Comparison of Reduced and Conventional Two-Phase Flash Calculations

Abstract

Phase-equilibrium calculations become computationally intensive in compositional simulation as the number of components and phases increases. Reduced methods were developed to address this problem, where the binary-interaction-parameter (BIP) matrix is approximated either by spectral decomposition (SD), as performed by Hendriks and van Bergen (1992), or with the twoparameter BIP formula of Li and Johns (2006). Several authors have recently stated that the SD method-and by reference all reduced methods-is 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 by use of optimized code and compilers.The results show that the SD method and its variants are not as fast as other reduced methods, and can be slower than the conventional approach when fewer than 10 components are used. These conclusions confirm the findings of recently published papers. The reason for the slow speed is 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 faster because the number of reduced parameters is fixed to six, which is independent of the number of components. Speed up in flash calculations for their formula is achieved for all fluids studied when more than six components are used. For example, for 10-component fluids, a speed up of 2-3 in the computational time for Newton-Raphson (NR) iterations is obtained compared with the conventional method modeled after minimization of Gibbs energy. The reduced method modeled after the linearized approach of Nichita and Graciaa (2011), which uses the twoparameter BIP formula of Li and Johns (2006), is also demonstrated to have a significantly larger radius of convergence than other reduced and conventional methods for five fluids studied. IntroductionGas injection achieves enhanced oil recovery (EOR) primarily by developing miscibility in situ. Compositional simulation of gasfloods is an important tool for recovery estimation, but a significant drawback is that compositional simulation is costly when the number of components and phases is large. One approach is to lump components into several pseudocomponents and to limit the number of phases that can form. Reducing the number of components, however, decreases the accuracy of the phase-behavior calculation in compositional simulation, and also the detailed type of compositional information required for better surface-facility designs. Fewer components also means that heavier components are not adequately represented and evaporation fronts will not be captured properly in simulation, necessitating the use of an unphysical parameter called the miscible residual oil saturation to force oil to be left behind. Thus, it is highly advantageous to use more components, not fewer, if methods for faster flash calculations are available.

A comparison of conventional and reduction approaches for phase equilibrium calculations

“…This is a common observation of the three recent publications on this matter [22][23][24]. Depending on how the comparison was done and on the implementation, the reported crossing point is around 15 in Haugen and Beckner [23], around 20 in Michelsen et al [22] (global time stability and flash using a Trust-region approach) and around 20 in Gorucu and Johns [24].…”

“…This work presents a comparison between conventional and reduction methods for phase equilibrium calculations, and is complementary with several recent papers [22][23][24] which questioned on the efficiency of the reduction methods as compared to conventional methods. Here, we have looked separately at the computational time spent by stability testing and flash calculations (per iteration and global).…”

“…The results show that flash calculations using the reduction methods are more efficient than conventional methods only for mixtures with many components (more than 20) and few non-zero binary interaction parameters (this is consistent with observations reported in Refs. [22][23][24]). …”

“…Previously, h have been used as independent variables by Kaul and Trasher [11] (for all BIPs equal to zero) and Pan and Firoozabadi [12]. Nichita and Graciaa's [16] reduction method was used by Michelsen et al [22], Haugen and Beckner [23], Gorucu and Johns [24,32] and Gaganis and Varotsis [33]. In Ref.…”

“…Several very recent papers (Michelsen et al [22], Haugen and Beckner [23], Gorucu and Johns [24]) have questioned on the efficiency of the reduction methods as compared to conventional methods. The common conclusion of these papers is that reduction methods become faster than conventional ones starting from a certain number of components in the mixture (about 20 if few components have non-zero BIPs).…”