Filtration constants

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. 

The terms in parentheses in Equation 13 are known as the filtration constants , and are often lumped together as parameters K and C where ... 

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 ... 

Filtration constants C and K can be determined on the basis of several measurements of filtrate volumes for different time intervals. 

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. 

Determine the filtration constants a and b, where a is the constant characterizing cake resistance related to 1 of filter area in sec/m, and b characterizes the resistance of the filter medium related to 1 m of filter area in sec./m. ... 

Using the filtration constants determined from the above question, determine the filtration time of a 5 m CaCOj suspension containing 5 % solids on the filter with 10 m area. The cake wetness is 40% and the solids density is 2,200 kg/m The density of the liquid is 1,000 kg/m Also determine the final filtration rate after 2 hrs. of operation. 

Substituting V2 = 0.75 V, in these two equations allows the filtration constants to found as ... 

The clogging effect can be considered as a reduction in the value of the surface filtration constant for practical purposes. Indeed, when clogging takes place, the surface filtration constant can be given by its initial value ko multiplied by a decreasing time function. This assumption is frequently used when the function is obtained from experiments [3.19, 3.20]. In our example, if we do not consider the friction (and heat transfer) we can note that only a concrete mass transfer problem can be associated with the membrane separation process. The first step before starting to build the general mathematical model, concerns the division of the system into different elementary sections. Indeed, we have a model for the filtration device (i.e. the membrane and its envelope), for the pump (P) and for the reservoir of concentrated suspension (RZ) (Fig. 3.7). 

The simulations shown in Figs. 3.10 and 3.12 were made for the following operating conditions 1, for the monodimensional model, the filter was considered to be composed of three identical membranes with a 0.5 m surface, the minimum permeate flow was imposed at 3.8 x 10 m /s, the initial value of the filtration constant ko = 33 x 10 m /m bar 2, in the second case, a 10 m long, 0.075 m high and 0.15 m wide filter was analyzed with a constant permeate flow rate while keeping the initial value of the filtration constant. A concentration of 10 kg/m was used for the fresh suspension. 

The target bich removes particles fi-om the liquid stream is the surfiice area of the bed media. If solids are deposited this sur ce area increases and, therefirre, the filtration constant should increase with time. However, pores within the bed will become increasingly clogged leading to straightening of flow channels with a consequent... 

Aa attemative approach to appfymg the en iiical quadratic equation is to consider a power function for each of the factors duch affect the fStration constant [Ives PLaivichitr,1965 Ives,1975], The filtration constant is again related to the microstructure changes within the bed (dq>osh porosity, maxianim specific deposit) ... 

The sinq)]ified ertq)irical model assumes that y = w = 0 and z- I, which leaves fewer constants in Equation (6.5) to be determined e q)erimenta]ly. Under these circumstances there should be a linear relation between the filtration constant and the specific deposh. This is the required assunption behind the bed depth service time (BDST) approach. 

There are many fiictors to be comadered in the design of a deq>-bed cility, the initial design may be based on some preliminary testwoik v hich needs to establish the efhdency of filtration of the medium ie. the filtration constant X and uses a knovdedge ofthe physical properties of the medium. 

The medium particle size must be chosen so that the settling velocity of the conq)onents is in the order anthracite, sand, garnet. Particle diametms of 1500, 750 and 550 jm respectively satisfy this requirement. The corresponding settling velocities are 0.083, 0.11 and 0.12 m s using the above correlation. Filtration tests onflie medium at these sizes reveal the following values of the filtration constants 0.5, 4 and 6 re ectively. Equation (6.3) can th be used with selected bed depths to provide an acceptable solution, one solution would be ... 

It is not pos le to provide values for the filtration constants, as these are dependent on the material to be ered, the flow conditions, fihration history, etc. They must be assessed by laboratory and pilot-scale tests. 

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