Equant Pores Research Articles

Amendment of different biochars changed pore characteristics and permeability of Ultisol macroaggregates identified by X-ray computed tomography (CT)

The addition of biochars produced by different feedstocks to soil affects soil aggregation, which has been shown to be critical for soil carbon sequestration, water holding capacity and plant growth. In this study, rice stalk biochar (RB) and canola stalk biochar (CB) produced at 350℃ were added to a Ultisol at the 1% rate. After a three-year incubation, the macroaggregates (5–6 mm) in soils were separated for quantification of pore structure using industrial X-ray computed tomography (CT) scanning. The RB and CB treatments significantly increased the total porosity and the ratio of connectivity to isolated porosity(C/I) in macroaggregates relative to CK treatments. The addition of biochars decreased the proportion of equant pores in the macroaggregates, while increased the proportion of irregular pores such as prolate and acircular pores, resulting in the high porosity heterogeneity in macroaggregates. The canola stalk biochar had a larger effect on the improvement of pore structure than rice stalk biochar, while having the opposite effect on pore throat structure. There was a positive correlation between porosity, connectivity and SOC in macroaggregates. Simulation results on water flow showed that the permeability for RB and CB treatments were 25.16 μm2 and 28.62 μm2, respectively, which were 116.7% and 146.5% higher than that of CK treatment (11.61 μm2). The results indicated that the biochars altered the pore structure of macroaggregates, potentially enhancing the functional services of macroaggregates such as SOC storage and hydraulic properties. The findings provided the detailed information on the effect of different biochar additions on pore structure in macroaggregates and simulated soil water movement within the macroaggregates, which is important for understanding the mechanism of biochars affecting soil aggregation and its functions.

Effects of different pore shapes on the pressure and frequency dependence of velocities of oil-saturated tight sandstone

The pressure dependence of elastic parameters of rocks is mainly controlled by the geometry of the pore space. In general, the compliant-stiff pore structure model can be used to reasonably describe this pressure dependence. However, our experiment measurements revealed that for tight sandstone rock with complex pore structures, the contribution of the compressibility of the stiff pores to the elastic modulus is significant. The dual porosity is not sufficient to explain the variation of ultrasonic velocity with pressure. For this reason, we adopted a triple pore structure to divide the rock pore space into equant pores, intermediate pores and compliant pores. Our laboratory measurement and model results show that this pore space division can better describe the pressure dependence of the elastic moduli of rocks. The low-frequency stress–strain measurements show that the fluid-saturated tight sandstone has obvious dispersion in the seismic frequency band, which is primarily attributed to the squirt flow effect. In order to study the pressure and frequency dependence of the elastic moduli of tight sandstone, we retrieved the geometric parameters of the pore structure from the pressure variation of the ultrasonic velocities under dry conditions. Based on this complex pore structure and the extension of the squirt flow model, we constructed an elaborate rock physics model to explain the pressure and frequency dependence of velocity. The model does not require adjustable parameters, and all parameters are measured and calculated by the laboratory, which improves the accuracy of theoretical modelling. The modified squirt flow model can be used to describe dispersion and attenuation in a wide frequency band, and fit well with the velocity measurements in both the low-frequency range and the ultrasonic frequency range under different pressures. Therefore, this rock physics model could be applied in the extraction of pore microstructure and fluid properties provided elastic moduli or velocities can be estimated accurately.

Integration of Multiscale Imaging of Nanoscale Pore Microstructures in Gas Shales

