DEVELOPMENT OF DISCRETIZATION AND COMPUTATIONAL ALGORITHMS FOR FILTRATION EQUATIONS IN OIL RESERVOIRS BASED ON THE FINITE DIFFERENCE METHOD
Keywords:
filtration equations; finite difference method; numerical discretization; computational algorithms; porous media flow; parallel computingAbstract
This paper is devoted to the development of discretization techniques and computational algorithms for solving filtration equations in oil reservoirs based on the finite difference method. The mathematical model of fluid flow in porous media is formulated using Darcy’s law and the mass conservation principle. Due to the heterogeneity of reservoir properties, nonlinearity of governing equations, and large spatial dimensions, analytical solutions are impractical, which necessitates the use of efficient numerical approaches.
A structured grid is employed to discretize the spatial domain, while implicit and semi-implicit time integration schemes are used to ensure numerical stability. Central difference approximations are applied to spatial derivatives, and harmonic averaging is utilized for transmissibility calculation in heterogeneous formations. The resulting system of algebraic equations is solved using iterative methods optimized for sparse matrices, which significantly reduces computational cost. Parallelization and adaptive time-stepping strategies are also incorporated to enhance computational efficiency for large-scale reservoir models.
The proposed finite difference–based algorithms demonstrate improved stability, accuracy, and scalability when applied to filtration problems in oil reservoirs. The results confirm that the developed approach is suitable for practical reservoir simulation tasks and can be effectively used for performance prediction and optimization in petroleum engineering applications.
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