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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Electrofracturing of Shale at Elevated Pressure

Electrofracturing deeply buried shale formations could be used to increase reservoir permeability and improve reservoir production without requiring large volumes of freshwater. This paper describes a novel experimental system and initial test results to electrofracture shale under high confining pressures. Core-scale laboratory testing was performed on twelve rock samples recovered from a shale gas reservoir. Each sample was subjected to confining pressures of 20.7 MPa (3000 psi) or 58.6 MPa (8000 psi), representative of overburden pressures at depth. Samples were then subjected to application of high voltage until specimen fracture. The experiments produced deformed samples with multiple fracture types, both parallel and oblique to bedding planes. Electrofracturing increased permeabilities by up to nine orders of magnitude for extended time periods. Rock fracture and throughgoing fractures were demonstrated. Computed tomography images revealed the creation of fractures and tube/tunnel flow channels, which resisted closure under hydrostatic pressures up to 58.6 MPa. The breakdown energy and permeability changes in the sample were independent of applied confining pressure. The cumulative energy input required for fracture depended on applied confining pressure and sample length. The energy required to fracture samples up to 9 cm in length is generally more than 0.5 kJ/cm, but no greater than 1 kJ/cm. Our results show that electrofracture of shales under confining pressure is possible and could be a possible water-free mechanism for reservoir stimulation.

04 OIL SHALES AND TAR SANDS↗
DOE OSTI2023

An adjoint-based optimization method for jointly inverting heterogeneous material properties and fault slip from earthquake surface deformation data

SUMMARY Analysis of tectonic and earthquake-cycle associated deformation of the crust can provide valuable insights into the underlying deformation processes including fault slip. How those processes are expressed at the surface depends on the lateral and depth variations of rock properties. The effect of such variations is often tested by forward models based on a priori geological or geophysical information. Here, we first develop a novel technique based on an open-source finite-element computational framework to invert geodetic constraints directly for heterogeneous media properties. We focus on the elastic, coseismic problem and seek to constrain variations in shear modulus and Poisson’s ratio, proxies for the effects of lithology and/or temperature and porous flow, respectively. The corresponding nonlinear inversion is implemented using adjoint-based optimization that efficiently reduces the cost function that includes the misfit between the calculated and observed displacements and a penalty term. We then extend our theoretical and numerical framework to simultaneously infer both heterogeneous Earth’s structure and fault slip from surface deformation. Based on a range of 2-D synthetic cases, we find that both model parameters can be satisfactorily estimated for the megathrust setting-inspired test problems considered. Within limits, this is the case even in the presence of noise and if the fault geometry is not perfectly known. Our method lays the foundation for a future reassessment of the information contained in increasingly data-rich settings, for example, geodetic GNSS constraints for large earthquakes such as the 2011 Tohoku-oki M9 event, or distributed deformation along plate boundaries as constrained from InSAR.

Geochemistry & Geophysics↗
NASA NTRS1986

Deformational sequence of a portion of the Michipicoten greenstone belt, Chabanel Township, Ontario

Detailed mapping at a scale of one inch = 400 feet is being carried out within a fume kill, having excellent exposure, located in the southwestern portion of the Michipicoten Greenstone Belt near Wawa, Ontario. The rocks are metasediments and metavolcanics of lower greenschist facies. U-Pb geochronology indicates that they are at least 2698 + or - 11 Ma old. The lithologic packages strike northeast to northwest, but the dominant strike is approximately east-west. Sedimentary structures and graded bedding are well preserved, aiding in the structural interpretation of this multiply deformed area. At least six phases of deformation within a relatively small area of the Michipicoten Greenstone Belt have been tentatively identified. These include the following structural features in approximate order of occurrence: (0) soft-sediment structures; (1) regionally overturned rocks, flattened pebbles, bedding parallel cleavage, and early, approximately bedding parallel faults; (2) northwest to north striking cleavage; (3) northeast striking cleavage and associated folds, and at least some late movement on approximately bedding parallel faults; (4) north-northwest and northeast trending faults; and (5) diabase dikes and associated fracture cleavages. Minor displacement of the diabase dikes occurs on faults that appear to be reactivated older structures.

