Comparison of reduced and conventional phase equilibrium calculations

Phase equilibrium calculations become computationally intensive in compositional simulation as the number of components and phases increase. Reduced methods were developed to address this problem where the binary interaction parameter (BIP) matrix is either approximated by spectral decomposition (Hendriks and van Bergen, 1992), or by using a two-parameter BIP formula (Li and Johns, 2006). Haugen and Beckner (2011) and Yan et al. (2011), however, recently stated that the spectral decomposition method, and by reference all reduced methods, are not as fast as previously reported in the literature. In this paper we present the first study that compares all eight reduced and conventional methods published to date using optimized code and compilers. The results show that the spectral decomposition method and its variants are not as fast as other reduced methods, and can be slower than the conventional approach when fewer than 20 components are used. The reason for the slow speed is the additional number of nested loops required in the code and the requirement that the code must allow for a variable number of eigenvalues. We show that the reduced method of Li and Johns (2006) and its variants, however, are significantly faster. Significant speed up in flash calculations is achieved for all fluids studied when more than six components are used. For example, for ten-component fluids, a speed up of 2 to 3 in the computational time for Newton-Raphson iterations are obtained compared to the conventional method based on minimization of Gibbs energy. We also demonstrate that the reduced method by Gorucu and Johns (2011, 2013), an offshoot of the Li and Johns (2006) reduced approach, is more robust than all other methods.