Lab scale tests performed on a cell broth with a viscosity of 5cP gave a specific cake resistance of 1 x 1011 cm/g and a negligible medium resistance. The cake solids (dry basis) per volume of filtrate was 15 g/liter. It is desired to operate a larger rotary vacuum filter (diameter 8 m and length 12 m) at a vacuum pressure of 80 kPA with a cake formation time of 20 s and a cycle time of 60 s. Determine the filtration rate in volumes/hr expected for the rotary vacuum filter?

473,400 L/h

Explanation:  

For an incompressible cake and negligible medium resistance, we can find the  volume of filtrate collected using the following equation:

    (1)          

Where:

: is the volume of filtrate collected  

A: is the filtration area  

: is the cake formation time = 20 s  

ΔP: is the vacuum pressure = 80 kPa  

μ: is the viscosity = 5 cP  

α: is the specific cake resistance = 1x10¹¹ cm/g  

ρ: is the cake solid per volume of filtrate = 15 g/L         

First, we need to convert the units:  

Now, we need to find the filtration area (A), which is equal to a cylinder area:    

where r: is the radius = 8/2 m and h: is the height of the side = 12 m.    

Now, we can calculate the volume of filtrate using equation (1):    

Finally, we can calculate the filtration rate in volumes/hr:  

I hope it helps you!