Limitations of Current Method-of-Characteristics (MOC) Methods Using Shock-Jump Approximations To Predict MMPs for Complex Gas/Oil Displacements

SPE Journal ◽  
2011 ◽  
Vol 16 (04) ◽  
pp. 743-750 ◽  
Author(s):  
Kaveh Ahmadi ◽  
Russell T. Johns ◽  
Kristian Mogensen ◽  
Rashed Noman
Keyword(s):  
Method Of Characteristics ◽  
Current Method ◽  
Gas Oil ◽  
Cell Models ◽  
Key Factors ◽  
Minimum Miscibility Pressure ◽  
Tie Lines ◽  
Reliable Methods ◽  
Tie Line ◽  
Shock Jump

Summary An accurate minimum miscibility pressure (MMP) is one of the key factors in miscible-gasflood design. There is a variety of experimental and analytical methods to determine the MMP, but the most-reliable methods are slimtube experiments, 1D slimtube simulations, mixing-cell models, and the fast key-tie-line approach using the method of characteristics (MOC). Direct comparisons of all these methods generally agree well, but there are cases in which they do not. No explanation has yet been given for these anomalies, although the MMP is critically important to recovery. The focus of this paper is to explain when current MOC results assuming that shocks exist from one key tie line to the next may not be reliable, and how to identify when this is the case. We demonstrate, using fluid characterizations from Middle East oils, that the MMPs using this MOC method can be more than 6,500 psia greater than those calculated using a recently developed mixing-cell method. The observed differences in the MMP increase substantially as the API gravity of the oil decreases, likely the result of the onset of L1-L2-V behavior. We show that the key tie lines determined using this MOC method do not control miscibility for such cases. We explain the reasons for these differences using simplified pseudoternary models and show how to determine when an error exists. We also offer a way to correct the MMP predictions using the MOC for these complex gas/oil displacements without solving for the complete compositional path.

Effect of Gas/Oil Capillary Pressure on Minimum Miscibility Pressure for Tight Reservoirs

SPE Journal ◽  
2019 ◽  
Vol 25 (02) ◽  
pp. 820-831 ◽  
Author(s):  
Kaiyi Zhang ◽  
Bahareh Nojabaei ◽  
Kaveh Ahmadi ◽  
Russell T. Johns
Keyword(s):  
Capillary Pressure ◽  
Hyperbolic Equations ◽  
Fluid Pressure ◽  
Gas Oil ◽  
Minimum Miscibility Pressure ◽  
Tight Reservoir ◽  
Tie Lines ◽  
Tight Reservoirs ◽  
Shale Reservoirs ◽  
The Impact

Summary Shale and tight reservoir rocks have pore throats on the order of nanometers, and, subsequently, a large capillary pressure. When the permeability is ultralow (k < 200 nd), as in many shale reservoirs, diffusion might dominate over advection, so that the gas injection might no longer be controlled by the multicontact minimum miscibility pressure (MMP). For gasfloods in tight reservoirs, where k > 200 nd and capillary pressure is still large, however, advection likely dominates over diffusive transport, so that the MMP once again becomes important. This paper focuses on the latter case to demonstrate that the capillary pressure, which has an impact on the fluid pressure/volume/temperature (PVT) behavior, can also alter the MMP. The results show that the calculation of the MMP for reservoirs with nanopores is affected by the gas/oil capillary pressure, owing to alteration of the key tie lines in the displacement; however, the change in the MMP is not significant. The MMP is calculated using three methods: the method of characteristics (MOC); multiple mixing cells; and slimtube simulations. The MOC method relies on solving hyperbolic equations, so the gas/oil capillary pressure is assumed to be constant along all tie lines (saturation variations are not accounted for). Thus, the MOC method is not accurate away from the MMP but becomes accurate as the MMP is approached when one of the key tie lines first intersects a critical point (where the capillary pressure then becomes zero, making saturation variations immaterial there). Even though the capillary pressure is zero for this key tie line, its phase compositions (and, hence, the MMP) are impacted by the alteration of all other key tie lines in the composition space by the gas/oil capillary pressure. The reason for the change in the MMP is illustrated graphically for quaternary systems, in which the MMP values from the three methods agree well. The 1D simulations (typically slimtube simulations) show an agreement with these calculations as well. We also demonstrate the impact of capillary pressure on CO2-MMP for real reservoir fluids. The effect of large gas/oil capillary pressure on the characteristics of immiscible displacements, which occur at pressures well below the MMP, is 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.

