A battery of cylindrical hollowfiber membranes is operated a

A battery of cylindrical hollow-fiber membranes is operated at steady state to concentrate a bacterial suspension from a fermenter. 350 kg min-1 broth is pumped through a stack of hollow-fiber membranes as shown. The broth contains 1% bacteria (by weight); the rest may be considered water. Buffer solution enters the annular space around the membrane tubes at a flow rate of 80 kg min-1; because broth in the membrane tubes is under pressure, water is forced across the membrane into the buffer. Cells in the broth are too large to pass through the membrane and pass out of the tubes as a concentrate. The aim of the membrane system is produce a cell suspension containing 6% biomass. (a) What is the flow rate of cell suspension from the membrane tubes? (b) What is the flow rate from the annular space? Assume the cells are not active, i.e. they do not grow. Assume further that the membrane does not allow any molecules other than water to pass from annulus to inner cylinder, or vice versa.

Solution

It is given-:

Buffer solution going into the hollow fibre membrane =, 80kg/min

Fermentation broth going into the membrane =350kg /min

As there is no reation taking place in this process therefore

Mass in = mass out Eq 1

If C is the concentrate and B is the buffer concentration then mass balance equation can be given as-:

3.5kg of bacteria in=0.06 *C con of bacteria out

C=58.3kg

The total mass balance can be given as-:

Buffer solution + Fermentation broth going into the membrane

=350+80kg

=430kg

Using Eq 1 we get-:

430kg total mass in =(C+B) kg of mass out

B=371.7 kg where C=58.3kg

Now water balance is given as-:

346. 5 kg water in= water out. Since broth contain 1% of bacteria that is 3.5kg and rest is water.

1.So the flow rate of cell concentrate from the membrane is 58.3kg /min

2.The flow rate of from the annular space is 371.7kg/min or 372kg/min.