scholarly journals On the Information Content of Coarse Data with Respect to the Particle Size Distribution of Complex Granular Media: Rationale Approach and Testing

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 601 ◽  
Author(s):  
Carlos García-Gutiérrez ◽  
Miguel Ángel Martín ◽  
Yakov Pachepsky
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Information Content ◽  
Granular Media ◽  
Initial Conditions ◽  
Physical Property ◽  
Conceptual Approach ◽  
Grain Sizes ◽  
Andersen Model

The particle size distribution (PSD) of complex granular media is seen as a mathematical measure supported in the interval of grain sizes. A physical property characterizing granular products used in the Andreasen and Andersen model of 1930 is re-interpreted in Information Entropy terms leading to a differential information equation as a conceptual approach for the PSD. Under this approach, measured data which give a coarse description of the distribution may be seen as initial conditions for the proposed equation. A solution of the equation agrees with a selfsimilar measure directly postulated as a PSD model by Martín and Taguas almost 80 years later, thus both models appear to be linked. A variant of this last model, together with detailed soil PSD data of 70 soils are used to study the information content of limited experimental data formed by triplets and its ability in the PSD reconstruction. Results indicate that the information contained in certain soil triplets is sufficient to rebuild the whole PSD: for each soil sample tested there is always at least a triplet that contains enough information to simulate the whole distribution.

scholarly journals Log-Cubic Method for Generation of Soil Particle Size Distribution Curve

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Songhao Shang
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Cross Validation ◽  
Interpolation Method ◽  
Physical Property ◽  
Particle Size Analysis ◽  
Soil Particle ◽  
Size Analysis ◽  
Particle Analysis

Particle size distribution (PSD) is a fundamental physical property of soils. Traditionally, the PSD curve was generated by hand from limited data of particle size analysis, which is subjective and may lead to significant uncertainty in the freehand PSD curve and graphically estimated cumulative particle percentages. To overcome these problems, a log-cubic method was proposed for the generation of PSD curve based on a monotone piecewise cubic interpolation method. The log-cubic method and commonly used log-linear and log-spline methods were evaluated by the leave-one-out cross-validation method for 394 soil samples extracted from UNSODA database. Mean error and root mean square error of the cross-validation show that the log-cubic method outperforms two other methods. What is more important, PSD curve generated by the log-cubic method meets essential requirements of a PSD curve, that is, passing through all measured data and being both smooth and monotone. The proposed log-cubic method provides an objective and reliable way to generate a PSD curve from limited soil particle analysis data. This method and the generated PSD curve can be used in the conversion of different soil texture schemes, assessment of grading pattern, and estimation of soil hydraulic parameters and erodibility factor.

scholarly journals Improved Parameterization of Fertilizer Particle Size Distribution

1998 ◽  
Vol 81 (5) ◽  
pp. 935-942 ◽  
Author(s):  
Edmund Perfect ◽  
Qiang Xu ◽  
David L Terry
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Goodness Of Fit ◽  
Physical Property ◽  
Distribution Functions ◽  
Parameter System ◽  
Common System ◽  
Best Parameter ◽  
Log Normal

Abstract Particle size distribution is an important physical property of granular fertilizers that influences their bulk behavior (e.g., packing and segregation). Several parameter systems for fertilizer particle size distributions are analyzed in this paper. The most common system used by the fertilizer industry is the SGN-UI system, where SGN is the size guide number (the median particle size) and Ul is the uniformity index (the 10th percentile particle size expressed as a percentage of the 95th percentile particle size). This 2-parameter system, however, has many limitations. For example, it does not give a distribution function. Furthermore, the Ul parameter does not accurately reflect the spread of particle sizes. It is therefore necessary to find a better parameterization system. Three size distribution functions (the log-normal, the Rosin-Rammler and the Gaudin-Schuhmann equations) were tested on a size distribution database composed of 377 samples from 7 fertilizer materials. Each function was fitted to the data by nonlinear regression. The Rosin-Rammler function is the best parameter system on the basis of an analysis of variance of the sum of squares of error from the nonlinear fits. Comparisons between the Rosin-Rammler and the SGN-UI parameters were also made. The Rosin- Rammler system is more accurate than the SGN-UI system, possesses the ability of prediction, and provides a measure of the goodness of fit. Therefore, the Rosin-Rammler system should be used to characterize size distribution of granular fertilizer materials instead of the SGN-UI system.

scholarly journals Particle size distribution and clay minerals in dryland soils of Aceh Besar, Indonesia

2021 ◽  
Vol 922 (1) ◽  
pp. 012013
Author(s):  
S Sufardi ◽  
T Arabia ◽  
K Khairullah ◽  
I Apriani
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Physical Properties ◽  
Bulk Density ◽  
Size Distribution ◽  
Clay Minerals ◽  
Physical Property ◽  
Soil Bulk Density ◽  
Soil Profiles ◽  
Physical Constraints

