Pressure filtration constant

The scale-up of conventional cake filtration uses the basic filtration equation (eq. 4). Solutions of this equation exist for any kind of operation, eg, constant pressure, constant rate, variable pressure—variable rate operations (2). The problems encountered with scale-up in cake filtration are in estabHshing the effective values of the medium resistance and the specific cake resistance. 

Traditionally, the average specific cake and medium resistances have been deterrnined from constant pressure experiments and the solution of the basic filtration equation for constant pressure which relates filtrate volume to time. This relationship is, in theory, paraboHc but deviations occur in practice. 

If ah of the nonfiltration operations are grouped together into a downtime, assumed to be fixed and known, an optimum filtration time in relation to p can be derived by optimizing the average dry cake production obtained from the cycle. Eor constant pressure filtration and where the medium resistance R and the specific cake resistance are constant, the fohowing equation appHes ... 

Filtration. In many mineral processing operations, filtration follows thickening and it is used primarily to produce a soHd product that is very low in moisture. Filtration equipment can be either continuous or batch type and either constant pressure (vacuum) or constant rate. In the constant pressure type, filtration rate decreases gradually as the cake builds up, whereas in the constant rate type the pressure is increased gradually to maintain a certain filtration rate as the cake resistance builds. The size of the device is specified by the required filter surface area. 

By operating cycle. Filtration may be intermittent (batch) or continuous. Batch filters may be operated with constant-pressure driving force, at constant rate, or in cycles that are variable with respect to both pressure and rate. Batch cycle can vary greatly, depending on filter area and sohds loading. 

Con.stant-pre.s.sure filtration. The actuating mechanism is compressed gas maintained at a constant pressure. 

Constant-Pressure Filtration For constant-pressure filtration Eq. (18-51) can be integrated to give the following relationships between total time and filtrate measurements ... 

For a given constant-pressure filtration, these may be simplified to 9... 

Constant-Rate Filtration For substantially incompressible cakes, Eq. (18-51) may be integrated for a constant rate of slurry feed to the filter to give the following equations, in which filter-medium resistance is treated as the equivalent constant-pressure component to be deducted from the rising total pressure drop to... 

In the filtration of small amounts of fine particles from liquid by means of bulky filter media (such as absorbent cotton or felt) it has been found that the preceding equations based upon the resistance of a cake of solids do not hold, since no cake is formed. For these cases, in which filtration takes place on the surface or within the interstices of a medium, analogous equations have been developed [Hermans and Bredee, J. Soc. Chem. Ind., 55T, 1 (1936)]. These are usefully summarized, for both constant-pressure and constant-rate conditions, by Grace [Am. In.st. Chem. Eng. J., 2, 323 (1956)]. These equations often apply to the clarification of such materials as sugar solutions, viscose and other spinning solutions, and film-casting dopes. 

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. 

With the above as an introduction, we now consider the important operational case of filtration performed under constant pressure. In practice, all the parameters defined above are nearly constant under steady state conditions except V and r, which are varied by the operator. We may therefore integrate the working expression for filtration over the limits of volume from 0 to V, and for residence time over the limits of 0 to x ... 

This expression shows the relationship between filtration time and filtrate volume. The equation is applicable to both incompressible or compressible calces, because at constant AP the values and x are constant. For constant AP, an increase in the filtrate volume results in a reduction in the filtration rate. If we assume a definite filtering apparatus and set up a constant temperature and filtration pressure, then the values of Rf, r , fi and AP will be constant. We now take note of the well-known filtration constants K and C, which are derived from the above expressions ... 

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. 

Filtration experiments in a prototype machine at constant pressure or constant rate permit determination of ax , as well as s and Rf, for a given sludge and filtering medium. Consequently, it is possible to predict the time required for the pressure drop to reach the desired level for a specified set of operating conditions. In the initial stages of filtration, the filter medium has no cake. Furthermore, AP is not zero but has a certain value corresponding to the filter medium resistance for a given rate. This initial condition is ... 

Design Example for a Batch Nutsche Filter Operation A batch Nutsche filter operates under constant pressure and maximum capacity with three stages filtration, washing and drying. The Nutsche filter with a 1 m filtration area operates under the following set of conditions ... 

When the space above the suspension is subjected to compressed gas or the space under the filter plate is under a vacuum, filtration proceeds under a constant pressure differential (the pressure in the receivers is constant). The rate of filtration decreases due to an increase in the cake thickness and, consequently, flow resistance. A similar filtration process results from a pressure difference due to the hydrostatic pressure of a suspension layer of constant thickness located over the filter medium. 

For a constant pressure drop and temperature filtration process all the parameters in Equation 9, except V and x, are constant. Integrating Equation 9 over the limits of 0 to V, from 0 to x, we obtain ... 

Filtration constants K and C can be experimentally determined, from which the volume of filtrate obtained over a specified time interval (for a certain filter, at the same pressure and temperature) can be computed. If process parameters are changed, new constants K and C can be estimated from Equations 14 and 15. Equation 16 may be further simplified by denoting tg as a constant that depends on K and C ... 

Substituting to into Equation 16, the equation of filtration under constant pressure conditions is ... 

When sludge is fed to a filter by a positive-displacement pump, the rate of filtration is nearly constant (i.e., dV/dr = constant). During constant-rate filtration, the pressure increases with an increase in cake thickness. Therefore, the principal variables are pressure and filtrate volume, or pressure and filtration time. Equation 9 is the principal design relation, which may be integrated for a constant-rate process. The derivative, dV/dr, may be replaced simply by V/t ... 

Constant-pressure drop filtration can result in saturation or blockage of the filter medium. The network of pores within the filter medium can become blocked because of one or a combination of the following situations ... 

CHE 440 Filtration Experiment... find the parameters (discussed below) that govern constant pressure drop cake filtration... 

The system described in question 4 has an auxiliary time of = 1800 sec. Determine the total filtration time at constant pressure drop, cake thickness and filtrate volume. 

A suspension is to be processed in a filter press to obtain 6 m of filtrate in 3 hours. A filtration test in the lab under the same pressure and cake thickness showed that the filtration constants for 1 m of filter area are as follows K = 20.7 x 10-4 mVhr and C = 1.45 x 10 m /m. Determine the size of the filter. 

The following data were obtained in a filtration test using a CaCOj suspension on a filter of area A = 500 cm at constant pressure ... 

Since for constant pressure filtration, the tjV versus Vdata can be linearized, as shown in Figure 4.15, the resistances of cake and cloth plus cake held up in cloth can be determined. The former value is usually fairly reproducible while the latter is often variable, being particularly sensitive to start up conditions when cloth blinding occurs. Such tests can be rerun at different pressures and the extent of cake compressibility determined. Similarly, a wash cycle can be introduced. 

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