Numerical Simulation Study using the Explicit Finite Difference Method for Petroleum Reservoir

The behavior of petroleum reservoirs is inherently complex, making it challenging to determine their performance for both single-fluid and multiphase production systems. To accurately estimate the recovery reserves of a reservoir, a comprehensive understanding of its geometry and internal flow characteristics is essential. Numerical simulation serves as a fundamental tool for reservoir engineers, offering an efficient and reliable method to predict reservoir mechanisms, evaluate pressure variations, and estimate in-place hydrocarbon yield. This study employs mathematical modeling concepts and numerical techniques to analyze the dynamic behavior of petroleum reservoir systems. A flow model based on Partial Differential Equations (PDEs), specifically the diffusivity equation for unsteady-state fluid flow in porous media, is developed and applied. The diffusivity equation is discretized and solved mathematically using the explicit finite difference method to approximate pressure distribution over time and space. The primary objective of this research is to investigate and analyze the pressure distribution that governs reservoir performance under varying conditions. Sensitivity analyses are conducted to evaluate the influence of grid spacing, time step, hydraulic diffusivity, and boundary conditions on pressure reservoir behavior within a Cartesian grid for a one-dimensional, single-phase reservoir. The findings are expected to provide insight into the relationship between reservoir properties and fluid dynamics, supporting improved prediction of reservoir behavior. Ultimately, this research contributes to the optimization of petroleum production strategies and enhances the understanding of reservoir engineering processes through quantitative simulation.