Fig. 4: Comparison of nanofiltration and extraction with global energy and carbon dioxide equivalent emissions reductions.

a, Preferred separation processes for solute–solute separations among nanofiltration and extraction, excluding solute concentration. b, Preferred solute concentration processes after solute–solute separation by nanofiltration and extraction. c, Parameter boundary (0% and 90% energy reduction) visualization of a kernel density estimation plot based on rejection selectivity (\(\varphi\)) and the difference in log partition coefficients (ΔlogP) for all solvents and membranes. The parameter boundaries create regions where either extraction or nanofiltration is preferred in terms of energy reduction. d, Scatter plot with a 90% energy reduction parameter boundary for a polyamide membrane in acetonitrile. e, Average energy reductions realized with nanofiltration compared with extraction and subsequent evaporation for different membranes in different solvents. The absence of values indicates no available data. f,g, Maps of carbon dioxide equivalent emissions reduction (f) and operating cost reduction (g) for solute separation. The data in a and b are based on a tenfold relative purity increase. For detailed specifications of feed and target compositions, see Supplementary Methods.