Answer to Question #126107 in Other for Yamuna Ganeson

Question

It is desired to filter a cell broth at a rate of 1700 liters/h on a rotary vacuum filter at a vacuum pressure of 70kPa. The cycle time for the drum will be 60 s, and the cake formation time (filtering time) will be 15 s. The broth to be filtered has a viscosity of 0.08 P and a cake solids (dry basis) per volume of filtrate of 10 g/l. From laboratory tests, the specific cake resistance has been determined to be 9 x 1010 cm/g. Determine the area of the filter that is required. The resistance of the filter can be neglected. 

 It is then desired to wash the product (antibiotic) out of the cake so that only 5% of the antibiotic in the cake is left after washing. The washing efficiency is 50%. Estimate the washing time per cycle that would be required. Assume that the filtered cake contains 70% water

Answer 1

t/(V/A)=$(\mu_0 \alpha\rho_c/2\Delta p)*(V/A)$

$A^2=$ $\mu_0 \alpha\rho_c V^2/2 \Delta pt$

In applying this equation, it is helpful to focus on the area of the drum, which is where the cake is being formed and where filtrate is being obtained. Thus, A is the area of that part of the drum. We can calculate the volume of filtrate that needs to be collected during the cake formation time of 15 s:

V=1700*15*(1/3600)=7.083

$A^2=$ (0.08*9*10¹⁰*10*7.083²*(1/10⁴)*(1/10²)⁴*(10³))/(2*70*15)=1.72 m⁴

A=1.3115 m²

The area A’ of the entire rotary vacuum filter can be calculated from the cake formation time (15s) and the total cycle time (60s) as

A'=(60/15)*1.3115=5.246

 washing efficiency of a filter cake

R'=(1-E/100)ⁿ

where R’ is the weight fraction of solute remaining in the cake after washing (on the basis of R’ = 1.0 before washing), E is the percentage wash efficiency, and n is the volume of wash liquid per volume of liquid in the unwashed cake. Substituting R’ = 0.05 and E = 50% into this equation gives n=4.32

 the relationship between the washing time t^w, and the cake formation time t^f is given by t_w=2nft_f

where f is the ratio of volume V_r of residual liquid in the cake to the volume of filtrate V_f after time t_f . Thus, we need to estimate the volume of residual liquid in the filter cake to determine t_w . At the end of the 15 s cake formation time,  weight of dry cake solids filtered=10*7.083=70.83

weight of water=(70/30) *70.83=165.27 g

f=V_r/V_f=0.165/7.33=0.0225

t_w=2nft_f=2*4.32*0.0225*15=2.916 s