Probabilistic Data-Driven Prediction of Wellbore Signatures in High-Dimensional Data Using Bayesian Networks
- Nastaran Bassamzadeh (University of Southern California) | Roger Ghanem (University of Southern California)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- August 2018
- Document Type
- Journal Paper
- 1,090 - 1,104
- 2018.Society of Petroleum Engineers
- Bayesian networks, Risk assessment, Probabilistic predictive models, Dimensionality reduction, Data-driven models
- 2 in the last 30 days
- 329 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
Accurate, data-driven, stochastic models for fluid-flow prediction in hydrocarbon reservoirs are of particular interest to reservoir engineers. Being computationally less costly than conventional physical simulations, such predictive models can serve as rapid-risk-assessment tools. In this research, we seek to probabilistically predict the oil-production rate at locations where limited data are observed using the available data at other spatial points in the oil field. To do so, we use the Bayesian network (BN), which is a modeling framework for capturing dependencies between uncertain variables in a high-dimensional system. The model is applied to a real data set from the Gulf of Mexico (GOM) and it is shown that BN is able to predict the production rate with 86% accuracy. The results are compared with neural-network and co-Kriging methods. Moreover, BN structure enables us to select the most-relevant variables for prediction, and thus we managed to reduce the input dimension from 36 to 17 variables while preserving the same prediction accuracy. Similarly, we use the local-linear-embedding (LLE) method as a feature-extraction tool to nonlinearly reduce the input dimension from 36 to 10 variables with negligible loss in accuracy. Accordingly, we claim that BN is a valuable modeling tool that can be efficiently used for probabilistic prediction and dimension reduction in the oil industry.
|File Size||1 MB||Number of Pages||15|
Ahmadi, M. A., Ebadi, M., Shokrollahi, A. et al. 2013. Evolving Artificial Neural Network and Imperialist Competitive Algorithm for Prediction Oil Flow Rate of the Reservoir. Appl. Soft Comput. 13 (2): 1085–1098. https://doi.org/10.1016/j.asoc.2012.10.009.
Bazargan, H., Christie, M., and Tchelepi, H. 2013. Efficient Markov Chain Monte Carlo Sampling Using Polynomial Chaos Expansion. Presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, 18–20 February. SPE-163663-MS. https://doi.org/10.2118/163663-MS.
Box, G. and Cox, D. 1964. An Analysis of Transformations. J. Royal Stat. Soc. B 26 (2): 211–252.
Bravo, C. E., Saputelli, L., Rivas, F. et al. 2014. State of the Art of Artificial Intelligence and Predictive Analytics in the E&P Industry: A Technology Survey. SPE J. 19 (4): 547–563. SPE-150314-PA. https://doi.org/10.2118/150314-PA.
Bromhal, G. S., Birkholzer, J., Mohaghegh, S. D. et al. 2014. Evaluation of Rapid Performance Reservoir Models for Quantitative Risk Assessment. Energy Procedia 63: 3425–3431. https://doi.org/10.1016/j.egypro.2014.11.371.
Cardoso, M. A. 2009. Reduced-Order Models for Reservoir Simulation. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 4–7 October. SPE-129636-STU. https://doi.org/10.2118/129636-STU.
Cardoso, M. A., Durlofsky, L., and Sarma, P. 2009. Development and Application of Reduced-Order Modeling Procedures for Subsurface Flow Simulation. Int. J. Numer. Meth. Eng. 77 (9): 1322–1350. https://doi.org/10.1002/nme.2453.
Chow, C. and Liu, C. 1968. Approximating Discrete Probability Distributions With Dependence Trees. IEEE Trans. Inform. Theory 14 (3): 462–467. https://doi.org/10.1109/TIT.1968.1054142.
Coifman, R. R. and Lafon, S. 2006. Diffusion Maps. Appl. Comput. Harmonic Anal. 21 (1): 5–30. https://doi.org/10.1016/j.acha.2006.04.006.
Cormen, T. H., Leiserson, C. E., Rivest, R. L. et al. 2009. Introduction to Algorithms, third edition. Cambridge, Massachusetts: MIT Press.
