Author Correction: Performance metrics for nanofiltration-based selective separation for resource extraction and recovery

Correction to: Nature Water https://doi.org/10.1038/s44221-023-00037-0, published online 9 March 2023.

In the original version of this article, an incorrect version of Fig. 4 was displayed. The original Fig. 4 was inconsistent with the source data uploaded. The source data were correct. The scale of the y-axes in Fig. 4d and the inset graphs of 4a and c have been updated. The data points have been replotted for the Local Mg²⁺ line in Fig. 4b and the “Local” line in Fig. 4e.

Additionally, two errors were found in the “Supplementary Codes” of the original Supplementary Information. The first error was in line 120, where “Pressure = 4” should be corrected to “Pressure = 6”. The second error was in line 124, where “A = 18” should be corrected to “A = 18.8”.

Three additional functions (namely, ‘PCF’, ‘licl’ and ‘mgcl2’) are needed to generate the source data for Fig. 4. These functions were called in the function “SDEM” and were not included in the submission or uploaded to GitHub. They have now been added in the corrected Supplementary Information and on GitHub.

An additional function (namely, ‘upsolver’) is needed to run the permeability fitting application in the Supplementary Code and was not included in the submission or upload to GitHub. This function has now been added in the corrected Supplementary Code package and on GitHub. We have also added more annotations and comments to the updated codes to improve interpretability.

The authors would also like to use this opportunity to make the following clarifications:

• 1. The “$x$” in Equation 5 is dimensionless (from 0 to 1) as it is the transmembrane coordinate normalized by the membrane thickness. Therefore, ion permeability ‘$P$’ has the same unit as velocity instead of diffusivity.

• 2. Molar concentration (mmol L^–1 or mM) is used throughout mass transfer modeling for coupon and module scale. Mass concentration (mg L^–1 and g L^–1) is used for defining and quantifying total salinity, purity and Mg/Li ratio (MLR), to be consistent with literature convention.