Holding tanks (or surge tanks) are used to handle changes in pressure and / or flow in many production processes. one example is the production of citric acid by fermentation using the fungus aspergillus niger. the cell culture takes 5 days in a production-scale bioreactor (basically a large tank). five separate bioreactors are used, each started (and harvested) on a different day. this involves pumping the contents of the bioreactor into a large holding tank at a flow rate q (in), with the liquid flowing out of this tank and into the rest of the downstream purification process at a constant flow rate q.
q (in) = 8000*t for 0 < t < 1 hr
q (in) = 8000 l/hr for 1 hr < t < 4 hr
q (in) = 0 for 4 hr < t < 24 hr
a) write down the mass balance equations describing the volume of liquid in the holding tank as a function of time over the first day assuming that the liquid is incompressible and that q (in) has units of l/hr. note that you should have 3 separate equations.
b) derive an expression for the volume of liquid in the holding tank as a function of time throughout the day assuming v (t=0) = v (o) (again, you will have 3 equations).
c) what is the value of q required to insure that the downstream process can be run continuously in a stable configuration (over many weeks)?
d) what is the minimum volume of the holding tank that would be needed for this facility? what volume would you recommend for the tank?