Simple and Robust Algorithm for Multiphase Equilibrium Computations at Temperature and Volume Specifications

Abstract

Summary Two-phase and three-phase equilibria are frequently encountered in a variety of industrial processes, such as carbon dioxide (CO2) injection for enhanced oil recovery in oil reservoirs, multiphase separation in surface separators, and multiphase flow in wellbores and pipelines. Simulation and engineering design of these processes using isothermal/isochoric (VT) multiphase equilibrium algorithms are sometimes more convenient than that using the conventional isothermal/isobaric (PT) algorithms. This work develops a robust algorithm for VT multiphase equilibrium calculations using a nested approach. The proposed algorithm is simple because a robust PT multiphase equilibrium algorithm is used in the inner loop without any further modifications, while an effective equation-solving method (i.e., Brent’s method; Brent 1971) is applied in the outer loop to solve the pressure corresponding to a given volume/temperature specification. The robustness of the VT algorithm is safeguarded by using a highly efficient trust-region-method-based PT algorithm. We demonstrate the good performance of the newly developed algorithm by applying it to calculate the isochores of fluid mixtures that exhibit both two-phase and three-phaseequilibria.

A Review of Phase Behavior Mechanisms of CO2 EOR and Storage in Subsurface Formations

“… PT and Px phase diagrams of oil sample G: (a) PT phase diagram with 70 mol % CO 2 injection; (b) Px phase diagram with CO 2 injection at 307.59 K . [Reproduced with permission from ref .…”

“…In traditional phase equilibrium calculations, Newton’s method is normally applied with the initial value provided by the successive substitution method. Although fast convergence can be reached by using these two methods, the convergence problem can frequently appear in the near-critical regions or along with the stability test limit locus . To overcome this limitation, Petitfrere and Nichita proposed a trust-region method for both stability tests and flash calculations.…”

“…Flowchart of the multiphase PT equilibrium calculation algorithm proposed by Pan et al [Reproduced with permission from ref . Copyright 2021, SPE.…”

“…Although great strides have been made in PT multiphase equilibrium calculations, robust algorithms with volume–temperature ( VT ) specifications for the CO 2 –crude oil mixture in low-temperature reservoirs are still missing until 2021. VT multiphase equilibrium calculation algorithms have proven to be computationally efficient in compositional simulations . Besides, such algorithms can be applied to help the design of storage tanks and the separation process .…”

“…Although the aforementioned methods are shown to be able to capture the phase boundaries of the CO 2 −oil mixtures, convergence problems are frequently encountered in the phase equilibria calculations. In order to avoid this problem, Petitfrere and Nichita, 145 Pan et al, 146 and Lu et al 139 developed efficient and robust algorithms for three-phase VL COd 2 L HC equilibrium calculations using the trust region method. Tens of millions of points are tested using these algorithms and not a single failure is encountered, which shows that these algorithms are robust and can be applied in compositional simulators for CO 2 injection in low-temperature reservoirs.…”