K-Values-Based Upscaling of Compositional Simulation
- Amir Salehi (Quantum Reservoir Impact and Stanford University) | Denis V. Voskov (Delft University of Technology) | Hamdi A. Tchelepi (Stanford University)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- April 2019
- Document Type
- Journal Paper
- 579 - 595
- 2019.Society of Petroleum Engineers
- Thermodynamics and Phase Behavior, Compositional Simulation, Upscaling, K-Values, Non-Equilibrium
- 2 in the last 30 days
- 233 since 2007
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Enhanced-oil-recovery (EOR) processes involve complex flow, transport, and thermodynamic interactions; as a result, compositional simulation is necessary for accurate representation of the physics. Flow simulation of compositional systems with high-resolution reservoir models is computationally intensive because of the large number of unknowns and the strong nonlinear interactions. Thus, there is a great need for upscaling methods of compositional processes. The complex multiscale interactions between the phase behavior and the heterogeneities lie at the core of the difficulty in constructing consistent upscaling procedures.
We use a mass-conservative formulation and introduce upscaled phase-molar-mobility functions for coarse-scale modeling of multiphase flow. These upscaled flow functions account for the subgrid effects caused by the absolute permeability and relative permeability variations, as well as the effects of compressibility. Upscaling of the phase behavior is performed as follows. We assume that instantaneous thermodynamic equilibrium is valid on the fine scale, and we derive coarse-scale equations in which the phase behavior may not necessarily be at equilibrium. The upscaled thermodynamic functions, which represent differences in the component fugacities, are used to account for the nonequilibrium effects on the coarse scale. We demonstrate that the upscaled phase-behavior functions transform the equilibrium phase space on the fine scale to a region of similar shape, but with tilted tie-lines on the coarse space. The numerical framework uses K-values that depend on the orientation of the tie-lines in the new nonequilibrium phase space and the sign of upscaled thermodynamic functions.
The proposed methodology is applied to challenging gas-injection problems with large numbers of components and highly heterogeneous permeability fields. The K-value-based coarse-scale operator produces results that are in good agreement with the fine-scale solutions for the quantities of interest, including the component overall compositions and saturation distributions.
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Aziz, K. and Wong, T. W. 1988. Considerations in the Development of Multipurpose Reservoir Simulation Models. Proc., 1st and 2nd International Forum on Reservoir Simulation, Alpbach, Austria, 12–16 September, 77–208.
Ballin, P. R., Clifford, P. J., and Christie, M. A. 2002. Cupiagua: Modeling of a Complex Fractured Reservoir Using Compositional Upscaling. SPE Res Eval & Eng 5 (6): 488–498. SPE-81409-PA. https://doi.org/10.2118/81409-PA.
Barker, J. W. and Dupouy, P. 1999. An Analysis of Dynamic Pseudo-Relative Permeability Methods for Oil-Water Flows. Petrol. Geosci. 5 (4): 385–394. https://doi.org/10.1144/petgeo.5.4.385.
Barker, J. W. and Fayers, F. J. 1994. Transport Coefficients for Compositional Simulation With Coarse Grids in Heterogeneous Media. SPE Advances Technology Series 2 (2): 103–112. SPE-22591-PA. https://doi.org/10.2118/22591-PA.
Barker, J. W. and Thibeau, S. 1997. A Critical Review of the Use of Pseudorelative Permeabilities for Upscaling. SPE Res Eval & Eng 12 (2): 138–143. SPE-35491-PA. https://doi.org/10.2118/35491-PA.
Bolling, J. D. 1987. Development and Application of a Limited-Compositional, Miscible Flood Reservoir Simulator. Presented at the SPE Symposium on Reservoir Simulation, San Antonio, Texas, 1–4 February. SPE-15998-MS. https://doi.org/10.2118/15998-MS.
Cao, H. 2002. Development of Techniques for General Purpose Simulators. PhD dissertation, Stanford University, Stanford, California.
