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.

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.

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.

A General Purpose Model for Multiphase Compositional Flow Simulation

2018 ◽  
Author(s):  
Shuhong Wu ◽  
Jiangyan Dong ◽  
Baohua Wang ◽  
Tianyi Fan ◽  
Hua Li
Keyword(s):  
Flow Simulation ◽  
General Purpose ◽  
Compositional Flow

A Negative-Flash Tie-Simplex Approach for Multiphase Reservoir Simulation

SPE Journal ◽  
2013 ◽  
Vol 18 (06) ◽  
pp. 1140-1149 ◽  
Author(s):  
Alireza Iranshahr ◽  
Denis V. Voskov ◽  
Hamdi A. Tchelepi
Keyword(s):  
Phase Behavior ◽  
Oil Recovery ◽  
Large Scale ◽  
Flow Simulation ◽  
Steam Injection ◽  
Compositional Simulation ◽  
Reservoir Flow ◽  
Wide Range ◽  
Tie Lines ◽  
Eor Processes

Summary Enhanced Oil Recovery (EOR) processes usually involve complex phase behavior between the injected fluid (e.g., steam, hydrocarbon, CO2, sour gas) and the in-situ rock-fluid system. Several fundamental questions remain regarding Equation-of-State (EOS) computations for mixtures that can form three, or more, phases at equilibrium. In addition, numerical and computational issues related to the proper coupling of the thermodynamic phase behavior with multi-component transport must be resolved to accurately and efficiently model the behavior of large-scale EOR processes. Previous work has shown that the adaptive tabulation of tie-simplexes in the course of a compositional simulation is a reliable alternative to the conventional EOS-based compositional simulation. In this paper, we present the numerical results of reservoir flow simulation with adaptive tie-simplex parameterization of the compositional space. We study the behavior of thermal-compositional reservoir displacement processes across a wide range of fluid mixtures, pressures, and temperatures. We show that our approach rigorously accounts for tie-simplex degeneration across phase boundaries. We also focus on the complex behavior of the tie-triangles and tie-lines associated with three-phase, steam injection problems in heterogeneous formations. Our studies indicate that the tie-simplex based simulation is a potential approach for fast EOS modeling of complex EOR processes.

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.

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.

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.

Tie-Simplex Parameterization for EOS-Based Thermal Compositional Simulation

SPE Journal ◽  
2010 ◽  
Vol 15 (02) ◽  
pp. 545-556 ◽  
Author(s):  
A.. Iranshahr ◽  
D.V.. V. Voskov ◽  
H.A.. A. Tchelepi
Keyword(s):  
Flow Simulation ◽  
Critical Surface ◽  
Compositional Simulation ◽  
Fixed Temperature ◽  
Accurate Treatment ◽  
Tie Lines ◽  
Critical Boundary ◽  
Order Of Magnitude ◽  
Compositional Space ◽  
Tie Line

Summary Thermodynamic equilibrium computations are usually the most time-consuming component in compositional reservoir flow simulation. A compositional space adaptive tabulation (CSAT) approach was developed as a preconditioner for equation of state (EOS) computations in isothermal compositional simulation. The compositional space is decomposed into sub- and supercritical regions. In the subcritical region, we adaptively parameterize the compositional space using a small number of tie-lines, which are assembled into a table. The critical surface is parameterized and used to identify supercritical compositions. The phase-equilibrium information for a composition is interpolated as a function of pressure using the tie-line table. We extend the CSAT approach to thermal problems. Given an overall composition at a fixed temperature, the boundary between sub- and supercritical pressures is represented by the critical tie-line and the corresponding minimal critical pressure (MCP). A small set of subcritical tie-lines is computed and stored for a given temperature. This process is repeated for the pressure and temperature ranges of interest, and a coarse (regular) tie-line table is constructed. Close to the critical boundary, a refined tie-line table is used. A combination of regular and refined interpolation improves the robustness of the tie-line search procedure and the overall efficiency of the computations. Several challenging problems, including an unstructured heterogeneous discrete fracture field model with 26 components, are used to demonstrate the robustness and efficiency of this general tie-line-based parameterization method. Our results indicate that CSAT provides accurate treatment of the near-critical region. Moreover, the computational efficiency of the method is at least an order of magnitude better than that of standard EOS-based reservoir simulation approaches. We also show the efficiency gains relative to standard techniques as a function of the number of gridblocks in the simulation model.

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