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- Volume 61, Issue 2, 2013
Geophysical Prospecting - 2 - Rock Physics for Reservoir Exploration, Characterisation and Monitoring, 2013
2 - Rock Physics for Reservoir Exploration, Characterisation and Monitoring, 2013
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Laboratory seismic monitoring of supercritical CO2 flooding in sandstone cores using the Split Hopkinson Resonant Bar technique with concurrent x‐ray Computed Tomography imaging
More LessABSTRACTAccurate estimation of CO2 saturation in a saline aquifer is essential for the monitoring of supercritical CO2 injected for geological sequestration. Because of strong contrasts in density and elastic properties between brine and CO2 at reservoir conditions, seismic methods are among the most commonly employed techniques for this purpose. However the relationship between seismic (P‐wave) velocity and CO2 saturation is not unique because the velocity depends on both wave frequency and the CO2 distribution in rock. In the laboratory, we conducted measurements of seismic properties of sandstones during supercritical CO2 injection. Seismic responses of small sandstone cores were measured at frequencies near 1 kHz, using a modified resonant bar technique (Split Hopkinson Resonant Bar method). Concurrently, saturation and distribution of supercritical CO2 in the rock cores were determined via x‐ray CT scans. Changes in the determined velocities generally agreed with the Gassmann model. However, both the velocity and attenuation of the extension wave (Young's modulus or ‘bar’ wave) for the same CO2 saturation exhibited differences between the CO2 injection test and the subsequent brine re‐injection test, which was consistent with the differences in the CO2 distribution within the cores. Also, a comparison to ultrasonic velocity measurements on a bedded reservoir rock sample revealed that both compressional and shear velocities (and moduli) were strongly dispersive when the rock was saturated with brine. Further, large decreases in the velocities of saturated samples indicated strong sensitivity of the rock's frame stiffness to pore fluid.
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Sensitivity of flow and elastic properties to fabric heterogeneity in carbonates
Authors Ravi Sharma, Manika Prasad, Mike Batzle and Sandra VegaABSTRACTCarbonate rocks are heterogeneous at various levels from deposition to diagenesis. Any existing depositional heterogeneity becomes more complex when carbonate rocks are in contact with polar fluids. Our experiments on carbonate rocks show that change in textural heterogeneity leads to heterogeneity in the distribution of storage and flow properties that may govern changes in saturation patterns. This would be akin to any carbonate reservoir with a mix of heterogeneous and homogeneous facies within a formation and their control on saturation distribution in response to a standard imbibition process. Associated with the saturation pattern heterogeneities, the resultant elastic property distributions also change. We quantify this heterogeneity and its effects on flow and seismic properties based on a few textural extremes of fabric heterogeneity in samples that can exist in any typical carbonate reservoir system. Our measurements show that textural heterogeneity can lead to anisotropy in permeability and in acoustic velocities. Permeability anisotropy measurements varied between 40% and 100% while acoustic velocity anisotropy measurements varied between 8% and 30% with lower values for homogeneous samples respectively. Under similar conditions of the saturation experiment (spontaneous imbibition at the benchtop and undrained pressure imbibition at 1000 psi), the imbibing brine replaced 97% of the pore volume in a homogeneous sample (porosity 20% and permeability 2.6 mD) compared to 80% pore volume in a heterogeneous sample (porosity 29% and permeability 23.4 mD). Furthermore, after pressure saturation, a change of +79% in the bulk modulus and ‐11% in the shear modulus is observed for homogeneous samples in comparison to +34% in the bulk modulus and −1% in the shear modulus for heterogeneous samples, with respect to the dry state moduli values of the samples. We also examined the uncertainties associated with Gassmann models of elastic properties due to variations in fluid saturations.
Our results provide significant information on the saturation and, with it, modulus variations that are often ignored during fluid substitution modelling in time‐lapse seismic studies in carbonate reservoirs. We show that the bulk modulus could vary by 45% and the shear modulus by 10% between homogeneous and heterogeneous patches of a reservoir after a water flooding sequence for secondary recovery. Our findings demonstrate the need to incorporate and couple such fabric‐controlled saturation heterogeneities in reservoir simulation and in seismic fluid substitution models.