Improved Multiple-Mixing-Cell Method for Accelerating Minimum Miscibility Pressure Calculations

SPE Journal ◽  
2019 ◽  
Vol 25 (04) ◽  
pp. 1681-1696 ◽  
Author(s):  
Haining Zhao ◽  
Zhengbao Fang
Keyword(s):  
Search Algorithm ◽  
Mixing Ratio ◽  
Gas Oil ◽  
Two Phase ◽  
Minimum Miscibility Pressure ◽  
Multiple Mixing ◽  
Calculation Process ◽  
Successive Substitution ◽  
Tie Line ◽  
Pressure Estimate

Summary An improved algorithm for accelerating minimum miscibility pressure (MMP) computation using the multiple-mixing-cell (MMC) methods is presented. The MMC method is widely used to accurately calculate the MMP. In this study, we proposed an acceleration algorithm toward original MMC method to directly locate the shortest key tie-line (TL) after a certain amount of contacts through the adjustment of the gas/oil mixing ratio during the calculation process. The algorithm contains the following key components: (1) mixing cell cutoff strategy to avoid unnecessary flash calculations; (2) gas/oil mixing ratio adjustment to prevent lost information on the shortest key TL during the cell cutoff process; (3) a search algorithm for pressure to improve the next step pressure estimate; (4) the fast and reliable two-phase flash implementation by combining full Newton method with recently proposed iteration variables and conventional successive substitution method. The improved MMC model is shown to be faster than the original MMC method in computing MMP.

Application of Multiple-Mixing-Cell Method To Improve Speed and Robustness of Compositional Simulation

SPE Journal ◽  
2015 ◽  
Vol 20 (03) ◽  
pp. 565-578 ◽  
Author(s):  
Mohsen Rezaveisi ◽  
Russell T. Johns ◽  
Kamy Sepehrnoori
Keyword(s):  
Phase Equilibrium ◽  
Gas Injection ◽  
Computational Time ◽  
Simulation Methods ◽  
K Value ◽  
Acceptable Accuracy ◽  
Multiple Mixing ◽  
Tie Lines ◽  
Tie Line ◽  
Equilibrium Calculations

Summary Standard equation-of-state-based phase equilibrium modeling in reservoir simulators involves computationally intensive and time-consuming iterative calculations for stability analysis and flash calculations. Therefore, speeding up stability analysis and flash calculations and improving robustness of the calculations are of utmost importance in compositional reservoir simulation. Prior knowledge of the tie-lines traversed by the solution of a gas-injection problem translates into valuable information with significant implications for speed and robustness of reservoir simulators. The solution of actual-gas-injection processes follows a very complex route because of dispersion, pressure variations, and multidimensional flow. The multiple-mixing-cell (MMC) method, originally developed to calculate minimum miscibility pressure of a gas-injection process, accounts for various levels of mixing of the injected gas and initial oil. This observation suggests that the MMC tie-lines developed upon repeated contacts may represent a significant fraction of the actual simulation tie-lines encountered. We investigate this idea and use three tie-line-based K-value-simulation methods for application of MMC tie-lines in reservoir simulation. In two of the tie-line-based K-value-simulation methods, we examine tabulation and interpolation of MMC tie-lines in a framework similar to the compositional-space adaptive-tabulation (CSAT) method. In the third method, we perform K-value simulations based on inverse-distance interpolation of K-values from MMC tie-lines. We demonstrate that for the displacements examined, the MMC tie-lines are sufficiently close to the actual simulation tie-lines and provide excellent coverage of the simulation compositional route. The MMC-based methods are then compared with the computational time by use of other methods of phase-equilibrium calculations, including a modified application of CSAT (an adaptive tie-line-based K-value simulation), a method using only heuristic techniques, and the standard method in an implicit-pressure/explicit-concentration-type reservoir simulator. The results show that tabulation and interpolation of MMC tie-lines significantly improve phase equilibrium and computational time compared with the standard approach, with acceptable accuracy. The results also show that computational performance of the MMC-based methods with only prior tie-line tables is very close to that of CSAT, which requires flash calculations during simulation. The K-value simulations by use of MMC-based tie-line-interpolation methods improve the total computational time up to 51% in the cases studied, with acceptable accuracy. The results suggest that MMC tie-lines represent a significant fraction of the actual tie-lines during simulation and can be used to significantly improve speed and robustness of phase-equilibrium calculations in reservoir simulators.

