An Extended Natural Variable Formulation for Compositional Simulation Based on Tie-Line Parameterization

A nonlinear formulation based on extension of natural variables set is proposed for modeling compositional two-phase flow in porous media. The focus here is on numerical general-purpose simulation using the fully implicit method. In the formulation, the phase fraction and the saturation change continuously in the immiscible region of the compositional space (i.e., sub-critical region). Inside the two-phase region, these variables are identical to the saturation and phase-fraction of the standard approach. In the single-phase regions, however, these saturation-like and phase-fraction-like variables can become negative, or larger that unity. We demonstrate that when this variable set is used, the equation-of-state (EoS)-based thermodynamic equilibrium computations are resolved completely within the global Newton loop. That is, need not to separate things into phase stability and flash computations. Compared to the standard natural variables approach, the number of global Newton iterations grows only slightly, but overall, the new approach leads to more efficient simulations. Moreover, the continuous variation of both the saturation and phase fraction across phase boundaries results in improved behavior of the nonlinear (Newton) solver. Two different strategies are used to deal with the densities. The first scheme honors the nonlinear dependence of the overall density on phase fractions and saturation, and the second employs a linearized relation for the overall density. Both schemes are compared with the standard natural variables formulation using several challenging compositional problems.