Pebble Size Research Articles

Addition of pebbles to a ball-mill to improve grinding efficiency

Ball-mills are used widely for secondary grinding. Loveday (2010) reported on laboratory tests in which small pebbles (7–25mm) were used in various proportions with balls. The optimum proportion of pebbles, by volume, was found to be about 25%. Substantial savings in power and ball consumption were achieved, with no loss in grinding capacity. However, continuous pilot-plant tests were disappointing, because the consumption of small pebbles was too high.The idea of using a mixture of balls and pebbles, at a mill speed suitable for ball-milling, was revisited in this investigation, using a normal spectrum of pebble sizes (19–75mm). Batch tests in a pilot-scale mill (0.57m diameter) were used to compare ball-milling to various ball/pebble mixtures. The mill power was measured online by monitoring lateral torque on a freely suspended motor and gearbox. Initial tests were done using pebbles from previous tests on gold ore, in combination with balls, to mill silica sand (0.6–1.5mm)The size distributions of the balls and the pebbles were calculated to simulate steady-state addition of balls (37.5mm) and partly-rounded pebbles (19–75mm). There was a reduction in pebble consumption, as expected, when using larger rounded pebbles, to about 6% of total production. The grinding capacity, when using a mixture containing 25% pebbles, was the same as that with balls alone, resulting in a 13% saving in energy and an implied saving in ball consumption of 25%.It was concluded that the use of a composite load for secondary grinding is a very attractive option. Further tests were done, using samples from a platinum mine, namely the feed to a secondary mill (ball-mill) and rounded pebbles from a primary AG mill. Grinding capacity was maintained over the range 0–30% pebbles, by volume, with savings in energy and ball consumption increasing progressively. At 25% pebbles, the saving in energy was 18% and the pebble consumption was about 7% of total production.The theory of pebble wear was developed during this investigation, for application to batch grinding tests. The size distribution of the pebbles was measured after each test and the theory was used to calculate the pebble wear rate (mmh−1) and the specific wear rate (kgh−1kg−1) for all screen fractions. The wear rate of pebbles in the presence of balls was higher than that for pebbles alone. When the proportion of pebbles in the mill charge was low (up to 30%), the larger pebbles wore away significantly faster than expected, based on a constant surface wear rate. This could be due to size segregation in the mill.

Numerical and experimental characterization of ceramic pebble beds under cycling mechanical loading

All solid breeder concepts considered to be tested in ITER (International Thermonuclear Experimental Reactor), make use of lithium-based ceramics in the form of pebble-packed beds as tritium breeder. A thorough understanding of the thermal and mechanical properties of the ceramic pebble beds under fusion relevant conditions is essential for the design of the breeder blanket modules of future fusion reactors. In this study, the effect of cyclic loading on the mechanical behaviour of pebble bed assemblies was investigated using a Discrete Element Method (DEM) code. The numerical simulations were compared with the experimental outcomes. The results of numerical simulations show that the pebble size distribution affects noticeably the stress-strain behaviour of the assemblies. A good qualitative agreement between experimental and simulation results was found in terms of difference between residual strains of consecutive cycles. An increase of the oedometric modulus with the compressive load was observed for all investigated compositions in both experimental and DEM simulations. The numerical results show an increase of the oedometric modulus (E) with progressive compaction of the assemblies due to the cycling loading, while no significant influence of the pebbles size distribution was observed.

Effective thermal conductivity of unary particulate bed

AbstractEffective thermal conductivity of a unary (mono‐sized) pebble bed depends on the physical properties of solid pebbles, physical properties and flow rate of fluid, temperature, coordination number of pebbles, and void fraction. The pebble size also plays an important role on the effective thermal conductivity of a unary pebble bed. To date, no theoretical justification for the same has been reported. In this present study an attempt was made to justify theoretically the dependence of the effective thermal conductivity on pebble size of a unary pebble bed filled with a stagnant fluid. A mathematical model has been developed to determine the effective thermal conductivity of a unary pebble bed with stagnant fluid. Different particle sizes (10 μm to 10 mm) were considered and modes of heat transfer were assumed to be conduction and convention only. Radiation mode of heat transfer was not considered. It was found that the effective thermal conductivity depends on the pebble size and the estimated values of the same were in close agreement with the reported experimental results.