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Computational elastic up‐scaling of sandstone on the basis of X‐ray micro‐tomographic images
ABSTRACTUp‐scaling the elastic properties of digitized rock volumes as obtained from X‐ray computer tomography (CT) imaging via computer simulations has the potential to assist and complement laboratory measurements. This computational up‐scaling approach remains a challenging task as the overall elastic properties are not only dependent on the elastic properties of individual grains but also on the hardly resolvable pore spaces between adjacent grains such as micro‐cracks. We develop a digitized rock image and elastic up‐scaling workflow based on general‐purpose and widely available software packages. Particular attention is paid to CT image processing including filtering, smoothing and segmentation. A strategy for optimal meshing for subsequent finite‐element modelling is also proposed. We apply this workflow to the micro‐tomographic image of a well‐consolidated, feldspatic sandstone sample and determine the up‐scaled bulk and shear moduli. These effective elastic moduli are compared to the moduli inferred from laboratory ultrasound measurements at variable effective stresses (0–70 MPa). We observe that the numerically up‐scaled elastic moduli correspond to the moduli at a certain effective stress level (50 MPa), beyond which the effective‐stress dependency follows a linear trend. This indicates that the computational up‐scaling approach yields moduli as if all compliant (soft) porosity was absent, i.e., microcracks are closed. To confirm this hypothesis, we estimate the amount of soft porosity on the basis of the double‐porosity theory (Shapiro, 2003) and find that at 50 MPa the soft porosity is indeed practically zero. We conclude that our computational elastic up‐scaling approach yields physically consistent effective moduli even if some geometrical features are below CT resolution. To account for these sub‐resolution features either theoretical or additional computational approaches can be used.
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A new Seismic Wave Attenuation Module to experimentally measure low‐frequency attenuation in extensional mode
Authors Claudio Madonna and Nicola TisatoABSTRACTA Seismic Wave Attenuation Module is developed to experimentally measure the attenuation in extensional‐mode QE−1 and the Young's modulus of copper jacketed, 60 mm long and 25.4 mm in diameter samples in a gas medium (Paterson) rig. The new module is suitable for natural rock samples and was tested under confining pressure up to 50 MPa and room temperature. The module is designed to operate at a strain < 10−6, for which rocks behave linearly. To calculate attenuation, both the applied force and the bulk shortening of the sample are measured employing linear variable differential transformers. This technique allows measuring samples with a high degree of heterogeneity. Attenuation at low‐seismic frequencies (10−2–102 Hz) is obtained for rocks at dry and various saturation conditions. We present a series of measurements on Berea sandstone in a room‐dry condition and saturated with different fluids: water and glycerine solutions with viscosities of 10 cP and 22 cP, respectively, at a confining pressure of 10 MPa and with a pore pressure of 1 MPa. The accuracy of the attenuation data expressed as a phase shift is 0.0019 rad.
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Compressive strength and elastic properties of a transversely isotropic calcareous mudstone
Authors Douglas Miller, Richard Plumb and Gregory BoitnottABSTRACTThis paper reports measurements of static and dynamic elastic properties plus compressive strength performed on a block of calcareous mudstone retrieved from an exploration well. Measurements of mechanical properties indicate that the mudstone is anisotropic with respect to all three properties. A detailed analysis of the elastic moduli computed using small unload reload cycles and simultaneous ultrasonic wave velocities shows both strong anisotropy and strong anelasticity. Surprisingly, the measurements are consistent with a mathematical description of a special type of anisotropic linear viscoelastic medium that is obtained by adding a set of compliant elements (e.g., contacts between clay particles, kerogen lenses, or micro‐fractures) to an isotropic viscoelastic solid. This medium is fully characterized by density plus four parameters defining the viscoelastic solid and the excess normal compliance associated with the compliant elements. The mathematical model predicts a full set of parameters characterizing a transversely isotropic medium with a vertical axis of symmetry (a ‘tiv’ medium) for both low‐ and high‐strain rate behaviour.
