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.

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.

Mechanisms for High Displacement Efficiency of Low-Temperature CO2 Floods

SPE Journal ◽  
2011 ◽  
Vol 16 (04) ◽  
pp. 751-767 ◽  
Author(s):  
R.. Okuno ◽  
R.T.. T. Johns ◽  
K.. Sepehrnoori
Keyword(s):  
Low Temperature ◽  
Phase Behavior ◽  
Phase Region ◽  
Displacement Efficiency ◽  
Two Phase ◽  
Fixed Temperature ◽  
Three Phase ◽  
Minimum Number ◽  
Rich Liquid ◽  
Reservoir Simulator

Summary CO2 floods at temperatures typically below 120°F can involve complex phase behavior, where a third CO2-rich liquid (L2) phase coexists with the oleic (L1) and gaseous (V) phases. Results of slimtube measurements in the literature show that an oil displacement by CO2 can achieve high displacement efficiency of more than 90% when three hydrocarbon phases coexist during the displacement. However, the mechanism for the high-displacement efficiency is uncertain because the complex interaction of phase behavior with flow during the displacement is not fully understood. In this paper, we present the first detailed study of three-phase behavior predictions and displacement efficiency for low-temperature CO2 floods. Four-component EOS models are initially used to investigate systematically the effects of pressure, temperature, and oil properties on development of three-phase regions and displacement efficiency. Multicomponent oil displacements by CO2 are then considered. We use a compositional reservoir simulator capable of robust three-phase equilibrium calculations. Results show that high displacement efficiency of low-temperature CO2 floods is a consequence of both condensing and vaporizing behavior. The L2 phase serves as a buffer between the immiscible V and L1 phases within the three-phase region. Components in the L1 phase first transfer efficiently to the L2 phase near a lower critical endpoint (LCEP). These oil components then transfer to the V phase near an upper critical endpoint (UCEP) at the trailing edge of the three-phase region. The CEPs are defined where two of the three coexisting phases merge in the presence of the other immiscible phase. Unlike two-phase displacements, condensation and vaporization of intermediate components occur simultaneously within the three-phase region. The simultaneous condensing/vaporizing behavior involving the CEPs is also confirmed for simulations of several west Texas oil displacements. Quaternary fluid models can predict qualitatively the complex displacements because four is the minimum number of components to develop CEP behavior in composition space at a fixed temperature and pressure.

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

Phase Equilibrium of Mg-Nd-Zn System near Mg-Nd Side at 400°C

2016 ◽  
Vol 873 ◽  
pp. 18-22
Author(s):  
Ming Li Huang ◽  
Xue Shen ◽  
Hong Xiao Li
Keyword(s):  
Solid Solution ◽  
Phase Equilibrium ◽  
Ternary Isothermal Section ◽  
Phase Region ◽  
X Ray Diffraction ◽  
Maximum Solubility ◽  
Two Phase ◽  
Solubility Range ◽  
Three Phase ◽  
Equilibrium Alloys

The equilibrium alloys closed to Mg-Nd side in the Mg-rich corner of the Mg-Zn-Nd system at 400°C have been investigated by scanning electron microscopy, electron probe microanalysis and X-ray diffraction. The binary solid solutions Mg12Nd and Mg3Nd with the solubility of Zn have been identified. The maximum solubility of Zn in Mg12Nd is 4.8at%, and Mg12Nd phase can be in equilibrium with Mg solid solution. However, only when the solubility range of Zn in 26at%~32.2at%, Mg3Nd can be in two-phase equilibrium with Mg solid solution. As the results, two two-phase regions as Mg+Mg12Nd and Mg+Mg3Nd and a three-phase region as Mg+Mg12Nd+Mg3Nd in Mg-Nd-Zn ternary isothermal section at 400°C have been identified.

Influence of Compressed Carbon Dioxide on the Oxidation of Cyclohexane with Hydrogen Peroxide in Acetic Acid

2006 ◽  
Vol 59 (3) ◽  
pp. 225 ◽  
Author(s):  
Liang Gao ◽  
Tao Jiang ◽  
Buxing Han ◽  
Baoning Zong ◽  
Xiaoxin Zhang ◽  
...  
Keyword(s):  
Carbon Dioxide ◽  
Hydrogen Peroxide ◽  
Acetic Acid ◽  
Binary System ◽  
Reaction System ◽  
Phase Region ◽  
Phase Behaviour ◽  
Phase System ◽  
Two Phase ◽  
Three Phase

The oxidation of cyclohexane with H2O2 in a compressed CO2/acetic acid binary system was studied at 60.0 and 80.0°C, at pressures up to 18 MPa, and with the zeolite TS-1 as catalyst. The phase behaviour of the reaction system was also observed. There are three fluid phases in the reaction system at lower pressure but two at higher pressures. In the three-phase region the yields of the products, cyclohexanol and cyclohexanone, increase considerably with increasing pressure and reaches a maximum near the phase-separating pressure. CO2 can thus enhance the reaction effectively. However, the effect of pressure on the yield is very limited after the transition to a two-phase system.

