In upstream petroleum engineering, models of the flow of hydrocarbons from the reservoir up to the sales point need to be developed. These models are used subsequently to design the production facilities and select the operating conditions so as to maximize production at minimum field development cost. As flow is considered within the reservoir as well as in the production wells and the surface conduit, such models incorporate fluid flow calculations in the porous medium and in pipelines of various configurations. Moreover, although the flowing fluids are non-reacting, the fact that they are complex mixtures comprised of thousands of components and that might exhibit multiphase equilibrium renders fluid simulation as a complex computational task. Indeed, individual phase fluid properties such as density and enthalpy play an important role to the solution of the continuity, momentum and energy equations.Today, modern computers capabilities allow for the detailed numerical solution of the governing flow and phase behaviour equations in reservoir simulators using very fine space grids and time discretization. Although, quite often, the simplifying Black Oil Model approach can be used to describe thermodynamic behaviour of reservoir fluids, when it comes to complex phase behaviour phenomena such as the ones encountered in Enhanced Oil Recovery methods and to near critical gas condensates, compositional simulation is the only credible alternative. During this type of simulation, cubic EoS models are called to directly provide fluid phase thermodynamic properties and for solving iteratively the phase stability and phase split problems which consume a great part of the total CPU time due to the complexity of the available algorithms. Note that it is this complexity that discourages operators from employing advanced, mathematically more complex, EoS models which would be able to capture more accurately the real fluids thermodynamic behaviour. On the other hand, the utilization of such advanced EoS models is a prerequisite when flow assurance issues are considered such as precipitation of asphaltenes, wax and hydrate formation.Despite recent developments in accelerating conventional phase behaviour calculations, soft computing remains a very attractive option for speeding them up. Some of the most pronounced methods, which seem to be extensively utilized, are proxy models to generate explicit solutions of the stability and phase split problems, the on-the-fly tabulation of phase behaviour results so as to be used repeatedly during the flow simulation as well as interpolation techniques to map directly the natural flow variables such as density and energy to pressure and temperature. Of these methods, the use of proxy models has shown excellent speedup by two orders of magnitude for many simulations of various reservoir fluid types. Such methods propose the development of two distinct explicit models, one that firstly classifies the composition under study as a stable or an unstable one and a second model that provides the values of the prevailing equilibrium coefficients if the fluid was proved to be unstable.