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Static and dynamic behaviour of compacted sand and clay: Comparison between measurements in Triaxial and Oedometric test systems
Authors M. H. Bhuiyan, R. M. Holt, I. Larsen and J.F. StenebråtenABSTRACTIn rock mechanics and rock physics, like in many other branches of research, it is important to compare results obtained in different kinds of apparatus that are meant to measure the same properties. Differences may in general be due to differences in samples, or in test procedures. Here we compare uniaxial compaction experiments in oedometric and triaxial tests systems, using brine‐saturated samples made from pure kaolinite or from Ottawa sand. Small differences in sample manufacturing or in initial loading of the specimens were found to cause significant differences in static behaviour and in ultrasonic velocities during the tests. The influence of differences in sample geometry (wide and thin samples in the oedometer versus long and slim samples in the triaxial set‐up) and the influence of different boundary conditions caused by the confining medium (steel in the oedometer, thin soft sleeve in the triaxial system) were studied, amongst others with the use of discrete particle modelling. Although the boundary conditions may have an influence, the most significant sources of discrepancy in our experiments were associated with the manufacturing and preparation of the samples to be tested. The test data show that the drained static compaction modulus for sand is close to its dynamic counterpart, while for kaolinite, the dynamic modulus is significantly larger than the static one.
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Specific surface area and pore‐size distribution in clays and shales
Authors Utpalendu Kuila and Manika PrasadABSTRACTOne of the biggest challenges in estimating the elastic, transport and storage properties of shales has been a lack of understanding of their complete pore structure. The shale matrix is predominantly composed of micropores (pores less than 2 nm diameter) and mesopores (pores with 2–50 nm diameter). These small pores in the shale matrix are mainly associated with clay minerals and organic matter and comprehending the controls of these clays and organic matter on the pore‐size distribution is critical to understand the shale pore network. Historically, mercury intrusion techniques are used for pore‐size analysis of conventional reservoirs. However, for unconventional shale reservoirs, very high pressures (> 414 MPa (60 000 psi)) would be required for mercury to access the full pore structure, which has potential pitfalls. Current instrumental limitations do not allow reliable measurement of significant portions of the total pore volume in shales. Nitrogen gas‐adsorption techniques can be used to characterize materials dominated by micro‐ and mesopores (2–50 nm). A limitation of this technique is that it fails to measure large pores (diameter >200 nm). We use a nitrogen gas‐adsorption technique to study the micro‐ and mesopores in shales and clays and compare the results from conventional mercury porosimetry techniques.
Our results on pure clay minerals and natural shales show that (i) they have a multiscale pore structure at different dimensions (ii) fine mesopores, with a characteristic 3 nm pore size obtained with N2 gas‐adsorption are associated with an illite‐smectite group of clays but not with kaolinite; (iii) compaction results in a decrease of pore volume and a reduction of pore size in the ‘inter‐aggregate’ macropores of the illite‐smectite clays while the fine ‘intra‐tachoid’ mesopores are shielded from compaction; (iv) for natural shales, mineralogy controls the pore‐size distributions for shales and the presence of micropores and fine mesopores in natural shales can be correlated with the dominance of the illite‐smectite type of clays in the rock. Our assessment of incompressible 3 nm sized pores associated with illite‐smectite clays provides an important building block for their mineral modulus.
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Anisotropic elastic moduli of carbonates and evaporites from the Weyburn‐Midale reservoir and seal rocks
Authors Jaime Meléndez Martínez and Douglas R. SchmittABSTRACTAssuming Vertical Transverse Isotropy (VTI) symmetry the elastic anisotropy as a function of confining pressure of four carbonates and one evaporite from the Williston sedimentary basin in Saskatchewan, Canada is investigated using the ultrasonic pulse transmission method. Ultrasonic P‐ and S‐ wave velocities are obtained from cylindrical plugs cut from a main sample along horizontal, vertical and 45° orientations with respect to the sample's presumed vertical axis of symmetry. The elastic constants were then calculated from the measured velocities and densities. Anisotropy was quantified by estimating Thomsen parameters (Thomsen 1986) from elastic constants. The results show that the samples are at the best weakly anisotropic. The presence of microcracks and pores as well as the heterogeneity of the samples play an important role in defining the P‐ and S‐ wave velocities. The weak anisotropy found in these samples suggests that ‘intrinsic’ properties of these rocks negligibly contribute to the anisotropy observed at the seismic scale.