PEBBLE ACCRETION AND THE DIVERSITY OF PLANETARY SYSTEMS

ABSTRACT This paper examines the standard model of planet formation, including pebble accretion, using numerical simulations. Planetary embryos that are large enough to become giant planets do not form beyond the ice line within a typical disk lifetime unless icy pebbles stick at higher speeds than in experiments using rocky pebbles. Systems like the solar system (small inner planets and giant outer planets) can form if icy pebbles are stickier than rocky pebbles, and if the planetesimal formation efficiency increases with pebble size, which prevents the formation of massive terrestrial planets. Growth beyond the ice line is dominated by pebble accretion. Most growth occurs early, when the surface density of the pebbles is high due to inward drift of the pebbles from the outer disk. Growth is much slower after the outer disk is depleted. The outcome is sensitive to the disk radius and turbulence level, which control the lifetime and maximum size of pebbles. The outcome is sensitive to the size of the largest planetesimals because there is a threshold mass for the onset of pebble accretion. The planetesimal formation rate is unimportant, provided that some large planetesimals form while the pebbles remain abundant. Two outcomes are seen, depending on whether pebble accretion begins while the pebbles are still abundant. Either multiple gas-giant planets form beyond the ice line, small planets form close to the star, and a Kuiper-belt-like disk of bodies is scattered outward by the giant planets; or no giants form and the bodies remain an Earth-mass or smaller.

Soft sediment deformation in the shallow submarine slope off Nice (France) as a result of a variably charged Pliocene aquifer and mass wasting processes

Along the Ligurian slope near Nice, southeastern France, a combination of natural and man-made factors govern slope stability, and contributed to a devastating tsunamigenic landslide near Nice airport in 1979. Based on a total of 72 gravity and Kullenberg cores we characterise the architecture and facies of the subbottom sediment. A total of six sedimentary facies types were observed, three of which represent the Pliocene–Holocene background sediment in the wider Nice area while another three are associated with the 1979 landslide and tsunami. The three primary facies types are soft silty clay/clayey silt, somewhat indurated silt/sand interbeds, and Pliocene conglomerates underlying the former. The three other facies are poorly sorted mass wasting deposits up to pebble size, silt representing the finer fraction of the mobilised mass, and a tsunami-related bed into which plant debris and artefacts got amalgamated.Accompanying geotechnical results attest that significant strength variations exist when comparing measurements from the narrow shelf, shelf break and shallow slope as well as the 1979 slide scar. Factors such as groundwater charging in the more permeable horizons further lower the effective stress and, in places, approach lithostatic. Above such permeable silt/sand beds, deformation of soft clay is observed, suggesting that leaching of ions from the clay mineral surfaces and frayed edges also facilitates weakening and creep, micro-slumping and folding. Elevated water supply as well as hydraulic fracturing of the clayey sediment is further attested by pipes of cm-diameter and several decimeters length, which entrained very soupy mud. In the shallowmost deposits in and landward of the slide scar, we also observe remnants from the catastrophic deposition associated with the 2–3m high tsunami wave triggered in 1979, as attested by amalgamated sea grass and artefacts. Based on our observations and measurements on core-scale and earlier models based on in situ CPTu, we suggest that a significant part of the Quaternary delta and slope apron deposits are prone to being mobilised without a large external trigger, so that all in all a high risk for a landslide event of considerable size off Nice international airport is identified.

Grain growth behavior of Li4SiO4 pebbles fabricated by agar method for tritium breeder

The Li4SiO4 tritium breeding pebbles will be filled in the blanket and used for 2 years or more at high temperatures, which would increase the grain size and affect tritium release. Hence, grain sizes of the Li4SiO4 pebbles fabricated by agar method were investigated, and two kinds of different silicon sources (crystal and amorphous SiO2) with different particle sizes were used. The particle size of SiO2 could affect grain size and density of the Li4SiO4 pebble. And the isothermal sintering was carried out to study the grain growth kinetics of Li4SiO4. The grain growth exponent (n) and the activation energy (Q) were calculated by the phenomenological kinetic equation. The calculated n values were 4.10, 3.98, 3.34 and 2.96, and corresponding Q values were 152.15, 147.99, 125.54 and 110.58kJ/mol, respectively. At the higher sintering temperatures (950 and 1000°C), the grain growth of Li4SiO4 was controlled by vapor transport.

