Predicting asphaltenes phase change is crucial in forecasting the occurrence and extent of their instability as an undesirable fraction of crude oil to prevent the consequences associated with asphaltene destabilization. One of the equations of state (EOS) that has emerged in the last decade as a capable tool for this purpose is the PC-SAFT EOS. This equation performs well; however, due to its several disadvantages including complication and time-consumption, this EOS is not suited well in petroleum engineering applications. To address these issues, we developed a fast and robust algorithm based on the three-phase Rachford-Rice equation for predicting the asphaltene phase envelope (APE). The newly developed algorithm was evaluated for five oil samples with or without gas injection in the temperature range of 100–500 °F and pressures up to 10,000 psia. The injected gases included methane, nitrogen, carbon dioxide, and natural gas. The results revealed that the APEs obtained using the proposed approach are in line with those reported in the literature. However, in terms of computation time, the proposed algorithm is four times faster than those developed based on minimizing Gibbs free energies. Consequently, the newly developed algorithm can reliably be employed to prevent the damages caused by asphaltene instability in oil reservoirs, near-wellbore region, perforations, downhole equipment, well column, as well as wellhead installations.