  Molecular dynamics simulations have been performed to determine the
three-phase coexistence temperature for a methane hydrate system in equilibrium
with a NaCl solution and a methane gas phase. The direct coexistence technique
is used following two approaches, one where the triple coexistence temperature
for a given NaCl concentration is narrow down and another where the
concentration at a given temperature is equilibrated. In both approaches the
results are consistent within the error bars. All simulations were carried out
at 400 bar and the range of concentrations explored extends up to a molality of
4 m. TIP4P/2005 for water molecules and a simple Lennard-Jones interaction site
for methane were used to simulate the system. Positive deviations from the
Lorentz-Berthelot energetic rule have been applied between methane and water
(i.e., increasing the attractive interaction between water and methane). Na$^+$
and Cl$^-$ ions were described by using the Madrid-2019 scaled charge model.
The role played by finite size effects in the calculation of the coexistence
line was analyzed by studying a system with larger number of molecules at a
given NaCl concentration. Overall, our simulations show that upon NaCl addition
to the liquid water phase, a shift in the three-phase equilibrium line to lower
temperatures is produced as occurs in the ice-NaCl(aq) system. The depression
of the three-phase coexistence line obtained at different concentrations is in
a very good agreement with the experimental results.
