Filtration time calculation

The volume of the plutonium peroxide slurry varied slightly depending upon the experimental conditions. This variance ranged from 23.k to 31.6 ml with an average of 30.1 ml. (These are buret readings and they do not include the volume of the section of the Filterometer containing the filter). To correct for this variation in volume, the relative filtration time calculated above was multiplied by the factor... 

Calculate the total filtration time of both steps and the volumes of filtrate, cake and separated slurry. Assume for these calculations that the operation is performed without any washing and dewatering stages. 

Calculate the required filtration time for 10 Liters of liquid through 1 m of filter area if tests have shown that 1 Liter of filtrate is obtained after 2.25 min. and 3.2 Liters after 14.5 min. from the start of the process. 

For q - 0 or Tb -> 0, Ucond - 0, and at q - <=° or xb -> <=°, Ucond -> u. That is, to increase the filter capacity, filtration time should be increased. However, such an increase is limited by the maximum allowable pressure drop which at constant operating conditions, establishes a maximum cake thickness. Let s consider the following example for the first case in this analysis. We wish to determine the capacity of a batch filter operating at a constant rate. The rate of filtration is q = 0. 1 X 10 3 m3/m2-s and the auxiliary time is 900 s. The solution to this problem is as follows. The filter capacity is characterized by the average conditional filtration rate, q. Values of ucord calculated are shown plotted in Figure 41. As shown, an increase in the amount of filtrate causes a sharp increase in filter capacity initially, with a limiting value of u attained eventually. 

If not, they were discarded. The second step taken to eliminate variabi1ity— in this case the variability within the 28 to 37 second range—involved the use of relative rather than absolute filtration times. Relative filtration times were calculated as follows (12) ... 

The reference interval for urinary calcium (UCa) for spot fasting or timed specimens collected after an overnight fast is less than 0.16 mg/100 mL (<0.04 mmol/L) of glomerular filtrate (GF), calculated by the following equation ... 

A volume fraction of 0.035 is needed to reach a half saturated support when the wet layer thickness becomes 45 pm. A filtration time of 5 min seems to be appropriate in order to be relatively independent from the filling and emptying time of the 1 m long tube. The desired viscosity can be calculated from Eq. (6.39). 

The slurry of Prob. 30.3 is to be filtered in a press having a total area of 8 m and operated at a constant pressure drop of 2 atm. The frames are 36 mm thick. Assume that the filter-medium resistance in the large press is the same as that in the laboratory filter. Calculate the filtration time required and the volume of filtrate obtained in one cycle. 

For regcle experiments, the above procedure was repeated three times. The permeate was collected, sampled and filtered another two times without redispersion of the cake. Samples were taken during each recycle step and the total feed volume was about 1.5 L. Membrane flux averaged over an interval of filtration was calculated as... 

Filter sizing based on flat disc tests usually consists of recording the filtration time, volume of suspension filtered and pressure drop across the filter. An estimate of the filter performance can be achieved by calculating the volmue of filtrate produced per unit time, for constant-pressure filtration, or the volume of filtrate per unit pressure, for constant-rate filtration. Inspection of these rates will show if the membrane is acceptable, and the investigator can decide on the volume filtered before the filtration becomes either too slow or excessive in pressure drop. This provides a volume filtrate per unit area value which can be used to proportion the areas to arrive at the required filter area. 

Finally, the process filtration will probably be performed over a difiierait time fi om that of the laboratory test, so it is usu to calculate the flux obtained in the laboratory on the basis of volume per unit time and filter area and to check that this is considerably in excess of that required by the process after having applied safety ctors to the process filtration area calculation (typically 1.5 or more). 

Assume unit area and compute filtration time required to produce various values of V. Calculate corre onding values of dry solids yield w=c V... 

A relationsh between the outer and inner cake diameters dj, d2 and filtration time is required for the calculation of the pressure-drop-time variation ... 

