What is membrane flux?
Flux is a critical metric for comparing, scaling and assessing general performance of a membrane.
Flux is essentially the permeate flow expressed over unit of time and membrane surface area. In SI units membrane flux is commonly expressed as liters/m2/hr.
Calculating Flux
In order to size a membrane for scale-up you will likely want to calculate membrane flux. A lab/pilot scale process typically involves recirculating retentate while removing the permeate. In order to get the most representative assessment of flux you will want to measure flux over the entire concentration process.
Example
Calculate the flux across a 400 cm2 membrane concentrating 1500 ml of protein solution 3 x, i.e 500 ml of retentate and 1000 ml of permeate.
The calculation is relatively easy but it's important to measure accurately. Follow the procedure below.
Measurement
1. Ensure all the lines and membrane are drained of any water that could effect you calculation.
2. Accurately weigh your starting feed solution. ( e.g. 1500 g)
3. Take a clean dry beaker and get the tare weight to collect you permeate solution.
4. Start recirculating you protein solution and bring the pump up to your target cross flow rate.
5. Once at the target crossflow, apply target back pressure and start the timer. (Note: if no back pressure required start timer as soon as reach target flow rate).
6. Once the concentration factor has been achieved, stop the system and the timer. Measure the exact permeate volume and retentate volume. Typically there will be some losses in the system.
Calculation
Permeate = 1035 ml
Minutes = 66
Membrane surface area = 400 cm2
Flux = Liters/m2/hr
Permeate Liters = 1.035 L
Hrs = 1.1
m2 --> 400/10000 =0.04
Flux --> 1.035/0.04/1.1 = 23.52 L/m2/hr
Scale-up
Using the flux one can easily estimate the required surface area.
For example, you would like to scale up to 1500 Liter batch, how much membrane surface area would you require?
There are a few factors to consider when determining membrane surface area.
- Time required to process it, ideally as fast as possible, however, the below factors need to be taken into account
- Hold up capacity, greater surface area = greater hold up capacity. This is important when it comes to collecting the final concentrate. For example, if your goal is to remove water and concentrate the protein solution then you will want to limit hold up capacity. The larger the hold up capacity the more you will be required to flush at the end of the batch to capture the protein and the more dilution of you concentrate.
- Membrane cost and size. Also a factor in choosing surface area. The more surface area the larger the pumps and size of the system.
For the above example,
Batch size = 1500 L
Concentrate = 500 L
Permeate =1000 L
Surface area/hr = Permeate/Flux --> 1000/23.52 = 42.51 m2
4"x40" spiral wound membrane = 6m2
No. 4" membranes --> 42.51/6 = 7.086
Multiply by 20% to ensure more capacity and allow for lower flux performance over time.
7.086*1.20 = 8.5 membrane to process 1000 liters/hr
Considering in the example above we are not concentrating to a very low volume relative to starting batch size, hold up capacity is not as much of a concern, therefore it would be reasonable to consider using 8 x 4" membranes.
Typical Membrane Fluxes (General Rule)
RO --> 15 to 25 L/m2/hr
NF --> 20 to 30 L/m2/hr
UF --> 25 to 50 L/m2/hr
MF --> No typical flux, dependent on process