DeGroot, M. H. 2005. Optimal Statistical Decisions, Vol. 82. Hoboken, New Jersey: John Wiley & Sons.
Fung, R. and Chang, K.-C. 1989. Weighing and Integrating Evidence for Stochastic Simulation in Bayesian Networks. Proc., Fifth Conference on Uncertainty in Artificial Intelligence, Windsor, Ontario, Canada, 18–20 August.
Geiger, D. and Heckerman, D. 1994. Learning Gaussian networks. Proc., Tenth International Conference on Uncertainty in Artificial Intelligence, Seattle, Washington, 29–31 July, 235–243. San Francisco: Morgan Kaufmann Publishers.
Giese, M. and Bratvold, R. B. 2011. Probabilistic Modeling for Decision Support in Integrated Operations. SPE Econ & Mgmt 3 (3): 173–185. SPE-127761-PA. https://doi.org/10.2118/127761-PA.
Gilks, W. R., Thomas, A., and Spiegelhalter, D. J. 1994. A Language and Program for Complex Bayesian Modelling. J. Royal Stat. Soc. D 43 (1): 169–177. https://doi.org/10.2307/2348941.
Graham, J., Rose, K., Bauer, J. et al. 2012. Integration of Spatial Data to Support Risk and Impact Assessments for Deep and Ultra-Deepwater Hydrocarbon Activities in the Gulf of Mexico. Report NETL-TRS-4-2012, Office of Fossil Energy, National Energy Technology Laboratory, US Department of Energy, Morgantown, West Virginia.
Heckerman, D. 1998. A Tutorial on Learning with Bayesian Networks. Dordrecht, The Netherlands: Springer ScienceþBusiness Media.
Henrion, M. 1988. Propagating Uncertainty in Bayesian Networks by Probabilistic Logic Sampling. Proc., Second Annual Conference on Uncertainty in Artificial Intelligence, Philadelphia, Pennsylvania, 8–10 August, Vol. 2, 149–164.
Khaninezhad, M. and Jafarpour, B. 2013. Bayesian History Matching and Uncertainty Quantification Under Sparse Priors: A Randomized Maximum Likelihood Approach. Presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, 18–20 February. SPE-163656-MS. https://doi.org/10.2118/163656-MS.
Khaz’ali, A., Farahani, F., and Ahmadabadi, M. 2011. Bayesian Network—A New Probabilistic Method for Petroleum Reservoir Production Prediction and History Matching. Pet. Sci. Technol. 29 (7): 745–757. https://doi.org/10.1080/10916460903468393.
Kohonen, T. 1998. The Self-Organizing Map. Neurocomput. 21 (1): 1–6. https://doi.org/10.1016/S0925-2312(98)00030-7.
Lam, W. and Bacchus, F. 1994. Learning Bayesian Belief Networks: An Approach Based on the MDL Principle. Computat. Intell. 10 (3): 269–293. https://doi.org/10.1111/j.1467-8640.1994.tb00166.x.
Lee, J. A. and Verleysen, M. 2007. Nonlinear Dimensionality Reduction, first edition. New York City: Springer.
Lim, J.-S. 2005. Reservoir Properties Determination Using Fuzzy Logic and Neural Networks From Well Data in Offshore Korea. J. Pet. Sci. Eng. 49 (3–4): 182–192. https://doi.org/10.1016/j.petrol.2005.05.005.
Martinelli, G., Eidsvik, J., Hokstad, K. et al. 2014. Strategies for Petroleum Exploration on the Basis of Bayesian Networks: A Case Study. SPE J. 19 (4): 564–575. SPE-159722-PA. https://doi.org/10.2118/159722-PA.
Maschio, C., Vidal, A. C., and Schiozer, D. J. 2008. A Framework to Integrate History Matching and Geostatistical Modeling Using Genetic Algorithm and Direct Search Methods. J. Pet. Sci. Eng. 63 (1–4): 34–42. https://doi.org/10.1016/j.petrol.2008.08.001.
