Filtration data correlation

The correlations used are based partly on theoretical consideration and partly on empirical observations. The basic filtration data are correlated by application of the classic cake-filtration equation, aided by various simplifying assumptions which are sufficiently valid for many (but not all) situations. Washing and drying correlations are of a more empirical nature but with strong experimental justification. If steam or thermal diying is being examined, additional correlations are required beyond those summarized below for such applications, it is advisable to consult an eqmpment manufacturer or refer to pubhshed technical papers for guidance. 

For the output variables, as shown in Figs. 9-15 and 9-16, the filtration time data correlated well with mean particle size (chord length) and the level of fines by Lasentec FBRM measurement and optical micrographs. This correlation enabled direct feedback of process performance (cake filtration resistance) based upon FBRM measurement. 

While research has developed a significant and detailed filtration theory, it is still so difficult to define a given liquid-solid system that it is both faster and more accurate to determine filter requirements by performing small-scale tests. Filtration theoiy does, however, show how the test data can best be correlated, and extrapolated when necessary, for use in scale-up calculations. 

Where the resistance of the precoat bed is significant in comparison to the resistance of the deposited solids, the thickness of the precoat bed effec tively controls the filtration rate. In some instances, the resistance of the deposited solids is veiy large with respec t to even a thick precoat bed. In this case, variations in thickness through the life of the precoat bed have relatively little effec t on filtration rate. This type of information readily becomes apparent when the filtration rate data are correlated. 

Wash Time Cake-washing time is the most difficult of the filtration variables to correlate. It is obviously desirable to use one which provides a single cni ve for all of the data. Filtration theory suggests three possible correlations [Eqs. (18-59) to (18-61)]. These are listed below, beginning with the easiest to use ... 

The examples which follow show how data from the correlations justpresented and a knowledge of thephysical characteristics of a particular filter are used to determine a filtration cycle and, subsequently, the size of the filter itself. The three examples which follow involve a disk, a drum belt, and a horizontal belt filter. 

Data set Number of correlations Total correlations Extended correlations0 Total After filtration Generation time... 

The following empirical dimensional equation [5], which is based on data for the UF of diluted blood plasma, can correlate the filtrate flux/p (cm min ) averaged over the hollow fiber of length/, (cm) ... 

Equation 8.7 [6] was obtained to correlate the experimental data on membrane plasmapheresis, which is the MF of blood to separate the blood cells from the plasma. The filtrate flux is affected by the blood velocity along the membrane. Since, in plasmapheresis, all of the protein molecules and other solutes will pass into the filtrate, the concentration polarization of protein molecules is inconceivable. In fact, the hydraulic pressure difference in plasmapheresis is smaller than that in the UF of plasma. Thus, the concentration polarization of red blood cells was assumed in deriving Equation 8.7. The shape of the red blood cell is approximately discoid, with a concave area at the central portion, the cells being approximately 1-2.5 pm thick and 7-8.5 pm in diameter. Thus, a value of r (= 0.000257 cm), the radius of the sphere with a volume equal to that of a red blood cell, was used in Equation 8.7. 

Filterability of slurries depends so markedly on small and unidentified differences in conditions of formation and aging that no correlations of this behavior have been made. In feet, the situation is so discouraging that some practitioners have dismissed existing filtration theory as virtually worthless for representing filtration behavior. Qualitatively, however, simple filtration theory is directionally valid for modest scale-up and it may provide a structure on which more complete theory and data can be assembled in the future. 

Figure 11.3. Laboratory test data with a vacuum leaf filter, (a) Rates of formation of dry cake and filtrate, (b) Washing efficiency, (c) Air flow rate vs. drying time, (d) Correlation of moisture content with the air rate, pressure difference AP, cake amount W Ib/sqft, drying time 6d min and viscosity of liquid Dahlstrom and Silverblatt, 1977).

Some data fitted to these equations by Tiller et al. (1979) are in Table 11.8 here the constant k is the same for both a and e, although this is not necessarily generally the case. Unfortunately, these data show that the parameters are not independent of the pressure range. Apparently the correlation problem has not been solved. Perhaps it can be concluded that insofar as the existing filtration theory is applicable to real filtering behavior, the approximation of Almy and Lewis may be adequate over the moderate ranges or pressures that are used commonly, somewhere between 0.5 and 5 atm. 

Spectrex ILI-1000 Particle Counter combines the Prototron with a Particle Profile Attachment (multichannel analyzer). The instrument has been used [118] for examining volcanic ash. AC Fine Dust was used for calibration in eight 5 pm steps, which indicated that accurate data was obtained for sizes above 2 pm. It has also been shown to correlate well with the more tedious filtration and counting method for large volume parenteral liquids [119]. Although semi-transparent containers or liquids reduce the amount of transmitted light flux, the instrument gives valid data for particulates in oil [120]. 

The probable success of correlation of cake resistivity in terms of all the factors that have been mentioned has not been great enough to have induced any serious attempts of this nature, but the effect of pressure has been explored. Although the a s can be deduced from filtration experiments, as done in Example 11.1, a simpler method is to measure them in a CP cell as described briefly later in this chapter. Equation (11.24) for the effect of pressure was proposed by Almy and Lewis (1912). Eor the materials of Figure 11.4(b), for instance, it seems to be applicable over at least moderate stretches of pressure. Incidentally, these resistances are not represented well by the Kozeny porosity function (1 — s)/s for substance 6, the ratio of resistivities at 100 and 1 psia is 22 and the ratio of the porosity functions is 2.6. The data of Table 11.7 also show a substantial effect of pressure on resistivity. 

Poola et al studied the renal excretion of pentamidine in the isolated perfused rat kidney, which is an established model to study the renal disposition of drugs and that correlates with in vivo disposition. The data showed that a combination of filtration, active secretion and passive reabsortion are involved in the renal disposition of pentamidine [150]. 

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