Three-phase free-water flash calculations using a new Modified Rachford–Rice equation (original) (raw)
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Multiphase equilibria for water/hydrocarbon mixtures are frequently encountered in hydrocarbon reservoirs. The presence of water in these mixtures can lead to a higher number of equilibrating phases, increasing the complexity of the multiphase split calculations. It is a common approach to treating water as the bulk free phase and performing only two-phase split calculations on the hydrocarbon-rich liquid phase and vapor phase. The free-water flash algorithm uses a different approach; it considers the effect of water presence on the overall phase equilibrium of water/hydrocarbon mixtures, albeit also assuming the aqueous phase to be pure water. The free-water algorithm might be less accurate in some cases where the solubility of methane in the aqueous phase cannot be neglected. In this study, a modified version of the free-water flash method previously developed by the authors, i.e., the so-called augmented free-water flash, is extended to perform three-phase vapor-oleic-aqueous (VOA) flash calculations for water/hydrocarbons mixtures on the basis of the assumption that only the existence of water and methane is considered in the aqueous phase. The flash package incorporating this augmented free-water method can handle the single-phase, two-phase, or three-phase equilibrium calculations. Example calculations made on two water/hydrocarbons mixtures demonstrate that the phase compositions and phase mole fractions calculated by augmented free-water method provide better predictions compared with the traditional free-water method since the solubility of methane is considered in the aqueous phase. Our new algorithm is also shown to be computationally more efficient than the conventional full three-phase flash algorithm. Therefore, the augmented free-water approach strikes a good balance between computational efficiency and prediction accuracy.
An Efficient Method to Calculate Three-Phase Free-Water Flash for Water−Hydrocarbon Systems
Industrial & Engineering Chemistry Research, 2003
Using the free-water assumption and a modified Rachford-Rice (MRR) equation proposed in this work, a novel method is developed to calculate the three-phase flash of water-hydrocarbon mixtures. In the method, the number of phases can be determined instantly, the computation is as fast as that of two-phase flash, and binary parameters between water and hydrocarbons are only optional. The efficiency of the developed method is demonstrated by its reduction to the accurate Scheffer equation, its good results for two real systems, and its favorable comparison with regular three-phase flash.
2017
In this work, we develop a robust and efficient algorithm to perform three-phase flash calculations for CO2/water/hydrocarbons mixtures on the basis of the assumption that only CO2 and water are considered in the aqueous phase. We name this new algorithm as the so-called augmented free-water flash, considering that it is a modified version of the conventional freewater flash which assumes the presence of pure water in the aqueous phase. The new algorithm is comprised of two loops: in the outer loop, we first develop a pragmatic method for initializing the equilibrium ratios of CO2 and water in the aqueous phase with respect to the reference phase (i.e., the hydrocarbon-rich liquid phase); in the inner loop, we solve the Rachford-Rice (RR) equation that has been simplified based on the augmented free-water assumption. Moreover, this new augmented free-water three-phase flash algorithm is incorporated into a flash package which can handle single-phase, two-phase, and three-phase equilibria calculations. The flash package first tests the stability of the feed. If the feed is found to be stable, a single-phase equilibrium can be concluded. Otherwise, the augmented free-water three-phase flash algorithm is initiated. If the phase fractions obtained from this augmented free-water three-phase algorithm do not belong to [0, 1] or if an open feasible region occurs during the iterations, two-phase flash will be conducted. The flash package that couples the augmented free-water flash requires less computational time and a fewer number of iterations than the conventional full three-phase flash package. Furthermore, the augmented free-water flash method has been extended to the methanecontaining hydrocarbons/water mixtures where the solubility of methane in the aqueous phase might not be negligible under certain conditions. Similarly, in the new algorithm, we only consider the presence of water and methane in the aqueous phase. The general framework of the iii flash algorithm is the same as the one that is previously developed for the CO2/hydrocarbons/water mixtures. But, we use the Wilson equation to initialize the K-values for the non-water components, but use the equation suggested by Lapene et al. (2010) to initialize the K-values for water. Two case studies have been used to test the performance of the new algorithm. The testing results show that the amount of methane dissolved in water is less than that of CO2 under the same conditions. But the solubility of methane in the aqueous phase can be also quite high at high-pressure/high-temperature conditions, justifying the use of our augmented algorithm (instead of the free-water algorithm) to perform flash computations for the methanecontaining hydrocarbons/water mixtures. The example calculations for water/hydrocarbon mixtures using the augmented free-water algorithm prove its robustness and effectiveness over a wide range of pressure and temperature. The results obtained by the augmented free-water method are more accurate than the traditional free-water method since the solubility of methane is considered in the augmented one. The computational time and number of iterations are significantly decreased with the use of the new flash package featuring the augmented algorithm. This is because of the following reasons: 1) A fewer number of parameters are involved in the calculations due to the use of the augmented free-water concept; 2) the number of iterations are reduced due to a more accurate initialization of equilibrium ratios compared with the conventional method; and 3) A fewer number of stability tests are required in the new flash package compared with the conventional method. iv ACKNOWLEDGMENTS My sincere gratitude would go first and foremost to my supervisor, Dr. Huazhou Andy Li who teaches me how to be a good researcher. Without his instruction and guidance, the present work would not have been accomplished. I'm also grateful to Dr. Zhehui Jin and Dr. Nobuo Maeda for being my examination committee members and providing constructive suggestions. My thanks would also go to my beloved parents: Mom (Fengyu Gao) and Dad (Xiangyang Pang), and my boyfriend (Jialin Shi) for their care and confidence in me. I would also wish to thank all my friends in Edmonton; their friendship is a treasure to me. In addition, I am thankful for the friendship and technical support provided by the past and present
Three-Phase Flash in Compositional Simulation Using a Reduced Method
SPE Journal, 2010
Summary CO2 flooding at low temperatures often results in three or more hydrocarbon phases. Multiphase compositional simulation must simulate such gasfloods accurately. Drawbacks of modeling three hydrocarbon phases are the increased computational time and convergence problems associated with flash calculations. Use of a reduced method is a potential solution to these problems. We first demonstrate the importance of using three-phase flash calculations in compositional simulation by investigating difficulties with two-phase equilibrium approximations proposed in the literature. We then extend an algorithm for reduced two-phase flash calculations to three-phase calculations and show the efficiency and robustness of our algorithm. The reduced three-phase flash algorithm is implemented in a multiphase compositional simulator to demonstrate the speed-up and increased robustness of simulations in various case studies. Results show that use of a two-phase equilibrium approximation in rese...
