Assisted History Matching for Fractured Reservoirs by Use of Hough-Transform-Based Parameterization
- Le Lu (University of Southern California) | Dongxiao Zhang (Peking University)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- October 2015
- Document Type
- Journal Paper
- 942 - 961
- 2015.Society of Petroleum Engineers
- history matching, fractured reservoirs, Hough transform
- 0 in the last 30 days
- 428 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 5.00|
|SPE Non-Member Price:||USD 35.00|
Successful production in fractured reservoirs is significantly dependent on knowledge of the location, orientation, and conductivity of the fractures. Early water breakthrough can be prevented and sweep efficiency can be improved with the help of comprehensive and accurate information of fracture distributions. However, it is a challenge to estimate fracture distributions by conventional-history-matching methods because of the complexity of such reservoirs. Although there has been great progress in assisted-history-matching techniques during the last 2 decades, estimating fracture distributions in fractured reservoirs is still inefficient because of the strong heterogeneity and spatial discontinuity of model parameters. The performance of assisted-history-matching methods, such as the ensemble Kalman filter, can be significantly degraded by the non-Gaussian distributions of the parameters, such as effective permeability and porosity. On the other hand, although the geometric shapes of fractures may be generated properly at the initial step, they are difficult to preserve after updating, which results in geologically unrealistic fracture-distribution maps. In this study, we develop an assisted-history-matching method for fractured reservoirs with a Hough-transform-based parameterization. The facies maps of fractured reservoirs are parameterized into Hough-function fields in a discrete Hough space, whereas each gridblock in the Hough domain represents a fracture defined by its two Cartesian coordinates: angle θ of its normal and ρ of its algebraic distance from the origin in the flow domain. The length and axial position of the fractures are defined by two additional parameters on the same grid. The Hough-function value of each gridblock in the Hough domain is used as the indicator of the existence of the fracture in the facies map. When this parameterization is implemented in assisted history matching, the parameter fields in the Hough space, instead of the facies maps, are updated conditional on the production history. An inverse transform is performed to generate facies maps for the reservoir simulator. Pointwise prior information, such as known fractures discovered from well-log data, as well as the statistics of fracture orientation, can be honored by the inverse transform throughout the history-matching process. Applications and the effectiveness of this method are demonstrated by 2D synthetic-waterflooding examples. The fracture distributions in reference fields are identified by this method, and updated models are capable of providing improved predictions for prolonged periods of production.
|File Size||2 MB||Number of Pages||20|
Aanonsen, S. I., Nævdal, G., Oliver, D. S., et al. 2009. The Ensemble Kalman Filter in Reservoir Engineering – A Review. SPE J. 14 (3): 393–412. SPE-117274-PA. http://dx.doi.org/10.2118/117274-PA.
Bocquet, M. and Sakov, P. 2012. Combining Inflation-Free and Iterative Ensemble Kalman Filters for Strongly Nonlinear Systems. Nonlinear Proc. Geoph. 19 (3): 383–399. http://dx.doi.org/10.5194/npg-19-383-2012.
Caers, J. 2003. History Matching Under Training-Image-Based Geological Model Constraints. SPE J. 8 (3): 218–226. SPE-74716-PA. http://dx.doi.org/10.2118/74716-PA.
Chang, H., Zhang, D. and Lu, Z. 2010. History Matching of Facies Distribution with the EnKF and Level Set Parameterization. J. Comput. Phys. 229 (20): 8011–8030. http://dx.doi.org/10.1016/j.jcp.2010.07.005.
Chen, Y. and Oliver, D. S. 2012. Ensemble Randomized Maximum Likelihood Method as an Iterative Ensemble Smoother. Math. Geosci. 44 (1): 1–26. http://dx.doi.org/10.1007/s11004-011-9376-z.
Chen, Y. and Oliver, D. S. 2013. Levenberg–Marquardt Forms of the Iterative Ensemble Smoother for Efficient History Matching and Uncertainty Quantification. Computat. Geosci. 17 (4): 689–703. http://dx.doi.org/10.1007/s10596-013-9351-5.
Dovera, L. and Della Rossa, E. 2007. Ensemble Kalman Filter for Gaussian Mixture Models. In Proc., EAGE Petroleum Geostatistics 2007, Cascais, Portugal, 10–14 September, A16. Utrecht, The Netherlands: EAGE Publications BV.
Duda, R. O. and Hart, P. E. 1972. Use of the Hough Transformation to Detect Lines and Curves in Pictures. Commun. ACM 15 (1): 11–15. http://dx.doi.org/10.1145/361237.361242.
Evensen, G. 1994. Sequential Data Assimilation with a Nonlinear Quasi-Geostrophic Model Using Monte Carlo Methods to Forecast Error Statistics. J. Geophys. Res.-Oceans 99 (C5): 10143-10162. http://dx.doi.org/10.1029/94JC00572.
Evensen, G. 2004. Sampling Strategies and Square Root Analysis Schemes for the EnKF. Ocean Dyn. 54 (6): 539–560. http://dx.doi.org/10.1007/s10236-004-0099-2.
Gu, Y. and Oliver, D. S. 2007. An Iterative Ensemble Kalman Filter for Multiphase Fluid Flow Data Assimilation. SPE J. 12 (4): 438–446. SPE-108438-PA. http://dx.doi.org/10.2118/108438-PA.
Hough, P. V. 1962. Method and Means for Recognizing Complex Patterns. US Patent No. US3069654 A.
Iglesias, M., Lin, K. and Stuart, A. 2014. Well-Posed Bayesian Geometric Inverse Problems Arising in Subsurface Flow. Inverse Probl. 30 (11): 114001. http://dx.doi.org/10.1088/0266-5611/30/11/114001.
