Study on the Application of the Tie-Line-Table-Look-Up-Based Methods to Flash Calculations in Compositional Simulations
- Wei Yan (CERE) | Abdelkrim Belkadi (Center for Energy Resources Engineering) | Erling Halfdan Stenby (Technical University of Denmark) | Michael Michelsen (DTU)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- May 2013
- Document Type
- Journal Paper
- 932 - 942
- 2013. Society of Petroleum Engineers
- 5.5.7 Streamline Simulation, 5.2.2 Fluid Modeling, Equations of State, 5.5 Reservoir Simulation
- 1 in the last 30 days
- 228 since 2007
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Flash calculation can be a time-consuming part in compositional reservoirsimulations, and several approaches have been proposed to speed it up. Onerecent approach is the shadow-region method that reduces the computation timemainly by skipping stability analysis for a large portion of the compositionsin the single-phase region. In the two-phase region, a highly efficientNewton-Raphson algorithm can be used with the initial estimates from theprevious step. Another approach is the compositional-space adaptive tabulation(CSAT) approach, which is based on tie-line table look-up (TTL). It savescomputation time by replacing rigorous phase-equilibrium calculations with thestored results in a tie-line table whenever the new feed composition is on oneof the stored tie-lines within a certain tolerance. In this study, a modifiedversion of CSAT, named the TTL method, has been proposed to investigate ifapproximation by looking up a tie-line table can save flash-computation time inthe two-phase region. The number of tie-lines stored for comparison and thetolerance set for accepting the feed composition are the key parameters in thismethod because they will influence the simulation speed and the accuracy ofsimulation results. We also proposed the tie-line distance-based approximation(TDBA) method, an alternative method to TTL, to obtain approximate flashresults in the two-phase region. The method uses the distance to a previoustie-line in the same gridblock to determine whether the approximation should bemade. Comparison between the shadow-region approach and the approximationapproach, including TTL and TDBA, has been made with a slimtube simulator bywhich the simulation temperature and the simulation pressure are set constant.It is shown that TDBA can significantly improve the speed in the two-phaseregion. In contrast, TTL, even with a precalculated tie-line table, is not soadvantageous compared with an efficient implementation of rigorous flash.Furthermore, we implemented TDBA in a compositional streamline simulator toapply TDBA to scenarios with pressure variation across the reservoir. We alsodiscussed how to extend TDBA to the general situation in which pressures ingridblocks are updated dynamically.
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Cao, H. 2002. Development of Techniques for General Purpose Simulators, PhDThesis, Stanford University, Stanford, California (2002).
Coats K.H. 1980. An Equation of State Compositional Model. SPE J. 20 (5): 363-376. http://dx.doi.org/10.2118/8284-PA.
Collins, D.A., Nghiem, L.X., Li, Y-K. et al. 1992. An Efficient Approach toAdaptive-Implicit Compositional Simulation with an Equation of State. SPERes Eng 7 (2): 259-264. http://dx.doi.org/10.2118/15133-PA.
Firoozabadi, A. and Pan, H. 2002. Fast and Robust Algorithm forCompositional Modeling: Part I—Stability Analysis Testing. SPE J. 7 (1): 78-89. http://dx.doi.org/10.2118/77299-PA.
Hendriks, E.M. 1988. Reduction Theorem for Phase Equilibrium Problems.Ind. Eng. Chem. Res. 27 (9): 1728-1732. http://dx.doi.org/10.1021/ie00081a027.
Jessen, K. 2000. Effective Algorithms for the Study of Miscible GasInjections Processes, PhD Diss., Technical University of Denmark, Lyngby,Denmark (March 2000).
Michelsen, M.L. 1982a. The Isothermal Flash Problem. Part I. Stability.Fluid Phase Equilibria 9 (1): 1-19. http://dx.doi.org/10.1016/0378-3812(82)85001-2.
Michelsen, M.L. 1982b. The Isothermal Flash Problem. Part II. Phase-SplitCalculation. Fluid Phase Equilibria 9 (1): 21-40.http://dx.doi.org/10.1016/0378-3812(82)85002-4.
Michelsen, M.L. 1986. Simplified Flash Calculations for Cubic Equations ofState. Ind. Eng. Chem. Process Des. Dev. 25 (1): 184-188.http://dx.doi.org/10.1021/i200032a029.
