Estimating dry rock frame moduli of high-resolution 3D digital rock images using the contact-mechanics-based effective medium approach

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. MR235-MR243
Author(s):  
Abdulla Kerimov ◽  
Jennie Cook ◽  
Nathan Lane ◽  
Dmitry Lakshtanov ◽  
Glen Gettemy
Keyword(s):  
High Resolution ◽  
Contact Mechanics ◽  
Prediction Accuracy ◽  
Elastic Moduli ◽  
Effective Medium Theory ◽  
Contact Stiffness ◽  
Effective Medium ◽  
Contact Radius ◽  
Ambient Conditions ◽  
Digital Rock

We have developed a method to estimate the dry frame elastic moduli of high-resolution 3D digital rock images using the contact-mechanics-based effective medium theory (EMT) model. The existing EMT models often are used to predict the effective dry frame elastic moduli of granular aggregates as a function of porosity, average number of contacts per grain, grain radius, contact radius, and contact stiffnesses of an elastic two-grain combination. But, it is almost impossible to measure the number of contacts per grain, contact radius distribution, or contact stiffness distribution in complex rocks. Therefore, explicit assumptions based on simplified microstructural geometries often are made to predict these contact properties in granular aggregates. As a result, the predictions of dry frame elastic moduli using EMT models may fail to match the observed properties because of numerous simplified assumptions, which can be violated in complex rocks. Our method uses the morphological contact properties (i.e., the grain-to-grain contact radius distribution, grain radius distribution, and coordination number distribution) directly extracted from 3D digital rock images to improve the prediction accuracy of dry frame elastic moduli using the EMT models. With integration of digital rocks technology, there is no longer a need to assume the size and shape of the grains, contact size, and number of contacts. The prediction accuracy of our method is validated on high-resolution 3D micro-CT digital rock images of miniplugs extracted from plugs with ultrasonic velocity measurements under dry conditions at different confining pressures. Image-computed dry frame elastic moduli using the EMT model are consistent with laboratory-measured moduli extrapolated to ambient conditions.

Estimating 3D elastic moduli of rock from 2D thin-section images using differential effective medium theory

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. MR211-MR219 ◽  
Author(s):  
Sadegh Karimpouli ◽  
Pejman Tahmasebi ◽  
Erik H. Saenger
Keyword(s):  
Porous Media ◽  
Thin Section ◽  
Elastic Moduli ◽  
Effective Medium ◽  
Physical Parameters ◽  
Reconstruction Method ◽  
Digital Rock ◽  
Aspect Ratios ◽  
Rock Structure ◽  
2D Images

Standard digital rock physics (DRP) has been extensively used to compute rock physical parameters such as permeability and elastic moduli. Digital images are captured using 3D microcomputed tomography scanners that are not widely available and often come with an excessive cost and expensive computation. Alternative DRP methods, however, benefit from the highly available low-cost 2D thin-section images and require a small amount of computer memory use and CPU. We have developed another alternative DRP method to compute 3D elastic parameters based on differential effective medium (DEM) theory. Our investigations indicate that the pore aspect ratio (PAR) is the most crucial factor controlling the elastic moduli of rock. Based on digital rock modeling in a dry calcite sample with 20% porosity, the bulk modulus is reduced by 51%, 80.7%, and 96.8% for aspect ratios of 1, 0.2, and 0.05, respectively. Similarly, the shear modulus is reduced by 52%, 73.8%, and 92.8% for the same PARs. These findings confirm the importance of the PAR in wave propagation through porous media. Such an evaluation, however, can be very expensive for 3D images because one requires using several of them for drawing a reliable conclusion. Therefore, we aim to capture the PAR distribution from 2D images. This distribution is, then, used to estimate 3D elastic moduli of sample by DEM equations. Three orthogonal 2D images were used and results indicated that 2D PARs in orthogonal orientations could address pore shapes more effectively. Moreover, a stochastic porous media reconstruction method was also used to generate more scenarios of rock structure and those of which that are not seen in 2D images. Results from Berea sandstone and Grosmont carbonate indicated that using only 2D images our proposed method could effectively estimate 3D elastic moduli of rock samples.

On microscale heterogeneity in granular media and its impact on elastic property estimation

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. D561-D571 ◽  
Author(s):  
Ratnanabha Sain ◽  
Tapan Mukerji ◽  
Gary Mavko
Keyword(s):  
Numerical Simulations ◽  
Contact Mechanics ◽  
Granular Media ◽  
Elastic Moduli ◽  
Effective Medium ◽  
Force Balance ◽  
Theoretical Treatment ◽  
Property Estimation ◽  
Stress Dependent ◽  
The Impact

We emphasize the existence of stress-dependent microscopic heterogeneities in granular media and their influence on macroscopic property estimation using numerical simulations. Although numerical simulations based on contact mechanics successfully reproduce experimental stress-dependent acoustic response of granular media, most contact-mechanics-based effective medium theories (EMTs) fail. We have determined that the main reason for this discrepancy is an inadequate theoretical treatment of micro-heterogeneities in structure, force, and stress. Under infinitesimal perturbations used for estimating elastic moduli, microheterogeneities lead to displacements or relaxations — typically ignored in EMT. These infinitesimal granular relaxations are necessary to comply with detailed force balance, but do not involve grain slip and hence do not depend on friction. Furthermore, we have found that these relaxations primarily depend on the “amount” of heterogeneity, which to a first order are dependent on stress only and are independent of mineralogy. In the absence of an effective medium framework to estimate such relaxation corrections, we have provided simulation-based corrections to account for the impact of heterogeneity on elastic moduli calculations in EMT.

scholarly journals Conditional reconstruction: An alternative strategy in digital rock physics