Quantification of the microstructures of shales is difficult due to their complexity which extends across many orders of magnitude of scale. Nevertheless, shale microstructures are extremely important, not only as shale gas resources but also as cap rocks in CCS resources, in geothermal reservoirs, and as a host to the long-term storage of radioactive materials. In this work, we have performed ultrahigh-resolution CT imaging (nano-CT), mercury injection porosimetry (MIP), and nitrogen adsorption experiments on a sample of gas shale for which we already have focused ion beam scanning electron microscopy (FIB-SEM) and high-resolution CT (micro-CT) data sets. The combination of these data sets has allowed us to examine the microstructure of the shale in unprecedented depth across a wide range of scales (from about 20 nm to 0.5 mm). Overall, the sample shows a porosity of 0.67 ± 0.009% from the nano-CT data, 0.0235 ± 0.003% from nitrogen adsorption, and 0.60 ± 0.07% from MIP, which compare with 0.10 ± 0.01%, 0.52 ± 0.05%, and 0.94 ± 0.09% from three FIB-SEM measurements and 0.06 ± 0.008% from one micro-CT measurement. The data vary due to the different scales at which each technique interrogates the rock and whether the pores are openly accessible (especially in the case of the nitrogen adsorption value). The measured kerogen fraction is 32.4 ± 1.45% from nano-CT compared with 34.8 ± 1.74%, 38.2 ± 1.91%, 41.4 ± 2.07%, and 44.5 ± 2.22% for three FIB-SEM and one micro-CT measurement. The pore size imaged by nano-CT ranged between 100 and 5000 nm, while the corresponding ranges were between 3 and 2000 nm for MIP analysis and between 2 and 90 nm for N2 adsorption. The distribution of pore aspect ratio and scale-invariant pore surface area to volume ratio (σ) as well as the calculated permeability shows the sample to have a high shale gas potential. Aspect ratios indicate that most of the pores that contribute significantly to pore volume are oblate, which is confirmed by the range of σ (3–13). Oblate pores have greater potential for interacting with other pores compared to equant and needle-shaped prolate pores as well optimizing surface area for gas to desorb from the kerogen into the pores. Permeability essays provide 2.61 ± 0.42 nD from the nano-CT data, 2.65 ± 0.45 nD from MIP, and (5.07 ± 0.02) × 10–4 nD from nitrogen adsorption, which are consistent with expectations for generic gas shales (i.e., tens of nD) and the measurements made previously on the same sample using FIB-SEM and micro-CT imaging techniques.

Poroacoustoelasticity for rocks with a dual-pore structure

Acoustoelasticity describes the interaction of acoustic waves with nonlinear elastic deformations, particularly the change of wave velocity due to initial stresses or strains in a predeformed body. The theory extends the strain energy to cubic terms (third-order elasticity) and allows for finite strains to model deformations at high confining pressures. However, the theory considers equant (stiff) pores but neglects the effects of soft (compliant) pores, such as microfractures, cracks, and grain contacts. Our main contribution is to include these effects. Application of the novel poroacoustoelasticity theory to ultrasonic measurements on carbonate samples at varying confining pressures provides a better fit for the measured data of pressure dependence of wave velocity. We have quantified the contribution of the compliant pores to the nonlinear behavior of the wave velocity and determined the relation between the threshold pressure (beyond which the theories with and without compliant pores yield the same velocity) and porosity and permeability. The extension of poroacoustoelasticity theory by incorporating a dual-pore structure provides better description for stress dependence of wave velocity in fluid-saturated heterogeneous rocks, which can be applicable in further field studies regarding reservoir characterization and in situ stress estimation.

Experimental Investigation on Static and Dynamic Bulk Moduli of Dry and Fluid-Saturated Porous Sandstones

