Dynamic Ranking of Multiple Realizations By Use of the Fast-Marching Method
- Mohammad Sharifi (Amirkabir University of Technology) | Mohan Kelkar (University of Tulsa Center for Reservoir Studies) | Asnul Bahar (Kelkar and Associates) | Tormod Slettebo (Kelkar and Associates)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2014
- Document Type
- Journal Paper
- 1,069 - 1,082
- 2014.Society of Petroleum Engineers
- 5.5 Reservoir Simulation, 5.1.5 Geologic Modeling, 5.5.7 Streamline Simulation
- Ranking, Fast Marching Method, Uncertainity
- 3 in the last 30 days
- 485 since 2007
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One of the great challenges in reservoir modeling is to understand and quantify the dynamic uncertainties in geocellular models. Uncertainties in static parameters are easy to identify in geocellular models. Unfortunately, those models contain at least one to two orders of magnitude more gridblocks than typical simulation models. This means that, without significant upscaling, the dynamic uncertainties in these models cannot easily be assessed. Further, if we would like to select only a few geological models that can be carried forward for future performance predictions, we do not have an objective method of selecting the models that can properly capture the dynamic-uncertainty range. One possible solution is to use a faster simulation technique, such as streamline simulation. However, even streamline simulation requires solving a pressure equation at least once. For highly heterogeneous reservoir models with multimillion cells and in the presence of capillary effect or expansion-dominated process, this can pose a challenge. If we use static permeability thresholds to determine the connected volume, it would not account for how tortuous the connection is between the connected gridblock and the well location. In this paper, we use the fast-marching method (FMM) as a computationally efficient method for calculating the pressure/front propagation time on the basis of reservoir properties. This method is based on solving an Eikonal equation by use of upwind finite-difference approximation. In this method, pressure/front location (radius of investigation) can be calculated as a function of time without running any flow simulation. We demonstrate that dynamically connected volume based on pressure-propagation time is a very good proxy for ultimate recovery from a well in the primary-depletion process. With a predetermined threshold propagation time, a large number of geocellular models can be ranked. FMM can be scaled almost linearly with the number of gridblocks in the model. Two main advantages of this ranking method compared with other methods are that this method determines dynamic connectivity in the reservoir and that it is computationally much more efficient. We demonstrate the validity of the method by comparing ranking of multiple geocellular realizations (on Cartesian grid with heterogeneous and anisotropic permeability) by use of FMM with ranking from flow simulation. This method will allow us to select the geological models that can truly capture the range of dynamic uncertainty very efficiently.
|File Size||1 MB||Number of Pages||14|
Ates, H., Bahar, A., El-Abd, S., et al. 2005. Ranking and Upscaling of Geostatistical Reservoir Models Using Streamline Simulation: A Field Case Study. SPE Res Eval & Eng 8 (1): 22–32. SPE-81497-PA. http://dx.doi.org/10.2118/81497-PA.
Ballin, P.R., Journel, A.G., and Aziz, K. 1992. Prediction of Uncertainty in Reservoir Performance Forecast. J Can Pet Technol 31 (4): 52–62. PETSOC-92-04-05. http://dx.doi.org/10.2118/92-04-05.
Barth, T.J. and Sethian, J.A. 1998. Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains. J. Comput. Phys. 145 (1): 1–40. http://dx.doi.org/10.1006/jcph.1998.6007.
Berre, I., Dahle, H.K., Karlsen, K.H., et al. 2002. Time-of-Flight + Fast Marching + Transport Collapse: An Alternative to Streamlines for Two-Phase Porous Media Flow with Capillary Forces. Proc., Computational Methods in Water Resources XIV, Vol. 2, 995–1002.
Berre, I., Karlsen, K.H., Lie, K.A., et al. 2005. Fast Computation of Arrival Times in Heterogeneous Media. Computat. Geosci. 9 (4): 179–201. http://dx.doi.org/10.1007/s10596-005-9002-6.
Carlini, E., Falcone, M., Hoch. Ph. 2013. A Generalized Fast Marching Method on Unstructured Triangular Meshes. SIAM J. Numer. Anal. 51 (6): 2999–3035. http://dx.doi.org/10.1137/110833610.
