Water that accompanies CO2 during its pipeline transport presents a hazard due to rust and dathrate formation. Rusty pipeline walls favors adsorption of water and other impurities as an additional aqueous phase over condensing out as liquid droplets. The Gibbs phase rule prohibits the system from reaching full equilibrium since the continuous flow provides an ongoing supply of all phases. We present a scheme for free energy minimization under constraints of mass and heat transport that can predict the phase distribution and corresponding compositions. Molecular dynamics simulations and the Gibbs-Duhem relation are used to derive consistent infinite dilution chemical potentials for CO2 and H2S dissolved in water and H2O and H2S dissolved in CO2. Simplified activity coefficient expressions are derived and applied to analysis of hydrate risk formation. Applications of our approach are illustrated by estimating the tolerable water concentration in CO2 before water forms hydrate directly or adsorbs onto the rust. This limit is substantially lower for adsorption onto rust as opposed to condensing out. Investigating the water behavior as a solute in CO2 highlights the question of whether it is thermodynamically feasible for water to dissolve as monomers or if it can thermodynamically benefit from forming dimers or clusters.