A spreadsheet to calculate the specific cake and medium resistances fi om constant-pressure filtration data if filtration time and volume filtrate are measured. Other required inputs are the total filtration pressure used, physical data on the slurry and the masses of wet and dry cake-or a sample of the cake. Cake moisture omtent is calculated from the last two inputs, and is needed for the calculation of mass of dry cake per unit volume filtrate and, hence the specific cake resistance from the gradient o the line of best fit between the time over filtrate volume plotted against filtrate volume. The example data were used in Figure 2.7, and the woriced exanqrle fidlowing that figure. Reference should be made to Equations (2.24) and (2.25). 

The results are calculated in mg/1 in addition to the drying temperature, the type of filter used, e.g. membrane filter 0A5 pm, and the filtration time after sampling must also be stated. If iron or manganese which was originally in solution and passed through the filter has separated out, then this should be stated too. 

It is possible to determine experimentally the volume of filtrate by filtration time, which can be calculated from the analysis of tiV versus V, as shown in Figure 2.4. Regarding the function obtained, it is possible to calculate the constants a and... 

EXAMPLE 14.2-3. Rate of yVashing and Total Filter Cycle Time At the end of the filtration cycle in Example 14.2-2, a total filtrate volume of 3.37 m is collected in a total time of 269.7 s. The cake is to be washed by through washing in the plate-and-frame press using a volume of wash water equal to 10% of the filtrate volume. Calculate the time of washing and the total filter cycle time if cleaning the filter takes 20 min. 

The equations for c may need to be modified when considering a batch filtration. Unless care is taken the entire batch of suspension can be filtered and the experiment can be continued with the result that undesirable cake deliquoring, and sometimes cake compression, occur. As seen in Figure 4.2 these phenomena manifest themselves on a t/F vs. V plot as a sharp deviation at longer filtration times, and hence larger volumes of filtrate. Should cake deliquoring occur then both and need to be adjusted in order to calculate correct values for specific cake resistance and the volume fraction of cake soUds (Q ) as the mass of wet cake recorded at the end of an experiment will be too low. When the volume of filtrate at the transition from cake formation to gas deliquoring is... 

Dry Solids or Filtrate Rate Filtration rate, expressed either in terms of diy solids or filtrate volume, may be plotted as a function of time on log-log paper. However, it is more convenient to delavthe rate calculation until the complete cycle of operations has been defined. 

It should be noted also that the intercept is difficult to determine accurately because of large potential experimental error in observing the time of the start of filtration and the time-volume correspondence during the first moments when the filtration rate is high. The value of / calculated from the intercept may vaiy appreciably from test to test, and will almost always be different from the value measured with clean medium in a permeability test. 

It is advisable to start a constant-pressure filtration test, like a comparable plant operation, at a low pressure, and smoothly increase the pressure to the desired operating level. In such cases, time and filtrate-quantity data shoulci not be taken until the constant operating pressure is reahzed. The value of r calculated from the extrapolated intercept then reflec ts the resistance of both the filter medium and that part of the cake deposited during the pressure-buildup period. When only the total mass of diy cake is measured for the tot cycle time, as is usually true in vacuum leaf tests, at least three runs of different lengths should be made to permit a rehable plot of 0/V against W. If rectification of the resulting three points is dubious, additional runs should be made. 

Constants K and C can be readily obtained from experiments conducted on a prototype machine, from whence the volume of filtrate obtained for a definite time interval (for a specified filter, at the same pressure and temperature) can be calculated. If process parameters are varied, new constants K and C can be estimated from the above expressions. The last expression can be further modified by denoting the constant r as = CVK, and substituting ... 

Constants C and K can be determined from several measurements of filtrate volumes taken at different time intervals. There are some doubts as to the actual constancy of C and K during constant pressure filtration. Constants C and K depend on r (specific volumetric cake resistance), which, in turn, depends on the pressure drop across the cake. This AP causes some changes in the cake, especially during the initial stages of filtration. When the cake is very thin, the main portion of the total pressure drop is exerted on the filter medium. As the cake becomes thicker, the pressure drop through the cake increases rapidly but then levels off to a constant value. Isobaric filtration shows insignificant deviation from the expressions developed. For approximate calculations, it is possible to neglect the resistance of the filter plate, provided the cake is not too thin. Then the filter plate resistance, Rf, is equal to zero, C = 0, and r = 0. Hence, a simplified equation is = Kr. 

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