Gibbs Energy Analysis of Phase Equilibria

Equations of state are used to predict or to match equilibrium fluid phase behavior for systems as diverse as distillation columns and miscible gas floods of oil reservoirs. The success of such simulations depends on correct predictions of the number and the compositions of phases present at a given temperature, pressure, and overall fluid composition. For example, recent research has shown that three or more phases may exist in equilibrium in CO floods. This paper shows why an equation of state can predict the incorrect number of phases or incorrect phase compositions. The incorrect phase descriptions still satisfy the usual restrictions on equality of chemical potentials of components in each phase and conservation of moles in the system. A new method and its mathematical proof are presented for determining when a phase equilibrium solution is incorrect. Examples of instances where incorrect predictions may be made are described. These include a binary system in which a two-phase solution may be predicted for a single-phase fluid and a multicomponent CO /reservoir oil system in which three or more phases may coexist. Introduction Advances in reservoir oil recovery methods have necessitated advances in methods for prediction of phase equilibria associated with those methods. It was long considered sufficient to approximate the reservoir behavior of oil and gas systems with models in which compositions of the phases in equilibrium were unimportant. In such a model, the amounts and properties of the phases are dependent on pressure and temperature only. Later, experience in production from condensate and volatile oil reservoirs showed that models incorporating compositional effects were required to simulate the phase equilibria adequately. This led to the use of convergence pressure correlations and subsequently to the development of more sophisticated equation of state methods for modeling and predicting phase equilibria. For adequate description of the compositional effects that occur in enhanced oil recovery processes such as CO and rich gas flooding, an equation-of-state approach is a virtual necessity. equilibrium The use of equations of state for phase prediction is not limited to the petroleum industry. Such equations also find wide use in basic chemical and physical research, and in the refining and chemical processing industries. Solution techniques for phase equilibrium problems are varied and depend to some extent on the application and equation of state used however, there are three restrictions that all phase equilibrium solutions must satisfy. First, material balance must be preserved. Second, for phases in equilibrium there must be no driving force to cause a net movement of any component from one phase to any other phase. In thermodynamic parlance, the chemical potentials for each component must be the same in all phases. Third, the system of predicted phases at the equilibrium state must have the lowest possible Gibbs energy at the system temperature and pressure. The requirement that the Gibbs energy of a system. at a given temperature and pressure, must be a minimum is a statement of the second law of thermodynamics, equivalent to the more common version requiring the entropy of an isolated system to be a maximum. The equivalence is demonstrated formally in Ref. 1, for example. If the Gibbs energy of a predicted equilibrium state is greater than that of another state that also satisfies Requirements 1 and 2, the state with the greater Gibbs energy is not thermodynamically stable. Requirements 1 and 2, material balance and equality of chemical potentials, are used commonly as the sole criteria for solution of phase equilibrium problems. SPEJ P. 731^