Shrady, C. H.↗
NASA NTRS2015

Petrology of Diogenite NWA 5480, A Pristine Olivine-Rich Deformed Harzburgite

Diogenites are achondrites that are part of the HED (howardite, eucrite, diogenite) meteorite group thought to originate from asteroid Vesta. This suite of igneous rocks offers a glimpse of early planetary differentiation and subsequent igneous processes. While eucrites represent asteroidal basaltic crust and howardites the impact brecciated surface, diogenites are samples of the mantle and lower crust. Most of them are orthopyroxene (Opx) dominated cumulates, although harzburgites and rare dunites have also been found. The majority of diogenites are impact breccias. This study describes NWA 5480, a pristine, i.e. hardly altered and minimally shocked, harzburgitic diogenite.

Peslier, A. H.↗
NASA NTRS1990

Block rotations, fault domains and crustal deformation in the western US

The aim of the project was to develop a 3D model of crustal deformation by distributed fault sets and to test the model results in the field. In the first part of the project, Nur's 2D model (1986) was generalized to 3D. In Nur's model the frictional strength of rocks and faults of a domain provides a tight constraint on the amount of rotation that a fault set can undergo during block rotation. Domains of fault sets are commonly found in regions where the deformation is distributed across a region. The interaction of each fault set causes the fault bounded blocks to rotate. The work that has been done towards quantifying the rotation of fault sets in a 3D stress field is briefly summarized. In the second part of the project, field studies were carried out in Israel, Nevada and China. These studies combined both paleomagnetic and structural information necessary to test the block rotation model results. In accordance with the model, field studies demonstrate that faults and attending fault bounded blocks slip and rotate away from the direction of maximum compression when deformation is distributed across fault sets. Slip and rotation of fault sets may continue as long as the earth's crustal strength is not exceeded. More optimally oriented faults must form, for subsequent deformation to occur. Eventually the block rotation mechanism may create a complex pattern of intersecting generations of faults.

Nur, Amos↗
DOE OSTI2020

More Than 40 yr of Potentially Induced Seismicity Close to the San Andreas Fault in San Ardo, Central California

Evidence for fluid–injection–induced seismicity is rare in California hydrocarbon basins, despite widespread injection close to seismically active faults. We investigate a potential case of injection–induced earthquakes associated with San Ardo oilfield operations that began in the early 1950s. The largest potentially induced events occurred in 1955 (M L 5.2) and 1985 (M w 4.5) within ~6 km from the oilfield. We analyze Synthetic Aperture Radar interferometric images acquired by Sentinel–1A/B satellites between 2016 and 2020 and find surface deformation of up to 1.5 cm/yr, indicating pressure–imbalance in parts of the oilfield. Fluid injection in San Ardo is concentrated within highly permeable rocks directly above the granitic basement at a depth of ~800 m. Seismicity predominantly occurs along basement faults at 6–13 km depths. Seismicity and wastewater disposal wells are spatially correlated to the north of the oilfield. Temporal correlations are observed over more than 40 yr with correlation coefficients of up to 0.71 for seismicity within a 24 km distance from the oilfield. Such large distances have not previously been observed in California but are similar to the large spatial footprint of injection in Oklahoma. Furthermore, the San Ardo seismicity shows anomalous clustering with earthquakes consistently occurring at close spatial proximity but long interevent times. Similar clustering has previously been reported in California geothermal fields and may be indicative of seismicity driven by long–term, spatially persistent external forcing.

58 GEOSCIENCES↗
DOE OSTI2020

Rapid Mineral Precipitation During Shear Fracturing of Carbonate-Rich Shales

Target subsurface reservoirs for emerging low-carbon energy technologies and geologic carbon sequestration typically have low permeability and thus rely heavily on fluid transport through natural and induced fracture networks. Sustainable development of these systems requires deeper understanding of how geochemically mediated deformation impacts fracture microstructure and permeability evolution, particularly with respect to geochemical reactions between pore fluids and the host rock. Here, a series of triaxial direct shear experiments was designed to evaluate how fractures generated at subsurface conditions respond to penetration of reactive fluids with a focus on the role of mineral precipitation. Calcite-rich shale cores were directly sheared under 3.5 MPa confining pressure using BaCl 2 -rich solutions as a working fluid. Experiments were conducted within an X-ray computed tomography (xCT) scanner to capture 4-D evolution of fracture geometry and precipitate growth. Three shear tests evidenced nonuniform precipitation of barium carbonates (BaCO 3 ) along through-going fractures, where the extent of precipitation increased with increasing calcite content. Precipitates were strongly localized within fracture networks due to mineral, geochemical, and structural heterogeneities and generally concentrated in smaller apertures where rock:water ratios were highest. The combination of elevated fluid saturation and reactive surface area created in freshly activated fractures drove near-immediate mineral precipitation that led to an 80% permeability reduction and significant flow obstruction in the most reactive core. While most previous studies have focused on mixing-induced precipitation, this work demonstrates that fluid–rock interactions can trigger precipitation-induced permeability alterations that can initiate or mitigate risks associated with subsurface energy systems.