Sensor-free and Sensor-based Heart-on-a-chip Platform: A Review of Design and Applications

2019 ◽  
Vol 24 (45) ◽  
pp. 5375-5385 ◽  
Author(s):  
Hao Wan ◽  
Chenlei Gu ◽  
Ying Gan ◽  
Xinwei Wei ◽  
Kai Zhu ◽  
...  
Keyword(s):  
Drug Efficacy ◽  
Recent Decade ◽  
Toxicity Assessment ◽  
Cell Models ◽  
Basic Definition ◽  
Key Factors ◽  
Human Organs ◽  
New Perspective ◽  
Approved Drugs ◽  
Human Specific

Drug efficacy and toxicity are key factors of drug development. Conventional 2D cell models or animal models have their limitations for the efficacy or toxicity assessment in preclinical assays, which induce the failure of candidate drugs or withdrawal of approved drugs. Human organs-on-chips (OOCs) emerged to present human-specific properties based on their 3D bioinspired structures and functions in the recent decade. In this review, the basic definition and superiority of OOCs will be introduced. Moreover, a specific OOC, heart-on-achip (HOC) will be focused. We introduce HOC modeling in the sensor-free and sensor-based way and illustrate the advantages of sensor-based HOC in detail by taking examples of recent studies. We provide a new perspective on the integration of HOC technology and biosensing to develop a new sensor-based HOC platform.

Equilibrium tie-line in PrOy–BaO–CuO ternary phase diagram around peritectic temperature of Pr1+xBa2−xCu3O7−δ

1998 ◽  
Vol 13 (1) ◽  
pp. 118-125 ◽  
Author(s):  
Minoru Tagami ◽  
Makoto Kambara ◽  
Takateru Umeda ◽  
Yuh Shiohara
Keyword(s):  
Phase Diagram ◽  
Ternary Phase ◽  
Ternary Phase Diagram ◽  
Peritectic Temperature ◽  
Air Atmosphere ◽  
Epma Analysis ◽  
Tie Lines ◽  
Growth Method ◽  
Quantitative Epma ◽  
Tie Line

This paper presents tie-lines between Pr1+xBa2−xCu3O7−δ and liquid on a PrOy –BaO–CuO ternary phase diagram at 965, 970, 975, 980, and 990 °C in air atmosphere, for which knowledge is necessary to fabricate composition controlled Pr1+xBa2−xCu3O7−δ single crystals by the solution growth method. Liquidus faces have been investigated by dipping MgO single crystal rods into the thermal equilibrium melt at various temperatures and analyzing the composition of the adhering melt by ICP. The compositions of Pr1+xBa2−xCu3O7−δ solid solution coexisting with various compositions of liquids were obtained by quantitative EPMA analysis of quenched melts. Tie-lines were calculated by applying the lever rule to these experimental data for solid compositions and liquidus faces. Furthermore, the relationships between solid solubilities and peritectic temperatures of Pr1+xBa2−xCu3O7−δ are reported.

