Filtration calculations

Filtration. .. Section, Title. 1. Terminology. 2. Filtration Models.2.1. Cake Filtration Calculation of the Pressure Drop.. .. http.7/www.wiley-vch.de/contents/ullmann/ull 10295.html [More Results From www.wiley-vch.de]... 

Continuous filtration. Calculation of cake impurity and liquid yield" by H Mondria ... 

Concentrate the combined filtrate and washings (W) to about half the original volume, and pour it into sUghtly more than the calculated amount of dilute hydrochloric acid (use a mixture of 30 ml. of concentrated hydrochloric acid and 30 ml. of ice-water) then add about 300 ml. of water. Collect the active aec.-octyl hydrogen phthalate (crude lA) as above (5). The weight of the air-dried ester is about half that of the dl-ester originally used (7). 

When the filtrate is sterile, the number 1 is substituted for the average total recovery and the value is expressed as greater than the calculated value. 

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. 

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. 

Scale-Up on Rate Filtration rates calculated from bench-scale data shouldbe multiplied by a factor of 0.8 for all types of commercial units which do not employ continuous washing of the filter medium and on which there is a possibility of filter-medium bhnding. For those units which employ continuous filter-medium washing, belt-type drum and horizontal units, the scale-up fac tor maybe increased to 0.9. The use of this scale-up fac tor assumes the following ... 

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. 

Scaling Up Test Results The results of small-scale tests are determined as dry weight of sohds or volume of filtrate per unit of area per cycle. This quantity multiplied by the number of cycles per day permits the calculation of either the filter area reqiiired for a stipulated daily capacity or the daily capacity of a specified plant filter. The scaled-up filtration area should be increased by 25 percent as a factor of uncertainty. In the calculation of cycle length, proper account must be made of the downtime of a batch filter. 

Belt Presses Belt presses were fiiUy described in the section on filtration. The description here is intended to cover only the parts and designs that apply expression pressure by a mechanism in adchtion to the normal compression obtained from tensioning the belts and pulling them over rollers of smaller and smaller diameters. The tension on the belt produces a squeezing pressure on the filter cake proportional to the diameter of the rollers. Normally, that static pressure is calculated as P = 2T/D, where P is the pressure (psi), T is the tension on the belts (Ib/hnear in), and D is the roller diameter. This calculation results in values about one-half as great as the measured values because it ignores pressure created by drive torque and some other forces [Laros, Advances in Filtration and Separation Technology, 7 (System Approach to Separation and Filtration Process Equipment), pp. 505-510 (1993)]. 

To the wa-propyl alcohol filtrate is added another i5o-g. portion of benzophenone and the solution is exposed to sunlight as in the first reduction. The benzopinacol which separates is filtered and dried. The yield in the second and subsequent runs is 142-143 g. (94-95 per cent of the calculated amount). This procedure can be repeated with the same filtrate until six or seven portions (900-1050 g.) of benzophenone have been reduced. 

In this subsection, basic design theory for preliminary sizing and specifying equipment are reviewed. Some sample design calculations are included. References cited at the end of tlie chapter can be consulted for more detailed information and design methods. For solid-liquid separation methods, the reader should refer to Liquid Filtration, 2" edition, by N. P. Cheremisinoff, Butterworth-Heinemarui Publishers (1998). 

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. 

The objective of this chapter is to provide an overview of filtration terminology and basic engineering principles, as well as calculation methods that describe the filtration process in a generalized way. The basis equations describing the generalized process of filtration have been around for nearly 100 years, and with few refinements, continue to be applied to modem design practices. 

Comparative calculations of specific capacities of different filters or their specific filter areas should be made as part of the evaluation. Such calculations may be performed on the basis of experimental data obtained without using basic filtration equations. In designing a new filtration unit after equipment selection, calculations should be made to determine the specific capacity or specific filtration area. Basic filtration equations may be used for this purpose, with preliminary experimental constants evaluated. These constants contain information on the specific cake resistance and the resistance of the filter medium. 

R.G. Holdich, 1990, Rotary Vacuum Filter Scale-up Calculations - and the use of Computer Spreadsheets, Filtration and Separation, 27, pp 435-439... 

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. 

Approximately 15 m of filtrate was removed from a suspension containing 20% by weight solids. The cake wetness is 30%. Calculate the amount of dry cake obtained. 

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. 

Thermo-diffusion calculations analyze the migration of hazardous material from compartment to compartment to release in containment. These calculations use physico-chemical parameters to predict the retention of hazardous materials by filtration, deposition on cold surfaces and other retention processes in the operation. Containment event trees aid in determining the amount, duration and types of hazardous material that leaves the containment. 

The current prototype code, is included because of being knowledge-based and its potential relevance for chemical releases. Presently, it calculates doses and consequences to facility workers from accidental releases of radioactive material. This calculation includes specifying material at risk and worker evacuation schemes, and calculating airborne release, flows between rooms, filtration, deposition, concentrations of released materials at various locations and worker exposures. 

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