A fully compositional numerical simulator for sequestration of CO2 and H2S in deep saline aquifers requires a large number of flash equilibrium calculations at each time step. Therefore, a robust and efficient flash solver is needed in order to resolve the thermodynamic equilibrium of systems composed of brine, CO2, and H2S, i.e., determine the equilibrium phases that emerge in the system, resolve the partitioning of the species among them, and calculate the phase molar fractions. In this work, we develop two fast and accurate flash equilibrium methods, the GeometricFlash and the ProgressiveFlash, for Brine-CO2 and Brine-CO2-H 2S systems. The temperature and pressure ranges are 12-100°C and 1-600 bar for Brine-CO2 systems and 12-100°C and 1-200 bar for Brine-CO2-H2S systems. In this study brine is a solution of NaCl in water. A serial and GPU-based parallel implementations of the above-mentioned flash equilibrium methods are developed for the computation of hundreds of thousands of flash equilibrium calculations. A performance analysis of the computations shows that the progressive flash is faster than the geometric one when executed in serial (on CPUs), while the geometric flash is slightly faster when solved on GPUs. Average speedups of 180 and 300 were achieved with the use of GPUs for the progressive and geometric flash method, respectively.