Energy consumption
The energy consumption for a stirred dead-end filtration cell consists of the power dissipated by a stirrer (Ps ) and the power for generating the applied pressure (Pa ). Thus the specific energy consumption (E ) in kWh per a kilogram of product during the filtration process is presented by
\(E=\frac{\int_{0}^{T}{\left(P_{s}+P_{a}\right)\text{dt}}}{M_{p}}=\frac{\int_{0}^{T}{\left(P_{s}+P_{a}\right)\text{dt}}}{YM_{f}}\)(35)
where T is the filtration time, Mp is the product mass in the permeate, Mf is the substrate mass added in the filtration system, Y is the yield.
\(P_{a}=QP\) (36)
where Q is permeate flow rate.
Power dissipated by a stirrer (Ps ) depends on the diameter of the impeller (Di ), dimensionless power number (NT ), the stirring angular velocity (ωo ), and the density of the fluid (ρ ) 29.Ps can be calculated using eq. (37)
\(P_{s}=N_{T}\rho\omega_{o}^{3}D_{i}^{5}\) (37)
To generate high surface stress for alleviating membrane fouling, the minimum stirrer speed used in our system was 100 rpm, which gave a Reynolds number of 1130. As the Reynolds number is larger than 100, theNT of the Rushton impeller is independent of the Reynolds number and can be approximated to 5.0 30.