Applying the Multilevel Monte Carlo Method for Heterogeneity-Induced Uncertainty Quantification of Surfactant/Polymer Flooding
- A. Alkhatib (Saudi Aramco) | M. Babaei (University of Manchester)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- August 2016
- Document Type
- Journal Paper
- 1,192 - 1,203
- 2016.Society of Petroleum Engineers
- Uncertainty Quantificaiton, Uncertainty in heterogeneity, Multi-level Monte Carlo, Chemical EOR
- 2 in the last 30 days
- 399 since 2007
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Reservoir heterogeneity can be detrimental to the success of surfactant/polymer enhanced-oil-recovery (EOR) processes. Therefore, it is important to evaluate the effect of uncertainty in reservoir heterogeneity on the performance of surfactant/polymer EOR. Usually, a Monte Carlo sampling approach is used, in which a number of stochastic reservoir-model realizations are generated and then numerical simulation is performed to obtain a certain objective function, such as the recovery factor. However, Monte Carlo simulation (MCS) has a slow convergence rate and requires a large number of samples to produce accurate results. This can be computationally expensive when using large complex reservoir models. This study applies a multiscale approach to improve the efficiency of uncertainty quantification. This method is known as the multilevel Monte Carlo (MLMC) method.
This method comprises performing a small number of expensive simulations on the fine-scale model and a large number of less-expensive simulations on coarser upscaled models, and then combining the results to produce the quantities of interest. The purpose of this method is to reduce computational cost while maintaining the accuracy of the fine-scale model. The results of this approach are compared with a reference MCS, assuming a large number of simulations on the fine-scale model. Other advantages of the MLMC method are its nonintrusiveness and its scalability to incorporate an increasing number of uncertainties.
This study uses the MLMC method to efficiently quantify the effect of uncertainty in heterogeneity on the recovery factor of a chemical EOR process, specifically surfactant/polymer flooding. The permeability field is assumed to be the random input. This method is first demonstrated by use of a Gaussian 3D reservoir model. Different coarsening algorithms are used and compared, such as the renormalization method and the pressure-solver method (PSM). The results are compared with running Monte Carlo for the fine-scale model while equating the computational cost for the MLMC method. Both of these results are then compared with the reference case, which uses a large number of runs of the fine-scale model. The method is then extended to a channelized non-Gaussian generated 3D reservoir model incorporating multiphase upscaling.
The results show that it is possible to robustly quantify spatial uncertainty for a surfactant/polymer EOR process while greatly reducing the computational requirement, up to two orders of magnitude compared with traditional Monte Carlo for both the Gaussian and non-Gaussian reservoir models. The method can be easily extended to other EOR processes to quantify spatial uncertainty, such as carbon dioxide (CO2) EOR. Other possible extensions of this method are also discussed.
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Aanonsen, S., Naevdal, G., Oliver, D. 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.
Aarnes, J. E. and Efendiev, Y. 2006. An Adaptive Multiscale Method for Simulation of Fluid Flow in Heterogeneous Porous Media. Multiscale Model. Simul. 5 (3): 918–939. http://dx.doi.org/10.1137/050645117.
Adams, W. and Schievelbein, V. 1987. Surfactant Flooding Carbonate Reservoirs. SPE Res Eng 2 (4): 619–626. SPE-12686-PA. http://dx.doi.org/10.2118/12686-PA.
Al Abri, K., Al-Mjeni, R., Al-Bulushi, K. et al. 2014. Reducing Key Uncertainties Prior to a Polymer Injection Trial in a Heavy Oil Reservoir in Oman. Presented at the SPE EOR Conference at Oil and Gas West Asia, Muscat, 31 March–2 April. SPE-169686-MS. http://dx.doi.org/10.2118/169686-MS.
Alkhatib, A, Babaei, M. and King, P. 2013. Decision Making under Uncertainty: Applying the Least Squares Monte Carlo Method in Surfactant Flooding Implementation. SPE J. 18 (4): 721–735. SPE-154467-PA. http://dx.doi.org/10.2118/154467-PA.
Barua, J., Prescott, T. and Haldorsen, H. 1986. Financial and Technical Decision Making for Surfactant Flooding. Presented at the SPE California Regional Meeting, Oakland, California, 2–4 April. SPE-15074-MS. http://dx.doi.org/10.2118/15074-MS.
Begg, S. H., Carter, R. R. and Dranfield, P. 1989. Assigning Effective Values to Simulator Gridblock Parameters for Heterogeneous Reservoirs. SPE Res Eng 4 (4): 455–463. SPE-16754-PA. http://dx.doi.org/10.2118/16754-PA.
