An Alternative to Streamlines for Flow Diagnostics on Structured and Unstructured Grids
- Mohammad Shahvali (Stanford University) | Bradley Mallison (Chevron Energy Technology Company) | Kaihong Wei (Chevron Energy Technology Company) | Herve Gross (Chevron Energy Technology Company)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 2012
- Document Type
- Journal Paper
- 768 - 778
- 2012. Society of Petroleum Engineers
- 5.5 Reservoir Simulation, 5.7.2 Recovery Factors, 5.6.5 Tracers
- 4 in the last 30 days
- 820 since 2007
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Streamline-based methods can be used as effective post-processing tools for assessing flow patterns and well allocation factors in reservoir simulation. This type of diagnostic information can be useful for a number of applications, including visualization, model ranking, upscaling validation, and optimization of well placement or injection allocation. In this paper, we investigate finite-volume methods as an alternative to streamlines for obtaining flow diagnostic information. Given a computed flux field, we solve the stationary transport equations for tracer and time of flight by use of either single-point upstream (SPU) weighting or a truly multidimensional upstream (MDU) weighting scheme. We use tracer solutions to partition the reservoir into volumes associated with injector/producer pairs and to calculate fluxes (well allocation factors) associated with each volume. The heterogeneity of the reservoir is assessed with time of flight to construct flow-capacity/storage-capacity (F-vs.-F) diagrams that can be used to estimate sweep efficiency. We compare the results of our approach with streamline-based calculations for several numerical examples, and we demonstrate that finite-volume methods are a viable alternative. The primary advantages of finite volume methods are the applicability to unstructured grids and the ease of implementation for general-purpose simulation formulations. The main disadvantage is numerical diffusion, but we show that a MDU weighting scheme is able to reduce these errors.
|File Size||3 MB||Number of Pages||11|
Aavatsmark, I. 2002. An Introduction to Multipoint FluxApproximations for Quadrilateral Grids. Comput. Geosci. 6(3-4): 405-432. http://dx.doi.org/10.1023/A:1021291114475.
Aavatsmark, I., Barkve, T., Bøe, Ø., and Mannseth, T. 1998.Discretizaton on unstructured grids for inhomogeneous, anisotropic media. PartII: Discussion And Numerical Results. SIAM J. Sci. Comput. 19 (5): 1717-1736. http://dx.doi.org/10.1137/S1064827595293594.
Aziz, K. and Settari, A. 1979. Petroleum ReservoirSimulation. Essex, UK: Elsevier Applied Science Publishers.
Batycky, R.P., Thiele, M.R., Baker, R.O., and Chugh, S.H. 2008.Revisiting Reservoir Flood-Surveillance Methods Using Streamlines. SPE ResEval & Eng 11 (2): 387-394. SPE-95402-PA. http://dx.doi.org/10.2118/95402-PA.
Datta-Gupta, A. and King, M.J. 2007. Streamline Simulation:Theory and Practice, No. 11. Richardson, Texas: Textbook Series, SPE.
DeBaun, D., Byer, T., Childs, P., et al. 2005. An ExtensibleArchitecture for Next Generation Scalable Parallel Reservoir Simulation. PaperSPE 93274 presented at the SPE Reservoir Simulation Symposium, Houston, 31January-2 February. http://dx.doi.org/10.2118/93274-MS.
Edwards, M.G. and Rogers, C.F. 1998. Finite volumediscretization with imposed flux continuity for the general tensor pressureequation. Comput. Geosci. 2 (4): 259-290. http://dx.doi.org/10.1023/A:1011510505406.
Eikemo, B., Berre, I., Dahle, H.K., Lie, K.A., and Natvig, J.R.2006. A discontinuous Galerkin method for computing time-of-flight indiscrete-fracture models. Proc., International Conference onComputational Methods in Water Resources (CMWR--XVI), Copenhagen, Denmark,19-22 June.
Eikemo, B., Lie, K.-A., Eigestad, G.T., and Dahle, H.K. 2009.Discontinuous Galerkin methods for advective transport in single-continuummodels of fractured media. Adv. Water Resour. 32 (4):493-506. http://dx.doi.org/10.1016/j.advwatres.2008.12.010.
Keilegavlen, E. 2010. Robust control volume methods forreservoir simulation on challenging grids. PhD thesis, University ofBergen, Bergen, Norway.
Kozdon, J., Mallison, B., and Gerritsen, M. 2009. RobustMulti-D Transport Schemes with Reduced Grid Orientation Effects. TransportPorous Media 78 (1): 47-75. http://dx.doi.org/10.1007/s11242-008-9281-1.
Kozdon, J., Mallison, B., and Gerritsen, M. 2011.Multidimensional upstream weighting for multiphase transport in porous media.Comput. Geosci. 15 (3): 399-419. http://dx.doi.org/10.1007/s10596-010-9211-5.
Lake, L.W. 1989. Enhanced Oil Recovery. EnglewoodCliffs, New Jersey: Prentice Hall.
Lamine, S. and Edwards, M.G. 2010. Higher OrderMultidimensional Upwind Convection Schemes for Flow in Porous Media onStructured and Unstructured Quadrilateral Grids. SIAM J. Sci. Comput. 32 (3): 1119-1139. http://dx.doi.org/10.1137/080727750.
Moinfar, A., Narr, W., Hui, M.-H., Mallison, B.T., and Lee,S.H. 2011. Comparison of Discrete-Fracture and Dual-Permeability Models forMultiphase Flow in Naturally Fractured Reservoirs. Paper SPE 142295 presentedat the SPE Reservoir Simulation Symposium, The Woodlands, Texas, USA, 21-23February. http://dx.doi.org/10.2118/142295-MS.
Natvig, J.R. and Lie, K.-A. 2008. Fast computation ofmultiphase flow in porous media by implicit discontinuous Galerkin schemes withoptimal ordering of elements. J. Comput. Phys. 227 (24):10108-10107. http://dx.doi.org/10.1016/j.jcp.2008.08.024.
Natvig, J.R., Lie, K.A., Eikemo, B., and Berre, I. 2007. Anefficient discontinuous Galerkin method for advective transport in porousmedia. Adv. Water Resour. 30 (12): 2424-2438. http://dx.doi.org/10.1016/j.advwatres.2007.05.015.
Schmalz, J.P. and Rahme, H.D. 1950. The Variation of WaterfloodPerformance with Variation in Permeability Profile. Prod. Monthly 15 (9): 9-12.
Shook, G.M. and Mitchell, K.M. 2009. A Robust Measure ofHeterogeneity for Ranking Earth Models: The F PHI Curve and Dynamic LorenzCoefficient. Paper Paper SPE 124625 presented at the SPE Annual TechnicalConference and Exhibition, New Orleans, 4-7 October. http://dx.doi.org/10.2118/124625-MS.
Thiele, M.R. and Batycky, R.P. 2003. Water InjectionOptimization Using a Streamline-Based Workflow. Paper SPE 84080 presented atthe SPE Annual Technical Conference and Exhibition, Denver, 5-8 October. http://dx.doi.org/10.2118/84080-MS.
Zhou, Y., Tchelepi, H.A., and Mallison, B.T. 2011. AutomaticDifferentiation Framework for Compositional Simulation on Unstructured Gridswith Multi-Point Discretization Schemes. Paper SPE 141592 presented at the SPEReservoir Simulation Symposium, The Woodlands, Texas, USA, 21-23 February. http://dx.doi.org/10.2118/141592-MS.