Fluid Phase Equilibria, 2012
For most phase equilibrium calculations, a non-linear function in one unknown, known as the Rachford-Rice equation for vapor-liquid equilibrium problems, needs to be solved for determining the molar fractions of the co-existing phases required for achieving the desired feed separation. Two issues appear when solving this type of equations. Firstly, the existence of as many asymptotes as the number of components present in the mixture splits these equations to a set of n − 1 branches, each one containing a different solution. Therefore, care should be taken to ensure that the obtained solution lies within the branch of interest. Secondly, conventional solution methods often exhibit slow convergence rates which is an issue when repeated solutions are required as in the case of compositional reservoir simulation and pipeline flow.
The Canadian Journal of Chemical Engineering, 1994
The paper presents a novel approach for the solution of the isothermal multiphase flash problem with particular application to systems exhibiting liquid-liquid-vapor equilibria. The approach includes a rigorous method for thermodynamic stability analysis as a first step and an efficient phase identification procedure. The stability analysis, exercised only once, uses a modification of the Gibbs tangent plane criterion. The identification procedure implements the results of the stability test in a sequence of liquid-liquid and liquid-vapor calculations only till the phase configuration with a minimum Gibbs energy is determined.
Three-phase equilibria using equations of state
AIChE Journal, 1974
It is demonstrated that a single equation of state may be used to describe all three phases in liquid-liquid-vapor equilibrium situations. Wilson's version of the Redlich-Kwong equation is shown to predict accurately the water solubility in normal paraffins with interaction parameters k12 = 0.50. A simple procedure for three-phase flash computations is presented. Results obtained using this procedure for the system methane, n-butane, water exhibit many of the characteristics of the experimental data of McKetta and Katz (1948). In particular, the water content of the vapor phase and the liquid hydrocarbon phase are accurately predicted.
A New Algorithm for Rachford-Rice for Multiphase Compositional Simulation
SPE Journal, 2010
Flash calculations for use in compositional simulation are more difficult and time-consuming as the number of equilibrium phases increases beyond two. Because of its complexity many simulators do not even attempt to incorporate three or more hydrocarbon phases even though such cases are important in many low-temperature gas floods, or for high temperatures where hydrocarbons can partition into water. Multiphase flash algorithms typically use successive substitution (SS) followed by Newton's method. For N P -phase flash calculations, (N P -1) Rachford-Rice (RR) equations are solved in every iteration step in SS, and depending on the choice of independent variables, in Newton's method. Solution of RR equations determines both compositions and amounts of phases for a fixed overall composition and set of K-values. A robust algorithm for RR is critical to obtain convergence in multiphase compositional simulation, and has not been satisfactorily developed unlike the traditional two-phase flash. In this paper, we develop an algorithm for RR equations for multiphase compositional simulation that is guaranteed to converge to the correct solution independent of the number of phases for both positive and negative flash calculations.
Two-Phase Flash for Tight Porous Media by Minimization of the Helmholtz Free Energy
Fluid Phase Equilibria, 2021
Thermodynamic modeling of phase behavior is one of the most fundamental components in the study of enhanced oil recovery by gas injection. Robust algorithms exist for multiphase equilibrium problems with no capillary pressure as commonly used in compositional reservoir simulation. However, various convergence problems have been reported even for simple two-phase split problems in the presence of capillary pressure by using the traditional algorithm based on minimization of the Gibbs free energy. In this research, the phase-split problem with capillary pressure is formulated by using the Helmholtz free energy for a given temperature and total volume. The algorithm is based on the successive substitution (SS) for updating K values, which is coupled with the volume update by using the pressure constraint equation. The robustness of the SS algorithm is improved by using the convexity information of the Helmholtz free energy. Case studies present phase-split problems with capillary pressure by using the developed algorithm and highlight several advantages of using the Helmholtz free energy over the Gibbs free energy. The improved robustness comes mainly from the involvement of a single energy surface regardless of the number of phases. The pressure variability that occurs during the phase-split calculation with capillary pressure is inherent in the Helmholtz free energy in volume space.