A method for estimating maximum static rainfall retention in pebble mulches used for soil moisture conservation

Mulching of agricultural fields and gardens with pebbles has long been practiced to conserve soil moisture in some semi-arid regions with low precipitation. Rainfall interception by the pebble mulch itself is an important part of the computation of the water balance for the pebble mulched fields and gardens. The mean equivalent diameter (MED) was used to characterize the pebble size. The maximum static rainfall retention in pebble mulch is based on the water penetrating into the pores of pebbles, the water adhering to the outside surfaces of pebbles and the water held between pebbles of the mulch. Equations describing the water penetrating into the pores of pebbles and the water adhering to the outside surface of pebbles are constructed based on the physical properties of water and the pebble characteristics. The model for the water between pebbles of the mulch is based on the basic equation to calculate the water bridge volume and the basic coordination number model. A method to calculate the maximum static rainfall retention in the pebble mulch is presented. Laboratory rain simulation experiments were performed to test the model with measured data. Paired sample t-tests showed no significant differences between the values calculated with the method and the measured data. The model is ready for testing on field mulches.

Application of a model to investigate the effective thermal conductivity of randomly packed fusion pebble beds

In our precious study, a prediction model, which calculates the effective thermal conductivity keff of mono-sized pebble beds, has been developed and validated. Based on this model, here the effects of these influencing factors such as pebble size, thermal radiation, contact area, filling gas, gas flow, gas pressure, etc. on the keff of randomly packed fusion pebble beds are studied and analyzed. The pebble beds investigated include Li4SiO4, Li2ZrO3, Li2TiO3, Li2O, Be and BeO pebble beds. In the current study, many important and meaningful conclusions are derived and some of them are similar to the existing research results. Particularly, some critters that under which conditions the effect of some influencing factors can be neglected or should be considered are also presented.

Fabrication of attractive Li4SiO4 pebbles with modified powders synthesized via surfactant-assisted hydrothermal method

Li4SiO4 pebbles have been widely studied as attractive tritium breeding materials in the fusion reactor blanket of international thermonuclear experimental reactor (ITER). In this work, surfactant-assisted hydrothermal method was first employed to prepare ultrafine ceramic powders for fabricating attractive Li4SiO4 pebbles. SEM analysis revealed that the introduction of sodium dodecyl sulfate could eliminate the particle aggregation to prepare monodispersed precursor powders, and thus generated the green bodies of pebble with homogeneous microstructure, which was helpful to eventually obtain high-quality Li4SiO4 pebbles. Moreover, the effects of sintering temperature on the grain size, relative density, and crush load of Li4SiO4 pebbles were also investigated. Li4SiO4 pebbles sintered at 700°C had a high crush load (average value 27.39N), small grain size (average value 0.57μm), satisfactory density (88.13%T.D.) and abundant pore structure, which were expected to show favorable tritium release behavior as a promising tritium breeding material for fusion reactor blanket.

Evolution of the Late Cretaceous Yongfeng-Chongren Basin in Jiangxi Province, southeast China: insights from sedimentary facies analysis and pebble counting

The Gan-Hang Belt in Southeast China is characterized by several igneous and siliciclastic basins associated with crustal extension during Late Mesozoic. The sedimentary evolution of the red basins is still poorly understood. In this study, sedimentary facies analysis and pebble counting were performed on outcrop sections of the Late Cretaceous Guifeng Group inthe Yongfeng-Chongren Basin in central Jiangxi Province. Thirty-five conglomerate outcrops were chosen to measure pebble lithology, size, roundness, weathering degree and preferred orientation. Results show that gravels are mostly fine to coarse pebbles and comprise dominantly quartzites, metamorphic rocks, granitoids and sandstones. Rose diagrams based on imbricated pebbles indicate variable paleocurrent directions. Combining with typical sedimentary structures and vertical successions, we suggest that the Guifeng Group were deposited in alluvial fan, river and playa lake depositional systems. The proposed depositional model indicates that the Hekou Formation represents the start-up stage of the faulted basin, accompanied by sedimentation in alluvial fan and braided river environments. Then this basin turned into a stable expansion stage during the deposition of the Tangbian Formation. Except for minor coarse sediments at the basin margin, the other area is covered with fine-grained sediments of lake and river environments. The Lianhe Formation, however, is once again featured by conglomerates, suggesting a probable tectonic event. Therefore, the study region possibly suffered two tectonic events represented by the conglomerates of the Hekou and Lianhe formations in the context of the crustal extension in Southeast China.