Knowledge of pressure-dependent static and dynamic moduli of porous reservoir rocks is of key importance for evaluating geological setting of a reservoir in geo-energy applications. We examined experimentally the evolution of static and dynamic bulk moduli for porous Bentheim sandstone with increasing confining pressure up to about 190 MPa under dry and water-saturated conditions. The static bulk moduli (Ks) were estimated from stress–volumetric strain curves while dynamic bulk moduli (Kd) were derived from the changes in ultrasonic P- and S- wave velocities (~ 1 MHz) along different traces, which were monitored simultaneously during the entire deformation. In conjunction with published data of other porous sandstones (Berea, Navajo and Weber sandstones), our results reveal that the ratio between dynamic and static bulk moduli (Kd/Ks) reduces rapidly from about 1.5 − 2.0 at ambient pressure to about 1.1 at high pressure under dry conditions and from about 2.0 − 4.0 to about 1.5 under water-saturated conditions, respectively. We interpret such a pressure-dependent reduction by closure of narrow (compliant) cracks, highlighting that Kd/Ks is positively correlated with the amount of narrow cracks. Above the crack closure pressure, where equant (stiff) pores dominate the void space, Kd/Ks is almost constant. The enhanced difference between dynamic and static bulk moduli under water saturation compared to dry conditions is possibly caused by high pore pressure that is locally maintained if measured using high-frequency ultrasonic wave velocities. In our experiments, the pressure dependence of dynamic bulk modulus of water-saturated Bentheim sandstone at effective pressures above 5 MPa can be roughly predicted by both the effective medium theory (Mori–Tanaka scheme) and the squirt-flow model. Static bulk moduli are found to be more sensitive to narrow cracks than dynamic bulk moduli for porous sandstones under dry and water-saturated conditions.

Effect of pressure and fluid on pore geometry and anelasticity of dolomites

The acoustic properties of rocks depend on porosity, pressure, and pore fluid and also on pore geometry. Anelasticity (attenuation and velocity dispersion) is more affected by crack aspect ratio and fraction (soft pores) than by equant (stiff) pores. To study this fact, we have performed ultrasonic measurements on two dolomite samples under variable pressure and fluid content, and used the EIAS (equivalent inclusion-average stress) model to obtain the crack aspect ratio and fraction from the bulk and shear moduli of the rock. The theory has an excellent agreement with the experimental data, and the results show that the crack attributes decrease with increasing differential pressure and are higher for a stiffer fluid. In fact, the interpretation of the experiments with the model shows that crack fraction and aspect ratio increase with the bulk modulus of the fluid (water and oil). Then, by extending the theory to all frequencies, using the Zener mechanical model, we obtain the phase velocities and quality factors as a function of frequency. Our findings reveal the importance of considering differential pressure and fluid type to analyze pore geometry and rock anelasticity.

A rock-physics model to determine the pore microstructure of cracked porous rocks

SUMMARY Determining rock microstructure remains challenging, since a proper rock-physics model is needed to establish the relation between pore microstructure and elastic and transport properties. We present a model to estimate pore microstructure based on porosity, ultrasonic velocities and permeability, assuming that the microstructure consists on randomly oriented stiff equant pores and penny-shaped cracks. The stiff pore and crack porosity varying with differential pressure is estimated from the measured total porosity on the basis of a dual porosity model. The aspect ratio of pores and cracks and the crack density as a function of differential pressure are obtained from dry-rock P- and S-wave velocities, by using a differential effective medium model. These results are used to invert the pore radius from the matrix permeability by using a circular pore model. Above a crack density of 0.13, the crack radius can be estimated from permeability, and below that threshold, the radius is estimated from P-wave velocities, taking into account the wave dispersion induced by local fluid flow between pores and cracks. The approach is applied to experimental data for dry and saturated Fontainebleau sandstone and Chelmsford Granite.

Pressure-dependent bulk compressibility of a porous granular material modeled by improved contact mechanics and micromechanical approaches: Effects of surface roughness of grains

The change of the mechanical properties of granular materials with pressure is an important topic associated with many industrial applications. In this paper we investigate the influence of hydrostatic pressure (Pe) on the effective bulk compressibility (Ceff) of a granular material by applying two modified theoretical approaches that are based on contact mechanics and micromechanics, respectively. For a granular material composed of rough grains, an extended contact model is developed to elucidate the effect of roughness of grain surfaces on bulk compressibility. At relatively low pressures, the model predicts that the decrease of bulk compressibility with pressure may be described by a power law with an exponent of -1/2 (i.e., Ceff ∝Pe−1/2), but deviates at intermediate pressures. At elevated pressures beyond full contact, bulk compressibility remains almost unchanged, which may be roughly evaluated by continuum contact mechanics. As an alternative explanation of pressure-dependent bulk compressibility, we suggest a micromechanical model that accounts for effects of different types of pore space present in granular materials. Narrow and compliant inter-granular cracks are approximated by three-dimensional oblate spheroidal cracks with rough surfaces, whereas the equant and stiff pores surrounded by three and four neighboring grains are modeled as tubular pores with cross sections of three and four cusp-like corners, respectively. In this model, bulk compressibility is strongly reduced with increasing pressure by progressive closure of rough-walled cracks. At pressures exceeding crack closure pressure, deformation of the remaining equant pores is largely insensitive to pressure, with almost no further change in bulk compressibility. To validate these models, we performed hydrostatic compression tests on Bentheim sandstone (a granular rock consisting of quartz with high porosity) under a wide range of pressure. The relation between observed microstructures and measured pressure-dependent bulk compressibility is well explained by both suggested models.

