scholarly journals The influence of the pore shape on the bulk modulus and the Biot coefficient of fluid-saturated porous rocks

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
A. P. S. Selvadurai ◽  
A. P. Suvorov
Keyword(s):  
Bulk Modulus ◽  
Pore Space ◽  
Pore Shape ◽  
Porous Rocks ◽  
Partially Saturated ◽  
Biot Coefficient ◽  
Stress Partitioning ◽  
Oblate Spheroids ◽  
Poroelastic Materials ◽  
Applied Stresses

Abstract Fluid-saturated rocks are multi-phasic materials and the mechanics of partitioning the externally applied stresses between the porous skeleton of the rock and the interstitial fluids has to take into consideration the mechanical behaviour of the phases. In these studies the porosity of the multi-phasic material is important for estimating the multi-phasic properties and most studies treat the porosity as a scalar measure without addressing the influence of pore shape and pore geometry. This paper shows that both the overall bulk modulus of a porous medium and the Biot coefficient depend on the shape of the pores. Pores with shapes resembling either thin oblate spheroids or spheres are considered. The Mori–Tanaka and the self-consistent methods are used to estimate the overall properties and the results are compared with experimental data. The pore density and the aspect ratio of the spheroidal pores influence the porosity of the geomaterials. For partially saturated rocks, the equivalent bulk modulus of the fluid–gas mixture occupying the pore space can also be obtained. The paper also examines the influence of the pore shape in estimating the Biot coefficient that controls the stress partitioning in fluid-saturated poroelastic materials.

Stochastic joint inversion of 2D seismic and seismoelectric signals in linear poroelastic materials: A numerical investigation

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. N19-N31 ◽  
Author(s):  
Abderrahim Jardani ◽  
André Revil ◽  
Evert Slob ◽  
Walter Söllner
Keyword(s):  
Bulk Modulus ◽  
Posterior Probability ◽  
Solid Phase ◽  
Joint Inversion ◽  
Layer Boundary ◽  
Partially Saturated ◽  
Poroelastic Materials ◽  
Posterior Probability Density ◽  
Porous Frame ◽  
Horizontal Layers

The interpretation of seismoelectrical signals is a difficult task because coseismic and seismoelectric converted signals are recorded simultaneously and the seismoelectric conversions are typically several orders of magnitude smaller than the coseismic electrical signals. The seismic and seismoelectric signals are modeled using a finite-element code with perfectly matched layer boundary conditions assuming a linear poroelastic body. We present a stochastic joint inversion of the seismic and seismoelectrical data based on the adaptive Metropolis algorithm, to obtain the posterior probability density functions of the material properties of each geologic unit. This includes the permeability, porosity, electrical conductivity, bulk modulus of the dry porous frame, bulk modulus of the fluid, bulk modulus of the solid phase, and shear modulus of the formations. A test of this approach is performed with a synthetic model comprising two horizontal layers and a reservoir partially saturated with oil, which is embedded in the second layer. The result of the joint inversion shows that we can invert the permeability of the reservoir and its mechanical properties.

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.

Exact equations for fluid and solid substitution

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. L21-L32 ◽  
Author(s):  
Nishank Saxena ◽  
Gary Mavko
Keyword(s):  
Shear Stress ◽  
Shear Modulus ◽  
Bulk Modulus ◽  
Fluid Substitution ◽  
Pore Shape ◽  
Effective Shear Modulus ◽  
Stiffness Measurement ◽  
Saturated Rock ◽  
Mean Stresses

We derived exact equations, elastic bulk and shear, for fluid and solid substitution in monomineralic isotropic rocks of arbitrary pore shape and suggested methods to obtain the required substitution parameters. We proved that the classical Gassmann’s bulk modulus equation for fluid-to-fluid substitution is exact for solid-to-solid substitution if compression-induced mean stresses (pressure) in initial and final pore solids are homogeneous and either the shear modulus of the substituted solid does not change or no shear stress is induced in pores. Moreover, when compression-induced mean stresses in initial and final pore solids are homogeneous, we evaluated exact generalizations of Gassmann’s bulk modulus equation, which depend on usually known parameters. For the effective shear modulus, we found general exactness conditions of Gassmann and other approximations. Using the new exact substitution equations, we interpreted that predicting solid-filled rock stiffness from a dry rock stiffness measurement requires more information (i.e., assumptions about the pore shape) compared to predicting the same from a fluid-saturated rock stiffness.