Brown, C. and Smith, P. 1984. The Evaluation of Uncertainty in Surfactant EOR Performance Prediction. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 16–19 September. SPE-13237-MS. http://dx.doi.org/10.2118/13237-MS.
Chai, C., Adamson, G., Lo, S. et al. 2011. St Joseph Chemical EOR Pilot - A Key De-risking Step Prior to Offshore ASP Full field Implementation. Presented at the SPE Enhanced Oil Recovery Conference, Kuala Lumpur, 19–21 July. SPE-144594-MS. http://dx.doi.org/10.2118/144594-MS.
Cheng, H., Shook, G., Taimur, M. et al. 2012. Interwell Tracer Tests to Optimize Operating Conditions for a Surfactant Field Trial: Design, Evaluation and Implications. SPE Res Eval & Eng 15 (2): 229–242. SPE-144899-PA. http://dx.doi.org/10.2118/144899-PA.
Cliffe, K., Giles, M., Scheichl, R. et al. 2011. Multilevel Monte Carlo Methods and Applications to Elliptic PDEs with Random Coefficients. Comput. Visual. Sci. 14 (1): 3–15. http://dx.doi.org/10.1007/s00791-011-0160-x.
Collier, N., Haji-Ali, A., Nobile, F. et al. 2014. A Continuation Multilevel Monte Carlo Algorithm. BIT Numer. Math. 55 (2): 399–432. http://dx.doi.org/10.1007/s10543-014-0511-3.
Delamaide, E., Tabary, R. and Rousseau, D. 2014. Chemical EOR in Low Permeability Reservoirs. Presented at the SPE EOR Conference at Oil and Gas West Asia, Muscat, 31 March–2 April. SPE-169673-MS. http://dx.doi.org/10.2118/169673-MS.
Durlofsky, L. 2005. Upscaling and Gridding of Fine Scale Geological Models for Flow Simulation. Oral presentation given at the 8th International Forum on Reservoir Simulation, Stresa, Italy, 20–24 June.
Efendiev, Y., Lliev, O. and Kronsbein, C. 2013. Multilevel Monte Carlo Methods Using Ensemble Level Mixed MsFEM for Two-Phase Flow and Transport Simulations. Computat. Geosci. 17 (5): 833–850. http://dx.doi.org/10.1007/s10596-013-9358-y.
Fletcher, A. and Morrison, G. 2008. Developing a Chemical EOR Pilot Strategy for a Complex, Low Permeability Water Flood. Presented at the SPE Symposium on Improved Oil Recovery, Tulsa, 19–23 April. SPE-112793-MS. http://dx.doi.org/10.2118/112793-MS.
Giles, M. 2008. Multilevel Monte Carlo Path Simulation. Oper. Res. 56 (3): 607–617.
Gogarty, W. 1976. Status of Surfactant or Micellar Methods. J Pet Technol 28 (1): 93–102. SPE-5559-PA. http://dx.doi.org/10.2118/5559-PA.
Green, D. and Willhite, G. 1998. Enhanced Oil Recovery. Richardson, Texas: Society of Petroleum Engineers.
Hammershaimb, E., Kuuskraa, V. and Stosur, G. 1983. Recovery Efficiency of Enhanced Oil Recovery Methods: A Review of Significant Field Tests. Presented at the SPE Annual Technical Conference and Exhibition, San Francisco, 5–8 October. SPE-12114-MS. http://dx.doi.org/10.2118/12114-MS.
Hankins, N. and Harwell, J. 1996. Case Studies for the Feasibility of Sweep Improvement in Surfactant-Assisted Waterflooding. J. Pet. Sci. Eng. 17 (1–2): 41–62. http://dx.doi.org/10.1016/S0920-4105(96)00055-1.
Heinrich, S. 2001. Multilevel Monte Carlo Methods. In Large-Scale Scientific Computing, ed. S. Margenov, J. Wasniewski, P. Yalamov, 58–67. Heidelberg, Germany: Springer Berlin Heidelberg.
Hilden, S. T., Lie, K.-A. and Raynaud, X. 2014. Steady-State Upscaling of Polymer Flooding. Oral presentation given at the ECMOR XIV 14th European Conference on the Mathematics of Oil Recovery, Sicily, Italy, 8–11 September.
