It appears that the phenomena occurring during filtration and rinsing are strongly affected by the grain shape and by derivative properties resulting from grain shape. Prior to being filled in the filter, the bed material is sieved through suitable sieves of predetermined mesh.
Obviously, it is not possible to obtain grains of single diameter, because if a bed is sieved through sieve with holes of, for example, 1. If a bed would be built of a perfectly spherical mineral, then a substitute diameter equal to arithmetical average of two extreme sieve hole sizes could be used for calculations. In actual situations however, one has to deal with minerals other than perfectly spherical, whereas crushed minerals may have shapes that are elongated, cylindrical, lamellar, pyramidal and even completely irregular. In such case, sieves may retain grains of dimensions other than the sieve hole size, as larger elongated particles may be among them as a result of vertical positioning of smallest dimensions or jamming of grains with largest dimensions, oriented horizontally.
For that reason, it was necessary to develop certain equivalent values to describe averaged parameters of beds.
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They include equivalent substitute diameter, sphericity shape factor and porosity. As the total volume of solid particles forming a fixed bed is smaller than the volume of the bed, the ratio of free spaces between these particles to bed volume is called porosity, which may be determined by different methods . For particles with regular shapes the sphericity may be determined on the base of that definition.
For particles with irregular shapes the sphericity is determined with approximate methods.
One of them is the measurement of three characteristic dimensions, which may be obtained with optical method, or density and volumetric, or gas-expansion methods . Razumow , as well as Cooke and Rowe , indicated that, for uniform spherical particles, porosity depends only on the number of points of contact of individual spheres and not on grain diameter.
Thus, theoretically, the porosity of such bed may range from 0. As in practice a bed is never built of uniform and perfect spheres, the porosity may deviate significantly from these values. The relationship between sphericity and porosity and the degree of compacting densification is presented in Fig. The relationship between sphericity, porosity and bed compacting  As may be seen, at specific sphericity, especially with shapes close to spherical, bed compacting affects the porosity quite significantly. This relationship is of significant importance for the practice, because the lower porosity the better water purification and the higher hydraulic losses during water flow through the bed.
In case of water purification filters, the use of a direct method of sphericity determination is not justified, because the filter always contains a bed built of a mixture of particles of different sphericities. In this way the sphericity was determined by many researchers for various minerals [4, 6].
In the intermediate flow range both terms assume negligible values. When the rinsing velocity is gradually increasing, water stream loosens the bed slowly and causes its lifting to a so-called fluid or fluidized state when the bed behaves like a liquid. This formula is correct within the fluid state of bed.
This velocity is designated as V i and it goes into the formula In their in-depth tests, Dharmajah and Cleasby  analyzed various minerals and attempted to find relationships between sphericity and densities of water and grains, granulation, porosity, etc. In addition to their own measurements, they utilized those by Gunasingham at al.
Table 1. The products were obtained in commercial quantities with mixed granulation. Therefore, the first step prior to actual testing was to prepare beds in suitable grain fractions. The beds were screened so as to enable grading of 10 following fractions: 3. The granulation ranges resulted from sieve set, used by the laboratory. A substitute diameter was assigned to each fraction range and for each bed.https://roepoconfatu.ga
As individual grain fractions contained grains of different shapes and sizes, limited only by the size of sieve, differing numbers of grains were added to the weighing vessel. In case of courser fractions 3. This growing number of grains for smaller granulations was used in order to reduce the effect of weighing error.
Density of minerals was determined by standard method  using pycnometer and denaturized alcohol.
Volumetric density may have different values, depending on the degree of grain compaction. Since filtration bed is quite loose during rinsing process, once it is ended, the bed is in the state of bulk-density conditions. That is why the porosity calculation utilized volumetric density determined by standard method [27, 29] with steel cylinders and funnels for continuous grain feeding. The microscope-inspections, as well as initial density and hydraulic testing, found out that some minerals exhibited significant internal porosity with consequent long degassing of grains when immersed in liquid.
This phenomenon applied primarily to diatomite and clinoptylolite, and less to chalcedonite, nevtraco and barite. Therefore, additional experiment was carried out by immersing grains of all beds in kerosene of density precisely determined by pycnometric method. Once the pores were filled with kerosene air bubbling has stopped , grains were removed onto a screen and left for kerosene to drip off. Seen under microscope, the internal pores in grains remained filled with kerosene with convex meniscus, while flat surfaces were covered with kerosene film.
In order to remove this excess of kerosene, the grains were gently rolled on paper of average absorptivity. The final stage was the weighing of grains with their pores filled with kerosene. The porosity value, as determined for each bed and each fraction from the formula 25 , was used in further tests and calculations. The sedimentation velocity was testing with use of a 2m-long column of transparent material PLEXI of internal diameter 52 mm. Appropriate levels were marked on column wall and the time of grain sinking was measured on sections of 0. The lengths of sections and sinking times became a basis for calculating of sedimentation velocity V s.
In order to obtain reliable results, the sedimentation velocity was measured for grains of each mineral and each fraction. The constancy of that temperature was observed, because water was taken from a well and, after its conditioning, was stored in tank. This tank of m 3 capacity is buried under ground under a quite thick layer of soil, thus ensuring constant temperature conditions inside.
The testing of bed expansion and head losses during water flow through the bed in both steady state and during fluidization was conducted with the use stand shown in Fig. Diagram of stand for bed testing The testing stand was built of a 2m-long transparent tube of PLEXI plastic material with internal diameter of 52 mm. A strainer, made of plastic filtration nozzle, with additional small holes drilled in its upper surface to enable rather uniform water flow, was installed in the lower part of the tube.
A gravel layer of quartz sand in granulation from 3. The height of the gravel layer ranged from Then a layer of tested bed was poured onto that gravel layer. Its height was 50 cm for courser beds and 40 cm — for beds of finer granulation. These heights resulted from the distance of the top surface of bed from column outlet, so as to allow for expected expansion and to avoid grain escape to drain.
These strata thicknesses were determined during earlier, preliminary tests. Each series of tests began by filling the column with water to approximately half of the height and with gravel layer filling.
Then water was pumped with high intensity through column inlet in order to fluidize the layer. This operation permitted removing of any impurities which could get in among gravel grains, and enabled obtaining flat horizontal top surface of that layer. The second part of measurements consisted in filling the tested bed on thus prepared gravel layer. Head losses were measured as a differences of water mirror levels in a piezometer connected to the column under the strainer, as well as the water mirror level in column resulting from installed overflow, through which water is drained after bed rinsing.
For this reason, two water mirror levels, in piezometer and column, were read during each measurement. The difference in readings showed the amount of head loss. As the measurement of pressure loss in filtration bed layer was the primary objective, all measurements were preceded by measurements of head loss in the strainer. They were carried out identically as described earlier, with the only difference that they were carried out with column without gravel layer and bed.
The second element that have to be accounted for were head losses in the flow through the gravel layer. The difference in approach here resulted from the fact that, while the strainer remained the same all the time, i.
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That is why each measurement of rinsing parameters consisted of two parts. Measurements were carried out identically as for water flow through the strainer. The head loss was therefore a sum of head losses in water flow through the strainer and through the gravel layer. The second part of measurements consisted in pouring the bed to be tested on a previously tested gravel layer.
Related [Journal] Filter Media (a Filtration + Separation publication). Volume 1. Issue 1
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