Incorporating pore geometry and fluid pressure communication into modeling the elastic behavior of porous rocks

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 106-117 ◽  
Author(s):  
Anthony L. Endres ◽  
Rosemary J. Knight
Keyword(s):  
Closed System ◽  
Elastic Moduli ◽  
Pore Space ◽  
Fluid Pressure ◽  
Continuous Distribution ◽  
Elastic Behavior ◽  
Pore Geometry ◽  
Porous Rocks ◽  
Low Frequencies ◽  
Poroelastic Theory

Inclusion‐based formulations allow an explicit description of pore geometry by viewing porous rocks as a solid matrix with embedded inclusions representing individual pores. The assumption commonly used in these formulations that there is no fluid pressure communication between pores is reasonable for liquid‐filled rocks measured at high frequencies; however, complete fluid pressure communication should occur throughout the pore space at low frequencies. A generalized framework is presented for incorporating complete fluid pressure communication into inclusion‐based formulations, permitting elastic behavior of porous rocks at high and low frequencies to be described in terms of a single model. This study extends previous work by describing the pore space in terms of a continuous distribution of shapes and allowing different forms of inclusion interactions to be specified. The effects of fluid pressure communication on the elastic moduli of porous media are explored by using simple models and are found to consist of two fundamental elements. One is associated with the cubical dilatation and governs the effective bulk modulus. Its magnitude is a function of the range of pore shapes present. The other is due to the extensional part of the deviatoric strain components and affects the effective shear modulus. This element is dependent on pore orientation, as well as pore shape. Using sandstone and granite models, an inclusion‐based formulation shows that large differences between high‐ and low‐frequency elastic moduli can occur for porous rocks. An analysis of experimental elastic wave velocity data reveals behavior similar to that predicted by the models. Quantities analogous to the open and closed system moduli of Gassmann‐Biot poroelastic theory are defined in terms of inclusion‐based formulations that incorporate complete fluid pressure communication. It was found that the poroelastic relationships between the open and closed system moduli are replicated by a large class of inclusion‐based formulations. This connection permits explicit incorporation of pore geometry information into the otherwise empirically determined macroscopic parameters of the Gassmann‐Biot poroelastic theory.

Squirt-flow seismic dispersion models: a comparison

2020 ◽  
Vol 222 (3) ◽  
pp. 2068-2082 ◽  
Author(s):  
Yongyang Sun ◽  
José M Carcione ◽  
Boris Gurevich
Keyword(s):  
Aspect Ratio ◽  
Pore Space ◽  
Crack Density ◽  
Fluid Pressure ◽  
Porous Rocks ◽  
Dispersion Models ◽  
Pore Characteristics ◽  
Low Frequencies ◽  
High Frequencies ◽  
Significant Difference

SUMMARY The anelastic properties of porous rocks depend on the pore characteristics, specifically, the pore aspect ratio and the pore fraction (related to the soft porosity). At high frequencies, there is no fluid pressure communication throughout the pore space and the rock becomes stiffer than at low frequencies, where the pore pressure is fully equilibrated. This causes a significant difference between the moduli at low and high frequencies, which is known as seismic dispersion and is commonly explained by the squirt-flow mechanism. In this paper, we consider and contrast three squirt-flow dispersion models: the modified Mavko–Jizba model, valid for a porous medium with arbitrary shapes of the pores and cracks, and two other models, based on idealized geometries of spheres and ellipsoids: the EIAS (equivalent inclusion-average stress) and CPEM (cracks and pores effective medium) models. We first perform analytical comparisons and then compute several numerical examples to demonstrate similarities and differences between the models. The analytical comparison shows that when the stiff pores are spherical and the crack density is small, the theoretical predictions of the three models are very close to each other. However, when the stiff pores are spheroids with an aspect ratio smaller than 1 (say, between 0.2 and 1), the predictions of inclusion based models are not valid at frequencies of ultrasonic measurements on rock samples. In contrast, the predictions of the modified Mavko–Jizba model are valid at ultrasonic frequencies of about 106 Hz, which is a typical frequency of laboratory measurements on core samples. We also introduce Zener-based bulk and shear dispersion indices, which are proportional to the difference between the high- and low-frequency stiffness moduli, and are a measure of the degree of anelasticity, closely related to the quality factors by view of the Kramers–Kronig relations. The results show that the three models yield similar moduli dispersion with very small differences when the crack density is relatively high. The indices versus crack density can be viewed as a template to obtain the crack properties from low- and high-frequency velocity measurements.

