Theory and software describing the transport of three-phase ( gas, liquid, solid) hyper-saline brines in porous media is developed using the Palliser - McKibbin description of the H2O - NaCl phase space. Six phase regions are recognised ( liquid, gas, liquid+ solid, gas + solid, liquid+ gas and liquid + gas + solid), and for each region the relevant thermodynamic states, choice of state variables, and phase compositions are described. A new simulation code, NaCl-TOUGH2, is described which is based on this theory. This extends the widely used simulator TOUGH2 with an additional component ( salt) and the six phase regions, and solves the equations for the conservation of water, salt and energy. As currently implemented, this code is valid for pressures from 1 to 1000 bar, temperatures from 10 to 620 degrees C, and salt mass fractions between 0 and 1.