Analysis of the applicability of parallel computing on Graphics Processing Unit for modeling problems based on the boundary element method

UDK: 004.02:622.276

DOI: 10.24887/0028-2448-2025-9-96-100

Key words: boundary element method (BEM), Graphics Processing Unit (GPU), parallel computing, programming model CUDA, filtration processes, petroleum industry, computational acceleration

Authors: B.M. Latypov (Ufa State Petroleum Technological University, RF, Ufa); E.V. Yudin (Gazprom Neft Companу Group, RF, Saint Petersburg); Z.A. Bogdanov(NEDRA LLC, RF, Saint Petersburg); S.I. Kogakov (Oil and Gas Production Tools LLC, RF, Krasnogorsk); N.S. Markov (NEDRA LLC, RF, Saint Petersburg)

This paper presents a comprehensive analysis of Graphics Processing Unit (GPU) acceleration technologies application for modeling filtration processes in oil and gas reservoirs using the boundary element method (BEM). The research addresses the critical need for computational time reduction in complex multi-well models featuring hydraulic fractures and heterogeneous boundaries, which is essential for real-time reservoir development optimization in the modern digitalized petroleum industry. The study provides detailed examination of architectural compatibility between GPU's massively parallel structure and the naturally decomposable nature of BEM computations, which are based on superposition principles of contributions from multiple sources. A comprehensive algorithmic adaptation strategy was developed, incorporating spatial-temporal decomposition, divergence minimization, efficient utilization of GPU's multi-level memory hierarchy, and optimization of data access patterns. The implementation utilizes programming model CUDA with specialized numerical integration techniques adapted for GPU architecture, including Gauss-Kronrod quadrature and exponential integral approximations optimized for parallel execution. Experimental verification on realistic industrial reservoir models demonstrated an average speedup of 77 times with peak performance reaching up to 126 times in individual iterations, while maintaining high computational accuracy (deviation less than 2,1 %). This enables dramatic reduction of simulation time from hours to minutes for complex reservoir systems, opening new possibilities for uncertainty analysis, multi-scenario calculations, and real-time reservoir development optimization.

References

1. Yudin E.V., Gubanova A.E., Krasnov V.A., Method for estimating the wells interference using field performance data (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2018, no. 8, pp. 64–69, DOI: https://doi.org/10.24887/0028-2448-2018-8-64-69

2. Yudin E.V., Poroshin I.O., Gruzdev I.E., Markov N.S., New approaches to rapid performance evaluation of wells in heterogeneous reservoirs (In Russ.), Neftyanoe khozyaystvo= Oil Industry, 2023, no. 10, pp. 61-67, DOI: https://doi.org/10.24887/0028-2448-2023-10-61-67

3. Yudin E.V., Modelirovanie fil’tratsii zhidkosti v neodnorodnykh sredakh dlya analiza i planirovaniya razrabotki neftyanykh mestorozhdeniy (Modeling of fluid filtration in heterogeneous environments for the analysis and planning of oilfield development): candidate of physical and mathematical sciences, Moscow, 2014.

4. Lubnin A.A. et al., System approach to planning the development of multilayer offshore fields, SPE-176690-MS, 2015, DOI: https://doi.org/10.2118/176690-MS

5. GOST 19.101-2024. Unified system for program documentation. Types of programs and program documents.

6. Basniev S.K., Dmitriev N.M., Rozenberg G.D., Neftegazovaya gidromekhanika (Oil and gas hydromechanics), Moscow-Izhevsk: Publ. of Institute of Computer Science, 2003, 479 p.

7. Kazemzadeh-Parsi M.J., Unsteady flow to a partially penetrating well in an unconfined aquifer using the boundary element method, Engineering Analysis with Boundary Elements, 2015, V. 50, pp. 50–56.

8. Aziz K., Settari A., Petroleum reservoir simulation, London: Applied Science Publishers, 1979, 476 p.

9. Kirk D.B., Hwu W.-M.W., Programming massively parallel processors: A hands-on approach, Morgan Kaufmann, 2016, 542 p.

10. Sanders J., Kandrot E., CUDA by example: An introduction to general-purpose GPU programming, Addison-Wesley Professional, 2010, 312 p.

11. Demidov D.E., Egorov A.G., Nuriev A.N., Solving computational fluid dynamics problems using NVIDIA CUDA technology (In Russ.), Uchenye zapiski Kazanskogo gos. universiteta. Seriya fiziko-matematicheskie nauki, 2010, V. 152, no. 1, pp. 142-154.