58 GEOSCIENCES↗
DOE OSTI2022

Subduction, Underplating, and Return Flow Recorded in the Cycladic Blueschist Unit Exposed on Syros, Greece

Exhumed high-pressure/low-temperature (HP/LT) metamorphic rocks provide insights into deep (~20–70 km) subduction interface dynamics. On Syros Island (Cyclades, Greece), the Cycladic Blueschist Unit preserves blueschist-to-eclogite facies oceanic- and continental-affinity rocks that record the structural and thermal evolution linked to Eocene subduction. Despite decades of research, the metamorphic and deformation history (P-T-D) and timing of subduction and exhumation are matters of ongoing discussion. We suggest that Syros comprises three coherent tectonic slices and that each slice underwent subduction, underplating, and syn-subduction return flow along similar P-T trajectories, but at progressively younger times. Subduction and exhumation are distinguished by lineations and ductile fold axis orientations, and are kinematically consistent with previous studies that document top-to-the-S-SW shear (prograde-to-peak subduction), top-to-the-NE shear (blueschist facies exhumation), and then E-W coaxial stretching (greenschist facies exhumation). Amphibole zonations record cooling during decompression, indicating return flow above a cold slab. Multi-mineral Rb-Sr isochrons and compiled metamorphic geochronology show that the three slices record distinct stages of peak subduction (53–52, ~50, and 45 Ma) that young with structural depth. Retrograde blueschist and greenschist facies fabrics span ~50–40 and ~43–20 Ma, respectively, and also young with structural depth. Synthesized data sets support a revised tectonic framework for Syros, involving subduction of structurally distinct coherent slices and simultaneous return flow of previously accreted tectonic slices in the subduction channel shear zone. Distributed, ductile, dominantly coaxial return flow in an Eocene-Oligocene subduction channel proceeded at rates of ~1.5–5 mm/yr and accommodated ~80% of the total exhumation of this HP/LT complex.

58 GEOSCIENCES↗
NASA NTRS1992

Effects of dispersed particulates on the rheology of water ice at planetary conditions

Effects of the initial grain size and the hard particulate impurities on the transient and the steady state flows of water ice I were investigated under laboratory conditions selected as appropriate for simulating those of the surfaces and interiors of large moons. The samples were molded with particulate volume fraction, phi, of 0.001 to 0.56 and particle sizes of 1 to 150 microns; deformation experiments were conducted at constant shortening rates of 4.4 x 10 exp -7 to 4.9 x 10 exp -4 per sec at pressures of 50 and 100 MPa and temperatures 77 to 223 K. The results obtained suggest that viscous drag occurs in the ice as it flows around hard particulates. Mixed-phase ice was found to be tougher than pure ice, extending the range of bulk plastic deformation vs. faulting to lower temperatures and higher strain rates. It is suggested that bulk planetary compositions of ice + rock (phi = 0.4-0.5) are roughly 2 orders of magnitude more viscous than pure ice, leading to thermal instability inside giant icy moons and possibly explaining the retention of crater topography on icy planetary surfaces.