Mineral Alteration and Fracture Influence on the Elastic Properties of Volcaniclastic Rocks

AbstractIn geothermal environments, the physical properties of rocks, such as porosity and alteration, are highly variable and control the reservoir's elastic and hydraulic properties. Elastic wave velocity in volcaniclastic rocks and their relation to fractures, pore shapes, and mineral alteration is mostly unknown. We measure ultrasonic P and S wave speeds on volcanic rocks from the Ngatamariki Geothermal Reservoir, New Zealand. Data clustering of wave speed versus porosity and density allow us to classify lithotypes of variable propylitic and phyllic mineral alteration. Wave speeds increase first due to porosity reduction as a result of mineral alteration and welding and, second, due to the high elasticity of alteration minerals (epidote, chlorite, and carbonates). We model the rock porosity as composed of equant pores and oblate‐spheroidal microfractures following an elastic effective medium model. For our samples, microfracture porosities range from 4% in the volcaniclastic tuffs to less than 1% in the ignimbrites, which we validate with pycnometer porosity data under effective pressure. We quantify that within one geological volcaniclastic formation, wave speeds vary up to 47% due to rock alteration and welding, while the effect of microfractures and changes in effective stress on wave speeds is secondary (up to 11%) but not negligible. From the experimental and numerical results we show that equant pores remain open at reservoir conditions (2,000 m) and can retain considerable porosity (10%). Our analysis has implications for microfracture and pore network characterization in geothermal reservoirs, in particular, in vapor‐dominated systems where matrix porosity and permeability play a role.

A Broadband Laboratory Study of the Seismic Properties of Cracked and Fluid‐Saturated Synthetic Glass Media

AbstractFor better understanding of frequency dependence (dispersion) of seismic wave velocities caused by stress‐induced fluid flow, broadband laboratory measurements were performed on a suite of synthetic glass media containing both equant pores and thermal cracks. Complementary forced oscillation, resonant bar, and ultrasonic techniques provided access to millihertz‐hertz frequencies, ~1 kHz frequency, and ~1 MHz frequency, respectively. The wave speeds or effective elastic moduli and associated dissipation were measured on samples under dry, argon‐ or nitrogen‐saturated, and water‐saturated conditions in sequence. The elastic moduli, in situ permeability, and crack porosity inferred from in situ X‐ray computed tomography all attest to strong pressure‐induced crack closure for differential (confining‐minus‐pore) pressures <30 MPa, consistent with zero‐pressure crack aspect ratios <4 × 10−4. The low permeabilities of these materials allow access to undrained conditions, even at subhertz frequencies. The ultrasonically measured elastic moduli reveal consistently higher shear and bulk moduli upon fluid saturation—diagnostic of the saturated‐isolated regime. For a glass rod specimen, containing cracks but no pores, saturated‐isolated conditions apparently persist to subhertz frequencies—requiring in situ aspect ratios (minimum/maximum dimension) <10−5. In marked contrast, the shear modulus measured at subhertz frequencies on a cracked glass bead specimen of 5% porosity, is insensitive to fluid saturation, consistent with the Biot‐Gassmann model for the saturated‐isobaric regime. The measured dispersion of the shear modulus approaches 10% over the millihertz‐megahertz frequency range for the cracked and fluid‐saturated media—implying that laboratory ultrasonic data should be used with care in the interpretation of field data.