Chen, Y. and Durlofsky, L. J. 2006. Efficient Incorporation of Global Effects in Upscaled Models of Two-Phase Flow and Transport in Heterogeneous Formations. Multiscale Model. Simul. 5 (2): 445–475. https://doi.org/10.1137/060650404.
Chen, Y., Durlofsky, L. J., Gerritsen, M. et al. 2003. A Coupled Local-Global Upscaling Approach for Simulating Flow in Highly Heterogeneous Formations. Adv. Water Resour. 26 (10): 1041–1060. https://doi.org/10.1016/S0309-1708(03)00101-5.
Christie, M. A. 1996. Upscaling for Reservoir Simulation. J Pet Technol 48 (11): 1004–1010. SPE-37324-JPT. https://doi.org/10.2118/37324-JPT.
Christie, M. A. and Blunt, M. J. 2001. Tenth SPE Comparative Solution Project: A Comparison of Upscaling Techniques. SPE Res Eval & Eng 4 (4): 308–317. SPE-72469-PA. https://doi.org/10.2118/72469-PA.
Christie, M. A. and Clifford, P. J. 1998. Fast Procedure for Upscaling Compositional Simulation. SPE J. 3 (3): 272–278. SPE-50992-PA. https://doi.org/10.2118/50992-PA.
Coats, K. H. 1980. An Equation of State Compositional Model. SPE J. 20 (5): 363–376. SPE-8284-PA. https://doi.org/10.2118/8284-PA.
Coats, K. H., Thomas, L. K., and Pierson, R. G. 2004. Simulation of Miscible Flow Including Bypassed Oil and Dispersion Control. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 26–29 September. SPE-90898-MS. https://doi.org/10.2118/90898-MS.
Darman, N. H., Pickup, G. E., and Sorbie, K. S. 2002. A Comparison of Two-Phase Dynamic Upscaling Methods Based on Fluid Potentials. Computat. Geosci. 6 (1): 5–27. https://doi.org/10.1023/A:1016572911992.
Durlofsky, L. J. 1991. Numerical Calculation of Equivalent Grid Block Permeability Tensors for Heterogeneous Porous Media. Water Resour. Res. 27 (5): 699–708. https://doi.org/10.1029/91WR00107.
Durlofsky, L. J. and Chen, Y. 2012. Uncertainty Quantification for Subsurface Flow Problems Using Coarse-Scale Models. In Numerical Analysis of Multiscale Problems: Lecture Notes in Computational Science and Engineering, Vol. 83, 163–202. Berlin: Springer.
Evazi, M. and Jessen, K. 2014. Dual-Porosity Coarse-Scale Modeling and Simulation of Highly Heterogeneous Geomodels. Transport Porous Med. 105 (1): 211–233. https://doi.org/10.1007/s11242-014-0367-7.
Farmer, C. L. 2002. Upscaling: A Review. Int. J. Numer. Meth. Fl. 40 (1–2): 63–78. https://doi.org/10.1002/fld.267.
Fayers, F. J., Barker, J. W., and Newley, T. M. J. 1989. Effects of Heterogeneities on Phase Behaviour in Enhanced Oil Recovery. Oral presentation given at ECMOR I–1st European Conference on the Mathematics of Oil Recovery, Cambridge, UK, 1 July.
Hui, M. H. 2005. Upscaling of Multiphase Flow Parameters for Modeling Near-Well and Miscible Displacements. PhD dissertation, Stanford University, Stanford, California.
Indrupskiy, I. M., Lobanova, O. A., and Zubov, V. R. 2016. Non-Equilibrium Phase Behavior of Hydrocarbons in Compositional Simulations and Upscaling. Oral presentation given at ECMOR XV–15th European Conference on the Mathematics of Oil Recovery, Amsterdam, 29 August–1 September.
Iranshahr, A., Chen, Y., and Voskov, D. V. 2014. A Coarse-Scale Compositional Model. Computat. Geosci. 18 (5): 797–815. https://doi.org/10.1007/s10596-014-9427-x.