Incorporating mechanisms of fluid pressure relaxation into inclusion‐based models of elastic wave velocities

Geophysics ◽  
2003 ◽  
Vol 68 (4) ◽  
pp. 1173-1181 ◽  
Author(s):  
S. Richard Taylor ◽  
Rosemary J. Knight
Keyword(s):  
Elastic Wave ◽  
Water Saturation ◽  
Laboratory Data ◽  
Fluid Pressure ◽  
P Wave ◽  
Porous Rocks ◽  
Low Frequencies ◽  
Wave Velocities ◽  
Exact Agreement ◽  
Flow Through

Our new method incorporates fluid pressure communication into inclusion‐based models of elastic wave velocities in porous rocks by defining effective elastic moduli for fluid‐filled inclusions. We illustrate this approach with two models: (1) flow between nearest‐neighbor pairs of inclusions and (2) flow through a network of inclusions that communicates fluid pressure throughout a rock sample. In both models, we assume that pore pressure gradients induce laminar flow through narrow ducts, and we give expressions for the effective bulk moduli of inclusions. We compute P‐wave velocities and attenuation in a model sandstone and illustrate that the dependence on frequency and water‐saturation agrees qualitatively with laboratory data. We consider levels of water saturation from 0 to 100% and all wavelengths much larger than the scale of material heterogeneity, obtaining near‐exact agreement with Gassmann theory at low frequencies and exact agreement with inclusion‐based models at high frequencies.

FORMATION VELOCITY AND DENSITY—THE DIAGNOSTIC BASICS FOR STRATIGRAPHIC TRAPS

Geophysics ◽  
1974 ◽  
Vol 39 (6) ◽  
pp. 770-780 ◽  
Author(s):  
G. H. F. Gardner ◽  
L. W. Gardner ◽  
A. R. Gregory
Keyword(s):  
Mineral Composition ◽  
Chemical Interaction ◽  
Sedimentary Rocks ◽  
Fluid Pressure ◽  
P Wave ◽  
Elastic Behavior ◽  
Reflection Coefficients ◽  
Porous Rocks ◽  
The Difference ◽  
Recent Sediments

A multiplicity of factors influence seismic reflection coefficients and the observed gravity of typical sedimentary rocks. Rock velocity and density depend upon the mineral composition and the granular nature of the rock matrix, cementation, porosity, fluid content, and environmental pressure. Depth of burial and geologic age also have an effect. Lithology and porosity can be related empirically to velocity by the time‐average equation. This equation is most reliable when the rock is under substantial pressure, is saturated with brine, and contains well‐cemented grains. For very low porosity rocks under large pressures, the mineral composition can be related to velocity by the theories of Voigt and Reuss. One effect of pressure variation on velocity results from the opening or closing of microcracks. For porous sedimentary rocks, only the difference between overburden and fluid pressure affects the microcrack system. Existing theory does not take into account the effect of microcrack closure on the elastic behavior of rocks under pressure or the chemical interaction between water and clay particles. The theory of Gassmann can be used to calculate the effect of different saturating fluids on the P-wave velocity of porous rocks. The effect may be large enough in shallow, recent sediments to permit gas sands to be distinguished from water sands on seismic records. At depths greater than about 6000 ft, however, the reflection coefficient becomes essentially independent of the nature of the fluid. Data show the systematic relationship between velocity and density in sedimentary rocks. As a result, reflection coefficients can often be estimated satisfactorily from velocity information alone.