Durham, William B.↗
NASA NTRS1997

Original Size and Shape of the Sudbury Structure

This paper presents new evidence bearing on the original size and shape of the Sudbury impact structure. Current opinion is almost unanimous that the structure is a multiring basin with an original diameter of about 200 km and a circular shape that has since been shortened in a northwest-southeast direction by Penokean deformation Evidence for this interpretation, collected chiefly from north of the Sudbury Igneous Complex (SIC), includes supposed outer rings on Landsat imagery, distant occurrences of "Sudbury breccia" (generally defined as pseudotachylite), shatter cone occurrences, and outliers of Huronian sedimentary rock thought to be down-faulted rings. New data from imaging radar and field work north of the SIC, however, contradict this evidence. Radar imagery shows no signs of the supposed outer rings mapped by earlier workers on Landsat images. The most prominent ring has been found to be a chance alignment of two independent fracture sets. Radar imagery from the CCRS Convair 580, with look direction almost normal to the north rim of the SIC, shows no evidence of the rings despite strong look azimuth highlighting. Radar imagery has shown many unmapped diabase dikes north of the SIC. Several exposures of supposed Sudbury breccia are associated with these dikes or with Nipissing diabase intrusions, in some cases actually inside the dikes or directly continuous with them. They appear to be igneous intrusion breccias with no relation to impact. Shock-wave interaction at lithologic contacts cannot be invoked for most of these, because they are part of a northwest trending swarm cutting the SIC in the North Range, and hence too young for an impact origin. Similar diabase-related breccias and pseudotachylite-like veins have been found far outside the Sudbury area between Chapleau and Thessalon. Shatter cones north of the SIC are few and poorly developed, perhaps due to the coarse-grained Footwall rock, and cannot be considered a continuous zone analogous to their occurrence on the South Range in Huronian rocks. Supposed down-faulted outliers of Huronian rocks north of the SIC show no consistent relation to faulting, and the Huronian/Archean contact is locally erosional. Radar imagery and field-checking confirm Rousell's conclusion that the North Range has undergone little or no Penokean deformation. T'his implies that the plan view outline of the crater (floor of the SIC) is original. Extrapolation of the North Range as part of a circular arc leads to an impossibly great diameter. It is concluded that although Penokean deformation largely accounts for the structure's shape, the original crater was not circular and was much smaller than 200 km across.

Lowman, P. D., Jr.↗
NASA NTRS2017

Physical Properties of the Stone Meteorites: Implications for the Properties of Their Parent Bodies

The physical properties of the stone meteorites provide important clues to understanding the formation and physical evolution of material in the Solar protoplanetary disk as well providing indications of the properties of their asteroidal parent bodies. Knowledge of these properties is essential for modeling a number of Solar System processes, such as bolides in planetary atmospheres, the thermal inertia of atmosphereless solid body surfaces, and the internal physical and thermal evolution of asteroids and rock-rich icy bodies. In addition, insight into the physical properties of the asteroids is important for the design of robotic and crewed reconnaissance, lander, and sample return spacecraft missions to the asteroids. One key property is meteorite porosity, which ranges from 0% to more than 40%, similar to the range of porosities seen in asteroids. Porosity affects many of the other physical properties including thermal conductivity, speed of sound, deformation under stress, strength, and response to impact. As a result of the porosity, the properties of most stone meteorites differ significantly from those of compact terrestrial rocks, whose physical properties have been used in many models of asteroid behavior. A few physical properties, such as grain density, magnetic susceptibility, and heat capacity are not functions of porosity. Taken together, the grain density and the magnetic susceptibility can be used to classify unweathered or minimally weathered ordinary chondrites. This provides a rapid screening technique to identify heterogeneous samples, classify new samples, and identify misclassified meteorites or interlopers in strewn fields.

Chondritic meteorites↗
NASA NTRS2023

Microstructural Changes and Pb Mobility During the Zircon to Reidite Transformation: Implications for Planetary Impact Chronology

