Numerical Simulation Study using the Explicit Finite Difference Method for Petroleum Reservoir
DOI:
https://doi.org/10.21512/comtech.v16i2.12191Keywords:
Numerical simulation, diffusivity equation, explicit finite difference methodAbstract
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.
Plum Analytics
References
Abou-Kassem, J. H., Islam, M. R., & Farouq Ali, S. M. (2020). Chapter 4 - Simulation with a block-centered grid. In J. H. Abou-Kassem, M. R. Islam, & S. M. Farouq Ali (Eds.), Petroleum Reservoir Simulation (Second Edition) (Second Edi, pp. 65–124). Gulf Professional Publishing. https://doi.org/10.1016/B978-0-12-819150-7.00004-9
Adak, M. (2020). Comparison of explicit and implicit finite difference schemes on diffusion equation. Springer Proceedings in Mathematics and Statistics, 320, 227–238. https://doi.org/10.1007/978-981-15-3615-1_15
Aliyu, B. K., Agency, D., Olatoyinbo, S. F., Agency, D., & Vehicle, U. A. (2021). Explicit and Implicit Solution to 2D Heat Equation. February. https://doi.org/10.13140/RG.2.2.10788.19840
Appau, P. O., Dankwa, O. K., & Brantson, E. T. (2019). A comparative study between finite difference explicit and implicit method for predicting pressure distribution in a petroleum reservoir. International Journal of Engineering, Science and Technology, 11(4), 23–40. https://doi.org/10.4314/ijest.v11i4.3
Contreras, F. R. L., Carvalho, D. K. E., Galindez-Ramirez, G., & Lyra, P. R. M. (2021). A nonlinear finite volume method coupled with a modified higher order MUSCL-type method for the numerical simulation of two-phase flows in non-homogeneous and non-isotropic oil reservoirs. Computers and Mathematics with Applications, 92, 120–133. https://doi.org/10.1016/j.camwa.2021.03.023
Galindez-Ramirez, G., Contreras, F. R. L., Carvalho, D. K. E., & Lyra, P. R. M. (2020). Numerical simulation of two-phase flows in 2-D petroleum reservoirs using a very high-order CPR method coupled to the MPFA-D finite volume scheme. Journal of Petroleum Science and Engineering, 192, 107220. https://doi.org/10.1016/j.petrol.2020.107220
Ghedira, A., Lataoui, Z., Benselama, A. M., Bertin, Y., & Jemni, A. (2025). Numerical simulation of incompressible two-phase flows with phase change process in porous media. Results in Engineering, 25, 103706. https://doi.org/10.1016/j.rineng.2024.103706
Keita, S., Beljadid, A., & Bourgault, Y. (2021). Efficient second-order semi-implicit finite element method for fourth-order nonlinear diffusion equations. Computer Physics Communications, 258, 107588. https://doi.org/10.1016/j.cpc.2020.107588
Kvashchuk, A., Klöfkorn, R., & Sandve, T. H. (2023). A second-order finite volume method for field-scale reservoir simulation. Transport in Porous Media, 150(1), 109–129. https://doi.org/10.1007/s11242-023-01999-1
Liu, H., & Luo, Y. (2022). An explicit method to calculate implicit spatial finite differences. Geophysics, 87(2), T157–T168. https://doi.org/10.1190/geo2021-0001.1
Maulindani, S. F., Abdassah, D., Marhaendrajana, & Prakoso, S. (2021). Reservoir simulation study for dual porosity model to determine characteristic of naturally fractured reservoir. 3rd International Conference on Earth Science, Mineral, and Energy, 2363, 020006. https://doi.org/10.1063/5.0061130
Maulindani, S. F., Abdassah, D., Marhaendrajana, T., Prakoso, S., & Fathaddin, M. T. (2021). Application of pressure type curve matching for characterizing the naturally fractured reservoir. Journal of Earth Energy Science, Engineering, and Technology, 4(1). https://doi.org/10.25105/jeeset.v4i1.9060
Mojumder, M. S. H., Haque, M. N., & Alam, M. J. (2023). Efficient finite difference methods for the numerical analysis of one-dimensional heat equation. Journal of Applied Mathematics and Physics, 11(10), 3099–3123. https://doi.org/10.4236/jamp.2023.1110204
Nascimento, J. C. S., Santos, A. dos, Pico Ortiz, C. E., & Pires, A. P. (2021). A fully implicit EOS based compositional two-phase transient flow simulator in wellbores. Journal of Petroleum Science and Engineering, 205(May). https://doi.org/10.1016/j.petrol.2021.108923
Raza, Q., & Wang, X. (2024). Numerical simulation of Boger nanofluids with heat source, magnetic field, and Cattaneo–Christov heat flux model between two parallel permeable porous plates via finite difference method. Case Studies in Thermal Engineering, 64(May), 105518. https://doi.org/10.1016/j.csite.2024.105518
Salomon, L., & Guilcher, P. M. (2024). Fully higher-order coupling of finite element and level set methods for two-phase flow with a new explicit projection method. Computers and Fluids, 275(February), 106245. https://doi.org/10.1016/j.compfluid.2024.106245
Sun, Q., & Ertekin, T. (2019). Reservoir Simulation: Problems and Solutions. https://doi.org/10.2118/9781613996935
Sun, Q., Zhang, R., Zhan, Q., Member, S., & Liu, Q. H. (2019). 3-D implicit – explicit hybrid finite difference / spectral element / finite element time domain method. IEEE Transactions on Antennas and Propagation, 67(8), 5469–5476.
Wang, S., Yu, C., Sang, G., Yu, R., & Cheng, F. (2020). An oil – water two-phase reservoir numerical simulation coupled with dynamic capillary force based on the full-implicit method. Computers and Mathematics with Applications, 79(9), 2527–2549. https://doi.org/10.1016/j.camwa.2019.11.013
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Sri Feni Maulindani, Andry Prima, Jati Arie Wibowo, Pauhesti Rusdi, Harin Widiyatni
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this journal agree to the following terms:
a. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License - Share Alike that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
b. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
c. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
 USER RIGHTS
 All articles published Open Access will be immediately and permanently free for everyone to read and download. We are continuously working with our author communities to select the best choice of license options, currently being defined for this journal as follows:
