The packing efficiency of inorganic particles in the system can have a large impact on the level of water required for runoff. However, the packing efficiency of the particles affected the stiffness of the plasticized material.
Mono- sized Ideal Spherical Packing
Experimental solids loading values for packing several sizes of mono-distributed spherical particles carried out by McGeary1 are shown in Table II. McGeary also determined through experiments that to ensure accurate packing information and eliminate vessel wall interference, the cylinder used to pack the particles must be at least an order of magnitude (10x) larger in diameter than the particles being packed.
Packing of a Binary system of spherical particles
The packing density increases as the ratio of coarse to fine particles increases, reaching a maximum of ~84% when the ratio reaches ~10:1 and remaining relatively constant up to 20:1. When the coarse to fine ratio exceeds 20:1, it shows a small change in packing density as shown in Figure 3.
Packing of continuous size distribution
Particle size and distribution effect on slurry and paste rheology
Sieve Analysis and Screening of Incoming Alumina
The particle size data from the siphon analysis and laser diffraction are in reasonable agreement. Based on the sieve analysis, the as-received T-64 material was passed through a series of screens (Table IV) to obtain six discrete particle size distributions.
Measuring Screened Material Via Laser Diffraction
The peak of each distribution measured by laser diffraction coincides with the large screen aperture in the scope series. The exception is the -400 mesh screened material, which has a much wider distribution than the other five materials because it includes all particles smaller than 37 microns. The reported values for the span of the distributions are consistent for the coarsest five screenings, showing relatively tight distributions compared to the as-received material.
The finest screening (-400 mesh) had a wider spread resulting in a span value approximately double that of the other materials. Air classification of the -400 mesh material was successful in creating two fairly discrete particle size distributions. The air classification resulted in the distribution of the -400 mesh material being tighter, with the +24 micron cut having a similar span to the coarser materials, but the -24 micron cut still being relatively broad compared to the rest of the materials.
Tap Density Procedure for Obtaining Packing Efficiency
The greater width in particle size distribution increases the overall packing efficiency of the material. Second, the packing efficiency response to tapping is different for the -24μ and as-received (group A in Figure 16) materials compared to the remaining materials (group B in Figure 16). The packing efficiency of the blended materials was measured using the same dry tap density procedure as the screened material.
The overall packing efficiency of the mixed materials reported in Figure 19 shows increasing packing efficiency as the coarse to fine particle size ratio increases at 5000 taps. The Furnas model has also been used to predict the packing efficiency of dispersions of particles. As shown in Figure 29, the stiffness of the material increases as the packing efficiency increases.
Extrusion Paste Pressure and Stiffness Measurements
Plasticizing wet material
The wet material was measured with a torque rheometer (Intelli-torque Plast-Corder Torque Rheometer, Brabender Technologies, Duisburg, Germany) and mixed at 50 RPM to a constant mixing energy measured at 50 KJ. The now plasticized material was then cut into ¼” pieces to prepare a series for extrusion pressure and stiffness measurements.
Rod and Ribbon Preparation for Measurement
The plasticized group was added to a test machine (Instron, Model 5569, Norwood Massachusetts) with a 25.4 mm diameter barrel and ram-style piston. At the exit of the barrel in the deadhead of the system for evaluation was attached a strong card. A vacuum of 25 inHg was drawn into the system for 1 minute to aerate the material.
Once the vacuum was applied, the piston compressed the material up to 1000kgf to consolidate and result in a uniform deaerated starting material. After compression, the piston was retracted to remove the force and the deadhead was removed and replaced with a 15mm diameter circular. Repeating the same process for the 15 mm bars, a 6 mm x 25.4 mm ribbon die was added to the barrel and five ribbons were extruded at 15 cm each for additional stiffness measurements.
Measuring Stiffness of Plasticized Material
Measuring Extrusion Pressure of Material
Once the rate was stabilized, the pressure at each shear rate was measured and recorded. Two capillary dies were used, one with a diameter of 1 mm and the other with a diameter of 1.5 mm. Two diameters were used to determine if the particles within a given distribution were too large and possibly exhibiting particle blockage.
The pressure delta between the 1.0 mm nozzle and the 1.5 mm nozzle was plotted against the median particle diameter (D50) for each distribution in Figure 12. The normalized pressure difference in Equation 6 shows a linear regression correlation coefficient (R2) was 0.093, indicating no correlation. If particle stoppage affected the 1.0 mm capillary data, it would be evident in an increased pressure as the particles became larger, resulting in a larger pressure delta between the 1.0 mm and 1.5 mm dies.
Die Wear Correction
To compare the pressure data from each run as the die increases in diameter, the shear rate is kept constant. To achieve a shear rate of 58 s-1 using the 1.67 mm die, the punch speed is calculated to be 9 mm/min. Using the recorded pressure at the adjusted speeds to keep the shear rate constant for the same material using the 1.67 mm and 2.4 mm dies resulted in pressures of 29.71 MPa and 20.06 MPa, respectively.
