Numerical models have become indispensable tools for investigating submarine hydrothermal systems and for relating seafloor observations to physicochemical processes at depth. Particularly useful are multiphase models that account for phase separation phenomena, so that model predictions can be compared to observed variations in vent fluid salinity. Yet, the numerics of multiphase flow remain a challenge. Here we present a novel hydrothermal flow model for the system H2O-NaCl able to resolve multiphase flow over the full range of pressure, temperature, and salinity variations that are relevant to submarine hydrothermal systems. The method is based on a 2-D finite volume scheme that uses a Newton-Raphson algorithm to couple the governing conservation equations and to treat the non-linearity of the fluid properties. The method uses pressure, specific fluid enthalpy, and bulk fluid salt content as primary variables, is not bounded to the Courant time step size, and allows for a direct control of how accurately mass and energy conservation is ensured. In a first application of this new model, we investigate brine formation and mobilization in hydrothermal systems driven by a transient basal temperature boundary condition-analogue to seawater circulation systems found at mid-ocean ridges. We find that basal heating results in the rapid formation of a stable brine layer that thermally insulates the driving heat source. While this brine layer is stable under steady-state conditions, it can be mobilized as a consequence of variations in heat input leading to brine entrainment and the venting of highly saline fluids.