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Rock physics modelling of 4D time‐shifts and time‐shift derivatives using well log data – a North Sea demonstration
Authors Per Avseth, Norunn Skjei and Åshild SkålnesABSTRACTRock physics models for fluid and stress dependency in reservoir rocks are essential for quantification and interpretation of 4D seismic signatures during reservoir depletion and injection. For siliciclastic sandstone reservoirs, the Gassmann theory successfully predicts changes in seismic properties associated with fluid changes. However, our ability to predict the sensitivity to pressure from first principles is poor, especially for cemented sandstones. In this study, we demonstrate how we can use a patchy cement rock physics model to quantify the combined effect of stress and fluid changes in terms of seismic time‐shifts and time‐shift derivatives during depletion or injection. The time‐shifts are estimated directly from well log data without core calibration of stress sensitivity. By assuming non‐uniform grain contacts where some grain contacts are cemented and others are loose, we can combine the contact theory for cemented sandstones with the contact theory for loose sands in order to predict stress sensitivity in a patchy cemented sandstone reservoir. Time‐shift derivatives are also useful estimates, as this parameter reveals which part of the reservoir is most stress sensitive and contributes most to the cumulative time‐shift.
We test out our new approach on well log data from Troll East, North Sea and compare the predicted time‐shifts with observed 4D seismic time‐shifts. We find that there are good agreements between predicted time‐shifts and observed time‐shifts. Furthermore, we confirm that there are local geological trends controlling the fluid and stress sensitivity of the reservoir sands on Troll East. In particular, we observe a lateral stiffening of the reservoir from west to east, probably associated with the tectonic and burial history of the area. The combined effect of a thinning gas cap and stiffening reservoir sands amplifies the eastward decrease in time‐shifts associated with reservoir depletion. We manage to disentangle these two effects using rock physics analysis. It is essential to identify and map the static rock stiffness spatial trends before interpreting time‐shifts and time‐shift derivatives in terms of dynamic (i.e., 4D) pressure and fluid changes.
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Modelling elastic anisotropy of dry rocks as a function of applied stress
Authors Mahyar Madadi, Marina Pervukhina and Boris GurevichABSTRACTWe propose an analytical model for seismic anisotropy caused by the application of an anisotropic stress to an isotropic dry rock. We first consider an isotropic, linearly elastic medium (porous or non‐porous) permeated by a distribution of discontinuities with random (isotropic) orientation (such as randomly oriented compliant grain contacts or cracks). The geometry of individual discontinuities is not specified. Instead, their behaviour is defined by a ratio B of the normal to tangential excess compliances.
When this isotropic rock is subjected to a compressive stress (isotropic or anisotropic), the specific surface area of cracks aligned parallel to a particular plane is reduced in proportion to the normal stress traction acting on that plane. This effect is modelled using the Sayers‐Kachanov non‐interactive approximation, which expresses the effect of cracks on the elastic compliance tensor as an integral over crack orientations. This integral is evaluated using the Taylor expansion of the stress dependency of the specific surface area of the cracks. This allows the analytical solution previously derived for small anisotropic stresses to be extended to large stresses. Comparison of the model predictions with the results of laboratory measurements shows a reasonable agreement for moderate magnitudes of uniaxial stress (up to 50 MPa).
While the model contains five independent parameters, the variation of the anisotropy pattern (which can be expressed by the ratios of Thomsen’s anisotropy parameters ε, δ and γ) with normalized stress is controlled by only two parameters: Poisson’s ratio ν of the unstressed rock and the compliance ratio B. The model predicts that the ε/γ ratio depends on both ν and B but varies only mildly with stress, while the ε/δ ratio varies between 0.8–1.1 in a wide range of values of ν and B. The latter observation implies that the anisotropy remains close to elliptical even for larger stresses (within the assumptions of the model).
The proposed model of stress‐induced anisotropy may be useful for differentiating stress‐induced anisotropy from that caused by aligned fractures. Conversely, if the cause of seismic anisotropy is known, then the anisotropy pattern allows one to estimate P‐wave anisotropy from S‐wave anisotropy.
