The study of phase behavior is important for the oil and gas industry. Many approaches have been proposed and developed for phase behavior calculation. In this thesis, an alternative method is introduced to study the phase behavior by means of minimization of Helmholtz free energy. For a system at fixed volume, constant temperature and constant number of moles, the Helmholtz free energy reaches minimum at the equilibrium state. Based on this theory, a stochastic method called Particle Swarm Optimization (PSO) algorithm, is implemented to compute the phase diagrams for several pure component and mixture systems. After comparing with experimental and the classical PT-ash calculation, we found the phase diagrams obtained by minimization of the Helmholtz Free Energy approach match the experimental and theoretical diagrams very well. Capillary effect is also considered in this thesis because it has a significant influence on the phase behavior of reservoir fluids. In this part, we focus on computing the phase envelopes, which consists of bubble and dew point lines. Both fixed and calculated capillary pressure from the Young-Laplace equation cases are introduced to study their effects on phase envelopes. We found that the existence of capillary pressure will change the phase envelopes. Positive capillary pressure reduces the dew point and bubble point temperatures under the same pressure condition, while the negative capillary pressure increases the dew point and bubble point temperatures. In addition, the change of contact angle and pore radius will affect the phase envelope. The effect of the pore radius on the phase envelope is insignificant when the radius is very large. These results may become reference for future research and study. Keywords: Phase Behavior; Particle Swarm Optimization; Capillary Pressure; Reservoir Fluids; Phase Equilibrium; Phase Envelope.