From their first discovery in the late 1970's, seafloor hydrothermal vent systems have been an intensive area of study in terms of characterizing the chemistry of their fluids, the biology that thrives around them, and the unique chimney structures that grow from the minerals precipitating from the fluids coming out of the seafloor. Predicting sub-seafloor fluid flow pathways and the dynamics of how these systems operate and evolve in the subsurface, however, still remains elusive due the paucity of holistic mathematical models of the chemical and physical processes that drive these systems. This research develops 2-D and 3-D mathematical models of fluid flow and reactive transport in high temperature mid-ocean ridge seafloor hydrothermal systems. Resulting models take into account mineral dissolution and precipitation and how these change basement permeability, fluid flow, and flow pathways. Goals are to test various hypotheses about what controls the distribution of focused and diffuse flow in high temperature seafloor hydrothermal systems, the extent of mineral precipitation, and the thermal/chemical conditions in the subsurface. The RST2D software package and modifications to it will be used to model the systems. The codes will permit fully-coupled reactive-flow investigations to be carried out which can examine the sensitivity of mid-ocean ridge hydrothermal vent systems to crustal structure, permeability, thermal conductivity, chemical dispersivity, and other geologic variables. Broader impacts of the work include integration of research and education and training graduate students in computational geoscience. Software that will be created during the course of the project builds infrastructure for science and has crossover potential to other fields, such as geothermal energy production and ore deposits. It will be made publicly available over the web. Results of the project will be presented to the public via lectures by participating faculty. The project will also support a PI from a gender under-represented in the sciences.