Iranshahr, A., Voskov, D. V., and Tchelepi, H. A. 2013a. A Negative-Flash Tie-Simplex Approach for Multiphase Reservoir Simulation. SPE J. 18 (6): 1140–1149. SPE-141896-PA. https://doi.org/10.2118/141896-PA.
Iranshahr, A., Voskov, D. V., and Tchelepi, H. A. 2013b. Tie-Simplex Based Compositional Space Parameterization: Continuity and Generalization to Multiphase Systems. AIChE J. 59 (5): 1684–1701. https://doi.org/10.1002/aic.13919.
Juanes, R. 2008. A Robust Negative Flash Based on a Parameterization of the Tie-Line Field. Fluid Phase Equilibr. 267 (1): 6–17. https://doi.org/10.1016/j.fluid.2008.02.009.
Kyte, J. R. and Berry, D. W. 1975. New Pseudo Functions to Control Numerical Dispersion. SPE J. 15 (4): 269–276. SPE-5105-PA. https://doi.org/10.2118/5105-PA.
Li, H. 2014. Compositional Upscaling for Individual Models and Ensembles of Realizations. PhD dissertation, Stanford University, Stanford, California.
Li, H. and Durlofsky, L. J. 2016. Upscaling for Compositional Reservoir Simulation. SPE J. 21 (3): 873–887. https://doi.org/10.2118/173212-PA.
Michelsen, M. L. 1982a. The Isothermal Flash Problem. Part I. Stability. Fluid Phase Equilibr. 9 (1): 1–19. https://doi.org/10.1016/0378-3812(82)85001-2.
Michelsen, M. L. 1982b. The Isothermal Flash Problem. Part II. Phase-Split Calculation. Fluid Phase Equilibr. 9 (1): 21–40. https://doi.org/10.1016/0378-3812(82)85002-4.
Ogunlana, D. O. and Mohanty, K. K. 2005. Compositional Upscaling in Fractured Reservoirs During Gas Recycling. J. Pet. Sci. Eng. 46 (1–2): 1–21. https://doi.org/10.1016/j.petrol.2004.11.004.
Orr, F. M. 2007. Theory of Gas Injection Processes. Holte, Denmark: Tie-Line Publications.
Pan, H. and Tchelepi, H. A. 2011. Compositional Flow Simulation Using Reduced-Variables and Stability-Analysis Bypassing. Presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, 21–23 February. SPE-142189-MS. https://doi.org/10.2118/142189-MS.
Peng, D. Y. and Robinson, D. B. 1976. A New Two-Constant Equation of State. Int. Eng. Chem. Fundamen. 15 (1): 59–64. https://doi.org/10.1021/i160057a011.
Peng, X., Du, Z., Liang, B., and Qi, Z. 2009. Darcy-Stokes Streamline Simulation for the Tahe-Fractured Reservoir With Cavities. SPE J. 14 (3): 543–552. SPE-107314-PA. https://doi.org/10.2118/107314-PA.
Rannou, G., Voskov, D. V., and Tchelepi, H. A. 2013. Tie-Line-Based K-Value Method for Compositional Simulation. SPE J. 18 (06): 1112–1122. SPE-167257-PA. https://doi.org/10.2118/167257-PA.
Rasmussen, C. P., Krejbjerg, K., Michelsen, M. L. et al. 2003. Increasing Computational Speed of Flash Calculations With Applications for Compositional, Transient Simulations. Presented at the SPE Annual Technical Conference and Exhibition, Denver, 5–8 October. SPE-84181-MS. https://doi.org/10.2118/84181-MS.
Remy, N., Boucher, A., and Wu, J. 2009. Applied Geostatistics With SGeMS: A User’s Guide. Cambridge, UK: Cambridge University Press.
Salehi, A. 2016. Upscaling of Compositional Flow Simulation Based on a Non-Equilibrium Formulation. PhD dissertation, Stanford University, Stanford, California.
Salehi, A., Voskov, D. V., and Tchelepi, H. A. 2012. Upscaling of Compositional Flow Simulation Based on a Non-Equilibrium Formulation. Oral presentation given at the American Geophysical Union Fall Meeting, San Francisco, 3–7 December.