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Applications of deterministic and stochastic rock physics modelling to anisotropic velocity model building
Authors Ran Bachrach, Konstantin Osypov, Dave Nichols, Yi Yang, Yangjun Liu and Marta WoodwardABSTRACTModern anisotropic depth imaging requires transverse isotropy velocity models. Because the surface seismic experiment alone cannot uniquely determine all transverse isotropy parameters, additional information is required. Traditional methods that use checkshots can only constrain anisotropy locally near the well and thus model building requires 3D extrapolation of well data. We propose to use rock physics. Rock physics compaction modelling of shales and sandy shales can be used to constrain and predict anisotropic parameters of sediments whose depositional environment is governed by compaction. In this study, we present several applications of rock physics modelling to anisotropic velocity model building. We show how both deterministic and stochastic rock physics modelling can be used for initial anisotropic velocity model building and as a constraint for anisotropic parameter estimation. In all cases, all predicted anisotropy models are physical and realizable in terms of effective medium theory and do not violate elasticity theory.
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The effect of anisotropy on the Young's moduli and Poisson's ratios of shales
More LessABSTRACTYoung's modulus and Poisson's ratio are required for geomechanics applications such as hydraulic fracture design, analysis of wellbore stability and rock failure, determination of in situ stress and assessment of the response of reservoirs and surrounding rocks to changes in pore pressure and stress. Shales are usually anisotropic and models that neglect shale anisotropy may fail to describe geomechanical behaviour correctly. Anisotropy in shales results from a partial alignment of anisotropic clay particles, kerogen inclusions, microcracks, low‐aspect ratio pores and layering. For shales, the Young's modulus measured parallel to bedding E1 is usually greater than the Young's modulus measured perpendicular to bedding E3. However, the Poisson's ratio ν31 corresponding to stress applied perpendicular to bedding and strain measured parallel to bedding can be greater than, equal to, or less than the Poisson's ratio ν12 for stress applied parallel to bedding and strain measured parallel to bedding.
For transverse isotropy, the elastic anisotropy resulting from a partial alignment of clay particles can be written in terms of the coefficients W200 and W400, which describe the impact of clay particle orientation on the anisotropy of shales. Disorder in the orientation of clay particles acts to reduce W400 faster than W200, since W400 is a higher order moment of the clay particle orientation distribution function than W200. This is confirmed by analysis of measured anisotropy parameters for shales. A partial alignment of clay particles is consistent with the measured Young's moduli for shales and with values of Poisson's ratio ν31 > ν12 but not with values ν31 < ν12. These values can be explained if there exist kerogen inclusions, microcracks, or low‐aspect ratio pores aligned parallel to the bedding plane.
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Seismic characterization of naturally fractured reservoirs using amplitude versus offset and azimuth analysis
Authors Mehdi E. Far, Colin M. Sayers, Leon Thomsen, De‐hua Han and John P. CastagnaABSTRACTP‐wave seismic reflection data, with variable offset and azimuth, acquired over a fractured reservoir can theoretically be inverted for the effective compliance of the fractures. The total effective compliance of a fractured rock, which is described using second‐ and fourth‐rank fracture tensors, can be represented as background compliance plus additional compliance due to fractures. Assuming monoclinic or orthotropic symmetry (which take into account layering and multiple fracture sets), the components of the effective second‐ and fourth‐rank fracture compliance tensors can be used as attributes related to the characteristics of the fractured medium. Synthetic tests indicate that using a priori knowledge of the properties of the unfractured medium, the inversion can be effective on noisy data, with S/N on the order of 2. Monte Carlo simulation was used to test the effect of uncertainties in the a priori information about elastic properties of unfractured rock. Two cases were considered with Wide Azimuth (WAZ) and Narrow Azimuth (NAZ) reflection data and assuming that the fractures have rotationally invariant shear compliance. The relative errors in determination of the components of the fourth‐rank tensor are substantially larger compared to the second‐rank tensor, under the same assumptions.
Elastic properties of background media, consisting in horizontal layers without fractures, do not cause azimuthal changes in the reflection coefficient variation with offset. Thus, due to the different nature of these properties compared to fracture tensor components (which cause azimuthal anomalies), simultaneous inversion for background isotropic properties and fracture tensor components requires additional constraints.