Effective medium modeling: How to efficiently infer porosity from seismic data?

Many geophysical studies in reservoir characterization focus on the variations in the elastic properties of rocks. They commonly involve seismic data, which are processed in terms of seismic attributes. These processed data still have to be related to the physical properties of the rock mass and the fluids saturating the pore space. This need motivated the development of research projects based upon the effective medium theory (EMT). We have used the EMT to infer porosity and also fracture data from seismic impedances in part of the Fort Worth Basin, Texas. The main idea was to take advantage of the available impedances to characterize porosity in terms of equant pores and cracks. We then focused on the volume fraction of spherical pores and crack density. Shortly thereafter, we developed an effective medium (EM) model that provided numerical responses for seismic impedances. These responses were then compared to the impedances obtained from stratigraphic inversion. The overall procedure consisted in adjusting the input parameters of the EMT model, which were the spherical porosity and the crack density, to minimize the impedance mismatch. Our case study involved two limestone formations of the Fort Worth Basin (the Marble Falls and Ellenburger Formations) and one shaly formation (the Barnett Shale). The results are promising — The EMT turns out to be a very useful tool to explain reservoir and geophysical data in terms of microstructural properties, in particular, for fractured reservoirs.

Permeability dependency on stiff and compliant porosities: a model and some experimental examples

The relation between porosity and permeability is not unique. We show that stress dependencies of both porosity and permeability can provide useful information clarifying this relation. We propose that comparison of the functional dependency of porosity and permeability on stress shows which part of the void space in rocks controls the permeability, the compliant porosity or the stiff porosity. The compliant porosity (including very thin cracks and grain-contact vicinities) usually controls the stress dependencies of elastic moduli of rocks. One then observes exponential-like dependencies of elastic properties on effective stress. Stress-induced deformation of stiff pores (equant pores) have less significance for stress dependencies of elastic properties on loadings of low to moderate magnitudes (several tens of MPa). However, such pores can play a significant role in the stress dependency of permeability. We propose a rather general model of permeability as a function of the stiff and compliant porosity. The model includes the possibility that, in different rocks, permeability can be controlled by stiff pores or, alternatively, by compliant pores, or, finally, by a combination of these. This model predicts a functional dependency of permeability on stress, ranging from power-law to exponential-law and to a mixed behavior of permeability in these situations, respectively. We show experimental results for four samples of sedimentary rocks from oil reservoirs of the Russian Perm region indicating these types of behavior.

THREE DIMENSIONAL CHARACTERIZATION OF SOIL MACROPOROSITY BY X-RAY MICROTOMOGRAPHY

Analysis of the soil pore system represents an important way of characterizing soil structure. Properties such as the shape and number of pores can be determined through soil pore evaluations. This study presents a three-dimensional (3D) characterization of the shape and number of pores of a sub-tropical soil. To do so, a second generation X-ray microtomograph equipped with a plain type detector was employed. A voltage of 120 kV and current of 80 mA was applied to the X-ray tube. The soil samples analyzed were collected at three different depths (0-10, 10-20, and 20-30 cm). The results obtained allowed qualitative (images) and quantitative (3D) analyses of the soil structure, revealing the potential of the microtomographic technique, as well as the study of differences in soil macroporosity at different depths. Macroporosity was 5.14 % in the 0-10 cm layer, 5.10 % in the 10-20 cm layer, and 6.64 % in the 20-30 cm layer. The macroporosity of unclassified pores (UN) was 0.30 % (0-10 and 10-20 cm) and 0.40 % (20-30 cm), while equant pores (EQ) had values of 0.01 % at the three depths under analysis.