A prediction model for the effective thermal conductivity of mono-sized pebble beds

A model is presented here to predict the effective thermal conductivity of porous medium packed with mono-sized spherical pebbles, and it is valid when pebbles’ size is far less than the characteristic length of porous medium just like the fusion pebble beds. In this model, the influences of parameters such as properties of pebble and gas materials, bed porosity, pebble size, gas flow, contact area, thermal radiation, contact resistance, etc. are all taken into account, and one method to couple the contact areas with bed strains is also developed and implemented preliminarily. Compared with available theoretical models, CFD numerical simulations and experimental data, this model is verified to be successful to forecast the bed effective thermal conductivity in various cases and its advantages are also showed obviously. Especially, the convection in pebble beds is focused on and a constant coefficient C to correlate the effect of gas flow is determined for the fully developed region of beds by numerical simulation, which is close to some experimental data.

Dropstones in Rosso Ammonitico-facies pelagic sediments of the Southern Alps (southern Switzerland and northern Italy)

Sparse isolated pebbles and cobbles of extraformational lithologies are occasionally found in fine-grained deep-water sediments. In the Middle and Upper Liassic deep-water marly limestones and marlstones of Rosso Ammonitico facies (Morbio and Rosso Ammonitico Lombardo Formations) in the western Southern Alps, Lombardy and Ticino, outsized ‘exotic’ clasts of volcanic and basement rocks occur sporadically. The clasts, of pebble size, are typically rounded. The rhyolitic volcanic clasts can be related to the Permian volcanic succession of the western Southern Alps, from which they must have been reworked; a quartzite pebble is obviously derived from the Hercynian basement. The clasts are best interpreted, in analogy to other occurrences, as dropstones transported to the site of final deposition by drift wood that occasionally occurs in the pelagic sediments. The only possible source area must be situated to the west of Lago Maggiore where the Permian volcanic suite was exposed in a fault block uplifted in the course of latest Triassic–Early Jurassic rifting.

Axial dispersion and mixing phenomena of the gas phase in a packed pebble-bed reactor

The knowledge and proper analyses of axial dispersion and the mixing phenomena of the coolant gas flow in the dynamic core of pebble-bed nuclear reactors are useful for safe design and efficient operation of these reactors. These processes can be characterized in terms of the residence time distribution and quantified in terms of the axial dispersion coefficient. Therefore, in this work, the axial dispersion coefficients of the gas phase and their residence time distributions were measured experimentally in a separate effect pilot-plant scale and cold-flow experimental setup of 0.3m in diameter, using a sophisticated and advanced gaseous tracer technique. The non-ideal flow of the gas phase in the pebble bed was described using the axial dispersion model (ADM). The effect of the gas velocity on the axial dispersion was investigated using a range of velocities from 0.01 to 2m/s, covering both the laminar and turbulent flow regimes. The effect of the bed structure (pebble size) on the axial dispersion coefficient was investigated, and the results indicate that the pebble size strongly affects axial dispersion and mixing in the packed pebble-bed reactor. The results show that the flow pattern of the gas phase does not deviate much from the idealized plug-flow condition at high flow rate, which depends on the gas flow rate and the bed structure of the pebble-bed. The present work provides insight on the extent of mixing and dispersion in the gas phase in the studied bed using an advanced gas dynamics technique and methodology that properly accounts for the external dispersion.

Preparation of β-Li2TiO3 pebbles by a modified indirect wet chemistry method

β-Li2TiO3 pebbles were fabricated by a modified indirect wet chemistry method. The first feature lies in that β-Li2TiO3 powders via hydrothermal method were used as raw materials. The second one lies in that a mixture of the acetone and carbon tetrachloride was used for formation and aging of the pebbles at room temperature. The phase identification of the β-Li2TiO3 sintered pebbles was conducted by the X-ray Diffraction analysis. The morphology of the sintered β-Li2TiO3 pebbles was observed by Field Emission Scanning Electron Microscope. The experimental results show that the β-Li2TiO3 pebbles with about 1.56mm in diameter, a better sphericity of 1.02 and relative sintered density of 95.8%T.D. are successfully fabricated when sintered at 1100°C for 6h in ambient conditions. The grains in the pebbles are polyhedral brick-shaped, and homogeneous in size distribution. The morphology evolution and relative density of the β-Li2TiO3 pebbles are governed by the sintering temperature, between 1050°C and 1150°C. More homogeneous in grain size, less porosity, and higher densification of the β-Li2TiO3 pebbles can be obtained at 1100°C.

