It involves albitization, which you have consistently maintained has no relevance to the output of sodium from the sea. I say this because you have consistently said that albitization has a value of 0 in the output column. This is wrong. The article of relevance is K. L. Von Damm, "Controls on the Chemistry and Temporal Variability of Seafloor Hydrothermal Fluids," in Humphris et al editors, Seafloor Hydrothermal Systems: Physical, Chemical, Biological and Geological Interactions, Geophysical Monograph 91, (Washington: American Geophysical Union, 1995), pp222-247. Von Damm states,
"Sodium is by far the most abundant cation in hydrothermal fluids, and as such, its cycle is tightly tied to that of chloride. Sodium is not conservative in water-rock reactions as is chloride, but has a major sink in the albitization of basalt. The largest sodium deficits with respect to chloride are found in high chlorinity fluids. In a few cases the Na/Cl ratio is slightly greater than in seawater and the cause of this is not well understood."(Von Damm, 1995, p. 238)
and
"Sodium, the most abundant cation, of necessity tracks chloride, but where it does not (i.e., the Na/Cl ratio is lower than the seawater value) provides our best evidence that albitization is an active process in hydrothermal vent systems. "(Von Damm, 1995 p. 240)