Filtration at constant pressure

Filtration at constant pressure is more frequently adopted in practice, although the pressure difference is normally gradually built up to its ultimate value. 

The final method of operation to consider is that of filtration at constant pressure and constant rate. This method is employed when pure liquid is filtered through a cake of constant thickness and a constant pressure differential exists across the cake. Cake washing by displacement may be considered as filtering of a washing liquid through a constant cake thickness at constant pressure and flowrate. The rate of... 

From Fig. 3.15 we can note that, by analogy to the 2 bar constant pressure case, example FIS shows a new special case where we have positive and small negative values in the concentrated suspension flow rate at the plant exit. This result can be explained by the background noise in the measurement of the flow of suspension. Nevertheless, the mean value of the flow rate is small but positive. If the efficiency of the filtration at constant pressure is given by the solid concentration ratio between the exit and fresh suspensions, then, as shown in Fig. 3.13, the ratio is always lower than 2 for operation case F2/1.6. For cases FI and FIS, this ratio increases permanently, non-uniformly and attains values over 12 g/1 in the proximity of the complete clogging state. 

In the case of filtration at constant pressure, flow volume recordings over time are used to calculate the flow rates. The origin of the vertical axis represents go and, as Vmax corresponds to a zero flow rate ... 

For constant-pressure filtration and washing, such as occur on vacuum filters, the filtration time and washing time can be related through the wash ratio if the wash liquor and filtrate are assumed to have similar physical properties. From the equation for incompressible filtration at constant pressure expressed in terms of a, ecffic resistance ... 

Machac and Crha developed plots which, like in Newtonian liquid filtration, have to be linear. The cake and medium resistances are then determined from the slope and the intercept, as is usual in filtration. The problem here is that, in filtration at constant pressure, the filtration velocity may vary widely and this requires the parameters K and n also to apply in a wide interval of the corresponding rate of shear. The way to relate the shear rates to filtration velocities is via the following equation ... 

For filtration at constant pressure drop we use Equation (6.27), which indicates that if we plot t/V versus V a straight line will have a gradient... 

A sludge is filtered in a plate and frame press (50-mm frames). Pressure rises to 500 kN/m in the first 3600 sec (one-fourth total filtrate obtained). The remaining filtration (at constant pressure) requires another 3600 sec. Cleaning and reassembling requires 900 sec. When a filter aid is used (cloths precoated to a depth of 1.6 mm), cloth resistance is reduced to one-fourth its former value. How will the overall throughput increase if precoat is applied in 180 sec ... 

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 ... 

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. 

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

A slurry is filtered in a plate and frame press containing 12 frames, each 0.3 m square and 25 mm thick. During the first 180 s, the filtration pressure is slowly raised to the final value of 400 kN/m2 and, during this period, the rate of filtration is maintained constant. After the initial period, filtration is carried out at constant pressure and the cakes are completely formed in a further 900 s. The cakes are then washed with a pressure difference of 275 kN/m2 for 600 s, using thorough washing. What is the volume of filtrate collected per cycle and how much wash water is used ... 

A sludge is filtered in a plate and frame press fitted with 25 mm frames. For the first 600 s the slurry pump runs at maximum capacity. During this period the pressure difference rises to 500 kN/m2 and a quarter of the total filtrate is obtained. The filtration takes a further 3600 s to a complete at constant pressure and 900 s is required for emptying and resetting the press. 

In the leaf filter, filtration is at constant pressure from the start. 

In the filter press, a volume V) of filtrate is obtained under constant rate conditions in time t, and filtration is then carried out at constant pressure. 

It may be possible to do a membrane autopsy to identify the foulant(s) and fouling mechanism. For microporous membranes the blocking law analysis [1], which uses permeate volume (V) vs. time (t) data, can supplement the observations. The generalized relationship at constant pressure and in dead-end filtration mode gives,... 

Example 4 Cycle time for maximum amount of production from a plate-and-frame filter press. Tests with a plate-and-frame filter press, operated at constant pressure, have shown that the relation between the volume of filtrate delivered and the time in operation can be represented as follows ... 

Total volume of filtrate in Time from start of filtration (0), h, at constant pressure difference of ... 

Figure 3.10 shows the details of the numerical-solving algorithm for the monodimensional. This numerical transposition has the capacity of being related with any available software. In Fig. 3.10, we can note that only the case of constant filtrate rate has been presented. Otherwise, when we operate at constant pressure, the filtrate rate decreases with the time due to the continuous clogging phenomenon. To simulate a constant pressure filtration, some changes in the computing program of Fig. 3.10 are necessary these modifications are shown in Fig. 3.11. It is easily observable that here the stop criterion has been completed with the decreasing of the solid concentration in the recycled suspension.

The main difference between the operation at constant filtrate flow rate and at constant pressure can be observed in Fig. 3.13. In the case of a constant filtrate flow rate, the solid concentration inside the unit increases permanently, whereas, at constant pressure, the solid concentration increases very quickly initially (up to 1200 s) and then decreases for all the remaining time. If we look at both Figs. 3.13 and 3.15 we can see that it is not possible to start with the considered conditions with a 2 bar constant pressure because, in these conditions, a negative value of the exit flow rate appears for the concentrated suspension (Fig. 3.15) and the solid concentration increases tremendously from 10 to 120 kg/m. ... 

Assume that the filtration is conducted at constant pressure. Then, after separating variables and integrating from 0 to tp and 0 and Vp, we obtain... 

A more conunon alternative are filtration methods generally relying on the time it takes for a given volume of eeU suspension to pass through micropore membranes at constant pressure (Sato et al., 1977). Although this method only gives average information on the... 

Example 30.2. Laboratory filtrations conducted at constant pressure drop on a slurry of CaCOj in H2O gave the data shown in Table 30.2. The filter area was 440 cm, the mass of solid per unit volume of filtrate was 23.5 g/L, and the temperature was 25°C. Evaluate the quantities a and as a function of pressure drop, and fit an empirical equation to the results for a. 

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