Accurate Resolution of Near-Well Effects in Upscaled Models Using Flow-Based Unstructured Local Grid Refinement
- Authors
- Mohammad Karimi-Fard (Stanford University) | Louis Durlofsky (Stanford University)
- DOI
- https://doi.org/10.2118/141675-PA
- Document ID
- SPE-141675-PA
- Publisher
- Society of Petroleum Engineers
- Source
- SPE Journal
- Volume
- 17
- Issue
- 04
- Publication Date
- December 2012
- Document Type
- Journal Paper
- Pages
- 1,084 - 1,095
- Language
- English
- ISSN
- 1086-055X
- Copyright
- 2012. Society of Petroleum Engineers
- Disciplines
- 4.1.2 Separation and Treating, 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation, 4.3.4 Scale, 5.8.8 Gas-condensate reservoirs, 5.5 Reservoir Simulation, 5.5.3 Scaling Methods, 5.2.1 Phase Behavior and PVT Measurements, 5.8.1 Tight Gas
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- 690 since 2007
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Summary
We present a new approach for representing wells in coarse-scale reservoir simulation models. The technique is based on an expanded well model concept which provides a systematic procedure for the construction of the near-well grid. The method proceeds by first defining an underlying fine-scale model, in which the well and any key near-well features such as hydraulic fractures are fully resolved using an unstructured grid. In the (coarse) simulation model, the geometry of the grid in the expanded well region, and the associated "radial" transmissibilities, are determined from the solution of a fine-scale, single-phase, well-driven flow problem. The coarse-scale transmissibilities outside of the well region are computed using existing local upscaling techniques or by applying a new global upscaling procedure. Thus, through use of near-well flow-based gridding and generalized local grid refinement, this methodology efficiently incorporates the advantages of highly-resolved unstructured grid representations of wells into coarse models. The overall model provided by this technique is compatible with any reservoir simulator that allows general unstructured cell-to-cell connections (model capabilities, in terms of flow physics, are defined by the simulator).
The expanded well-modeling approach is applied to challenging 3D problems involving injection and production in a low-permeability heterogeneous reservoir, tight-gas production by a hydraulically-fractured well, and production in a gas-condensate reservoir. In the first two cases, where it is possible to simulate the fine-grid unstructured model, results using the expanded well model closely match the reference solutions, while standard approaches lead to significant error. In the gas-condensate example, which involves a nine-component compositional model, the reference solution is not computed, but the solution using the expanded well model is shown to be physically reasonable while standard coarse-grid solutions show large variation under grid refinement.
| File Size | 1 MB | Number of Pages | 12 |
References
Aavatsmark, I. and Klausen, R.A. 2003. Well Index in Reservoir Simulationfor Slanted and Slightly Curved Wells in 3D Grids. SPE J. 8(1): 41-48. SPE-75275-PA.http://dx.doi.org/10.2118/75275-PA.
Aavatsmark, I., Barkve, T., Bøe, Ø. et al. 1998.Discretizaton onunstructured grids for inhomogeneous, anisotropic media. Part I: Derivation ofthe methods. SIAM J. Sci. Comput. 19 (5): 1700-1716. http://dx.doi.org/10.1137/S1064827595293582.
Al-Mohannadi, N.S., Ozkan, E., and Kazemi, H. 2007.Grid-System Requirementsin Numerical Modeling of Pressure-Transient Tests in Horizontal Wells.SPERes Eval&Eng 10 (2): 122-131. SPE-92041-PA.http://dx.doi.org/10.2118/92041-PA.
Aouizerate, G., Durlofsky, L., and Samier, P. 2012. New models for heaterwells in subsurface simulations, with application to the in situ upgrading ofoil shale.Comput.Geosci. 16 (2): 519-533. http://dx.doi.org/10.1007/s10596-011-9263-1.
Blanc, G., Ding, D.Y., Ene, A. et al. 1998. Transient productivity index fornumerical well test simulations. In Reservoir Characterization: RecentAdvances, ed. R.A. Schatzinger and J.F. Jordan, No. 71, 163-174. Tulsa,Oklahoma: AAPG Memoir, AAPG Publications.
Cao, H. 2002. Development of techniques for general purposesimulators.PhD dissertation, Stanford University, Stanford, California.
Chen, Y., Durlofsky, L.J., Gerritsen, M. et al. 2003. A coupled local-globalupscaling approach for simulating flow in highly heterogeneousformations.Adv. Water Resour. 26 (10): 1041-1060. http://dx.doi.org/10.1016/S0309-1708(03)00101-5.
Ding, D.Y. 2010.Modeling Formation Damage for Flow Simulations at ReservoirScale.SPE J. 15 (3): 737-750. SPE-121805-PA.http://dx.doi.org/10.2118/121805-PA.
Ding, Y. 1995. Scaling-up in the Vicinity of Wells in Heterogeneous Field.Paper SPE 29137 presented at the SPE Reservoir Simulation Symposium, SanAntonio, Texas, USA, 12-15 February. http://dx.doi.org/10.2118/29137-MS.
Durlofsky, L.J. 1991. Numerical Calculation of Equivalent Grid BlockPermeability Tensors for Heterogeneous Porous Media.Water Resour. Res. 27 (5): 699-708. http://dx.doi.org/10.1029/91WR00107.
Durlofsky, L.J., Milliken, W.J., and Bernath, A. 2000.Scaleup in theNear-Well Region.SPE J. 5 (1): 110-117. SPE-61855-PA.http://dx.doi.org/10.2118/61855-PA.
