Cake rate calculation

A mixture of iron, ferric chloride and water is added to the toluene solution. The mixture is heated to reflux and concentrated hydrochloric acid is added dropwise at a rate calculated to keep the mixture refluxing vigorously. After the hydrochloric acid Is all added, the refluxing is continued by the application of heat for several hours. A siliceous filter aid is then added to the cooled reaction mixture and the material is removed by filtration. The filter cake is washed four times, each time with 90 ml of benzene. The organic layer is then separated from the filtrate. The water layer is acidified to a pH of 2 and extracted three times with 90 ml portions of benzene. 

Determination of the effect of pressure drop and g-forces on flow rate and liquid content is the chief objective of tests involving compactible cakes. Accurate calculation of parameters in constitutive equations [Equation (22.29)] generally requires that a relatively wide range of... 

Filtration tests can be carried out with quite simple apparatus where the objectives are principally twofold. Firstly, cake formation rate is required for preliminary equipment selection, and secondly parameters such as cake specific resistance and solids concentration values are needed, ideally as functions of the applied pressure/vacuum, for filter sizing and filtration rate calculations (Tarleton, 1998a,b Tarleton and Wakeman, 1994c, 1999 Wakeman and Tarleton, 1990, 1991a, 1994a). 

Equation (5) is equivalent to stating that sublimation and subsequent transport of 1 g of water vapor into the chamber demands a heat input of 650 cal (2720 J) from the shelves. The vial heat transfer coefficient, Kv, depends upon the chamber pressure, Pc and the vapor pressure of ice, P0, depends in exponential fashion upon the product temperature, Tp. With a knowledge of the mass transfer coefficients, Rp and Rs, and the vial heat transfer coefficient, Kv, specification of the process control parameters, Pc and 7 , allows Eq. (5) to be solved for the product temperature, Tp. The product temperature, and therefore P0, are obviously determined by a number of factors, including the nature of the product and the extent of prior drying (i.e., the cake thickness) through Rp, the nature of the container through Kv, and the process control variables Pc and Ts. With the product temperature calculated, the sublimation rate is determined by Eq. (4). 

Filtration is carried out in a plate and frame filter press, with 20 frames 0.3 m square and 50 mm thick, and the rate of filtration is maintained constant for the first 300 s. During this period, the pressure is raised to 350 kN/m2, and one-quarter of the total filtrate per cycle is obtained. At the end of the constant rate period, filtration is continued at a constant pressure of 350 kN/m2 for a further 1800 s, after which the frames are full. The total volume of filtrate per cycle is 0.7 m3 and dismantling and refitting of the press takes 500 s. It is decided to use a rotary drum filter, 1.5 m long and 2.2 m in diameter, in place of the filter press. Assuming that the resistance of the cloth is the same in the two plants and that the filter cake is incompressible, calculate the speed of rotation of the drum which will result in the same overall rate of filtration as was obtained with the filter press. The filtration in the rotary filter is carried out at a constant pressure difference of 70 kN/m2, and the filter operates with 25 per cent of the drum submerged in the slurry at any instant. 

A rotary drum with a filter area of 3 m3 operates with an internal pressure of 71.3 kN/m2 below atmospheric and with 30 per cent of its surface submerged in the slurry. Calculate the rate of production of filtrate and the thickness of cake when it rotates at 0.0083 Hz, if the filter cake is incompressible and the filter cloth has a resistance equal to that of 1 mm of cake. 

It is decided to use a rotary drum filter, 1.5 m long and 2.2 m in diameter, in place of the filter press. Assuming that the resistance of the cloth is the same in the two plants and that the filter cake is incompressible, calculate the speed of rotation of the drum which will result in the same overall rate of filtration as was obtained with the filter press. The filtration in the rotary filter is carried out at a constant pressure difference of 70 kN/m2, and the filter operates with 25 per cent of the drum submerged in the slurry at any instant. 

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. 

Related Calculations. In constant-rate (as opposed to constant-pressure) filtration, v = qt and wc = cqt. Then, from Eq. (14.3), the average specific filtration resistance aav = (p — p )/(ncq2t), where Pi is the pressure at the interface of the filter medium and the cake. Constant-rate filtrations are usually operated at above 10 lbf/in2 (69 kPa), and this equation is accurate enough for most purposes. At... 

The equations for sizing rotary-drum filters are summarized in Table 6.18. Equation 6.18.1 is the liquid mass balance. In this procedure, y is a mass fraction. Because the cake is wet, the liquid entering the filter will be less then the liquid leaving. Equation 6.18.2 is the solids mass balance, assuming that all the solids in the slurry are removed. Solve Equation 6.18.2 for the cake formation rate, me. Then, solve Equation 6.18.1 for the filtrate volumetric flow rate, V2. Next, calculate the filtration area from Equation 6.18.5 and the dmm area from Equation 7.18.6. Finally, select a standard rotary filter from Table 6.20. The calculation procedure for sizing a rotary filter is outlined in Table 6.19. Example 6.5 illustrates the sizing procedure. 

Calculate the rate of wet cake formation, me, from Equation 6.18.2. 

Vacuum drum filters, 319 air flow rates, 328 applications, 332 cycle design, 328 flowsketch, 326 laboratory test data, 312 minimum cake thickness, 328 operation, calculation example, 312,... 

On-line measurements of cake thickness during filter-system operation have not been feasible in most systems. However, when the pressure drop across the filter system, the gas flow rate, and the particle concentration in the incoming gases are measured, these data can be used to calculate the mass of filter cake on each filter. The overall pressure drop can be modeled as ... 

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