Singular value decomposition (SVD) and resolution matrix analysis can be used to predict fracture inversion efficacy before acquiring data. Therefore, they can be used to determine the optimal seismic survey design for inversion of fracture parameters. However, results of synthetic inversion in some cases are not consistent with resolution matrix results and resolution matrix results are reliable only after one can see a consistent and robust behaviour in inversion of synthetics with different noise levels.
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Rock physics interpretation of heterogeneous and anisotropic turbidite reservoirs
Authors Pavel Golikov, Per Avseth, Alexey Stovas and Ran BachrachABSTRACTIn this paper, we create rock physics templates for heterogeneous and anisotropic thin‐bedded sand‐shale intervals as a function of group angle, net‐to‐gross, saturation and porosity as variable parameters. These templates are basically cross‐plots of acoustic impedance versus P‐ to S‐velocity ratio. We apply these templates to interpret well log data from a vertical and a deviated well, respectively, in a North Sea turbidite system. We are able to infer the shale anisotropic elastic moduli and Thomsen parameters by comparing the measured velocities in a deviated well with the velocities in an adjacent vertical well. Our modeling captures the observed trends in the data as we go from a vertical well to a deviated well through a heterogeneous reservoir saturated with light oil and water. We can clearly see how the reservoir properties changes due to the presence of anisotropy. We also perform an AVO sensitivity study as a function of heterogeneity and hydrocarbon saturation.
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Laboratory determination of the full electrical resistivity tensor of heterogeneous carbonate rocks at elevated pressures
Authors Laurence North, Angus I. Best, Jeremy Sothcott and Lucy MacGregorABSTRACTWe describe a measurement system capable of determining the full resistivity tensor of core samples at elevated, geologically representative, pressures using a galvanic method. It is suitable for heterogeneous rocks where it is difficult to measure tensorial resistivity without bias from sample selection and heterogeneity. We demonstrate the efficacy of the system using both synthetic data and measurements on carbonate rock core samples. The apparatus employs a computer controlled array of 16 electrodes to inject current into, and measure boundary voltages on, a 5 cm diameter cylindrical sample. A computationally efficient FE algorithm is used to retrieve the full resistivity tensor from the measured voltages. The algorithm uses isotropic Finite Element code to calculate anisotropic solutions for samples of arbitrary geometry. Initial results from Jurassic limestone and Triassic dolomite samples, reveal cm‐scale heterogeneity and significant bulk anisotropy consistent with rock fabric observed in X‐ray Computed Tomography scan images.
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Modelling electrical conductivity for earth media with macroscopic fluid‐filled fractures
Authors James G. Berryman and G. Michael HoverstenABSTRACTEffective‐medium theories for either highly conductive or more resistive electrical inclusions in a moderately conducting background medium are presented for modelling macroscopic (i.e., large‐scale) fluid‐filled fractures or cracks in a potential reservoir rock or granular medium. Conductive fluids are most often brine and the resistive fluids of interest are oil, gas, air and/or CO2. Novel features of the presentation for conductive fluids include results for both non‐interacting inclusions (using a Maxwell approximation) and for interacting inclusions (via a self‐consistent effective‐medium scheme). The anisotropic analysis is specifically designed to handle reservoirs with multiple orientations (usually three orthogonal sets) of oblate spheroidal cracks/fractures, while also having arbitrary aspect ratios. But these aspect ratios are strictly <1, thus excluding spherical pores and simple granular media – both already widely studied by others. Results show that the self‐consistent approximation depends on fracture aspect ratio α and that this approximation becomes important when fracture porosity is about φ= 1% for aspect ratio α≃ 0.05, or φ= 3% for aspect ratio α≃ 0.10. It is shown that the self‐consistent analysis is most important when the fractures have a very small aspect ratio — the inferred reason being that the fracture (or crack) number density (ρc≡φ/α) then becomes very high and the fracture relative spacing correspondingly very small for any fixed value of porosity (but with decreasing values of the aspect ratio). Hybrid methods (combining self‐consistent and non‐self consistent formulas) are also developed to deal with high volume fractions and multiple sets of fractures having different aspect ratios. Whenever possible and appropriate, the results are also compared to rigorous bounds, including the Wiener bounds and the Hashin‐Shtrikman bounds, in order to provide one type of partial validation of the methods being developed.
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Volumes & issues
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Volume 72 (2023 - 2024)
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