Salehi, A., Voskov, D. V., and Tchelepi, H. A. 2013. Thermodynamically Consistent Transport Coefficients for Upscaling of Compositional Processes. Presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, 18–20 February, SPE-163576-MS. https://doi.org/10.2118/163576-MS.
Shirangi, M. G. and Durlofsky, L. J. 2015. Closed-Loop Field Development Under Uncertainty by Use of Optimization With Sample Validation. SPE J. 20 (5): 908–922. SPE-173219-PA. https://doi.org/10.2118/173219-PA.
Stone, H. L. 1991. Rigorous Black Oil Pseudo Functions. Presented at the SPE Symposium on Reservoir Simulation, Anaheim, California, 17–20 February. SPE-21207-MS. https://doi.org/10.2118/21207-MS.
Volkov, O. and Voskov, D. V. 2016. Effect of Time Stepping Strategy on Adjoint-Based Production Optimization. Computat. Geosci. 20 (3): 707–722. https://doi.org/10.1007/s10596-015-9528-1.
Voskov, D. 2012. An Extended Natural Variable Formulation for Compositional Simulation Based on Tie-Line Parameterization. Transport Porous Med. 92 (3): 541–557. https://doi.org/10.1007/s11242-011-9919-2.
Voskov, D. V. and Tchelepi, H. A. 2009a. Compositional Space Parameterization: Theory and Application for Immiscible Displacements. SPE J. 14 (3): 431–440. SPE-106029-PA. https://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. SPE J. 14 (3): 441–449. SPE-113492-PA. https://doi.org/10.2118/113492-PA.
Voskov, D. V. and Tchelepi, H. A. 2012. Comparison of Nonlinear Formulations for Two-Phase Multi-Component EOS Based Simulation. J. Pet. Sci. Eng. 82–83 (February–March): 101–111. https://doi.org/10.1016/j.petrol.2011.10.012.
Wallstrom, T. C., Christie, M. A., Durlofsky, L. J. et al. 2002. Effective Flux Boundary Conditions for Upscaling Porous Media Equations. Transport Porous Med. 46 (2–3): 139–153. https://doi.org/10.1023/A:1015075210265.
Wu, X. H., Parashkevov, R., Stone, M. et al. 2008. Global Scale-Up on Reservoir Models With Piecewise Constant Permeability Field. J. Algorithm. Computat. Technol. 2 (2): 223–247. https://doi.org/10.1260/174830108784646643.
Zaydullin, R. 2011. Direct Discretization of the Tie-Line Space for Compositional Flow Simulation. Master’s thesis, Stanford University, Stanford, California.
Zhang, B. and Okuno, R. 2015. Modeling of Capacitance Flow Behavior in EOS Compositional Simulation. J. Pet. Sci. Eng. 131 (July): 96–113. https://doi.org/10.1016/j.petrol.2015.04.014.
Zhang, P., Pickup, G. E., and Christie, M. A. 2008. A New Practical Method for Upscaling in Highly Heterogeneous Reservoir Models. SPE J. 13 (1): 68–76. SPE-103760-PA. https://doi.org/10.2118/103760-PA.
Zhou, Y. 2012. Parallel General-Purpose Reservoir Simulation With Coupled Reservoir Models and Multi-Segment Wells. PhD dissertation, Stanford University, Stanford, California.
Zhou, Y., Tchelepi, H. A., and Mallison, B. T. 2011. Automatic Differentiation Framework for Compositional Simulation on Unstructured Grids With Multi-Point Discretization Schemes. Presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, 21–23 February. SPE-141592-MS. https://doi.org/10.2118/141592-MS.
Zubov, V. R., Indrupskiy, I. M., and Bogachev, K. Y. 2016. Compositional Simulator With Non-Equilibrium Phase Transitions. Presented at the SPE Russian Petroleum Technology Conference and Exhibition, Moscow, 24–26 October. SPE-182001-MS. https://doi.org/10.2118/182001-MS.