The aim is to eliminate inorganic carbon for isotopic analysis (13C an 14C) of organic C. DOM has been concentrated by reverse osmosis from river water samples.
I suggest you read the article : Patrick Albéric Université d’Orléans-CNRS/INSU UMR 6113 “LC/MS stable isotope analysis of dissolved organic carbon in stream and soil Waters. ”
Author manuscript, published in "Rapid Communications in Mass Spectrometry 25 (2011).
If you analyze it as freeze dried material, you can follow protocols to remove inorganic carbon from soils and sediments, keeping in mind that you might have much less carbonates in your solids and therefore reducing the amount of acid to minimize negative effects on the elemental analyzer. Some people prefer adding acid into tin or silver capsules, other fumigate their capsules in HCl vapor. It depends probably on which method is established in your lab.
On the other hand we use a TOC analyzer coupled to a Picarro CO2 isotope analyzer. In this case you keep using a liquid sample, the DOC or TOC is digested and the resulting CO2 is analyzed. An acidification step prior to analysis removed DIC, as in a normal TOC/DOC analyzer.
For fluffy freeze dried samples, some times you can just 'fume' the sample with HCL vapor for a bit (I've used ~8hrs, but probably overkill) and re-lyophilize the sample or just put it under vacuum for a while to remove any water or HCL adsorbed.
A simple method for fuming just uses a glass desiccator. pour a mL or so of conc. HCL in the bottom put the sample tray and sample (unsealed so the HCL vapor can reach it) in, close the lid to the desicator and let diffusion do it's thing.
You can also pH adjust (very carefully) your samples before freezedrying them to ensure the DIC volatilizes during sublimation.