Effects of porosity and crack density on the compressive strength of rocks

We analyzed a compilation of previously published and new data on the uniaxial compressive strength (UCS) of various rock types using the pore-emanated crack and the wing crack models. While previous empirical studies have highlighted the strong control of porosity over the strength, the comparison with the pore-emanated crack model demonstrates that the pore size can be another microstructural parameter that exerts strong influence on the UCS of a rock that contains significant equant pores. We proposed an analytical simplification of the Ashby and Sammis wing crack model for uniaxial compression. Our model explicitly shows the relation between the UCS and the initial level of damage and/or the crack density in a rock. Our analysis also reveals that the normalized fracture toughness for ultimate failure is always significantly larger than the normalized fracture toughness for wing crack initiation. It is therefore more appropriate to consider two different parameters for the toughness in the micromechanical analysis. To gain insights into the physics of the Coulomb criterion, we derived analytic approximations for the empirical failure parameters with reference to the sliding wing crack model. The internal friction coefficient can be approximated as related linearly to the friction coefficient of the sliding crack, and the difference between the two coefficients has a logarithmic dependence on the square root of the crack density.

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

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.

Dispersion of elastic moduli in a porous-cracked rock: Theoretical predictions for squirt-flow

Crustal rocks contain variable amount of both cracks and equant pores depending on tectonic and thermal stresses but also on their geological origin. Crack damage and porosity change result in effects on elastic waves velocities. When rocks are fluid saturated, dispersion of the P- and S-waves should be taken into account. This paper deals with frequency dispersion of elastic moduli in a fluid saturated porous and cracked rock with the assumption that squirt-flow is the dominant process. We develop a theoretical approach to calculate both high (HF) and low (LF) frequency bulk and shear moduli. The HF moduli are derived from a new effective medium model, called CPEM, with an isotropic distribution of pores or cracks with idealized geometry, respectively spheres and ellipsoids. LF moduli are obtained by taking HF dry moduli from the CPEM and substituting into Gassmann's equations. In the case of a porosity only supported by equant pores, the calculated dispersion in elastic moduli is equal to zero. In the case of a crack porosity, no bulk dispersion is predicted but a shear dispersion appears. Finally in the general case of a mixed porosity (pores and cracks), dispersion in bulk and in shear is predicted. Our results show that the maximum dispersion is predicted for a mixture of pores and spheroidal cracks with a very small aspect ratio (≤ 10 − 3 ). Our theoretical predictions are compared to experimental data obtained during hydrostatic experiment performed on a basaltic rock and a good agreement is observed. We also used our theoretical model to predict elastic waves velocities and Vp/Vs ratio dispersion. We show that the P-waves dispersion can reach almost 20% and the Vp/Vs dispersion a maximum value of 9% for a crack porosity of about 1%. Since laboratory data are ultrasonic measurements and field data are obtained at much lower frequencies, these results are useful for geophysicists to interpret seismic data in terms of fluid and rock interactions.

Frequency and fluid effects on elastic properties of basalt: Experimental investigations

In order to investigate the effects of fluid and frequency on the elastic properties, we performed hydrostatic experiments on an Icelandic basalt specimen under both dry and saturated conditions. This basalt is characterized by a bimodal porosity, i.e., cracks and equant pores. The elastic properties ‐bulk moduli in our case‐ were investigated under high pressure through two experimental methods: (1) a classical one using ultrasonic P‐ and S‐waves velocities (frequency 106 Hz), (2) and a new one, using oscillation tests (frequency 10−2 Hz). In dry condition, experimental data show no significant difference between high (HF) and low (LF) frequency bulk moduli. However, in saturated conditions, two effects are highlighted: a physico‐chemical effect emphasized by a difference between drained and dry moduli, and a squirt‐flow effect evidenced by a difference between HF and LF undrained moduli.