Without the shear rate adjustment, the pressure for the 1.67mm die would have been 32.82MPa, which means there is a maximum of a 3MPa error when the correction is not used. Although the correction was used as it was, accounting for the shift difference would not change the outcome of this paper. Accept linear wear from 1.67mm to 2.4mm between; runs 34 and 70, respectively, the run-to-run decrease in pressure was calculated as 0.9%.
Determining Methocel Level
For each methocel concentration and excess liquid level shown in Figure 14, capillary entry pressure and penetrometer stiffness were measured. As the methocel concentration increases, the slope of pressure versus stiffness also decreases (unable to extrude lowest water level for 10% methocel due to particle jamming). Operation above 25 MPa pressure becomes increasingly difficult due to die and equipment strength challenges.
Below 10 MPa pressure, formation problems related to too little pressure (peripheral flow uniformity) begin to introduce. Methocel concentration levels above 20% would likely work for the extrusion process, resulting in an acceptable compressive and stiffness window. 20% methocel solution provides the pressure and stiffness in a window that balances pressure, stiffness and drying/baking ability.
Determining Packing Efficiency Using Tap Density
Packing Efficiency of Scalped Material
As reported in Table VI, the calculated span of the as-received distribution is much larger than that of the screened materials. There is a clear increase in the slope for the -24 µm and received material in the range of 25-500 taps compared to the remaining materials. This change in slope can be attributed to the low flow density of the -24 micron cut; more taps are needed to achieve the initial consolidation (due to the higher cohesive forces of the finest particles).
Alternatively, the difference may be due to the time it takes for the larger particles to move by pressing in order for the smaller particles to fill the interstitial. As particle size decreases, particle cohesion increases requiring more energy to consolidate. The modified Carr index shown in Figure 18 is reported for values calculated from 0-500 taps and 500-5000 taps to show the impact of using fine particles on the initial tapping sequence.
Packing Efficiency of 70:30 Blended Material
The sieved materials were mixed in a 70:30 coarse to fine particle size ratio to produce a range of increased packing efficiencies. Using the Carr's Index and separating the tap density data into 0-500 and 500-5000 taps, the distributions are divided into two groups as shown in Figure 20. The overall Carr's Index is increased for the mixed materials compared to the screened monodistributed materials, indicating increased resistance to flow as packing efficiency increases.
The -24 μm materials are to the right of the green line in Figure 18. The Carr index increases as the fine content increases, providing evidence of increased cohesive forces contributing to the change in slope of the tap density curves for finer materials. For the purpose of this article, packing efficiency at 5000 taps is assumed to be an accurate representation of particle packing in a paste.
Experimental Packing Efficiency Versus Models
Although the extent of packing efficiency is different, probably due to particle density, both sets of data show almost the same "critical" ratio of coarse to fine (10:1). The Furnas model uses the packing efficiency of the original distributions to predict the packing efficiency of the ratio of the two. Where PEc and PEf are the packing efficiency of the coarse and fine distribution, respectively, F1 is a function of the volume fraction of fines Xf and F2 is a function of the size ratio of coarse and fine particles (R).
Where C2 is equal to 4 based on best fit curves for experimental data given by Furnas.4 Based on this model, the theoretical packing efficiency is calculated and compared with the measured packing efficiency (Table VII) in Figure 24. As shown in Table VI. this distribution has the broadest particle size distribution with a range almost twice as large as the remaining distributions. The wide distribution could explain the reduced packing efficiency compared to the Furnas model prediction, effectively increasing the coarse portion of the 70:30 coarse to fine ratio.
Determining Critical Excess Liquid for capillary Flow
Percent excess fluid is used and not total fluid because the excess fluid is a consistent measurement regardless of packing efficiency. As described in Figure 25, a packed bed with particles in the spaces shown would have an overall reduced fluid at the same excess fluid level as the packing shown. The materials in Figure 26 were selected to produce a range of uniform packing efficiency mono-distributed materials centered around different particle sizes as well as varying coarse to fine bi-modal particle size distributions to produce a range of packing efficiencies.
The second slope describes a much higher reduction in pressure as a critical excess liquid level is reached to allow free particle flow. The point where the two slopes intersect in Figure 27 is reported as the critical percent excess liquid for each distribution. However, a range of 4% is enough to confidently report that there is a real trend and shows that the excess fluid required for capillary flow is consistently in the range of 55-73% packing efficiency.
Determining Material Stiffness at Critical Excess Liquid
The stiffness of the different packing efficiency materials converges to zero between a low 30% and a low 40% excess liquid (4-7 times the critical excess liquid level). A reasonable explanation for this phenomenon is that as packing efficiency increases, interactions between particles also increase. These data make it possible to predict stiffness at critical excess fluid based on packing efficiency data.
The trend in packaging efficiency as the ratio of coarse to fine particles increases was almost indistinguishable from the McGeary model. Both model and experimental data showed maximum packing efficiency at a coarse-to-fine ratio of 10:1. Determine whether softer particles such as talc or clay have the same packing efficiency behavior as aluminum oxide.
