Study of Perturbation Designs for the Partially Separable Objective Function With Gradient-Based Optimizations in History Matching
- Didier Yu Ding (IFP Energies Nouvelles) | Francois McKee (IFP Energies Nouvelles)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- April 2013
- Document Type
- Journal Paper
- 495 - 507
- 2013. Society of Petroleum Engineers
- 4.1.5 Processing Equipment, 5.5 Reservoir Simulation, 5.5.8 History Matching, 5.1.9 Four-Dimensional and Four-Component Seismic, 4.1.2 Separation and Treating
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- 272 since 2007
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Assisted history matching is widely used to constrain reservoir models by integrating well-production data and/or 4D seismic data. However, history matching generally requires a large number of reservoir simulations, which are very CPU time-consuming, in the optimization procedure. In this paper, we present a new technique that allows us to reduce the number of reservoir simulations for the gradient-based optimization method in history matching.
The new method is based on the partial separability of the objective function with local components referred to the wells and/or the seismic zones. How to choose a good perturbation design for the gradient computation is the main issue. In this paper, the graph-coloring algorithm is applied to determine "independent" components and parameters for a partially separable function, and analytical test functions are proposed for the selection of perturbation designs. This method can significantly reduce the number of reservoir simulations for a partially separable objective function in history matching.
|File Size||2 MB||Number of Pages||13|
Abacioglu, Y., Oliver, D.S., and Reynolds, A.C. 2001. Efficient reservoirhistory matching using subspace vectors. Comput. Geosci. 5(2): 151-172. http://dx.doi.org/10.1023/A:1013155928900.
Bissel, R., Sharma, Y., and Killough, J.E. 1994. History Matching Using theMethod of Gradients: Two Case Studies. Paper SPE 28590 presented at the SPEAnnual Technical Conference and Exhibition, New Orleans, 25-28 September. http://dx.doi.org/10.2118/28590-MS.
Brélaz, D. 1979. New methods to color the vertices of a graph. Commun.ACM 22 (4): 251-256. http://dx.doi.org/10.1145/359094.359101.
Chavent, G., Dupuy, M., and Lemonnier, P. 1975. History Matching by Use ofOptimal Control Theory. SPE J. 15 (1): 74-86. SPE-4627-PA.http://dx.doi.org/10.2118/4627-PA.
Chu, L., Reynolds, A.C., and Oliver, D.S. 1995. Computation of sensitivitycoefficients for conditioning the permeability field to well-test data. InSitu 19 (2): 179-223.
Ding, D.Y. 2011. Development of a Data Partition Technique forGradient-Based Optimization Methods in History Matching. SPE J. 16 (3): 582-593. SPE-130473-PA. http://dx.doi.org/10.2118/130473-PA.
Gosselin, O., Cominelli, A., van den Berg, S. et al. 2000. A gradient-basedapproach for history matching of both production and 4D seismic data. Paperpresented at the 7th European Conference on the Mathematics of Oil Recovery(ECMOR), Baveno, Italy, 5-8 September.
Handels, M., Zandvliet, M.J., Brouwer, D.R. et al. 2007. Adjoint-BasedWell-Placement Optimization Under Production Constraints. Paper SPE 105797presented at the SPE Reservoir Simulation Symposium, Houston, 26-28 February.http://dx.doi.org/10.2118/105797-MS.
Hossain, A.K.M.S. and Steihaug, T. 1998. Computing a sparse Jacobian matrixby rows and columns. Optimization Methods and Software 10(1): 33-48. http://dx.doi.org/10.1080/10556789808805700.
Hu, L.Y., Blanc, G., and Noetinger, B. 2001. Gradual Deformation andIterative Calibration of Sequential Stochastic Simulations. Math. Geol. 33 (4): 475-489.
Landa, J.L. and Horne, R.N. 1997. A Procedure to Integrate Well Test Data,Reservoir Performance History and 4-D Seismic Information into a ReservoirDescription. Paper SPE 38653 presented at the SPE Annual Technical Conferenceand Exhibition, San Antonio, Texas, USA, 5-8 October. http://dx.doi.org/10.2118/38653-MS.
Maschio, C. and Schiozer, D.J. 2008. A New Methodology for Assisted HistoryMatching Using Independent Objective Functions. Petroleum Science andTechnology 26 (9): 1047-1062. http://dx.doi.org/10.1080/10916460701208389.
Newsam, G.N. and Ramsdell, J.D. 1983. Estimation of Sparse JacobianMatrices. SIAMJournal on Algebraic and Discrete Methods 4(3): 404-418. http://dx.doi.org/10.1137/0604041.
Nocedal, J. and Wright, S.J. 2006. Numerical Optimization, secondedition. New York: Series in Operations Research and Financial Engineering,Springer.
Oliver, D.S., Reynolds, A.C., and Liu, N. 2008. Inverse Theory forPetroleum Reservoir Characterization and History Matching. Cambridge, UK:Cambridge University Press.
Roggero, F. and Hu, L.Y. 1998. Gradual Deformation of ContinuousGeostatistical Models for History-Matching. Paper SPE 49004 presented at theSPE Annual Technical Conference and Exhibition, New Orleans, 27-30 September.http://dx.doi.org/10.2118/49004-MS.
Roggero, F., Ding, D.Y., Berthet, P. et al. 2007. Matching of ProductionHistory and 4D Seismic Data—Application to the Girassol Field, Offshore Angola.Paper SPE 109929 presented at the SPE Annual Technical Conference andExhibition, Anaheim, California, USA, 11-14 November. http://dx.doi.org/10.2118/109929-MS.
Saltelli, A., Tarantola, S., Campolongo, F. et al. 2004. SensitivityAnalysis in Practice: A Guide to Assessing Scientific Models. West Sussex,UK: John Wiley & Sons.
Sarma, P., Aziz, K., and Durlofsky, L.J. 2005. Implementation of AdjointSolution for Optimal Control of Smart Wells. Paper SPE 92864 presented at theSPE Reservoir Simulation Symposium, The Woodlands, Texas, USA, 31 January-2February. http://dx.doi.org/10.2118/92864-MS.
Sedighi, F. and Stephen, K.D. 2009. Faster Convergence in Seismic HistoryMatching by Efficient Parameter Searching. Paper SPE 121210 presented at theEUROPEC/EAGE Conference and Exhibition, Amsterdam, 8-11 June. http://dx.doi.org/10.2118/121210-MS.
Touzani, S., Busby, D., and Antoniadis, A. 2010. A Comparison of ScreeningMethods for High Dimensional Input Problems. Paper presented at the 12thEuropean Conference on the Mathematics of Oil Recovery (ECMOR XII), Oxford, UK,6-9 September.
Yadav, S., Heim, R., Bryant, S. et al. 2007. Optimal Regional Delineation ina Reservoir for Efficient History Matching. Paper SPE 108994 presented at theSPE Annual Technical Conference and Exhibition, Anaheim, California, USA, 11-14November. http://dx.doi.org/10.2118/108994-MS.