Petroelastic Model PEM for a Highly Heterogeneous Cretaceous Reservoir in Middle East

2021 ◽  
Author(s):  
Rafael Ignacio Celma ◽  
Nepal Singh ◽  
Kamal Ouldamer ◽  
Pascal Debec
Keyword(s):  
Middle East ◽  
Aspect Ratio ◽  
Pore Space ◽  
Elastic Behavior ◽  
Pore Geometry ◽  
Elastic Model ◽  
Reservoir Properties ◽  
Sonic Log ◽  
Seismic Acquisition ◽  
4D Seismic

Abstract The objective of this project is to simulate elastic logs (sonic P, sonic S and density) through a Petroelastic Model (PEM) for a complex lithology reservoir in the Middle East, that later will be used as input for a new 4D seismic feasibility study. A log conditioning (despike, depth shift, hydrocarbon correction and normalization) and comprehensive petrophysical analysis was first performed, to obtain lithology volumetric, porosity and saturation, that later were used as input for the PEM. Some wells with recorded P and S sonic log were used to conduct different cross plots of elastic properties (e.g. Vp/Vs vs. Acoustic Impedance) in order to understand how lithology, porosity and saturation affect the elastic parameters of the reservoir. After understanding and assessing the elastic behavior with the reservoir properties, three approaches to construct a PEM were tested on this reservoir. The first approach used to construct PEM applying Hashin Shtrikman (H-S) mixt, considering the solid part as a mixture of dolomite and limestone and pore space filled with a mix of oil and water. This model is limited because assumes a homogenous geometry of the pores. To address the pore geometry a Kuster Toksoz (K-T) approach was subsequently tested but the challenge was that there was no clear organization of the aspect ratio (either by lithofacies or petrophysical groups) so the original logs were used to control of the aspect ratio trough a fit function. The third approach was to use a function that models the incompressibility model of the frame (Kdry) with porosity. The result of H-S was a good agreement in the low porosity areas but in the porous intervals, it is observed that the velocities were quite high due the effect of the pore geometry that was not properly assessed by H-S. Despite reasonable reconstructions, K-T was limited by the impossibility to apply it to the wells without sonic P and S (uncalibrated aspect ratio) or a fortiori to a 3D grid. For the Kdry vs. Porosity function the result was very successful since the function is not dependent on the pore geometry, and addresses the ratio issue between solid and pore space. Then with the help of the Gassman Equation, the final Incompressibility Mix Module (Kmix) was calculated and a reconstructed sonic P and S were available for all the wells. The PEM was coded in order to deploy over a 3D property model hence a volumetric elastic model was available to assess the feasibility for new seismic acquisition.

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 3D Finite Element Analysis of Rotary Instruments in Root Canal Dentine with Different Elastic Moduli

2021 ◽  
Vol 11 (6) ◽  
pp. 2547 ◽  
Author(s):  
Carlo Prati ◽  
João Paulo Mendes Tribst ◽  
Amanda Maria de Oliveira Dal Piva ◽  
Alexandre Luiz Souto Borges ◽  
Maurizio Ventre ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Root Canal ◽  
Elastic Moduli ◽  
Reaction Force ◽  
Von Mises Stress ◽  
Elastic Behavior ◽  
Element Analysis ◽  
Heat Treated ◽  
Von Mises

The aim of the present investigation was to calculate the stress distribution generated in the root dentine canal during mechanical rotation of five different NiTi endodontic instruments by means of a finite element analysis (FEA). Two conventional alloy NiTi instruments F360 25/04 and F6 Skytaper 25/06, in comparison to three heat treated alloys NiTI Hyflex CM 25/04, Protaper Next 25/06 and One Curve 25/06 were considered and analyzed. The instruments’ flexibility (reaction force) and geometrical features (cross section, conicity) were previously investigated. For each instrument, dentine root canals with two different elastic moduli(18 and 42 GPa) were simulated with defined apical ratios. Ten different CAD instrument models were created and their mechanical behaviors were analyzed by a 3D-FEA. Static structural analyses were performed with a non-failure condition, since a linear elastic behavior was assumed for all components. All the instruments generated a stress area concentration in correspondence to the root canal curvature at approx. 7 mm from the apex. The maximum values were found when instruments were analyzed in the highest elastic modulus dentine canal. Strain and von Mises stress patterns showed a higher concentration in the first part of curved radius of all the instruments. Conventional Ni-Ti endodontic instruments demonstrated higher stress magnitudes, regardless of the conicity of 4% and 6%, and they showed the highest von Mises stress values in sound, as well as in mineralized dentine canals. Heat-treated endodontic instruments with higher flexibility values showed a reduced stress concentration map. Hyflex CM 25/04 displayed the lowest von Mises stress values of, respectively, 35.73 and 44.30 GPa for sound and mineralized dentine. The mechanical behavior of all rotary endodontic instruments was influenced by the different elastic moduli and by the dentine canal rigidity.

