Optimum filtration time cycle

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 ... 

It may be noted, as a consequence of these relationships, that the filtration time for a given quantity of filtrate is proportional to the square of the thickness of the cake at the end of the filtration. Maximum filter productivity WIA(6 + 6 under batchwise constant-pressure filtration, with the medium resistance neglected, is obtained when the filtration time 6 is equal to the downtime 0, which is the sum of the time required to remove the product cake and to prepare the medium for the next cycle. The greater the resistance of the filter medium and the longer the preparation downtime, the longer is the optimum filtration time and the thicker is the optimum cake. 

When the medium resistance R is small compared with Ihe specific cake resistance o. the second term in the above equation becomes ncgligibk and the optimum hltnttion time t r, becomes equal to downtime r,/. For any other ease, r, is always greater than r,. It follows, therefore, that the filtration time should be at least equal lo the sum of the other nonliltntlion periods involved in the cycle. 

A worked example showing how basic filtration data can be used to assess the optimum cycle time, and hence filter area required to complete a clarification of a v etable oil using precoat filtration on a pressure leaf filter. The filtration is assumed to be constant rate, after having formed a precoat of 2 mm on the pressure leaves prior to clarification. The cleaning and reforming of the precoat takes iproximately 30% of the total cycle time, hence active filtration time is only 70% of any given cycle time. The analysis is based on a 14 h working and 350 days per year. These are easily altered in cells D15 and D16, respectively. 

Optimum cycle time during batch filtration... 

At the optimum cycle time giving the maximum output of filtrate per 24 h,... 

Column 6 contains the filtrate volume for time of 15 min. These values are frequently used to obtain the optimum amount of filter aid. They indicate that the maximum flow rate results from adding perlite when/= 0.33. However, the cycle rates in colnmns 8 and 9 show that the optimum dose of filter aid is/= 0.2. The example clearly shows that the choice of a filter aid and the value of / should be based on a cycle analysis and not on v versns t data. 

This system is designed for fine slimy sohds that would not be retained on a filter cloth. The capture mechanism is a combination of surface and depth filtration so some feed suspension particles will penetrate into the precoat layer. It is a matter of ejqperhnentation to find the optimum depth of precoat cut which will preserve a high filtration rate with a long overall cycle time. 

This infotmation can be used to calculate the optimum cycle time and filtration cycles per day for various assumed levels of the average specific resistance a. Hie corresponding Vf p cycle and the fih area requiremaits are listed in the table below. 

These results iadicate that as the fiherahility of the material reduces, so does the optimum cycle time. Practical e q>eiieiice [Bosley, 1986] suggests that difficuh-to-fiher materials, e.g. alum sludge or hi protdn containing materials require thin cake filtration conditions, with cake thicknesses 1.5-2.0 cm Read% filtered materials are generally produced optimally as thicker cakes, iq) to 7.0 cm in thickness. This e qieiience points to the usefiihiess of the models discussed here, in process calculations and plant q>edfications. 

Various cycle times are used in column A flrom 1 to 8 h, the optimum, i.e. lowest cost per unit volume of filtrate, is 2 h. Alternatively, the lowest total annual cost is given by a 3 hour cycle, but with a significantly lower yield of cleaned oil. 

By repeated use of simulations for a given cycle configuration it is possible to identify the optimum cake thickness to be formed during the overall filtration process. The optimum is application specific and a compromise between the efficiency of cycle operations and the overall economics and time scale of the filter cycle operation. It is clear that the effects of other process parameters on filter performance can also be readily assessed using simulations. 

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