Study on the Application of the Tie-Line-Table-Look-Up-Based Methods to Flash Calculations in Compositional Simulations

SPE Journal ◽  
2013 ◽  
Vol 18 (05) ◽  
pp. 932-942 ◽  
Author(s):  
Wei Yan ◽  
Abdelkrim Belkadi ◽  
Michael L. Michelsen ◽  
Erling H. Stenby
Keyword(s):  
Computation Time ◽  
Phase Region ◽  
General Situation ◽  
Shadow Region ◽  
Two Phase ◽  
Feed Composition ◽  
Simulation Speed ◽  
Recent Approach ◽  
Tie Lines ◽  
Tie Line

Summary Flash calculation can be a time-consuming part in compositional reservoir simulations, and several approaches have been proposed to speed it up. One recent approach is the shadow-region method that reduces the computation time mainly by skipping stability analysis for a large portion of the compositions in the single-phase region. In the two-phase region, a highly efficient Newton-Raphson algorithm can be used with the initial estimates from the previous step. Another approach is the compositional-space adaptive-tabulation (CSAT) approach, which is based on tie-line table look-up (TTL). It saves computation time by replacing rigorous phase-equilibrium calculations with the stored results in a tie-line table whenever the new feed composition is on one of the stored tie-lines within a certain tolerance. In this study, a modified version of CSAT, named the TTL method, has been proposed to investigate if approximation by looking up a tie-line table can save flash-computation time in the two-phase region. The number of tie-lines stored for comparison and the tolerance set for accepting the feed composition are the key parameters in this method because they will influence the simulation speed and the accuracy of simulation results. We also proposed the tie-line distance-based approximation (TDBA) method, an alternative method to TTL, to obtain approximate flash results in the two-phase region. The method uses the distance to a previous tie-line in the same grid-block to determine whether the approximation should be made. Comparison between the shadow-region approach and the approximation approach, including TTL and TDBA, has been made with a slimtube simulator by which the simulation temperature and the simulation pressure are set constant. It is shown that TDBA can significantly improve the speed in the two-phase region. In contrast, TTL, even with a precalculated tie-line table, is not so advantageous compared with an efficient implementation of rigorous flash. Furthermore, we implemented TDBA in a compositional streamline simulator to apply TDBA to scenarios with pressure variation across the reservoir. We also discussed how to extend TDBA to the general situation in which pressures in grid-blocks are updated dynamically.

Analytical Solutions for Gas Displacements With Bifurcating Phase Behavior

SPE Journal ◽  
2014 ◽  
Vol 19 (05) ◽  
pp. 943-955 ◽  
Author(s):  
Saeid Khorsandi ◽  
Kaveh Ahmadi ◽  
Russell T. Johns
Keyword(s):  
Phase Behavior ◽  
Analytical Solutions ◽  
Phase Region ◽  
Co2 Injection ◽  
Two Phase ◽  
Complex Phase ◽  
Three Phase ◽  
Tie Lines ◽  
Tie Line ◽  
Composition Path

Summary Minimum miscibility pressure (MMP) is one of the most important parameters in the design of a successful gasflooding process. The most-reliable methods to calculate the MMP are based on slimtube experiments, 1D slimtube simulations, mixing-cell calculations, and the analytical methods known as the method of characteristics (MOC). The calculation of MMP by use of MOC is the fastest method because it relies solely on finding the key tie lines in the displacement path. The MOC method for MMP estimation in its current form assumes that the composition path is a series of shocks from one key tie line to the next. For some oils, however, these key tie lines do not control miscibility, and the MMP calculated by use of the key-tie line approach can be significantly in error. The error can be as high as 5,000 psia for heavier oils or CO2 displacements at low temperature in which three-phase hydrocarbon regions can exist (L1–L2–V). At higher pressures, the two- or three-phase region can split (or bifurcate) into two separate two-phase regions (L1–L2 and L1–V regions). Thus, for the MMP calculation from MOC to be correct, we must calculate the entire composition path for this complex phase behavior, instead of relying on the shock assumption from one key tie line to the next. In this paper, the MOC-composition route is developed completely for the bifurcating phase-behavior displacement for pure CO2 injection by use of a simplified pseudoternary system that is analogous to the complex phase behavior observed for several real displacements with CO2. We develop the MOC analytical solutions by honoring all constraints required for a unique solution—velocity, mass balance, entropy, and solution continuity. The results show that a combination of shocks and rarefaction waves exists along the nontie-line path, unlike previous MOC solutions reported to date. We show that by considering the entire composition path, not just the key tie lines, the calculated MMP agrees with the mixing-cell method. We also show that, in this complex ternary displacement, the displacement mechanism has features of a both condensing and vaporizing (C/V) drive, which was thought to be possible only for gasfloods with four or more components. For pure CO2 injection, the solution also becomes discontinuous for oils that lie on the tie line envelope curve. Finally, we show that shock paths within the two-phase region are generally curved in composition space and that there is no MMP for some oil compositions considered in the displacements by CO2. Recovery can be large even though the MMP is not reached.