Masoudi, P., Asgarinezhad, Y., and Tokhmechi, B. 2015. Feature Selection for Reservoir Characterisation by Bayesian Network. Arab. J. Geosci. 8 (5): 3031–3043. https://doi.org/10.1007/s12517-014-1361-7.
Mohaghegh, S. 2000a. Virtual-Intelligence Applications in Petroleum Engineering: Part 1—Artificial Neural Networks. J Pet Technol 52 (9): 64–73. SPE-58046-JPT. https://doi.org/10.2118/58046-JPT.
Mohaghegh, S. 2000b. Virtual-Intelligence Applications in Petroleum Engineering: Part 3—Fuzzy Logic. J Pet Technol 52 (11): 82–87. SPE-62415-JPT. https://doi.org/10.2118/62415-JPT.
Mohaghegh, S. D. 2005. Recent Developments in Application of Artificial Intelligence in Petroleum Engineering. J Pet Technol 57 (4): 86–91. SPE-89033-JPT. https://doi.org/10.2118/89033-JPT.
Murphy, K. P. 2012. Machine Learning: A Probabilistic Perspective. Cambridge, Massachusetts: MIT Press.
Nagarajan, R., Scutari, M., and Lèbre, S. 2013. Bayesian Networks in R with Applications in Systems Biology, Vol. 48. New York City: Springer.
Roweis, S. T. and Saul, L. K. 2000. Nonlinear Dimensionality Reduction by Locally Linear Embedding. Science 290 (5500): 2323–2326. https://doi.org/10.1126/science.290.5500.2323.
Saad, G. and Ghanem, R. 2009. Characterization of Reservoir Simulation Models Using a Polynomial Chaos-Based Ensemble Kalman Filter. Water Resour. Res. 45 (4): W04417. https://doi.org/10.1029/2008WR007148.
Saltelli, A., Annoni, P., Azzini, I. et al. 2010. Variance Based Sensitivity Analysis of Model Output. Design and Estimator for the Total Sensitivity Index. Comput. Phys. Commun. 181 (2): 259–270. https://doi.org/10.1016/j.cpc.2009.09.018.
Schlumberger. 2014. Eclipse Reservoir Engineering Software, https://www.software.slb.com/products/eclipse?tab=Overview.
Scutari, M. 2010. Learning Bayesian Networks with the bnlearn R Package. J. Stat. Software 35 (3): 1–22.
Silpngarmlers, N., Guler, B., Ertekin, T. et al. 2002. Development and Testing of Two-Phase Relative Permeability Predictors Using Artificial Neural Networks. SPE J. 7 (3): 299–308. SPE-79547-PA. https://doi.org/10.2118/79547-PA.
Tenenbaum, J. B., de Silva, V., and Langford, J. C. 2000. A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science 290 (5500): 2319–2323. https://doi.org/10.1126/science.290.5500.2319.
Thimmisetty, C., Khodabakhshnejad, A., Jabbari, N. et al. 2015. Multiscale Stochastic Representation in High-Dimensional Data Using Gaussian Processes with Implicit Diffusion Metrics. In Dynamic Data-Driven Environmental Systems Science, ed. S. Ravela and A. Sandu, 157–166. New York City: Springer.
Velez-Langs, O. 2005. Genetic Algorithms in Oil Industry: An Overview. J. Pet. Sci. Eng. 47 (1–2): 15–22. https://doi.org/10.1016/j.petrol.2004.11.006.
Wyllie, M. R. J. and Gardner, G. H. F. 1958. The Generalized Kozeny-Varman Equation. World Oil 146 (4): 121–128.
Zerafat, M. M.., Ayatollahi, S., Mehranbod, N. et al. 2011. Bayesian Network Analysis as a Tool for Efficient EOR Screening. Presented at the SPE Enhanced Oil Recovery Conference, Kuala Lumpur, 19–21 July. SPE-143282-MS. https://doi.org/10.2118/143282-MS.
Zhang, Y. and Sahinidis, N. V. 2012. Uncertainty Quantification in CO2 Sequestration Using Surrogate Models From Polynomial Chaos Expansion. Ind. Eng. Chem. Res. 52 (9): 3121–3132. https://doi.org/10.1021/ie300856p.