Abstract Soil particle size distribution is a fundamental physical property affecting other soil properties. This research aims to determine the distribution of soil particles and the composition of clay minerals on each layer of the horizon in four soil profiles (P1, P2, P3, and P4) with different parent materials in the dryland of Aceh Besar district which includes Entisols Jantho, Andisols Saree, Inceptisols Cucum, and Oxisols Lembah Seulawah. Particle size distribution (or texture) and bulk density (BD) were analyzed in the laboratory. Soil structure and consistency were observed directly in the field. The type of clay minerals was identified by X-ray diffraction, while Fe, Al, and Si-oxide were extracted by dithionite-citrate solution. The results shown that the particle size distribution and the physical properties of dryland soils of Aceh Besar vary between soil orders. Andisols Saree has better physical properties than the physical properties of other soils and low bulk density. The Al, Fe, and Si fractions and clay mineral composition in the soil profiles also vary considerably between soil orders. The Andisols are dominated by allophane minerals (amorphous fractions) while Entisols, Inceptisols and Oxisols consist of mixed minerals of feldspar, quartz, halloysite, goethite, and other clay minerals. These soil orders have some soil physical constraints i.e. high soil bulk density, low water holding capacity and poor soil structures. Improvements in the physical properties of the soil on Aceh Besar dryland are indispensable to improve the quality of the soil.

Modelling of the Movement of a Prolate Particle in the Steady State Flow of a Non-Newtonian Fluid in an Inclined Annulus With Inner String Rotation

2019 ◽  
Author(s):  
Eric Cayeux
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Cross Section ◽  
Slip Velocity ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Bulk Fluid ◽  
Tool Joint

Abstract The determination of the slip velocity, or whether a solid particle will sediment, during its transport is of prime importance for hole cleaning evaluations during drilling operations. Yet, this task is complexified by the asymmetry of the annulus when the central pipe axis does not coincide with the borehole central line and when the inner string rotates, especially since drilling fluids typically follow a yield stress power law rheological behavior. This paper describes the modelling of the movement of a particle in such conditions yet with the following simplifications: the inner tube is eccentric but has a uniform movement, the shape of the particle is assimilated to a prolate, the change of shear rates in the fluid around the slipping particle is neglected and collisions between particles are not considered. Otherwise, gravitational effects are incorporated by accounting for the mass density difference between the particle and the surrounding fluid mixture and by considering the borehole inclination. The particle spin is also estimated as it plays an important role in the determination of the drag and lift forces. The solution to the differential equations that describe the time evolution of the position and orientation of the particle, depend largely upon the initial conditions. Therefore, an ensemble of boundary conditions is generated at a starting cross-section along the annulus and the resulting particle trajectories are estimated. It is then possible to estimate a probabilistic slip velocity for particles of the considered dimensions, far away from the entrance region. This probabilistic approach allows to define a critical transport fluid velocity as the lower limit of the bulk fluid velocity by which no particle risk to settle. Similarly, one can define a critical settling fluid velocity as the upper limit of the bulk fluid velocity where every particle will sediment regardless of the initial conditions. With the described modelling of the particle movement and its associated statistical methods, it is possible to quantitatively estimate the spatial distribution of particles in any cross-section. For those particles that get trapped between the tool-joint and the borehole, it is then possible to estimate their size reduction by grinding, resulting from the rotation of the tool-joint on the borehole wall. The grinding process impacts the particle size distribution passed a tool-joint. By applying this method iteratively up to the annulus outlet, it is possible to estimate the particle size distribution of the drill-cuttings when they arrive at the shale-shakers.

Aspects of particle attachment in filtration

2006 ◽  
Vol 6 (4) ◽  
pp. 125-134 ◽  
Author(s):  
J. Kim ◽  
D.F. Lawler
Keyword(s):  
Particle Size ◽  
Zeta Potential ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Granular Media ◽  
Early Stage ◽  
Particle Removal ◽  
Specific Chemical ◽  
Ph Values ◽  
Initial Stage

Granular media filtration is used almost universally as the last particle removal process in conventional water treatment plants, but every particle cannot be removed. Laboratory-scale filtration experiments were performed at a filtration velocity of 5 m/h using spherical glass beads with mean diameter of 0.55 mm as collectors; the 10 cm depth ensured particles would be in the effluent. Particle suspensions (Min-U-Sil 5) with 1.7 μm mean particle size were filtered at pH values of 3.0, 4.0, and 5.0, all above the isoelectric point (near pH 2.0). Zeta potential distribution (ZPD) and particle size distribution (PSD) of influent and effluent particles were measured. More favorable particles, i.e. particles with smaller surface charge, were well attached to the collectors during the early stage of filtration. This selective attachment of the lower charged particles caused the ZPD of the effluent to move to a more negative range. However, the ZPD did not keep moving to a more negative range during later stages of filtration, and this result was thought to be caused by two reasons: ripening effects and detachment of flocs. In the early stages of filtration, particles were captured better at pH 3.0 than at the higher pH values (as expected), but this trend reversed at a cumulative hydraulic loading (CHL) of only 5–10 m3/m2. Particle breakoff apparently occurs as flocs of particles that are initially captured individually, as indicated by the trends for different particle sizes. At pH 3.0, particles in the 3–5 μm range had worse removal after a CHL of 5 m3/m2, whereas removal improved through the entire CHL of 20 m3/m2 for all size particles at pH 4.0. Chemical parameters such as zeta potential can be important during the initial stage of filtration, but their importance can decrease over time depending on the specific chemical conditions. The influent particle size distribution and the removal of certain size particles during the initial stage can significantly influence ripening which, in turn, can influence the overall particle removal efficiency. Better initial particle removal does not necessarily mean better overall particle removal.

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