The actual task of petroleum geophysics is to solve the problem of multicomponent multiphase flow in a porous medium. At the same time, the development of effective parallel algorithms is an urgent task for modeling processes of this type. For these purposes, the authors carried out the following works.
The problem of modeling the movement of a multicomponent multiphase liquid in a porous medium was solved. The equations describing fluid movement were linearized by the Newton-Raphson method and the resulting system of linear equations was solved using the generalized minimal residuals method (GMRES) with the Incomplete Lower-Upper factorization (ILU(0)) preconditioner. As a result, the problem was solved by the developed algorithm called Newton-ILU(0)-GMRES. A parallel program using the MPI standard and a fragmented program in the LuNA language for shared memory systems were developed and implemented.
After analyzing the results of the previous work, it was decided to optimize the parallel GMRES algorithm, since the parallel program was not effective enough. Bottlenecks were identified, in particular Arnoldi orthogonalization, which negatively affected the effectiveness of the parallel program. An optimized version of the GMRES parallel algorithm was developed and implemented, which avoids the loss of parallel execution efficiency on Arnoldi orthogonalization. The developed program was tested and the results were analyzed. Comparisons were made with the previous version of the developed method.

Recently, modern information technology are used in many fields of industry, and using parallel computation can enhance the performance of numerical simulation. So in this study, we use the high-performance computing technologies to solve the problem of numerical simulations of a polymer flooding process of oil recovery. The range of applications of polymers have been progressively increased. It began to be used rapidly in various fields of science and technology, including chemistry, pharmacology, and chemical and petroleum engineering. Polymer flooding is best for improving sweep in reservoirs where fractures do not cause severe channeling, also it is one of the enhanced oil recovery technique that has been successfully applied in many fields of projects, especially in chemical and petroleum engineering. The viscosity of water is increased by injecting polymer into the reservoir, and this process highly improved the efficiency of water flooding process.
This study aims to develop a hybrid (Open MP+ MPI + CUDA) parallel computing model associated with oil recovery by polymer flooding. The model developed is general enough to analyze a polymer flooding for oil recovery. The main purpose of this study is a comparative analysis of the parallel algorithm computing results on different technologies, in order to show the results of each of Open MP, MPI, CUDA, and hybrid of these three techniques for solving oil recovery problems. The computing results of parallel algorithms were compared and analyzed. Numerical model are developed and the results of these modeling is presented.
Studying these models of parallel algorithms run on the high-performance computer, and the results enhance the program performances and decrease the implementation time. So, we draw the conclusion that these models are suitable for large-scale numerical calculations and Open MP-MPI-CUDA hybrid model can increase the performance of numerical simulations of a polymer flooding process and achieve higher speedup.