# Membrane Performance Calculator

## Step 1. Water permeability coefficient,

can also be calculated using solutes, but read the note on how to do it correctly.

The presence of solutes in a feed solution will increase the osmotic pressure difference across the membrane (∆πf = πf – πp), reducing the net effective driving force. To account for this when calculating , the following equation needs to be used:

Note: ∆πf can be calculated here. The feed-side mass transfer coefficient (kf) can be calculated here.

## Step 2. Observed solute rejection,

Note: is generally reported between 0 and 100%, but it should be a value between 0 and 1 for the calculation of (step 4)

## Step 3. Solute flux,

Note: taken from step 2

## Step 4. Solute permeability coefficient,

Note: , , , and taken from steps 2–3. can be considered equal to the feed-side mass transfer coefficient (kf) for single-solute solutions. Details for calculating kf can be found here. If unavailable, kf and ksol can be roughly estimated as 100 L m-2 h-1. For more information on the estimation of and , please see the page concentration polarization here

## Step 5. Real rejection, and water-salt permselectivity,/

Note: ∆πf can be calculated here. Details for calculating can be found here. If unavailable, can be roughly estimated as 100 L m-2 h-1. For more information on the estimation of and , please see the page concentration polarization here. Rg, T, and VW are the ideal gas constant (cm3 bar K-1 mol-1), temperature (K), and molar volume of water (cm3 mol-1), respectively. All other values taken from steps 1 and 4.

## Step 6. Diffusive Water and Solute Permeabilities, and

Note: and taken from steps 4–5. The factor of 2.778×10-12 is for unit conversion to cm2 s-1 when using units of nm for δ and L m-2 h-1 for B.

## References

•  J. R. Werber, et al., The critical need for increased selectivity, not increased water permeability, for desalination membranes, Environ. Sci. Technol. Lett. 3 (2016) 112–120.
•  G.M. Geise, et al., Fundamental water and salt transport properties of polymeric materials, Prog. Polym. Sci. 39 (2014) 1–42.
•  D.R. Paul, Relation between hydraulic permeability and diffusion in homogeneous swollen membranes, J. Polym. Sci. B Polym. Phys. 11 (1973) 289–296.