We report two-phase Monte Carlo (MC) simulations of the binary water-acid gas mixtures at high temperature and high pressure. Simulations are performed in the Np(N)AT ensemble in order to reproduce the pressure dependence of the interfacial tensions of the water-CO2 and water-H2S mixtures. The interfacial tension of the binary water-CO2 mixture is determined from 5 to 45 MPa along the isotherm T = 383 K. Water-H2S interfacial tensions are computed along one supercritical isotherm (T = 393 K) in a pressure range of 1 - 15 MPa. The temperature and pressure conditions investigated here by the MC simulations are typical of the geological storage conditions of these acid gases. The coexisting densities and the compositions of the water-rich and acid-gas-rich phases are compared with experiments and with data calculated from Gibbs ensemble Monte Carlo (GEMC) simulations.