Development of Robust Trust-Region Algorithms for Multiphase Equilibrium Calculations
Creators: Xu, Lingfei
Publisher: name: University of Alberta Library
Year: 2023

<p>Crude oil, as a major type of fossil fuels, is a mixture mainly made up of hydrocarbons. One important research topic relevant to the extraction, transportation, and storage of these hydrocarbon mixtures is the study of multiphase equilibria under specified specifications, especially the pressure-temperature (PT) specification. In the CO2 injection process for enhanced oil recovery (EOR), the vapor-liquid-liquid (VLL) equilibria, consisting of a vapor phase (V), a solvent-rich liquid phase (L2), and an oil-rich liquid phase (L1), are frequently encountered. A robust PT equilibrium calculation algorithm, which quantitively determines the number of phases, phase fractions, and phase compositions, is a fundamental module that is required in the reliable compositional simulations of multiphase flows. However, the development of such an algorithm is challenging, because detecting the second liquid hydrocarbon phase can be a challenging task. To address this issue, Pan et al. (2019) proposed a robust multiphase (up to three phases) equilibrium calculation framework, where the state-of-the-art trust-region solvers developed by Petitfrere and Nichita (2014) were embedded into their framework. Such a framework consists of a series of implementation of two key subroutines, namely stability test (Michelsen, 1982a) and flash calculation (Michelsen, 1982b). The new trust-region-based algorithms (Petitfrere and Nichita, 2014) are successfully applied in both stability test and flash calculation to address the convergence difficulties that may be encountered when running the conventional Newton-based method.<br>
Inspired by the trust-region method applied in the flash calculation algorithms (Petitfrere and Nichita, 2014; Pan et al., 2019), we build a new hybrid trust-region-based flash calculation algorithm based on a different formulation. In the new formulation, the logarithms of equilibrium ratios (lnK) and phase fractions are the independent variables that are solved simultaneously. Advantages of such a simultaneous solution strategy include that the explicit solution of the phase fractions (i.e., solving the Rachford-Rice equation; Rachford and Rice, 1952) is not needed in each iteration and the well-scaled variable lnK is treated as the independent variable. We build a new robust equilibrium calculation framework embedding the new flash calculation algorithm as a subroutine. Case studies indicate that the new hybrid flash calculation can generate digital multiphase phase diagrams in a more robust and efficient manner than the conventional approach. <br>
Besides, considering that the conventional Newton-based method is still the major solution method for envelope constructions, we propose new trust-region-based phase envelope construction algorithms aiming to improve the computational efficiency and robustness. A trust-region-based algorithm is first proposed for two-phase envelope constructions. Example calculations show that the new construction algorithm is more cost-effective and robust than the conventional Newton-based algorithm. We then extend this base algorithm to three-phase envelope constructions. More specifically, the extended algorithm handles the calculation of multiphase envelopes involving two-phase envelopes, three-phase envelopes, and three-phase points (i.e., the intersection point of a two-phase envelope and a three-phase region). We successfully construct a total of 15 multiphase envelopes for 15 mixtures (including hydrocarbon-CO2, hydrocarbon-water, hydrocarbon-asphaltene mixtures), without encountering a single failure. We also observe that the new trust-region-based algorithm significantly enhances the computational efficiency of multiphase envelope constructions. </p>