An Artificial Intelligence-Based Nonlinear Solver for Hydrocarbon Reservoir Simulations
- Mohammad Ebadi (Skolkovo Institute of Science and Technology) | Yashar Bezyan (Concordia University) | Seyed Hassan Zabihifar (Bauman Moscow State Technical University) | Dmitry Koroteev (Skolkovo Institute of Science and Technology)
- Document ID
- Society of Petroleum Engineers
- SPE Europec featured at 82nd EAGE Conference and Exhibition, 8-11 December, Amsterdam, The Netherlands
- Publication Date
- Document Type
- Conference Paper
- 2020. Society of Petroleum Engineers
- 5 Reservoir Desciption & Dynamics, 7.6 Information Management and Systems, 7 Management and Information, 5.5 Reservoir Simulation, 7.6.7 Neural Networks, 7.6.6 Artificial Intelligence
- Nonlinear PDEs, Adaptive neural networks, Initial guesses, Newtonâ€™s method, Hydrocarbon reservoir simulation
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- 27 since 2007
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The reservoir simulation is based on the solving of second-order nonlinear Partial Differential Equations (PDEs). Following the high-level of nonlinearity or irregular boundaries, analytical solutions are not applicable to solve the supposed PDEs. To numerically solve the PDEs, applying nonlinear solvers are recommended. Dependencies on derivatives and proper initial guesses are the main disadvantages of classic solvers. To overcome the mentioned obstacles, solving supposed equations based on Adaptive Neural Network (ANN) has been introduced.
The algorithm starts by introducing an initial set into the Nonlinear Simultaneous Algebraic Equations (NSAE). The outputs are compared with the desired matrix of zeros to generate the required error. The calculated vectors of errors and its derivation are firstly employed to update the ANN weights through applying the adaption laws, and secondly, create the input vector to run the ANN. The outputs of the ANN are considered as corrections to be made to the initial set. Then, the corrected initial set is reintroduced into equations. The procedure continues iteratively until the outputs of equations meet the required level of accuracy.
By taking advantages of the adaptive laws, the outputs of the presented algorithm have successfully been matched with answers of the classic solvers, but with less computational costs. The convergence of the shown algorithm has practically been examined by assuming various mathematical types of initial sets. The implemented algorithm has been robust enough to converge for different forms of the initial sets, even for invalid values like minus numbers. However, records indicate that the convergence rates are strongly dependent on the values of initial sets. Following the sensitivity analysis over the primary model of ANN lead to the optimized network, which could solve the supposed NSAE three times faster. It has been interpreted that the number of neurons (NN), the diagonal coefficient matrix of error (λ), and the adaptive coefficient (Fw) have the most significant impacts on the performance of the algorithm.
In contrast to Newton's method as the most well-known nonlinear solver, the launched algorithm does not require any proper initial guesses. Moreover, the absolute independence of computing the partial derivatives of the Jacobian matrix and its inversion, which causes a notable reduction of computational costs, is the other remarkable advantage of the proposed approach. The represented algorithm can be taken as the platform to develop the next generation of simulators working based on machine learning.
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Ahmadi, MohammadAl Mohammad Ebadi, Payam Soleimani Marghmaleki, and Mohammad Mahboubi Fouladi. 2014. "Evolving Predictive Model to Determine Condensate-to-Gas Ratio in Retrograded Condensate Gas Reservoirs." Fuel 12 4: 241–57. 10.1016/j.fue1.2014.01.073.
Ahmadi, Mohammad Ali, Mohammad Ebadi, Amin Shokrollahi, and Seyed Mohammad Javad Majidi. 2013. "Evolving Artificial Neural Network and Imperialist Competitive Algorithm for Prediction Oil Flow Rate of the Reservoir." Applied Soft Computing 13 (2): 1085–98. 10.1016/j.asoc.2012.10.009.
Ahmadi, Mohammad Ali, Mohammad Ebadi, and Arash Yazdanpanah. 2014. "Robust Intelligent Tool for Estimating Dew Point Pressure in Retrograded Condensate Gas Reservoirs: Application of Particle Swarm Optimization." Journal of Petroleum Science and Engineering 123: 7–19. 10.1016/j.petro1.2014.05.023.
Ahmed,Tarek. 2010. "Fundamentals of Reservoir Fluid Flow." In Reservoir Engineering Handbook, Fourth, 331483. Elsevier. 10.1016/B978-1-85617-803-7.50014-6.
Ahmed, Tarek, and Paul D. McKinney. 2005. "Well Testing Analysis." In Advanced Reservoir Engineering, edited by Tarek Ahmed and Paul D B T - Advanced Reservoir Engineering McKinney, 1–147. Burlington: Elsevier. 10.1016/B978-075067733-2/50003-4.
Awadalla, Tarek, and Denis Voskov. 2018. "Modeling of Gas Flow in Confined Formations at Different Scales." Fuel 234 (September): 1354–66. 10.1016/j.fue1.2018.08.008.