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. D465-D477 ◽  
Author(s):  
Sadegh Karimpouli ◽  
Pejman Tahmasebi
Keyword(s):  
High Resolution ◽  
Elastic Moduli ◽  
Rock Physics ◽  
Image Resolution ◽  
Work Flow ◽  
Physical Parameters ◽  
Reconstruction Algorithms ◽  
Digital Rock Physics ◽  
Digital Rock ◽  
Carbonate Formation

Digital rock physics (DRP) is a newly developed method based on imaging and digitizing of 3D pore and mineral structure of actual rock and numerically computing rock physical properties, such as permeability, elastic moduli, and formation factor. Modern high-resolution microcomputed tomography scanners are used for imaging, but these devices are not widely available, and 3D imaging is also costly and it is a time-consuming procedure. However, recent improvements of 3D reconstruction algorithms such as crosscorrelation-based simulation and, on the other side, the concept of rock physical trends have provided some new avenues in DRP. We have developed a modified work flow using higher order statistical methods. First, a high-resolution 2D image is divided into smaller subimages. Then, different stochastic subsamples are generated based on the provided 2D subimages. Eventually, various rock physical parameters are calculated. Using several subsamples allows extracting rock physical trends and better capturing the heterogeneity and variability. We implemented our work flow on two DRP benchmark data (Berea sandstone and Grosmont carbonate) and a thin-section image from the Grosmont carbonate formation. Results of realization models, pore network modeling, and autocorrelation functions for the real and reconstructed subsamples reveal the validity of the reconstructed models. Furthermore, the agreement between static and dynamic methods indicates that subsamples are representative volume elements. Average values of the subsamples’ properties follow the reference trends of the rock sample. Permeability trends pass the actual results of the benchmark samples; however, elastic moduli trends find higher values. The latter can be due to image resolution and voxel size, which are generated by imaging tools and reconstruction algorithms. According to the obtained results, this strategy can be introduced as a valid and accurate method where an alternative method for standard DRP is needed.

A numerical study on reflection coefficients of fractured media

Geophysics ◽  
2007 ◽  
Vol 72 (4) ◽  
pp. D61-D67 ◽  
Author(s):  
Oliver S. Krüger ◽  
Erik H. Saenger ◽  
Steven J. Oates ◽  
Serge A. Shapiro
Keyword(s):  
Effective Medium Theory ◽  
Numerical Study ◽  
Crack Density ◽  
Effective Medium ◽  
Numerical Results ◽  
Reflection Coefficients ◽  
Medium Theory ◽  
Application Range ◽  
Digital Rock ◽  
Effective Medium Theories

Effective-medium theories can be used to predict reflection coefficients of an interface between an unfractured layer overlying a fractured half-space. In 2D and 3D computer simulations, we analyze wavefields that are emitted by an explosion line or point source and reflected from a fractured area in a digital rock model. The reflection coefficients from the simulations are compared to several predictions given by static effective-medium theories. The agreement between our numerical results and the theoretical reflection coefficients is best for differential effective-medium schemes in 2D as well as in 3D. This result agrees with previously published numerical static and numerical transmission-time experiments. By varying the wavelength to crack-length ratio, we consider the application range of different effective-medium theories. We observe good agreement with theoretical predictions even for a ratio equal to 9. An angle-dependent analysis of the reflected amplitude of our numerical results is also compared to results given by effective-medium theory in combination with exact reflection-coefficient formulas. As expected, the fluctuations of the reflection coefficients decrease for wider angles. In our 3D digital rock models, we vary the crack density and the infill of the crack (i.e., water [cold and hot] and oil [cold and hot]).

scholarly journals Spectral Induced Polarization Survey with Distributed Array System for Mineral Exploration: Case Study in Saudi Arabia

Minerals ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 769 ◽  
Author(s):  
Fouzan A. Alfouzan ◽  
Abdulrahman M. Alotaibi ◽  
Leif H. Cox ◽  
Michael S. Zhdanov
Keyword(s):  
Effective Medium Theory ◽  
Coupling Effect ◽  
Pilot Project ◽  
Drill Hole ◽  
Induced Polarization ◽  
Effective Medium ◽  
Inductive Coupling ◽  
Geothermal Resources ◽  
Spectral Induced Polarization ◽  
Distributed Array

The Saudi Arabian Glass Earth Pilot Project is a geophysical exploration program to explore the upper crust of the Kingdom for minerals, groundwater, and geothermal resources as well as strictly academic investigations. The project began with over 8000 km2 of green-field area. Airborne geophysics including electromagnetic (EM), magnetics, and gravity were used to develop several high priority targets for ground follow-up. Based on the results of airborne survey, a spectral induced polarization (SIP) survey was completed over one of the prospective targets. The field data were collected with a distributed array system, which has the potential for strong inductive coupling. This was examined in a synthetic study, and it was determined that with the geometries and conductivities in the field survey, the inductive coupling effect may be visible in the data. In this study, we also confirmed that time domain is vastly superior to frequency domain for avoiding inductive coupling, that measuring decays from 50 ms to 2 s allow discrimination of time constants from 1 ms to 5 s, and the relaxation parameter C is strongly coupled to intrinsic chargeability. We developed a method to fully include all 3D EM effects in the inversion of induced polarization (IP) data. The field SIP data were inverted using the generalized effective-medium theory of induced polarization (GEMTIP) in conjunction with an integral equation-based modeling and inversion methods. These methods can replicate all inductive coupling and EM effects, which removes one significant barrier to inversion of large bandwidth spectral IP data. The results of this inversion were interpreted and compared with results of drill hole set up in the survey area. The drill hole intersected significant mineralization which is currently being further investigated. The project can be considered a technical success, validating the methods and effective-medium inversion technique used for the project.

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