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In order to explain the observed time-dependent salinity variations in seafloor hydrothermal vent fluids, quasi-numerical and fully numerical fluid flow models of the NaCl-H2O system are constructed. For the quasi-numerical model, a simplified treatment of phase separation of seawater near an igneous dike is employed to obtain rough estimates of the thickness and duration of the two-phase zone, the amount of brine formed, and its distribution in the subsurface. For the fully numerical model, the equations governing fluid flow, the thermodynamic relations between various quantities employed, and the coupling of these elements together in a time marching scheme is discussed. The fully numerical model is benchmarked against previously published heat pipe and Elder problem simulation results, and is shown to be largely in agreement with those results. A number of simulation results are presented in the context of two-phase flow and phase separation within the framework of the single pass model. It is found that a quasi-stable two-phase (liquid + vapor) zone at depth below the hydrothermal discharge outlet gives rise to vent fluid with lower than normal seawater salinity. Additionally, it is shown that increasing the spatial extent of the two-phase zone can lower vent fluid salinity. The numerical approach used in this thesis is able to generate salinity patterns predicted by a widely held conceptual model of vent fluid salinity variation, and may be able to explain the vent fluid salinities and temperatures found at the Main Endeavour Vent Field on the Juan de Fuca Ridge, as this approach is able to produce simulated vent fluid salinities that match observed values from the Endeavour Field vents Dante and Hulk.