Cruz, P. 2000. Reservoir Management Decision-Making in the Reference of Geological Uncertainity. PhD dissertation, Stanford University, Stanford, California (2000).
Datta-Gupta, A., Xie, J., Gupta, N., et al. 2011. Radius of Investigation and its Generalization to Unconventional Reservoirs. J Pet Technol (July): 52–55.
Daungkaew, S., Hollaender, F., and Gringarten, A.C. 2000. Frequently Asked Questions in Well Test Analysis. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, 1–4 October. SPE-63077-MS. http://dx.doi.org/10.2118/63077-MS.
Deutsch, C.V. and Srinivasan, S. 1996. Improved Reservoir Management Through Ranking Stochastic Reservoir Models. Presented at the SPE/DOE Improved Oil Recovery Symposium, Tulsa, Oklahoma, 21–24 April. SPE-35411-MS. http://dx.doi.org/10.2118/35411-MS.
Farag, A. and Hassouna, M. 2005. Theoretical Foundations of Tracking Monotonically Advancing Fronts using Fast Marching Level Set Method. Technical Report, Department of Electrical and Computer Engineering and Computer Vision and Image Processing Laboratory, University of Louisville, Louisville, Kentucky (February 2005).
Gillberg, T., Hjelle, Ø., and Bruaset, A. M. 2012. Accuracy and Efficiency of Stencils for the Eikonal Equation in Earth Modelling. Computat. Geosci. 16 (4): 933–952. http://dx.doi.org/10.1007/s10596-012-9296-0.
Hassouna, M.S. and Farag, A. 2007. Multi-Stencils Fast Marching Methods: A Highly Accurate Solution to the Eikonal Equation on Cartesian Domains. IEEE Trans. Pattern Anal. 29 (9): 1563–1574. http://dx.doi.org/10.1109/TPAMI.2007.1154.
Hysing, S.R. and Turek, S. 2005. The Eikonal equation: Numerical Efficiency vs. Algorithmic Complexity on Quadrilateral Grids. Proc., Algoritmy 2005 Conference on Scientific Computing, 22–31.
Karlsen, K.H., Lie, K.A., and Risebro, N.H. 2000. A Fast Marching Method for Reservoir Simulation. Computat. Geosci. 4 (2): 185–206. http://dx.doi.org/10.1023/A:1011564017218.
Kuchuk, F. J. 2009. Radius of Investigation for Reservoir Estimation from Pressure Transient Well Tests. Presented at the SPE Middle East Oil and Gas Show and Conference, Bahrain, 15–18 March. SPE-120515-MS. http://dx.doi.org/10.2118/120515-MS.
Kulkarni, K.N., Datta-Gupta, A., and Vasco, D.W. 2001. A Streamline Approach for Integrating Transient Pressure Data into High-Resolution Reservoir Models. SPE J. 6 (3): 273–282. SPE-74135-PA. http://dx.doi.org/10.2118/74135-PA.
Lee, W. J. 1982. Well Testing. Richardson, Texas: Textbook Series, SPE.
McLennan, J.A. and Deutsch, C.V. 2005. Selecting Geostatistical Realizations by Measures of Discounted Connected Bitumen. Presented at the SPE International Thermal Operations and Heavy Oil Symposium, Calgary, Alberta, Canada, 1–3 November. SPE-98168-MS. http://dx.doi.org/10.2118/98168-MS.
Natvig, J. R. and Lie, K. A. 2008. Fast Computation of Multiphase Flow in Porous Media by Implicit Discontinuous Galerkin Schemes with Optimal Ordering of Elements. J. Comput. Phys. 227 (24): 10108–10124. http://dx.doi.org/10.1016/j.jcp.2008.08.024.
Natvig, J. R., Lie, K. A., Eikemo, B., et al. 2007. An Efficient Discontinuous Galerkin Method for Advective Transport in Porous Media. Adv. Water Resour. 30 (12): 2424–2438. http://dx.doi.org/10.1016/j.advwatres.2007.05.015.
Osako, I., Datta-Gupta, A., and King, M. J. 2004. Timestep Selection During Streamline Simulation Through Transverse Flux Correction. SPE J. 9 (4): 450–464. SPE-79688-PA. http://dx.doi.org/10.2118/79688-PA.
