Reservoir hydrocarbons exist as vapour, liquid or solid phases. A phase is defined as a part of a system which is physically distinct from other parts by definite boundaries. The reservoir oil may form a gas phase during the pressure depletion process. The evolved gas initially remains dispersed in the oil phase before forming large mobile clusters. The subject of phase behaviour focuses only on the state of equilibrium, where no changes will occur with time if the system is left at the prevailing constant pressure and temperature. The system reaches equilibrium when it attains its minimum energy level. The assumption of equilibrium between fluid phases in contact in a reservoir is valid in engineering applications, in most cases; fluids at equilibrium are also referred to as saturated fluids. The objective of this thesis work is to review the phase behaviour computations using a cubic EOS existing as a FORTRAN code implementation. This program is used to compute phase equilibria solutions for phase envelope representation of pressure versus temperature. Phase envelope representation near the critical conditions requires accurate and very robust saturation pressure determination. The first goal of this work was to improve the saturation pressure computations of the existing program. Furthermore, a new algorithm should be implemented to allow for the computation of fixed quality lines within the two-phase region for various types of hydrocarbon reservoir fluids.