During the pilot scale studies, a $1000$L batch of cell culture was filtered using a module

that had the following parameters: $(4$ points$)$

V volume of filtrate

A area of the filter, $=0\mathrm{.}5$ m$2$

C Weight of the cake deposited per volume of the filtrate, $=1750$ kg$/$m$3$

Ap Pressure drop across the filter, $=2$ x $105$ pa

$r_m$ Specific resistance of the filter medium $=12{10}^{10}{m}^{-1}$

$$ Average specific resistance of the cakc $=2{10}^5\frac{m}{k}g$

$$ Viscosity of the filtrate $=3{10}^{-3}k\frac{g}{m}-s$

a$.$ Estimate the time to filter the $1000L.$

b$.$ A $5000$L batch of cell culture must be filtered using dead end lilter $($depth

filtration technique$).$ Assuming that a filter similar to the one used in the pilot

studies $($with all the parameters being same except filter size$)$ will be used for

scaleup, what is the size of the filter if the $5000L$ batch must be processed in one

hour?

Use the following equations $($Ruth Equation$)$ for depth filtration

$V^2+2V{V}_0=Kt$

$K=(\frac{2{}^2}{C})p,V_0=\frac{r_m}{G}$