Progress and Challenges of Integrated Machine Learning and Traditional Numerical Algorithms: Taking Reservoir Numerical Simulation as an Example

Xu Chen, Kai Zhang (), Zhenning Ji, Xiaoli Shen, Piyang Liu (), Liming Zhang, Jian Wang and Jun Yao
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Xu Chen: School of Petroleum Engineering, China University of Petroleum (East China), 66 West Changjiang Road, Qingdao 266580, China
Kai Zhang: School of Petroleum Engineering, China University of Petroleum (East China), 66 West Changjiang Road, Qingdao 266580, China
Zhenning Ji: Petroleum Technology Research Institute of PetroChina Changqing Oilfield Company, 35 Weiyang Road, Xi’an 610100, China
Xiaoli Shen: Petroleum Technology Research Institute of PetroChina Changqing Oilfield Company, 35 Weiyang Road, Xi’an 610100, China
Piyang Liu: Civil Engineering School, Qingdao University of Technology, 777 Jialingjiang East Road, Qingdao 266520, China
Liming Zhang: School of Petroleum Engineering, China University of Petroleum (East China), 66 West Changjiang Road, Qingdao 266580, China
Jian Wang: College of Science, China University of Petroleum (East China), 66 West Changjiang Road, Qingdao 266580, China
Jun Yao: School of Petroleum Engineering, China University of Petroleum (East China), 66 West Changjiang Road, Qingdao 266580, China

Mathematics, 2023, vol. 11, issue 21, 1-44

Abstract: Machine learning techniques have garnered significant attention in various engineering disciplines due to their potential and benefits. Specifically, in reservoir numerical simulations, the core process revolves around solving the partial differential equations delineating oil, gas, and water flow dynamics in porous media. Discretizing these partial differential equations via numerical methods is one cornerstone of this simulation process. The synergy between traditional numerical methods and machine learning can enhance the precision of partial differential equation discretization. Moreover, machine learning algorithms can be employed to solve partial differential equations directly, yielding rapid convergence, heightened computational efficiency, and accuracies surpassing 95%. This manuscript offers an overview of the predominant numerical methods in reservoir simulations, focusing on integrating machine learning methodologies. The innovations in fusing deep learning techniques to solve reservoir partial differential equations are illuminated, coupled with a concise discussion of their inherent advantages and constraints. As machine learning continues to evolve, its conjunction with numerical methods is poised to be pivotal in addressing complex reservoir engineering challenges.

Keywords: machine learning; reservoir numerical simulation; reservoir engineering; numerical methods; partial differential equation solving (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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