Modeling of coupled processes in the geology near a high-level nuclear waste repository is similar to the modeling of coupled Thermo-Hydro-Mechanical-Chemical (THMC) processes that occur in magma-hydrothermal systems. Former Professor Denis Norton and his colleagues at the Geoscience Department at University of Arizona studied magma-hydrothermal systems extensively. These hydro-thermal codes were verified by obtaining excellent matches between calculated δ 18 O–values and measured δ 18 O–values in three principal rock units: basalt, gabbro, and gneiss. This paper reviews the concept of transport theory used in the formulation of the conservation principle used to model the hydrothermal systems. In addition, the paper reviews conservation of mass, momentum, energy, and chemical component equations as applied to the multicomponent-multiphase systems related to hydrothermal systems and obtains parallels to reaction rates and radionuclide transport in the geology of a high level nuclear water repository. Further, this paper compares published results obtained by other researchers modeling coupled THMC process in the geology of high-level nuclear waste repositories.