Mass transfer in low water-rock ratio systems such as those anticipated for long-term disposal of high-level nuclear waste as well as natural environments have heretofore been modeled for the most part by computational schemes for water dominated systems. That is, the solid phase is titrated in small increments into a large amount of aqueous phase that was previously equilibrated with all aqueous species. Following addition of each small amount of the solid phase, the aqueous phase is re-equilibrated and new solid phases may be precipitated and/or destroyed as constrained by the minimization of the Gibbs function until no further changes in either phase takes place. This generalized method for tracing reaction paths was first conceptualized and developed by Helgeson et al. (1969, 1970) and adopted by most subsequent mass transfer geochemical modeling computer programs: e.g., EQ3/6 (Wolery, 1979), PHREEQE (Parkhurst, 1980), CHILLER (Reed, 1982), and The Geochemist's Workbench (Bethke, 1992). Although these programs have admirably addressed a myriad of geochemical problems involving water-rock interactions, they are not suitable for systems in extremely dry environments. On the other hand, computer models that minimize the free energy directly such as HCh (Shvarov & Bastrakov, 1999) are well-suited to modeling the titration of water into rock. For example, in the classic mass transfer example of Helgeson, KAlSi3O8 was titrated into H2O-HCl(pH=4)resulting in a sequence of various minerals that dissolved and precipitated as the titration proceeded. When water is titrated into K-feldspar, this sequence is for the most part reversed. Owing to the very small amount of water, however, the concentrations of the aqueous species exceeds by many orders of magnitude those for the case where KAlSi3O8 is titrated into water. These very concentrated solutions produced in systems with low water-rock ratios, have important implications to the dissolution of the waste form as well as to the corrosion of waste package resulting in a need to re-evaluate the overall integrity of repositories for high-level nuclear waste. Examples of changes in mineralization, as well as changes in solution compositions, have been calculated for mass transfer under extremely dry conditions from 25 to 250 C.