Anisotropy of elastic wave velocities in deformed shales: Part 2 — Modeling results

This study was devoted to the interpretation of the evolution of elastic wave velocities in anisotropic shales that are subjected to deformation experiments in the laboratory. A micromechanical model was used to describe the macroscopic effective elastic properties and anisotropy of the rock in terms of its microscopic features, such as intrinsic anisotropy and crack/pore geometry. The experimental data (reported in Part 1) were compared quantitatively with the micromechanical model predictions to gain some insight into the microstructural behavior of the rock during deformation. The inversion of the experimental data using the micromechanical model was carried out by means of a numerical minimization of the least-squares distance between data and model in terms of effective compliances. Under isotropic mechanical loading, the overall behavior of the dry shale is consistent with the closure of crack-like pores, which are aligned in theplane of symmetry of the transversely isotropic background matrix. Those cracks represent a low fraction of the total porosity, but they have a strong effect on elastic wave velocities. The data are consistent with an initial (horizontal) crack density of 0.07. Crack closure also is evidenced at early stages of axial loading applied perpendicular to the shale bedding plane, whereas crack density increases significantly as axial stress is increased. Interpretation of the wet experiment is less straightforward, although some preliminary conclusions could be drawn. Under isotropic stress, crack closure also is evidenced, whereas crack density remains constant at the early stages of deviatoric loading. When axial peak stress is approached, crack density increases drastically, which likely indicates onset and development of vertical cracking. Wet experiments probably are more complex because water is likely to be expelled from crack-like pores toward equant pores in response to the mechanical loading.

Role of void space geometry in permeability evolution in crustal rocks at elevated pressure

A key consequence of the presence of void space within rock is their significant influence upon fluid transport properties. In this study, we measure changes in elastic wave velocities (P and S) contemporaneously with changes in permeability and porosity at elevated pressure for three rock types with widely different void space geometries: a high‐porosity sandstone (Bentheim), a tight sandstone (Crab Orchard), and a microcracked granodiorite (Takidani). Laboratory data are then used with the permeability models of Guéguen and Dienes and Kozeny‐Carman to investigate the characteristics that different void space geometries impart to measured permeabilities. Using the Kachanov effective medium theory, elastic wave velocities are inverted, permitting the recovery of crack density evolution with increasing effective pressure. The crack densities are then used as input to the microcrack permeability model of Guéguen and Dienes. The classic Kozeny‐Carman approach of Walsh and Brace is also applied to the measured permeability data via a least squares fit in order to extract tortuosity data. We successfully predict the evolution of permeability with increasing effective pressure, as directly measured in experiments, and report the contrast between permeability changes observed in rock where microcracks or equant pores dominate the microstructure. Additionally, we show how these properties are affected by anisotropy of the rock types via the measured anisotropic fabrics in each rock. The combined experimental and modeling results illustrate the importance of understanding the details of how rock microstructure changes in response to an external stimulus in predicting the simultaneous evolution of different rock physical properties.

Pressure‐dependent seismic response of fractured rock

Effects of external stress and pore pressure variations on the seismic signature of fractured rocks remain of interest to geoscientists and practicing geophysicists. Commonly, the effects are modeled theoretically, assuming fracture faces to be rough surfaces contacting each other via the surface asperities. The model proposed here differs from other models of this kind in that (1) fracture roughness is described by a single parameter and (2) a controlled degree of hydraulic connectivity between fractures and equant pores is introduced. This adds to the model's convenience and makes it applicable to a wide variety of reservoirs. The model predictions of seismic velocities in fractured rock at variable stress are consistent with experimental data. For fixed effective stress, the model predictions coincide with those obtained using the model with ellipsoidal fractures of certain average aspect ratio and the same fracture porosity.Apart from known effects, the model introduced predicts an amplification of the stress variation influence on fracturing‐induced anisotropy with an increase of connected equant porosity, a decrease of VP/VSwith effective stress, and implicit frequency dependence of the VP/VSrelation. It is also shown that amplitude versus offset (AVO) anomalies caused by fluid replacement can be seriously distorted if the fluid replacement is accompanied by significant variations of pore pressure, as, for example, at intense gas production. Neglecting these effects can lead to erroneous conclusions on shear modulus dependence on the pore fluid type. Qualitatively, in rocks with azimuthally aligned fracturing, the increase of effective stress affects AVO gradient in about the same way as the increase of water saturation parameter Vw. In contrast, the AVO intercept is not affected by variations of effective stress, while fluid replacement effect on the intercept is significant. Potentially, this can help distinguish the effects of pore pressure variations and fluid replacement on the AVO attributes.