Evidence for pebbles in comets

When the EPOXI spacecraft flew by Comet 103P/Hartley 2, it observed large particles floating around the comet nucleus. These particles are likely low-density, centimeter- to decimeter-sized clumps of ice and dust. While the origin of these objects remains somewhat mysterious, it is possible that they are giving us important information about the earliest stages of our Solar System’s formation. Recent advancements in planet formation theory suggest that planetesimals (or cometestimals) may grow directly from the gravitational collapse of aerodynamically concentrated small particles, often referred to as “pebbles.” Here we show that the particles observed in the coma of 103P are consistent with the sizes of pebbles expected to efficiently form planetesimals in the region that this comet likely formed, while smaller pebbles are may be expected in the majority of comets, whose chemistry is often indicative of formation in the colder, outer regions of the protoplanetary disk.

Short term displacements of marked pebbles in the swash zone: Focus on particle shape and size

Abstract In this paper, two short term experiments with tracers on a mixed beach are presented. The aim was to understand how the size and shape of pebbles can affect their transport under low energy conditions. Sediment transport was studied by means of RFID technology to univocally monitor every single marked pebble. A size subdivision of injected pebbles was conducted based on three classes (“Big” from − 5.5 to − 6.5 phi; “Medium”, from − 5 to − 5.5 phi; and “Small”, from − 4.5 to − 5 phi). Two recoveries were realised 6 and 24 h after the injection. During a single day, the wave motion was very low in the first experiment and low to moderate in the second (never exceeding 0.4 m). The results showed that discs are less dynamic than spheres but can cover greater distances. Regarding the sediment size, “Big” pebbles are less dynamic if compared to finer classes, and they move preferentially down the swash zone towards the step or do not move up-slope if already at the step. Very low and steady energy conditions facilitate cross-shore and offshore movement of pebbles, rather than a slight raise in wave height producing predominant longshore transport even with non-marginal displacements. Low to moderate energy conditions can also produce some trend displacement based on the pebble shape even though T-tests showed that shape was not statistically significant for pebble displacement. The displacements of “Medium” and “Small” sized pebbles show a statistical dissimilarity compared to the “Big” ones. To refine the velocity estimation necessary to initiate pebble movement, the threshold velocity formulas known up to now should involve the shape parameter, especially for the short term. Better knowledge of the relationship between the sediment's characteristics and dynamics is critical to forecast the durability of replenishment material and to establish the suitability of fill material relative to native beach material. Hence, a better understanding of the role of particle characteristics is necessary.

Tendency towards sphericity symmetry of pebbles: The rate change of volume with surface

The primary effect of rocks and stones tending to erode towards sphericity symmetry can be identified with the rate change of volume with surface. Marble pebbles of various shapes and sizes are recorded and modeled mathematically as ellipsoids. The rate change of volume with surface dV/dA is computed for flat-shaped pebbles where the thickness dimension is assumed to be unity. Invoked is the hypothesis that the change of shape and size of pebbles can be characterized by a master curve derived from dA/dL, the 2D version of dV/dA. The sphericity symmetry is assumed to be concerned with the preference of roundness to slenderness regardless of the surface roughness, smoothness and the mineralogical composition. The erosiveness and abrasiveness of the surface and time effects can interact with sphericity, which is an issue beyond the scope of this work.

