Numerical modeling of two-phase flow in the sodium chloride-water system with applications to seafloor hydrothermal systems

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. Under the assumption that heat transfer occurs mainly by thermal conduction it is shown that, for a two-meter wide dike, the maximum width of the two phase zone is approximately 20 cm and that a zone of halite is deposited near the dike wall. The two-phase zone is mainly filled with vapor. After 13 days, the two-phase zone begins to disappear at the base of the system, and disappears completely by 16 days. The results of this simplified model agree reasonably well with transient numerical solutions for the analogous two-phase flow in a pure water system. The seafloor values of vapor salinity given by the model are compared with vapor salinity data from the "A" vent at 9-10°N on the East Pacific Rise and it is argued that either non-equilibrium thermodynamic behavior or near-surface mixing of brine with vapor in the two-phase region may explain the discrepancies between model predictions and data. 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 thermodynamic relations are expressed in terms of equations of state, and the latter are shown to vary both smoothly and physically in P-T-X space. In particular, vapor salinity values near the vapor-liquid-halite coexistence surface are shown to be in strong agreement with recently measured values. 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. Additionally, code output from an approximately one-dimensional scenario is compared to the analytic solution of the classical one-dimensional thermal advection-diffusion equation, and it is found that the numerical output and analytic solution are in strong agreement. 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, a model that has been shown to be useful in the study of seafloor hydrothermal systems. 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, even with the average temperature of the two-phase zone held constant. As the two-phase zone evolves, brine of high salinity and density collects at the bottom of the system and is held there primarily via the effect of vapor on the liquid phase's relative permeability; however, it is found that lowering the temperature of the heat source until the two-phase zone vanishes and allowing the system to evolve for some time results in the flushing of this brine from the system. The resulting pattern of vent fluid salinities resembles that described in a widely held conceptual model of vent fluid salinity variation in seafloor hydrothermal systems, where low salinity fluids emerge from venting systems during early stages, and high salinity fluids emerge at later stages as brine is flushed from the system. The effect of varying the permeability is investigated, and it is found that peaks in vent fluid salinities occur later in time for lower permeabilities than one might expect for a simple linear relationship. Finally, it is argued that the numerical approach used in this thesis 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.