Multiphase equilibria for CO2/water/hydrocarbons mixtures are frequently encountered in using CO2 for flooding or storing CO2 in depleted reservoirs. The presence of an aqueous phase in multiphase equilibrium poses difficulties associated with how to ensure the convergence of stability test. The free-water assumption, where the aqueous phase is considered as pure water, provides a better solution to this problem compared with the conventional full three-phase flash method. As for CO2/hydrocarbons/water mixtures, the free-water assumption might not be valid since the solubility of CO2 in the aqueous phase may not be negligible. This research presents a robust and efficient algorithm to perform three-phase flash calculation for CO2/hydrocarbons/water mixtures based on the assumption that only the presence of CO2 and water is considered in the aqueous phase, i.e., the so-called augmented free-water concept. The new algorithm is comprised of two loops. In the outer loop, we first develop a pragmatic method for initializing the equilibrium ratios of CO2 and water in the aqueous phase with respect to the reference phase (i.e., the hydrocarbon-rich liquid phase). In the inner loop, we solve the Rachford-Rice (RR) equation that has been simplified based on the augmented free-water assumption. In addition, we incorporate this new augmented free-water three-phase flash algorithm to a flash package which can deal with the single-phase, two-phase, and three-phase equilibria. Both positive and negative flashes have been applied in the flash package. Also, a new criterion is developed to properly switch between two-phase flash and three-phase flash; such criterion has been used as the supplementary judgment for the negative flash, which is proven to be reliable and efficient after extensive testing. The example calculations using the new algorithm show that the augmented free-water method is more accurate than the traditional free-water method since the solubility of CO2 is considered in the augmented one. The flash package that couples the augmented free-water flash requires less computational time and a fewer number of iterations than the conventional full three-phase flash package. (C) 2017 Elsevier B.V. All rights reserved.