Scale-up of a Rotary Vacuum Filter A rotary vacuum filter is...

Scale-up of a Rotary Vacuum Filter A rotary vacuum filter is available with an area of 200 m2 and vacuum pressure of 75 kPa. Filter leaf tests have been performed on a cell broth with a viscosity of 5 cp. The leaf tests gave a specific cake resistance of 1 × 1011 cm/g and a medium resistance of 1 × 108 cm?1. The cake solids (dry basis) per volume of filtrate was 15 g/liter. It is desired to operate the large filter with a cycle time of 45 s and a cake formation time of 10 s. What is the filtration rate expected for the rotary vacuum filter? How significant is the medium resistance?

Scale-up of a Rotary Vacuum Filter A rotary vacuum filter is available with an
area of 200 m2
and vacuum pressure of 75 kPa. Filter leaf tests have been performed
on a cell broth with a viscosity of 5 cp. The leaf tests gave a specific cake resistance of
1 × 1011 cm/g and a medium resistance of 1 × 108
cm?1. The cake solids (dry basis) per
volume of filtrate was 15 g/liter. It is desired to operate the large filter with a cycle time
of 45 s and a cake formation time of 10 s. What is the filtration rate expected for the
rotary vacuum filter? How significant is the medium resistance?

Key Concepts

Medium Resistance

Medium resistance refers to the resistance offered by the filtering medium itself, independent of the cake layer. Its significance is determined by comparing it to the cake resistance; if the medium resistance is much lower, it can often be neglected, but if it is comparable, it will affect the overall filtration rate and must be considered in design calculations.

Specific Cake Resistance

Specific cake resistance is a measure of the relative difficulty for a liquid to flow through a deposited cake. Expressed as resistance per unit mass of cake, it is fundamental in evaluating the filtration process via Darcy's law, where higher values indicate greater difficulty in fluid flow and thus contribute significantly to the overall filtration resistance.

Filtration Rate Prediction Using Darcy’s Law

Darcy’s law is the foundational principle used to predict filtration rates by relating the volumetric flow rate through the filter to the applied pressure difference and the combined resistances (from both the cake and the medium). Understanding and applying this law is key to calculating expected performance in filtration systems.

Rotary Vacuum Filter

A rotary vacuum filter is a continuous filtration device in which a rotating drum covered with a porous medium is partially submerged in the feed slurry. Vacuum is applied to draw the liquid through the cake formed on the drum surface while leaving solids behind. This equipment is widely used in industrial processes for the effective separation of solids and liquids.

Scale-up of Filtration Equipment

Scaling up filtration processes involves using data from laboratory or pilot tests to predict the performance of full-scale equipment. It requires the extrapolation of parameters such as filter area, cycle times, and resistance values to ensure that an industrial system can achieve the desired throughput and efficiency while maintaining proper process dynamics.

Cycle Time and Cake Formation Time

Cycle time and cake formation time are operational parameters that define the duration of each filtration cycle and the time available for cake buildup, respectively. These timeframes are crucial in continuous processes because they impact the overall capacity and efficiency of the filter; the cycle must be designed to accommodate proper cake formation to achieve effective separation.

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