In a 3-stage continuous ultrafiltration process, a solution is concentrated from 5 gm/Liter to 50 gm/Liter of protein. The final retentate is to have a flow rate of 1000 L/hr. The rejection coefficient of the protein is 0.95. The membrane flux (liter/meter^2/Hour) is :

J=50.82exp(-0.01626 * C) where C is the protein concentration.

Assuming the permeate flows rate from each membrane is equal (p1=p2=p3), and using the rule of thumb:

J (avg) = J (final) + 0.333 * [J (initial) - J (final)]

Calculate the membrane areas A1, A2, and A3 to described the operation described above. Also calculate the % protein recovery.