The Critical Composition Method A New Convergence Pressure Method
Authors: Rowe Allen M. 
Published: December 2007

Abstract
A considerable quantity of experimental hydrocarbon K-factor data has been correlated as a function of component identity, temperature, pressure and convergence pressure. To utilize these correlations effectively, convergence pressure must be determined accurately, particularly for volatile mixtures near their critical states. This paper presents phase diagrams that illustrate physically the meaning of convergence pressure. A new method, referred to hereafter as the "critical composition method", will be outlined for calculating convergence pressure. An example calculation has been included to illustrate how to use this new technique.

Introduction
The principle of hydrocarbon phase composition calculations as applied to such diverse problems as optimizing separator performance or predicting fluid compositions at various stages of reservoir depletion is the same. Usually, temperature, pressure and the numbers of moles of the various components of the fluid contained in a given volume are known. Questions answered by the phase calculation are what fraction of the total mass of fluid exists in each of the equilibrium phases, and what are the mole fractions of die various components in the two phases?To answer these questions the Natural Gasoline Supplymen's Assoc. (NGSMA) has correlated a considerable quantity of K-factor data as a function of temperature, pressure, component identity and convergence pressure. To use these correlations to obtain the best answers possible, one must be able to calculate the convergence pressure. This is particularly true for over-all fluid compositions in the neighborhood of the critical state.

STATEMENT OF THEORY
Use of convergence pressure as a combating parameter is based on a postulate similar to the law of corresponding states used in correlating PVT data of hydrocarbon gases. This postulate, which proposes convergence pressure as a correlating parameter, has been stated as follows: "The equilibrium vaporization constant for one component in a complex system is the same as the equilibrium constant at the same temperature and pressure for the same number or kind of components, providing only that the convergence pressures of the two systems are exactly the same at the same temperature and that the components are of the same homologous series. This law, as with all laws of physics, cannot be proven theoretically. It can only be justified by experimental data supporting its premises. Arguments have been made that this law violates Gibb's phase rule. For example, consider a four-component system. By Gibb's phase rule, which is thermodynamically rigorous, f = c - P+ 2 = 4, for a four-component, two-phase system. Thus, four independent intensive variables must be specified to establish completely all the intensive variables of the equilibrium phases. On the other hand, according to convergence pressure theory only three variables need be specified for any mixture containing four different components. These variables are temperature, pressure and convergence pressure. Thus, the two laws appear to be in conflict. However, the convergence pressure postulate is more restrictive than Gibb's phase rule. It applies only to mixtures of the same homologous series. Hence, these two concepts are not in disagreement.

PHASE DIAGRAMS DESCRIBING CONVERGENCE PRESSURE
This paper presents phase diagrams grading from the simple two-component system to the more complex four-component system to illustrate convergence pressure.
SPEJ
P. 54ˆ