APPLICATION OF PARALLEL ALGORITHMS FOR THE NUMERICAL SOLUTION OF DYNAMICALLY INTERCONNECTED OIL FILTRATION EQUATIONS

Abstract

This article investigates the application of parallel algorithms to the numerical solution of dynamically interconnected oil filtration equations that arise in modeling multiphase flow in porous media. The mathematical formulation of the problem is based on mass conservation laws and Darcy’s law, leading to a coupled system of nonlinear partial differential equations describing pressure and saturation dynamics in heterogeneous reservoirs. Due to the large scale and high computational complexity of such models, classical sequential numerical methods become inefficient for practical simulations.

To address this limitation, modern discretization techniques combined with domain decomposition and parallel computing strategies are employed. The computational domain is partitioned into subdomains, allowing simultaneous calculations on multiple processors and significantly reducing execution time. The study analyzes the stability, accuracy, and scalability of the proposed parallel approach and evaluates its computational efficiency compared to traditional methods. The results demonstrate that parallel algorithms substantially accelerate simulations while preserving numerical reliability, enabling large-scale and high-resolution reservoir modeling. The proposed methodology can be effectively applied in petroleum engineering practice for forecasting, optimization, and management of oil field development.