Study of elastic moduli and thermal properties of RMnO3 (R = La, Nd) compounds

2014 ◽  
Vol 03 (02) ◽  
pp. 1450011 ◽  
Author(s):  
Dinesh Varshney ◽  
Dinesh Choudhary
Keyword(s):  
Heat Capacity ◽  
Thermal Properties ◽  
Elastic Moduli ◽  
Systematic Investigation ◽  
Elastic Behavior ◽  
Repulsive Interaction ◽  
Interionic Interaction ◽  
Einstein Temperature ◽  
Capacity Calculation ◽  
Increasing Temperature

In this paper, we develop a theoretical model for quantitative analysis of temperature-dependent heat capacity calculation of the magnetoresistance compounds RMnO 3 ( R = La , Nd ). The results on heat capacity obtained by us are in good agreement with the measured values. An effective interionic interaction potential (EIoIP) with the long-range Coulomb, van der Waals (vdW) interaction and short-range repulsive interaction up to second neighbor ions within the Hafemeister and Flygare approach was formulated to estimate the Debye and Einstein temperature and was found to be consistent with the available experimental data. In addition, the properties studied are the cohesive energy, molecular force constant, Restrahlen frequency and Gruneisen parameter. After characterizing thermal properties, a systematic investigation of elastic behavior has been undertaken and it has been found that the elastic moduli are decreasing continuously with increasing temperature.

Modes of Wave Propagation and Dispersion Relations in Inclusion Reinforced Composite Plates

2010 ◽  
Author(s):  
Yu Cheng Liu ◽  
Jin Huang Huang
Keyword(s):  
Composite Plate ◽  
Elastic Moduli ◽  
Lamb Waves ◽  
Plate Thickness ◽  
Composite Plates ◽  
Dispersion Relations ◽  
Elastic Behavior ◽  
Effective Elastic Moduli ◽  
Aspect Ratios ◽  
Reinforced Composite

This paper mainly analyzes the wave dispersion relations and associated modal pattens in the inclusion-reinforced composite plates including the effect of inclusion shapes, inclusion contents, inclusion elastic constants, and plate thickness. The shape of inclusion is modeled as spheroid that enables the composite reinforcement geometrical configurations ranging from sphere to short and continuous fiber. Using the Mori-Tanaka mean-field theory, the effective elastic moduli which are able to elucidate the effect of inclusion’s shape, stiffness, and volume fraction on the composite’s anisotropic elastic behavior can be predicted explicitly. Then, the dispersion relations and the modal patterns of Lamb waves determined from the effective elastic moduli can be obtained by using the dynamic stiffness matrix method. Numerical simulations have been given for the various inclusion types and the resulting dispersions in various wave types on the composite plate. The types (symmetric or antisymmetric) of Lamb waves in an isotropic plate can be classified according to the wave motions about the midplane of the plate. For an orthotropic composite plate, it can also be classified as either symmetric or antisymmetric waves by analyzing the dispersion curves and inspecting the calculated modal patterns. It is also found that the inclusion contents, aspect ratios and plate thickness affect propagation velocities, higher-order mode cutoff frequencies, and modal patterns.