Jakobsen, S. and Hovland, F. 1994. Surfactant Flooding: Technical and Economical Conditions to Succeed. Presented at the SPE/DOE Improved Oil Recovery Symposium, Tulsa, 17–20 April. 17–20 April. http://dx.doi.org/10.2118/27824-MS.
Karim, M. and Krabbenhoft, K. 2010. New Renormalization Schemes for Conductivity Upscaling in Heterogeneous Media. Transport Porous Med. 85 (3): 677–690. http://dx.doi.org/10.1007/s11242-010-9585-9.
King, P. R. 1989. The Use of Renormalization for Calculating Effective Permeability. Transport Porous Med. 4 (1): 37–58. http://dx.doi.org/10.1007/BF00134741.
Kossack, C. and Bilhartz, H. 1976. The Sensitivity of Micellar Flooding to Reservoir Heterogeneities. Presented at the SPE Improved Oil Recovery Symposium, Tulsa, 22–24 March. SPE-5808-MS. http://dx.doi.org/10.2118/5808-MS.
Krogstad, S., Lie, K., Møyner, O. et al. 2015. MRST-AD – an Open-Source Framework for Rapid Prototyping and Evaluation of Reservoir Simulation Problems. Presented at the SPE Reservoir Simulation Symposium, Houston, 23–25 February. SPE-173317-MS. http://dx.doi.org/10.2118/173317-MS.
Lake, L. W. 1989. Enhanced Oil Recovery. Englewood Cliffs, New Jersey: Prentice Hall.
Lie, K., Krogstad, S., Ligaarden, I. et al. 2012. Open-Source MATLAB Implementation of Consistent Discretisations on Complex Grids. Computat. Geosci. 16 (2): 297–322. http://dx.doi.org/10.1007/s10596-011-9244-4.
Lowry, P., Ferrell, H. and Dauben, D. 1986. A Review and Statistical Analysis of Micellar-Polymer Field Test Data. Topical report, National Petroleum Technology Office, US Department of Energy, Tulsa, November 1986.
Masalmeh, S., Wei, L., Blom, C. et al. 2014. EOR Options for Heterogeneous Carbonate Reservoirs Currently Under Waterflooding. Presented at the Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, 10–13 November. SPE-171900-MS. http://dx.doi.org/10.2118/171900-MS.
Muller, F., Jenny, P. and Meyer, D. 2013. Multilevel Monte Carlo for Two Phase Flow and Buckley-Leverett Transport in Random Heterogeneous Porous Media. J. Computat. Phys. 250 (1 October): 685–702. http://dx.doi.org/10.1016/j.jcp.2013.03.023.
Pope, G., Wang, B. and Tsaur, K. 1979. A Sensitivity Study of Micellar/Polymer Flooding. SPE J. 19 (6): 357–368. SPE-7079-PA. http://dx.doi.org/10.2118/7079-PA.
Schlumberger. 2014. Eclipse Reservoir Engineering Software, http://www.slb.com/content/services/software/recent/.
Schneiderman, H. and Kanade, T. 2004. Object Detection Using the Statistics of Parts. Int. J. Comput. Vision 56 (3): 151–177. http://dx.doi.org/10.1023/B:VISI.0000011202.85607.00.
Sheng, J. 2011. Modern Chemical Enhanced Oil Recovery: Theory and Practice. Burlington, Massachusetts: Elsevier.
Stanford Geostatistical Modeling Software (SGeMS). 2012. Remy, N., Boucher, A. and Wu, J. http://sgems.sourceforge.net/
Stoll, W., AlShureqi, H., Finol, J. et al. 2011. Alkaline/Surfactant/Polymer Flood: From the Laboratory to the Field. SPE J. 14 (6): 702–712. SPE-129164-PA. http://dx.doi.org/10.2118/129164-PA.
Thomas, S. 2006. Chemical EOR: The Past – Does It Have a Future? SPE-108828-DL.
Wallstrom, T., Hou. S., Christie, M. et al. 1999. Accurate Scale Up of Two Phase Flow Using Renormalization and Nonuniform Coarsening. Computat. Geosci. 3 (1): 69–87. http://dx.doi.org/10.1023/A:1011570724061.
Warren, J. and Price, H. 1961. Flow in Heterogeneous Porous Media. SPE J. 1 (3): 153–169. SPE-1579-G. http://dx.doi.org/10.2118/1579-G.
Wen, X.-H. and Chen, W. H. 2006. Real-Time Reservoir Model Updating Using Ensemble Kalman Filter with Confirming Options. SPE J. 11 (4): 431–442. SPE-92991-PA. http://dx.doi.org/10.2118/92991-PA.