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.

Modeling squirt dispersion and attenuation in fluid-saturated rocks using pressure dependency of dry ultrasonic velocities

Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. WA157-WA168 ◽  
Author(s):  
Osni Bastos de Paula ◽  
Marina Pervukhina ◽  
Dina Makarynska ◽  
Boris Gurevich
Keyword(s):  
Aspect Ratio ◽  
Elastic Properties ◽  
Elastic Moduli ◽  
Pore Space ◽  
Geometrical Parameters ◽  
Laboratory Measurements ◽  
Significant Linear Trend ◽  
Aspect Ratios ◽  
Pressure Dependency ◽  
Dispersion And Attenuation

Modeling dispersion and attenuation of elastic waves in fluid-saturated rocks due to squirt flow requires the knowledge of a number of geometrical parameters of the pore space, in particular, the characteristic aspect ratio of the pores. These parameters are usually inferred by fitting measurements on saturated rocks to model predictions. To eliminate such fitting and thus make the model more predictive, we propose to recover the geometrical parameters of the pore space from the pressure dependency of elastic moduli on dry samples. Our analysis showed that the pressure dependency of elastic properties of rocks (and their deviation from Gassmann’s prediction) at ultrasonic frequencies is controlled by the squirt flow between equant, stiff, and so-called intermediate pores (with aspect ratios between [Formula: see text]). Such intermediate porosity is expected to close at confining pressures of between 200 and 2000 MPa, and thus cannot be directly obtained from ultrasonic experiments performed at pressures below 50 MPa. However, the presence of this intermediate porosity is inferred from the significant linear trend in the pressure dependency of elastic properties of the dry rock and the difference between the bulk modulus of the dry rock computed for spherical pores and the measured modulus at 50 MPa. Moreover, we can infer the magnitude of the intermediate porosity and its characteristic aspect ratio. Substituting these parameters into the squirt model, we have computed elastic moduli and velocities of the water-saturated rock and compared these predictions against laboratory measurements of these velocities. The agreement is good for a number of clean sandstones, but not unexpectedly worse for a broad range of shaley sandstones. Our predictions showed that dispersion and attenuation caused by the squirt flow between compliant and stiff pores may occur in the seismic frequency band. Confirmation of this prediction requires laboratory measurements of elastic properties at these frequencies.

Digital rock physics and laboratory considerations on a high-porosity volcanic rock

2020 ◽  
Author(s):  
Laura L. Schepp ◽  
Benedikt Ahrens ◽  
Martin Balcewicz ◽  
Mandy Duda ◽  
Mathias Nehler ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Elastic Properties ◽  
Effective Properties ◽  
Rock Physics ◽  
Numerical Results ◽  
High Porosity ◽  
Effective Elastic Properties ◽  
Digital Rock Physics ◽  
Digital Rock ◽  
Laboratory Investigations

<p>Microtomographic imaging techniques and advanced numerical simulations are combined by digital rock physics (DRP) to obtain effective physical material properties. The numerical results are typically used to complement laboratory investigations with the aim to gain a deeper understanding of physical processes related to transport (e.g. permeability and thermal conductivity) and effective elastic properties (e.g. bulk and shear modulus). The present study focuses on DRP and laboratory techniques applied to a rock called reticulite, which is considered as an end-member material with respect to porosity, stiffness and brittleness of the skeleton. Classical laboratory investigations on effective properties, such as ultrasonic transmission measurements and uniaxial deformation experiments, are very difficult to perform on this class of high-porosity and brittle materials.</p><p>Reticulite is a pyroclastic rock formed during intense Hawaiian fountaining events. The open honeycombed network has a porosity of more than 80 % and consists of bubbles that are supported by glassy threads. The natural mineral has a strong analogy to fabricated open-cell foams. By comparing experimental with numerical results and theoretical estimates we demonstrate the potential of digital material methodology with respect to the investigation of porosity, effective elastic properties, thermal conductivity and permeability</p><p>We show that the digital rock physics workflow, previously applied to conventional rock types, yields reasonable results for a high-porosity rock and can be adopted for fabricated foam-like materials. Numerically determined effective properties of reticulite are in good agreement with the experimentally determined results. Depending on the fields of application, numerical methods as well as theoretical estimates can become reasonable alternatives to laboratory methods for high porous foam-like materials.</p>

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.