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>

A dynamic elastic model for squirt-flow effect and its application on fluid-viscosity-associated velocity dispersion in reservoir sandstones

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. MR201-MR212
Author(s):  
Zhi-Qiang Yang ◽  
Tao He ◽  
Chang-Chun Zou
Keyword(s):  
Velocity Dispersion ◽  
Pore Space ◽  
Pore Fluid ◽  
Quantitative Prediction ◽  
Elastic Model ◽  
Fluid Viscosity ◽  
Porous Rocks ◽  
S Wave ◽  
Flow Effect ◽  
Reservoir Sandstones

Velocity dispersion is a common phenomenon for fluid-charged porous rocks and carries important information on the pore structure and fluid in reservoir rocks. Previous ultrasonic experiments had measured more significant non-Biot velocity dispersion on saturated reservoir sandstones with increasing pore-fluid viscosity. Although wave-induced local squirt-flow effect could in theory cause most of the non-Biot velocity dispersion, its quantitative prediction remains a challenge. Several popular models were tested to predict the measured velocities under undrained conditions, but they either underestimated the squirt-flow effect or failed to simultaneously satisfy P- and S-wave velocity dispersions (especially for higher viscosity fluids). Based on the classic double-porosity theory that pore space is comprised of mainly stiff/Biot’s porosity and minor compliant porosity, an effective “wet frame” was hypothesized to account for the squirt-flow effect, whose compliant pores are filled with a hypothesized fluid with dynamic modulus. A new dynamic elastic model was then introduced by extending Biot theory to include the squirt-flow effect, after replacing the dry-frame bulk/shear moduli with their wet-frame counterparts. In addition to yielding better velocity predictions for P- and S-wave measurements of different fluid viscosities, the new model is also more applicable because its two key tuning parameters (i.e., the effective aspect ratio and porosity of compliant pores) at in situ reservoir pressure could be constrained with laboratory velocity measurements associated with pore-fluid viscosities.

scholarly journals Effective thermal conductivity of partially saturated porous rocks

2007 ◽  
Vol 44 (3-4) ◽  
pp. 811-833 ◽  
Author(s):  
C. Gruescu ◽  
A. Giraud ◽  
F. Homand ◽  
D. Kondo ◽  
D.P. Do
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Porous Rocks ◽  
Partially Saturated

Effective-Stress Coefficients of Porous Rocks Involving Shocks and Loading/Unloading Hysteresis

SPE Journal ◽  
2020 ◽  
pp. 1-24
Author(s):  
Faruk Civan
Keyword(s):  
Effective Stress ◽  
Power Law ◽  
Rock Properties ◽  
Porous Rocks ◽  
Limit Values ◽  
Biot Coefficient ◽  
Rock Formations ◽  
Porosity Ratio ◽  
Basic Power ◽  
Power Law Equation

Summary A critical review, examination, and clarification of the various issues and problems concerning the definition and dependence of the effective-stress coefficients of porous-rock formations is presented. The effective-stress coefficients have different values for different rock properties because the physical mechanisms of rock deformation can affect the various rock properties differently. The alteration of petrophysical properties occurs by the onset of various rock-deformation/damaging processes, including pore collapsing and grain crushing, and affects the values of the effective-stress coefficients controlling the different petrophysical properties of rock formations. The slope discontinuity observed in the effective-stress coefficients of naturally or induced fractured-rock formations during loading/unloading, referred to as a shock effect, is essentially related to deformation of fractures at less than the critical effective stress and deformation of matrix at greater than the critical effective stress. The hysteresis observed in the effective-stress coefficients of heterogeneous porous rocks during loading/unloading is attributed to elastic deformation under the fully elastic predamage conditions, and/or irreversible pore-structure-alteration/deformation processes. A proper correlation of the Biot-Willis coefficient controlling the bulk volumetric strain is developed using the data available from various sources in a manner to meet the required endpoint-limit conditions of the Biot-Willis coefficient, ranging from zero to unity. The modified power-law equation presented in this paper yields a physically meaningful correlation because it successfully satisfies the low-end- and high-end-limit values of the Biot-Willis coefficient and also provides a better quality match of the available experimental data than the semilogarithmic equation and the popular basic power-law equation. It is shown that the semilogarithmic correlation cannot predict the values of the Biot coefficient beyond the range of the data because it generates unrealistic values approaching the negative infinity for the Biot coefficient for the low-permeability/porosity ratio and unrealistically high values approaching the positive infinity for the high-permeability/porosity ratio. The basic power-law equation is not adequate either because it can only satisfy the low-end value but cannot satisfy the high-end value of the Biot coefficient. The correlation developed in this paper from the modified power-law equation is effectively applicable over the full range of the Biot-Willis coefficient, extending from zero to unity. To the best of the author’s knowledge, this paper is the first to present an effective theory and formulation of the convenient correlation of the Biot-Willis poroelastic coefficient that not only satisfies both of the two endpoint-limit values of the Biot-Willis coefficient but also produces the best match of the available experimental data.

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