Michelsen, M.L. 1998. Speeding up the Two-Phase PT-Flash, with Applicationsfor Calculation of Miscible Displacement. Fluid Phase Equilibria 143 (1-2): 1-12. http://dx.doi.org/10.1016/S0378-3812(97)00313-0.
Michelsen, M.L. 2010. Speed Control in Compositional Reservoir Simulation.Paper presented at the Annual Discussion Meeting of the Center for EnergyResources Engineering, Technical University of Denmark, Helsingør, Denmark,9-11 June.
Michelsen, M.L. and Mollerup, J. 2007. Thermodynamic Models: Fundamentalsand Computational Aspects, second edition, Holte, Denmark: Tie-linePublications.
Michelsen, M.L., Yan, W., and Stenby, E.H. 2013. A Comparative Study ofReduced-Variables-Based Flash and Conventional Flash. SPE J. (in press).http://dx.doi.org/10.2118/154477-PA.
Mifflin, R.T., Watts, J.W., and Weiser, A. 1991. A Fully Coupled, FullyImplicit Reservoir Simulator for Thermal and Other Complex Reservoir Processes.Paper SPE 21252 presented at the SPE Symposium on Reservoir Simulation,Anaheim, California, 17-20 February. http://dx.doi.org/10.2118/21252-MS.
Orr, F.M. 2007. Gas Injection Processes, Holte, Denmark: Tie-LinePublications.
Pan, H. and Firoozabadi, A. 2003. Fast and Robust Algorithm forCompositional Modeling: Part II--Two-Phase Flash Computations. SPE J. 8 (4): 380-391. http://dx.doi.org/10.2118/87335-PA.
Peng, D.-Y. and Robinson, D.B. 1976. A New Two-Constant Equation of State.Ind. Chem. Eng. Fund. 15 (1): 59-64. http://dx.doi.org/10.1021/i160057a011.
Rasmussen, C.P., Krejbjerg, K., Michelsen, M.L. et al. 2006. Increasing theComputational Speed of Flash Calculations with Applications for CompositionalTransient Simulations. SPE Res Eval & Eng 9 (1): 32-38.http://dx.doi.org/ 10.2118/84181-PA.
Soave, G. 1972. Equilibrium Constants from a Modified Redlich-Kwong Equationof State. Ind. Chem. Eng. Sci. 27 (6): 1197-1203. http://dx.doi.org/10.1016/0009-2509(72)80096-4.
Thiele, M.R., Batycky, R.P., and Blunt, M.J. 1997. A Streamline-Based 3DField-Scale Compositional Reservoir Simulator. Paper SPE 38889 presented at theSPE Annual Technical Conference and Exhibition, San Antonio, Texas, 5-8October. http://dx.doi.org/10.2118/38889-MS.
Voskov, D.V. and Tchelepi, H.A. 2008. Compositional Space Parameterizationfor Miscible Displacement Simulation. Transp. in Porous Media 75 (1): 111-128. http://dx.doi.org/10.1007/s11242-008-9212-1.
Voskov, D.V. and Tchelepi, H.A. 2009a. Compositional Space Parameterization:Theory and Application for Immiscible Displacements. SPE J. 14(3): 431-440. http://dx.doi.org/10.2118/106029-PA.
Voskov, D.V. and Tchelepi, H.A. 2009b. Compositional Space Parameterization:Multicontact Miscible Displacements and Extension to Multiple Phases. SPEJ. 14 (3): 441-449. http://dx.doi.org/10.2118/113492-PA.
Voskov, D.V. and Tchelepi, H.A. 2009c. Tie-simplex Based MathematicalFramework for Thermodynamical Equilibrium Computation of Mixtures with anArbitrary Number of Phases. Fluid Phase Equilibria 283(1-2): 1-11. http://dx.doi.org/10.1016/j.fluid.2009.04.018.
Yan, W., Michelsen, M.L., Stenby, E.H. et al. 2004. Three-PhaseCompositional Streamline Simulation and Its Application to WAG. Paper SPE 89440presented at the SPE/DOE Symposium on Improved Oil Recovery, Tulsa, Oklahoma,17-21 April. http://dx.doi.org/10.2118/89440-MS.
Zick, A.A. 1986. A Combined Condensing/Vaporizing Mechanism in theDisplacement of Oil by Enriched Gases. Paper SPE 15493 presented at the SPEAnnual Technical Conference and Exhibition, New Orleans, Louisiana, 5-8October. http://dx.doi.org/10.2118/15493-MS.