Subpixel determination of wormhole tip position in 4D tomography of dissolving limestone cores

2021 ◽  
Author(s):  
Rishabh Prakash Sharma ◽  
Max P. Cooper ◽  
Anthony J.C. Ladd ◽  
Piotr Szymczak
Keyword(s):  
Flow Field ◽  
Pore Space ◽  
Nonlinear Process ◽  
Linear Interpolation ◽  
Flow Fields ◽  
Porous Rocks ◽  
Dissolution Experiment ◽  
Novel Approach ◽  
Highly Nonlinear ◽  
Computed Microtomography

<p>Dissolution of porous rocks by reactive fluids is a highly nonlinear process resulting in a variety of dissolution patterns, the character of which depends on physical conditions such as flow rate and reactivity of the fluid. Long, finger-like dissolution channels, “wormholes”, are the main subject of interest in the literature, however, the underlying dynamics of their growth remains unclear. </p><p>While analyzing the tomography data on wormhole growth.  one open question is to define the exact position of the tip of the wormhole. Near the tip the wormhole gradually thins out and the proper resolution of its features is hindered by the finite spatial resolution of the tomographs. In particular, we often observe in the near-tip region several disconnected regions of porosity growth, which - as we hypothesized - are connected by the dissolution channels at subpixel scale. In this study, we show how these features can be better resolved by using numerically calculated flow fields in the reconstructed pore-space. </p><p>We used 70 micrometers, 16-bit grayscale X-ray computed microtomography (XCMT) time series scans of limestone cores, 14mm in diameter and 25mm in length. Scans were performed during the entire dissolution experiment with an interval of 8 minutes. These scans were further processed using a 3-phase segmentation proposed by Luquot et al.[1], in which grayscale voxels are converted to macro-porosity, micro-porosity and grain phases from their grayscale values. The macro-porous phase is assigned a porosity of 1, while the grain phase is assigned 0. Micro-porous regions are assigned an intermediate value determined by linear interpolation between pore and grain threshold using grayscale values. An OpenFOAM based, Darcy-Brinkman solver, porousFoam, is then used to calculate the flow field in this extracted porosity field. </p><p>Porosity contours reconstructed from the tomographs show some disconnected porosity growth near the tip region which later become part of the wormhole in subsequent scans. We have used a novel approach by including the micro-porosity phase in pore-space to calculate the flow-fields in the near-tip region. The calculated flow fields clearly show an extended region of focused flow in front of the wormhole tip, which is a manifestation of the presence of a wormhole at the subpixel scale. These results show that micro-porosity plays an important role in dissolution and 3-phase segmentation combined with the flow field calculations is able to capture the sub-resolved dissolution channels. </p><p> </p><p> [1] Luquot, L., Rodriguez, O., and Gouze, P.: Experimental characterization of porosity structure and transport property changes in limestone undergoing different dissolution regimes, Transport Porous Med., 101, 507–532, 2014</p>

Chemotaxis under flow disorder shapes microbial dispersion in porous media 

2021 ◽  
Author(s):  
Pietro de Anna ◽  
Amir A. Pahlavan ◽  
Yutaka Yawata ◽  
Roman Stocker ◽  
Ruben Juanes
Keyword(s):  
Porous Media ◽  
Dispersion Coefficient ◽  
Pore Space ◽  
Low Flow ◽  
Pore Scale ◽  
Porous Rocks ◽  
Chemical Gradients ◽  
Deep Earth ◽  
Bacterium Bacillus Subtilis ◽  
Bacterium Bacillus

<div> <div> <div> <p>Natural soils are host to a high density and diversity of microorganisms, and even deep-earth porous rocks provide a habitat for active microbial communities. In these environ- ments, microbial transport by disordered flows is relevant for a broad range of natural and engineered processes, from biochemical cycling to remineralization and bioremediation. Yet, how bacteria are transported and distributed in the sub- surface as a result of the disordered flow and the associ- ated chemical gradients characteristic of porous media has remained poorly understood, in part because studies have so far focused on steady, macroscale chemical gradients. Here, we use a microfluidic model system that captures flow disorder and chemical gradients at the pore scale to quantify the transport and dispersion of the soil-dwelling bacterium Bacillus subtilis in porous media. We observe that chemotaxis strongly modulates the persistence of bacteria in low-flow regions of the pore space, resulting in a 100% increase in their dispersion coefficient. This effect stems directly from the strong pore-scale gradients created by flow disorder and demonstrates that the microscale interplay between bacterial behaviour and pore-scale disorder can impact the macroscale dynamics of biota in the subsurface.</p> </div> </div> </div>

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