In this work, we developed an extended surface complexation model (SCM) that successfully fits all tested zeta-potential data (63 in total) of synthetic calcite and three natural carbonates (Iceland spar, Indiana limestone, "SME" rock from a Middle East field) in brines with divalent ions in a wide range of ionic strengths (0.001-0.5 M). To develop this extended model, our previous reported SCM is first optimized by incorporating the zeta-potential of synthetic calcite in a wide range of ionic strength (0.001-0.5 M) along with previously published data for parameter refitting. The model is then applied to predict the surface charge of synthetic calcite in concentrated solutions up to 5 M NaCl to reveal the role of high salinity in calcite wettability. Eventually, the model is extended to fit the zeta-potential of natural carbonates by adding surface reactions for impurities such as silica and organic-based carboxylic acids. The coverage of the organic impurities is found to be essential for explaining why the zeta-potential of natural carbonates is more negative compared to that of synthetic calcite. Naphthenic acid (assumed to have one carboxylic group) and humic/fulvic acid (assumed to have six carboxylic groups) are tested in the model calculation as possible sources of surface impurities to demonstrate the effect of the number of carboxylic groups in the acid molecule. Finally, the effect of a humic acid pretreatment on the zeta-potential of synthetic calcite is investigated experimentally to verify the assumption that absorbed organic impurities on the calcite surface contribute significantly to a more negatively charged natural carbonate surface when compared to that of pure calcite surfaces.