Ternary mixtures of phosphonium ionic liquids + organic solvents + water

2008 ◽  
Vol 80 (6) ◽  
pp. 1325-1335 ◽  
Author(s):  
Shahana A. Chowdhury ◽  
Janet L. Scott ◽  
Douglas R. MacFarlane
Keyword(s):  
Ionic Liquids ◽  
Organic Solvents ◽  
Ternary Phase ◽  
Single Phase ◽  
Ternary Mixtures ◽  
Green Solvents ◽  
Ternary Phase Diagrams ◽  
Tie Lines ◽  
Extraction Processes ◽  
Tie Line

Ionic liquids (ILs) and water are both potentially green solvents that are useful in a variety of extraction processes. This report presents the ternary phase diagrams and tie-line data of trihexyl(tetradecyl)phosphonium dicyanamide [P6,6,6,14][DCA], phosphonium bis(2,4,4-trimethylpentyl)phosphinate [P6,6,6,14][((CH3)3C5H8)2PO2], and 1-ethyl-3-methylimidazolium ethylsulfate [emim][C2H5SO4] ILs in organic solvents (ethanol, acetonitrile, toluene) and water. [P6,6,6,14][DCA] and [P6,6,6,14][((CH3)3C5H8)2PO2] tended to yield emulsions when combined with water and ethanol, while [emim][C2H5SO4] combined with toluene and water provided two clear phases of reasonable viscosity. The compositions of the ternary mixtures were determined to obtain the tie-lines. A noticeable difference was observed for the tie-lines of the same IL (e.g., [P6,6,6,14][DCA]) with different organic solvents (ethanol and acetonitrile) and water mixtures. In all cases, the addition of ethanol eventually produced a single phase.

scholarly journals III. On certain ternary alloys. Part V. Determination of various critical curves, and their tie-lines and limiting points

1892 ◽  
Vol 50 (302-307) ◽  
pp. 372-395 ◽  
Keyword(s):  
Graphical Representation ◽  
Conjugate Point ◽  
Critical Curve ◽  
Ternary Mixtures ◽  
Ternary Alloys ◽  
Conjugate Points ◽  
Critical Curves ◽  
Tie Lines ◽  
Tie Line

The triangular method of graphical representation suggested by Sir G. G. Stokes, and described in Part IV (‘Roy. Soc. Proc.,’ vol. 49, p. 174), substantially amounts to the tracing out of a curve (“ critical curve”) which shall express the saturation of the solvent C with a mixture in given variable proportions of the other two constituents, A, B ; the variation being such that any given point on the curve is related to some other point (“ conjugate point ”) in a way given by the consideration that all mixtures of the three constituents, A, B, C, represented by points lying on the line (“ tie-line ”) joining these two conjugate points (“ ideal ” alloys, or mixtures), will separate into two different ternary mixtures corresponding with the two points respectively ; whereas any mixture of the same constituents, repre­sented by a point lying outside the critical curve, will form a “ real ” alloy, or mixture, not separating spontaneously into two different fluids but existing as a stable homogeneous whole.

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.

Co-existing Pyroxenes in Igneous Assemblages: a Re-evaluation of the Existing Data on Tie-line Orientations

1961 ◽  
Vol 98 (4) ◽  
pp. 333-343 ◽  
Author(s):  
G. M. Brown
Keyword(s):  
Intersection Point ◽  
Ternary Diagram ◽  
Wide Range ◽  
Tie Lines ◽  
Point Of Intersection ◽  
Tie Line ◽  
Existing Data

AbstractTie-line data are presented for twelve analysed igneous pyroxene pairs, from which it is demonstrated that a precise point of intersection, at or close to Wo75 En25 in the ternary diagram, does not exist. Eight tie-lines for pyroxene pairs from ultrabasic nodules in basalts are also considered. The tie-lines for metamorphic pyroxenes are compared with the igneous, and are shown to intersect over a similarly wide range, the average (Ca82 Mg18) being the same for both assemblages. It is shown that no conclusions can be drawn as to the genesis of the pyroxene assemblage, from the assumption of a characteristic tie-line intersection point. Optical determinations are considered, and shown to be of little practical value in this particular problem.

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