Rawlinson, N. and Sambridge, M. 2005. The Fast Marching Method: An Effective Tool for Tomographics Imaging and Tracking Multiple Phases in Complex Layered Media. Explor. Geophys. 36 (4): 341–350. http://dx.doi.org/10.1071/EG05341.
Scheidt, C. and Caers, J. 2009a. Bootstrap Confidence Intervals for Reservoir Model Selection Techniques. Computat. Geosci. 14 (2): 369–382. http://dx.doi.org/10.1007/s10596-009-9156-8.
Scheidt, C. and Caers, J. 2009b. Uncertainty Quantification in Reservoir Performance Using Distances and Kernel Methods–Application to a West Africa Deepwater Turbidite Reservoir. SPE J. 14 (4): 680–692. SPE-118740-PA. http://dx.doi.org/10.2118/118740-PA.
Sethian, J. A. 1996. A Fast Marching Level Set Method for Monotonically Advancing Fronts. Proc. Natl. Acad. Sci. USA 93 (4): 1591–1595. http://dx.doi.org/10.1073/pnas.93.4.1591.
Sethian, J. A. 2001. Evolution, Implementation and Application of Level Set and Fast Marching Methods for Advancing Fronts. J. Comput. Phys. 169 (2): 503–55. http://dx.doi.org/10.1006/jcph.2000.6657.
Sethian, J. A. 1999. Level Sets Methods and Fast Marching Methods, second edition. Cambridge, UK: Cambridge University Press.
Sethian, J. A. and Popovici, A. M. 1999. 3-D Traveltime Computation Using the Fast Marching Method. Geophys. 64 (2): 516–523. http://dx.doi.org/10.1190/1.1444558.
Sethian, J. A. and Vladimirsky, A. 2000. Fast Methods for the Eikonal and Related Hamilton-Jacobi Equations on Unstructured Meshes. Proc. Natl. Acad. Sci. USA 97 (11): 5699–5703. http://dx.doi.org/10.1073/pnas.090060097.
Shahvali, M., Mallison, B., Wei, K., et al. 2012. An Alternative to Streamlines for Flow Diagnostics on Structured and Unstructured Grids. SPE J. 17 (3): 768–778. SPE-146446-PA. http://dx.doi.org/10.2118/146446-PA.
Thiele, M. R. 2001. Streamline Simulation. Oral presentation given at the 6th International Forum on Reservoir Simulation, Schloss Fuschl, Austria, 3–7 September.
Vasco, D., Keers, H., and Karasaki, K. 2000. Estimation of Reservoir Properties using Transient Pressure Data: An Asymptotic Approach. Water Resour. Res. 36 (12): 3447–3465. http://dx.doi.org/10.1029/2000WR900179.
Virieux, J., Flores-Luna, C., and Gilbert, D. 1994. Asymptotic Theory for Diffusive Electromagnetic Imaging. Geophys. J. Int. 119 (3): 857–868. http://dx.doi.org/10.1111/j.1365-246X.1994.tb04022.x.
Xie, J., Datta-Gupta, A., and Hill, A.D. 2011. Improved Characterization and Performance Assessment of Shale Gas Wells by Integrating Stimulated Reservoir Volume and Production Data. Presented at the SPE Eastern Regional Meeting, Columbus, Ohio, 1 October. SPE-148969-MS. http://dx.doi.org/10.2118/148969-MS.
Xie, J., Gupta, N., King, M.J, et al. 2012. Depth of Investigation and Depletion Behavior in Unconventional Reservoirs Using Fast Marching Methods. Presented at the SPE Europec/EAGE Annual Conference, Copenhagen, Denmark, 4–7 June. SPE-154532-MS. http://dx.doi.org/10.2118/154532-MS.
Yatziv, L., Bartesaghi, A., and Sapiro, G. 2006. O(N) Implementation of the Fast Marching Algorithm. J. Comp. Phys. 212 (2): 393–399. http://dx.doi.org/10.1016/j.jcp.2005.08.005.
Zhang, Y., Yang, C., King, M. J., et al. 2013. Fast-Marching Methods for Complex Grids and Anisotropic Permeabilities: Application to Unconventional Reservoirs. Presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, 18–20 February. SPE-163637-MS. http://dx.doi.org/10.2118/163637-MS.