Impact events modify and leave behind a complex history of rock metamorphism on terrestrial planets. Evidence for an impact event may be recorded in physical changes to minerals, such as mineral deformation and formation of high P-T polymorphs, but also in the form of chemical fingerprints, such as enhanced elemental diffusion and isotopic mixing. Here we explore laboratory shock-induced physical and chemical changes to zircon and feldspar, the former of which is of interest because its trace elements abundances and isotope ratios are used extensively in geochemistry and geochronology. To this end, a granular mixture of Bishop Tuff sanidine and Kuehl Lake zircon, both with well characterized Pb isotope compositions, was prepared and then shocked via a flat plate accelerator. The peak pressure of the experiment, as calculated by the impedance matching method, was ~24 GPa although a broader range of P-T conditions is anticipated due to starting sample porosity. Unshocked and shocked materials were characterized via scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), and Raman spectroscopy. These methods show that the starting zircon material had abundant metamict regions, and the conversion of the feldspar to glass in the post-shock material. Analyses of the shocked product also yielded multiple occurrences of the high-pressure ZrSiO 4 polymorph reidite, with some domains up to 300 μm across. The possibility of U-Pb system disturbance was evaluated via laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS) and secondary ion mass spectrometry (SIMS). The isotopic data reveal that disturbance of the U-Pb geochronometer in the reidite was minimal (<2% for the main U-Pb geochronometers). To better constrain the P-T conditions during the shock experiment, we complement impedance matching pressure calculations with iSALE2D impact simulations. The simulated results yield a range of P-T conditions experienced during the experiment and show that much of the sample may have reached >30 GPa, which is consistent with formation of reidite. In the recovered shocked material, we identified lamellae of reidite, some of which interlock with zircon lamellae. Reidite {112} twins were identified, which we interpret to have formed to reduce stress between the crystal structure of the host zircon and reidite. These two findings support the interpretation that shear transformation enabled the transition of zircon to reidite. The size and presence of reidite found here indicate that this phase is probably common in impact-shocked crustal rocks that experienced ~25 to ~35 GPa, especially when the target material has porosity. Additionally, shock loading of the zircon and transformation to reidite at these pressures in porous materials is unlikely to significantly disturb the U-Pb system in zircon and that the reidite inherits the primary U and Pb elemental and isotopic ratios from the zircon.

Bishop Tuff↗
DOE OSTI2023

Effects of anisotropic shale creep on the stress and permeability evolution of a geological nuclear waste repository

To ensure long-term safety and performance, geological nuclear waste repositories require low-permeability barriers such as bentonite buffers and/or shale host rock. Shale is not only known for its low permeability but also for its trend to undergo time-dependent deformation (i.e., creep), which could heal damage, but the effects of shale creep on the long-term performance of nuclear waste repositories have not been clearly understood. In particular, the anisotropic nature of shale (i.e., bedding) could have a significant effect on its creep behavior, and consequently, on the long-term performance of nuclear waste repositories. In this research, numerical simulations were carried out with the objective of showing the effects of anisotropic shale creep on the stress and permeability evolution of a generic geological nuclear waste repository in shale. The TOUGH-FLAC simulator, a thermo-hydromechanically (THM) coupled numerical code, was used for the simulations. To achieve the objective, comparisons were performed between the results of anisotropic shale creep simulations and those of different simulation cases, namely, no creep (i.e., elastic), isotropic creep, and long-term creep shale cases. Results of the comparisons show that the elastic and isotropic creep shale cases respectively led to the overestimation and underestimation of stress and permeability in the repository, whereas the long-term creep shale case, which accumulated greater creep in later periods than in earlier periods, helped to keep large shear and tensile stresses from developing while maintaining compressive spherical stress, resulting in consistently low permeability levels. These results indicate that performance assessments with elastic and isotropic creep formation models will provide the upper and lower bound estimates of stress and permeability, while more reasonable estimates will be given by an anisotropic creep formation model, and that shale with long-term creep characteristics will be beneficial in many aspects of the safety and performance of nuclear waste repositories.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS1975

Shock-induced deformation features in terrestrial peridot and lunar dunite

Single crystals of terrestrial olivine were experimentally shock-loaded along the 010 line to peak pressures 280, 330, and 440 kbar, and the resulting deformation features were compared to those in olivine from lunar dunite 72415. Recovered fragments were examined to determine the orientation of the planar fractures. With increasing pressure the percentage of pinacoids and prisms decreases, whereas the percentage of bipyramids increases. The complexity of the distribution of bipyramids also increases with increasing pressure. Other shock-induced deformation features, including varying degrees of recrystallization, are found to depend on pressure, as observed by others. Lunar dunite 72415 was examined and found to contain olivine with well-developed shock-deformation features. The relative proportion of pinacoid, prism, and bipyramid planar fractures measured for olivine from 72415 indicates that this rock appears to have undergone shock pressure in the range 330-440 kbar. If this dunite was brought to the surface of the moon as a result of excavation of an Imbrium event-sized impact crater, the shock-pressure range experienced by the sample and the results of cratering calculations suggest that it could have originated no deeper than 50-150 km.