Iglesias, M. A. 2014. Iterative Regularization for Ensemble Data Assimilation in Reservoir Models. Computat. Geosci. 19 (1): 1–36. http://dx.doi.org/10.1007/s10596-014-9456-5.
Iglesias, M. A. and McLaughlin, D. 2011. Level-Set Techniques for Facies Identification in Reservoir Modeling. Inverse Probl. 27 (3): 035008. http://dx.doi.org/10.1088/0266-5611/27/3/035008.
Jafarpour, B. and Khodabakhshi, M. 2011. A Probability Conditioning Method (PCM) for Nonlinear Flow Data Integration into Multipoint Statistical Facies Simulation. Math. Geosci. 43 (2): 133–164. http://dx.doi.org/10.1007/s11004-011-9316-y.
Jafarpour, B. and McLaughlin, D. B. 2008. History Matching with an Ensemble Kalman Filter and Discrete Cosine Parameterization. Computat. Geosci. 12 (2): 227–244. http://dx.doi.org/10.1007/s10596-008-9080-3.
Khodabakhshi, M. and Jafarpour, B. 2011. Multipoint Statistical Characterization of Geologic Facies from Dynamic Data and Uncertain Training Images. Presented at the SPE Reservoir Characterisation and Simulation Conference and Exhibition, Abu Dhabi, UAE, 9–11 October. SPE-146935-MS. http://dx.doi.org/10.2118/146935-MS.
Levenberg, K. 1944. A Method for the Solution of Certain Problems in Least Squares. Q. Appl. Math. 2: 164–168.
Liu, N. and Oliver, D. S. 2005a. Critical Evaluation of the Ensemble Kalman Filter on History Matching of Geologic Facies. SPE Res Eval & Eng 8 (6): 470–477. SPE-92867-PA. http://dx.doi.org/10.2118/92867-PA.
Liu, N. and Oliver, D. S. 2005b. Ensemble Kalman Filter for Automatic History Matching of Geologic Facies. J. Pet. Sci. Eng. 47 (3): 147–161. http://dx.doi.org/10.1016/j.petrol.2005.03.006.
Lorentzen, R. J., Nævdal, G. and Shafieirad, A. 2012. Estimating Facies Fields by Use of the Ensemble Kalman Filter and Distance Functions--Applied to Shallow-Marine Environments. SPE J. 3 (1): 146–158. SPE-143031-PA. http://dx.doi.org/10.2118/143031-PA.
Moreno, D. and Aanonsen, S. 2007. Stochastic Facies Modelling Using the Level Set Method. Proc., EAGE Petroleum Geostatistics 2007, Cascais, Portugal, 10–14 September, A18. Utrecht, The Netherlands: EAGE Publications BV.
Nejadi, S. and Leung, J. 2012. Integration of Production Data for Estimation of Natural Fracture Properties in Tight Gas Reservoirs Using Ensemble Kalman Filter. Presented at the SPE Canadian Unconventional Resources Conference, Calgary, Alberta, Canada, 30 October–1 November. SPE-162783-MS. http://dx.doi.org/10.2118/162783-MS.
Oliver, D. S. and Chen, Y. 2011. Recent Progress on Reservoir History Matching: A Review. Computat. Geosci. 15 (1): 185–221. http://dx.doi.org/10.1007/s10596-010-9194-2.
Peters, L., Arts, R. J., Brouwer, G. K., et al. 2010. Results of the Brugge Benchmark Study for Flooding Optimization and History Matching. SPE Res Eval & Eng 13 (3): 391–405. http://dx.doi.org/10.2118/119094-PA.
Ping, J. and Zhang, D. 2013. History Matching of Fracture Distributions by Ensemble Kalman Filter Combined with Vector Based Level Set Parameterization. J. Pet. Sci. Eng. 108 (August): 288–303. http://dx.doi.org/10.1016/j.petrol.2013.04.018.
Ping, J. and Zhang, D. 2014. History Matching of Channelized Reservoirs With Vector-Based Level-Set Parameterization. SPE J. 19 (3): 514–529. SPE-169898-PA. http://dx.doi.org/10.2118/169898-PA.
Sakov, P., Oliver, D. S. and Bertino, L. 2012. An Iterative EnKF for Strongly Nonlinear Systems. Mon. Weathe Rev. 140 (6): 1988–2004. http://dx.doi.org/10.1175/MWR-D-11-00176.1.
Schlumberger 2007. Eclipse Reference Manual 2007.2. http://www.software.slb.com/products/foundation/Pages/eclipse.aspx.
Skjervheim, J.-A., Evensen, G., Aanonsen, S. I., et al. 2005. Incorporating 4D Seismic Data in Reservoir Simulation Models Using Ensemble Kalman Filter. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, 9–12 October. SPE-95789-MS. http://dx.doi.org/10.2118/95789-MS.
Strebelle, S. 2002. Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics. Math. Geol. 34 (1): 1–21. http://dx.doi.org/10.1023/A:1014009426274.
van Leeuwen, P. J. and Evensen, G. 1996. Data Assimilation and Inverse Methods in Terms of a Probabilistic Formulation. Mon. Weather Rev. 124 (12): 2898–2913. http://dx.doi.org/10.1175/1520-0493(1996)124%3C2898:DAAIMI%3E2.0.CO;2.
Zhang, D. and Lu, Z. 2004. An Efficient, High-Order Perturbation Approach for Flow in Random Porous Media via Karhunen–Loeve and Polynomial Expansions. J. Comput. Phys. 194 (2): 773–794. http://dx.doi.org/10.1016/j.jcp.2003.09.015.