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.

Phase-Behavior Properties of CO2 - Reservoir Oil Systems

1978 ◽  
Vol 18 (01) ◽  
pp. 20-26 ◽  
Author(s):  
Ralph Simon ◽  
A. Rosman ◽  
Erdinc Zana
Keyword(s):  
Interfacial Tension ◽  
Phase Behavior ◽  
Single Phase ◽  
Phase Region ◽  
Experimental Phase ◽  
Two Phase ◽  
Co2 Concentrations ◽  
Liquid Phases ◽  
Compositional Simulator ◽  
To Come

February 1978 Original manuscript received in Society of Petroleum Engineers office Jan. 14, 1977. Paper accepted for publication Aug. 15, 1977. Revised manuscript received Sept. 21, 1977. Paper (SPE 6387) was presented at the SPE-AIME Permian Basin Oil and Gas Recovery Conference, held in Midland, Tex., March 10-11, 1977. Abstract This paper presents experimental phase behavior data on two CO2-reservoir oil systems at reservoir pressures and temperatures. pressures and temperatures. The data includepressure-composition diagrams with bubble points, dew points, and critical points;vapor-liquid equilibrium compositions and related K values;vapor and liquid densities compared with values calculated by the Redlich-Kwong equation of state;vapor and liquid viscosities compared with predictions by the Lobrenz-Bray-Clark correlation; andinterfacial tensions for six vapor-liquid mixtures compared with values calculated by the Weinaug-Katz parachor equation. These and other published data contribute to development of the generalized correlations needed by reservoir and production engineers for evaluating, designing, and efficiently operating CO2-injection projects. projects Introduction This paper presents experimental phase behavior data for two CO2-reservoir oil systems. These data are used in predicting the performance of CO2 floods with a compositional simulator. The simulator calculates vapor and liquid compositions, densities, viscosities, and interfacial tensions to describe the phase behavior as the injected CO2 advances through phase behavior as the injected CO2 advances through the reservoir. The simulator predictions are used to evaluate proposed projects and to design and efficiently operate approved ones. The data in this paper consist of pressure-composition diagrams with bubble points, pressure-composition diagrams with bubble points, dew points, and critical points; and compositions, densities, viscosities, and interfacial tensions of vapors and liquids in equilibrium in the two-phase region. These data were obtained by the experimental procedure shown in Fig. 1. procedure shown in Fig. 1. We have compared our measured data with values calculated by existing methods: Redlich-Kwong equation for densities, Lohrenz-Bray-Clark correlation for viscosities, and the Weinaug-Katz parachor equation for interfacial tension. We found parachor equation for interfacial tension. We found that these published methods give acceptable agreement in some areas, but in general, they are not satisfactory for engineering purposes. Therefore, we conclude that improved calculation methods are needed for CO2 systems. For the special case of compositional simulator applications, we devised a technique for obtaining satisfactory calculated density, viscosity, and interfacial tension values. This technique is discussed in the section on "Measurements vs Calculations." We believe that our data, along with previously published information and information yet to come, published information and information yet to come, will advance the development of satisfactory correlations, thus reducing the need for extensive laboratory studies of individual systems. PRESSURE-COMPOSITION DIAGRAMS PRESSURE-COMPOSITION DIAGRAMS OIL A Ten mixtures of CO2 and Reservoir Oil A were prepared. These mixtures contained CO2 concentrations prepared. These mixtures contained CO2 concentrations of 0, 20, 40, 55, 60, 65. 70, 75, 80, and 90 mol percent. At 130 degrees F, pressure traverses were made with each mixture. These traverses started in the single-phase region at a pressure above the bubble (or dew) points and lowered the pressure in discrete steps, passing from the single-phase into the two-phase region. At each step, the vapor and liquid volumes were measured. The results are described in Fig. 2A. At 130 degrees F, the critical point of the CO2-Reservoir Oil A system (where intensive properties of the gas and liquid phases were equal) properties of the gas and liquid phases were equal) is 2,570 psia and 60-mol percent CO2. OIL B Eight mixtures of CO2 and Reservoir Oil B also were prepared and studied in the visual cell at 255 degrees F. CO2 concentrations for these mixtures were 0, 20, 40, 55, 65, 75, 80, and 85 mol percent. The pressure was varied from 800 to 6,100 psia, and the pressure was varied from 800 to 6,100 psia, and the relative vapor and liquid volumes measured. The results are given in Fig. 2B. The critical point of the CO2-Reservoir Oil B system at 255 degrees F is 4,890 psia and 74-mol percent CO2. psia and 74-mol percent CO2. SPEJ P. 20

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.

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