CFD Analysis for the Hydrodynamics and Heat Transfer in Packed Pebble Bed

Lithium titanate (Li2TiO3) and lithium orthosilicate (Li4SiO4) are the promising solid breeder materials for the fusion reactors. Packed bed of Li2TiO3 or Li4SiO4 pebbles is considered in the fusion reactor blanket for in situ production of tritium and for this a good effective thermal conductivity of the pebble bed is necessary. In recent past, Mandal et al. [26] studied the hydrodynamics and heat transfer properties of bed of lithium titanate pebbles at different operating conditions viz., gas flow rates, pebble sizes, bed wall temperatures, etc. In the present study laminar, k – ε and low Reynolds k – ε model have been used to simulate the hydrodynamics and heat transfer data of Li2TiO3 pebble bed. The computational fluid dynamics (CFD)-simulated hydrodynamics results have been compared with hydrodynamics and heat transfer results of bed of Li2TiO3 pebbles reported by Mandal et al. [26] and others. It was found that k – ε and low Reynolds number k – ε model shows better agreement with experimental results. The CFD study were carried out using low Reynolds k – ε model for pebble bed of different materials viz. Li2TiO3, Li4SiO4 and alumina (Al2O3). The effect of flow rate, pebble size, wall temperature, solid properties viz. thermal conductivity and specific heat on effective thermal conductivity and overall heat transfer coefficient has been discussed in this paper.

Formation of pebble-pile planetesimals

The first stage of planet formation is the accumulation of dust and ice grains into mm-cm-sized pebbles. These pebbles can clump together through the streaming instability and form gravitationally bound pebble 'clouds'. Pebbles inside such a cloud will undergo mutual collisions, dissipating energy into heat. As the cloud loses energy, it gradually contracts towards solid density. We model this process and investigate two important properties of the collapse: (i) the timescale of the collapse and (ii) the temporal evolution of the pebble size distribution. Our numerical model of the pebble cloud is zero-dimensional and treats collisions with a statistical method. We find that planetesimals with radii larger than 100 km collapse on the free-fall timescale of about 25 years. Lower-mass clouds have longer pebble collision timescales and collapse much more slowly, with collapse times of a few hundred years for 10-km-scale planetesimals and a few thousand years for 1-km-scale planetesimals. The mass of the pebble cloud also determines the interior structure of the resulting planetesimal. The pebble collision speeds in low-mass clouds are below the threshold for fragmentation, forming pebble-pile planetesimals consisting of the primordial pebbles from the protoplanetary disk. Planetesimals above 100 km in radius, on the other hand, consist of mixtures of dust (pebble fragments) and pebbles which have undergone substantial collisions with dust and other pebbles. The Rosetta mission to the comet 67P/Churyumov-Gerasimenko and the New Horizons mission to Pluto will both provide valuable information about the structure of planetesimals in the Solar System. Our model predicts that 67P is a pebble-pile planetesimal consisting of primordial pebbles from the Solar Nebula, while the pebbles in the cloud which contracted to form Pluto must have been ground down substantially during the collapse.

Event sedimentation in low‐latitude deep‐water carbonate basins, Anegada passage, northeast Caribbean

AbstractThe Virgin Islands and Whiting basins in the Northeast Caribbean are deep, structurally controlled depocentres partially bound by shallow‐water carbonate platforms. Closed basins such as these are thought to document earthquake and hurricane events through the accumulation of event layers such as debris flow and turbidity current deposits and the internal deformation of deposited material. Event layers in the Virgin Islands and Whiting basins are predominantly thin and discontinuous, containing varying amounts of reef‐ and slope‐derived material. Three turbidites/sandy intervals in the upper 2 m of sediment in the eastern Virgin Islands Basin were deposited between ca. 2000 and 13 600 years ago, but do not extend across the basin. In the central and western Virgin Islands Basin, a structureless clay‐rich interval is interpreted to be a unifite. Within the Whiting Basin, several discontinuous turbidites and other sand‐rich intervals are primarily deposited in base of slope fans. The youngest of these turbidites is ca. 2600 years old. Sediment accumulation in these basins is low (<0.1 mm year−1) for basin adjacent to carbonate platform, possibly due to limited sediment input during highstand sea‐level conditions, sediment trapping and/or cohesive basin walls. We find no evidence of recent sediment transport (turbidites or debris flows) or sediment deformation that can be attributed to the ca. M7.2 1867 Virgin Islands earthquake whose epicentre was located on the north wall of the Virgin Islands Basin or to recent hurricanes that have impacted the region. The lack of significant appreciable pebble or greater size carbonate material in any of the available cores suggests that submarine landslide and basin‐wide blocky debris flows have not been a significant mechanism of basin margin modification in the last several thousand years. Thus, basins such as those described here may be poor recorders of past natural hazards, but may provide a long‐term record of past oceanographic conditions in ocean passages.