Liquid-Liquid Equilibria for Acetone + Several Citrates Aqueous Two-Phase Systems at Different Temperatures

2012 ◽  
Vol 549 ◽  
pp. 30-35
Author(s):  
Shi Ping Hu ◽  
Juan Han ◽  
Yong Sheng Yan ◽  
Yu Tao Hu
Keyword(s):  
Ternary Systems ◽  
Data Fitting ◽  
Potassium Citrate ◽  
Liquid Equilibrium ◽  
Two Phase ◽  
Different Temperatures ◽  
Tie Lines ◽  
Aqueous Two Phase Systems ◽  
Phase Systems ◽  
Tie Line

Liquid-liquid equilibria for the three kinds of the ternary systems acetone + ammonium, sodium or potassium citrate + water have been determined at T= (273.15, 283.15, and 298.15) K. Binodal curves, tie-lines, and integrated phase diagrams for the ternary systems are given. The data of the experimental bimodal curve are described with a four-parameter equation. The result also shows the temperature has little influence on the liquid-liquid equilibrium within the investigated range. The tie-line data calculated according to the bimodal data fitting equation and the lever arm rule were satisfactorily described by using the Othmer-Tobias and Bancroft equations, and the result conform the reliability of the calculation method and corresponding tie-line data.

The f.c.c.+tetragonal two-phase region of the Cu–Ni–Zn system

1983 ◽  
Vol 16 (1) ◽  
pp. 99-102 ◽  
Author(s):  
O. S. Mayall
Keyword(s):  
Tetragonal Phase ◽  
Lattice Spacing ◽  
Single Phase ◽  
Phase Region ◽  
Unit Cell ◽  
Unit Cell Parameters ◽  
Two Phase ◽  
Cell Parameters ◽  
Tie Lines

The f.c.c. + tetragonal two-phase region of the Cu–Ni–Zn system has been delineated, and unit-cell parameters along the boundaries determined. Apparently anomalous parameter measurements prevented the determination of the tie lines. A pattern of diffraction broadening from the tetragonal phase common to both the two-phase and single-phase regions was related to the variation in lattice spacing of the tetragonal phase along the boundary. Reasons for this broadening are discussed.

Tie Simplex Based Parameterization for Compositional Reservoir Simulation

2008 ◽  
Author(s):  
Denis Voskov ◽  
Hamdi A. Tchelepi
Keyword(s):  
Method Of Characteristics ◽  
Flow Simulation ◽  
Deep Understanding ◽  
General Purpose ◽  
Two Phase ◽  
Compositional Flow ◽  
Reservoir Flow ◽  
Tie Lines ◽  
Solution Route ◽  
Tie Line

In this work, we generalize the Compositional Space Parameterization (CSP) approach, which was originally developed for compositional two-phase reservoir flow simulation. Tie-line based parameterization methods [1]–[3] were motivated by insights obtained from MOC (Method of Characteristics) theory. The MOC based analytical theory [4] has provided deep understanding of the interactions between thermodynamics and flow. In our adaptive framework, tie-lines are used to represent the solution route of multi-component multiphase displacements. The tie-line information is used as a preconditioner for EOS computations in general-purpose compositional flow simulation.

scholarly journals Ternary Phase Diagram of Model Dentin Adhesive Exposed to Over-wet Environments

2011 ◽  
Vol 90 (12) ◽  
pp. 1434-1438 ◽  
Author(s):  
Q. Ye ◽  
J. Park ◽  
J.S. Laurence ◽  
R. Parthasarathy ◽  
A. Misra ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Ternary Phase Diagram ◽  
Water System ◽  
Phase Region ◽  
Partial Phase Diagram ◽  
Conjugate Pair ◽  
Two Phase ◽  
Phase Partitioning ◽  
Equilibrium Partition ◽  
Tie Lines

When adhesives and/or composites are bonded to the tooth, water in the environment can interfere with proper interface formation. Formation of water blisters and phase separation at the adhesive/dentin interface have appeared as new types of bond defects. To better understand this problem, we determined the near-equilibrium partition of the hydrophobic/hydrophilic components when exposed to over-wet environments. Model methacrylate-based adhesives were mixed with different amounts of water to yield well-separated aqueous and resin phases. It was found that less than 0.1% BisGMA but nearly one-third of the HEMA diffused into the aqueous phase, leaving the remaining resin phase relatively hydrophobic. A partial phase diagram was created for the ternary BisGMA/HEMA/water system. All the experimental phase partitioning data were plotted, and the points lay on a binodal curve that separated the single-phase region from the two-phase region. We obtained the 3 tie lines by connecting the 2 points of each conjugate pair of the phase partitioning data from the 3 sets of tripartite mixtures. Information about solubility, water miscibility, distribution ratio, and phase partitioning behavior could be obtained quantitatively. This type of phase diagram will provide a more thorough understanding of current adhesive performance and elucidate directions for further improvement.