Snee, L. W.↗
DOE OSTI2022

Effects of time-dependent deformation of shale on the integrity of a geological nuclear waste repository

Safety assessment of geological nuclear waste repositories is essential for the permanent disposal of spent nuclear fuels and high-level radioactive waste. The long-term integrity of the host rock as well as the engineered barrier system (e.g., bentonite buffer) surrounding nuclear waste canisters is of particular importance as decay heat from nuclear waste canisters, which will last over thousands of years, significantly disturbs the thermo-hydromechanical (THM) state of the repository. In this study, THM coupled simulations were carried out to investigate the effect of time-dependent deformation (i.e., creep) of shale on the long-term integrity of a generic subsurface nuclear waste repository. The Norton-Bailey creep model, which is also known as the Lemaitre-Menzel-Schreiner model, was employed to simulate the power-law type creep that is observed in shales. The TOUGH-FLAC simulator was employed for the THM coupled modeling of the repository. The objective of this study is to assess the effect of creep in different shales (i.e., high creep shale vs. low creep shale) on long-term stress and permeability changes in the repository. Results show potential advantages of constructing repositories in the high creep shale, as deviatoric stress levels in the formation decreased to zero in 100 years since the emplacement of nuclear waste canisters and the permeability also decreased to the undamaged, intrinsic levels in 10,000 years. Also, mean effective stress levels in the bentonite buffer increased by 100% in the high creep shale case relative to the low creep shale case at 10,000 years due to creep-induced contraction of the nuclear waste disposal tunnel. However, in earlier periods (e.g., 1000 years), the stress levels in the bentonite buffer were twice smaller in the high creep shale case than in the low creep shale case, which shows a tradeoff between the intermediate- (~1000 years) and long-term (>10,000 years) compaction levels in the bentonite buffer depending on the creep characteristics of the host shale.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Modeling the dynamic response of rock masses with multiple compliant fluid saturated joint sets—Part I: Mesoscale simulations

Recently a mesoscale model was developed that includes thermomechanically consistent constitutive equations with dissipation due to porous compaction, inelastic distortional deformation rate, and slipping on persistent dry joint surfaces. In this Part I of a two-part paper, we describe enhancements of the mesoscale model which include: normal compliance with hysteresis, non-persistent joints with finite area, joint sets with angular deviation, and the weakening effect of fluid pressure in the joints. Examples study the influences of these effects on average strength. These computationally expensive simulations are used to inspire functional forms in a continuum model, described in Part II, which is needed for large scale simulations of real applications.

42 ENGINEERING↗
DOE OSTI2020

Impact of the adhesion-force lever-arm “a” on the Rock ‘n’ Roll resuspension model and how to compute it from contact mechanics

The paper proposes a methodology to fill a gap in the context of mechanistic particle resuspension models related to the adhesion and lift force lever arms ( a ): to date, only one experimental observation exists from a centrifuge experiment with a specific particle/surface pair which found r P / a = 100 and assumed that the contact points were symmetric with respect to the particle center. However, the Reeks and Hall’s (2001) model is highly sensitive to this parameter, which therefore cannot be used as-is for different particle diameters or materials. This paper proposes a methodology to compute the adhesion and lift force lever arms ( a A and a L , respectively) based on Atomic Force Microcopy (AFM) surface roughness measurements and contact mechanics arguments. In practice, a spherical, perfectly smooth particle is brought in contact (computationally) with the measured surface roughness and is then rotated by the point of contact to determine the two or more asperities over which the particle would sit on the surface. A method to compute the asperity radius of curvature is devised to compute the asperity deformation and the correct partitioning of the total deformation between the particle and the asperity is presented. For the glass surface under consideration, the asperity deformation was negligible, i.e., it was below the van der Waals radius, which is the limit of applicability of contact mechanics. The Reeks and Hall’s (2001) model is then extended to account for the joint probability of a A and a L . Significant differences in particle resuspended after a day in common atmospheric conditions are found between the approach that uses the lever-arm distributions or their mean values. Also, important differences are found when comparing the lever-arm distribution and r P / a = 100. Hence, one should be cautious of using r P / a = 100 for surface/particle pairs differing from those in the original study. Finally, limits of applicability of the theories used are presented together with considerations regarding how to extend the method to non-spherical particles and different materials.

42 ENGINEERING↗