Compositional parametrization for multi-phase flow in porous media

In this work we generalize the Compositional Space Parameterization (CSP) approach, which was originally developed for two-phase compositional problems. The extension is valid for an arbitrary number of phases, regardless of the number of components. The compositional space is considered to be a high-dimensional simplex, and the phase behavior is represented using a low dimensional tie-simplex parameterization. For example, in the three-phase case, the space is parameterized using tie-triangles and tie-lines for three- and two-phase regions, respectively. This parameterization improves the accuracy of the phase behavior representation as well as the efficiency of various types of computation for compositional flow. One application of this approach is to speed up standard multi-component phase behavior computations. For general purpose compositional simulation, Compositional Space Adaptive Tabulation (CSAT) can be used to avoid most of the redundant Equation of State calculations. A Supercritical State Criteria algorithm, which is based on adaptive tabulation of the critical tie-simplex, is used to handle the super-critical region. Results of several challenging tests of practical interest indicate that the CSAT strategy is quite robust, and that it leads to an order of magnitude gain in computational efficiency. This strategy is valid for systems with any number of phases and components. Another application area for our CSP framework is to speed up standard thermodynamic computations for complex mixtures. For such systems, the methodology is generalized in terms of a multi-phase tie-simplex description, where one finds the closest tie-simplex and uses it as an initial guess for the computations. For better tie-simplex estimation, interpolation based on triangulation is used. For cases with wide variation in pressure and temperature, linear interpolation of the tie-simplex for these variables is adequate. The methodology is demonstrated using several challenging examples.