Reaction Sintering of β-Si3N4/α'-Sialon Ceramics

1992 ◽  
Vol 287 ◽  
Author(s):  
S. Boskovic ◽  
K.J. Lee ◽  
T.Y. Tien
Keyword(s):  
Solid Solution ◽  
Applied Pressure ◽  
Phase Region ◽  
Reaction Sintering ◽  
Two Phase ◽  
Sintering Aid ◽  
Third Phase ◽  
Solid Solution Region ◽  
Tie Lines ◽  
Solution Region

ABSTRACTCompositions in the α'-SiAlON-√-Si3N4 solid solution region in the system Si,Al,Y/N,O which contained a third phase as a sintering aid were prepared. Mixtures of starting materials were reaction sintered to full densities without applied pressure. Phases were identified and lattice parameters of β' and √ph ases were measured and compared with standards. The results were used to construct β'-SiAION-√-Si3N4 solidsolution tie lines in the two phase region. As expected, the specimens with a higher β'-SiAION content showed higher hardness and lower toughness values.

Tie lines in a two-phase region in the Cu–Ni–Zn system

1979 ◽  
Vol 12 (4) ◽  
pp. 360-364 ◽  
Author(s):  
O. S. Mayall ◽  
A. Mathew
Keyword(s):  
Phase Region ◽  
Two Phase ◽  
Tie Lines

Interface Stability of Ti(Sil−yGey)2 and Si1−x Gex Alloys

1995 ◽  
Vol 402 ◽  
Author(s):  
D. B. Aldrich ◽  
F. M. D'Heurle ◽  
D. E. Sayers ◽  
R. J. Nemanich
Keyword(s):  
Solid Solution ◽  
Solid Phase ◽  
Equilibrium Diagram ◽  
Two Phase ◽  
Germanium Content ◽  
Tie Lines ◽  
Two Phases ◽  
Silicon And Germanium ◽  
Classical Thermodynamics ◽  
Tie Line

AbstractThe stability of C54 Ti(Si1−yGey)2 films in contact with Si1−xGex substrates was investigated. The titanium germanosilicide films were formed from the Ti − Si1−xGex solid phase metallization reaction. It was observed that Ti(Si1−yGey) 2 initially forms with the same germanium content as the Si1−x Gex substrate (i.e., y = x). Following the initial formation of TiM2 (M = Sil−yGey), silicon and germanium from the substrate diffuse into the TiM2 layer, the composition of the TiM2 changes, and Si1−z Gez precipitates form along the TiM2 grain boundaries. The germanium content of the Ti(Sil−y Gey)2 decreases, and the Sil−z Gez precipitates are germanium rich such that y < x < z. This instability of the TiM2 film and the dynamics of the germanium segregation were examined using the Ti-Si-Ge ternary equilibrium diagram. The relevant region of the ternary diagram is the two phase domain limited by a Si-Ge solid solution and a TiSi2 − TiGe2 solid solution. In this study first approximation Ti(Sil−y Gey)2 -to- Sil−xGex tie lines were calculated on the basis of classical thermodynamics. The tie line calculations indicate that for C54 Ti(Sil−yGey)2 to be stable in contact with Sil−xGex, the compositions of the two phases in equilibrium must be such that y < x. The specific compositions of the two phases in equilibrium depend on the temperature and the relative quantities of the two phases. The dynamic processes by which the Ti(Si1−yGey)2/Si1−x. Gex, system progresses from the as-formed state (y = x) to the equilibrium state (y < x) can be predicted using the tie line calculations.

Solution Properties and Phase Behavior of Ammonium Hexylene Octyl Succinate in Water and Water-Oil System

1970 ◽  
Vol 3 (1) ◽  
Author(s):  
Md. Hamidul Kabir ◽  
Ravshan Makhkamov ◽  
Shaila Kabir
Keyword(s):  
Critical Micelle Concentration ◽  
Phase Behavior ◽  
Liquid Crystalline ◽  
Carbon Number ◽  
Phase Region ◽  
Solution Properties ◽  
Middle Phase ◽  
Two Phase ◽  
Lamellar Liquid Crystal ◽  
Drug Ingredient

The solution properties and phase behavior of ammonium hexylene octyl succinate (HOS) was investigated in water and water-oil system. The critical micelle concentration (CMC) of HOS is lower than that of anionic surfactants having same carbon number in the lipophilic part. The phase diagrams of a water/ HOS system and water/ HOS/ C10EO8/ dodecane system were also constructed. Above critical micelle concentration, the surfactant forms a normal micellar solution (Wm) at a low surfactant concentration whereas a lamellar liquid crystalline phase (La) dominates over a wide region through the formation of a two-phase region (La+W) in the binary system. The lamellar phase is arranged in the form of a biocompatible vesicle which is very significant for the drug delivery system. The surfactant tends to be hydrophilic when it is mixed with C10EO8 and a middle-phase microemulsion (D) is appeared in the water-surfactant-dodecane system where both the water and oil soluble drug ingredient can be incorporated in the form of a dispersion. Hence, mixing can tune the hydrophile-lipophile properties of the surfactant. Key words: Ammonium hexylene octyl succinate, mixed surfactant, lamellar liquid crystal, middle-phase microemulsion. Dhaka Univ. J. Pharm. Sci. Vol.3(1-2) 2004 The full text is of this article is available at the Dhaka Univ. J. Pharm. Sci. website

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