Fung, L.S.K., Buchanan, L., and Sharma, R. 1994. Hybrid-CVFE Method forFlexible-Grid Reservoir Simulation.SPE Res Eng 9 (3):188-194. SPE-25266-PA.http://dx.doi.org/10.2118/25266-PA.
Gong, B., Karimi-Fard, M., andDurlofsky, L.J. 2008.Upscaling DiscreteFracture Characterizations to Dual-Porosity, Dual-Permeability Models forEfficient Simulation of Flow With Strong Gravitational Effects. SPE J.13 (1): 58-67. SPE-102491-PA.http://dx.doi.org/10.2118/102491-PA.
Hassanpour, R.M., Manchuk, J.G., Leuangthong, O. et al. 2010. Calculation ofPermeability Tensors for Unstructured Gridblocks.J Can Pet Technol 49 (10): 65-74. SPE-141305-PA.http://dx.doi.org/10.2118/141305-PA.
Heinemann, Z.E., Brand, C.W., Munka, M. et al. 1991. Modeling ReservoirGeometry With Irregular Grids. SPE Res Eng 6 (2): 225-232.SPE-18412-PA.http://dx.doi.org/10.2118/18412-PA.
Jiang, Y. 2007. Techniques for modeling complex reservoirs and advancedwells.PhD thesis, Stanford University, Stanford, California.
Kamath, J. 2007. Deliverability of Gas-Condensate Reservoirs--FieldExperiences and Prediction Techniques. Distinguished Author Series, J PetTechnol 59 (4): 94-99. SPE-103433-PA.
Karimi-Fard, M. 2008. Grid optimization to improve orthogonality oftwo-point ?ux approximation for unstructured 3D fractured reservoirs. Paperpresented at the 11th European Conference on the Mathematics of Oil Recovery(ECMOR XI), Bergen, Norway, 8-11 September.
Karimi-Fard, M. and Durlofsky, L.J. 2009.Detailed Near-WellDarcy-Forchheimer Flow Modeling and Upscaling on Unstructured 3D Grids. PaperSPE 118999 presented at the SPE Reservoir Simulation Symposium, The Woodlands,Texas, USA, 2-4 February. http://dx.doi.org/10.2118/118999-MS.
Karimi-Fard, M., Durlofsky, L.J., and Aziz, K. 2004.An EfficientDiscrete-Fracture Model Applicable for General-Purpose ReservoirSimulators.SPE J. 9 (2): 227-236. SPE-88812-PA.http://dx.doi.org/10.2118/88812-PA.
Karimi-Fard, M., Gong, B., and Durlofsky, L.J. 2006. Generation ofcoarse-scale continuum flow models from detailed fracture characterizations.Water Resour. Res. 42 (10): W10423. http://dx.doi.org/10.1029/2006WR005015.
Kenyon, D. and Behie, G.A. 1987. Third SPE Comparative Project: Gas Cyclingof Retrograde Condensate Reservoirs. J Pet Technol39 (8):981-997. SPE-12278-PA.http://dx.doi.org/10.2118/12278-PA.
King, M.J. and Mansfield, M. 1999. Flow Simulation of Geologic Models.SPE Res Eval&Eng 2 (4): 351-367. SPE-57469-PA.http://dx.doi.org/10.2118/57469-PA.
Lee, S.H. and Milliken, W.J. 1993. The Productivity Index of an InclinedWell in Finite-Difference Reservoir Simulation. Paper SPE 25247 presented atthe SPE Symposium on Reservoir Simulation, New Orleans, 28 February-3 March. http://dx.doi.org/10.2118/25247-MS.
Mlacnik, M.J. and Heinemann, Z.E. 2003.Using Well Windows in Full FieldReservoir Simulation.SPE Res Eval&Eng 6 (4): 275-285.SPE-85709-PA.http://dx.doi.org/10.2118/85709-PA.
Palagi, C.L. and Aziz, K. 1994. Modeling Vertical and Horizontal Wells WithVoronoi Grid.SPE Res Eng 9 (1): 15-21. SPE-24072-PA.http://dx.doi.org/10.2118/24072-PA.
Peaceman, D.W. 1983. Interpretation of Well-Block Pressures in NumericalReservoir Simulation WithNonsquare Grid Blocks and Anisotropic Permeability.SPE J. 23 (3): 531-543. SPE-10528-PA.http://dx.doi.org/10.2118/10528-PA.
Prévost, M., Lepage, F., Durlofsky, L.J. et al. 2005.Unstructured 3Dgridding and upscaling for coarse modelling of geometrically complexreservoirs.Pet. Geosci. 11 (4): 339-345. http://dx.doi.org/10.1144/1354-079304-657.
Si, H. 2004. TetGen: A Quality Tetrahedral Mesh Generator andThree-Dimensional Delaunay Triangulator, Ver. 1.3 software. Berlin, Germany:Weierstrass Institute for Applied Analysis and Stochastics.
Wolfsteiner, C., Durlofsky, L.J., and Aziz, K. 2003. Calculation of wellindex for nonconventional wells on arbitrary grids.Comput.Geosci.7 (1): 61-82. http://dx.doi.org/10.1023/A:1022431729275.
Zhou, Y. and King, M.J. 2011.Improved Upscaling for Flow Simulation of TightGas Reservoir Models. Paper SPE 147355 presented at the SPE Annual TechnicalConference and Exhibition, Denver, 30 October-2 November. http://dx.doi.org/10.2118/147355-MS.
