) ◽  
pp. 2495
Author(s):  
Belén Ferrer ◽  
María-Baralida Tomás ◽  
David Mas
Keyword(s):  
Cross Correlation ◽  
Pore Space ◽  
Digital Camera ◽  
Experimental Methods ◽  
Image Correlation ◽  
Rock Surface ◽  
Experimental Setup ◽  
Porous Rocks ◽  
Porous Sandstone ◽  
Variable Displacement

Some materials undergo hygric expansion when soaked. In porous rocks, this effect is enhanced by the pore space, because it allows water to reach every part of its volume and to hydrate most swelling parts. In the vicinity, this enlargement has negative structural consequences as adjacent elements support some compressions or displacements. In this work, we propose a normalized cross-correlation between rock surface texture images to determine the hygric expansion of such materials. We used small porous sandstone samples (11 × 11 × 30 mm3) to measure hygric swelling. The experimental setup comprised an industrial digital camera and a telecentric objective. We took one image every 5 min for 3 h to characterize the whole swelling process. An error analysis of both the mathematical and experimental methods was performed. The results showed that the proposed methodology provided, despite some limitations, reliable hygric swelling information by a non-contact methodology with an accuracy of 1 micron and permitted the deformation in both the vertical and horizontal directions to be explored, which is an advantage over traditional linear variable displacement transformers.

scholarly journals Modelling the elastic mechanical properties of bioactive glass-derived scaffolds

2020 ◽  
Vol 6 (1) ◽  
pp. 50-56
Author(s):  
Francesco Baino ◽  
Elisa Fiume
Keyword(s):  
Elastic Properties ◽  
Poisson’S Ratio ◽  
Mechanical Performance ◽  
Solid Material ◽  
Poisson's Ratio ◽  
Predictive Capability ◽  
Shear Moduli ◽  
Wide Range ◽  
Constitutive Parameters ◽  
The Relationship

AbstractPorosity is known to play a pivotal role in dictating the functional properties of biomedical scaffolds, with special reference to mechanical performance. While compressive strength is relatively easy to be experimentally assessed even for brittle ceramic and glass foams, elastic properties are much more difficult to be reliably estimated. Therefore, describing and, hence, predicting the relationship between porosity and elastic properties based only on the constitutive parameters of the solid material is still a challenge. In this work, we quantitatively compare the predictive capability of a set of different models in describing, over a wide range of porosity, the elastic modulus (7 models), shear modulus (3 models) and Poisson’s ratio (7 models) of bioactive silicate glass-derived scaffolds produced by foam replication. For these types of biomedical materials, the porosity dependence of elastic and shear moduli follows a second-order power-law approximation, whereas the relationship between porosity and Poisson’s ratio is well fitted by a linear equation.

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