Elastic properties of rock salt: Laboratory measurements and Gulf of Mexico well-log analysis

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. D303-D317 ◽  
Author(s):  
Jingjing Zong ◽  
Robert R. Stewart ◽  
Nikolay Dyaur ◽  
Michael T. Myers
Keyword(s):  
Gulf Of Mexico ◽  
Elastic Properties ◽  
Rock Salt ◽  
Model Building ◽  
Complex Geometry ◽  
Rock Physics ◽  
P Wave ◽  
Elastic Behavior ◽  
Laboratory Measurements ◽  
Wave Velocities

Rock salt (essentially halite) is a special type of sedimentary rock that has played a large role throughout tectonic and economic history. The unique physical properties of halite (ductility, low density, flowability, and impermeability) can be critical factors in hydrocarbon traps and underground storage. However, seismic imaging and interpretation can be challenging when salt structures are present due to their complex geometry and large impedance contrasts relative to surrounding rocks. To investigate the properties of rock salt in terms of elastic parameters, we use ultrasonic laboratory measurements and well logs. In the laboratory, we have analyzed the effects of composition, crystalline structure, pressure, and temperature on the elastic behavior of a variety of rock salt samples. The samples include pure halite (>95 wt%) from the Gulf of Mexico (GOM) area, argillaceous rock salt from the Zipaquirá Mine, Colombia, and crystalline salt from the Goderich Mine, Canada. Current measurements suggest that the GOM salt cores behave isotropically in general. The Zipaquirá salt samples show velocity and density variations on account of their heterogeneous composition. The Goderich halite crystals display distinct cubic anisotropy. Measurements on the GOM samples at varying confining pressures and temperatures indicate that increasing pressure elevates velocity whereas increasing temperature decreases velocity. From the analysis of 145 log suites from boreholes drilled through rock salt in the northern GOM, we found that, within the salt formations, P-wave velocities increased slightly with depth (approximately [Formula: see text] per km). The S-wave velocities from three wells range from 2280 to [Formula: see text]. Bulk densities from all the wells cluster at [Formula: see text]. These laboratory and log measurements provide new values for the elastic properties of rock salt, which can assist in velocity model building, synthetic seismogram generation, and the understanding of the rock physics of halite.

Rock-physics transforms and scale of investigation

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. MR75-MR88 ◽  
Author(s):  
Jack Dvorkin ◽  
Uri Wollner
Keyword(s):  
Elastic Properties ◽  
Rock Physics ◽  
Clay Content ◽  
Pore Fluid ◽  
Petrophysical Properties ◽  
Reflection Seismology ◽  
Physics Model ◽  
Well Data ◽  
Rock Physics Model ◽  
Seismic Scale

Rock-physics “velocity-porosity” transforms are usually established on sets of laboratory and/or well data with the latter data source being dominant in recent practice. The purpose of establishing such transforms is to (1) conduct forward modeling of the seismic response for various geologically plausible “what if” scenarios in the subsurface and (2) interpret seismic data for petrophysical properties and conditions, such as porosity, clay content, and pore fluid. Because the scale of investigation in the well is considerably smaller than that in reflection seismology, an important question is whether the rock-physics model established in the well can be used at the seismic scale. We use synthetic examples and well data to show that a rock-physics model established at the well approximately holds at the seismic scale, suggest a reason for this scale independence, and explore where it may be violated. The same question can be addressed as an inverse problem: Assume that we have a rock-physics transform and know that it works at the scale of investigation at which the elastic properties are seismically measured. What are the upscaled (smeared) petrophysical properties and conditions that these elastic properties point to? It appears that they are approximately the arithmetically volume-averaged porosity and clay content (in a simple quartz/clay setting) and are close to the arithmetically volume-averaged bulk modulus of the pore fluid (rather than averaged saturation).

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