PARALLEL IMPLEMENTATION OF MUSKAT-LEVERTT EQUATION USING CUDA
DOI:
https://doi.org/10.26577/JMMCS2023v119i3a9Keywords:
HPC, CUDA, waterflooding, Capillary pressure, SaturationAbstract
Capillary pressure plays a crucial role in waterflooding by influencing the displacement of oil by water in reservoir rocks. It is influenced by factors such as pore size distribution, wettability, and pore connectivity. Understanding and accounting for capillary pressure in the design and implementation of waterflooding operations can lead to improved oil recovery from reservoirs. In this work, to investigate the effects of capillary pressure in the waterflooding process in porous media, a one-dimensional numer-ical model is proposed, and the execution time of the serial model is computed. In the serial model, the absolute permeability, water and oil viscosity are considered as constant. In order to speed up the execu-tion time of the serial model, the high-performance computing technology CUDA is used, and the re-sults (execution time and speedup) on different threads are calculated. The results of serial and CUDA parallel models for the effects of capillary pressure are presented and analyzed.
References
Paul Willhite G. (1986)., "Waterflooding." , Society of petroleum engineers, Richardson, TX, Textbook Series Volume, 3: 1-7.
Ming Yang, Cunliang Chen, Yu Wang, Xiaohui Wu, Dong Ma,Buckley S.E., Leverett M.C. (1942) Mechanism of Fluid Displacement in Sands , Transactions AIME, Vol.146, pp.107-116.
Brooks R. H., Corey A. T. , Hydraulic properties of porous media , Hydrology Paper 3 (1964), 27.
Gray W., Hassanizadeh S.,"Paradoxes and Realities in Unsaturated Flow Theory" , Water Resources Research, 27 (1991), 1847–1854.
Gray W., Hassanizadeh S., "Unsaturated Flow Theory Including Interfacial Phenomena" , Water Resources Research 27 (1991), 1855–1863.
Hassanizadeh S., Gray W., "Thermodynamic basis of capillary pressure in porous media" , Water Resources Research 29 (1993), 3389–3406.
HassanizadehS., Celia M., Dahle H.,"Dynamic Effect in the Capillary Pressure-Saturation Relationship and its Impacts
on Unsaturated Flow" , Vadose Zone Journal 1 (2002), 38–57.
Das D., Hassanizadeh S., Rotter B., Ataie-Ashtiani B.,"A Numerical Study of MicroHeterogeneity Effects on Upscaled
Properties of Two-Phase Flow in Porous Media" , Transport in Porous Media 56 (2004), 329–350.
Beliaev, Hassanizadeh S., "A Theoretical Model of Hysteresis and Dynamic Effects in the Capillary Relation for Two-phase
Flow in Po-rous Media" , Transport in Porous Media 43 (2001), 487–510.
NVIDIA’s Next Generation CUDA Compute Architecture: Kepler GK110, 2012, Available:
http://www.nvidia.com/content/PDF/kepler/NVIDIA-KeplerGK110-ArchitectureWhitepaper.pdf.
Wilt N., The Cuda Handbook: A Comprehensive Guide to GPU Programming , Pearson Education, 2013.
C. Nvidia , Programming guide, ed,2008.
Sanders J., Kandrot E., CUDA by Example: An Introduction to General-Purpose GPU Programming, Addison-Wesley Professional, 2010.
Kirk D.B., Wen-mei W.H., Programming Massively Parallel Processors: A Hands-On Approach , Newnes, 2012.
Beisembetov I. K., Bekibaev T. T., Assilbekov B. K., Zhapbasbayev U. K., Kenzhaliev B. K.,"High-performance computing in oil recovery simulation based on CUDA.", Proceedings of 10th World Congress on Computational Mechanics. Sao- Paulo, Brazil(2012).
Akhmed-Zaki D.Zh., Daribayev B.S., Imankulov T.S., Turar O.N, "High-performance computing of oil recovery problem on a mobile platform using cuda technology" , Eurasian Journal Of Mathematical And Computer Applications , Volume 5, Issue 2 (2017) 4–13.
Ayham Zaza, Abeeb A. Awotunde, Faisal A. Fairag, Mayez A. Al-Mouhamed, "A CUDA-based parallel multi-phase oil reservoir simulator" , Computer Physics Communications (2016),
Pawel Czarnul, "Investigation of Parallel Data Processing Using Hybrid High-Performance CPU + GPU Systems and CUDA Streams" , Computing and Informatics , Vol. 39, 2020, 510–536.