Batista Fernandes, Bruno Ramon, Francisco Marcondes, and Kamy Sepehrnoori. 2018. "Development of a Fully Implicit Approach with Intensive Variables for Compositional Reservoir Simulation." Journal of Petroleum Science and Engineering 169 (May): 317–36. 10.1016/j.petrol.2018.05.039.
Bezyan, Yashar, Mohammad Ebadi, Shahab Gerami, Roozbeh Rafati, Mohammad Sharifi, and Dmitry Koroteev. 2019. "A Novel Approach for Solving Nonlinear Flow Equations: The next Step towards an Accurate Assessment of Shale Gas Resources." Fuel 236 (May 2018): 622–35. 10.1016/j.fue1.2018.08.157.
Cusini, Matteo, Barnaby Fryer, Cor van Kruijsdijk, and Hadi Hajibeygi. 2018. "Algebraic Dynamic Multilevel Method for Compositional Flow in Heterogeneous Porous Media." Journal of Computational Physics 354 (February): 593–612. 10.1016/j.jcp.2017.10.052.
Deb, Pulok Kanti, Farhana Akter, Syed Ahmad Imtiaz, and M. Enamul Hossain. 2017. "Nonlinearity and Solution Techniques in Reservoir Simulation: A Review." Journal of Natural Gas Science and Engineering 46 (October): 845–64. 10.1016/j.jngse.2017.07.031.
Ebadi, Mohammad, and Dmitry Koroteev. 2019. "Towards a Reliable Determination of Saturation Pressure: A Hybrid of Mouth Brooding Fish MBF Algorithm and Flash Calculations." In SPE/IATMI Asia Pacific Oil & Gas Conference and Exhibition. Society of Petroleum Engineers. 10.2118/196427-MS.
Ewing, Richard E. 1983. The Mathematics of Reservoir Simulation. Edited by Richard E. Ewing. Society for Industrial and Applied Mathematics. 10.1137/1.9781611971071.
Gonzalez, Mario H., Richard F. Bukacek, and Anthony L. Lee. 1967. "The Viscosity of Methane." Society of Petroleum Engineers Journal 7 (01): 75–79. 10.2118/1483-PA.
Jianyu, Li, Luo Siwei, Qi Yingjian, and Huang Yaping. 2003. "Numerical Solution of Elliptic Partial Differential Equation Using Radial Basis Function Neural Networks." Neural Networks 16 (5-6): 729–34. 10.1016/S0893-6080(03)00083-2.
Li, Guimei, and Zhezhao Zeng. 2008. "A Neural-Network Algorithm for Solving Nonlinear Equation Systems." In 2008 International Conference on Computational Intelligence and Security, 20–23.Suzhou: IEEE. 10.1109/CIS.2008.65.
Magrefidn, A. Alberto, and Ioannis K. Argyros. 2018. "Newton's Method." In A Contemporary Study of Iterative Methods, 276: 37–47. Elsevier. 10.1016/B978-0-12-809214-9.00003-6.
Raja, MuhammadAsif Zahoor, and Siraj-ul-Islam Ahmad. 2014. "Numerical Treatment for Solving One-Dimensional Bratu Problem Using Neural Networks." Neural Computing and Applications 24 (3-4): 549–61. 10.1007/s00521-012-1261-2.
Satter, Abdus, and Ghulam M. Iqbal. 2016. "Petroleum Reservoir Management Processes." In Reservoir Engineering, 137–53. Elsevier. 10.1016/B978-0-12-800219-3.00008-5.
Shekari Beidokhti, R., and A. Malek. 2009. "Solving Initial-Boundary Value Problems for Systems of Partial Differential Equations Using Neural Networks and Optimization Techniques." Journal of the Franklin Institute 346 (9): 898–913. 10.1016/j.jfranklin.2009.05.003.
Shirvany, Yazdan, Mohsen Hayati, and Rostam Moradian. 2009. "Multilayer Perceptron Neural Networks with Novel Unsupervised Training Method for Numerical Solution of the Partial Differential Equations." Applied Soft Computing 9 (1): 20–29. 10.1016/j.asoc.2008.02.003.
Slotine, Jean-Jacques E, and Weiping, Li. 1991. Applied Nonlinear Control. Vol. 199. Prentice hall Englewood Cliffs, NJ. http://cds.cem.ch/record/1228283.
Wilson, Adam. 2017. "Technique Blends Dimensionless Numbers and Data Mining To Predict Recovery Factors." Journal of Petroleum Technology 69 (10): 88–90. 10.2118/1017-0088-JPT.
Younis, Rami, Hamdi A. Tchelepi, and Khalid Aziz. 2010. "Adaptively Localized Continuation-Newton Method--Nonlinear Solvers That Converge All the Time." SPE Journal 15 (02): 526–44. 10.2118/119147-PA.